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VENKATESHWARA OPEN UNIVERSITY MICROECONOMIC THEORY www.vou.ac.in

MICROECONOMIC THEORY MICROECONOMIC THEORY

MA [MEC-102]

VENKATESHWARA

OPEN UNIVERSITYwww.vou.ac.in MICROECONOMIC THEORY

MA [MEC-102] BOARD OF STUDIES Prof Lalit Kumar Sagar Vice Chancellor

Dr. S. Raman Iyer Director Directorate of Distance Education

SUBJECT EXPERT Bhaskar Jyoti Neog Assistant Professor Dr. Kiran Kumari Assistant Professor Ms. Lige Sora Assistant Professor Ms. Hage Pinky Assistant Professor

CO-ORDINATOR Mr. Tauha Khan Registrar

Authors Dr. S.L. Lodha, (Units: 1.2, 1.4, 1.6, 1.7, 5.2, 5.3.1, 5.4, 9.4, 10.2, 10.3, 10.3.2) © Dr. S.L. Lodha, 2019 D.N. Dwivedi, (Units: 1.3, 1.5, 1.8, 2.2-2.4, 3.2-3.3, 3.4.1-3.4.2, 4.2-4.4, 5.3, 5.5-5.6, 6.2-6.4, 6.5.2-6.7, 7.2-7.4, 8.2-8.5.2, 8.6, 9.2-9.3, 10.2.1-10.2.2) © D.N. Dwivedi, 2019 Dr. Renuka Sharma & Dr. Kiran Mehta, (Units: 3.4.3-3.4.5, 7.5, 8.7) © Dr. Renuka Sharma & Dr. Kiran Mehta, 2019 Vikas Publishing House (Units: 1.0-1.1, 1.9-1.13, 2.0-2.1, 2.5-2.9, 3.0-3.1, 3.4, 3.5-3.9, 4.0-4.1, 4.5-4.9, 5.0-5.1, 5.7-5.11, 6.0-6.1, 6.5-6.5.1, 6.8-6.12, 7.0-7.1, 7.6-7.10, 8.0-8.1, 8.5.3, 8.8-8.12, 9.0-9.1, 9.5-9.9, 10.0-10.1, 10.3.1, 10.4-10.8) © Reserved, 2019

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Syllabi Mapping in Book

Unit-I : Consumer’s Choice under Certainty Unit 1: Consumer’s Choice Preference ordering and utility function – Utility maximization and Marshallian under Certainty demand function– Indirect utility function and cost/expenditure duality (Pages 3-39) between constrained utility maximization and constrained cost minimisation – Hicksian demand function – Properties of budget line and demand function: Engle aggregation, Cournot aggregation, homogeneity – Linear expenditure system – An overview of estimation of demand functions.

Unit-II : Theory of Production Unit 2: Theory of Production Production function – Returns to scale and returns to a factor- Elasticity of (Pages 41-70) factor substitution – Types of production function: Homogeneous production function, Cobb-Douglas, CES production functions and its properties – Derivation of Cobb-Douglas and Leontief production functions from CES production function.

Unit-III : Theory of Cost and Factor Pricing Unit 3: Theory of Cost and Derivation of cost function from production function – Technical progress Factor Pricing (Hicksian and Harrodian version) and factor shares – Theories of distribution: (Pages 71-100) Marginal Productivity theory and Euler’s theorem, Ricardo, Kalecki and Kaldor.

Unit-IV : Theory of Market Unit 4: Theory of Market Critique of perfect competition as a market form – Actual market forms: (Pages 101-139) Duopoly, oligopoly and monopolistic competition – Cournot and Stackelberg’s model of duopoly – Collusive oligopoly: Cartel.

Unit-V : Game Theoretic Approach to Economics Unit 5: Game Theoretic Two-person zero-sum and non-zero sum game – Pure strategy, maximin and Approach to Economics minimax - saddle point, and minimax theorem – mixed strategy, its solution – (Pages 141-156) Two person co-operative game, non-co-operative game – dominated strategy – Prisoner’s dilemma and its repetition – Nash equilibrium – application of game theory to oligopoly.

Unit-VI : Alternative Theories of the Firm Unit 6: Alternative The traditional theory of firm and its critical evaluation – Baumol’s revenue Theories of Firm maximization model – Williamson’s model of managerial discretion – (Pages 157-178) Managerial firm vs. entrepreneurial firm – Marris’s model of managerial enterprise – Limit pricing theory.

Unit-VII : Theory of General Equilibrium Unit 7: Theory of General Principles of general equilibrium, existence, uniqueness and stability Equilibrium (Walrasian and Marshallian conditions of stability) – Walrasian general (Pages 179-206) equilibrium system – Computable general equilibrium.

Unit-VIII : Welfare Economics Unit 8: Welfare Economics Pareto Optimality, Pareto Optimality conditions: Consumption, production (Pages 207-239) and exchange, critical evaluation of Pareto Optimality – Compensation tests: Kaldor, Hicks and Scitovsky and Little’s criterion – Social welfare function – Arrow’s Impossibility Theorem. Unit-IX : Choice under Uncertainty and Risk Unit 9: Choice under Difference between Uncertainty and risk; classes of measures: associative Uncertainty and Risk measure, ordinal and cardinal measures, Axioms of Neumann-Morgenstern (Pages 241-260) (N-M) utility, Characteristics of N-M utility index; relationship between the shape of the utility function and behaviour towards risk, elasticity of marginal utility and risk aversion; absolute and relative risk aversion.

Unit-X : Economics of Imperfect Information Unit 10: Economics of Information and decision making under certainty and uncertainty – Imperfect Information Asymmetric information, adverse selection, moral hazard and signalling – (Pages 261-280) Applications to insurance and lemons markets. CONTENTS

INTRODUCTION 1-2 UNIT 1 CONSUMER’S CHOICE UNDER CERTAINTY 3-39 1.0 Introduction 1.1 Unit Objectives 1.2 Preference Ordering and Utility Function 1.2.1 Utility Functions (Numerical Preference Rankings) 1.3 Utility Maximization and Marshallian Demand Function 1.3.1 Cardinal Utility Approach to Consumer Demand (Marshallian Approach) 1.3.2 Total and Marginal Utility 1.3.3 Consumer Equilibrium 1.3.4 Derivation of Individual Demand Curve for a Commodity 1.4 Indirect Utility Function and Cost/Expenditure Function Duality between Constrained Utility Maximization and Constrained Cost Minimization 1.4.1 Slutsky Equation 1.5 Hicksian Demand Function 1.5.1 Assumptions of Ordinal Utility Approach 1.5.2 Meaning and Nature of Indifference Curve 1.5.3 Marginal Rate of Substitution (MRS) 1.5.4 Properties of Indifference Curves 1.6 Properties of Budget Line and Demand Function 1.6.1 Engel Aggregation and Cournot Aggregation 1.7 Linear Expenditure System 1.8 Overview of Estimation of Demand Functions 1.8.1 Linear Demand Function 1.8.2 Non-Linear Demand Function 1.8.3 Multi-variate or Dynamic Demand Function: Long-Term Demand Function 1.9 Summary 1.10 Key Terms 1.11 Answers to ‘Check Your Progress’ 1.12 Questions and Exercises 1.13 Further Reading UNIT 2 THEORY OF PRODUCTION 41-70 2.0 Introduction 2.1 Unit Objectives 2.2 Production Function 2.3 Returns to Scale and Returns to a Factor 2.3.1 Short-run Laws of Production: Production with One Variable Input 2.3.2 Isoquants 2.3.3 Law of Returns to Scale 2.3.4 Elasticity of Factor Substitution 2.4 Types of Production Function 2.4.1 Homogenous Production Function 2.4.2 Cobb-Douglas Function and Derivations 2.4.3 CES Production Function and its Properties and Derivation of Leontief Function 2.5 Summary 2.6 Key Terms 2.7 Answers to ‘Check Your Progress’ 2.8 Questions and Exercises 2.9 Further Reading UNIT 3 THEORY OF COST AND FACTOR PRICING 71-100 3.0 Introduction 3.1 Unit Objectives 3.2 Derivation of Cost Function from Production Function 3.2.1 Short-run Cost-output Relations 3.2.2 Cost Curves and the Law of Diminishing Returns 3.2.3 Output Optimization in the Short-run 3.3 Technical Progress: Hicksian Version 3.3.1 Harrodian Version of Technical Progress 3.4 Theories of Distribution 3.4.1 Marginal Productivity Theory 3.4.2 Euler’s Theorem 3.4.3 Ricardian Theory of Income Distribution 3.4.4 Kalecki’s Theory 3.4.5 Kaldor’s Saving Investment Model of Distribution and Growth 3.5 Summary 3.6 Key Terms 3.7 Answers to ‘Check Your Progress’ 3.8 Questions and Exercises 3.9 Further Reading UNIT 4 THEORY OF MARKET 101-139 4.0 Introduction 4.1 Unit Objectives 4.2 Critique of Perfect Competition as a Market Form 4.2.1 Price Determination under Perfect Competition 4.2.2 Equilibrium of the Firm in Short-run 4.2.3 Derivation of Supply Curve 4.3 Actual Market Forms: Monopolistic Competition, Oligopoly and Duopoly 4.3.1 Price Determination under Pure Monopoly 4.3.2 Pricing and Output Decisions under Oligopoly 4.3.3 Cournot and Stackleberg’s Model of Duopoly 4.4 Collusive Oligopoly: Cartel 4.4.1 Joint Profit Maximization Model 4.4.2 Cartel and Market-sharing 4.5 Summary 4.6 Key Terms 4.7 Answers to ‘Check Your Progress’ 4.8 Questions and Exercises 4.9 Further Reading UNIT 5 GAME THEORETIC APPROACH TO ECONOMICS 141-156 5.0 Introduction 5.1 Unit Objectives 5.2 Two-person Zero-sum and Non-zero Sum Game 5.2.1 Non-Zero-Sum Games 5.3 Pure Strategy, Maximin and Minimax 5.3.1 Saddle Point and Minimax 5.4 Mixed Strategy and Randomization 5.4.1 Two-Person Cooperative and Non-cooperative Game 5.4.2 Dominant Strategy 5.5 Prisoner’s Dilemma and its Repetition 5.5.1 Relevance of Prisoners’ Dilemma to Oligopoly 5.6 Application of Game Theory to Oligopoly 5.6.1 Nash Equilibrium 5.7 Summary 5.8 Key Terms 5.9 Answers to ‘Check Your Progress’ 5.10 Questions and Exercises 5.11 Further Reading UNIT 6 ALTERNATIVE THEORIES OF FIRM 157-178 6.0 Introduction 6.1 Unit Objectives 6.2 Traditional Theory of Firm and its Critical Evaluation 6.3 Baumol’s Revenue Maximization Model 6.3.1 Baumol’s Model without Advertising 6.3.2 Baumol’s Model with Advertising 6.3.3 Criticism of Baumol’s Model 6.4 Williamson’s Model of Managerial Discretion 6.4.1 Simple Version of Williamson’s Model 6.4.2 Firm’s Equilibrium: Graphical Presentation 6.5 Managerial Firm vs Entrepreneurial Firm 6.5.1 Entrepreneurial Firms 6.5.2 Cyert-March Model of Firms 6.6 Marris’ Model of Managerial Enterprise 6.6.1 Financial Policy for Balanced Growth 6.6.2 Shortcomings of Marris Theory 6.7 Limit Pricing Theory 6.7.1 Bain’s Model of Limit Pricing 6.8 Summary 6.9 Key Terms 6.10 Answers to ‘Check Your Progress’ 6.11 Questions and Exercises 6.12 Further Reading UNIT 7 THEORY OF GENERAL EQUILIBRIUM 179-206 7.0 Introduction 7.1 Unit Objectives 7.2 Principles of General Equilibrium 7.3 Existence, Uniqueness and Stability 7.3.1 Existence 7.3.2 Uniqueness 7.3.3 Stability 7.3.4 Evaluation 7.4 Walrasian Approach to General Equilibrium 7.4.1 Walrasian General Equilibrium Model 7.4.2 Process of Automatic Adjustment 7.5 Computable General Equilibrium 7.5.1 Arrow-Debreu Model and Polynomial Time Algorithm 7.5.2 Arrow-Debreu Pricing: Equilibrium 7.5.3 General Equilibrium under Uncertainty 7.6 Summary 7.7 Key Terms 7.8 Answers to ‘Check Your Progress’ 7.9 Questions and Exercises 7.10 Further Reading UNIT 8 WELFARE ECONOMICS 207-239 8.0 Introduction 8.1 Unit Objectives 8.2 Meaning and Nature of Welfare Economics 8.2.1 Nature of Welfare Economics 8.3 Pareto Optimality 8.3.1 Pareto’s Welfare Economics 8.3.2 Criticism of Pareto Optimality 8.4 Pareto Optimality Conditions: Consumption, Production and Exchange 8.4.1 Pareto Optimality under Perfect Competition 8.4.2 Externalities and Pareto Optimality 8.4.3 Indivisibilities and Pareto Optimality 8.5 Compensation Tests 8.5.1 Kaldor-Hicks’ Compensation Criterion 8.5.2 Scitovsky’s Double-Criterion 8.5.3 Little’s Criterion 8.6 Social Welfare Function 8.7 Arrow’s Impossibility Theorem 8.8 Summary 8.9 Key Terms 8.10 Answers to ‘Check Your Progress’ 8.11 Questions and Exercises 8.12 Further Reading UNIT 9 CHOICE UNDER UNCERTAINTY AND RISK 241-260 9.0 Introduction 9.1 Unit Objectives 9.2 Difference between Uncertainty and Risk 9.3 Classes of Measures: Ordinal and Cardinal Measures 9.3.1 Axioms of Neumann-Morgenstern (N-M) Utility 9.4 Relationship between Shape of Utility Function and Behaviour towards Risk 9.4.1 Elasticity of Marginal Utility and Risk Aversion 9.4.2 Absolute and Relative Risk Aversion 9.5 Summary 9.6 Key Terms 9.7 Answers to ‘Check Your Progress’ 9.8 Questions and Exercises 9.9 Further Reading UNIT 10 ECONOMICS OF IMPERFECT INFORMATION 261-280 10.0 Introduction 10.1 Unit Objectives 10.2 Information and Decision Making under Certainty and Uncertainty 10.2.1 Investment Decisions under Certainty 10.2.2 Investment Decisions under Uncertainty 10.3 Asymmetric Information 10.3.1 Adverse Selection and Signalling 10.3.2 Moral Hazard and its Application to Insurance 10.4 Summary 10.5 Key Terms 10.6 Answers to ‘Check Your Progress’ 10.7 Questions and Exercises 10.8 Further Reading Introduction INTRODUCTION

Economics has two major branches: (i) Microeconomics, and (ii) Macroeconomics. NOTES Both micro and macro-economics are applied to business analysis and decision-making— directly or indirectly. Operational issues are of internal nature. Internal issues include all those problems which arise within the business organization and fall within the purview and control of the management. Some of the basic internal issues are: (i) choice of business and the nature of product, i.e., what to produce; (ii) choice of size of the firm, i.e., how much to produce; (iii) choice of technology, i.e., choosing the factor-combination; (iv) choice of price, i.e., how to price the commodity; (v) how to promote sales; (vi) how to face price competition; (vii) how to decide on new investments; (viii) how to manage profit and capital; (ix) how to manage an inventory, i.e., stock of both finished goods and raw materials. These problems may also figure in forward planning. Microeconomics deals with such questions confronted by managers of business enterprises. The following microeconomic theories deal with most of these questions. Demand theory deals with consumers’ behaviour. It answers such questions as: How do the consumers decide whether or not to buy a commodity? How do they decide on the quantity of a commodity to be purchased? When do they stop consuming a commodity? How do the consumers behave when price of the commodity, their income and tastes and fashions, etc., change? At what level of demand, does changing price become inconsequential in terms of total revenue? The knowledge of demand theory can, therefore, be helpful in making the choice of commodities, finding the optimum level of production and in determining the price of the product. Production theory explains the relationship between inputs and output. It also explains under what conditions costs increase or decrease; how total output behaves when units of one factor (input) are increased keeping other factors constant, or when all factors are simultaneously increased; how can output be maximized from a given quantity of resources; and how can the optimum size of output be determined? Production theory, thus, helps in determining the size of the firm, size of the total output and the amount of capital and labour to be employed, given the objective of the firm. Price theory explains how price is determined under different kinds of market conditions; when price discrimination is desirable, feasible and profitable; and to what extent advertising can be helpful in expanding sales in a competitive market. Thus, price theory can be helpful in determining the price policy of the firm. Price and production theories together, in fact, help in determining the optimum size of the firm. Profit making is the most common objective of all business undertakings. But, making a satisfactory profit is not always guaranteed because a firm has to carry out its activities under conditions of uncertainty with regard to: (i) demand for the product, (ii) input prices in the factor market, (iii) nature and degree of competition in the product market, and (iv) price behaviour under changing conditions in the product market, etc. Therefore, an element of risk is always there even if the most efficient techniques are used for predicting the future and even if business activities are meticulously planned. The firms are, therefore, supposed to safeguard their interest and avert or minimize the possibilities of risk. Profit theory guides firms in the measurement and management of profit, in making allowances for the risk premium, in calculating the pure return on capital and pure profit and also for future profit planning. Self-Instructional Material 1 Introduction Capital like all other inputs, is a scarce and expensive factor. Capital is the foundation of business. Its efficient allocation and management is one of the most important tasks of the managers and a determinant of the success level of the firm. The major issues related to capital are (i) choice of investment project, (ii) assessing the efficiency NOTES of capital, and (iii) most efficient allocation of capital. Knowledge of capital theory can contribute a great deal in investment-decision making, choice of projects, maintaining the capital, capital budgeting, etc. This book deals with the theories of microeconomics. This book, Microeconomic Theory, is written in a self-instructional format and is divided into ten units. Each unit begins with an ‘Introduction’ to the topic followed by an outline of the ‘Unit Objectives’. The content is then presented in a simple and easy-to- understand manner, and is interspersed with ‘Check Your Progress’ questions to test the reader’s understanding of the topic. A list of ‘Questions and Exercises’ is also provided at the end of each unit, and includes short-answer as well as long-answer questions. The ‘Summary’ and ‘Key Terms’ section are useful tools for students and are meant for effective recapitulation of the text.

Self-Instructional 2 Material Consumer’s Choice UNIT 1 CONSUMER’S CHOICE under Certainty UNDER CERTAINTY NOTES Structure 1.0 Introduction 1.1 Unit Objectives 1.2 Preference Ordering and Utility Function 1.2.1 Utility Functions (Numerical Preference Rankings) 1.3 Utility Maximization and Marshallian Demand Function 1.3.1 Cardinal Utility Approach to Consumer Demand (Marshallian Approach) 1.3.2 Total and Marginal Utility 1.3.3 Consumer Equilibrium 1.3.4 Derivation of Individual Demand Curve for a Commodity 1.4 Indirect Utility Function and Cost/Expenditure Function Duality between Constrained Utility Maximization and Constrained Cost Minimization 1.4.1 Slutsky Equation 1.5 Hicksian Demand Function 1.5.1 Assumptions of Ordinal Utility Approach 1.5.2 Meaning and Nature of Indifference Curve 1.5.3 Marginal Rate of Substitution (MRS) 1.5.4 Properties of Indifference Curves 1.6 Properties of Budget Line and Demand Function 1.6.1 Engel Aggregation and Cournot Aggregation 1.7 Linear Expenditure System 1.8 Overview of Estimation of Demand Functions 1.8.1 Linear Demand Function 1.8.2 Non-Linear Demand Function 1.8.3 Multi-variate or Dynamic Demand Function: Long-Term Demand Function 1.9 Summary 1.10 Key Terms 1.11 Answers to ‘Check Your Progress’ 1.12 Questions and Exercises 1.13 Further Reading

1.0 INTRODUCTION

Consumers face different types of choice problems. They have choice problems when there is no uncertainty involved, i.e., choosing under the conditions of certainty. They choose from a given set of mutually exclusive feasible outcomes. They know what each of the outcomes represents. They also know that they will get any of the outcomes they choose. Besides this problem of choice under certainty, there are two other types of choice problems: the problem of choice under strategic uncertainty and the problem of choice under non-strategic uncertainty. In this unit, you will learn about consumer choice under certainty. In consumer’s choice under certainty, an action is the choice of a consumption bundle; the set of possible actions, for any given income and set of prices, is the set of consumption bundles satisfying the budget constraint; and the choice rule is maximization in accordance with the ordering expressing the individual’s preference pattern.

Self-Instructional Material 3 Consumer’s Choice under Certainty 1.1 UNIT OBJECTIVES

After going through this unit, you will be able to: NOTES • Discuss the concept of preference ordering and utility function • Explain the Marshallian demand function and utility maximization • Assess indirect utility function and the duality between constrained utility maximization and constrained cost minimization • Explain the characteristics of Hicksian demand function • Evaluate the properties of budget line and demand function and Engel and Cournot aggregation • Describe the linear expenditure system • Give an overview of estimation of demand functions

1.2 PREFERENCE ORDERING AND UTILITY FUNCTION

When we look at it in terms of economics, ‘preference is the ordering of alternatives based on their relative utility, a process which results in an optimal ‘choice’ (whether real or theoretical)’. It is purely the factors of taste that determines the character of the individual’s preferences, independent of the individual’s income, price considerations or consideration of goods’ availability. Human behaviour can be predicted with the help of scientific methods and many important decisions of life can also be modelled through scientific methods. Economists are generally not interested in the underlying reasons of the preferences in themselves, instead they show an interest in the theory of choice since it provides a stage for empirical demand analysis. Therefore, preference ordering is a formal apparatus used by an economist to model a consumers’ taste. Let us quickly look at how preference ordering is done. Resnik xPy ≡ the individual has a preference for x over y yPx ≡ the individual has a preference for y over x xIy ≡ the individual is indifferent between x and y Strict preference: Example xPy just in case the individual prefers x over y and not vice versa. Alternative

Weak preference: It is represented by using  so it is x  y just in case the agent either prefers x over y or is indifferent between them. So to sum up: We define indifference as xIy ≡ x  y and y  x. ≡ Self-Instructional We define strict preference as xPy x  y and not xIy. 4 Material Ordering Conditions Consumer’s Choice under Certainty (O1) (Reflexivity) x  x - the individual has a preference for x or is indifferent between x and x NOTES (O2) (Transitivity) If x  y and y  z, then x  z. - if the individual has a preference for x over y and y over z, then the individual has a preference of x over z (O3) (Connectedness) For any outcomes x and y, x  y or y  x - for any two outcomes, one of them is (weakly) preferred Corollaries 1. All of Resnik’s ordering conditions 2. Results about Indifference (a) xIx follows from (O1). So indifference is reflexive. (b) xIy implies yIx, by definition. So indifference is symmetric. (c) If xIy and yIz, then x  z and z  x, so xIz. So indifference is transitive. • Indifference as an equivalence relation • Outcomes fall into indifference classes Points of Justification • (O1) as given above is unproblematic. • (O2) as given above is much discussed and is seen to be empirically false. • (O3) as given above is the most unreasonable constraint. 1.2.1 Utility Functions (Numerical Preference Rankings) In economics, utility function is an important concept that measures preferences over a set of goods and services. Proposition: If (O1) - (O3) are satisfied by a preference ordering, then it is possible to assign to each outcome x a number u(x), which is referred to as the utility of x, such that: • u(x) > u(y) iff xPy • u(x) = u(y) iff xIy u is referred to as a utility scale or a utility function. Ordinal transformations An ordinal transformation t(u) is a function in which for every utility value u and v, t(u) ≥t(v) iff u≥v Positive linear transformations t(u) = a u + b, where a > 0 Interval scales are utility functions that have been specified up to a positive linear transformation.

Self-Instructional Material 5 Consumer’s Choice Following is a list of criteria that are used for the purpose of evaluating decision under Certainty principles. • Ability to take advantage of opportunities NOTES • Arbitrariness • Intuitive counterexamples • Invariance under expansion of options • Invariance under ordinal transformations • Probabilistic pre-suppositions Maximin Rule (a) Easier version • Locate each act’s minimum value. • Select the act with the minimum value as maximal. (b) Lexical version • If there is a tie, maximize the next-to-minimum value, and so on. Rationale: Conservatism—it prevents worst outcome. Objections: • Intuitive counter-examples • Lost opportunities • Probabilistic pre-suppositions Minimax Regret • Regret value for each act-state pair: MAX value for state—value for the pair • For each act, locate the maximum regret value in its row • Select the act which minimizes the maximum regret value • This can be a lexical rule in event of a tie Rationale: Helps in making the decision that will minimize lost opportunity. Objections: • Intuitive counter examples • Is not invariant under act expansion • Is not invariant under ordinal transformations; presupposes an interval scale The ‘best average’ rule • For each act, locate MAX and MIN in its row • Compute AVG = (MAX + MIN) / 2 • Select the act that will maximize AVG Rationale: Prevents such acts that could prove catastrophic and also such acts that miss out on great opportunities.

Self-Instructional 6 Material Objections Consumer’s Choice under Certainty • Pre-supposes interval scale • Same counter-example as for Minimax Regret NOTES Principle of Insufficient Reason • Consider every state equally probable • Maximize expected utility on this basis (Shortcut: Sum utilities for the row, and choose the maximal row.) Rationale: When there is no good reason to assign any probabilities, assign them all equal probability. Objections • Arbitrariness of assumption of equi-probability • Incoherence of the equi-probability assumption • Possibility of catastrophe • Pre-supposes interval scale

1.3 UTILITY MAXIMIZATION AND MARSHALLIAN DEMAND FUNCTION

The consumers demand a commodity because they derive or expect to derive utility from that commodity. The expected utility from a commodity is the basis of demand for it. Though ‘utility’ is a term of common usage, it has a specific meaning and use in the analysis of consumer demand. Meaning of Utility The concept of utility can be looked upon from two angles—from the commodity angle and from the consumer’s angle. From the commodity angle, utility is the want-satisfying property of a commodity. From the consumer’s angle, utility is the psychological feeling of satisfaction, pleasure, happiness or well-being which a consumer derives from the consumption, possession or the use of a commodity. There is a subtle difference between the two concepts which must be borne in mind. The concept of a want-satisfying property of a commodity is ‘absolute’ in the sense that this property is ingrained in the commodity irrespective of whether one needs it or not. For example, a pen has its own utility irrespective of whether a person is literate or illiterate. Another important attribute of the ‘absolute’ concept of utility is that it is ‘ethically neutral’ because a commodity may satisfy a frivolous or socially immoral need, e.g., alcohol, drugs or a profession like prostitution. Check Your Progress On the other hand, from a consumer’s point of view, utility is a post-consumption 1. Why do economists phenomenon as one derives satisfaction from a commodity only when one consumes or show an interest in uses it. Utility in the sense of satisfaction is a ‘subjective’ or a ‘relative’ concept. In the the theory of subjective sense, utility is a matter of one’s own feeling of satisfaction. In the relative choice? 2. What is utility sense: (i) a commodity need not be useful for all, for example, cigarettes do not have any function? utility for non-smokers, and meat has no utility for strict vegetarians; (ii) utility of a

Self-Instructional Material 7 Consumer’s Choice commodity varies from person to person and from time to time; and (iii) a commodity under Certainty need not have the same utility for the same consumer at different points of times, at different levels of consumption and at different moods of a consumer. In consumer analysis, only the ‘subjective’ concept of utility is used. NOTES There are two approaches to consumer demand analysis: Cardinal utility approach or Marshallian approach and ordinal utility approach or Hicks-Allen approach. The hicksian approach is described later. 1.3.1 Cardinal Utility Approach to Consumer Demand (Marshallian Approach) The central theme of the consumption theory is the analysis of utility maximizing behaviour of the consumer. The fundamental postulate of the consumption theory is that all the consumers—individuals and households—aim at utility maximization and all their decisions and actions as consumers are directed towards utility maximization. The specific questions that the consumption theory seeks to answer are : (i) How does a consumer decide the optimum quantity of a commodity that he or she chooses to consume, i.e., how does a consumer attain his/her equilibrium? (ii) How does he or she allocate his/her total consumption expenditure on various commodities he/she consumes so that his/her total utility is maximized? As mentioned above, the theory of consumer behaviour postulates that consumers seek to maximize their total utility or satisfaction. On the basis of this postulate, consumption theory explains how a consumer attains the level of maximum satisfaction under the following assumptions. Assumptions: The cardinal utility approach to consumer analysis makes the following assumptions. (i) Rationality: It is assumed that the consumer is a rational being in the sense that he/she satisfies his/her wants in the order of their preference. That is, he/she buys that commodity first which yields the highest utility and that last which gives the least utility. (ii) Limited money income: The consumer has a limited money income to spend on the goods and services he or she chooses to consume. Limitedness of income, along with utility maximization objective makes the choice between goods inevitable. (iii) Maximization of satisfaction: Every rational consumer intends to maximize his/her satisfaction from his/her given money income. (iv) Utility is cardinally measurable: The cardinalists assumed that utility is cardinally measurable and that utility of one unit of a commodity equals the money a consumer is prepared to pay for it or 1 util = 1 unit of money. (v) Diminishing marginal utility: Consumption of a commodity is subject to the law of diminishing marginal utility, i.e., the utility derived from the successive units of a commodity goes on decreasing as a consumer consumes more and more units of the commodity. This is an axiom of the theory of consumer behaviour. (vi) Constant marginal utility of money: The cardinal utility approach assumes that marginal utility of money remains constant whatever the level of a consumer’s income. This assumption is necessary to keep the scale of measuring rod of utility fixed. It is important to recall in this regard that cardinalists used ‘money’ as a measure of utility. Self-Instructional 8 Material (vii) Utility is additive: Cardinalists assumed not only that utility is cardinally Consumer’s Choice measurable but also that utility derived from various goods and services by a under Certainty consumer can be added together to obtain the total utility. For example, suppose a person consumes X number of goods. His total utility can be expressed as: NOTES TU = UX1 + UX2 + UX3 + ...... + UXn

where X1, X2, ... Xn denote the total quantities of the various goods consumed. 1.3.2 Total and Marginal Utility Before we proceed to explain and illustrate the law of diminishing marginal utility, let us explain the concept of total and marginal utility used in the explanation of the law of diminishing marginal utility. Total utility: Assuming that utility is measurable and additive, total utility may be defined as the sum of the utilities derived by a consumer from the various units of goods and services he consumes. Suppose a consumer consumes four units of a commodity, X, at a time and derives utility as u1, u2, u3 and u4. His total utility (TUx) from commodity X can be measured as follows.

TUx = u1 + u2 + u3 + u4

If a consumer consumes n number of commodities, his total utility, TUn, will be the sum of total utilities derived from each commodity. For instance, if the consumption goods are X, Y and Z and their total respective utilities are Ux, Uy and Uz, then:

TUn = Ux + Uy + Uz Marginal utility: The marginal utility is another most important concept used in economic analysis. Marginal utility may be defined in a number of ways. It is defined as the utility derived from the marginal unit consumed. It may also be defined as the addition to the total utility resulting from the consumption (or accumulation) of one additional unit. Marginal Utility (MU) thus refers to the change in the Total Utility (i.e., DTU) obtained from the consumption of an additional unit of a commodity. It may be expressed as: TU MU = Q

where TU = total utility, and ∆Q = change in quantity consumed by one unit. Another way of expressing marginal utility (MU), when the number of units consumed is n, can be as follows.

MU of nth unit = TUn – TUn–1 Having explained the concept of total utility (TU) and marginal utility (MU), let us now discuss the law of diminishing marginal utility. Law of Diminishing Marginal Utility Let us begin our study of consumer demand with the law of diminishing marginal utility. The law of diminishing marginal utility is one of the fundamental laws of economics. This law states that as the quantity consumed of a commodity increases, the utility derived from each successive unit decreases, consumption of all other commodities remaining the same. In simple words, when a person consumes more and more units of a commodity per unit of time, e.g., rasgullas, keeping the consumption of all other commodities constant, the utility which he derives from the successive rasgullas he Self-Instructional Material 9 Consumer’s Choice consumes goes on diminishing. This law applies to all kinds of consumer goods—durable under Certainty and non-durable sooner or later. To explain the law of diminishing marginal utility, let us suppose that a consumer consumes 6 units of a commodity X and his/her total and marginal utility derived from NOTES various units of X are as given in Table 1.1. Table 1.1 Total and Marginal Utility Schedules of X

No. of units Total Marginal consumed utility utility 1 30 30 2 50 20 3 60 10 4 65 5 5 60 – 5 6 45 – 15

As shown in Table 1.1, with the increase in the number of units consumed per unit of time, the TU increases but at a diminishing rate. The diminishing rate of increase in the total utility gives the measure of marginal utility. The diminishing MU is shown in the last column of the table. Figure 1.1 illustrates graphically the law of diminishing MU. The rate of increase in TU as the result of increase in the number of units consumed is shown by the MU curve in Figure 1.1. The downward sloping MU curve shows that marginal utility goes on decreasing as consumption increases. At 4 units consumed, the TU reaches its maximum level, i.e., 65 utils. Beyond this, MU becomes negative and TU begins to decline. The downward sloping MU curve illustrates the law of diminishing marginal utility.

x 50 U M

d 40 TU n x a

x

U 30 T – y t i l

i 20 t U 10

0 1234567 –10 Quantity MUx

Fig. 1.1 Diminishing Marginal Utility

Why the MU decreases: The utility gained from a unit of a commodity depends on the intensity of the desire for it. When a person consumes successive units of a commodity, his need is satisfied by degrees in the process of consumption and the intensity of his need goes on decreasing. Therefore, the utility obtained from each successive unit goes on decreasing. Necessary conditions: The law of diminishing marginal utility holds only under certain conditions. These conditions are referred to as the assumptions of the law. The

Self-Instructional 10 Material assumptions of the law of diminishing marginal utility are listed below. Consumer’s Choice under Certainty First, the unit of the consumer good must be a standard one, e.g., a cup of tea, a bottle of cold drink, a pair of shoes or trousers, etc. If the units are excessively small or large, the law may not hold. NOTES Second, the consumer’s taste or preference must remain the same during the period of consumption. Third, there must be continuity in consumption. Where a break in continuity is necessary, the time interval between the consumption of two units must be appropriately short. Fourth, the mental condition of the consumer must remain normal during the period of consumption. Otherwise, the law of diminishing MU may not apply. Given these conditions, the law of diminishing marginal utility holds universally. In some cases, e.g., accumulation of money, collection of hobby items like stamps, old coins, rare paintings and books, melodious songs, etc. the marginal utility may initially increase, but eventually it does decrease. As a matter of fact, the law of marginal utility generally operates universally. 1.3.3 Consumer Equilibrium From economic analysis point of view, a consumer is a utility maximizing entity. From theoretical point of view, therefore, a consumer is said to have reached his equilibrium position when he has maximized the level of his satisfaction, given his resources and other conditions. Technically, a utility-maximizing consumer reaches his equilibrium position when allocation of his consumption expenditure is such that the last penny spent on each commodity yields the same utility. How does a consumer reach this position? Given the assumptions, a rational and utility-maximizing consumer consumes commodities in the order of their utilities. He picks up first the commodity which yields the highest utility followed by the commodity yielding the second highest utility and so on. He switches his expenditure from one commodity to another in accordance with their marginal utilities. He continues to switch his expenditure from one commodity to another till he reaches a stage where MU of each commodity is the same per unit of expenditure. This is the state of consumer’s equilibrium. Consumer’s equilibrium is analysed under two conditions: • A consumer consuming only one commodity • A consumer consuming many commodities Let us first explain and illustrate consumer’s equilibrium in a simple case assuming that the consumer spends his total income on only one commodity. (i) Consumer’s equilibrium: (one-commodity case.) We explain and illustrate here consumer’s equilibrium in a simple one-commodity model. Suppose that a consumer with certain money income consumes only one commodity, X. Since both his money income and commodity X have utility for him, he can either spend his money income on commodity X or retain it

in the form of asset. If the marginal utility of commodity X, (MUx), is greater

than marginal utility of money (MUm) as asset, a utility-maximizing consumer

will exchange his money income for the commodity. By assumption, MUx is subject to diminishing returns (assumption 5), whereas marginal utility of

money (MUm) as an asset remains constant (assumption 6). Therefore, the Self-Instructional Material 11 Consumer’s Choice consumer will exchange his money income on commodity X so long as MU under Certainty x > Px(MUm), Px being the price of commodity X and MUm = 1 (constant). The utility-maximizing consumer reaches his equilibrium, i.e., the level of maximum satisfaction, where: NOTES MUx = Px (MUm) Alternatively, the consumer reaches equilibrium point where, MU x = 1 Pxm() MU Consumer’s equilibrium in a single commodity model is graphically illustrated

in Figure 1.2. The horizontal line Px (MUm) shows the constant utility of

money weighted by the price of commodity X (i.e., Px) and MUx curve

represents the diminishing marginal utility of commodity X. The Px (MUm)

line and MUx curve interest at point E. Point E indicates that at quantity

OQx consumed, MUx = Px (MUm). Therefore, the consumer is in equilibrium

at point E. At any point above point E, MUx > Px (MUx). Therefore, the utility maximizing consumer would exchange his money for commodity X,

and will increase his total satisfaction because his gain in terms of MUx is

greater than his loss in terms of MUm. This condition exists till he reaches

point E. And, at any point below E, MUx < Px (MUm). Therefore, if he

consumes more than OQx, he loses more utility than he gains. He is therefore a net loser. The consumer can, therefore, increase his satisfaction by reducing his consumption. This means that at any point other than E, consumer’s total satisfaction is less than maximum. Therefore, point E is the point of equilibrium. e c i r P

d E

n Px Pxm (MU ) a

U M

MUx O Qx Quantity

Fig. 1.2 Consumer’s Equilibrium (ii) Consumer’s equilibrium in multicommodity case: (the law of equi- marginal utility.) In the previous section, we have explained consumer’s equilibrium assuming that the consumer consumes a single commodity. In real life, however, a consumer consumes multiple number of goods and services. So the question arises: How does a consumer consuming multiple goods reach his equilibrium? In this section, we explain consumer’s equilibrium in the multi-commodity case.

Self-Instructional 12 Material The law of equi-marginal utility explains the consumer’s equilibrium in a Consumer’s Choice multi-commodity model. This law states that a consumer consumes various under Certainty goods in such quantities that the MU derived per unit of expenditure on each good is the same. In other words, a rational consumer spends his income on various goods he consumes in such a manner that each rupee NOTES spent on each good yields the same MU. Let us now explain consumer’s equilibrium in a multi-commodity model. For the sake of simplicity, however, we will consider only a two-commodity case. Suppose that a consumer consumes only two commodities, X and Y,

their prices being Px and Py, respectively. Following the equilibrium rule of the single commodity case, the consumer will distribute his income between commodities X and Y, so that:

MUx = Px (MUm) and MUy = Py (MUm) Given these conditions, the consumer is in equilibrium where:

MU MU y x = ...(1.1) Pxmym()() MU P MU Since, according to assumption (6), MU of each unit of money (or each rupee) is constant at 1, Eq. (1.1) can be rewritten as:

MU x MU y ...(1.2) PPxy

MUxx P or ...(1.3) MUyy P Equation (1.2) leads to the conclusion that the consumer reaches his equilibrium when the marginal utility derived from each rupee spent on the two commodities X and Y is the same. The two-commodity case can be used to generalize the rule for consumer’s equilibrium for a consumer consuming a large number of goods and services with a given income and at different prices. Supposing, a consumer consumes A to Z goods and services, his equilibrium condition may be expressed as:

MUAB MU MU Z  MU m ...(1.3) PPAB P Z Equation (1.3) gives the law of equi-marginal utility. It is important to note that, in order to achieve his equilibrium, what a utility maximizing consumer intends to equalize is not the marginal utility of each commodity he consumes, but the marginal utility per unit of his money expenditure on various goods and services. 1.3.4 Derivation of Individual Demand Curve for a Commodity We have explained, in the preceding sections, the consumer’s equilibrium using one- commodity and multi-commodity models. The theory of consumer’s equilibrium provides a convenient basis for the derivation of the individual demand curve for a commodity. Marshall was the first economist to explicitly derive the demand curve from the

Self-Instructional Material 13 Consumer’s Choice consumer’s utility function. Marshall gave the equilibrium condition for the consumption under Certainty of a commodity, say X, as MUx = Px (MUm). Using this equilibrium condition, consumer’s equilibrium has been illustrated in Fig. 1.2. The same logic can be used to derive consumer’s demand curve for commodity X. NOTES The derivation of individual demand curve for the commodity X is illustrated in Figure 1.3 (a) and 1.3 (b). Let us first look at Figure 1.3 (a). Suppose price of X is

initially given at P3 and the consumer is in equilibrium at point E1 where MUx = P3

(MUm). Here, equilibrium quantity is OQ1. Now if price of the commodity X falls to P2,

the consumer reaches a new equilibrium position at point E2 where MUx = P2 (MUm). Similarly, if price falls further, he/she buys and consumes more to maximize his/her satisfaction. This behaviour of the consumer can be used to derive his/her demand curve for commodity X.

(a)

E1 P P3m (MU ) y 3 t i l i t

u E2

l P P (MU ) a 2 2m n i g r E3 a P (MU ) P1 1m M

MUx

O Q1 Q2 Q3

Quantity

(b) J P3

e K

c P

i 2 r P L P1

Dx

O Q1 Q2 Q3

Quantity

Fig. 1.3 Derivation of Demand Curve

Figure 1.3 (a) reveals that when price is P3, equilibrium quantity is OQ1. When

price decreases to P2, equilibrium point shifts downward to point E2 at which equilibrium

quantity is OQ2. Similarly, when price decreases to P1 and the P (MUm) line shifts

downward, the equilibrium point shifts to E3 and equilibrium quantity is OQ3. Note that when price goes on decreasing, the corresponding quantity goes on decreasing. This means that as price decreases, the equilibrium quantity increases. This inverse price- quantity relationship is the basis of the law of demand. The inverse price and quantity relationship is shown in panel (b) of Figure 1.3.

The price-quantity combination corresponding to equilibrium point E3 is shown at point J. Self-Instructional 14 Material Consumer’s Choice Similarly, the price-quantity combinations corresponding to equilibrium points, E2 and E1 are shown at points K and L, respectively. By joining points J, K and L we get the under Certainty individual’s demand curve for commodity X. The demand curve Dx in panel (b) is the usual downward sloping Marshallian demand curve. NOTES Demand under variable MUm: We have explained above the consumer’s equilibrium and derived the demand curve under the assumption that MUm remains constant. This analysis holds even if MUm is assumed to be variable. This aspect is explained below.

Suppose MUm is variable—it decreases with increase in stock of money and vice versa. Under this condition, if price of a commodity falls and the consumer buys only as many units as he did before the fall in price, he saves some money on this commodity. As a result, his stock of money increases and his MUm decreases, whereas MUx remains unchanged because his stock of commodity remains unchanged. As a result, his MUx exceeds his MUm. When a consumer exchanges money for commodity, his stock of money decreases and stock of commodity increases. As a result, MUm increases and

MUx decreases. The consumer, therefore, exchanges money for commodity until MUx

= MUm. Consequently, demand for a commodity increases when its price falls.

1.4 INDIRECT UTILITY FUNCTION AND COST/ EXPENDITURE FUNCTION DUALITY BETWEEN CONSTRAINED UTILITY MAXIMIZATION AND CONSTRAINED COST MINIMIZATION

The Marshallian demand function provides us with a solution to the below given problem of consumer utility maximization in which the consumer is faced with price vector p and his income is Y. maxu (x) s.t. p x Y x Typically, the Marshallian demand is denoted for good j as xj (p; Y). The indirect utility function depicts the level of utility that is achieved in prices p and income Y.

v (p, Y) = u (x1 (p, Y), x2 (p, Y), ..., xn (p,Y)) Marshallian demand xj (pj; p-j; Y) is the optimal quantity (i.e. .solution) of input j, chosen for a given parameter vector. Consider the parameter ‘own price’, i.e. pj. As Check Your Progress pj changes to p0j, the optimal solution is expected to change to xj. This represents 3. State an important ‘demand’, which is a sort of the relationship between the chosen quantity and parameters. attribute of the absolute concept of Generally, Marshallian demand is considered ‘uncompensated demand’ as it solves the utility. new optimal level of input without factoring in the consideration that the agent now 4. State the central theme of the achieves a different level of utility. If there is a change in the input demand xii( p , p- i,Y ) consumption theory. 5. Define total utility. will cause a new level of indirect utility, (p , p- i,Y ) . i 6. When does a utility- Marshallian demand curve plots out the relationship that exists between a good’s maximizing consumer reach his quantity and its price xj (pj, p–j, Y) with the quantity chosen optimally by an agent, with equilibrium every other demand parameters being constant. position?

Self-Instructional Material 15 Consumer’s Choice Graphical Interpretation of Marshallian Demand under Certainty

When a parameter p’j changes to P”j, there is a change in the trade off (slope) or MRS. For the purpose of optimization, the agent will move his indifference curve I as much as NOTES possible, to get a new solution bundle for Marshallian demand. Quantity of y As the price px of x falls...... quantity of x demanded rises.

P'x

P"x

Px"' U U 3 U1 2

x x x x1 x2 x3 Quantity of x ' " "' Quantity of x i = p' +p i = p"+p x y x y i = px "'+ py

Fig. 1.4 Graphical Interpretation of Marshallian Demand

Hence, it is possible to decompose the reaction of the consumer into income and

substitution effects when pj changes. Substitution Effect When there is a change in pj, despite the individual still being on an indifference curve, there will be a change in his optimal choice xj since MRS needs to be same as the new price ratio. Intuitively, when there is any change in pj, it renders the good less attractive in comparison with the margin and it brings in substitution to pull the purchasing away from it. Income Effect When there is a change in pj, despite MRS remaining same, the buyer’s optimal choice xj will change due to the fact that there is a change in real income and the buyer needs to shift to a new indifference curve. Intuitively, when there is a change in pj, the cost of infra marginal units of good j changes and this leads to a change in the budget set and thus utility. Income effect and substitution are both rejected by Marshallian demand. Substitution effect: Hold utility u constant, but allow relative price of good x to change. Income effect: Hold trade-off between goods x and y constant, shift out ‘real income’.

Self-Instructional 16 Material Quantity of y Consumer’s Choice under Certainty

The substitution effect is the movement from point A to point C NOTES

A C The individual substitution good x for good y because it is now U 1 relatively cheaper Quantity of x Substitution effect

Quantity of y

The income effect is the movement B from point C to point B If x is a normal good, A C the individual will buy U 2 more because 'real'

U1 income increased Quantity of x Income effect Fig. 1.5 Substitution and Income Effect

In the Hicksian demand function, one can find a solution to the below mentioned problem of consumer expenditure minimization when the consumer is faced with price vector p and must achieve utility level u. min p x s.t.u (x) u x

Typically, the Hicksian demand for good j is denoted as hj (p, u) . The expenditure function depicts the expenditure level needed to achieve utility u, in the presence of prices p. e (p, u) = p · h (p, u)

Hicksian demand hj (pj, p–j, u) is the optimal quantity (solution) of input j, selected for a given parameter vector, constrained for a fixed utility level u. Consider: There are two things that happen when price pj changes to p’j. Graphical Interpretation of Hicksian Demand When there is a change in parameter P′j and it becomes p′'j, the trade-off (slope) or MRS will change but utility is held constant. In the process of optimization, the agent remains on the same indifference curve in obtaining the new solution bundle for Hicksian demand.

Self-Instructional Material 17 Consumer’s Choice under Certainty Holding utility constants, as price falls... Quantity of y slope = NOTES ... Quantity demanded rises.

slope =

slope =

Quantity of x Quantity of x

Fig. 1.6 Graphical Interpretation of Hicksian Demand

Use can be made of Shephard’s lemma to find Hicksian demand function for good j directly from the expenditure function by simple partial differentiation. Shephard’s lemma is represented as:

epj (p, u) = hj (p, u) Intuitively, the first-order effect of a price increase on expenditure is that we pay more for each unit of the good that we are currently consuming. According to the Shephard’s lemma, the cost minimizing point of any given good j with price pj is unique. It is believed that a consumer would purchase a unique ideal amount of each item so that he can keep the cost minimum at obtaining a certain level of utility given the market price of goods. 1.4.1 Slutsky Equation Expenditure maximization and utility minimization are dual problems. Formally, x (p, Y) = h (p, v (p,Y)) The bundle of goods that solves the utility maximization problem (Marshallian) with prices p and income Y also solves the expenditure minimization problem (Hicksian) with prices p and utility target v (p, Y). h (p, u) = x (p, e (p, u)) The bundle of goods that solve the expenditure minimization problem (Hicksian) with prices p and utility target u also solves the utility maximization problem (Marshallian) with prices p and income e (p, u). This duality allows us to derive the Slutsky equation, which relates changes in the Marshallian demand to changes in Hicksian demand. Slutsky Decomposition Equation The change in demand due to price can be decomposed into a substitution effect and an income effect.

Self-Instructional 18 Material Consumer’s Choice xhjj x j under Certainty x j ppjj Y Demand response Substitution Income to price changes effect effect NOTES Proof. 1. Start from duality equation (2) for good j

xj (p, e (p, u)) = hj (p, u)

2. Differentiate with respect to pj

xjj(p, eu (p, )) xeu (p, (p, )) eu( p, ) hj(p, u)

pj Y ppjj 3. Substitute in the following identities eu(p, ) = hj (p, u) (from Shephard’s lemma) p j Y=e (p, u) (Budget Constraint: income = expenditure)

hj (p, u)=xj (p, Y) (from duality) leading to

xYjj(p, ) xY (p, ) huj(p, ) xYj (p, ) pYjj p 4. Rearrange to obtain the result Consider the substitution effect. This is exactly the definition of the Hicksian demand curve, which gives us the effect on demand of price changes, after we have negated any effects on overall utility. The negative slope of the Hicksian demand curve tells us that this term is always negative. Consider the income effect. Intuitively, the first order effect on our budget when

x j pj rises by a dollar is that we are xj dollars poorer. We scale this response by which Y tells us how sensitive demand for good j is to changes in wealth.

x j A normal good is one where > 0. This effect reinforces the substitution Y effect.

x j On the other hand, an inferior good is one where < 0. The income effect Y would then counteract the substitution effect. The following is a useful schematic that shows how the utility maximization problem (UMP) and expenditure minimization problem (EMP) are connected.

Self-Instructional Material 19 Consumer’s Choice UMP EMP under Certainty Slutsky Equation x ()p,w h ()p,u

NOTES h (p,u ) = Roy's e (p,u ) identity p x (p,w ) = h ( p , V ( p ,w)) h (p,u ) = x( p , e( p , u ))

u= V( p, e(p,u )) V ()p,w e ()p,u w= e( p, V(p,w ))

Fig. 1.7 Connection between UMP and EMP

1.5 HICKSIAN DEMAND FUNCTION

Unlike Marshall, modern economists—Hicks in particular—have used the ordinal utility concept to analyse consumer’s behaviour. This is called ordinal utility approach. Hicks has used a different tool of analysis called indifference curve or equal utility curve to analyse consumer behaviour. In this section, we will first explain the indifference curve and then explain consumer’s behaviour through the indifference curve technique. Let us first look at the assumptions of the ordinal utility approach. 1.5.1 Assumptions of Ordinal Utility Approach The assumptions of ordinal utility approach are as follows: 1. Rationality: As under cardinal utility approach, under ordinal utility approach also, the consumer is assumed to be a rational being. Rationality means that a consumer aims at maximizing his total satisfaction given his income and prices of the goods and services. To maximize his/her total utility, he/she spends his/her first rupee on the commodity which yields maximum utility. 2. Ordinal utility: Indifference curve analysis assumes that utility is only ordinally expressible. That is, the consumer can only reveal the order of his preference for different goods or basket of goods.

Check Your Progress 3. Transitivity and consistency of choice: Consumer’s choices are assumed to be transitive. Transitivity of choice means that if a consumer prefers A to B and 7. Fill in the blanks with appropriate B to C, then he prefers A to C. Or, if he treats A = B and B = C, then he treats A terms. = C. Consistency of choice means that if he prefers A to B in one period, he will (i) According to the not prefer B to A in another period or even treat them as equal. ______, the cost 4. Non satiety: It is also assumed that the consumer has not reached the point of minimizing saturation in case of any commodity. This implies that the consumer is not over point of any supplied with goods in question. Therefore, a consumer always prefers a larger given good j quantity of all the goods. with price pj is unique. 5. Diminishing marginal rate of substitution: The marginal rate of substitution is (ii) ______the rate at which a consumer is willing to substitute one commodity (X) for another plots out the (Y) so that his total satisfaction remains the same. This rate is given as ∆Y/∆X. relationship that exists between a The ordinal utility approach assumes that ∆Y/∆X goes on decreasing when a good’s quantity consumer continues to substitute X for Y. and its price.

Self-Instructional 20 Material 1.5.2 Meaning and Nature of Indifference Curve Consumer’s Choice under Certainty An indifference curve may be defined as the locus of points, each representing a different combination of two substitute goods, which yield the same utility or level of satisfaction to the consumer. Therefore, he is indifferent between any two combinations of goods NOTES when it comes to making a choice between them. Such a situation arises because he consumes a large number of goods and services and often finds that one commodity can be substituted for another. It gives him an opportunity to substitute one commodity for another, if need arises and to make various combinations of two substitutable goods which give him the same level of satisfaction. If a consumer is faced with such combinations, he would be indifferent between the combinations. When such combinations are plotted graphically, it produces a curve called indifference curve. An indifference curve is also called isoutility curve or equal utility curve. For example, let us suppose that a consumer makes five combinations a, b, c, d and e of two substitute commodities, X and Y, as presented in Table 1.2. All these combinations yield the same level of satisfaction indicated by U. Table 1.2 Indifference Schedule of Commodities X and Y

Combination Units of Units of Total Commodity Y + Commodity X = Utility

a = 25 + 3 = U b = 15 + 6 = U c = 8 + 10 = U d = 4 + 17 = U e = 2 + 30 = U

Table 1.2 is an indifference schedule—a schedule of various combinations of two goods, between which a consumer is indifferent. The last column of the table shows an undefined utility (U) derived from each combination of X and Y. The combinations a, b, c, d and e given in Table 1.2 are plotted and joined by a smooth curve (as shown in Figure 1.8). The resulting curve is known as an indifference curve. On this curve, one can locate many other points showing different combinations of X and Y which yield the same level of satisfaction. Therefore, the consumer is indifferent between the combinations which may be located on the indifference curve. Indifference map: We have drawn a single indifference curve in Figure 1.8 on the basis of the indifference schedule given in Table 1.2. The combinations of the two commodities, X and Y, given in the indifference schedule or those indicated by the indifference curve are by no means the only combinations of the two commodities. The consumer may make many other combinations with less of one or both of the goods— each combination yielding the same level of satisfaction but less than the level of satisfaction indicated by the indifference curve IC in Figure 1.8. As such, an indifference curve below the one given in Figure 1.8 can be drawn, say, through points f, g and h. Similarly, the consumer may make many other combinations with more of one or both the goods—each combination yielding the same satisfac-tion but greater than the satisfaction indicated by IC. Thus, another indifference curve can be drawn above IC, say, through points j, k and l as shown in Figure 1.8. This exercise may be repeated as many times as one wants, each time generating a new indifference curve.

Self-Instructional Material 21 Consumer’s Choice under Certainty 0 3

25 a Y NOTES

y j 20 t i d o

m b m

15 f o C k 10 c

8 g

6 i

5 d h e IC 24

O 3 5 6910 15 17 20 25 30

Commodity X

Fig. 1.8 Indifference Curve

In fact, the space between X and Y axes is known as the indifference plane or commodity space. This plane is full of finite points and each point on the plane indicates a different combination of goods X and Y. Intuitively, it is always possible to locate any two or more points indicating different combinations of goods X and Y yielding the same satisfaction. It is thus possible to draw a number of indifference curves without intersecting

or touching the other, as shown in Figure 1.9. The set of indifference curves IC1, IC2,

IC3 and IC4 drawn in this manner make the indifference map. It is important to note here that utility represented by each upper IC is higher than that on the lower ones. For

example, the utility represented by IC2 is greater than utility represented by IC1. In

terms of utility, IC1 < IC2 < IC3 < IC4. Y

y t i d o m m o C

(Quantity per unit of of unit per time) (Quantity IC4 IC3 IC2

IC1

O Commodity X (Quantity per unit of time)

Fig. 1.9 The Indifference Map

1.5.3 Marginal Rate of Substitution (MRS) An indifference curve is formed by substituting one good for another. The MRS is the rate at which one commodity can be substituted for another, the level of satisfaction remaining the same. The MRS between two commodities X and Y, may be defined as the quantity of X which is required to replace one unit of Y or quantity of Y required to replace one unit of X, in the combination of the two goods so that the total utility remains Self-Instructional 22 Material the same. This implies that the utility of X (or Y) given up is equal to the utility of Consumer’s Choice additional units of Y (or X). The MRS is expressed as ∆Y/∆X, moving down the curve. under Certainty

Diminishing MRS: The basic postulate of ordinal utility theory is that MRSy,x (or MRSx,y) decreases. It means that the quantity of a commodity that a consumer is willing to sacrifice for an additional unit of another goes on decreasing when he goes on substituting NOTES one commodity for another. The diminishing MRSx,y obtained from different combinations of X and Y given in Table 1.2 are given in Table 1.3. Table 1.3 The Diminishing MRS between Commodities X and Y

Indifference Points Combinations Change in Y Change in X MRSy, x Y + X (– ∆Y) (∆X) (∆Y/∆X)

a 25 + 3 – – – b 15 + 6 – 10 3 – 3.33 c 8 + 10 – 7 4 – 1.75 d 4 + 17 – 4 7 – 0.60 e 2 + 30 – 2 13 – 0.15

As Table 1.3 shows, when the consumer moves from point a to b on his indifference curve (Figure 1.8) he gives up 10 units of commodity Y and gets only 3 units of commodity X, so that: −∆Y −10 MRS = = = −3.33 yx, ∆X 3 As he moves down from point b to c, he gives up 7 units of Y for 4 units of X, giving Y 7 MRS 1.75 yx, X 4

The MRSy, x goes on decreasing as the consumer moves further down along the indifference curve, from point c through points d and e. The diminishing marginal rate of substitution causes the indifference curves to be convex to the origin. Why does the MRS diminish? (i) Diminishing subjective marginal utility: The MRS decreases along the IC curve because, in most cases, no two goods are perfect substitutes for one another. In case any two goods are perfect substitutes, the indifference curve will be a straight line with a negative slope and constant MRS. Since most goods are not perfect substitutes, the subjective value attached to the additional quantity (i.e., subjective MU) of a commodity decreases fast in relation to the other commodity whose total quantity is decreasing. Therefore, when the quantity of one commodity (X) increases and that of the other (Y) decreases, the subjective MU of Y increases and that of X decreases. Therefore, the consumer becomes increasingly unwilling to sacrifice more units of Y for one unit of X. But, if he is required to sacrifice additional units of Y, he will demand increasing units of X to maintain the level of his satisfaction. That is the reason why MRS decreases. (ii) Decreasing ability to sacrifice a good: When combination of two goods at a point on indifference curve is such that it includes a large quantity of one commodity (Y) and a small quantity of the other commodity (X), then consumer’s capacity to Self-Instructional Material 23 Consumer’s Choice sacrifice Y is greater than to sacrifice X. Therefore, he can sacrifice a larger under Certainty quantity of Y in favour of a smaller quantity of X. For example, at combination a (see the indifference schedule, Table 1.2), the quantity of Y (25 units) is much larger than that of X (3 units). That is why the consumer is willing to sacrifice 10 NOTES units of Y for 3 unit of X. This is an observed behavioural rule that the consumer’s willingness and capacity to sacrifice a commodity is greater when its stock is greater and it is lower when the stock of a commodity is smaller. Besides, as mentioned above, the MRS decreases also because of the law of the diminishing MU. The MU of a commodity available in larger quantity is lower than that of a commodity available on smaller quantity. Therefore, the consumer has to sacrifice a large quantity of Y for a small quantity of X in order to maintain total utility at the same level. These are the reasons why MRS between the two substitute goods decreases all along the indifference curve. 1.5.4 Properties of Indifference Curves Indifference curves drawn for two normal substitute goods have the following four basic properties: • Indifference curves have a negative slope • Indifference curves are convex to the origin • Indifference curves do not intersect nor are they tangent to one another • Upper indifference curves indicate a higher level of satisfaction These properties of indifference curves, in fact, reveal the consumer’s behaviour, his choices and preferences. They are, therefore, very important in the modern theory of consumer behaviour. Let us now look into their implications. 1. Indifference curves have a negative slope: In the words of Hicks, ‘so long as each commodity has a positive marginal utility, the indifference curve must slope downward to the right’, as shown in Figure 1.10.

P IC for Imperfect Substitutes Y

y t i d

o IC for Perfect

m Substitutes m o C (Per unit of time)

IC O Commodity X S (Per unit of time)

Fig. 1.10 Normal Indifference Curves

Figure 1.10 shows two IC curves: (i) A curvilinear IC (ii) A straight line IC as shown by the line PS The curvilinear IC represents IC for two imperfect substitute goods whereas straight line PS represents IC for two perfect substitute goods. In both the cases, the IC has a downward or a negative slope. The negative slope of an indifference

Self-Instructional 24 Material curve implies: (a) that the two commodities can be substituted for each other; and Consumer’s Choice (b) that if the quantity of one commodity decreases, quantity of the other under Certainty commodity must increase so that the consumer stays at the same level of satisfaction. If quantity of the other commodity does not increase simultaneously, the bundle of commodities will decrease as a result of decrease in the quantity of NOTES one commodity. And, a smaller bundle of goods is bound to yield a lower level of satisfaction. 2. Indifference curves are convex to origin: Indifference curves are not only negatively sloped, but are also convex to the origin. The convexity of the indifference curves implies two properties: (i) The two commodities are imperfect substitutes for one another (ii) The marginal rate of substitution (MRS) between the two goods decreases as a consumer moves along an indifference curve. The MRS decreases because of an observed fact that if a consumer substitutes one commodity (X) for another (Y), his willingness to sacrifice more units of Y for one additional unit of X decreases, as quantity of Y decreases. There are two reasons for this: (i) no two commodities are perfect substitutes for one another, and (ii) MU of a commodity increases as its quantity decreases and vice versa, and, therefore, more and more units of the other commodity are needed to keep the total utility constant. 3. Indifference curves can neither intersect nor be tangent with one another: If two indifference curves intersect or are tangent with one another, it reflects two rather impossible conclusions: (i) that two equal combinations of two goods yield two different levels of satisfaction, and (ii) that two different combinations— one being larger than the other—yield the same level of satisfaction. Such conditions are impossible if the consumer’s subjective valuation of a commodity is greater than zero. Besides, if two indifference curves intersect, it would mean negation of consistency or transitivity assumption in consumer’s preferences.

Let us now see what happens when two indifference curves, IC1 and IC2, intersect each other at point A (Figure 1.11). Point A falls on both the indifference curves,

IC1 and IC2. It means that the same basket of goods (OM of X + AM of Y) yields different levels of utility below and above point A on the same indifference curve. Y

y t i d o m

m A o

C B IC2

C

IC1

O M N Commodity X Fig. 1.11 Intersecting indifference Curves

The inconsistency that two different baskets of X and Y yield the same level of utility can be proved as follows. Consider two other points—point B on indifference

curve IC2 and point C on indifference curve IC1 both being on a vertical line. Self-Instructional Material 25 Consumer’s Choice Points A, B and C represent three different combinations of commodities X and Y, under Certainty yielding the same utility. Let us call these combinations as A, B and C, respectively. Note that combination A is common to both the indifference curves. The intersection

of the two ICS implies that in terms of utility, NOTES A = B and A = C ∴ B = C But if B = C, it would mean that in terms of utility, ON of X + BN of Y = ON of X + CN of Y Since ‘ON of X’ is common to both the sides, it would mean that BN of Y = CN of Y But as Figure 1.11 shows, BN > CN. Therefore, combinations B and C cannot be equal in terms of satisfaction. The intersection, therefore, violates the transitivity rule which is a logical necessity in indifference curve analysis. The same reasoning is applicable when two indifference curves are tangent with each other. 4. Upper indifference curves represent a higher level of satisfaction than the lower ones: An indifference curve placed above and to the right of another represents a higher level of satisfaction than the lower one. In Figure 1.12,

indifference curve IC2 is placed above the curve IC1. It represents, therefore, a higher level of satisfaction. The reason is that an upper indifference curve contains all along its length a larger quantity of one or both the goods than the lower indifference curve. And a larger quantity of a commodity is supposed to yield a greater satisfaction than the smaller quantity of it, provided MU > 0.

b Y

f o

y c t i t n a

u d Y Q a

IC2

IC1

O X Quantity of X Check Your Progress Fig. 1.12 Comparison between Lower and Upper Indifference Curves 8. Define an indifference curve. For example, consider the indifference curves IC1 and IC2 in Figure 1.12. Let us 9. What is the marginal begin at point a. The vertical movement from point a on the lower indifference rate of substitution curve IC1, to point b on the upper indifference curve IC2, means an increase in the (MRS)? quantity of Y by ab, the quantity of X remaining the same (OX). Similarly, a horizontal 10. What are the movement from point a to d means a greater quantity (ad) of commodity X, quantity properties that the of Y remaining the same (OY). The diagonal movement, i.e., from a to c, means a convexity of the indifference curves larger quantity of both X and Y. Unless the utility of additional quantities of X and Y imply? are equal to zero, these additional quantities will yield additional utility. Therefore,

the level of satisfaction indicated by the upper indifference curve (IC2) would always be greater than that indicated by the lower indifference curve (IC1). Self-Instructional 26 Material Consumer’s Choice 1.6 PROPERTIES OF BUDGET LINE AND DEMAND under Certainty FUNCTION

Indifference curve shows the satisfaction of the consumers where a higher indifference NOTES curve proves to have a higher level of consumer satisfaction. A consumer, thus, in order to reach his highest indifference curve would try to maximize his satisfaction. But for maximizing his satisfaction, he needs to pay more and more for the goods he purchases. There comes a point when he realizes that he has a limited money income with which he needs to purchase goods. Therefore, his satisfaction level would depend on the prices of the goods and the money income. To understand the consumer’s equilibrium, there is a need of understanding the budget line which is introduced into the indifference curve analysis which represents the prices of the goods and consumer’s money income. The budget line demonstrates all those combinations of two goods which the consumer can purchase by spending his given money income on the two goods at their given prices. A budget line is a straight line due to the fact that budget line is derived from a linear budget equation:

M = XPx + YPy and where this line intercepts with the axes is the maximum or highest amount of a commodity that can be purchased, if no other commodity is purchased.

Y

' A1 Y '

y t

i A d o

m A2 m o C

O X B2 B B1 Commodity 'X'

Fig. 1.13 A Budget Line

There is also a negative slope to the budget line. The line slopes downward as it moves from left to right. This negative slope gets established mathematically with noticing coefficient of ‘X’, i.e., – PX/PY when we rearrange the budget equation in the following manner:

–PX M Y = X+ PPYY

(PX, PY > 0) In mathematical terms, the budget line’s slope is coefficient of ‘X’ or derivative Y/ X in the equation given above. So, the budget line’s slope is negative of the price Self-Instructional Material 27 Consumer’s Choice ratio, i.e., – P /P In case where both the commodities ‘X’ and ‘Y’ have the same price, under Certainty x y. there must be a 45 degree angle of the budget line with both X and Y axis. A budget line that is flattened implies that on the X axis, the relative price of the commodity is lower. Geometrically, the budget line’s slope is considered to be the ratio of NOTES OB/OA meaning perpendicular/base or tan 8. Here, OB is the units of commodity ‘Y’ which can be purchased by the consumer when his total income is spent on purchasing ‘Y’.

It is equal to consumer’s income divided by the price of commodity ‘Y’ or M/Py. In the same manner, OA is the units of commodity ‘X’ which can be purchased by the

consumer when his total income is spent on purchasing ‘X’. It is equal to M/Px. So, budget line AB’s slope will be:

OB/OA = (M/Py)/(M/Px) = Px/Py It is also possible to work out the value of OB and OA with using X = 0 and Y = 0 in budget equation to obtain:

OB or Y = M/Py and OA or X = M/Px These are Y-intercept and X-intercept respectively. So, the budget line’s slope will be:

OB/OA = Px/Py. When interpreted in economic terms, on purchasing a single unit less of ‘X’, the

individual makes a saving equal to Px. The individual can employ this saved amount to

buy PX/PY units of ‘Y’.

Therefore, Px/Py or slope of the budget line represents the rate at which commodity ‘Y’ is substituted for commodity ‘X’ or the number of units of ‘Y’ that the consumer

needs to give up for an additional unit of ‘X’. If PX/PY or budget line’s slope is 2, it shows commodity ‘X’ has a price which is twice the price of commodity ‘Y’. Till the ratio of the price does not change, the budget line’s slope will remain the same. In case for the consumer’s same budget, there is a rise and fall in the prices of both commodities by the same proportion, the budget line will have an outward and inward parallel shift in the two cases, respectively, as given below. If the change in the two commodities’ price is not proportionate, the shift in the budget line will happen in a non-parallel manner. Additionally, in case the prices of both the commodities and also of the consumer’s budget changes in the same proportion, there will be no change in the budget line. In such a case, there is an offsetting of the change in the two commodities’ prices by the corresponding change that has taken place in the consumer’s income. Also, if there is no change in the price of the commodities while there is an increase (decrease) in the consumer’s income, there will be a parallel outward (inward) shift in the budget line as shown in Figure1.13. This is because now the consumer has the capacity to purchase more (less) as the income has increased (decreased). With this there will be an increase (decrease) in ‘X’ as well as ‘Y’ intercepts, in the two cases respectively. In each one of the case, the budget line’s slope of the budget will be the same. In the budget line, there is a representation of the combination of just two commodities which are purchasable by the individual. It specifies the real purchasing power or real income which is available to the consumer. Due to this, the budget line is also known as real income line. As the budget line’s diagram does not show monetary Self-Instructional 28 Material units, one cannot use it to find the price of a commodity. Nevertheless, one can use the Consumer’s Choice budget line’s slope to find out the price ratio of the two commodities. under Certainty The budget line displays the boundary line (dividing line), below which is the region that contains the two commodities’ attainable combinations. The right angled triangle that is created between the axes and the budget line is known as ‘feasible NOTES consumption choice set’ or ‘budget set’. The part that lies above the boundary line will be out of reach for the consumer based on the consumer’s income and the two commodities’ price. Hence, the concept of scarcity is reinforced by the budget line implying that it is not possible for the consumer to have unlimited amount of anything or everything. There will be a change in the slope as well as the position of the budget line in case the price of even one commodity changes while the income remains the same. Consider that the consumer’s income as well as the price of commodity ‘X’ remains unchanged while there is a fall in the price of commodity ‘Y’. In such a situation, the consumer will be in a position to buy more units of commodity ‘Y’ and the same quantity of commodity ‘X’. This will lead to a shift in the budget line just at the time when its end touches the Y-axis. This will increase Y – intercept. In Figure 1.14 (a), there is an outward shift in the budget line from BA to BA1, making it steeper. The budget line’s slope (provided by the two commodities’ price ratio) goes up from OA/OB to OA/OB. If the price rises for commodity ‘Y’, fewer units of the commodity will be purchasable by the consumer. Due to this there will be an inward shift in the budget line to BA2. This will decrease Y-intercept. In this case, there will be a decrease in the budget line’s slope to OA2/OB. If there is a change in the price of commodity ‘X’ while the price of commodity ‘Y’ and the consumer’s income remains the same, there will be a shift in the budget line only at its end touching the X-axis (Figure 1.14 (b)). If there is a fall in the price of commodity ‘X’, the consumer has the capacity to purchase additional units of commodity ‘X’. In this case, there will be an outward shift in the budget line, increasing the intercept on X-axis. In the graph given below, there is a shift in the budget line from AB to AB1. When there is a rise in the price of commodity ‘X’, the consumer is in a position to buy fewer units of commodity ‘X’. So, there is an inward shift in the budget line to

AB1. The new budget line is relatively flatter and steeper in the two cases, respectively.

Y Y

A1 A ' Y '

y t

i A d o m

m A2 o C Commodity 'Y' Commodity

X O B X O B2 B B1 Commodity 'X' Commodity 'X' (a) (b) Fig. 1.14 Shifts in Budget Line Due to Change in Price of Only One Commodity Self-Instructional Material 29 Consumer’s Choice When there is a need to depict greater than two commodities on a budget line, under Certainty one must isolate the commodity that is more important, and depict it on the X-axis. The rest of the commodities then get bundled together and are known as ‘composite commodity’ or money income, and are represented on the Y-axis. In a situation like this NOTES one, the budget line will be equal to the price of the commodity on the X-axis, meaning the money income is divided by the available number of units of commodity ‘X’. 1.6.1 Engel Aggregation and Cournot Aggregation Engel aggregation and Cournot aggregation are the properties of Marshallian demand curve. They both are restrictions that are imposed by theory on the systems of demand functions. They provide cross-equation restrictions which can be used for the purpose of empirical testing. Both of the aggregations begin with budget constraints which is equality in equilibrium. In case of Engel aggregation, the effect of change that takes place in expenditure due to the change in income has to be equal to the change in income. In case of Cournot aggregation, the effect of change that occurs in a single price needs to sum up to zero.

1.7 LINEAR EXPENDITURE SYSTEM

Several alternative formulation have been used to represent household demand systems. Examples include the almost ideal demand systems by Deaton and Muellbaucer, the Rotterdam model by Theil, and Barten, and the linear expenditure system (LES) by Stone. It has been observed a theoretically consistent demand system permits imposition of the general restrictions of classical demand theory. These restrictions are as follows: (a) Adding-up: Value of total demands equals total expenditure (b) Homogeneity: Demands are homogeneous of degree zero in total expenditure and prices (c) Symmetry: Cross-price derivatives of the Hicksian demands are symmetric (d) Negativity: Direct substitution effects are negative for the Hicksian demands The linear expenditure system is the most commonly used in CGE (Computable General Equilibrium) analysis due to convention and because it allows representation of subsistence consumption, in addition to satisfying the above restrictions. Here, we provide an overview of the LES demand system and its adaptation to the CGE framework. Linear expenditure system specifies the median voter utility function in: Check Your Progress Stone Geary form as under: U = β In(g-m ) + (1-β) in (x-m ). 11. What does a m g x consumer do to m is often considered as a subsistence level of consumption. m can be regarded attain his highest x x indifference curve? as a minimum required for local public services which depends on the median voter 12. What does a budget preferences. line demonstrate? The local public expenditure function is derived from the following programme 13. What does Engel MAX U (x, g) subject to y = p g + p x: and Cournot m m g x aggregation stand P g = p m + β(y –pgm –p m ) for? g g g m g x x n Self-Instructional With ∑ βi = 1 and i = I,… n. 30 Material i=1 Consumer’s Choice Pg g is measured by per capita expenditure in each municipality and pg is measured by the tax share. under Certainty The specification is a (simplified) linear expenditure system (LES) if we consider only two goods. The LES was derived by Stone (1954) by imposing theoretical restrictions (adding up, homogeneity and symmetry) on a general linear formulation of demand. NOTES In this framework, some minimum level of each good has to be consumed, irrespective of its price or the consumer’s income. So, the median voter first purchases the minimum level of each good, and the left-over income is then allocated in fixed proportion β to the demand for local goods. Since public spending is usually characterized by inertia, this specification is then particularly suited to account for these features of the fiscal process. Here, as we are only interested in the demand for municipal public goods, we suppose that the minimal private consumption can be incorporated in parameter γ . bb pg=mm m +βγ ( y − m −) gbb gm g The income elasticity may be written as: b m g ∂qy1 β b E(gi/ymi ) = with ω = ∂yq1 ω ym In addition, price elasticities are not constrained to increase with price, which distinguishes it from the linear form:

mg E (g / pg) = –1+(1–β ) g Thus, the income elasticity is always positive, and the municipal public goods are always normal goods since the marginal budget share β is positive. Furthermore, as 0 < β < 1, price elasticity is greater than –1 and the demand is inelastic.

1.8 OVERVIEW OF ESTIMATION OF DEMAND FUNCTIONS

A function is a symbolic statement of a relationship between the dependent and the independent variables. Demand function states the relationship between the demand for a product (the dependent variable) and its determinants (the independent variables). Let us consider a very simple case of market demand function. Suppose all the determinants of the aggregate demand for commodity X, other than its price, remain constant. This is a case of a short-run demand function. In the case of a short-run demand function, quantity demanded of X, (Dx) depends on its price (Px). The market demand function can then be symbolically written as

Dx = f (Px) ...(1.4)

In this function, Dx is a dependent and Px is an independent variable. The function

(1.4) reads ‘demand for commodity X (i.e., Dx) is the function of its price (Px)’. It implies that a change in Px (the independent variable) causes a change in Dx (the dependent variable). The function (1.4) however does not reveal the change in Dx for a given percentage change in Px, i.e., it does not give the quantitative relationship between Dx Self-Instructional Material 31 Consumer’s Choice and Px. When the quantitative relationship between Dx and Px is known, the demand under Certainty function may be expressed in the form of an equation. For example, a linear demand function is written as: D = a – bP ...(1.5) NOTES x x where ‘a’ is a constant, denoting total demand at zero price and b = ∆D/∆P, is

also a constant—it specifies the change in Dx in response to a change in Px. The form of a demand function depends on the nature of demand-price relationship. The two most common forms of demand functions are linear and non-linear demand function. Here we briefly discuss the linear and non-linear forms of demand functions. 1.8.1 Linear Demand Function A demand function is said to be linear when ∆D/∆P is constant and the function it results in is a linear demand curve. Eq. (1.5) represents a linear form of the demand function. Assuming that in an estimated demand function a = 100 and b = 5, demand function Eq. (1.5) can be written as:

Dx = 100 – 5Px ...(1.6) By substituting numerical values for Px, a demand schedule may be prepared as given in Table 1.4. Table 1.4 Demand Schedule

Px Dx = 100 – 5 Px Dx

0 Dx = 100 – 5 × 0 100

5 Dx = 100 – 5 × 5 75

10 Dx = 100 – 5 × 10 50

15 Dx = 100 – 5 × 15 25

20 Dx = 100 – 5 × 20 0 This demand schedule when plotted, gives a linear demand curve as shown in ∆ Figure 1.15. As can be seen in Table 1.4, each change in price, i.e., Px = 5 and each ∆ ∆ ∆ corresponding change in quantity demanded, i.e., Dx = 25. Therefore, Dx/ Px = b = 25/5 = 5 throughout. That is why demand function Eq. (1.6) produces a linear demand curve.

Fig. 1.15 Linear Demand Function Self-Instructional 32 Material Price Function Consumer’s Choice under Certainty From the demand function, one can easily obtain the price function. For example, given the demand function Eq. (1.5), the price function may be written as follows.

aD NOTES P = x x b a 1 P = D x bb x

Assuming a/b = a1 and 1/b = b1, the price function may be written as:

Px = a1 – b1 Dx ...(1.7) 1.8.2 Non-Linear Demand Function A demand function is said to be non-linear or curvilinear when the slope of the demand curve, (∆P/∆D) changes all along the curve. A non-linear demand function yields a demand curve instead of a demand line, as shown in Figure 1.16. A non-linear demand function takes the form of a power function of the form given below.

Dx = aPx–b …(1.8) a − b and Dx = …(1.9) Pcx + where a > 0, b > 0 and c > 0.

Fig. 1.16 Non-linear Demand Function

1.8.3 Multi-variate or Dynamic Demand Function: Long-Term Demand Function We have discussed above a single variable demand function, i.e., one with price as a single independent variable. This may be termed as a short-term demand function. In the long run, however, neither the individual nor the market demand for a product is determined by any one of its determinants because other determinants do not remain constant. The long-run demand for a product depends on the composite impact of all its determinants operating simultaneously. Therefore, for the purpose of estimating long- term demand for a product, all its relevant determinants are taken into account. They are then expressed in a functional form. The function describes the relationship between Self-Instructional Material 33 Consumer’s Choice the demand (a dependent variable) and its determinants (the independent or explanatory under Certainty variables). A demand function of this kind is called a multi-variate or dynamic demand

function. For instance, consider this statement: the demand (Dx) for a commodity X,

depends on its price (Px), consumer’s money income M, price of its substitute Y, (Py),

NOTES price of complementary goods (Pc) and consumer’s taste (T) and advertisement expenditure (A). This statement can be expressed in a functional form as,

Dx = f (Px, M, Py, Pc, T, A) ...(1.10) The demand function (1.10) describes the demand for commodity X which depends

on such determinants as Px, M, Py, Pc, T and A. If the relationship between Dx and the

quantifiable independent variables, Px, M, Py, Pc and A is of linear form, the estimable form of the demand function is expressed as:

Dx = a + bPx + cM + dPy + gPc + jA ...(1.11) where ‘a’ is a constant term and constants b, c, d, e, g and j are the coefficients

of relation between Dx and the respective independent variables. In a market demand function for a product, other independent variables, viz., size of population (N) and a measure of income distribution, i.e., Gini-coefficient, (G) may also be included.

1.9 SUMMARY

In this unit, you have learnt that, • When we look at it in terms of economics, ‘preference is the ordering of alternatives based on their relative utility, a process which results in an optimal “choice” (whether real or theoretical)’. • Human behaviour can be predicted with the help of scientific methods and many important decisions of life can also be modelled through scientific methods. Economists are generally not interested in the underlying reasons of the preferences in themselves, instead they show an interest in the theory of choice since it provides a stage for empirical demand analysis. • In economics, utility function is an important concept that measures preferences over a set of goods and services. • The consumers demand a commodity because they derive or expect to derive utility from that commodity. The expected utility from a commodity is the basis of demand for it. Check Your Progress • The concept of utility can be looked upon from two angles—from the commodity 14. Why is the linear angle and from the consumer’s angle. From the commodity angle, utility is the expenditure system most commonly want-satisfying property of a commodity. From the consumer’s angle, utility is used in CGE the psychological feeling of satisfaction, pleasure, happiness or well-being which (Computable a consumer derives from the consumption, possession or the use of a commodity. General Equilibrium)? • The central theme of the consumption theory is the analysis of utility maximizing 15. What is a function? behaviour of the consumer. The fundamental postulate of the consumption theory 16. On what does the is that all the consumers—individuals and households—aim at utility maximization long-run demand and all their decisions and actions as consumers are directed towards utility for a product maximization. depend?

Self-Instructional 34 Material • Assuming that utility is measurable and additive, total utility may be defined as the Consumer’s Choice sum of the utilities derived by a consumer from the various units of goods and under Certainty services he consumes. • The marginal utility is another most important concept used in economic analysis. Marginal utility may be defined in a number of ways. It is defined as the utility NOTES derived from the marginal unit consumed. It may also be defined as the addition to the total utility resulting from the consumption (or accumulation) of one additional unit. Marginal Utility (MU) thus refers to the change in the Total Utility (i.e., ∆TU) obtained from the consumption of an additional unit of a commodity. • The law of diminishing marginal utility is one of the fundamental laws of economics. This law states that as the quantity consumed of a commodity increases, the utility derived from each successive unit decreases, consumption of all other commodities remaining the same. • From economic analysis point of view, a consumer is a utility maximizing entity. From theoretical point of view, therefore, a consumer is said to have reached his equilibrium position when he has maximized the level of his satisfaction, given his resources and other conditions. • The law of equi-marginal utility explains the consumer’s equilibrium in a multi- commodity model. This law states that a consumer consumes various goods in such quantities that the MU derived per unit of expenditure on each good is the same. • Marshallian demand curve plots out the relationship that exists between a good’s quantity and its price with the quantity chosen optimally by an agent, with every other demand parameters being constant. • The change in demand due to price can be decomposed into a substitution effect and an income effect. • Unlike Marshall, the modern economists—Hicks in particular—have used the ordinal utility concept to analyse consumer’s behaviour. This is called ‘ordinal utility approach’. • An indifference curve may be defined as the locus of points, each representing a different combination of two substitute goods, which yield the same utility or level of satisfaction to the consumer. • An indifference curve is formed by substituting one good for another. The Marginal Rate of Substitution is the rate at which one commodity can be substituted for another, the level of satisfaction remaining the same. • The negative slope of an indifference curve implies: (a) that the two commodities can be substituted for each other; and (b) that if the quantity of one commodity decreases, quantity of the other commodity must increase so that the consumer stays at the same level of satisfaction. • Indifference curve shows the satisfaction of the consumers where a higher indifference curve proves to have a higher level of consumer satisfaction. A consumer, thus, in order to reach his highest indifference curve would try to maximize his satisfaction. • To understand the consumer’s equilibrium, there is a need of understanding the budget line which is introduced into the indifference curve analysis which represents the prices of the goods and consumer’s money income. The budget line Self-Instructional Material 35 Consumer’s Choice demonstrates all those combinations of two goods which the consumer can under Certainty purchase by spending his given money income on the two goods at their given prices. • In the budget line, there is a representation of the combination of just two NOTES commodities which are purchasable by the individual. It specifies the real purchasing power or real income which is available to the consumer. Due to this, the budget line is also known as real income line. • Engel aggregation and Cournot aggregation are the properties of Marshallian demand curve. They both are restrictions that are imposed by theory on the systems of demand functions. • Several alternative formulation have been used to represent household demand systems. Examples include the almost ideal demand systems by Deaton and Muellbauer, the Rotterdam model by Theil, and Barten, and the linear expenditure system (LES) by Stone. • The linear expenditure system is the most commonly used in CGE (Computable General Equilibrium) analysis due to convention and because it allows representation of subsistence consumption, in addition to satisfying the above restrictions. • The LES was derived by Stone (1954) by imposing theoretical restrictions (adding up, homogeneity and symmetry) on a general linear formulation of demand. • A function is a symbolic statement of a relationship between the dependent and the independent variables. Demand function states the relationship between the demand for a product (the dependent variable) and its determinants (the independent variables). • The long-run demand for a product depends on the composite impact of all its determinants operating simultaneously. Therefore, for the purpose of estimating long-term demand for a product, all its relevant determinants are taken into account.

1.10 KEY TERMS

• Preference: It is the ordering of alternatives based on their relative utility, a process which results in an optimal ‘choice’ (whether real or theoretical). • Utility function: In economics, utility function is an important concept that measures preferences over a set of goods and services. • Utility: It is the psychological feeling of satisfaction, pleasure, happiness or well- being which a consumer derives from the consumption, possession or the use of a commodity. • Total utility: Assuming that utility is measurable and additive, total utility may be defined as the sum of the utilities derived by a consumer from the various units of goods and services he consumes. • Marginal utility: It is defined as the utility derived from the marginal unit consumed. • Indifference curve: An indifference curve may be defined as the locus of points, each representing a different combination of two substitute goods, which yield the same utility or level of satisfaction to the consumer.

Self-Instructional 36 Material • Budget line: It demonstrates all those combinations of two goods which the Consumer’s Choice consumer can purchase by spending his given money income on the two goods at under Certainty their given prices.

1.11 ANSWERS TO ‘CHECK YOUR PROGRESS’ NOTES

1. Economists show an interest in the theory of choice since it provides a stage for empirical demand analysis. 2. In economics, utility function is an important concept that measures preferences over a set of goods and services. 3. An important attribute of the absolute concept of utility is that it is ethically neutral because a commodity may satisfy a frivolous or socially immoral need, e.g., alcohol, drugs or a profession like prostitution. 4. The central theme of the consumption theory is the analysis of utility maximizing behaviour of the consumer. 5. Assuming that utility is measurable and additive, total utility may be defined as the sum of the utilities derived by a consumer from the various units of goods and services he consumes. 6. A utility-maximizing consumer reaches his equilibrium position when allocation of his consumption expenditure is such that the last penny spent on each commodity yields the same utility. 7. (i) Shephard’s Lemma (ii) Marshallian demand curve 8. An indifference curve may be defined as the locus of points, each representing a different combination of two substitute goods, which yield the same utility or level of satisfaction to the consumer. 9. The marginal rate of substitution is the rate at which one commodity can be substituted for another, the level of satisfaction remaining the same. 10. The convexity of the indifference curves implies two properties: • The two commodities are imperfect substitutes for one another. • The marginal rate of substitution (MRS) between the two goods decreases as a consumer moves along an indifference curve. 11. Indifference curve shows the satisfaction of the consumers where a higher indifference curve proves to have a higher level of consumer satisfaction. A consumer, thus, in order to reach his highest indifference curve would try to maximize his satisfaction. 12. The budget line demonstrates all those combinations of two goods which the consumer can purchase by spending his given money income on the two goods at their given prices. 13. Engel aggregation and Cournot aggregation are the properties of Marshallian demand curve. They both are restrictions that are imposed by theory on the systems of demand functions. 14. The linear expenditure system is the most commonly used in CGE (computable general equilibrium) analysis due to convention and because it allows representation of subsistence consumption, in addition to satisfying the above restrictions. Self-Instructional Material 37 Consumer’s Choice 15. A function is a symbolic statement of a relationship between the dependent and under Certainty the independent variables. 16. The long-run demand for a product depends on the composite impact of all its determinants operating simultaneously. NOTES 1.12 QUESTIONS AND EXERCISES

Short-Answer Questions 1. What is preference? What is preference ordering? 2. What is utility? What are the two angles from which utility can be viewed? 3. State the law of diminishing marginal utility. What are the assumptions of the law of diminishing marginal utility? 4. When does a consumer reach his equilibrium? 5. Illustrate and derive the individual demand curve for a commodity. 6. What is the Shephard’s Lemma? 7. How can the Slutsky equation be derived? 8. What is an indifference map? Illustrate with the help of a diagram. 9. What is a budget line? Why is the budget line also referred to as real income line? 10. What is the linear expenditure system? Who developed this system? 11. What is a demand function? 12. Write a note on linear demand function. Long-Answer Questions 1. Discuss the concept of preference ordering and utility function. 2. Describe the meaning of utility and the Marshallian approach to consumer demand. 3. What is total and marginal utility? Discuss the law of diminishing marginal utility in detail. 4. Assess the analysis of consumer’s equilibrium. 5. Discuss the indirect utility function and the connection between utility maximization problem (UMP) and expenditure minimization problem (EMP). 6. With regard to Hicksian demand function, discuss the nature and properties of indifference curves. 7. Discuss the properties of budget line and Engel and Cournot aggregation. 8. Give an overview of the linear expenditure system and its adaptation to the CGE (Computable General Equilibrium). 9. Give an overview of estimation of demand functions.

Self-Instructional 38 Material Consumer’s Choice 1.13 FURTHER READING under Certainty

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. NOTES Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional Material 39

Theory of Production UNIT 2 THEORY OF PRODUCTION

Structure NOTES 2.0 Introduction 2.1 Unit Objectives 2.2 Production Function 2.3 Returns to Scale and Returns to a Factor 2.3.1 Short-run Laws of Production: Production with One Variable Input 2.3.2 Isoquants 2.3.3 Law of Returns to Scale 2.3.4 Elasticity of Factor Substitution 2.4 Types of Production Function 2.4.1 Homogenous Production Function 2.4.2 Cobb-Douglas Function and Derivations 2.4.3 CES Production Function and its Properties and Derivation of Leontief Function 2.5 Summary 2.6 Key Terms 2.7 Answers to ‘Check Your Progress’ 2.8 Questions and Exercises 2.9 Further Reading

2.0 INTRODUCTION

Whatever the objective of business firms, achieving optimum efficiency in production or minimizing cost for a given production is one of the prime concerns of business managers. In fact, the very survival of a firm in a competitive market depends on their ability to produce at a competitive cost. Therefore, managers of business firms endeavour to minimize the production cost of a given output or, in other words, maximize the output from a given quantity of inputs. In their effort to minimize the cost of production, the fundamental questions that managers are faced with are: (i) How can production be optimized or cost minimized? (ii) How does output respond to change in quantity of inputs? (iii) How does technology matter in reducing the cost of production? (iv) How can the least-cost combination of inputs be achieved? (v) Given the technology, what happens to the rate of return when more plants are added to the firm? The theory of production provides a theoretical answer to these questions through abstract models built under hypothetical conditions. The production theory may, therefore, not provide solutions to the real life problems. But it does provide tools and techniques to analyse the real-life production conditions and to find solutions to the practical business problems. This unit discusses the theory of production. Production theory deals with quantitative relationships—technical and technological relations—between inputs (especially labour and capital) and output. It further explains laws of variable proportions and returns to scale.

Self-Instructional Material 41 Theory of Production 2.1 UNIT OBJECTIVES

After going through this unit, you will be able to: NOTES • Discuss production function as a mathematical presentation of input-output relationship • Describe the short-run laws of production and the law of diminishing returns to a variable input • Distinguish between laws of returns to variable proportions and laws of returns to scale • Analyse the elasticity of factor substitution • Discuss the types of production function • State and illustrate the Cobb-Douglas production function • Evaluate the CES production function and its properties

2.2 PRODUCTION FUNCTION

Production function is a mathematical presentation of input-output relationship. More specifically, a production function states the technological relationship between inputs and output in the form of an equation, a table or a graph. In its general form, it specifies the inputs on which depends the production of a commodity or service. In its specific form, it states the quantitative relationships between inputs and output. Besides, the production function represents the technology of a firm, of an industry or of the economy as a whole. A production function may take the form of a schedule or a table, a graphed line or curve, an algebraic equation or a mathematical model. But each of these forms of a production function can be converted into its other forms. A real-life production function is generally very complex. It includes a wide range of inputs, viz., (i) land and building; (ii) labour including manual labour, engineering staff and production manager, (iii) capital, (iv) raw material, (v) time, and (vi) technology. All these variables enter the actual production function of a firm. The long-run production function is generally expressed as: Q = f (LB, L, K, M, T, t) where LB = land and building L = labour, K = capital, M = raw materials, T = technology and t = time. The economists have however reduced the number of input variables used in a production function to only two, viz., capital (K) and labour (L), for the sake of convenience and simplicity in the analysis of input-output relations. A production function with two variable inputs, K and L, is expressed as: Q = f (L, K) The reasons for excluding other inputs are following. Land and building (LB), as inputs, are constant for the economy as a whole, and hence they do not enter into the aggregate production function. However, land and building are not a constant variable for an individual firm or industry. In the case of individual firms, land and building are lumped with ‘capital’.

Self-Instructional 42 Material In case of ‘raw materials’ it has been observed that this input ‘bears a constant Theory of Production relation to output at all levels of production’. For example, cloth bears a constant relation to the number of garments. Similarly, for a given size of a house, the quantity of bricks, cement, steel, etc. remains constant, irrespective of the number of houses constructed. To consider another example, in car manufacturing of a particular brand or size, the NOTES quantity of steel, number of the engine, and number of tyres and tubes are fixed per car. Therefore, raw materials are left out of production function. So is the case, generally, with time and space. Also, technology (T) of production remains constant over a period of time. That is why, in most production functions, only labour and capital are included. We will illustrate the tabular and graphic forms of a production function when we move on to explain the laws of production. Here, let us illustrate the algebraic or mathematical form of a production function. It is this form of production function that is most commonly used in production analysis. To illustrate the algebraic form of production function, let us suppose that a coal mining firm employs only two inputs—capital (K) and labour (L)—in its coal production activity. As such, the general form of its production function may be expressed as:

QC = f (K, L) …(2.1) where QC = the quantity of coal produced per time unit, K = capital, and L = labour. The production function (2.1) implies that quantity of coal produced depends on the quantity of capital (K) and labour (L) employed to produce coal. Increasing coal production will require increasing K and L. Whether the firm can increase both K and L or only L depends on the time period it takes into account for increasing production, i.e., whether the firm considers a short-run or a long-run. By definition, as noted above, short-run is a period in which supply of capital is inelastic. In the short-run, therefore, the firm can increase coal production by increasing only labour since the supply of capital in the short run is fixed. Long-run is a period in which supply of both labour and capital is elastic. In the long-run, therefore, the firm can employ more of both capital and labour. Accordingly, there are two kinds of production functions: (i) Short-run production function (ii) Long-run production function The short-run production function or what may also be termed as ‘single variable input production function’, can be expressed as: Q = f (KL , ), where K is a constant …(2.2a) For example, suppose a production function is expressed as: Q = bL where b = ∆Q/∆L gives constant return to labour. In the long-term production function, both K and L are included and the function takes the following form. Q = f (K, L) …(2.2b) As mentioned above, a production function can be expressed in the form of an equation, a graph or a table, though each of these forms can be converted into its other forms. We illustrate here how a production function in the form of an equation can be Self-Instructional Material 43 Theory of Production converted into its tabular form. Consider, for example, the Cobb-Douglas production function—the most famous and widely used production function—given in the form of an equation as: Q = AKaLb …(2.3) NOTES (where K = Capital, L = Labour, and A, a and b are parameters and b = 1 – a) Production function (2.3) gives the general form of Cobb-Douglas production function. The numerical values of parameters A, a and b, can be estimated by using actual factory data on production, capital and labour. Suppose numerical values of parameters are estimated as A = 50, a = 0.5 and b = 0.5. Once numerical values are known, the Cobb-Douglas production function can be expressed in its specific form as follows. Q = 50 K0.5 L0.5 This production function can be used to obtain the maximum quantity (Q) that can be produced with different combinations of capital (K) and labour (L). The maximum quantity of output that can be produced from different combinations of K and L can be worked out by using the following formula.

Q = 50KL or Q= 50 K L

For example, suppose K = 2 and L = 5. Then:

Q 50 2 5 158

and if K = 5 and L = 5, then:

Q 50 5 5 250 Similarly, by assigning different numerical values to K and L, the resulting output can be worked out for different combinations of K and L and a tabular form of production function can be prepared. Table 2.1 shows the maximum quantity of a commodity that can be produced by using different combinations of K and L, both varying between 1 and 10 units. Table 2.1 Production Function in Tabular Form

Table 2.1 shows the units of output that can be produced with different combinations of capital and labour. The figures given in Table 2.1 can be graphed in a three-dimensional diagram. Self-Instructional 44 Material We now move on to explain the laws of production, first with one variable input Theory of Production and then with two variable inputs. We will then illustrate the laws of production with the help of production function. Before we proceed, it is important to note here that four combinations of K and L—10K + 1L, 5K + 2L, 2K + 5L and 1K + 10L—produce the same output, i.e., 158 units. NOTES When these combinations of K and L producing the same output are joined by a line, it produces a curve as shown in the table. This curve is called ‘isoquant’. An isoquant is a very important tool used to analyse input-output relationship.

2.3 RETURNS TO SCALE AND RETURNS TO A FACTOR

We will now discuss the law of variable proportions and returns to scale. 2.3.1 Short-run Laws of Production: Production with One Variable Input The laws of production state the relationship between output and input. In the short-run, input-output relations are studied with one variable input (labour), other inputs (especially, capital) held constant. The laws of production under these conditions are called the ‘laws of variable proportions’ or the ‘laws of returns to a variable input’. In this section, we explain the ‘laws of returns to a variable input’. Law of Diminishing Returns to a Variable Input The law of diminishing returns states that when more and more units of a variable input are used with a given quantity of fixed inputs, the total output may initially increase at increasing rate and then at a constant rate, but it will eventually increase at diminishing rates. That is, the marginal increase in total output decreases eventually when additional units of a variable factor are used, given quantity of fixed factors. Assumptions: The law of diminishing returns is based on the following assumptions: (i) Labour is the only variable input, capital remaining constant (ii) Labour is homogeneous (iii) The state of technology is given (iv) Input prices are given To illustrate the law of diminishing returns, let us assume (i) that a firm (say, the coal mining firm in our earlier example) has a set of mining machinery as its capital (K) fixed in the short-run, and (ii) that it can employ only more mine-workers to increase its coal production. Thus, the short-run production function for the firm will take the following form.

Qc = f(L), K constant Let us assume also that the labour-output relationship in coal production is given by a hypothetical production function of the following form.

3 2 Check Your Progress Qc = – L + 15L + 10L …(2.4) Given the production function (2.4), we may substitute different numerical values 1. Define production function. for L in the function and work out a series of Q , i.e., the quantity of coal that can be c 2. What is a long-run? 3. What is an isoquant?

Self-Instructional Material 45 Theory of Production produced with different number of workers. For example, if L = 5, then by substitution, we get:

3 2 Qc = – 5 + 15 × 5 + 10 × 5 = – 125 + 375 + 50 NOTES = 300 A tabular array of output levels associated with different number of workers from 1 to 12, in our hypothetical coal-production example, is given in Table 2.2 (Cols. 1 and 2).

What we need now is to work out marginal productivity of labour (MPL) to find the trend in the contribution of the marginal labour and average productivity of

labour (APL ) to find the average contribution of labour.

Marginal productivity of labour (MPL ) can be obtained by differentiating the production function (2.4). Thus, ∂Q MP = = – 3L2 + 30L + 10 …(2.5) L ∂L

By substituting numerical value for labour (L) in Equation (2.5), MPL can be obtained at different levels of labour employment. However, this method can be used only where labour is perfectly divisible and ∂L → 0. Since, in our example, each unit of L = 1, calculus method cannot be used.

Alternatively, where labour can be increased at least by one unit, MPL can be obtained as

MPL = TPL – TPL–1

The MPL worked out by this method is presented in Col. 3 of Table 2.2. Average productivity of labour (APL) can be obtained by dividing the production function by L. Thus, −+LLL3215 + 10 AP = L L = –L2 + 15L + 10 ...(2.6)

Now APL can be obtained by substituting the numerical value for L in Equation

(2.6). APL obtained by this method is given in Col. 4 of Table 2.2. Table 2.2 Three Stages of Production

No. of Workers Total Product Marginal Average Stages of (N) (TPL) Product* Product Production (tonnes) (MPL) (APL) (based on MPL) (1) (2) (3) (4) (5) 1 24 24 24 I 2 72 48 36 Increasing 3 138 66 46 returns 4 216 78 54 5 300 84 60 6 384 84 64 7 462 78 66 II 8 528 66 66 Diminishing 9 576 48 64 returns 10 600 24 60 11 594 – 6 54 III 12 552 – 42 46 Negative returns

Self-Instructional *MPL = TPn – TPn–1. MPL calculated by differential method will be different from that given in Col. 3. 46 Material The information contained in Table 2.2 is presented graphically in panels (a) and Theory of Production

(b) of Figure 2.1. Panel (a) of Figure 2.1 presents the total product curve (TPL) and panel (b) presents marginal product (MPL) and average product (APL) curves. The TPL schedule demonstrates the law of diminishing returns. As the curve TPL shows, the total output increases at an increasing rate till the employment of the 5th worker, as indicated NOTES by the increasing slope of the TPL curve. (See also Col. 3 of the table). Employment of the 6th worker contributes as much as the 5th worker. Note that beyond the employment of the 6th worker, although TPL continues to increase (until the 10th worker), the rate of increase in TPL (i.e., MPL) begins to fall. This shows the operation of the law of diminishing returns.

Fig. 2.1 Total, Average and Marginal Products

The three stages in production: Table 2.2 and Figure 2.1 present the three usual stages in the application of the laws of diminishing returns.

In stage I, TPL increases at increasing rate. This is indicated by the rising MPL till the employment of the 5th and 6th workers. Given the production function (2.4), the 6th worker produces as much as the 5th worker. The output from the 5th and the 6th workers represents an intermediate stage of constant returns to the variable factor, labour.

In stage II, TPL continues to increase but at diminishing rates, i.e., MPL begins to decline. This stage in production shows the law of diminishing returns to the variable factor. Total output reaches its maximum level at the employment of the 10th worker.

Beyond this level of labour employment, TPL begins to decline. This marks the beginning of stage III in production. To conclude, the law of diminishing returns can be stated as follows. Given the employment of the fixed factor (capital), when more and more workers are employed, the return from the additional worker may initially increase but will eventually decrease. Factors behind the laws of returns: As shown in Figure 2.1, the marginal productivity of labour (MPL) increases is stage I, whereas it decreases in stage II. In other words, in stage I, law of increasing returns is in operation and in stage II, the law of diminishing returns is in application. The reasons which underlie the application of the laws of returns in stages I and II may be described as follows. Self-Instructional Material 47 Theory of Production One of the important factors causing increasing returns to a variable factor is the indivisibility of fixed factor (capital). The minimum size of capital is given as it cannot be divided to suit the number of workers. Therefore, if labour is less than its optimum number, capital remains underutilized. Let us suppose that optimum capital-labour NOTES combination is 1:6. If capital is indivisible and less than 6 workers are employed, then capital would remain underutilized. When more and more workers are added, utilization of capital increases and also the productivity of additional worker. The second and the most important reason for increase in labour productivity is the division of labour that becomes possible with the employment of additional labour, until optimum capital-labour combination is reached. Once the optimum capital-labour ratio is reached, employment of additional workers amounts to substitution of capital with labour. But, technically, there is a limit to which one input can be substituted for another. That is, labour cannot substitute for capital beyond a limit. Hence, to replace the same amount of capital, more and more workers will have to be employed because per worker marginal productivity decreases. Also, with increasing number of workers, capital remaining the same, capital-labour ratio goes on decreasing. As a result, productivity of labour begins to decline. This marks the beginning of the second stage. Application of the Law of Diminishing Returns The law of diminishing returns is an empirical law, frequently observed in various production activities. This law, however, may not apply universally to all kinds of productive activities since it is not as true as the law of gravitation. In some productive activities, it may operate quickly, in some its operation may take a little longer time and in some others, it may not appear at all. This law has been found to operate in agricultural production more regularly than in industrial production. The reason is, in agriculture, natural factors play a predominant role whereas man-made factors play the major role in industrial production. Despite the limitations of the law, if increasing units of an input are applied to the fixed factors, the marginal returns to the variable input decrease eventually. Law of diminishing returns and business decisions: The law of diminishing returns as presented graphically has a relevance to the business decisions. The graph can help in identifying the rational and irrational stages of operations. It can also tell the business managers the number of workers (or other variable inputs) to apply to a given fixed input so that, given all other factors, output is maximum. As Figure 2.1 exhibits, capital is presumably underutilized in stage I. So, a firm operating in stage I is required to increase labour, and a firm operating in stage III is required to reduce labour, with a view to maximizing its total production. From the firm’s point of view, setting an output target in stages I and III is irrational. The only meaningful and rational stage from the firm’s point of view is stage II in which the firm can find answer to the question ‘how many workers to employ’. Figure 2.1 shows that the firm should employ a minimum of 7 workers and a maximum of 10 workers even if labour is available free of cost. This means that the firm has a limited choice—ranging from 7 to 10 workers. How many workers to employ against the fixed capital and how much to produce can be answered, only when the price of labour, i.e., wage rate, and that of the product are known. We will answer these questions now.

Self-Instructional 48 Material Determining Optimum Employment of Labour Theory of Production It may be recalled from Figure 2.1 that an output maximizing coal-mining firm would like to employ 10 workers since at this level of employment, the output is maximum. The firm can, however, employ 10 workers only if workers are available free of cost. But NOTES labour is not available free of cost—the firm is required to pay wages to the workers. Therefore, the question arises as to how many workers will the firm employ—10 or less or more than 10—to maximize its profit. A simple answer to this question is that the number of workers to be employed depends on the output that maximizes the firm’s profit, given the product price and the wage rate. This point can be proved as follows. Profit is maximum where: MC = MR In our example here, since labour is the only variable input, marginal cost (MC) equals marginal wages (MW), i.e., MC = MW. As regards MR, in case of factor employment, the concept of marginal revenue productivity (MRP) is used. The marginal revenue productivity is the value of product resulting from the marginal unit of variable input (labour). In specific terms, marginal revenue productivity (MRP) equals marginal physical productivity (MPL) of labour multiplied by the price (P) of the product, i.e.,

MRP = MPL × P For example, suppose that the price (P) of coal is given at ` 10 per quintal. Now,

MRP of a worker can be known by multiplying its MPL (as given in Table 2.2) by `10. For example, MRP of the 3rd worker (see Table 2.2) equals 66  10 = ` 660 and of the

4th worker, 78  10 = ` 780. Likewise, if the entire column (MPL) is multiplied by ` 10, it gives us a table showing marginal revenue productivity of workers. Let us suppose that wage rate (per time unit) is given at ` 660. Given the wage rate, the profit maximizing firm will employ only 8 workers because at this employment, MRP = wage rate = MRP of 8th worker; 66  10 = ` 660. If the firm employs the 9th worker, his MRP = 48  10 = ` 480 < ` 660. Clearly, the firm loses ` 180 on the 9th worker. And, if the firm employees less than 8 workers, it will not maximize profit.

Graphic illustration The process of optimum employment of variable input (labour) is illustrated graphically in Figure 2.2. When relevant series of MRP is graphed, it produces a MRP curve like one shown in Figure 2.2. Similarly, the MRP curve for any input may be drawn and compared with MC (or MW) curve. Labour being the only variable input, in our example, let us suppose that wage rate in the labour market is given at OW (Figure 2.2). When wage rate is constant, average wage (AW) equals the marginal wage (MW) i.e., AW = MW, for the entire range of employment in the short-run. When AW = MW, the supply of labour is shown by a straight horizontal line, as shown by the line AW = MW. With the introduction of MRP curve and AW = MW line (Figure 2.2), a profit maximizing firm can easily find the maximum number of workers that can be optimally employed against a fixed quantity of capital. Once the maximum number of workers is determined, the optimum quantity of the product is automatically determined.

Self-Instructional Material 49 Theory of Production

NOTES

Fig. 2.2 Determination of Labour Employment in the Short-Run

The marginality principle of profit maximization says that profit is maximum when MR = MC. This is a necessary condition of profit maximization. Figure 2.2 shows that MRP = MW (= MC ) are equal at point P, the point of intersection between MRP and AW = MW. The number of workers corresponding to this point is ON. A profit maximizing firm should, therefore, employ only ON workers. Given the number of workers, the total output can be known by multiplying ON with average labour productivity (AP). 2.3.2 Isoquants We have discussed in the preceding section the technological relationship between inputs and output assuming labour to be the only variable input, capital held constant. Now we will discuss the relationship between inputs and output under the condition that both the inputs, capital and labour, are variable factors. In the long-run, supply of both the inputs is supposed to be elastic and firms can hire larger quantities of both labour and capital. With larger employment of capital and labour, the scale of production increases. The technological relationship between changing scale of inputs and output is explained under the laws of returns to scale. The laws of returns to scale can be explained through the production function and isoquant curve technique. The most common and simple tool of analysis is isoquant curve technique. We will, therefore, first introduce and elaborate on this tool of analysis. The laws of return to scale will then be explained through isoquant curve technique. The laws of returns to scale through production function will be explained in the next section. The term ‘isoquant’ has been derived from the Greek word iso meaning ‘equal’ and Latin word quantus meaning ‘quantity’. The ‘isoquant curve’ is, therefore, also known as ‘equal product curve’ or ‘production indifference curve’. An isoquant curve can be defined as the locus of points representing various combinations of two inputs—capital and labour—yielding the same output. An ‘isoquant curve’ is analogous to an ‘indifference curve’, with two points of distinction: (a) an indifference curve is made of two consumer goods while an isoquant curve is constructed of two producer goods (labour and capital), and (b) an indifference curve assumes a level of satisfaction whereas an isoquant measures output of a commodity. An idea of isoquant can be had from the curve connecting 158 units from four different combinations of capital and labour given in Table 2.3. Isoquant curves are drawn on the basis of the following assumptions: • There are only two inputs, viz., labour (L) and capital (K), to produce a commodity X Self-Instructional 50 Material • Both L and K and product X are perfectly divisible Theory of Production • The two inputs—L and K—can substitute each other but at a diminishing rate as they are imperfect substitutes • The technology of production is given NOTES

Fig. 2.3 Isoquant Curves

Given these assumptions, it is technically possible to produce a given quantity of commodity X with various combinations of capital and labour. The factor combinations are so formed that the substitution of one factor for the other leaves the output unaffected.

This technological fact is presented through an isoquant curve (IQ1 = 100) in Figure 2.3.

The curve IQ1 all along its length represents a fixed quantity, 100 units of product X. This quantity of output can be produced with a number of labour-capital combinations. For example, points A, B, C, and D on the isoquant IQ1 show four different combinations of inputs, K and L, as given in Table 2.3, all yielding the same output—100 units. Note that movement from A to D indicates decreasing quantity of K and increasing number of L. This implies substitution of labour for capital such that all the input combinations yield the same quantity of commodity X, i.e., IQ1 = 100. Table 2.3 Capital Labour Combinations and Output

Points Input Combinations Output K+ L

A OK4 + OL1 = 100

B OK3 + OL2 = 100

C OK2 + OL3 = 100

D OK1 + OL4 = 100 Properties of Isoquant Curves Isoquants, i.e., production indifference curves, have the same properties as consumer’s indifference curves. Properties of isoquants are explained below in terms of inputs and output. (a) Isoquants have a negative slope: An isoquant has a negative slope in the economic region and in the economic range of isoquant. The economic region is the region on the production plane and economic range of isoquant is the range in which substitution between inputs is technically feasible. Economic region is also known as the product maximizing region. The negative slope of the isoquant implies substitutability

Self-Instructional Material 51 Theory of Production between the inputs. It means that if one of the inputs is reduced, the other input has to be so increased that the total output remains unaffected. For example, movement from A to B on IQ1 (Figure 2.3) means that if K4 K3 units of capital are removed from the production process, L1L2 units of labour have to be brought in to maintain the same level NOTES of output. (b) Isoquants are convex to the origin: Convexity of isoquants implies two things: (i) substitution between the two inputs, and (ii) diminishing marginal rate of technical substitution (MRTS) between the inputs in the economic region. The MRTS is defined as:

−∆K MRTS = = slope of the isoquant ∆L In plain words, MRTS is the rate at which a marginal unit of labour can substitute a marginal unit of capital (moving downward on the isoquant) without affecting the total output. This rate is indicated by the slope of the isoquant. The MRTS decreases for two reasons: (i) no factor is a perfect substitute for another, and (ii) inputs are subject to diminishing marginal returns. Therefore, more and more units of an input are needed to replace each successive unit of the other input. For example, suppose various units of K (minus sign ignored) in Figure 2.3 are equal, i.e.,

K1 = K2 = K3 the corresponding units of L substituting K go (in Figure 2.3) on increasing, i.e.,

L1 < L2 < L3 As a result, MRTS = ∆K/∆L goes on decreasing, i.e.,

∆K ∆K ∆K 1 > 2 > 3 ∆L1 ∆L2 ∆L3 (c) Isoquants are non-intersecting and non-tangential: The intersection or tangency between any two isoquants implies that a given quantity of a commodity can be produced with a smaller as well as a larger input-combination. This is untenable so long as marginal productivity of inputs is greater than zero. This point can be proved graphically. Note that in Figure 2.4, two isoquants intersect each other at point M. Consider two other points—point J on isoquant marked Q1 = 100 and point K on isoquant marked Q2 = 200 such that points K and J fall on a vertical line KL2, denoting the same amount of labour (OL2) but different units of capital—KL2 units of capital at point K and JL2 units of capital at point J. Note that point M is common to both the isoquants. Given the definition of isoquant, one can easily infer that a quantity that can be produced with the combination of K and L at point M can be produced also with factor combination at points J and K. On the isoquant Q1 = 100, factor combinations at points M and J yield 100 units of output. And, on the isoquant Q2 = 200, factor combinations at M and K yield 200 units of output. Since point M is common to both the isoquants, it follows that input combinations at J and K are equal in terms of output. This implies that in terms of output,

OL2(L) + JL2(K) = OL2(L) + KL2(K)

Since OL2 is common to both the sides, it means,

JL2(K) = KL2(K) Self-Instructional 52 Material But it can be seen in Figure 2.4 that, Theory of Production

JL2(K) < KL2(K)

NOTES

Fig. 2.4 Intersecting Isoquants

But the intersection of the two isoquants means that JL2 and KL2 are equal in terms of their output. This is wrong. That is why isoquants will not intersect or be tangent to each other. If they do, it violates the laws of production. (d) Upper isoquants represent higher level of output: Between any two isoquants, the upper one represents a higher level of output than the lower one. The reason is, an upper isoquant has a larger input combination, which, in general, produces a larger output. Therefore, upper isoquant has a higher level of output.

Fig. 2.5 Comparison of Output at Two Isoquants

For instance, IQ2 in Figure 2.5 will always indicate a higher level of output than

IQ1. For, any point at IQ2 consists of more of either capital or labour or both. For example, consider point a on IQ1 and compare it with any point at IQ2. The point b on

IQ2 indicates more of capital (ab), point d more of labour (ad) and point c more of both, capital and labour. Therefore, IQ2 represents a higher level of output (200 units) than

IQ1 indicating 100 units.

Self-Instructional Material 53 Theory of Production Isoquant Map and Economic Region of Production An isoquant map is a set of isoquants presented on a two-dimensional plane as shown by isoquants Q1, Q2, Q3 and Q4 in Figure 2.6. Each isoquant shows various combinations of two inputs that can be used to produce a given quantity of output. An NOTES upper isoquant is formed by a greater quantity of one or both the inputs than the input combination indicated by the lower isoquants. For example, isoquant Q2 indicates a greater input-combination than that shown by isoquant Q1 and so on.

Fig. 2.6 Isoquant Map

In the isoquant map, each upper isoquant indicates a larger input-combination than the lower ones, and each successive upper isoquant indicates a higher level of output than the lower ones. This is one of the properties of the isoquants. For example,

if isoquant Q1 represents an output equal to 100 units, isoquant Q2 represents an output greater than 100 units. As one of the properties of isoquants, no two isoquants can intersect or be tangent to one another. Economic region: Economic region is that area of production plane in which substitution between two inputs is technically feasible without affecting the output. This area is marked by locating the points on the isoquants at which MRTS = 0. A zero MRTS implies that further substitution between inputs is technically not feasible. It also determines the minimum quantity of an input that must be used to produce a given output. Beyond this point, an additional employment of one input will necessitate employing additional units of the other input. Such a point on an isoquant may be obtained by drawing a tangent to the isoquant and parallel to the vertical and horizontal axes, as shown by dashed lines in Figure 2.6. By joining the resulting points a, b, c and d, we get a line called the upper ridge line, Od. Similarly, by joining the points e, f, g and h, we get the lower ridge line, Oh. The ridge lines are locus of points on the isoquants where the marginal products (MP) of the inputs are equal to zero. The upper ridge line implies that MP of capital is zero along the line, Od. The lower ridge line implies that MP of labour is zero along the line, Oh. The area between the two ridge lines, Od and Oh, is called ‘economic Region’ or ‘technically efficient region’ of production. Any production technique, i.e., capital-labour combination, within the economic region is technically efficient to produce a given output. And, any production technique outside this region is technically inefficient since it requires more of both inputs to produce the same quantity of output.

Self-Instructional 54 Material Other Forms of Isoquants Theory of Production We have introduced above a convex isoquant that is most widely used in traditional economic theory. The shape of an isoquant, however, depends on the degree of substitutability between the factors in the production function. The convex isoquant presented in Figure 2.3 assumes a continuous substitutability between capital and labour NOTES but at a diminishing rate. The economists have, however, observed other degrees of substitutability between K and L and have demonstrated the existence of three other kinds of isoquants. 1. Linear isoquants: A linear isoquant is presented by the line AB in Figure 2.7. A linear isoquant implies perfect substitutability between the two inputs, K and L. The isoquant AB indicates that a given quantity of a product can be produced by using only capital or only labour or by using both. This is possible only when the two factors, K and L, are perfect substitutes for one another. A linear isoquant also implies that the MRTS between K and L remains constant throughout.

Fig. 2.7 Linear Isoquant

The mathematical form of the production function exhibiting perfect substitutability of factors is given as follows. If Q = f(K, L) then, Q = aK + bL ...(2.7) The production function (2.7) means that the total output, Q, is simply the weighted sum of K and L. The slope of the resulting isoquant from this production function is given by – b/a. This can be proved as shown below. Given the production function (2.7),

∂Q ∂Q MP = = a and MP = = b K ∂K L ∂L

MPL MP − b Since MRTS = and L = MPK MPK a − b Therefore, MRTS = = slope of the isoquant a The production function exhibiting perfect substitutability of factors is, however, unlikely to exist in the real world production process.

Self-Instructional Material 55 Theory of Production 2. Isoquants with fixed factor-proportion or L-shaped isoquants: When a production function assumes a fixed proportion between K and L, the isoquant takes ‘L’ shape, as shown by isoquants Q1 and Q2 in Figure 2.8. Such an isoquant implies zero substitutability between K and L. Instead, it assumes perfect complementarity between NOTES K and L. The perfect complementarity assumption implies that a given quantity of a commodity can be produced by one and only one combination of K and L and that the proportion of the inputs is fixed. It also implies that if the quantity of an input is increased and the quantity of the other input is held constant, there will be no change in output. The output can be increased only by increasing both the inputs proportionately.

As shown in Figure 2.8, to produce Q1 quantity of a product, OK1 units of K and

OL1 units of L are required. It means that if OK1 units of K are being used, OL1 units of

labour must be used to produce Q1 units of a commodity. Similarly, if OL1 units of labour

are employed, OK1 units of capital must be used to produce Q1. If units of only K or only

L are increased, output will not increase. If output is to be increased to Q2, K has to be

increased by K1K2 and labour by L1L2. This kind of technological relationship between K and L gives a fixed proportion production function. A fixed-proportion production function, called Leontief function, is given as:

Q = f(K, L) = min (aK, bL) …(2.8) where ‘min’ means that Q equals the lower of the two terms, aK and bL. That is, if aK > bL, Q = bL and if bL > aK, then Q = aK. If aK = bL, it would mean that both K and L are fully employed. Then the fixed capital labour ratio will be K/L = b/a. In contrast to a linear production function, the fixed-factor-proportion production function has a wide range of application in the real world. One can find many techniques of production in which a fixed proportion of labour and capital is fixed. For example, to run a taxi or to operate a photocopier, one needs only one labour. In these cases, the machine-labour proportion is fixed. Any extra labour would be redundant. Similarly, one can find cases in manufacturing industries where capital-labour proportions are fixed. 3. Kinked isoquants or linear programming isoquants: The fixed proportion production function (Figure 2.8) assumes that there is only one technique of production, and capital and labour can be combined only in a fixed proportion. It implies that to double the production, one would require doubling both the inputs, K and L. The line OB (Figure 2.8) shows that there is only one factor combination for a given level of output. In real life, however, the businessmen and the production engineers find in existence many, but not infinite, techniques of producing a given quantity of a commodity, each technique having a different fixed proportion of inputs. In fact, there is a wide range of machinery available to produce a commodity. Each machine requires a fixed number of workers to work it. This number varies from machine to machine. For example, 40 persons can be transported from one place to another by two methods: (i) by hiring 10 taxis and 10 drivers, or (ii) by hiring a bus and one driver. Each of these methods is a different process of production and has a different fixed proportion of capital and labour. Handlooms and power looms are other examples of two different factor proportions. One can similarly find many such processes of production in manufacturing industries, each process having a different fixed-factor proportion.

Self-Instructional 56 Material Theory of Production

NOTES

Fig. 2.8 The L-Shaped Isoquant

Let us suppose that for producing 10 units of a commodity, X, there are four different techniques of production available. Each technique has a different fixed factor- proportion, as given in Table 2.4. Table 2.4 Alternative Techniques of Producing 100 Units of X

S. No. Technique Capital + Labour Capital/labour ratio 1 OA 10 + 2 10:2 2 OB 6 + 3 6:3 3 OC 4 + 6 4:6 4 OD 3 + 10 3:10 The four hypothetical production techniques, as presented in Table 2.4, have been graphically presented in Figure 2.9. The ray OA represents a production process having a fixed factor-proportion of 10K:2L. Similarly, the other three production processes having fixed capital-labour ratios 6:3, 4:6 and 3:10 have been shown by the rays OB, OC and OD respectively. Points A, B, C and D represent four different production techniques. By joining the points, A, B, C and D, we get a kinked isoquant, ABCD. Each of the points on the kinked isoquant represents a combination of capital and labour that can produce 100 units of commodity X. If there are other processes of production, many other rays would be passing through different points between A and B, B and C, and C and D, increasing the number of kinks on the isoquant ABCD. The resulting isoquant would then resemble the typical isoquant. But there is a difference— each point on a typical isoquant is technically feasible, but on a kinked isoquant, only kinks are the technically feasible points. The kinked isoquant is used basically in linear programming. It is, therefore, also called linear programming isoquant or activity analysis isoquant. 2.3.3 Law of Returns to Scale Having introduced the isoquants—the basic tool of analysis—we now return to the laws of returns to scale. The laws of returns to scale explain the behaviour of output in response to a proportional and simultaneous change in inputs. Increasing inputs proportionately and simultaneously is, in fact, an expansion of the scale of production.

Self-Instructional Material 57 Theory of Production When a firm expands its scale, i.e., it increases both the inputs proportionately, then there are three technical possibilities: (i) Total output may increase more than proportionately NOTES (ii) Total output may increase proportionately (iii) Total output may increase less than proportionately Accordingly, there are three kinds of returns to scale: (i) Increasing returns to scale (ii) Constant returns to scale (iii) Diminishing returns to scale So far as the sequence of the laws of ‘returns to scale’ is concerned, the law of increasing returns to scale is followed by the law of constant and then by the law of diminishing returns to scale. This is the most common sequence of the laws. Let us now explain the laws of returns to scale with the help of isoquants for a two-input and single output production system. 1. Increasing returns to scale When inputs, K and L, are increased at a certain proportion and output increases more than proportionately, it exhibits increasing returns to scale. For example, if quantities of both the inputs, K and L, are successively doubled and the resultant output is more than doubled, the returns to scale is said to be increasing. The increasing returns to scale is illustrated in Figure 2.9. The movement from point a to b on the line OB means doubling the inputs. It can be seen in Figure 2.9 that input-combination increases from 1K + 1L to 2K + 2L. As a result of doubling the inputs, output is more than doubled: it increases from 10 to 25 units, i.e., an increase of 150 per cent. Similarly, the movement from point b to point c indicates 50 per cent increase in inputs as a result of which the output increases from 25 units to 50 units, i.e., by 100 per cent. Clearly, output increases more than the proportionate increase in inputs. This kind of relationship between the inputs and output shows increasing returns to scale.

Fig. 2.9 Increasing Returns to Scale

Factors behind increasing returns to scale There are at least three plausible reasons for increasing returns to scale. (i) Technical and managerial indivisibilities: Certain inputs, particularly mechanical

Self-Instructional equipment and managers, used in the process of production are available in a given size. 58 Material Such inputs cannot be divided into parts to suit small scale of production. For example, Theory of Production half a turbine cannot be used and one-third or a part of a composite harvester and earth- movers cannot be used. Similarly, half of a production manager cannot be employed, if part-time employment is not acceptable to the manager. Because of indivisibility of machinery and managers, given the state of technology, they have to be employed in NOTES a minimum quantity even if scale of production is much less than the capacity output. Therefore, when scale of production is expanded by increasing all the inputs, the productivity of indivisible factors increases exponentially because of technological advantage. This results in increasing returns to scale. (ii) Higher degree of specialization: Another factor causing increasing returns to scale is higher degree of specialization of both labour and machinery, which becomes possible with increase in scale of production. The use of specialized labour suitable to a particular job and of a composite machinery increases productivity of both labour and capital per unit of inputs. Their cumulative effects contribute to the increasing returns to scale. Besides, employment of specialized managerial personnel, e.g., administrative manager, production manager, sales manager and personnel manager, contributes a great deal in increasing production. (iii) Dimensional relations: Increasing returns to scale is also a matter of dimensional relations. For example, when the length and breadth of a room (15′ × 10′ = 150 sq. ft.) are doubled, then the size of the room is more than doubled: it increases to 30′ × 20′ = 600 sq. ft. When diameter of a pipe is doubled, the flow of water is more than doubled. In accordance with this dimensional relationship, when the labour and capital are doubled, the output is more than doubled and so on.

2. Constant returns to scale When the increase in output is proportionate to the increase in inputs, it exhibits constant returns to scale. For example, if quantities of both the inputs, K and L, are doubled and output is also doubled, then the returns to scale are said to be constant. Constant returns to scale are illustrated in Figure 2.10. The lines OA and OB are ‘product lines’ indicating two hypothetical techniques of production with optimum capital-labour ratio. The isoquants marked Q = 10, Q = 20 and Q = 30 indicate the three different levels of output. In the figure, the movement from points a to b indicates doubling both the inputs. When inputs are doubled, output is also doubled, i.e., output increases from 10 to 20. Similarly, the movement from a to c indicates trebling inputs—K increase to 3K and L to 3L. This leads to trebling the output—from 10 to 30.

Fig. 2.10 Constant Returns to Scale Self-Instructional Material 59 Theory of Production Alternatively, movement from point b to c indicates a 50 per cent increase in both labour and capital. This increase in inputs results in an increase of output from 20 to 30 units, i.e., a 50 per cent increase in output. In simple words, a 50 per cent increase in inputs leads to a 50 per cent increase in output. This relationship between a proportionate NOTES change in inputs and the same proportional change in outputs may be summed up as follows. 1K + 1L  10 2K + 2L  20 3K + 3L  30 This kind of relationship between inputs and output exhibits constant returns to scale. The constant returns to scale are attributed to the limits of the economies of scale. With expansion in the scale of production, economies arise from such factors as indivisibility of fixed factors, greater possibility of specialization of capital and labour, use of more efficient techniques of production, etc. But there is a limit to the economies of scale. When economies of scale reach their limits and diseconomies are yet to begin, returns to scale become constant. The constant returns to scale take place also where factors of production are perfectly divisible and where technology is such that capital- labour ratio is fixed. When the factors of production are perfectly divisible, the production function is homogeneous of degree 1 showing constant returns to scale. 3. Decreasing Returns to Scale The firms are faced with decreasing returns to scale when a certain proportionate increase in inputs, K and L, leads to a less than proportionate increase in output. For example, when inputs are doubled and output is less than doubled, then decreasing returns to scale is in operation. The decreasing returns to scale is illustrated in Figure 2.11. As the figure shows, when the inputs K and L are doubled, i.e., when capital-labour combination is increased from 1K + 1L to 2K + 2L, the output increases from 10 to 18 units. This means that when capital and labour are increased by 100 per cent, output increases by only 80 per cent. That is, increasing output is less that the proportionate increase in inputs. Similarly, movement from point b to c indicates a 50 per cent increase in the inputs. But, the output increases by only 33.3 per cent. This exhibits decreasing returns to scale.

Fig. 2.11 Decreasing Return to Scale

Self-Instructional 60 Material Causes of diminishing return to scale Theory of Production The decreasing returns to scale are attributed to the diseconomies of scale. The economists find that the most important factor causing diminishing returns to scale is ‘the diminishing return to management’, i.e., managerial diseconomies. As the size of NOTES the firms expands, managerial efficiency decreases. Another factor responsible for diminishing returns to scale is the limitedness or exhaustibility of the natural resources. For example, doubling of coal mining plant may not double the coal output because of limitedness of coal deposits or difficult accessibility to coal deposits. Similarly, doubling the fishing fleet may not double the fish output because availability of fish may decrease in the ocean when fishing is carried out on an increased scale. 2.3.4 Elasticity of Factor Substitution As you have studied, the concept of the marginal rate of technical substitution (MRTS) decreases along the isoquant. MRTS refers only to the slope of an isoquant, i.e., the ratio of marginal changes in inputs. It does not reveal the substitutability of one input for another—labour for capital—with changing combination of inputs. The economists have devised a method of measuring the degree of substitutability of factors, called the elasticity of factor substitution. The elasticity of substitution ( ) is formally defined as the percentage change in the capital-labour ratio (K/L) divided by the percentage change in marginal rate of technical substitution (MRTS), i.e., Percentage change in KL σ = Percentage change in MRTS

∂(KL /)( KL /) σ or = ∂()()MRTS MRTS Since all along an isoquant, K/L and MRTS move in the same direction, the value of is always positive. Besides, the elasticity of substitution ( ) is ‘a pure number, independent of the units of the measurement of K and L, since both the numerator and the denominator are measured in the same units’. The concept of elasticity of factor substitution is graphically presented in Figure 2.12. The movement from point A to B on the isoquant IQ, gives the ratio of change in MRTS. The rays OA and OB represent two techniques of production with different factor intensities. While line OA indicates capital intensive technique, line OB indicates labour intensive technique. The shift from OA to OB gives the change in factor intensity. The ratio between the two factor intensities measures the substitution elasticity.

Fig. 2.12 Graphic Derivation of Elasticity of Substitution Self-Instructional Material 61 Theory of Production The value of substitution elasticity depends on the curvature of the isoquants. It varies between 0 and , depending on the nature of production function. It is, in fact, the production function that determines the curvature of the various kinds of isoquants. For example, in case of fixed-proportion production function [see Equation (2.8)] yielding an NOTES L-shaped isoquant, = 0. If production function is such that the resulting isoquant is linear (see Figure 2.7), =  And, in case of a homogeneous production function of degree 1 of the Cobb-Douglas type, = 1.

2.4 TYPES OF PRODUCTION FUNCTION

The laws of returns to scale may be explained more precisely through a production function. Let us assume a production function involving two variable inputs (K and L) and one commodity X. The production function may then be expressed as:

Qx = f (K, L) …(2.9)

where Qx denotes the quantity of commodity X. Let us also assume that the production function is homogeneous. A production function is said to be homogeneous when all the inputs are increased in the same proportion and the proportion can be factored out. And, if all the inputs are increased by a certain proportion (say, k) and output increases in the same proportion (k), then production is said to be homogeneous of degree 1. This kind of production function may be expressed as follows.

kQx = f (kK, kL) …(2.10) or = k (K, L) A homogeneous production function of degree 1, as given in Equation (2.10), implies constant returns to scale. Equation (2.10) shows that increase in inputs, K and

L, by a multiple of k, increases output, Qx, by the same multiple (k). This means constant returns to scale. The constant returns to scale may not be applicable at all the levels of increase in inputs. Increasing inputs K and L in the same proportion may result in increasing or diminishing returns to scale. In other words, it is quite likely that if all the inputs are increased by a certain proportion, output may increase more or less than proportionately. Check Your Progress For example, if all the inputs are doubled, the output may not be doubled—it may increase 4. List the by less than or more than double. Then the production function may be expressed as: assumptions on which the law of hQ = f (kK, kL) …(2.11) diminishing returns x is based. where h denotes h-times increase in Qx, as a result of k-times increase in inputs, K and 5. Why does capital L. The proportion h may be greater than k, equal to k, or less than k. Accordingly, it remain underutilized reveals the three laws of returns to scale: when labour is less than its optimum (i) If h = k, production function reveals constant returns to scale. number? (ii) If h > k, it reveals increasing returns to scale. 6. What is the marginal revenue (iii) If h < k, it reveals decreasing returns to scale. productivity? 7. When do firms face This aspect has been elaborated in the following section. decreasing returns to scale?

Self-Instructional 62 Material 2.4.1 Homogenous Production Function Theory of Production In case of a homogeneous production function of degree 1 [Equation (2.10)], k has an exponent equal to 1, i.e., k = k1. It means that if k has an exponent equal to 1, the production function is homogeneous of degree 1. But, all the production functions need NOTES not be homogeneous of degree 1. They may be homogeneous of a degree less or greater than 1. It means that the exponent of k may be less than 1 or greater than 1. Let us assume that exponent of k is r, where r  1. A production function is said to be of degree r when all the inputs are multiplied by k and output increases by a multiple of kr. That is, if: f (kK, kL) = kr(K, L) = kr Q …(2.12) then function (2.12), is homogeneous of degree r. From the production function (2.12), we can again derive the laws of returns to scale. (i) If k > 1 and r < 1, it reveals decreasing returns to scale (ii) If k > 1 and r > 1, it reveals increasing returns to scale (iii) If k > 1 and r = 1, it means constant returns to scale For example, consider a multiplicative form of production function i.e., Q = K0.25 L0.50 …(2.13) If K and L are multiplied by k, and output increases by a multiple of h then, hQ = (kK)0.25 (kL)0.50 By factoring out k, we get, hQ = k0.25+0.50 [K0.25 L0.50] = k0.75 [K0.25 L0.50] …(2.14) In Equation (2.14), h = k0.75 and r = 0.75. This means that r < 1 and, thus, h < k. Production function (2.13), therefore, shows decreasing returns to scale. Now consider another production function given as: Q = K0.75 L1.25 X0.50 …(2.15) If K, L and X are multiplied by k, Q increases by a multiple of h then: hQ = (kK)0.75 (kL)1.25 (kX)0.50 By factoring out k, we get: hQ = k(0.75+1.25+0.50) [K0.75 L1.25 X0.50] = k2.5 [K0.75 L1.25 X0.50] Here h = k2.5 where 2.5 = r and r > 1. So h > k. Therefore, function (2.15) gives increasing returns to scale. Similarly, if in a production function, h = kr and r = 1, the production function gives constant returns to scale. 2.4.2 Cobb-Douglas Function and Derivations One of the widely used production functions is the power function. The most popular production function of this category is ‘Cobb-Douglas Production Function’ of the form Q = AKa Lb …(2.16) Self-Instructional Material 63 Theory of Production where A is a positive constant; a and b are positive fractions; and b = 1 – a. The Cobb-Douglas production function is often used in its following form. Q = AKa L1–a …(2.17)

NOTES Properties of Cobb-Douglas production function A power function of this kind has several important properties. First, the multiplicative form of the power function (2.16) can be changed into its log- linear form as: log Q = log A + a log K + b log L …(2.18) In its logarithmic form, the function becomes simple to handle and can be empirically estimated using linear regression analysis. Second, power functions are homogeneous and the degree of homogeneity is given by the sum of the exponents a and b. If a + b = 1, then the production function is homogeneous of degree 1 and implies constant returns to scale. Third, parameters a and b represent the elasticity co-efficient of output for inputs K and L, respectively. The output elasticity co-efficient () in respect of capital may be defined as proportional change in output as a result of a given change in K, keeping L constant. Thus, ∂∂QQ Q K ∈ = = ⋅ …(2.19) k ∂∂KK K Q By differentiating the production function Q = AKaLb with respect to K and substituting the result in Equation (2.19), we can find the elasticity co-efficient. We know that: ∂Q = a AKa–1 Lb ∂K By substituting the values for Q and Q/K in Equation (2.19), we get:

K ∈ = a AKa–1 Lb  = a …(2.20) k AKab L Thus, output-elasticity coefficient for K is ‘a’. The same procedure may be adopted to show that b is the elasticity co-efficient of output for L. Fourth, constants a and b represent the relative share of inputs, K and L, in total output Q. The share of K in Q is given by: ∂Q ⋅ K ∂K Similarly, the share of L in Q is given by:

∂Q ⋅ L ∂L

The relative share of K in Q can be obtained as:

∂Q 1 a AKab−1 L. K K ⋅ = = a ∂L Q AKab L Similarly, it can be shown that b gives the relative share of L in Q. Self-Instructional 64 Material Finally, Cobb-Douglas production function in its general form, Q = Ka L1– a implies that at Theory of Production zero cost, there will be zero production. Some Input-Output Relationships Some of the concepts used in production analysis can be easily derived from the Cobb- NOTES Douglas production function as shown below. (i) Average product (AP) of L and K: 1–a APL = A (K/L)

1 APK = A (L/K) (ii) Marginal product of L and K:

MPL = a.A (K/L) a = a (Q/L)

MPK = (a – 1) A (L/K) a = (1 – a) Q/K (iii) Marginal rate of technical substitution:

MP aK =L = ⋅ MRTSLk,  MPK 1− a L

2.4.3 CES Production Function and its Properties and Derivation of Leontief Function In addition to the Cobb-Douglas production function, there are other forms of production function, viz., ‘constant elasticity substitution’ (CES), ‘variable elasticity of substitution’ (VES), Leontief-type, and linear-type. Of these, the constant elasticity substitution (CES) production function is more widely used, apart from Cobb-Douglas production function. We will, therefore, discuss the CES production function briefly. The CES production function is expressed as: Q = A[αK–β + (1 – α)L–β]–1/β ... (2.21) or Q = A[αL–β + (1 – α)K–β]–1/β (A > 0, 0 < < 1, and > – 1) where L = labour, K = capital, and A, and are the three parameters. An important property of the CES production function is that it is homogeneous of degree 1. This can be proved by increasing both the inputs, K and L, by a constant factor and finding the final outcome. Let us suppose that inputs K and L are increased by a constant factor m. Then the production function given in Equation (2.21) can be written as follows. Q  = A[ (mK)– + (1 – ) (mL) – ] – 1/ ...(2.22) = A[m– { K – + (1 – )L– }] – 1/ = (m– )– 1/  A[ K – + (1 – ) L– ] – 1/

Since the term A[ K – + (1 – ) L– ] – 1/ in Equation (2.21) = Q, by substitution, we get: Q′ = mQ

Self-Instructional Material 65 Theory of Production Thus, the CES production function is homogeneous of degree 1. Given the production function (2.21), the marginal product of capital (K) can be obtained as:

β+1 NOTES δαQQ = ⋅ β  δKA K and of labour (L) as:

β+1 δQQ1 −α  = ⋅ β  δKA L The rate of technical substitution (RTS ) can be obtained as:

β +1 α L RTS =  1−α K

Merits of CES production function CES production function has certain advantages over the other functions: • It is a more general form of production function • It can be used to analyse all types of returns to scale • It removes many of the problems involved in the Cobb-Douglas production function. Limitations: The CES production function has, its own limitations. Some economists claim that it is not a general form of production function as it does not stand the empirical test. In other words, it is difficult to fit this function to empirical data. Also, Uzawa finds that it is difficult to generalize this function to n-number of factors. Besides, in this production function, parameter combines the effects of two factors, K and L. When there is technological change, given the scale of production, homogeneity parameter may be affected by both the inputs. This production function does not provide a measure to separate the effects on the productivity of inputs.

2.5 SUMMARY

In this unit, you have learnt that: • Production function is a mathematical presentation of input-output relationship. More specifically, a production function states the technological relationship Check Your Progress between inputs and output in the form of an equation, a table or a graph. 8. When is a • A real-life production function is generally very complex. It includes a wide range production function of inputs, viz., (i) land and building; (ii) labour including manual labour, engineering said to be staff and production manager, (iii) capital, (iv) raw material, (v) time, and (vi) homogeneous? technology. 9. Name the most popular production • Land and building (LB), as inputs, are constant for the economy as a whole, and function of the hence they do not enter into the aggregate production function. However, land power function category. and building are not a constant variable for an individual firm or industry. In the 10. List the advantages case of individual firms, land and building are lumped with ‘capital’. of CES production • Long-run is a period in which supply of both labour and capital is elastic. In the function. long-run, therefore, the firm can employ more of both capital and labour.

Self-Instructional 66 Material • There are two kinds of production functions: Theory of Production o Short-run production function o Long-run production function • An isoquant is a very important tool used to analyse input-output relationship. NOTES • The laws of production state the relationship between output and input. In the short-run, input-output relations are studied with one variable input (labour), other inputs (especially, capital) held constant. The laws of production under these conditions are called the ‘laws of variable proportions’ or the ‘laws of returns to a variable input’. • Given the employment of the fixed factor (capital), when more and more workers are employed, the return from the additional worker may initially increase but will eventually decrease. • One of the important factors causing increasing returns to a variable factor is the indivisibility of fixed factor (capital). The minimum size of capital is given as it cannot be divided to suit the number of workers. • The law of diminishing returns is an empirical law, frequently observed in various production activities. This law, however, may not apply universally to all kinds of productive activities since it is not as true as the law of gravitation. • The marginal revenue productivity is the value of product resulting from the marginal unit of variable input (labour). • The technological relationship between changing scale of inputs and output is explained under the laws of returns to scale. The laws of returns to scale can be explained through the production function and isoquant curve technique. • An isoquant curve can be defined as the locus of points representing various combinations of two inputs—capital and labour—yielding the same output. • Isoquants, i.e., production indifference curves, have the same properties as consumer’s indifference curves. • The intersection or tangency between any two isoquants implies that a given quantity of a commodity can be produced with a smaller as well as a larger input- combination. This is untenable so long as marginal productivity of inputs is greater than zero. • Between any two isoquants, the upper one represents a higher level of output than the lower one. The reason is, an upper isoquant has a larger input combination, which, in general, produces a larger output. Therefore, upper isoquant has a higher level of output. • Economic region is that area of production plane in which substitution between two inputs is technically feasible without affecting the output. • The kinked isoquant is used basically in linear programming. It is, therefore, also called linear programming isoquant or activity analysis isoquant. • There are three kinds of returns to scale: o Increasing returns to scale o Constant returns to scale o Diminishing returns to scale

Self-Instructional Material 67 Theory of Production • The constant returns to scale are attributed to the limits of the economies of scale. With expansion in the scale of production, economies arise from such factors as indivisibility of fixed factors, greater possibility of specialization of capital and labour, use of more efficient techniques of production, etc. NOTES • The firms are faced with decreasing returns to scale when a certain proportionate increase in inputs leads to a less than proportionate increase in output. • A production function is said to be homogeneous when all the inputs are increased in the same proportion and the proportion can be factored out. • One of the widely used production functions is the power function. The most popular production function of this category is ‘Cobb-Douglas Production Function’. • In addition to the Cobb-Douglas production function, there are other forms of production function, viz., ‘constant elasticity substitution’ (CES), ‘variable elasticity of substitution’ (VES), Leontief-type, and linear-type. • CES production function has certain advantages over the other functions: o It is a more general form of production function. o It can be used to analyse all types of returns to scale. o It removes many of the problems involved in the Cobb-Douglas production function.

2.6 KEY TERMS

• Production function: It is a mathematical presentation of input-output relationship. More specifically, a production function states the technological relationship between inputs and output in the form of an equation, a table or a graph. • Isoquant: An isoquant is a very important tool used to analyse input-output relationship. • Empirical law: Laws that are verifiable or provable by means of observation or experiment are called empirical law. • Marginal revenue productivity: It is the value of product resulting from the marginal unit of variable input (labour). • Isoquant curve: It can be defined as the locus of points representing various combinations of two inputs—capital and labour—yielding the same output.

2.7 ANSWERS TO ‘CHECK YOUR PROGRESS’

1. Production function is a mathematical presentation of input-output relationship. More specifically, a production function states the technological relationship between inputs and output in the form of an equation, a table or a graph. 2. Long-run is a period in which supply of both labour and capital is elastic. In the long-run, therefore, the firm can employ more of both capital and labour. 3. An isoquant is a very important tool used to analyse input-output relationship.

Self-Instructional 68 Material 4. The law of diminishing returns is based on the following assumptions: Theory of Production (i) Labour is the only variable input, capital remaining constant (ii) Labour is homogeneous (iii) The state of technology is given NOTES (iv) Input prices are given 5. One of the important factors causing increasing returns to a variable factor is the indivisibility of fixed factor (capital). The minimum size of capital is given as it cannot be divided to suit the number of workers. Therefore, if labour is less than its optimum number, capital remains underutilized. 6. The marginal revenue productivity is the value of product resulting from the marginal unit of variable input (labour). 7. The firms are faced with decreasing returns to scale when a certain proportionate increase in inputs leads to a less than proportionate increase in output. 8. A production function is said to be homogeneous when all the inputs are increased in the same proportion and the proportion can be factored out. 9. One of the widely used production functions is the power function. The most popular production function of this category is ‘Cobb-Douglas production function’. 10. CES production function has certain advantages over the other functions: (i) It is a more general form of production function. (ii) It can be used to analyse all types of returns to scale. (iii) It removes many of the problems involved in the Cobb-Douglas production function.

2.8 QUESTIONS AND EXERCISES

Short-Answer Questions 1. Why is a real-life production function complex? What does it include? 2. How is a production function, in case of two variable inputs, expressed? What are the reasons for excluding other inputs in the production function? 3. There are two kinds of production functions. What are they? 4. What does the law of diminishing returns state? 5. State why is the law of diminishing returns found to operate in agricultural production more regularly than in industrial production. 6. What is an isoquant curve? How is it different from an indifference curve? 7. What are the three kinds of returns to scale? 8. Determine whether the following production functions show constant, increasing or decreasing returns to scale: (a) Q = L0.60 K0.40 (b) Q = 5K0.5 L0.3 (c) Q = 4L + 2K 9. List the merits and limitations of CES production function.

Self-Instructional Material 69 Theory of Production Long-Answer Questions 1. Discuss production function as a mathematical presentation of input-output relationship. Also, discuss its types. NOTES 2. Describe the short-run laws of production and the law of diminishing returns to a variable input. 3. Explain the term isoquants and its properties. 4. Assess the other degrees of substitutability of isoquants excluding the convex isoquant. 5. Distinguish between laws of returns to variable proportions and laws of returns to scale. 6. What are the factors that cause increasing returns to scale? What are the reasons for diminishing returns to scale? 7. Critically analyse the elasticity of factor substitution. 8. Discuss the types of production function. 9. Illustrate the Cobb-Douglas production function. What are the properties of this function?

2.9 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional 70 Material Theory of Cost and UNIT 3 THEORY OF COST AND Factor Pricing FACTOR PRICING NOTES Structure 3.0 Introduction 3.1 Unit Objectives 3.2 Derivation of Cost Function from Production Function 3.2.1 Short-run Cost-output Relations 3.2.2 Cost Curves and the Law of Diminishing Returns 3.2.3 Output Optimization in the Short-run 3.3 Technical Progress: Hicksian Version 3.3.1 Harrodian Version of Technical Progress 3.4 Theories of Distribution 3.4.1 Marginal Productivity Theory 3.4.2 Euler’s Theorem 3.4.3 Ricardian Theory of Income Distribution 3.4.4 Kalecki’s Theory 3.4.5 Kaldor’s Saving Investment Model of Distribution and Growth 3.5 Summary 3.6 Key Terms 3.7 Answers to ‘Check Your Progress’ 3.8 Questions and Exercises 3.9 Further Reading

3.0 INTRODUCTION

Factor prices together with factor employment determine the share of each factor in the national income. For example, the share of labour income in the national income equals the national average wage rate multiplied by the number of workers. Thus, the theory of factor pricing also explains how national income is distributed between the various factors of production. Therefore, the theory of factor pricing is also known as theory of distribution. In fact, theories of factor pricing were developed to answer the question how national income is distributed between the factors of production. Distribution of national income among the various factors of production is called distribution of incomes. The founders of classical economics, especially Adam Smith and David Ricardo, were concerned with functional distribution of national income among the three basic factors of production—land, labour and capital. Smith and Ricardo attempted to answer the questions, ‘What determines the income of each group—the land owners, the labour and the capitalist in the total income?’ and how is the distribution of total income affected by economic growth? Another aspect of national income distribution is the group distribution of incomes, i.e., distribution of the total income among the various income groups. The size-distribution of national income classifies the society among the various income groups, e.g., high income, middle income, and low income groups. This kind of income distribution has a greater relevance in the context of social justice and social welfare. The theory of factor pricing is not fundamentally different from the product pricing. Both factor and commodity prices are determined essentially by the interaction of demand

Self-Instructional Material 71 Theory of Cost and and supply forces. Though there are differences in factors which determine demand for Factor Pricing and supply of commodities and of factors of production. Demand curves for both commodities and factors are derived demand curves. While demand for a commodity is derived from its marginal utility schedule, demand for a factor is derived from its NOTES marginal productivity schedule. There are, however, differences on the supply side. While supply of a product depends mainly on its marginal cost, the supply of factors of production depends on a number of factors which vary from factor to factor. In this unit, we will discuss the theories of factor price determination based on demand for and supply of the factors and the derivation of the cost function from production function.

3.1 UNIT OBJECTIVES

After going through this unit, you will be able to: • Derive cost function from production function • Assess the Hicksian and Harrodian versions of technical progress • Explain the marginal productivity theory and Euler’s theorem • Explain the Ricardian theory of income distribution and its implication • Discuss Kaldor’s saving investment model of distribution and growth • Explain Kalecki’s theory of income distribution

3.2 DERIVATION OF COST FUNCTION FROM PRODUCTION FUNCTION

Cost function is a symbolic statement of the technological relationship between cost and output. In its general form, it is expressed by an equation. Cost function can be expressed also in the form of a schedule and a graph. In fact, tabular, graphical, and algebraic equation forms of cost function can be converted in the form of each other. Going by its general form, total cost (TC) function is expressed as follows. TC = f (Q) This form of cost function tells only that there is a relationship between TC and output (Q). But it does not tell the nature of relationship between TC and Q. Since there is a positive relationship between TC and Q, cost function must be written as: TC = f (Q), ∆TC/∆Q > 0 This cost function means that TC depends on Q and that increase in output (Q) causes increase in TC. The nature and extent of this relationship between TC and Q depends on the product and technology. For example, cost of production increases at a constant rate in case of clothes, furniture and building, given the technology. In case raw materials and labour become scarce as production increases, cost of production increases at increasing rate. In case of agricultural products, cost of production increases first at decreasing rate and then at increasing rate. When these three kinds of TC and Q relationships are estimated on the basis of actual production and cost data, three different kinds of cost functions emerge as given in table 3.1.

Self-Instructional 72 Material Table 3.1 Kinds of Cost Functions and Change in TC Theory of Cost and Factor Pricing Nature of Cost Function Cost Function Change in TC Linear TC = a + bQ TC increases at constant rate Quadratic TC = a + bQ + Q2 TC increases at increasing rate NOTES Cubic TC = a + bQ – Q2 + Q3 TC increases first at decreasing rate than at increasing rate These cost functions are explained further and illustrated below graphically. 3.2.1 Short-run Cost-output Relations The theory of cost deals with the behaviour of cost in relation to a change in output. In other words, the cost theory deals with cost-output relations. The basic principle of cost behaviour is that the total cost increases with increase in output. This simple statement of an observed fact is of little theoretical and practical importance. What is of importance from a theoretical and managerial point of view is not the absolute increase in the total cost but the direction of change in the average cost (AC) and the marginal cost (MC). The direction of change in AC and MC—whether AC and MC decrease or increase or remain constant—depends on the nature of the cost function. The specific form of the cost function depends on whether the time framework chosen for cost analysis is short-run or long-run. It is important to recall here that some costs remain constant in the short-run while all costs are variable in the long-run. Thus, depending on whether cost analysis pertains to short-run or to long run, there are two kinds of cost functions: (i) Short-run cost functions, and (ii) Long-run cost functions Accordingly, the cost output relations are analysed in short-run and long-run framework. In this section, we will analyse the short-run cost-output relations by using cost function. The long-run cost-output relations are discussed in the following section. Cost Concepts used in Cost Analysis Before we discuss the cost-output relations, let us first look at the cost concepts and the components used to analyse the short-run cost-output relations. The basic analytical cost concepts used in the analysis of cost behaviour are total, average and marginal costs. The total cost (TC) is defined as the actual cost that must be incurred to produce a given quantity of output. The short-run TC is composed of two major elements: (i) total fixed cost (TFC), and (ii) total variable cost (TVC). That is, in the short-run, TC = TFC + TVC ...(3.1) As mentioned earlier, TFC (i.e., the cost of plant, machinery building, etc.) remains fixed in the short-run, whereas T VC varies with the variation in the output. For a given quantity of output (Q), the average total cost (AC), average fixed cost (AFC) and average variable cost (AVC) can be defined as follows:

TC T FC TVC AC = QQ

Self-Instructional Material 73 Theory of Cost and TFC Factor Pricing AFC = Q TVC AVC = NOTES Q and AC = AFC + AVC ...(3.2) Marginal cost (MC) is defined as the change in the total cost divided by the change in the total output, i.e., TC MC = ...(3.3) Q TC or as the first derivative of cost function, i.e., . Q Note that since ∆TC = ∆TFC + ∆TVC and, in the short-run, ∆TFC = 0, therefore, ∆TC = ∆TVC. Furthermore, under the marginality concept, where ∆Q = 1, MC = ∆TVC. Now we turn to cost function and derivation of cost curves. Short-run Cost Functions and Cost Curves The cost-output relations are determined by the cost function and are exhibited through cost curves. The shape of the cost curves depends on the nature of the cost function. Cost functions are derived from actual cost data of the firms. Given the cost data, estimated cost functions may take a variety of forms, yielding different kinds of cost curves. The cost curves produced by linear, quadratic and cubic cost functions are illustrated below. 1. Linear cost function: A linear cost function takes the following form. TC = a + bQ …(3.4) (where TC = total cost, Q = quantity produced, a = TFC, and b = ∂TC/∂Q). Given the cost function (Equation 3.4), AC and MC can be obtained as follows. TC a bQ a AC = + b Q QQ TC and MC = b Q Note that since ‘b’ is a constant factor, MC remains constant throughout in case of a linear cost function. Assuming an actual cost function given as: TC = 60 + 10Q …(3.5) the cost curves (TC, TVC and TFC) are graphed in Figure 3.1. Given the cost function (Equation 3.5), 60 AC = + 10 Q and MC = 10

Self-Instructional 74 Material 200 Theory of Cost and Factor Pricing 180 160 TC

140 Q 10 0 + t 120 6 s = NOTES o TC C 100 Q TVC 10 = 80 VC TFC = 60 T 60 TFC 40 20

0 1 234567891011 Output Fig. 3.1 Linear Cost Functions

Figure 3.1 shows the behaviour of TC, TVC and TFC. The straight horizontal line shows TFC and the line marked TVC = 10Q shows the movement in TVC. The total cost function is shown by TC = 60 + 10Q. More important is to notice the behaviour of AC and MC curves in Figure 3.2. Note that in case of a linear cost function MC remains constant, while AC continues to decline with the increase in output. This is so simply because of the logic of the linear cost function.

Fig. 3.2 AC and MC Curves Derived from Linear Cost Function

2. Quadratic cost function: A quadratic cost function is of the form: TC = a + bQ + Q2 ....(3.6) where a and b are constants. Given the cost function (Equation 3.6), AC and MC can be obtained as follows.

TC a bQ Q2 a AC = + b + Q ...(3.7) Q QQ

TC MC = = b + 2Q ...(3.8) Q Let us assume that the actual (or estimated) cost function is given as: TC = 50 + 5Q + Q2 …(3.9) Given the cost function (Equation 3.9), Self-Instructional Material 75 Theory of Cost and 50 C Factor Pricing AC = + Q + 5 and MC = = 5 + 2Q Q Q The cost curves that emerge from the cost function (3.9) are graphed in NOTES Figure 3.3 (a) and (b). As shown in panel (a), while fixed cost remains constant at 50, TVC is increasing at an increasing rate. The rising TVC sets the trend in the total cost (TC). Panel (b) shows the behaviour of AC, MC and AVC in a quadratic cost function. Note that MC and AVC are rising at a constant rate whereas AC first declines and then increases.

(a) 200 (b) 60 180

160 2 50

t Q s 140 + o 5Q 40

C

120 + 2 l 0 a 5 t 100 = Q o + 30 C T Q T 5 80 = C 20 MC 60 TV 50 FC (= 50) AC

40 costs Marginal and Average 10 AVC 20 0 1 234567891011 1 2345678910 11 Output (Q) Output (Q) Fig. 3.3 Cost Curves Derived from a Quadratic Cost Function

3. Cubic cost function: A cubic cost function is of the form: TC = a + bQ – cQ2 + Q3 …(3.10) where a, b and c are the parametric constants. From the cost function (3.10), AC and MC can be derived as follows.

23 TC a bQ cQ Q a AC = = + b – cQ + Q2 QQ Q TC and MC = = b – 2cQ + 3Q2 Q Let us suppose that the cost function is empirically estimated as: TC = 10 + 6Q – 0.9Q2 + 0.05Q3 …(3.11) Given the cost function (3.12), the TVC funstion can be derived as: TVC = 6Q – 0.9Q2 + 0.05Q3 …(3.12) The TC and TVC, based on Equations (3.11) and (3.12), respectively, have been calculated for Q = 1 to 16 and presented in Table 3.1. The TFC, TVC and TC have been graphically presented in Figure 3.4. As the figure shows, TFC remains fixed for the whole range of output, and hence, takes the form of a horizontal line—TFC. The TVC curve shows that the total variable cost first increases at a decreasing rate and then at an increasing rate with the increase in the output. The rate of increase can be obtained from the slope of the TVC curve. The pattern of change in the TVC stems directly from the law of increasing and diminishing returns to the variable inputs. As output increases, larger quantities of variable inputs are required to produce the same quantity of output due to diminishing returns. This causes a subsequent increase in the variable cost for producing the same output. Self-Instructional 76 Material Theory of Cost and Factor Pricing 80

70 TC

TVC 60 NOTES

50 t s o C 40

30

20

10 TFC

0 246810 12 14 16 18 Output Fig. 3.4 TC, TFC and TVC Curves

Table 3.2 Cost-Output Relations

Q FC TVC TC AFC AVC AC MC (1) (2) (3) (4) (5) (6) (7) (8)

0 10 0.0 10.00 — — — — 1 10 5.15 15.15 10.00 5.15 15.15 5.15 2 10 8.80 18.80 5.00 4.40 9.40 3.65 3 10 11.25 21.25 3.33 3.75 7.08 2.45 4 10 12.80 22.80 2.50 3.20 5.70 1.55 5 10 13.75 23.75 2.00 2.75 4.75 0.95 6 10 14.40 24.40 1.67 2.40 4.07 0.65 7 10 15.05 25.05 1.43 2.15 3.58 0.65 8 10 16.00 26.00 1.25 2.00 3.25 0.95 9 10 17.55 27.55 1.11 1.95 3.06 1.55 10 10 20.00 30.00 1.00 2.00 3.00 2.45 11 10 23.65 33.65 0.90 2.15 3.05 3.65 12 10 28.80 38.80 0.83 2.40 3.23 5.15 13 10 35.75 45.75 0.77 2.75 3.52 6.95 14 10 44.80 54.80 0.71 3.20 3.91 9.05 15 10 56.25 66.25 0.67 3.75 4.42 11.45 16 10 70.40 80.40 0.62 4.40 5.02 14.15

From Equations (3.11) and (3.12), we may derive the behavioural equations for AFC, AVC and AC. Let us first consider AFC. (a) Average fixed cost (AFC): As already mentioned, the costs that remain fixed for a certain level of output make the total fixed cost in the short-run. The fixed cost is represented by the constant term ‘a’ in Equation (3.10) and a = 10 as given in Equation (3.11). We know that: TFC AFC = ....(3.13) Q Self-Instructional Material 77 Theory of Cost and Substituting 10 for TFC in Equation 3.13, we get: Factor Pricing 10 AFC = ....(3.14) Q NOTES Equation (3.14) expresses the behaviour of AFC in relation to change in Q. The behaviour of AFC for Q from 1 to 16 is given in Table 3.2 (col. 5) and presented graphically by the AFC curve in Figure 3.5. The AFC curve is a rectangular hyperbola. (b) Average variable cost (AVC): As defined above, AVC = TVC/Q. Given the TVC function (Equation 3.12), we may express AVC as follows.

6QQ 0.923 0.05 Q AVC = Q = 6 – 0.9Q + 0.05Q2 ...(3.15) Having derived the AVC function in Equation (3.15), we may easily obtain the behaviour of AVC in response to change in Q. The behaviour of AVC for Q = 1 to 16 is given in Table 3.2 (col. 6), and graphically presented in Figure 3.5 by the AVC curve.

16 MC

14

C 12 M

d n a

10 C A

,

C 8 V A

, C

F 6 AC A AVC 4

2

AFC O 2 4 6 8 10 12 14 16 Output Fig. 3.5 Short-run AFC, AVC, AC and MC Curves

Critical value of AVC: From Equation (3.9), we may compute the critical value of Q in respect of AVC. The critical value of Q (in respect of AVC) is one that minimizes AVC. The AVC will be minimum when its rate of decrease equals zero. This can be accomplished by differentiating Equation (3.15) and setting it equal to zero. Thus, critical value of Q can be obtained as:

AVC Critical value of Q = = – 0.9 + 0.10 Q = 0 Q 0.10 Q = 0.9 Q = 9 In our example, the critical value of Q = 9. This can be verified from Table 3.1. The AVC is minimum (1.95) at output 9.

Self-Instructional 78 Material Theory of Cost and TC (c) Average cost (AC): The average cost (AC) is defined as AC = . Factor Pricing Q

Substituting Equation (3.11) for TC in the above equation, we get: NOTES 10 6QQ 0.923 0.05 Q AC = Q

10 = + 6 – 0.9Q + 0.05Q2 ...(3.16) Q The Equation (3.16) gives the behaviour of AC in response to change in Q. The behaviour of AC for Q = 1 to 16 is given in Col. 7 of Table 3.2 and graphically presented in Figure 3.5 by the AC curve. Note that AC curve is U-shaped. Minimization of AC: One objective of business firms is to minimize AC of their product or, which is the same as, to optimize the output. The level of output that minimizes AC can be obtained by differentiating Equation (3.16) and setting it equal to zero. Thus, the optimum value of Q can be obtained as follows.

AC 10 0.9 0.1Q = 0 QQ2 When simplified (multiplied by Q2) this equation takes the quadratic form as: – 10 – 0.9Q2 + 0.1Q3 = 0 or Q3 – 9Q2 – 100 = 0 ...(3.17) By solving equation (3.17) we get Q = 10. Thus, the critical value of output in respect of AC is 10. That is, AC reaches its minimum at Q = 10. This can be verified from Table 3.2. (d) Marginal cost (MC): The concept of marginal cost (MC) is useful particularly in economic analysis. MC is technically the first derivative of the TC function. Given the TC function in Equation (3.11), the MC function can be obtained as:

TC MC = = 6 – 1.8Q + 0.15Q2 ...(3.18) Q Equation (3.18) represents the behaviour of MC. The behaviour of MC for Q = 1 to 16 computed as MC = TCn– TCn–1 is given in Table 3.2 (col. 8) and graphically presented by the MC curve in Figure 3.5. The critical value of Q with respect to MC is 6 or 7. This can be seen from Table 3.2. 3.2.2 Cost Curves and the Law of Diminishing Returns Now we return to the law of variable proportions and explain it through the cost curves. Figures 3.4 and 3.5 represent the cost curves conforming to the short-term law of production, i.e., the law of diminishing returns. Let us recall the law: it states that when more and more units of a variable input are applied, other inputs held constant, the returns from the marginal units of the variable input may initially increase but it decreases eventually. The same law can also be interpreted in terms of decreasing and increasing costs. The law can then be stated as, if more and more units of a variable input are applied to a given amount of a fixed input, the marginal cost initially decreases, but eventually increases. Both interpretations of the law yield the same information—one in Self-Instructional Material 79 Theory of Cost and terms of marginal productivity of the variable input, and the other in terms of the Factor Pricing marginal cost. The former is expressed through a production function and the latter through a cost function. Figure 3.5 presents the short-run laws of return in terms of cost of production. As NOTES the figure shows, in the initial stage of production, both AFC and AVC are declining because of some internal economies. Since AC = AFC + AVC, AC is also declining. This shows the operation of the law of increasing returns to the variable input. But beyond a certain level of output (i.e., 9 units in our example), while AFC continues to fall, AVC starts increasing because of a faster increase in the TVC. Consequently, the rate of fall in AC decreases. The AC reaches its minimum when output increases to 10 units. Beyond this level of output, AC starts increasing which shows that the law of diminishing returns comes into operation. The MC curve represents the change in both the TVC and TC curves due to change in output. A downward trend in the MC shows increasing marginal productivity of the variable input mainly due to internal economy resulting from increase in production. Similarly, an upward trend in the MC shows increase in TVC, on the one hand, and decreasing marginal productivity of the variable input, on the other. Some important relationships between costs used in analysing the short-run cost- behaviour may now be summed up as follows: (a) Over the range of output both AFC and AVC fall, AC also falls because AC = AFC + AVC. (b) When AFC falls but AVC increases, change in AC depends on the rate of change in AFC and AVC. (i) If decrease in AFC > increase in AVC, then AC falls (ii) If decrease in AFC = increase in AVC, AC remains constant (iii) If decrease in AFC < increase in AVC, then AC increase (c) The relationship between AC and MC is of a varied nature. It may be described as follows: (i) When MC falls, AC follows, over a certain range of initial output. When MC is falling, the rate of fall in MC is greater than that of AC, because in the case of MC the decreasing marginal cost is attributed to a single marginal unit while, in case of AC, the decreasing marginal cost is distributed over the entire output. Therefore, AC decreases at a lower rate than MC. (ii) Similarly, when MC increases, AC also increases but at a lower rate for the reason given in (i). There is, however, a range of output over which the relationship does not exist. Compare the behaviour of MC and AC over the range of output from 6 to 10 units (Figure 3.5). Over this range of output, MC begins to increase while AC continues to decrease. The reason for this can be seen in Table 3.2: when MC starts increasing, it increases at a relatively lower rate which is sufficient only to reduce the rate of decrease in AC—not sufficient to push the AC up. That is why AC continues to fall over some range of output even if MC increases. (iii) The MC curve intersects the AC at its minimum point. This is simply a mathematical relationship between MC and AC curves when both of them are obtained from the same TC function. In simple words, when AC is at its minimum, it is neither increasing nor decreasing: it is constant. When AC is constant, AC = MC. That is the point of intersection.

Self-Instructional 80 Material 3.2.3 Output Optimization in the Short-run Theory of Cost and Factor Pricing Optimization of output in the short-run has been illustrated graphically in Figure 3.5. Let us suppose that a short-run cost function is given as: TC = 200 + 5Q + 2Q2 …(3.19) NOTES We have noted above that an optimum level of output is one that equalizes AC and MC. In other words, at optimum level of output, AC = MC. Given the cost function in Equation (3.19), 200 5QQ 2 2 200 AC = = + 5 + 2Q ... (3.20) Q Q TC and MC = = 5 + 4Q ... (3.21) Q By equating AC and MC equations, i.e., Equations (3.20) and (3.21), respectively, and solving them for Q, we get the optimum level of output. Thus,

200 Q + 5 + 2Q = 5 + 4Q, 200 = 2Q Q 2Q2 = 200 or Q = 10 Thus, given the cost function (3.19), the optimum output is 10.

3.3 TECHNICAL PROGRESS: HICKSIAN VERSION

There is an assumption that technology of production remains unchanged over the reference period. In the real world, however, technological progress does take place. Technological progress means a given quantity of output can be produced with less quantity of inputs or a given quantity of inputs can produce a greater quantity of output. This means a downward shift in the production function (the isoquant) towards the point of origin (O).

Check Your Progress 1. What is the basic principle of cost behaviour? 2. What are the basic analytical cost concepts used in the analysis of cost behaviour? Fig. 3.6 Technological Progress Neutral Fig. 3.7 Technological Progress Capital-Deepening 3. On what does the shape of the cost curves depend?

Self-Instructional Material 81 Theory of Cost and Technological progress is graphically shown in Figure 3.6. A given level of output Factor Pricing is shown by isoquants I, I′ and I″. That is, all three isoquants, I, I′, I″ represent the same level of output. The downward (or leftward) shift in the isoquant from the position of I to I′ and NOTES from I′ to I″ means that a given level of output can be produced with decreasing quantities of labour and capital represented by points a, b and c. This is possible only with technological progress. The movement from a towards c shows technological progress. The slope of the ray, OP, shows the constant capital-labour ratio. According to J. R. Hicks, technological progress may be classified as neutral, capital-deepening and labour-deepening. Technological progress is neutral if, at constant

K/L, the marginal rate of technical substitution of capital for labour i.e., MRTSl,k remains constant. The neutral technological progress is illustrated in Figure 3.6. At each equilibrium

point, MRTSl,k = w/r. When technological progress is neutral, both K/L and w/r remain unchaged. It follows that relative factor share remains unchanged when technological progress is neutral. Capital-deepening technological progress is illustrated in Figure 3.7. Technological

progress is capital-deepening when, at a constant capital/labour ratio (K/L), MRTSl,k

declines. It implies that, at constant K/L, MPk increases relative to MPl. Therefore, at

equilibrium w/r declines, as r increases relative to w, because w = VMPl. Consequently, the relative factor share changes in favour of K. That is, share of capital in the total output increases while that of labour decreases.

Technological progress is labour-deepening when, at a given K/L, the MRTSl,k increases. Labour-deepening technological progress is illustrated in Figure 3.8. It can be shown, following the above reasoning, that under labour-deepening technological progress, the share of labour in the total output increases while that of capital increases.

Fig. 3.8 Labour Deepening Technological Progress

3.3.1 Harrodian Version of Technical Progress From the 1930s to the 1970s many economists debated the classification of technological progress into neutral, labour- or capital-saving inventions. One of them was R. F. Harrod, who defined neutral inventions as those in which the capital-output ratio remains unaffected at a certain rate of interest. Harrodain technical change is obtained by capturing the essential technical interdependence of the system, characterised by the fact that commodity capital is reproducible. Here, there is no compulsion to include the price, only technology is employed. Therefore, the Harrodian concept is, on this premise, equal to the ‘standard’ Hicksian Self-Instructional 82 Material counterpart in that technology alone is being considered. Harrod developed a path- Theory of Cost and breaking theory of economic growth, i.e., the capital accumulation growth theory— Factor Pricing popularly known as Harrod-Domar growth theory. Harrod’s growth model is an extension of Keynesian short-term analysis of full employment and income theory. It provides ‘a more comprehensive long period theory NOTES of output’. Harrod and Domar had in their separate writings concerned themselves with the conditions and requirements of steady economic growth. Although their models differ in details, their conclusions are substantially the same. Their models are, therefore, known as Harrod-Domar growth model. Central Theme of Harrod Growth Model Harrod considers capital accumulation as a key factor in the process of economic growth. They emphasise that capital accumulation (i.e., net investment) has a double role to play in economic growth. It generates income, on the one hand, and increases production capacity of the economy, on the other. For example, establishment of a new factory generates income for those who supply labour, bricks, steel, cement, machinery and equipment and at the same time, it increases the total capital stock and thereby, the production capacity of the economy. The new income generated creates demand for goods and services. A necessary condition of economic growth is that the new demand (or spending) must be adequate enough to absorb the output generated by increase in capital stock or else there will be excess or idle production capacity. This condition should be fulfilled year after year in order to maintain full employment and to achieve steady economic growth in the long-run. This is the central theme of Harrod growth model. Let us now describe the Harrod model of economic growth in its formal form. Assumptions of Harrod growth model Harrod model assumes a constant capital-output ratio. That is, it assumes a simple production function with a constant capital-output co-efficient. At macro level, the model assumes that the national output is proportional to the total stock of capital. The assumption may thus be expressed as: Y = kK …(3.22) Where Y = national output; K = total stock of capital and k = output/capital ratio (i.e., the reciprocal of capital/output ratio). Since output/capital ratio is assumed to be constant, any increase in national output (∆Y) must be equal to k-times ∆K, i.e.: ∆Y = k ∆K …(3.23) It follows from Eq. (3.23) that growth in national output (∆Y) per time unit depends on and is limited by the growth in capital stock (∆K). If economy is assumed to be in equilibrium and the existing stock of capital is fully employed. Eq. (3.23) tells also how much additional capital (∆K) will be required to produce a given quantity of additional output (∆Y). Since increase in capital stock (∆K) in any period equals the net investment (I) of that period, Eq. (3.23) may be rewritten as: ∆Y =k I …(3.24)

Self-Instructional Material 83 Theory of Cost and Another important assumption of the Harrod model is that the society saves a Factor Pricing constant proportion (s) of the national income, (Y), i.e.: S = sY …(3.25) NOTES Where S = savings per unit of time, and s = marginal propensity to save. And, at equilibrium level of output, the desired savings equals the desired investment, i.e.: S =I = sY …(3.26) Given these assumptions, the growth rate, defined as ∆Y/Y, may be obtained as follows. If the term sY is substituted for I in Eq. (3.24) and both sides are divided by Y, it gives:

∆Y = k · s …(3.27) Y As Eq. (3.27) shows, the rate of growth equals the output/capital ratio (k) times marginal propensity to save (s). Since, growth rate ∆Y/Y, pertains to the condition that I = S, this may also be called equilibrium growth rate, which implies capacity utilisation of capital stock. This growth rate fulfills the expectations of the entrepreneurs. Therefore, this growth rate has been termed as warranted growth rate,’ (Gw), to use Harrod’s symbol. Harrod defines Gw as ‘that rate of growth which, if it occurs, will leave all parties satisfied that they have produced neither more nor less than the right amount.’ According to Harrod model, economic growth can be achieved either by increasing marginal propensity to save and increasing simultaneously the stock of capital, or by increasing the output/capital ratio. When marginal propensity to save increases overall savings increase. Savings transmuted into investment increases income and production capacity of the nation. Increase in income leads in increases in demand for goods so that additional output generated through additional investment is absorbed. On the other hand, increase in production capacity in one period creates more income in the following periods. Higher incomes lead to higher savings and investment and till higher income in the subsequent periods. In this process, the investment increases at an accelerated rate based on the principle of acceleration. This proposition of Harrod model is based on the assumption that warranted

growth rate (Gw) is equal to the actual or realized growth rate (Gr), i.e., expected growth rate is always realised. This is possible only under the following simplifying assumptions of the model: • mpc remains constant • Output/capital ratio remains constant • Technology of production is given • Economy is initially in equilibrium • There is no government expenditure and no foreign trade • There are no lags in adjustments (a) between demand and supply, and (b) between saving and investment Since these assumptions make the model economy unrealistic, the warranted (or expected) growth rate may not always be equal to the actual (realized) growth rate. And if warranted and actual growth rates are not equal, it will lead to economic instability.

Self-Instructional 84 Material Capital Accumulation and Labour Employment Theory of Cost and Factor Pricing We have so far discussed Harrod model confining to only one aspect of the model, i.e., accumulation of capital and growth. Let us now discuss another important aspect of the model, i.e., employment of labour. In Harrod model labour can be introduced to the NOTES model under the assumptions that: • Labour and capital are perfect complements, instead of substitutes, for each other • Capital/labour ratio is constant Given these assumptions, economic growth can take place only so long as the potential labour force is not fully employed. Thus, the potential labour supply imposes a limit on economic growth at the full employment level. It implies that: • Growth will take place beyond the full employment level only if supply of labour increases • Actual growth rate would be equal to warranted growth rate only if growth rate of labour force equals the warranted growth rate However, if labour force increases at a lower rate, the only way to maintain the growth rate is to bring in the labour-saving technology. Under this condition the long- term growth rate will depend on (i) growth rate of labour force (∆L/L) and the rate of progress in labour-saving technology (i.e., the rate at which capital substitutes labour, m). Thus, the maximum growth rate that can be sustained in the long-run will be equal to ∆ L/L plus m. Harrod calls this growth rate as natural growth rate (Gn). (c) Harrod Growth Model is a razor-edge model The major defect of the Harrod model is that the parameters used in this model, viz., capital/output ratio, marginal propensity to save, growth rate of labour force, progress rate of labour-saving technology, are all determined independently out of the model. The model therefore does not ensure the equilibrium growth rate in the long-run. Even the slightest change in the parameters will make the economy deviate from the path of equilibrium. That is why this model is sometimes called as ‘razor-edge model’.

3.4 THEORIES OF DISTRIBUTION

Distribution theory, in economics, is the systematic attempt to account for the sharing of the national income among the owners of the factors of production—land, labour, and Check Your Progress capital. 4. What is The theory of distribution takes cognizance of three noticeable sets of problems. technological These are as follows: progress? • 5. What according to Personal distribution problems: How is the national income distributed among Harrod and Domar people? is the key factor in • Functional distribution problems: What decides the prices of the factors of the process of economic growth? production? 6. State one • Share in national problems and share of labour, capital and land: How is the assumption of the national income disseminated proportionally among the factors of production? Harrod model. 7. State the major Even though the three sets of problems are apparently interconnected, they should defect of the Harrod not be confused with one another. Economists were distrustful of the potential of any model. considerable development in the lot of those at the foundation of the income allocation. Self-Instructional Material 85 Theory of Cost and They questioned the shortage of productive land and the propensity of population to rise Factor Pricing faster than the means of survival limits imposed on distributive justice. David Ricardo, in his book On the Principles of Political Economy and Taxation (1817), apprehended that the landlords would obtain a bigger share of the national income while capitalists NOTES would get fewer and less and that this change in allocation would lead to economic stagnation. 3.4.1 Marginal Productivity Theory The neo-classical approach to factor price determination is based on marginal productivity theory of factor. Marginal productivity theory is regarded as the general micro-theory of factor price determination. It provides an analytical framework for the analysis of determination of factor prices. The origin of marginal productivity concept can be traced into the writings of economic thinkers of the nineteenth century. The earliest hint of the concepts of ‘marginal product’ and its use in the determination of ‘natural wage’ appeared in Von Thunen’s Der Isolierte Staat (1826). Later, the concept also appeared, in Samnel Mountifont Longfield’s Lectures on Political Economy (1834) and in Henry George’s Progress and Poverty (1879). It was, in fact, John Bates Clark who had developed the marginal productivity theory as an analytical tool of analysing wage determination. According to Clark, the marginal productivity principle is a complete theory of wages, which could be well applied to other factors of production also. Although many theorists, including Marshall and Hicks, have objected to the marginal productivity theory being regarded as theory of wages or as theory of distribution, it is regarded as a sound theory of factor price determination. Strictly speaking, marginal productivity theory offers only a theory of demand for a factor of production. The marginal productivity theory provides an analytical framework for deriving the demand for a factor which is widely used in modern economic analysis. The factor demand curve, derived on the basis of its marginal productivity, combined with factor supply curve, gives the factor price determination. The derivation of factor demand curve is explained below with reference to labour. Marginal Productivity and Factor Demand Demand for a factor is a derived demand: It is derived on the basis of the marginal productivity of a factor. Firms demand factors of production—land, labour, capital—- because they are productive. Factors are demanded not merely because they are productive but also because the resulting product has a market value. Thus, demand for a factor of production depends on the existence of demand for the goods and services that a factor of production can create. The derivation of factor demand has been explained with reference to labour demand. Demand for a single factor: Labour The demand for a variable factor depends on the value of its marginal productivity. Therefore, we shall first derive the value of marginal productivity (VMP) curve of

labour. The VMPL for labour is drawn from the marginal productivity curve (MPL). The

MPL curve is shown in Figure 3.9. The curve MPL shows diminishing returns to the

variable factor—labour. If we multiply the MPL at each level of employment a constant

Self-Instructional 86 Material price Px, we get the value of marginal physical product curve, as shown by the curve Theory of Cost and Factor Pricing VMPL = MPL. Px. It is this curve which is the basis of demand curve for labour. The derivation of labour demand curve is illustrated in the following section.

NOTES

Fig. 3.9 MPL and VMPL Curves

Derivation of a firm’s labour

A firm’s demand curve for labour is derived on the basis of the VMPL curve on the following assumptions for the sake of simplicity in the analysis. (i) Firm’s objective is to maximize profit and profit condition is MR=MC=w. (ii) The firm uses a single variable factor, labour and the price of labour, wages (w), is constant.

(iii) The firm produces a single commodity whose price is constant at Px.

Given the assumptions and the VMPL curve, we can now derive the firm’s demand curve for labour. As assumed above, a profit maximising firm produces a quantity of output at which its MR=MC=w. This profit-maximization rule can be interpreted as a profit-maximizing firm increases its output upto the point at which the marginal cost of available factor (labour) employed equals the value of its product. In other words, a profit-maximizing firm employs a factor till the marginal cost of the variable factor (labour) equals the value of the marginal product of the factor (i.e., VMPL). The short-run equilibrium of the profit-maximising firm is illustrated in Figure

3.10. The VMPL curve shows the value of marginal product of labour, the only variable factor. The SL lines present the labour supply curves for an individual firm [assumption

(b)], at the constant wage rates. The VMPL curve and SL3 line intersect each other at point E3, where VMPL= W3. The profit-maximizing firm will, therefore, employ only OL1 units of labour. By employing OL1 units of labour, the firm maximizes its profit. Given these conditions, any additional employment of labour will make W3 > VMPL. Hence, the total profit will decrease by W3 – VMPL. Similarly, if one unit less of labour is employed, VMPL will be greater than W3 and the total profit is reduced by VMPL – W3.

Thus, given the VMPL and SL3, the profit maximizing firm will demand only OL1 units of labour.

Self-Instructional Material 87 Theory of Cost and Factor Pricing

NOTES

Fig. 3.10 MPL and VMPL Curves The above analysis can be extended to derive the firm’s demand curve for labour.

If wage rate falls to OW2 firm’s equilibrium point shifts from point E3 to E2 increasing the

demand for labour from OL1 to OL2. Similarly, when wage rate falls further to OW1,

firm’s equilibrium shifts downward to E1 causing an increase in the demand for labour to

OL3. To summarize, when wage rate is OW3, demand for labour OL1; when wage rate

falls to OW2, demand for labour increases to OL2; and when wage rate falls further to

OW1, labour demand increases to OL3. Obviously, as wage rate falls, demand for labour increases. This relationship between the wage rate and labour demand gives a usual

downward sloping demand curve for labour, which is, by definition, the same as VMPL curve. It may now be concluded that individual demand curve for a single variable

factor (e.g., labour) is given by its value of marginal product curve (VMPL) or its marginal

revenue product curve (MRPL). When all the firms of an industry are using a single variable factor, industry’s demand for labour is a horizontal summation of the individual demand curve. Factor Price Determination in Perfect Market

We have derived above the market demand curve for labour, as shown by curve D2 in

Figure 3.11. The labour supply curve is shown through the curve SL. The labour supply

curve (SL) shows that labour supply increases in wage rate. The tools may now be applied to illustrate the factor price (wage) determination in perfectly competitive markets. Figure 3.11 shows the determination of wage in a competitive market. As shown in the figure, the demand curve for and supply curve of labour intersect each other at point P, where demand for and supply of labour are equal at OL, and wage-rate is determined at OW. This wage rate will remain stable in a competitive market so long as demand supply conditions do not change. This final analysis of factor price determination gives a brief analysis of marginal productivity theory of factor price determination with reference to labour. But it applies to other factors also.

Self-Instructional 88 Material Theory of Cost and Factor Pricing

NOTES

Fig. 3.11 Determination of Wages in a Perfectly Competitive Market

3.4.2 Euler’s Theorem One of the earlier proofs to the distribution of national income according to marginal productivity of production factors was provided by Swiss mathematician Leonard Euler (1701–83), which is known as Euler Theorem. Euler Theorem demonstrates that if production function is homogeneous of degree one (which exhibits constant returns to scale), then: ∂ ∂ Q = ⋅+ ⋅ ...(3.28) ∂ ∂ ∂ ∂ ∂ ∂ Since Q/ L = MPl and Q/ K = MPk, Eq. (3.28) takes the form,

Q = MPl·L + MPk·K This may be proved as follows. A production function, Q = f (L, K), is homogeneous of degree v if: f(λ L, λ K) = λv · f(L, K) ...(3.29) By differentiating Eq. (3.29) with respect to λ, we get:

L· +⋅

= ν·λν–1 f(L, K)

When return to scale is constant, ν = 1, and then Eq. (3.29) may be written as:

Q = L (MPl) + K (MPk) = f (L, K)

Thus, Q = MPl·L + MPk·K Multiplying MP by the price of product, P, we get:

P·Q = (MPl·P) L + (MPk·P) K

= VMPl·L + VMPk·K

If VMPl = w and VMPk = r, then: P·Q = w·L + r·K It is thus, proved that if each factor is paid a sum equal to its VMP, the total value of product is exhausted. This is Euler’s product exhaustion theorem.

Self-Instructional Material 89 Theory of Cost and 3.4.3 Ricardian Theory of Income Distribution Factor Pricing Income distribution (as per the economics concept) is how a nation’s total GDP is dispersed amongst its population. David Ricardo opined that the principle issue of political economy NOTES was the laws governing the distribution of income. He was a successful broker who developed a theoretical model popularly known as ‘corn laws’. The corn laws imposed tariffs on the import of agricultural products, which led to an increase in their prices, domestically. Then there emerged a struggle between the interest of landlords and manufacturing concerns over economic policy and control of parliament. The significance of David Ricardo’s model is that it was one of the initial models used in economics, intended at the amplification that how income is distributed or dispersed in society. The Ricardian model is based upon certain assumptions. These assumptions are as under: 1. There is only one industry, i.e., agriculture 2. There is only one good, i.e., grain 3. There are three kinds of people in the economy, i.e., capitalists, workers and landlords (i) Capitalists: The capitalist start their process of economic growth with saving and investment. The reward for it is in the form of profits (P). The profits are obtained after making payment of wages and rents out of gross revenues. The capital can be divided into fixed capital and working capital. Machine is an example of fixed capital and wage fund (WF) is an example of working capital in Ricardo’s model of income distribution. (ii) Workers: The workers get wages (w) as a reward of their work. They represent the labour force of the economy. (iii) Landlords: They provide land to allow production (y) to take place in the economy and the in return they get rent (R) as a reward. 4. The principle of margin applies to labour. The marginal product of labour along with average product of land is decreasing. 5. Says’ law is applicable which says that supply creates its own demand. It further elaborates that whatever is saved is invested. 6. Agriculture is labour intensive and manufacturing is capital intensive. 7. Land is fixed and differs in fertility. 8. Law of diminishing returns is prevailing which affects labour and land. Labour is considered as a variable factor of production and land is considered as fixed factor of production. Table 3.3 Increases in Output (in plots of land of decreasing quality →)

No. of workers (each A B C D E F with one shovel) 1 50 45 40 35 30 25 2 45 40 35 30 25 20 3 40 35 30 25 20 15 4 35 30 25 20 15 10 5 30 25 20 15 10 5 Self-Instructional 6 25 20 15 10 5 0 90 Material 9. Principle of economic surplus is prevailing which says that the profits are Theory of Cost and determined on the basis of surplus production. Factor Pricing

Y

P NOTES D C RENT A A P B N

R PROFITS P O K M

C W WAGES O X LABOUR M

Fig. 3.12 P-AP and P-MP Curves

As explained in the Figure 3.12, the y-axis measures the quantities of ‘corn’ which is the output of all agricultural land and x-axis measures the amount of labour employed on agriculture land. At a given state of knowledge and natural environment, the P-AP curve represents the product per unit of labour and curve P-MP represents the marginal product of the labour. These two curves are the result of assumption of diminishing returns. The corn-output is determined at a place where the quantity of labour is given, for any given working force, OM total output is represented by the rectangle OCDM. Rent is determined through the difference in product of labour on ‘marginal’ land and product on average land, or the difference between average and marginal labour productivity which is dependent upon the elasticity of P-AP curve. Implication of the Theory In the short run, the corn laws result in raising the price of agricultural product. It leads to cultivation of marginal or less fertile land to earn profits. It raises the demand for more fertile land and leads to increased rents because of competitive bids. The increased rent paid to landlords cause reduced profits and percentage profit per unit of wage. The lesser the profits the lesser is the savings which reduces the investment or accumulation of capital. And as per Say’s law, lesser investment causes slow economic growth. Therefore, the policy recommendation is in favour of a laissez faire economy. And it suggests corn laws to be eliminated. Therefore, by redistribution of income to capitalists can push the economic growth. Ricardo believed there was a coincidence in the interest of capitalists and interest of society, and contradiction in the interest of landlords and interest of society. In the long run, the growth in population causes use of marginal land and increased rents for and reduced profits which disappear gradually. At this stationary state of the economy, there is no accumulation of profits and capitalism ceases. Ricardo is pessimistic of the long run and says that economy can do better in the short run. Therefore, Ricardo concluded that there is no benefit of worrying about long- term growth of an economy. It is just a waste of time. And instead of worrying about the steady state of economy, the more important issue to be considered is how to distribute the output among different classes of the society. He was of the opinion that ultimately there will be no increase in the total output of an economy. Therefore, it is more important to find out ways on how to share limited output of the economy. It is to be shared among different sectors rather than considering more on the methods of making economy richer. The following quotation of Ricardo gives a glimpse of his theory. Self-Instructional Material 91 Theory of Cost and ‘Political economy, you think, is an enquiry into the nature and causes of wealth. Factor Pricing I think it should rather be called an enquiry into the laws which determine the division of produce of industry amongst the classes that concur in its formation. No law can be laid down respecting quantity, but a tolerably correct one can be laid down respecting NOTES proportions. Every day I am more satisfied that the former enquiry is vain and delusive, and the latter the only true object of the science.’ (David Ricardo, ‘Letter to T. R. Malthus’, October 9, 1820, in Collected Works, Vol. VIII: p.278-9). 3.4.4 Kalecki’s Theory Income distribution plays an important task in Michal Kalecki’s theory of effective demand. According to Kalecki, output and employment depend on capitalist spending, and on the share of profits in national income. Kalecki’s theory of income distribution is closely attached with his theory of price determination, and the latter is associated with his vision that recent capitalism is distinguished by market imperfections, equally on the labour market and on the product market. By centering on these imperfections, Kalecki obtained two vital dissimilarities between perfect and imperfect competition. The primary difference is that in perfect competition, for any particular firm production is not restricted by demand, nevertheless by costs and prices. Because individual firms facade a horizontal demand curve, they are cost inhibited, in that by vaguely lowering their price they can put up for sale whatsoever quantity they desire as long as marginal cost is under the market price. On the contrary, in the case of imperfect competition firms are demand- constrained, as they would freely produce extra if only they could put up for sale at the existing or a somewhat lower price; but they cannot, since their supply has an impact on the price. As a result, while alteration in the level of aggregate demand origin price deviation when competition is ideal, it requires also, or only, a quantity deviation when competition is imperfect. The next disparity is that firms in perfect competition function essentially in the growing element of their marginal cost curves. In contrast, the theory of imperfect competition forecast surplus ability as a long-term characteristic. An imperative feature of this proposal is that firms can now function in the stable part of their marginal constant cost curves. Collectively, both propositions indicate, primary, that prices stay comparatively stable in the face of deviation in demand. Conversely, as regards income distribution, author implies that when demand changes this need not engross a change in income shares, providing the degree of market imperfection does not vary. This guided Kalecki to hypothesize that the allocation of income is determined by the price/unit cost ratio, or degree/amount of monopoly, a word summarizing a diversity of oligopolistic and monopolistic factors. It is worth highlighting that Kalecki’s model does not entail price inflexibility. In a state of perfect competition, price rigidity arises normally as an estimate to partial price adjustment. On the contrary, in imperfect competition prices are understood to adjust as quickly as necessary; producers supply whatsoever is demanded at the price which they have put in their greatest interests. This comment can assist understanding the essential difference made by Kalecki between price whose changes, in perfect competitive market, are mainly determined by altering in the costs of productions and those prices whose changes, in imperfect competitive market, are dogged mainly by changes in demand, illuminating particularly this difference is not based on disparity on pace of price modification but on disparity in industrial structure and in costs condition. Self-Instructional 92 Material Kalecki in 1954 posited, generally speaking, changes in the prices of finished Theory of Cost and goods are ‘cost-determined’, while changes in the prices of raw materials, inclusive of Factor Pricing primary foodstuffs, are ‘demand-determined’. With his hypothesis of income distribution, Kalecki further developed his hypothesis of efficient demand. He had previously revealed that, for a specified distribution of NOTES income between profits and wages, changes in profits would carry about alteration in the similar route of output and employment. At the moment, he added that for an agreed level of capitalist expenses and consequently for a known level of profits, income redistribution amid workers and capitalists, will aggravate an alteration in aggregate demand and by means of it in the level of output and employment. The fundamental cause is the diverse inclination to consume between workers and capitalists. There is a well-built complementarily among income distribution and income determination, which establish appearance in the thought that even although the profit share depends on the degree of monopoly, the profit level stays exclusively determined by the level of capitalist expenses. This proposal is critical. On the one side, it highlights that difference in the degree of monopoly influence output and employment merely by moving effective demand through workers’ expenditure. On the other hand, it demonstrates that if wages drop (climb), profits will not get high (go down) since they are totally determined by capitalist investment and expenditure, which are doubtful to change either in the present period or in the subsequent just because wages (or the wage share) altered. However, Kalecki’s crucial intention on the reasons of unemployment under capitalism does not necessitate this theory of income distribution. Nevertheless, the later should be taken into account as it is practical under contemporary capitalism, even as it completes and strengthens Kalecki’s theory of effective demand. Lastly, Kalecki’s theory of income distribution permits defining a novel examination of the wages-employment association, first in reviewing the association between real wages and output by centering on defects on the product markets, and next in reviewing the association among money wages and employment by centering on both limitations on the labour and product market. Kalecki’s Theory of Income Distribution To seize the general idea of Kalecki’s theory of income distribution, let us take the case of a vertically integrated industry. To make the study simpler, we suppose that all workers are productive workers and that the productivity of labour is known and are stable. Furthermore, we describe gross profits as the distinction between the total value of production and total prime costs, which are completely made up of wages in this simplify case. It can be simply seen that income distribution in an industry is entirely determined by the ability of firms to repair their prices in relative to prime unit costs. Precisely, the higher (lower) the price/unit-costs ratio, the higher (lower) the share of profits in respect to gross value added will be. The perception following the previous analysis is the subsequent. Let us presume that in the industry under consideration the wage rate and productivity per worker are known. Then, if firms lift up prices, the price-cost ratio, and the unit profit margin will go up. However, now workers will be capable to purchase a lesser share of the output (or the value added) of the industry than earlier, whereas capitalists will be capable to purchase a higher share of the value added. Income distribution will vary, adjacent to wages and in support of profits. Additionally, we may believe that in any known industry, the senior the monopolistic control of firms on the market, the higher their ability to fix high prices (in relation to their costs). As a result, the superior the monopolistic power of firms, and the superior the relative share of profits in Self-Instructional Material 93 Theory of Cost and income in the industry have a tendency to be. This is perhaps the rationale why Kalecki Factor Pricing named ‘degree of monopoly’ the price-cost ratio of the industry. Certainly, the latter is expected to be prejudiced by the strength of the monopolization existing in the industry. But the ‘degree of monopoly’ is a diverse and extremely exact term in Kalecki’s theory, NOTES as it submits exclusively to the price-cost ratio, and is definite by numerous factors. One, but only one of these factors is the strength of the monopolization of the market. 3.4.5 Kaldor’s Saving Investment Model of Distribution and Growth The major thought underlying the post or neo-Keynesian theories of growth and distribution is that of aggregate savings regulating to an autonomously known quantity of aggregate investment. The alteration of savings to investment, relatively than the other way round, is noticed to be a middle message of Keynes’s General Theory (cf. Keynes, CW, VII). As Keynes highlighted in the year next to the publication of his book, ‘the initial novelty’ of The General Theory ‘lies in my maintaining that it is not the rate of interest, but the level of income which ensures equality between saving and investment.’ The post-Keynesian theories of growth and distribution are fundamentally an issue of the principle of the multiplier, developed by Richard Kahn (1931) and then accepted by Keynes. There are basically two channels by means of which the modification of savings to investment can catch position. As Nicholas Kaldor said, the theory of the multiplier can be ‘otherwise applied to determination of association between prices and wages, stipulation is that level of output is taken as known, or to the determination of the level of employment, if distribution (i.e., the association between prices and wages) is taken as known. That is to say, in situations of repeatedly complete capital exploitation and complete employment of labour, the modification of savings to investment is foreseen to be resulted via prices varying relative to money wages and consequently a rearrangement of income among wages and profits or classes of income beneficiaries. In circumstances of less than complete exploitation of the capital stock and of the labour force, in contrast, savings can alter to investment by means of a change in the level of capital exploitation and the level of employment, not including any noticeable alteration in the real wage rate, at least in limits. Kaldor’s Theory of Distribution Kaldor unites Keynes’s thought that investment concludes savings, with class differences in economy. He employs the consequential device to clarify income distribution in complete employment. Investment produces saving equivalent to it. When thrift diverges between classes, this saving can arrive from an augment in income, or a raise in the share of profits. Thus, the saving-investment equality can be used to elucidate the intensity of income or its distribution. Kaldor utilizes it to elucidate distribution by abolishing the outcome of investment on income. Income is attached to a scientifically dogged level by assuming full employment. Alteration in investment has no consequence on output. The saving equivalent to investment is supplied by alter in class shares, protected by price alteration at full employment. Thus, full employment is the underpinning or foundation of the theory. Salient features of this model are as follows: • By making the saving rate flexible, a steady growth rate of the economy can be achieved. • Dissimilar to neo-classical economists, the capital-output ratio stays fixed and stable. Self-Instructional 94 Material • This model declines the production function approach. However, it somewhat, Theory of Cost and initiates the function of technical progress. Factor Pricing • In neo-classical model the investment function has not been initiated. But this model also gives the investment function which is based on that investment which is associated with one labourer. NOTES • In this model the conjectures of full employment and perfect competition have been surrendered. Full employment assumption of the model Kaldor considers that full employment is a reasonable depiction of the post 1945 economy, and of ‘stylized facts’ of above a hundred years. This conviction has been robustly challenged. Kaldor also attempts to give hypothetical reasons for his conviction in the possibility of full employment. Specially, he undertakes to explain that full employment equilibrium or balance is constant, using the concepts of aggregate supply and demand curves. Nevertheless, it appears that on Kaldor’s own logic, full employment is instable and momentary (short-lived), although it is underemployment equilibrium which is constant. Consequently Kaldor’s hypothetical cover of full employment is imaginative. Underemployment equilibrium is reasonable and was first established by the general theory. And it cannot be fought that the general theory is ‘true at each instant of time’ and untrue in the long run. Certainly, the statement of full employment is fundamentally nearer to neo-classical than Keynesians. Kaldor and the Neo-classical Now the question is ‘How does Kaldor transmit to the neo-classical theory of distribution?’ At the aggregate level, Kaldor’s theory contends with the neo-classical theory supported by the marginal productivity relation. In the single product neo-classical world, the wage level equivalents marginal product of labour at full employment. The elasticity of output with revere to labour gives the share of labour. Therefore, the wage share is specified by technology and the size of the labour force. It cannot alter even if investment does. Noticeably, Kaldor’s theory is mismatched with the aggregate descriptions of the neo-classical principle. It has been recommended that Kaldor’s theory does not establish the same dare in a many commodity world. Various economists say that Kaldor’s theory is unfinished in this framework since it has nothing to articulate on relative prices. Others have recommended that in a many commodity world, relative prices could modify to convince both Kaldorian and neo-classical conditions of equilibrium. In such a case, the marginal productivity circumstance could be said to ‘complete’ Kaldor’s theory. Criticism of this model • According to Luigi L. Pasinetti, there subsists a logical imperfection in Kaldor’s arguments as he authorizes the labouring class to build the savings, however these savings are neither ploughed in capital addition, nor they create income. He added to this and says that if any nation is deficient in the investing class and there are no profits, afterward how shall the growth rate be determined. • Kaldor presumes that the saving rate stays fixed. But assuming this he disregards the consequences of ‘life-cycle’ on savings and work.

Self-Instructional Material 95 Theory of Cost and • Kaldor model is unsuccessful in explaining that behavioural system which could Factor Pricing notify that distribution of income will be such like that the stable growth is involuntarily achieved.

NOTES 3.5 SUMMARY

In this unit, you have learnt that: • Cost function is a symbolic statement of the technological relationship between cost and output. In its general form, it is expressed by an equation. Cost function can be expressed also in the form of a schedule and a graph. • The theory of cost deals with the behaviour of cost in relation to a change in output. In other words, the cost theory deals with cost-output relations. The basic principle of cost behaviour is that the total cost increases with increase in output. • Depending on whether cost analysis pertains to short-run or to long run, there are two kinds of cost functions: o Short-run cost functions o Long-run cost functions • The basic analytical cost concepts used in the analysis of cost behaviour are total, average and marginal costs. • The cost-output relations are determined by the cost function and are exhibited through cost curves. The shape of the cost curves depends on the nature of the cost function. Cost functions are derived from actual cost data of the firms. • As output increases, larger quantities of variable inputs are required to produce the same quantity of output due to diminishing returns. This causes a subsequent increase in the variable cost for producing the same output. • Technological progress means a given quantity of output can be produced with less quantity of inputs or a given quantity of inputs can produce a greater quantity of output. • According to J. R. Hicks, technological progress may be classified as neutral, Check Your Progress capital-deepening and labour-deepening. 8. What does the marginal • Both Harrod and Domar consider capital accumulation as a key factor in the productivity theory process of economic growth. They emphasise that capital accumulation (i.e., net say? investment) has a double role to play in economic growth. 9. What are the assumptions for • Harrod model assumes a constant capital-output ratio. That is, it assumes a simple derivation of a firm’s production function with a constant capital-output co-efficient. demand curve for labour? • According to Harrod model, economic growth can be achieved either by increasing 10. What is the marginal propensity to save and increasing simultaneously the stock of capital, or significance of David by increasing the output/capital ratio. Ricardo’s model? • The major defect of the Harrod model is that the parameters used in this model, 11. What is the main argument of viz., capital/output ratio, marginal propensity to save, growth rate of labour force, Kalecki’s theory of progress rate of labour-saving technology, are all determined independently out of income distribution? the model. 12. What devices does • In economics, distribution refers to the way income, wealth or national income is Kaldor employ for income distribution? shared or distributed among the people or the factors of production—land, labour and capital. Self-Instructional 96 Material • The neo-classical approach to factor price determination is based on marginal Theory of Cost and productivity theory of factor. Marginal productivity theory is regarded as the Factor Pricing general micro-theory of factor price determination. • According to Clark, the marginal productivity principle is a complete theory of wages, which could be well applied to other factors of production also. NOTES • Firms demand factors of production—land, labour, capital—-because they are productive. Factors are demanded not merely because they are productive but also because the resulting product has a market value. • One of the earlier proofs to the distribution of national income according to marginal productivity of production factors was provided by the Swiss mathematician, Leonard Euler (1701–83), which is known as Euler Theorem. • Income distribution (as per the economics concept) is how a nation’s total GDP is dispersed amongst its population. • David Ricardo developed a theoretical model popularly known as ‘corn laws’. • The corn laws were actually imposing the tariffs on the import of agricultural products which caused increase in the price of agricultural products domestically. • The significance of David Ricardo’s model is that it was one of the initial models used in economics, intended at the amplification that how income is distributed or dispersed in society. • In the short run, the corn laws results in raising the price of agricultural product. It leads to the cultivation of marginal or less fertile land too to earn profits. • Ricardo concluded that there is no benefit of worrying about the long term growth of an economy. • Income distribution plays important task in Kalecki’s theory of effective demand. • Kalecki’s theory of income distribution is closely attached with his theory of price determination, and the latter is associated with his vision that recent capitalism is distinguished by market imperfections, equally on the labour market and on the product market. • The major thought underlying the post or neo-Keynesian theories of growth and distribution is that of aggregate savings regulating to an autonomously known quantity of aggregate investment. • The post-Keynesian theories of growth and distribution are fundamentally an issue of the principle of the multiplier, developed by Richard Kahn (1931) and then accepted by Keynes. • Kaldor unites Keynes’s thought that investment concludes savings, with class differences in economy. • The saving-investment equality can be used to elucidate the intensity of income or its distribution. • Kaldor’s theory contends with the neo-classical theory supported by the marginal productivity relation. • According to Prof. Pasinetti there subsists a logical imperfection in Kaldor’s arguments as he authorize the labouring class to build the savings, however these savings are neither ploughed in capital addition, nor they create income.

Self-Instructional Material 97 Theory of Cost and Factor Pricing 3.6 KEY TERMS

• Cost function: It is a symbolic statement of the technological relationship between NOTES cost and output. • Total cost (TC): It is defined as the actual cost that must be incurred to produce a given quantity of output. • Technological progress: It means a given quantity of output can be produced with less quantity of inputs or a given quantity of inputs can produce a greater quantity of output.

3.7 ANSWERS TO ‘CHECK YOUR PROGRESS’

1. The basic principle of cost behaviour is that the total cost increases with increase in output. 2. The basic analytical cost concepts used in the analysis of cost behaviour are total, average and marginal costs. 3. The shape of the cost curves depends on the nature of the cost function. 4. Technological progress means a given quantity of output can be produced with less quantity of inputs or a given quantity of inputs can produce a greater quantity of output. 5. Both Harrod and Domar consider capital accumulation as a key factor in the process of economic growth. They emphasise that capital accumulation (i.e., net investment) has a double role to play in economic growth. 6. Harrod model assumes a constant capital-output ratio. That is, it assumes a simple production function with a constant capital-output co-efficient. 7. The major defect of the Harrod model is that the parameters used in this model, viz., capital/output ratio, marginal propensity to save, growth rate of labour force, progress rate of labour-saving technology, are all determined independently out of the model. 8. Marginal productivity theory is regarded as the general micro-theory of factor price determination. It provides an analytical framework for the analysis of determination of factor prices. 9. A firm’s demand curve for labour is derived on the basis of the VMPL curve on the following assumptions for the sake of simplicity in the analysis. (i) Firm’s objective is to maximise profit and profit condition is MR=MC=w. (ii) The firm uses a single variable factor, labour and the price of labour, wages (w), is constant.

(iii) The firm produces a single commodity whose price is constant at Px. 10. The significance of David Ricardo’s model is that it was one of the initial models used in economics, intended at the amplification that how income is distributed or dispersed in society. 11. Kalecki’s theory of income distribution is closely attached with his theory of price determination, and the latter is associated with his vision that recent capitalism is distinguished by market imperfections, equally on the labour market and on the Self-Instructional product market. 98 Material 12. Kaldor unites Keynes’s thought that investment concludes savings, with class Theory of Cost and differences in economy. He employs the consequential device to clarify income Factor Pricing distribution in complete employment.

3.8 QUESTIONS AND EXERCISES NOTES

Short-Answer Questions 1. What is cost function? How can it be expressed? 2. What are the two kinds of cost functions? 3. What is the average cost? How can it be minimized? 4. How does Hicks classify technological progress? 5. What is the central theme of the Harrod growth model? Outline the Harrod model of growth and derive warranted rate of growth from the model. 6. What are the conditions in Harrod growth model under which warranted growth rate equals the actual growth rate? Why is this model called a razor-edge model? 7. Write a short note on marginal productivity theory. 8. Ricardo’s model is based upon certain assumptions. What are these assumptions, state briefly? 9. What are the features of Kaldor’s saving investment model? Long-Answer Questions 1. How can the cost function be derived from production function? Explain. 2. Discuss the short-run cost functions and cost curves. 3. Assess the Hicksian and Harrodian version of technical progress. 4. What are the theories of distribution? Explain the marginal productivity theory and Euler’s theorem in detail. 5. Explain the Ricardian theory of income distribution and its implication. 6. Discuss Kaldor’s saving investment model of distribution and growth. 7. Explain Kalecki’s theory of income distribution. 8. Why and how does Kaldor’s distribution theory contend the neo-classical theory? 9. Illustrate the cost curves produced by linear, quadratic and cubic cost functions with the help of equations.

3.9 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra.

Self-Instructional Material 99 Theory of Cost and Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Factor Pricing Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. NOTES Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional 100 Material Theory of Market UNIT 4 THEORY OF MARKET

Structure NOTES 4.0 Introduction 4.1 Unit Objectives 4.2 Critique of Perfect Competition as a Market Form 4.2.1 Price Determination under Perfect Competition 4.2.2 Equilibrium of the Firm in Short-run 4.2.3 Derivation of Supply Curve 4.3 Actual Market Forms: Monopolistic Competition, Oligopoly and Duopoly 4.3.1 Price Determination under Pure Monopoly 4.3.2 Pricing and Output Decisions under Oligopoly 4.3.3 Cournot and Stackleberg’s Model of Duopoly 4.4 Collusive Oligopoly: Cartel 4.4.1 Joint Profit Maximization Model 4.4.2 Cartel and Market-sharing 4.5 Summary 4.6 Key Terms 4.7 Answers to ‘Check Your Progress’ 4.8 Questions and Exercises 4.9 Further Reading

4.0 INTRODUCTION

In the economic sense, a market is a system by which buyers and sellers bargain for the price of a product, settle the price and transact their business—buy and sell a product. Personal contact between the buyers and sellers is not necessary. In some cases, e.g., forward sale and purchase, even immediate transfer of ownership of goods is not necessary. Market does not necessarily mean a place. The market for a commodity may be local, regional, national or international. What makes a market is a set of buyers, a set of sellers and a commodity. Buyers are willing to buy and sellers are willing to sell, and there is a price for the commodity. In this unit you will learn about the theory of price and output determination under perfect competition in both short-run and long-run. Here, two basic points need to be noted at the outset. One, the main consideration behind the determination of price and output is to achieve the objective of the firm. Two, although there can be various business objectives, traditional theory of price and output determination is based on the assumption that all firms have only one and the same objective to achieve, i.e., profit maximization. You will also learn about the actual market forms and price determination under monopoly, duopoly and oligopoly.

4.1 UNIT OBJECTIVES

After going through this unit, you will be able to: • Discuss perfect competition as a market form and discuss its features • Analyse the equilibrium of a firm under the conditions of perfect competition in the short-run

• Explain price determination under a pure monopoly Self-Instructional Material 101 Theory of Market • Explain and illustrate the determination of equilibrium price and output under monopolistic competition in the short-run • Analyse pricing and output decisions under oligopoly NOTES • Assess duopoly as a form of oligopoly and describe the various models of duopoly • Evaluate the cartel model of collusive oligopoly

4.2 CRITIQUE OF PERFECT COMPETITION AS A MARKET FORM

Perfect competition refers to a market condition in which a very large number of buyers and sellers enjoy full freedom to buy and to sell a homogenous good and service and they have perfect knowledge about the market conditions, and factors of production have full freedom of mobility. Although this kind of market situation is a rare phenomenon, it can be located in local vegetable and fruit markets. Another area which was often considered to be perfectly competitive is the stock market. However, stock market are controlled and regulated in India and a few big market players influence the market conditions in a serious and dangerous way. Therefore, stock market in India is not perfectly competitive.

Features of Perfect Competition The following are the main features or characteristics of a perfectly competitive market. (i) Large number of buyers and sellers: Under perfect competition, the number of sellers is assumed to be so large that the share of each seller in the total supply of a product is very small or insignificant. Therefore, no single seller can influence the market price by changing his supply or can charge a higher price. Therefore, firms are price- takers, not price-makers. Similarly, the number of buyers is so large that the share of each buyer in the total demand is very small and that no single buyer or a group of buyers can influence the market price by changing their individual or group demand for a product. (ii) Homogeneous product: The goods and services supplied by all the firms of an industry are assumed to be homogeneous or almost identical. Homogeneity of the product implies that buyers do not distinguish between products supplied by the various firms of an industry. Product of each firm is regarded as a perfect substitute for the products of other firms. Therefore, no firm can gain any competitive advantage over the other firms. This assumption eliminates the power of all the firms to charge a price higher than the market price. (iii) Perfect mobility of factors of production: Another important characteristic of perfect competition is that the factors of production are freely mobile between the firms. Labour can freely move from one firm to another or from one occupation to another, as there is no barrier to labour mobility—legal, language, climate, skill, distance or otherwise. There is no trade union. Similarly, capital can also move freely from one firm to another. No firm has any kind of monopoly over any industrial input. This assumption guarantees that factors of production—land, labour, capital, and entrepreneurship—can enter or quit a firm or the industry at will. (iv) Free entry and free exist: There is no legal or market barrier on the entry of new firms to the industry. Nor is there any restriction on the exit of the firms from the Self-Instructional 102 Material industry. A firm may enter the industry or quit it at its will. Therefore, when firms in the Theory of Market industry make supernormal profit for some reason, new firms enter the industry. Similarly, when firms begin to make losses or more profitable opportunities are available elsewhere, firms are free to leave the industry. (v) Perfect knowledge: Both buyers and sellers have perfect knowledge about the NOTES market conditions. It means that all the buyers and sellers have full information regarding the prevailing and future prices and availability of the commodity. As Marshall put it, ‘ ... though everyone acts for himself, his knowledge of what others are doing is supposed to be generally sufficient to prevent him from taking a lower or paying a higher price than others are doing.’ Information regarding market conditions is available free of cost. There is no uncertainty in the market. (vi) No government interference: Government does not interfere in any way with the functioning of the market. There are no discriminatory taxes or subsidies; no licencing system, no allocation of inputs by the government, or any other kind of direct or indirect control. That is, the government follows the free enterprise policy. Where there is intervention by the government, it is intended to correct the market imperfections if there are any. (vii) Absence of collusion and independent decision-making by firms: Perfect competition assumes that there is no collusion between the firms, i.e., they are not in league with one another in the form of guild or cartel. Nor are the buyers in any kind of collusion between themselves. There are no consumers’ associations. This condition implies that buyers and sellers take their decisions independently and they act independently. Perfect vs. pure competition Sometimes, a distinction is made between perfect competition and pure competition. The differences between the two is a matter of degree. While ‘perfect competition’ has all the features mentioned above, under ‘pure competition’, there is no perfect mobility of factors and perfect knowledge about market-conditions. That is, perfect competition less ‘perfect mobility’ and ‘perfect knowledge’ is pure competition. ‘Pure competition’ is ‘pure’ in the sense that it has absolutely no element of monopoly. The perfect competition, with characteristics mentioned above is considered as a rare phenomenon in the real business world. The actual markets that approximate to the conditions of a perfectly competitive market include markets for stocks and bonds, and agricultural market (mandis). Despite its limited scope, perfect competition model has been widely used in economic theories due to its analytical value. 4.2.1 Price Determination under Perfect Competition Under perfect competition, an individual firm does not determine the price of its product. Price for its product is determined by the market demand and market supply. In Figure 4.1 (a) the demand curve, DD', represents the market demand for the commodity of an industry as a whole. Likewise, the supply curve, SS′, represents the total supply created by all the firms of the industry (derivation of industry’s supply curve has been shown in a following section). As Figure 4.1 (a) shows, market price for the industry as a whole is determined at OP. This price is given for all the firms of the industry. No firm has power to change this price. At this price, a firm can sell any quantity. It implies that the demand curve for an individual firm is a straight horizontal line, as shown by the line dd′in Figure 4.1 (b), with infinite elasticity. Self-Instructional Material 103 Theory of Market (a) (b) D S′ e c i ′ NOTES r P d d P Price

S D′

O O Market Demand and Supply Demand for Individual Firm

Fig. 4.1 Determination of Market Price and Demand for Individual Firms

No control over cost: Because of its small purchase of inputs (labour and capital), a firm has no control over input prices. Nor can it influence the technology. Therefore, cost function for an individual firm is given. This point is, however, not specific to firms in a perfectly competitive market. This condition applies to all kinds of market except in case of bilateral monopoly. What are the firm’s options? The firm’s option and role in a perfectly competitive market are very limited. The firm has no option with respect to price and cost. It has to accept the market price and produce with a given cost function. The only option that a firm has under perfect competition is to produce a quantity that maximizes its profits given the price and cost. Under profit maximizing assumption, a firm has to produce a quantity which maximizes its profit and attains its equilibrium. 4.2.2 Equilibrium of the Firm in Short-Run A profit maximizing firm is in equilibrium at the level of output which equates its MC = MR. However, the level of output which meets the equilibrium condition for a firm varies depending on cost and revenue functions. The nature of cost and revenue functions depends on whether one is considering short-run or long-run. While the revenue function is generally assumed to be given in both short and long runs, the short- run cost function is not the same in the short and long-runs. The short-run cost function is different from the long-run cost function because in the short run, some inputs (e.g., capital) are held constant while all factors are variable in the long-run. Here, we will discuss firm’s short-run equilibrium. Assumptions: The short-run equilibrium of a firm is analysed under the following assumptions. • Capital is fixed but labour is variable • Prices of inputs are given • Price of the commodity is fixed • The firm is faced with short-run U-shaped cost curves The firm’s equilibrium in the short-run is illustrated in Figure 4.2. Price of a commodity is determined by the market forces—demand and supply—in a perfectly competitive market at OP. The firms, therefore, face a straight-line, horizontal demand curve, as shown by the line P = MR. The straight horizontal demand line implies that price equals marginal revenue, i.e., AR = MR. The short-run average and marginal cost curves are shown by SAC and SMC, respectively.

Self-Instructional 104 Material Theory of Market SMC SAC

E C P = MR A P

d NOTES n a

C M

, P′ E′ R M

OQ Output Fig. 4.2 Short-run Equilibrium of the Firm

It can be seen in Figure 4.2 that SMC curve intersects the P = MR line at point E, from below. At point E, therefore, SMC = MR. A perpendicular drawn from point E to the output axis determines the equilibrium output at OQ. It can be seen in the figure that output OQ meets both the first and the second order conditions of profit maximization. At output OQ, therefore, profit is maximum. The output OQ is, thus, the equilibrium output. At this output, the firm is in equilibrium and is making maximum profit. Firm’s total pure profit is shown by the area PEE′P′ which equals PP′ × OQ where PP′ is the per unit super normal profit at output OQ. Does a firm always make profit in the short-run?: Figure 4.2 shows that a firm makes supernormal profit in the shor-run. A question arises here: Does a firm make always a supernormal profit in the short-run? The answer is ‘not necessarily’. As a matter of fact, in the shor-run, a firm may make a supernormal profit or a normal profit or even make losses. Whether a firm makes abnormal profits, normal profits or makes losses depends on its cost and revenue conditions. If its short-run average cost (SAC) is below the price (P = MR) at equilibrium (Figure 4.2), the firm makes abnormal or pure profits. If its SAC is tangent to P = MR, as shown in Figure 4.3 (a), the firm makes only normal profit as it covers only its SAC which includes normal profit. But, if its SAC falls above the price (P = MR), the firm makes losses. As shown in Figure 4.3 (b), the total loss equals the area PP′E′E (= PP′ × OQ), while per unit loss is PP′ = EE′.

(a) (b) SAC SMC SAC SMC e c i r E′ P

d E P = MR P

n P = MR

a P P′ s

t E s o C Costs and Price

O Q O Q Output Output Fig. 4.3 Short-run Equilibrium of Firm with Normal and Losses

Self-Instructional Material 105 Theory of Market Shut-down or close-down point: In case a firm is making loss in the short-run, it must minimize its losses. In order to minimize its losses, it must cover its short-run average variable cost (SAVC). The behaviour of short-run average variable cost is shown by the curve SAVC in Figure 4.4. A firm unable to recover its minimum SAVC will have to NOTES close down. The firm’s SAVC is minimum at point E where it equals the MC. Note that SMC intersects SAVC at its minimum level as shown in Figure 4.4.

SMC SAC SAVC e c i r P

d n a

t E P = MR s

o P C

AFC

O Q Output Fig. 4.4 Shut-down Point

Another condition which must be fulfilled is P = MR = SMC. That is, for loss to be minimum, P = MR = SMC = SAVC. This condition is fulfilled at point E in Figure 4.4. At point E, the firm covers only its fixed cost and variable cost. It does not make any profit—rather it makes losses. The firm may survive for a short period but not for long. Therefore, point E denotes the ‘shut-down point’ or ‘break-down point’, because at any price below OP, it pays the firm to close down as it minimizes its loss. 4.2.3 Derivation of Supply Curve The supply curve of an individual firm is derived on the basis of its equilibrium output. The equilibrium output, determined by the intersection of MR and MC curves, is the optimum supply by a profit maximizing (or cost minimizing) firm. Under the condition of increasing MC, a firm will increase supply only when price increases. This forms the basis of a firm’s supply curve. The derivation of supply curve of a firm is illustrated in Figure 4.5 (a) and (b). As the figure shows, the firm’s SMC passes through point M on its SAVC. The point M marks the minimum of firm’s SAVC which equals MQ1. The firm must recover its SAVC = MQ1 to remain in business in the short-run. Point M is the shut- down point in the sense that if price falls below OP1, it is advisable for the firm to close down. However, if price increases to OP2, the equilibrium point shifts to R and output increases to OQ2. Note that at output OQ2, the firm covers its SAC and makes normal profit. Let the price increase further to OP3 so that equilibrium output rises to OQ3. When price rises to OP4, the equilibrium output rises to OQ4 and the firm makes abnormal profit. By plotting this information, we get a supply curve (SS′) as shown in Figure 4.5 (b).

Self-Instructional 106 Material (a) (b) Theory of Market

SMC S

P P C P4 P4 M SAC d

n T T a P P NOTES 3 3

R SAVC Price M R R , P2 P2 e c i r M M P P1 P1 S

O Q1 Q2 Q3 Q4 O Q1 Q2 Q3 Q4 Output Output Fig. 4.5 Derivation of a Firm’s Supply Curve

Derivation of industry’s supply curve The industry supply curve, or what is also called market supply curve, is the horizontal summation of the supply curve of the individual firms. If cost curves of the individual firms of an industry are identical, their individual supply curves are also identical. In that case, industry supply curve can be obtained by multiplying the individual supply at various prices by the number of firms. In the shor-run, however, the individual supply curves may not be identical. If so, the market supply curve can be obtained by summing horizontally the individual supply curves. Let us consider only two firms having their individual supply curves as S1 and S2 as shown in Figure 4.6 (a). At price OP1, the market supply equals P1A + P1B. Suppose P1A + P1B equals P1M as shown in Figure 4.6 (b). [Note that output scale in part (b) is different from that in part (a).] Similarly, at price OP2, the industry supply equals P2C + P2C or 2(P2C) = P2N as shown in Figure 4.6 (b). In the same way, point T is located. By joining the points M, N and T, we get the market or industry supply curve, SS′. (a) (b)

S1 S2 S′ D E P3 P3 T e c i r C

P P Price P 2 2 N Check Your Progress P1 P1 A M B S 1. Under perfect competition, why O Output O Output cannot a single seller Fig. 4.6 Derivation of the Industry Supply Curve influence market price? 2. What is the role of 4.3 ACTUAL MARKET FORMS: MONOPOLISTIC the government under perfect COMPETITION, OLIGOPOLY AND DUOPOLY competition? 3. Under perfect We are concerned in this section with the question: How is the price of a commodity competition, how is the price of a determined in different kinds of markets? The determination of price of a commodity product of an depends on the number of sellers and the number of buyers. Barring a few cases, e.g., individual firm occasional phases in share and property markets, the number of buyers is larger than the determined? number of sellers. The number of sellers of a product in a market determines the nature 4. When is a profit and degree of competition in the market. The nature and degree of competition makes maximizing firm in equilibrium? the structure of the market. Depending on the number of sellers and the degree of competition, the market structure is broadly classified as given in Table 4.1. Self-Instructional Material 107 Theory of Market Table 4.1 Types of Market Structures

Market structure No. of firms and Nature of Control Method of degree of industry over price marketing production where NOTES differentiation prevalent 1. Perfect Large no. of Financial mar- None Market Competition firms with kets and some exchange homogenous farm products or auction products 2. Imperfect Competition: (a) Monopol- Many firms with Manufacturing: Some Competitive istic com- real or perceived tea, toothpastes, advertising, petition product differen- TV sets, shoes, quality rivalry tiation refrigerators, etc.

(b) Oligopoly Little or no pro- Aluminium, steel, Some Competitive, duct differentia- cigarettes, cars, advertising, tion passenger cars, quality etc. rivalry

(c) Monopoly A single prod- Public utilities: Considera- Promotional ucer, without Telephones, ble but advertising if close substitute Electricity, etc. usually supply regulated is large

Source: Samuelson, P.A. and W.D. Nordhaus, Economics, McGraw-Hill, 15th Edn., 1995, p. 152. Market Structure and Pricing Decisions The market structure determines a firm’s power to fix the price of its product a great deal. The degree of competition determines a firm’s degree of freedom in determining the price of its product. The degree of freedom implies the extent to which a firm is free or independent of the rival firms in taking its own pricing decisions. Depending on the market structure, the degree of competition varies between zero and one. And, a firm’s discretion or the degree of freedom in setting the price for its product varies between one and none in the reverse order of the degree of competition. As a matter of rule, the higher the degree of competition, the lower the firm’s degree of freedom in pricing decision and control over the price of its own product and vice versa. Let us now see how the degree of competition affects pricing decisions in different kinds of market structures. Under perfect competition, a large number of firms compete against each other for selling their product. Therefore, the degree of competition under perfect competition is close to one, i.e., the market is highly competitive. Consequently, firm’s discretion in determining the price of its product is close to none. In fact, in perfectly competitive market, price is determined by the market forces of demand and supply and a firm has to accept the price determined by the market forces. If a firm uses its discretion to fix the price of its product above or below its market level, it loses its revenue and profit in either case. For, if it fixes the price of its product above the ruling price, it will not be able to sell its product, and if it cuts the price down below its market level, it will not be able to cover its average cost. In a perfectly competitive market, therefore, firms have little or no choice in respect to price determination. As the degree of competition decreases, firm’s control over the price and its discretion in pricing decision increases. For example, under monopolistic competition, where degree of competition is high but less than one, the firms have some discretion in Self-Instructional 108 Material setting the price of their products. Under monopolistic competition, the degree of freedom Theory of Market depends largely on the number of firms and the level of product differentiation. Where product differentiation is real, firm’s discretion and control over the price is fairly high and where product differentiation is nominal or only notional, firm’s pricing decision is highly constrained by the prices of the rival products. NOTES The control over the pricing discretion increases under oligopoly where degree of competition is quite low, lower than that under monopolistic competition. The firms, therefore, have a good deal of control over the price of their products and can exercise their discretion in pricing decisions, especially where product differentiation is prominent. However, the fewness of the firms gives them an opportunity to form a cartel or to make some settlement among themselves for fixation of price and non-price competition. In case of a monopoly, the degree of competition is close to nil. An uncontrolled monopoly firm has full control over the price of its product. A monopoly, in the true sense of the term, is free to fix any price for its product, of course, under certain constraints, viz., (i) the objective of the firm, and (ii) demand conditions. The theory of pricing explains pricing decisions and pricing behaviour of the firms in different kinds of market structures. In this section, we will describe the characteristics of different kinds of market structures and price determination in each type of market in a theoretical framework. We begin with price determination under monopoly. 4.3.1 Price Determination under Pure Monopoly The term pure monopoly means an absolute power of a firm to produce and sell a product that has no close substitute. In other words, a monopolized market is one in which there is only one seller of a product having no close substitute. The cross elasticity of demand for a monopoly product is either zero or negative. A monopolized industry is a single-firm industry. Firm and industry are identical in a monopoly setting. In a monopolized industry, equilibrium of the monopoly firm signifies the equilibrium of the industry. However, the precise definition of monopoly has been a matter of opinion and purpose. For instance, in the opinion of Joel Deal, a noted authority on managerial economics, a monopoly market is one in which ‘a product of lasting distinctiveness, is sold. The monopolized product has distinct physical properties recognized by its buyers and the distinctiveness lasts over many years.’ Such a definition is of practical importance if one recognizes the fact that most of the commodities have their substitutes varying in degree and it is entirely for the consumers/users to distinguish between them and to accept or reject a commodity as a substitute. Another concept of pure monopoly has been advanced by E. H. Chamberlin who envisages monopoly as the control of all goods and services by the monopolist. But such a monopoly has hardly ever existed, hence his definition is questionable. In the opinion of some authors, any firm facing a sloping demand curve is a monopolist. This definition, however, includes all kinds of firms except those under perfect competition. For our purpose here, we use the general definition of pure monopoly, i.e., a firm that produces and sells a commodity which has no close substitute. Causes and Kinds of Monopolies The emergence and survival of a monopoly firm is attributed to the factors which prevent the entry of other firms into the industry and eliminate the existing ones. The barriers to entry are, therefore, the major sources of monopoly power. The main barriers to entry are: Self-Instructional Material 109 Theory of Market • Legal restrictions or barriers to entry of new firms • Sole control over the supply of scarce and key raw materials • Efficiency in production NOTES • Economies of scale (i) Legal restrictions: Some monopolies are created by law in the public interest. Most of the erstwhile monopolies in the public utility sector in India, e.g., postal, telegraph and telephone services, telecommunication services, generation and distribution of electricity, Indian Railways, Indian Airlines and State Roadways, etc., were public monopolies. Entry to these industries was prevented by law. Now most of these industries are being gradually opened to the private sector. Also, the state may create monopolies in the private sector also, through licence or patent, provided they show the potential of and opportunity for reducing cost of production to the minimum by enlarging size and investing in technological innovations. Such monopolies are known as franchise monopolies. (ii) Control over key raw materials: Some firms acquire monopoly power because of their traditional control over certain scarce and key raw materials which are essential for the production of certain goods, e.g., bauxite, graphite, diamond, etc. For instance, Aluminium Company of America had monopolized the aluminium industry before World War II because it had acquired control over almost all sources of bauxite supply. Such monopolies are often called ‘raw material monopolies’. The monopolies of this kind emerge also because of monopoly over certain specific knowledge of technique of production. (iii) Efficiency in production: Efficiency in production, especially under imperfect market conditions, may be the result of long experience, innovative ability, financial strength, availability of market finance at lower cost, low marketing cost, managerial efficiency, etc. Efficiency in production reduces cost of production. As a result, a firm’s gains higher the competitive strength and can eliminate rival firms and gain the status of a monopoly. Such firms are able to gain governments’ favour and protection. (iv) Economies of scale: The economies of scale are a primary and technical reason for the emergence and existence of monopolies in an unregulated market. If a firm’s long-run minimum cost of production or its most efficient scale of production almost coincides with the size of the market, then the large-size firm finds it profitable in the long-run to eliminate competition through price cutting in the short-run. Once its monopoly is established, it becomes almost impossible for the new firms to enter the industry and survive. Monopolies created on account of this factor are known as natural monopolies. A natural monopoly may emerge out of the technical conditions of efficiency or may be created by law on efficiency grounds. Pricing and Output Decision: Short-run Analysis As under perfect competition, pricing and output decisions under monopoly are based on profit maximization hypothesis, given the revenue and cost conditions. Although cost conditions, i.e., AC and MC curves, in a competitive and monopoly market are generally identical, revenue conditions differ. Revenue conditions, i.e., AR and MR curves, are different under monopoly—unlike a competitive firm, a monopoly firm faces a downward sloping demand curve. The reason is a monopolist has the option and power to reduce Self-Instructional the price and sell more or to raise the price and still retain some customers. Therefore, 110 Material given the price-demand relationship, demand curve under monopoly is a typical downward Theory of Market sloping demand curve. When a demand curve is sloping downward, marginal revenue (MR) curve lies below the AR curve and, technically, the slope of the MR curve is twice that of AR curve. NOTES The short-run revenue and cost conditions faced by a monopoly firm are presented in Figure 4.7. Firm’s average and marginal revenue curves are shown by the AR and MR curves, respectively, and its short-run average and marginal cost curves are shown by SAC and SMC curves, respectively. The price and output decision rule for profit maximizing monopoly is the same as for a firm in the competitive industry.

Fig. 4.7 Price Determination under Monopoly: Short-run As noted earlier, profit is maximized at the level of output at which MC = MR. Given the profit maximization condition, a profit maximizing monopoly firm chooses a price-output combination at which MR = SMC. Given the firm’s cost and revenue curves in Figure 4.7, its MR and SMC intersect at point N. An ordinate drawn from point N to X- axis, determines the profit maximizing output for the firm at OQ. At this output, firm’s MR = SMC. The ordinate NQ extended to the demand curve (AR = D) gives the profit maximizing price at PQ. It means that given the demand curve, the output OQ can be sold per time unit at only one price, i.e., PQ (= OP1). Thus, the determination of output simultaneously determines the price for the monopoly firm. Once price is fixed, the unit and total profits are also simultaneously determined. Hence, the monopoly firm is in a state of equilibrium. At output OQ and price PQ, the monopoly firm maximizes its unit and total profits. Its per unit monopoly or economic profit (i.e., AR – SAC) equals PQ – MQ = PM. Its total profit, p = OQ × PM. Since OQ = P2M, p = P2M × PM = area P1PMP2 as shown by the shaded rectangle. Since in the short-run, cost and revenue conditions are not expected to change, the equilibrium of the monopoly firm will remain stable. Determination of Monopoly Price and Output: Algebraic Solution The determination of price and output by a monopoly firm in the short-run is illustrated above graphically (see Figure 4.7). Here, we present an algebraic solution to the problem of determination of equilibrium price output under monopoly. Suppose demand and total cost functions for a monopoly firm are given as follows. Demand function: Q = 100 – 0.2 P …(4.1.1) Price function : P = 500 – 5Q ...(4.1.2) 2 Self-Instructional Cost function : TC = 50 + 20Q + Q ...(4.2) Material 111 Theory of Market The problem before the monopoly firm is to find the profit maximizing output and price. The problem can be solved as follows. We know that profit is maximum at an output that equalizes MR and MC. So the first step is to find MR and MC from the demand and cost function respectively. We NOTES have noted earlier that MR and MC are the first derivation of TR and TC functions respectively. TC function is given, but TR function is not. So, let us find TR function first. We know that: TR = P.Q Since P = 500 – 5Q, by substitution, we get TR = (500 – 5Q) Q TR = 500Q – 5Q2 ...(4.3) Given the TR function (4.3), MR can be obtained by differentiating the function. ∂TR MR = = 500 – 10Q ∂Q Likewise, MC can be obtained by differentiating the TC function (4.2). ∂TR MC = ∂Q = 20 + 2Q Now that MR and MC are known, profit maximizing output can be easily obtained. Recall that profit is maximum where MR = MC. As given above, MR = 500 – 10Q and MC = 20 + 2Q By substitution, we get profit maximizing output as: MR = MC 500 – 10Q = 20 + 2Q 480 = 12Q Q = 40 The output Q = 40 is the profit maximizing output. Now profit maximizing price can be obtained by substituting 40 for Q in the price function (4.1.2). Thus, P = 500 – 5 (40) = 300 Profit maximizing price is ` 300. Total profit ( ) can be obtained as follows. π = TR – TC By substitution, we get: π = 500Q – 5Q2 – (50 + 20Q + Q2) = 500Q – 5Q2 – 50 – 20Q – Q2 By substituting profit maximizing output (40) for Q, we get: = 500(40) – 5(40)(40) – 50 – 20(40) – (40 × 40) = 20,000 – 8,000 – 50 – 800 – 1600 = 9,550 Total maximum profit comes to ` 9,550. Self-Instructional 112 Material Does a monopoly firm always earn economic profit? Theory of Market There is no certainty that a monopoly firm will always earn an economic or supernormal profit. Whether a monopoly firm earns economic profit or normal profit or incurs loss depends on: NOTES • Its cost and revenue conditions • Threat from potential competitors • Government policy in respect of monopoly If a monopoly firm operates at the level of output where MR = MC, its profit depends on the relative levels of AR and AC. Given the level of output, there are three possibilities. • If AR > AC, there is economic profit for the firm • If AR = AC, the firm earns only normal profit • if AR < AC, though only a theoretical possibility, the firm makes losses

Monopoly Pricing and Output Decision in the Long-Run The decision rules regarding optimal output and pricing in the long-run are the same as in the short-run. In the long-run, however, a monopolist gets an opportunity to expand the size of its firm with a view to enhance its long-run profits. The expansion of the plant size may, however, be subject to such conditions as: (a) size of the market, (b) expected economic profit and (c) risk of inviting legal restrictions. Let us assume, for the time being, that none of these conditions limits the expansion of a monopoly firm and discuss the price and output determination in the long-run. The equilibrium of monopoly firm and its price and output determination in the long-run is shown in Figure 4.8. The AR and MR curves show the market demand and marginal revenue conditions faced by the monopoly firm. The LAC and LMC show the long-run cost conditions. It can be seen in Figure 4.8, that monopoly’s LMC and MR intersect at point P determining profit maximizing output at OQ2. Given the AR curve, the price at which the total output OQ2 can be sold is P2Q2. Thus, in the long-run, equilibrium output will be OQ2 and price P2Q2. This output-price combination maximizes monopolist’s long-run profit. The total long-run monopoly profit is shown by the rectangle LMSP2.

Fig. 4.8 Equilibrium of Monopoly in the Long-run It can be seen in Figure 4.8 that compared to short-run equilibrium, the monopolist produces a larger output and charges a lower price and makes a larger Self-Instructional Material 113 Theory of Market monopoly profit in the long-run. In the short-run, monopoly’s equilibrium is determined

at point A, the point at which SMC1 intersects the MR curve. Thus, monopoly’s short- run equilibrium output is OQ1 which is less than long-run output OQ2. But the short- run equilibrium price P1Q1 is higher than the long-run equilibrium price P2Q2. The NOTES total short-run monopoly profit is shown by the rectangle JP1TK which is much smaller than the total long-run profit LP2SM. This, however, is not necessary: it all depends on the short-run and long-run cost and revenue conditions. It may be noted at the end that if there are barriers to entry, the monopoly firm

may not reach the optimal scale of production (OQ2) in the long-run, nor can it make full utilization of its existing capacity. The firm’s decision regarding plant expansion and full utilization of its capacity depends solely on the market conditions. If long-run market conditions (i.e., revenue and cost conditions and the absence of competition) permit, the firm may reach its optimal level of output.

Price Discrimination Under Monopoly Price discrimination means selling the same or slightly differentiated product to different sections of consumers at different prices, not commensurate with the cost of differentiation. Consumers are discriminated on the basis of their income or purchasing power, geographical location, age, sex, colour, marital status, quantity purchased, time of purchase, etc. When consumers are discriminated on the basis of these factors in regard to price charged from them, it is called price discrimination. There is another kind of price discrimination. The same price is charged from the consumers of different areas while cost of production in two different plants located in different areas is not the same. Some common examples of price discrimination, not necessarily by a monopolist, are given below: • Physicians and hospitals, lawyers, consultants, etc., charge their customers at different rates mostly on the basis of the latter’s ability to pay • Merchandise sellers sell goods to relatives, friends, old customers, etc., at lower prices than to others and offer off-season discounts to the same set of customers • Railways and airlines charge lower fares from the children and students, and for different class of travellers • Cinema houses and auditoria charge differential rates for cinema shows, musical concerts, etc. • Some multinationals charge higher prices in domestic and lower prices in foreign markets, called ‘dumping’ • Lower rates for the first few telephone calls, lower rates for the evening and night trunk-calls; higher electricity rates for commercial use and lower for domestic consumption, etc. are some other examples of price discrimination. Necessary Conditions First, different markets must be separable for a seller to be able to practice discriminatory pricing. The markets for different classes of consumers must be so separated that buyers of one market are not in a position to resell the commodity in the other. Markets are separated by: (i) geographical distance involving high cost of transportation, i.e., domestic versus foreign markets; (ii) exclusive use of the commodity, e.g., doctor’s services; (iii) lack of distribution channels, e.g., transfer of electricity from domestic use (lower rate) to industrial use (higher rate). Self-Instructional 114 Material Second, the elasticity of demand for the product must be different in different Theory of Market markets. The purpose of price discrimination is to maximize the profit by exploiting the markets with different price elasticities. It is the difference in the elasticity which provides monopoly firm with an opportunity for price discrimination. If price elasticities of demand in different markets are the same, price discrimination would reduce the profit by reducing NOTES demand in the high price markets. Third, there should be imperfect competition in the market. The firm must have monopoly over the supply of the product to be able to discriminate between different classes of consumers, and charge different prices. Fourth, profit maximizing output must be much larger than the quantity demanded in a single market or by a section of consumers. Pricing and Output Decisions under Monopolistic Competition The model of price and output determination under monopolistic competition developed by Edward H. Chamberlin in the early 1930s dominated the pricing theory until recently. Although the relevance of his model has declined in recent years, it has still retained its theoretical flavour. Chamberlin’s model is discussed below. Monopolistic competition is defined as market setting in which a large number of sellers sell differentiated products. Monopolistic competition has the following features: • Large number of sellers • Free entry and free exit • Perfect factor mobility • Complete dissemination of market information • Differentiated product Monopolistic vs Perfect Competition Monopolistic competition is, in many respects, similar to perfect competition. There are, however, three big differences between the two. (i) Under perfect competition, products are homogeneous, whereas under monopolistic competition, products are differentiated. Products are differentiated generally by a different brand name, trade mark, design, colour and shape, packaging, credit terms, quality of after-sales service, etc. Products are so differentiated that buyers can easily distinguish between the products supplied by different firms. Despite product differentiation, each product remains a close substitute for the rival products. Although there are many firms, each one possesses a quasi-monopoly over its product. (ii) There is another difference between perfect competition and monopolistic competition. While decision-making under perfect competition is independent of other firms, in monopolistic competition, firms’ decisions and business behaviour are not absolutely independent of each other. (iii) Another important factor that distinguishes monopolistic competition from perfect competition is the difference in the number of sellers. Under perfect competition, the number of sellers is very large as in case of agricultural products, retail business and share markets, whereas, under monopolistic competition, the number of sellers is large but limited—50 to 100 or even more. What is more important, conceptually, is that the number of sellers is so large that each seller expects that his/her business decisions, tactics and actions will go unnoticed and will not be retaliated by the rival firms. Self-Instructional Material 115 Theory of Market Monopolistic competition, as defined and explained above, is most common now in retail trade with firms acquiring agencies and also in service sectors. More and more industries are now tending towards oligopolistic market structure. However, some industries in India, viz., clothing, fabrics, footwear, paper, sugar, vegetable oils, coffee, spices, NOTES computers, cars and mobile phones have the characteristics of monopolistic competition. Let us now explain the price and output determination models of monopolistic competition developed by Chamberlin. Price and Output Decision in the Short-run Although monopolistic competition is characteristically close to perfect competition, pricing and output decisions under this kind of market are similar to those under monopoly. The reason is that a firm under monopolistic competition, like a monopolist, faces a downward sloping demand curve. This kind of demand curve is the result of: (i) a strong preference of a section of consumers for the product and (ii) the quasi-monopoly of the seller over the supply. The strong preference or brand loyalty of the consumers gives the seller an opportunity to raise the price and yet retain some customers. Besides, since each product is a substitute for the other, the firms can attract the consumers of other products by lowering their prices. The short-term pricing and output determination under monopolistic competition is illustrated in Figure 4.9. It gives short-run revenue and cost curves faced by the monopolistic firm.

Fig. 4.9 Price-Output Determination under Monopolistic Competition

As shown in the figure, firm’s MR intersects its MC at point N. This point fulfills the necessary condition of profit-maximization at output OQ. Given the demand curve, this output can be sold at price PQ. So the price is determined at PQ. At this output and price, the firm earns a maximum monopoly or economic profit equal to PM per unit of

output and a total monopoly profit shown by the rectangle P1PMP2. The economic profit, PM (per unit) exists in the short-run because there is no or little possibility of new firms entering the industry. But the rate of profit would not be the same for all the firms under monopolistic competition because of difference in the elasticity of demand for their products. Some firms may earn only a normal profit if their costs are higher than those of others. For the same reason, some firms may make even losses in the short- run.

Self-Instructional 116 Material Price and Output Determination in the Long-Run Theory of Market The mechanism of price and output determination in the long-run under monopolistic competition is illustrated graphically in Figure 4.10. To begin the analysis, let us suppose that, at some point of time in the long-run, firm’s revenue curves are given as AR1 and NOTES MR1 and long-run cost curves as LAC and LMC. As the figure shows, MR1 and LMC intersect at point M determining the equilibrium output at OQ2 and price at P2Q2. At price P2Q2, the firms make a supernormal or economic profit of P2T per unit of output. This situation is similar to short-run equilibrium.

Fig. 4.10 The Long-Run Price and Output Determination under Monopolistic Competition

Let us now see what happens in the long run. The supernormal profit brings about two important changes in a monopolistically competitive market in the long run. First, the supernormal profit attracts new firms to the industry. As a result, the existing firms lose a part of their market share to new firms. Consequently, their demand curve shifts downward to the left until AR is tangent to LAC. This kind of change in the demand curve is shown is Figure 4.10 by the shift in AR curve from AR1 to AR2 and the

MR curve from MR1 to MR2. Second, the increasing number of firms intensifies the price competition between them. Price competition increases because losing firms try to regain or retain their market share by cutting down the price of their product. And, new firms in order to penetrate the market set comparatively low prices for their product. The price competition increases the slope of the firms’ demand curve or, in other words, it makes the demand curve more elastic. Note that AR2 has a greater slope than AR1 and MR2 has a greater slope than

MR1. The ultimate picture of price and output determination under monopolistic competition is shown at point P1 in Figure 4.10. As the figure shows, LMC intersects

MR2 at point N where firm’s long-run equilibrium output is determined at OQ1 and price at P1Q1. Note that price at P1Q1 equals the LAC at the point of tangency. It means that under monopolistic competition, firms make only normal profit in the long-run. Once all the firms reach this stage, there is no attraction (i.e., super normal profit) for the new firms to enter the industry, nor is there any reason for the existing firms to quit the industry. This signifies the long-run equilibrium of the industry.

Self-Instructional Material 117 Theory of Market To illustrate the price and output determination under monopolistic competition through a numerical example, let us suppose that the initial demand function for the firms is given as: Q = 100 – 0.5P NOTES 1 1 or P1 = 200 – 2Q1 …(4.4)

Given the price function (4.4), firms’ TR1 function can be worked out as:

TR1 = P1 . Q1 = (200 – 2Q1)Q1 2 = 200Q1 – 2Q1 …(4.5)

The marginal revenue function (MR1) can be obtained by differentiating the TR1 function (4.5). Thus,

MR1 = 200 – 4Q1 …(4.6) Suppose also that firms’ TC function is given as: TC = 1562.50 + 5Q – Q2 + 0.05Q3 …(4.7) Given the firms’ TC function, LAC can be obtained as: TC 1562.50+−+ 5QQ23 0.05 Q LAC = = Q Q 1562.50 = + 5 – Q + 0.05Q2 …(4.8) Q We get firms’ LMC function by differentiating its TC function (4.7). Thus, LMC = 5 – 2Q + 0.15Q2 …(4.9) Let us now work out the short-run equilibrium levels of output and price that

maximize firms’ profit. The profit maximizing output can be obtained by equating MR1 and LMC functions given in Eqs. (4.6) and (4.9), respectively, and solving for Q1. That is,

MR1 = LMC 2 200 – 4Q1 = 5 – 2Q + 0.15Q …(4.10)

For uniformity sake, let us replace Q in MC function as Q1 and solve the Eq. (4.10) for Q1. 2 200 – 4Q1 = 5 – 2Q1 + 0.15Q1 2 195 = 2Q1 + 0.15Q1

Q1 = 30 Thus, profit maximizing output in the short-run equals 30.

Let us now find firms’ equilibrium price (P1), LAC and supernormal profit. Price P1 can be obtained by substituting 30 for Q1 in the price function (4.4).

P1 = 200 – 2Q1 = 200 – 2(30) = 140 Thus, firms’ equilibrium price is determined at ` 140. Firms’ LAC can be obtained by substituting equilibrium output 30 for Q in function (4.8). Thus, 1562.50 LAC = + 5 – 30 + 0.05 (30 × 30) = 72.08 Self-Instructional 30 118 Material Thus, the short-run equilibrium condition gives the following data. Theory of Market Equilibrium output = 30

P1 = 140 LAC = 72.08 NOTES

Supernormal profit = AR1 – LAC = 140 – 72.08 = 67.92 (per unit of output) Let us now see what happens in the long-run. As already mentioned, the existence of supernormal profit attracts new firms to the industry in the long-run. Consequently, old firms lose a part of their market share to the new firms. This causes a leftward shift in their demand curve with increasing slope. Let us suppose that given the long-run TC function, firms’ demand function in the long-run takes the following form.

Q2 = 98.75 – P2

and P2 = 98.75 – Q2 …(4.11) To work out the long-run equilibrium, we need to find the new TR function

(TR2) and the new MR function (MR2) corresponding to the new price function (4.11). For this, we need to first work out the new TR function (TR2).

TR2 = P2 ⋅ Q2 = (98 ⋅ 75 – Q2) Q2 2 = 98 ⋅ 75Q2 – Q2 …(4.12)

We get MR2 by differentiating TR function (4.12). Thus,

MR2 = 98 ⋅ 75 – 2Q2 …(4.13)

The long-run equilibrium output can now be obtained by equating MR2 with the LMC function (4.9). For the sake of uniformity, we designate Q in the LMC function as Q2. The long-run equilibrium output is then determined where:

MR2 = LMC 2 or 98 ⋅ 75 – 2Q2 = 5 – 2Q2 + 0 ⋅ 15Q2 2 93 ⋅ 75 = 0 ⋅ 15Q2 2 625 = Q2

Q2 = 25

One of the conditions of the long-run equilibrium is that AR2 or P2 must be equal to LAC. Whether this condition holds can be checked as follows.

P2 = AR2 = LAC

1562.5 2 98 ⋅ 75 – Q2 = + 5 – Q + 0 ⋅ 05Q Q2 By substitution, we get: 1562.5 98 ⋅ 75 – 25 = + 5 – 25 + 0 ⋅ 05 (25)2 25

73 ⋅ 75 = 62.50 – 20 + 31 ⋅ 25 = 73 ⋅ 75 It is thus, mathematically proved that in the long-run, firm’s P = AR = LAC and it earns only a normal profit.

Self-Instructional Material 119 Theory of Market Non-price Competition: Selling Cost and Equilibrium In the preceding section, we have presented Chamberlin’s analysis of price competition and its effect on the firm’s equilibrium output and profits under monopolistic competition. NOTES Chamberlin’s analysis shows that price competition results in the loss of monopoly profits. All firms are losers: there are no gainers. Therefore, firms find other ways and means to non-price competition for enlarging their market share and profits. The two most common forms of non-price competition are product innovation and advertisement. Product innovation and advertisement go on simultaneously. In fact, the successful introduction of a new product depends on its effective advertisement. Apart from advertisement expenses, firms under monopolistic competition incur other costs on competitive promotion of their sales, e.g., expenses on sales personnel, allowance to dealers, discounts to customers, expenses on displays, gifts and free samples to customers, additional costs on attractive packaging of goods, etc. All such expenses plus advertisement expenditure constitute firm’s selling cost. Incurring selling cost increases sales, but with varying degrees. Generally, sales increase initially at increasing rates, but eventually at decreasing rates. Consequently, the average cost of selling (ASC) initially decreases but ultimately it increases. The ASC curve is, therefore, U-shaped, similar to the conventional AC curve. This implies that total sales are subject to diminishing returns to increasing selling costs. Non-price competition through selling cost leads all the firms to an almost similar equilibrium. Chamberlin calls it ‘Group Equilibrium’. We discuss here Chamberlin analysis of firm’s group equilibrium. Selling Cost and Group Equilibrium To analyse group equilibrium of firms with selling costs, let us recall that the main objective of all firms is to maximize their total profit. When they incure selling costs, they do so with the same objective in mind. All earlier assumptions regarding cost and revenue curves remain the same. The analysis of group equilibrium is presented in Figure 4.11. Suppose APC represents firms’ average production cost and competitive price is given

at OP3. None of the firms incurs any selling cost. Also, let all the firms be in equilibrium at point E where they make only normal profits.

Fig. 4.11 Selling Costs and Group Equilibrium

Now suppose that one of the firms incurs selling cost so that its APC added with

average selling costs (ASC) rises to the position of the curve APC + ASC1 and its total Self-Instructional sale increases to OQ4. At output OQ4, the firm makes supernormal profits of P3PMP2. 120 Material This profit is, however, possible only so long as other firms do not incur selling cost on Theory of Market their products. If other firms do advertise their products competitively and incure the same amount of selling cost, the initial advantage to the firm advertising first disappears and its output falls to OQ2. In fact, all the firms reach equilibrium at point A and produce

OQ2 units. But their short-sightedness compels them to increase their selling cost because NOTES they expect to reduce their APC by expanding their output. With increased selling cost, their APC + ASC curve shifts further upward. This process continues until APC + ASC rises to APC + ASC2 which is tangent to the AR = MR line. This position is shown by point B. Beyond point B, advertising is of no avail to any firm. The equilibrium will be stable at point B where each firm produces OQ3 and makes only normal profit. Critical Appraisal of Chamberlin’s Theory Chamberlin’s theory of monopolistic competition propounded in the early 1930s is still regarded to be a major contribution to the theory of pricing. In fact, there is no better theoretical explanation of price determination under monopolistic competition. However, his theory has been criticized on both theoretical and empirical grounds. Let us now look into its theoretical weaknesses and empirical relevance. First, Chamberlin assumes that monopolistic competitors act independently and their price manoeuvring goes unnoticed by the rival firms. This assumption has been questioned on the ground that firms are bound to be affected by decisions of the rival firms since their products are close substitutes for one another and, therefore, they are bound to react. Second, Chamberlin’s model implicitly assumes that monopolistically competitive firms do not learn from their past experience. They continue to commit the mistake of reducing their prices even if successive price reductions lead to decrease in their profits. Such an assumption can hardly be accepted. Third, Chamberlin’s concept of industry as a ‘product group’ is ambiguous. It is also incompatible with product differentiation. In fact, each firm is an industry by virtue of its specialized and unique product. Fourth, his ‘heroic assumptions’ of identical cost and revenue curves are questionable. Since each firm is an industry in itself, there is a greater possibility of variations in the costs and revenue conditions of the various firms. Fifth, Chamberlin’s assumption of free entry is also considered to be incompatible with product differentiation. Even if there are no legal barriers, product differentiation and brand loyalties are in themselves barriers to entry. Finally, so far as empirical validity of Chamberlin’s concept of monopolistic competition is concerned, it is difficult to find any example in the real world to which his model of monopolistic competition is relevant. Most markets that exist in the real world may be classified under perfect or pure competition, oligopoly or monopoly. It is, therefore, alleged that Chamberlin’s model of monopolistic competition analyzes an unrealistic market. Some economists, e.g., Cohen and Cyert, hold the position that the model of monopolistic competition is not a useful addition to economic theory because it does not describe any market in the real world. Despite the above criticism, Chamberlin’s contribution to the theory of price cannot be denied. Chamberlin was the first to introduce the concept of differentiated product and selling costs as a decision variable and to offer a systematic analysis of these factors. Another important contribution of Chamberlin is the introduction of the concept Self-Instructional Material 121 Theory of Market of demand curve based on market share as a tool of analysing behaviour of firms, which later became the basis of the kinked-demand curve analysis. 4.3.2 Pricing and Output Decisions under Oligopoly NOTES Oligopoly is defined as a market structure in which there are a few sellers selling homogeneous or differentiated products. Where oligopoly firms sell a homogeneous product, it is called pure or homogeneous oligopoly. For example, industries producing bread, cement, steel, petrol, cooking gas, chemicals, aluminium and sugar are industries characterized by homogeneous oligopoly. And, where firms of an oligopoly industry sell differentiated products, it is called differentiated or heterogeneous oligopoly. Automobiles, television sets, soaps and detergents, refrigerators, soft drinks, computers, and cigarettes are some examples of industries characterized by differentiated or heterogeneous oligopoly. Be it pure or differentiated, ‘oligopoly is the most prevalent form of market organization in the manufacturing sector of the industrial nations…’. In non-industrial nations like India also, a majority of big and small industries have acquired the features of oligopoly market. The market share of 4 to 10 firms in 84 big and small industries of India is given below.

Market share (%) No. of industries 1 – 24.9 8 25 – 49.9 11 50 – 74.9 15 75 – 100 50 Total 84

As the data presented above shows, in India, in 50 out of 84 selected industries, i.e., in about 60 per cent industries, 4 to 10 firms have a 75 per cent or more market share which gives a concentration ratio of 0.500 or above. All such industries can be classified under oligopoly. The factors that give rise to oligopoly are broadly the same as those for monopoly. The main sources of oligopoly are described here briefly. 1. Huge capital investment: Some industries are by nature capital-intensive, e.g., manufacturing automobiles, aircraft, ships, TV sets, computers, mobile phones, refrigerators, steel and aluminium goods, etc. Such industries require huge initial investment. Therefore, only those firms which can make huge investment can enter these kinds of industries. In fact, a huge investment requirement works as a natural barrier to entry to the oligopolistic industries. 2. Economies of scale: By virtue of huge investment and large scale production, the large units enjoy absolute cost advantage due to economies of scale in production, purchase of industrial inputs, market financing, and sales organization. This gives the existing firms a comparative advantage over new firms in price competition. This also works as a deterrent for the entry of new firms. 3. Patent rights: In case of differentiated oligopoly, firms get their differentiated product patented which gives them an exclusive right to produce and market the patented commodity. This prevents other firms from producing

Self-Instructional 122 Material the patented commodity. Therefore, unless new firms have something new to Theory of Market offer and can match the existing products in respect of quality and cost, they cannot enter the industry. This keeps the number of firms limited. 4. Control over certain raw materials: Where a few firms acquire control over almost the entire supply of important inputs required to produce a certain NOTES commodity, new firms find it extremely difficult to enter the industry. For example, if a few firms acquire the right from the government to import certain raw materials, they control the entire input supply. 5. Merger and takeover: Merger of rival firms or takeover of rival firms by the bigger ones with a view to protecting their joint market share or to put an end to waste of competition is working, in modern times, as an important factor that gives rise to oligopolies and strengthens the oligopolistic tendency in modern industries. Mergers and takeovers have been one of the main features of recent trend in Indian industries. Features of Oligopoly Let us now look at the important characteristics of oligopolistic industries. 1. Small number of sellers: As already mentioned, there is a small number of sellers under oligopoly. How small is the number of sellers in oligopoly markets is difficult to specify precisely for it depends largely on the size of the market. Conceptually, however, the number of sellers is so small that the market share of each firm is large enough for a single firm to influence the market price and the business strategy of its rival firms. The number may vary from industry to industry. Some examples of oligopoly industries in India and market share of the dominant firms in 1997-98 is given below.

Industry No. of firms Total market share (%) Ice-cream 4 100.00 Bread 2 100.00 Infant Milk food 6 99.95 Motorcycles 5 99.95 Passenger cars 5 94.34 Cigarettes 4 99.90 Fruit Juice, pulp & conc. 10 98.21 Fluorescent lamps 3 91.84 Automobile tyres 8 91.37

Source: CMIE, Industries and Market Share, August 1999. 2. Interdependence of decision-making: The most striking feature of an oligopolistic market structure is the interdependence of oligopoly firms in their decision-making. The characteristic fewness of firms under oligopoly brings the firms in keen competition with each other. The competition between the firms takes the form of action, reaction and counter-action in the absence of collusion between the firms. For example, car companies have changed their prices following the change in price made by one of the companies. They have introduced new model in competition with one another. Since the number of firms in the industry is small, the business strategy of each firm in respect of pricing, advertising and product modification is closely watched by the rival firms and it evokes imitation and retaliation. What is equally important is that firms initiating a new business strategy anticipate and take into account the possible counter-action by the rival firms. This is called interdependence of oligopoly firms. Self-Instructional Material 123 Theory of Market An illuminating example of strategic manoeuvring is cited by Robert A. Meyer. To quote the example, one of the US car manufacturing companies announced in one year in the month of September an increase of $ 180 in the price list of its car model. Following it, a few days later a second company announced an increase NOTES of $ 80 only and a third announced an increase of $ 91. The first company made a counter move: it announced a reduction in the enhancement in the list price from $ 180 to $ 71. This is a pertinent example of interdependence of firms in business decisions under oligopolistic market structure. In India, when Maruti Udyog Limited (MUL), announced a price cut of ` 24,000 to ` 36,000 in early 2005 on its passenger cars, other companies followed suit. However, price competition is not the major form of competition among the oligopoly firms as price war destroys the profits. A more common form of competition is non-price competition on the basis of product differentiation, vigorous advertising and provision to survive. 3. Barriers to entry: Barriers to entry to an oligopolistic industry arise due to such market conditions as: (i) huge investment requirement to match the production capacity of the existing ones, (ii) economies of scale and absolute cost advantage enjoyed by the existing firms, (iii) strong consumer loyalty to the products of the established firms based on their quality and service and (iv) preventing entry of new firms by the established firms through price cutting. However, the new entrants that can cross these barriers can and do enter the industry, though only a few, that too mostly the branches of MNCs survive. 4. Indeterminate price and output: Another important feature, though a controversial one, of the oligopolistic market structure is the indeterminateness of price and output. The characteristic fewness and interdependence of oligopoly firms makes derivation of the demand curve a difficult proposition. Therefore, price and output are said to be indeterminate. However, price and output are said to be determinate under collusive oligopoly. But, there too, collusion may last or it may break down. An opposite view is that price under oligopoly is sticky, i.e., if price is once determined, it tends to stabilize. 4.3.3 Cournot and Stackleberg’s Model of Duopoly Oligopoly is a form of market in which there are a few sellers selling homogeneous or differentiated products. Economists do not specify how few are the sellers in an oligopolistic market. However, two sellers is the limiting case of oligopoly. When there are only two sellers, the market is called duopoly. The most basic form of oligopoly is a duopoly where a market is dominated by a small number of companies and where only two producers exist in one market. A duopoly is also referred to as a biopoly. Similar to a monopoly, a duopoly too can have the same impact on the market only if both the players connive on prices or output. There are three principal duopoly models—Cournot, Bertrand Model and Stackleberg’s model of duopoly. Both of them are discussed below. (i) Cournot’s duopoly model Augustine Cournot, a French economist, was the first to develop a formal oligopoly model in 1838. He formulated his oligopoly theory in the form of a duopoly model

Self-Instructional 124 Material which can be extended to oligopoly model. To illustrate his model, Cournot made the Theory of Market following assumptions. (a) There are two firms, each owning an artesian mineral water well. (b) Both the firms operate their wells at zero marginal cost. NOTES (c) Both of them face a demand curve with constant negative slope. (d) Each seller acts on the assumption that his competitor will not react to his decision to change his output—Cournot’s behavioural assumption. On the basis of this model, Cournot has concluded that each seller ultimately supplies one-third of the market and both the firms charge the same price. And, one- third of the market remains unsupplied. Cournot’s duopoly model is presented in Figure 4.12. The demand curve for mineral water is given by the AR curve and firm’s MR by the MR curve. To begin with, let us suppose that there are only two sellers A and B, but initially, A is the only seller of mineral water in the market. By assumption, his MC = 0. Following the profit maximizing rule, he sells quantity OQ where his MC = 0 = MR, at price OP2. His total profit is OP2PQ.

D e c

i P r P2 P

R P′ P1

O Q N M MR Quantity Fig. 4.12 Price and Output Determination under Duopoly: Cournot’s Model

Now let B enter the market. He finds that the market open to him is QM which is half of the total market. That is, he can sell his product in the remaining half of the market. B assumes that A will not change his output because he is making maximum profit. Specifically, B assumes that A will continue to sell OQ at prices OP2. Thus, the market available to B is QM and the relevant part of the demand curve is PM. Given his demand curve PM, his MR curve is given by the curve PN which bisects QM at point N where QN = NM. In order to maximize his revenue, B sells QN at price OP1. His total revenue is maximum at QRP′N which equals his total profit. Note that B supplies only QN = 1/4 = (1/2)/2 of the market. Let us now see how A’s profit is affected by the entry of B. With the entry of B, ′ price falls to OP1. Therefore, A s expected profit falls to OP1RQ. Faced with this situation,

A assumes, in turn, that B will not change his output QN and price OP1 as he is making maximum profit. Since QN = 1/4th of the market, A assumes that he has 3/4 ( = 1 – 1/4) of the market available to him. To maximize his profit, A supplies 1/2 of the unsupplied market (3/4), i.e., 3/8 of the market. It is noteworthy that A′s market share has fallen from 1/2 to 3/8.

Self-Instructional Material 125 Theory of Market Now it is B’s turn to react. Following Cournot’s assumption, B assumes that A will continue to supply only 3/8 of the market and the market open to him equals 1 – 3/8 = 5/8. To maximize his profit under the new conditions, B supplies 1/2 × 5/8 = 5/16 of the market. It is now for A to reappraise the situation and adjust his price and output NOTES accordingly. This process of action and reaction continues in successive periods. In the process, A continues to lose his market share and B continues to gain. Eventually, a situation is reached when their market share equals 1/3 each. Any further attempt to adjust output produces the same result. The firms, therefore, reach their equilibrium where each one supplies one-third of the market and both charge the same price. The actions and reactions and equilibrium of the sellers A and B, according to Cournot’s model, are presented in Table 4.2. Table 4.2 Determination of Market Share

Period Seller A Seller B 11 11 1 I (1) 22 22 4 1 13 1 35 II 1 1 2 48 2 8 16 1 5 11 1 11 21 III 1 1 2 16 32 2 32 64 1 21 43 1 43 85 IV 1 1 2 64 128 2 128 256 …… … …… … 1 11 1 11 N 1 1 2 33 2 33

Note: Arrows show the direction of actions and reactions of sellers A and B. Cournot’s equilibrium solution is stable. For, given the action and reaction, it is not possible for any of the two sellers to increase their market share as shown in the last row of the table. Cournot’s model of duopoly can be extended to a general oligopoly model. For example, if there are three sellers in the industry, each one of them will be in equilibrium when each firm supplies 1/4 of the market. The three sellers together supply 3/4 of the total market, 1/4 of the market remaining unsupplied. Similarly, when there are four firms each one of them supply 1/5th of the market and 1/5th of the market remains unsupplied. The formula for determining the share of each seller in an oligopolistic market is: Q ÷ (n + 1) where Q = market size, and n = number of sellers. Algebraic solution of duopoly: Cournot’s model can also be presented algebraically. Let us suppose that the market demand function is given by linear function as: Q = 90 – P ...(4.14) As noted above, under zero cost condition, profit is maximum where MC = MR = 0 and when MR = 0, the profit maximizing output is 1/2 (Q). Let us suppose that when A is the only seller in the market, his profit-maximizing

output is QA which is determined by the profit maximizing rule under zero cost condition. A′s market share can be written as: Q = 1/2 (90 – P) ...(4.15) Self-Instructional A 126 Material When seller B enters the market, his profit maximizing output is determined as follows. Theory of Market

QB = 1/2 [(1/2(90 – P)] ...(4.16)

Thus, the respective shares of sellers A and B are fixed at QA and QB. The division of market output may be expressed as: NOTES

Q = QA + QB = 90 – P ...(4.17) The demand function for A may now be expressed as:

QA = (90 – QB) – P ...(4.18) and for B as:

QB = (90 – QA) – P ...(4.19)

Given the demand function (4.18), the market open to A (at P = 0) is 90 – QB. The profit maximizing output for A will be: 90 Q Q = B ...(4.20) A 2 and for B, it will be: 90 Q Q = A ...(4.21) B 2 The equations (4.20) and (4.21) represent the reaction functions of sellers A and B, respectively. For example, consider equation (4.20). The profit maximizing output of

A depends on the value of QB, i.e., the output which B is assumed to produce. If B ′ chooses to produce 30 units (i.e., QB = 30), then A s profit maximizing output = [(90 – 30)1/2] = 30. If B chooses to produce 60 units, A′s profit maximizing output = (90 – 60) 1/2 = 15. Thus, equation (4.21) is A′s reaction function. It can similarly be shown that equation (4.21) is B′s reaction function.

Fig. 4.13 Reaction Functions and Equilibrium: Cournot’s Model

The reaction functions of A and B are graphed in Figure 4.13. The reaction function PM shows how A will react on the assumptions that B will not react to changes in his output once B’s output is fixed. The reaction function CD shows a similar reaction of B. The two reaction functions intersect at point E. It means that the assumptions of A and

Self-Instructional Material 127 Theory of Market B coincide at point E and here ends their action and reaction. Point E is, therefore, the point of stable equilibrium. At this point, each seller sells only 30 units. The same result can be obtained by equating the two reaction equations (4.20) and (4.21). The market slope of A and B can be obtained by equating A′s and B′s NOTES reaction functions (4.20) and (4.21), respectively. That is, market equilibrium lies where:

90QQBA 90 22

Since, QB = (90 – QA)/2, by substitution, we get first term as: 90 (90Q ) / 2 Q = A A 2 QA = 30 Thus, both the sellers are in equilibrium at their respective output of 30. The market output will be 60 units. Given the market demand curve, market price will be P = 90 – Q = 90 – 60 = ` 30. As mentioned above, the duopoly model can be extended to oligopoly market. Criticism of Cournot’s model: As we have seen above, Cournot’s model is logically sound and yields a stable equilibrium solution. His model has, however, been criticized on the following grounds. First, Cournot’s behavioural assumption, specifically assumption (d) above, is said to be naive as it implies that firms continue to make wrong calculations about the behaviour of the rival firms even though their calculations are proved wrong. For example, each seller continues to assume that his rival will not change his output even though he finds frequently that his rival does change his output. Second, Cournot assumed zero cost of production, which is not realistic. However, even if this assumption is ignored, Cournot’s results are not affected. (ii) Bertrand model of non-collusive oligopoly Bertrand, a French mathematician, criticised Cournot’s model and developed his own model of duopoly in 1883. Bertrand’s model differs from Cournot’s model in respect of its behavioural assumption. While under Cournot’s model, each seller assumes his rival’s output to remain constant, under Bertrand’s model each seller determines his price on the assumption that his rival’s price, rather than his output, remains constant. Bertrand’s model concentrates on price-competition. His analytical tools are reaction functions of the duopolists. Reaction functions of the duopolists are derived on the basis of isoprofit curves. An isoprofit curve, for a given level of profit, is drawn on the basis of various combinations of prices charged by rival firms. Assuming two firms A and B, the two axis of the plane on which isoprofit curves are drawn measure one each the prices of the two firms. Isoprofit curves of the two firms are convex to their respective price axis, as shown in Figures 4.14 and 4.15. Isoprofit curves of firm A

are convex to its price-axis PA (Figure 4.13) and those of firm B are convex to PB (Figure 4.15).

Self-Instructional 128 Material Theory of Market

NOTES

Fig. 4.14 A’s Reaction Curve

Fig. 4.15 B’s Reaction Curve

To explain the implication of an isoprofit curve, consider curve A in Figure 4.14. It shows that A can earn a given profit from the various combinations of its own and its rival’s price. For example, price combinations at points a, b and c on isoprofit curve A1, yield the same level of profit. If firm B fixes its price PB1, firm A has two alternative prices, PA1 and PA2, to make the same level of profits. When B reduces its price, A may either raise its price or reduce it. A will reduce its price when he is at point c and raise its price when he is at point a. But there is a limit to which this price adjustment is possible. This point is given by point b. So there is a unique price for A to maximize its profits. This unique price lies at the lowest point of the isoprofit curve. The same analysis applies to all other isoprofit curves. If we join the lowest points of the isoprofit curves A1, A2 and

A3, we get A’s reaction curve. Note that A’s reaction curve has a rightward slant. This is so because, isoprofit curve tend to shift rightward when A gains market from its rival B.

Fig. 4.16 Duopoly Equilibrium: Bertand’s Model Self-Instructional Material 129 Theory of Market Following the same process, B’s reaction curve may be drawn as shown in Figure 4.15. The equilibrium of duopolists suggested by Bertrand’s model may be obtained by putting together the reaction curves of the firms A and B as shown in Figure 4.16. The reaction curves of A and B intersect at point E where their expectations materialise. NOTES Point E is therefore equilibrium point. This equilibrium is stable. For, if anyone of the firms deviates from the equilibrium point, it will generate a series of actions and reactions between the firms which will lead them back to point E. Criticism Bertrand’s model has however been criticised on the same grounds as Cournot’s model. Bertrand’s implicit behavioural assumption that firms never learn from their past experience is naive. Furthermore, if cost is assumed to be zero, price will fluctuate between zero and the upper limit of the price, instead of stabilizing at a point. (iii) Stackelberg model of non-collusive oligopoly Stackelberg, a German economist, developed, his leadership model of duopoly in 1930. His model is an extension of Cournot’s model. Stackelberg assumes that one of the duopolists (say A) is sophisticated enough to play the role of a leader and the other (say B) acts as a follower. The leading duopolist A recognizes that his rival firm B has a definite reaction function which A uses into his own profit function and maximizes his profits. Suppose market demand function is Q = 90 – P and B’s reaction function is given as in Equation (4.22), i.e., − QB = …(4.22) Now, let A incorporate B’s reaction function into the market function and formulate his own demand function as:

QA = 90 – QB – P …(4.23)

Since QB = (90 – QA)/2, Equation (4.23) may be written as: − − − QA =

+− or QA =

or 2QA = 90 + QA – 2P …(4.24)

QA = 90 – 2P Thus, by knowing B’s reaction function, A is able to determine his own demand function. Following the profit-maximization rule, A will fix his output at 45 units (= 90/2), i.e., half of the total demand at zero price. Now, if seller A produces 45 units and seller B sticks to his own reaction function, he will produce: − QB = = 22.5 units ...(4.25) Thus, the industry output will be: 45 + 22.5 = 67.5. Self-Instructional 130 Material The problem with Stackelberg’s model is that it does not decide as to which of the Theory of Market firms will act as leader (or follower). If each firm assumes itself to be the leader and the other to be the follower then Stackelberg’s model will be indeterminate with unstable equilibrium. NOTES 4.4 COLLUSIVE OLIGOPOLY: CARTEL

The oligopoly models discussed in the previous section are based on the assumption that the oligopoly firms act independently; they are in competition with one another; and there is no collusion between the firms. The oligopoly models of this category are called non-collusive models. In reality, however, oligopoly firms are found to have some kind of collusion or agreement—open or secret, explicit or implicit, written or unwritten, and legal or illegal—with one another for at least three major reasons. First, collusion eliminates or reduces the degree of competition between the firms and gives them some monopolistic powers in their price and output decisions. Second, collusion reduces the degree of uncertainty surrounding the oligopoly firms and ensures profit maximization. Third, collusion creates some kind of barriers to the entry of new firms. The models that deal with the collusive oligopolies are called collusive oligopoly models. Collusion between firms may take many forms depending on their relative strength and objective of collusion, and on whether collusion is legal or illegal. There are, however, two major forms of collusion between the oligopoly firms: (i) cartel, i.e., firms’ association, and (ii) price leadership agreements. Accordingly, the collusive oligopoly models that economists have developed to explain the price determination under oligopoly can be classified as: (i) Cartel models (ii) Price leadership models Cartel Models: Collusive Models

Oligopoly cartels: A form of collusion: A cartel is a formal organization of the oligopoly Check Your Progress firms in an industry. A general purpose of cartels is to centralize certain managerial 5. What does the decisions and functions of individual firms in the industry, with a view to promoting market structure and common benefits. Cartels may be in the form of open or secret collusion. Whether degree of open or secret, cartel agreements are explicit and formal in the sense that agreements competition determine? are enforceable on the member firms not observing the cartel rules or dishonouring the 6. Define pure agreements. Cartels are, therefore, regarded as the perfect form of collusion. Cartels monopoly. and cartel type agreements between the firms in manufacturing and trade are illegal in 7. Name the two most most countries. Yet, cartels in the broader sense of the term exist in the form of trade common forms of associations, professional organizations and the like. non-price competition. A cartel performs a variety of services for its members. The two services of 8. Who was the first central importance are (i) fixing price for joint profit maximization; and (ii) market- economist to sharing between its members. Let us now discuss price and output determination under developed a formal oligopoly model in the cartel system. 1838? 4.4.1 Joint Profit Maximization Model 9. What is the assumption of Let us suppose that a group of firms producing a homogeneous commodity forms a Stackleberg’s model of non-collusive cartel aiming at joint profit maximization. The firms appoint a central management board oligopoly? with powers to decide (i) the total quantity to be produced; (ii) the price at which it must Self-Instructional Material 131 Theory of Market be sold; and (iii) the share of each firm in the total output. The cartel board is provided with cost figures of individual firms. Besides, it is supposed to obtain the necessary data required to formulate the market demand (AR) curve. The cartel board calculates the marginal cost (MC) and marginal revenue (MR) for the industry. In a sense, the cartel NOTES board holds the position of a multiplant monopoly. It determines the price and output for each firm in the manner a multiplant monopoly determines the price and output for each of its plants. The model of price and output determination for each firm is presented in Figure 4.17. It is assumed for the sake of convenience that there are only two firms, A and B, in the cartel. Their respective cost curves are given in the first two panels of Figure 4.17. In the third panel, AR and MR curves represent the revenue conditions of the industry. The MC curve is the summation of mc curves of the individual firms. The MC and MR curves intersect at point C determining the industry output at OQ. Given the industry output, the market price is determined at PQ. Now, under the cartel system, the industry output OQ has to be so allocated between firms A and B that their individual MC = MR. The share of each firm in the industry output, OQ, can be obtained by drawing a line from point C and parallel to X-

axis through mc2 and mc1. The points of intersection c1 and c2 determine the profit maximizing output for firms A and B, respectively. Thus, the share of firms A and B, is

determined at OQA and OQB, respectively, where OQA + OQB = OQ. At these outputs, they maximize their respective profits.

Firm A Firm B Industry

MC = mc12 + mc mc1 P Pw Pw Pw ac1 mc2 e

c ac

i 2 r c2 AR P Price Price C c1

MR

O QA O QB O Q = Qab + Q Output Output Output Fig. 4.17 Price and Output Determination Under Cartel

Problems in joint profit maximization: Although the above solution to joint profit maximization by cartel looks theoretically sound, William Fellner gives the following reasons why profits may not be maximized jointly. First, it is difficult to estimate market demand curve ‘accurately since each firm thinks that the demand of its own product is more elastic than the market demand curve because its product is a perfect substitute for the product of other firms. Second, an accurate estimation of industry’s MC curve is highly improbable for lack of adequate and correct cost data. If industry’s MC is incorrectly estimated, industry output can be only incorrectly determined. Hence joint profit maximization is doubtful. Third, cartel negotiations take a long time. During the period of negotiation, the composition of the industry and its cost structure may change. This may render demand and cost estimates irrelevant, even if they are correct. Besides, if the number of firms increases beyond 20 or so, cartel formation becomes difficult, or even if it is formed, it breaks down soon. Self-Instructional 132 Material Fourth, there are ‘chiselers’ who have a strong temptation to give secret or Theory of Market undeclared concessions to their customers. This tendency in the cartel members reduces the prospect of joint profit maximization. Fifth, if cartel price, like monopoly price, is very high, it may invite government attention and interference. For the fear of government interference, members may not NOTES charge the cartel price. Sixth, another reason for not charging the cartel price is the fear of entry of new firms. A high cartel price which yields monopoly profit may attract new firms to the industry. To prevent the entry of new firms, some firms may decide on their own not to charge the cartel price. Lastly, yet another reason for not charging the cartel price is the desire to build a public image or good reputation. Some firms may, to this end, decide to charge only a fair price and realise only a fair profit. 4.4.2 Cartel and Market-Sharing The market-sharing cartels are more common because this kind of collusion permits a considerable degree of freedom in respect of style and design of the product, advertising and other selling activities. There are two main methods of market allocations: (a) non- price competition agreement, and (b) quota system. (a) Non-price competition agreement: The non-price competition agreements are usually associated with loose cartels. Under this kind of arrangement between firms, a uniform price is fixed and each firm is allowed to sell as much as it can at the cartel price. The only requirement is that firms are not allowed to reduce the price below the cartel price. The cartel price is, however, a bargain price. While low-cost firms press for a low price, the high-cost firms press for a higher price. But the cartel price is so fixed by mutual consent that all member firms are able to make a reasonable profits. However, firms are allowed to compete with one another in the market on a non-price basis. That is, they are allowed to change the style of their product, innovate new designs and to promote their sales without reducing their price below the level of cartel price. Whether this arrangement works or breaks down depends on the cost conditions of the individual firms. If some firms expect to increase their profits by violating the price agreements, they will indulge in cheating by charging a lower price. This may lead to a price-war and the cartel may break down. (b) Quota system: The second method of market-sharing is quota system. Under this system, the cartel fixes a quota of market-share for each firm. There is no uniform principle by which quota is fixed. In practice, however, the main considerations are: (i) bargaining ability of a firm and its relative importance in the industry, (ii) the relative sales or market share of the firm in pre-cartel period, and (iii) production capacity of the firm. The choice of the base period depends on the bargaining ability of the firm. Fixation of quota is a difficult problem. Nevertheless, some theoretical guidelines for market sharing are suggested as follows. A reasonable criterion for ideal market- sharing can be to share the total market between the cartel members in such proportions that the industry’s marginal cost equals the marginal cost of individual firms. This criterion is illustrated in Figure 4.18 assuming an oligopoly industry consisting of only two firms, A and B. The profit maximizing output of the industry is OQ. The industry output OQ is so shared between the two firms A and B that their individual MC equals industry’s MC. As Self-Instructional Material 133 Theory of Market shown in Figure 4.18, at output OQA, MC of firm A equals industry’s marginal cost, MC,

and at output OQB, MC of firm B equals industry’s MC. Thus, under quota system, the

quota for firms A and B may be fixed as OQA and OQB, respectively. Given the quota allocation, the firm may set different prices for their product depending on the position NOTES and elasticity of their individual demand curves. This criterion is identical to the one adopted by a multiplant monopolist in the short-run, to allocate the total output between the plants.

(a) Firms A (b) Firms B (c) Industry

Price MCA Price MCB Price

PM PM R MC=MC +MC PM AB

C ARM

MRM ARA ARB MRA MRB

OQA OQB OQQ = QA + QB Quantity Quantity Quantity Fig. 4.18 Quota Allocation under Cartel Agreements

Another reasonable criterion for market-sharing under quota system is equal market-share for equal firms. This criterion is applicable where all firms have identical cost and revenue curves. This criterion also leads to a monopoly solution. It resembles Chamberlin’s duopoly model. To illustrate equal market sharing through quota allocation, let us assume that there are only two firms, A and B. Their AR, MR and MC curves are presented in Figure 4.18 (a) and 4.18 (b). The market revenue and cost curves, which are obtained by summing the individual revenue and cost curves, respectively, are presented in panel (c) of the figure. The industry output is determined at OQ. The share of each firm, which

maximizes their profits, is so determined that OQ = OQA + OQB, Given the identical cost

and revenue conditions, OQA = OQB. That is, market is divided equally between firms A and B. This result can be obtained also by drawing an ordinate from the point where

price line (PM) intersects the MRM, i.e., from point R. The market output OQ is divided equally between firms A and B. It may be noted at the end that cartels do not necessarily create the conditions for price stability in an oligopolistic market. Most cartels are loose. Cartel agreements are generally not binding on the members. Cartels do not prevent the possibility of entry of new firms. On the contrary, by ensuring monopoly profits, cartels create conditions Check Your Progress which attract new firms to the industry. Besides, ‘chiselers’ and ‘free-riders’ create 10. What are the two conditions for instability in price and output. major forms of collusion between the oligopoly 4.5 SUMMARY firms? 11. What is a cartel? In this unit, you have learnt that: 12. Why are the market-sharing • Perfect competition refers to a market condition in which a very large number of cartels more common? buyers and sellers enjoy full freedom to buy and to sell a homogenous good and service and they have perfect knowledge about the market conditions, and factors Self-Instructional of production have full freedom of mobility. 134 Material • Under perfect competition, the number of sellers is assumed to be so large that Theory of Market the share of each seller in the total supply of a product is very small or insignificant. Therefore, no single seller can influence the market price by changing his supply or can charge a higher price. Therefore, firms are price-takers, not price-makers. • Government does not interfere in any way with the functioning of the market. NOTES There are no discriminatory taxes or subsidies; no licencing system, no allocation of inputs by the government, or any other kind of direct or indirect control. That is, the government follows the free enterprise policy. • A profit maximising firm is in equilibrium at the level of output which equates its MC = MR. However, the level of output which meets the equilibrium condition for a firm varies depending on cost and revenue functions. • The supply curve of an individual firm is derived on the basis of its equilibrium output. The equilibrium output, determined by the intersection of MR and MC curves, is the optimum supply by a profit maximising (or cost minimising) firm. • The industry supply curve, or what is also called market supply curve, is the horizontal summation of the supply curve of the individual firms. If cost curves of the individual firms of an industry are identical, their individual supply curves are also identical. In that case, industry supply curve can be obtained by multiplying the individual supply at various prices by the number of firms. • In the economic sense, a market is a system by which buyers and sellers bargain for the price of a product, settle the price and transact their business—buy and sell a product. • The market structure determines a firm’s power to fix the price of its product a great deal. The degree of competition determines a firm’s degree of freedom in determining the price of its product. • Under perfect competition, a large number of firms compete against each other for selling their product. Therefore, the degree of competition under perfect competition is close to one, i.e., the market is highly competitive. • Under monopolistic competition, the degree of freedom depends largely on the number of firms and the level of product differentiation. Where product differentiation is real, firm’s discretion and control over the price is fairly high and where product differentiation is nominal or only notional, firm’s pricing decision is highly constrained by the prices of the rival products. • The term pure monopoly means an absolute power of a firm to produce and sell a product that has no close substitute. • As under perfect competition, pricing and output decisions under monopoly are based on profit maximization hypothesis, given the revenue and cost conditions. • The decision rules regarding optimal output and pricing in the long-run are the same as in the short-run. In the long-run, however, a monopolist gets an opportunity to expand the size of its firm with a view to enhance its long-run profits. • Price discrimination means selling the same or slightly differentiated product to different sections of consumers at different prices, not commensurate with the cost of differentiation. • Monopolistic competition is defined as market setting in which a large number of sellers sell differentiated products.

Self-Instructional Material 135 Theory of Market • Chamberlin’s analysis shows that price competition results in the loss of monopoly profits. All firms are losers: there are no gainers. Therefore, firms find other ways and means to non-price competition for enlarging their market share and profits. NOTES • Chamberlin was the first to introduce the concept of differentiated product and selling costs as a decision variable and to offer a systematic analysis of these factors. Another important contribution of Chamberlin is the introduction of the concept of demand curve based on market share as a tool of analysing behaviour of firms, which later became the basis of the kinked-demand curve analysis. • Oligopoly is defined as a market structure in which there are a few sellers selling homogeneous or differentiated products. • The most striking feature of an oligopolistic market structure is the interdependence of oligopoly firms in their decision-making. The characteristic fewness of firms under oligopoly brings the firms in keen competition with each other. • The most basic form of oligopoly is a duopoly where a market is dominated by a small number of companies and where only two producers exist in one market. A duopoly is also referred to as a biopoly. • Augustine Cournot, a French economist, was the first to develop a formal oligopoly model in 1838. He formulated his oligopoly theory in the form of a duopoly model which can be extended to oligopoly model. • Bertrand, a French mathematician, criticised Cournot’s model and developed his own model of duopoly in 1883. Bertrand’s model differs from Cournot’s model in respect of its behavioural assumption. • Stackelberg, a German economist, developed, his leadership model of duopoly in 1930. His model is an extension of Cournot’s model. Stackelberg assumes that one of the duopolists is sophisticated enough to play the role of a leader and the other acts as a follower. • There are two major forms of collusion between the oligopoly firms: (i) cartel, i.e., firms’ association, and (ii) price leadership agreements. • A cartel is a formal organization of the oligopoly firms in an industry. A general purpose of cartels is to centralize certain managerial decisions and functions of individual firms in the industry, with a view to promoting common benefits. • A cartel performs a variety of services for its members. The two services of central importance are (i) fixing price for joint profit maximization; and (ii) market- sharing between its members. • The market-sharing cartels are more common because this kind of collusion permits a considerable degree of freedom in respect of style and design of the product, advertising and other selling activities. • It may be noted at the end that cartels do not necessarily create the conditions for price stability in an oligopolistic market. Most cartels are loose. Cartel agreements are generally not binding on the members. Cartels do not prevent the possibility of entry of new firms. On the contrary, by ensuring monopoly profits, cartels create conditions which attract new firms to the industry. Besides, ‘chiselers’ and ‘free- riders’ create conditions for instability in price and output.

Self-Instructional 136 Material Theory of Market 4.6 KEY TERMS

• Perfect competition: It refers to a market condition in which a very large number of buyers and sellers enjoy full freedom to buy and to sell a homogenous good and NOTES service and they have perfect knowledge about the market conditions, and factors of production have full freedom of mobility. • Pure monopoly: It means an absolute power of a firm to produce and sell a product that has no close substitute. • Price discrimination: It means selling the same or slightly differentiated product to different sections of consumers at different prices, not commensurate with the cost of differentiation. • Monopolistic competition: It is defined as market setting in which a large number of sellers sell differentiated products. • Oligopoly: It is defined as a market structure in which there are a few sellers selling homogeneous or differentiated products.

4.7 ANSWERS TO ‘CHECK YOUR PROGRESS’

1. Under perfect competition, the number of sellers is assumed to be so large that the share of each seller in the total supply of a product is very small or insignificant. Therefore, no single seller can influence the market price by changing his supply or can charge a higher price. 2. Under perfect competition, a government does not interfere in any way with the functioning of the market. There are no discriminatory taxes or subsidies; no licencing system, no allocation of inputs by the government, or any other kind of direct or indirect control. That is, the government follows the free enterprise policy. 3. Under perfect competition, an individual firm does not determine the price of its product. Price for its product is determined by the market demand and market supply. 4. A profit maximising firm is in equilibrium at the level of output which equates its MC = MR. However, the level of output which meets the equilibrium condition for a firm varies depending on cost and revenue functions. 5. The market structure determines a firm’s power to fix the price of its product a great deal. The degree of competition determines a firm’s degree of freedom in determining the price of its product. 6. The term pure monopoly means an absolute power of a firm to produce and sell a product that has no close substitute. 7. The two most common forms of non-price competition are product innovation and advertisement. 8. Augustine Cournot, a French economist, was the first to develop a formal oligopoly model in 1838. He formulated his oligopoly theory in the form of a duopoly model which can be extended to oligopoly model.

Self-Instructional Material 137 Theory of Market 9. Stackelberg, a German economist, developed, his leadership model of duopoly in 1930. His model is an extension of Cournot’s model. Stackelberg assumes that one of the duopolists is sophisticated enough to play the role of a leader and the other acts as a follower. NOTES 10. There are two major forms of collusion between the oligopoly firms: (i) cartel, i.e., firms’ association, and (ii) price leadership agreements. 11. A cartel is a formal organization of the oligopoly firms in an industry. A general purpose of cartels is to centralize certain managerial decisions and functions of individual firms in the industry, with a view to promoting common benefits. 12. The market-sharing cartels are more common because this kind of collusion permits a considerable degree of freedom in respect of style and design of the product, advertising and other selling activities.

4.8 QUESTIONS AND EXERCISES

Short-Answer Questions 1. What are the features of perfect competition? 2. Distinguish between perfect and pure competition. 3. What is the relative position of a firm in a perfectly competitive industry? How does it choose its price and output? 4. Under what market conditions a firm is a price taker? 5. On what does the degree of freedom depend under monopolistic competition? 6. What is a natural monopoly? How does it emerge? 7. What is monopolistic competition? 8. Differentiate between monopolistic and perfect competition. 9. Why has the Chamberlin’s theory of monopolistic competition been criticized? 10. What is a duopoly? 11. State Bertrand’s model of non-collusive oligopoly. 12. State the reasons for a collusion or agreement in oligopoly firms. 13. Why is the cartel model regarded as the perfect form of collusion? Long-Answer Questions 1. Discuss perfect competition as a market form. Also, discuss its features. 2. Analyse the equilibrium of a firm under the conditions of perfect competition in the short-run? Discuss in this regard the importance of AR, AC, MR and MC under perfect competition. 3. Explain price determination under a pure monopoly. Also, differentiate between monopolistic and perfect competition. 4. Explain and illustrate the determination of equilibrium price and output under monopolistic competition in the short-run. How does a firm’s long-run equilibrium differ from its short-run equilibrium? 5. Write a critique on Chamberlin’s model of pricing. Self-Instructional 138 Material 6. Critically analyse pricing and output decisions under oligopoly. Theory of Market 7. Assess duopoly as a form of oligopoly. Also, describe the various models of duopoly. 8. Evaluate the cartel model of collusive oligopoly. 3. Do you agree that perfect competition leads to optimum size of the firm? Give NOTES reasons for your answer. 10. Suppose price function of a monopoly firm is given as P = 405 – 4Q and its total cost (TC) function is given as TC = 40 + 5Q + Q2 Find the following. (a) Total revenue function; (b) Average revenue function; (c) Profit maximizing monopoly output; and (d) Profit maximizing price. 11. Suppose firms under monopolistic competition face a uniform demand function as given below.

Q1 = 100 – 0.5P1 And their total cost (TC) function is given as TC = 1562.50 + 5Q – Q2 + 0.05Q3 When new firms enter the industry, the demand function for each firm changes to

Q2 = 98.75 – P2 Find answers to the following questions. (a) What was the motivation for the new firms to enter the industry? (b) How are the equilibrium price and output of the old firms affected by the entry of the new firms?

4.9 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill. Self-Instructional Material 139

Game Theoretic UNIT 5 GAME THEORETIC Approach to Economics APPROACH TO ECONOMICS NOTES Structure 5.0 Introduction 5.1 Unit Objectives 5.2 Two-person Zero-sum and Non-zero Sum Game 5.2.1 Non-Zero-Sum Games 5.3 Pure Strategy, Maximin and Minimax 5.3.1 Saddle Point and Minimax 5.4 Mixed Strategy and Randomization 5.4.1 Two-Person Cooperative and Non-cooperative Game 5.4.2 Dominant Strategy 5.5 Prisoner’s Dilemma and its Repetition 5.5.1 Relevance of Prisoners’ Dilemma to Oligopoly 5.6 Application of Game Theory to Oligopoly 5.6.1 Nash Equilibrium 5.7 Summary 5.8 Key Terms 5.9 Answers to ‘Check Your Progress’ 5.10 Questions and Exercises 5.11 Further Reading

5.0 INTRODUCTION

In this unit, we discuss the game theory approach to explain the strategic interaction among the oligopoly firms. This approach uses the apparatus of game theory—a mathematical technique—to show how oligopoly firms play their game of business. The first systematic attempt was made in this field by John von Neumann and Oskar Margenstern. Though their work was followed by many others, Martin Shubik is regarded as the ‘most prominent proponent of the game-theory approach’ who ‘seems to believe that the only hope for the development of a general theory of oligopoly is the game theory’. The game theory is the choice of the best alternative from the conflicting options. Though his hope does not seem to be borne out by further attempts in this area, the usefulness of game theory in revealing the intricate behavioural pattern of the oligopoly firms cannot be denied. In this unit, you will get acquainted with the two-person zero- sum and non-zero sum game; the concept of pure strategy, maximin and minimax in the game theory; the minimax theorem and the saddle point in the game theory; the concept of a dominant strategy; the prisoners’ dilemma game; the application of the game theory to oligopolistic market, and Nash equilibrium as a strategy used by firms.

5.1 UNIT OBJECTIVES

After going through this unit, you will be able to: • Describe the two-person zero-sum and non-zero sum game • Discuss the concept of pure strategy, maximin and minimax in the game theory

• Evaluate the minimax theorem and the saddle point in the game theory Self-Instructional Material 141 Game Theoretic • Assess the concept of a dominant strategy Approach to Economics • Describe the Prisoners’ Dilemma Game • Explain the application of the game theory to oligopolistic market NOTES • Analyse Nash equilibrium as a strategy used by firms

5.2 TWO-PERSON ZERO-SUM AND NON-ZERO SUM GAME

A key objective of game theory is to determine the optimal strategy for each player. A strategy is a rule or plan of action for playing the game. In a zero-sum game, there is no destruction or creation of wealth. Therefore, if the game is a two-person zero-sum game, the loss of one player is gain to the other, hence, that which is won by one player has been lost by the other player. This leads to the player sharing no common interests. Zero-sum games are of two general types: those games where there is perfect information and those games where there is no perfect information. In a game which is played with perfect information, each player has knowledge of the outcomes of all the previous moves. Some games that fall in this category are noughts and crosses, and chess. In such games, there exists a minimum of one ‘best’ for every player to play. While it is not essential that the best strategy for a player will make the player the victor, it will certainly keep his losses to a minimum. To take an example, in noughts and crosses, there is a strategy that will always prevent you from losing but there is no strategy that will not make you win each time. While an optimal strategy exists, players might not always be able to find the strategy, as in the case of chess. Zero-sum games with imperfect information are the ones where the players are not aware of all the previous moves. Generally, the reason for this is that all the players have to make their move at the same time. A good example of such a game is rock- paper-scissors. 5.2.1 Non-Zero-Sum Games There is a huge difference between the theory of zero-sum games and non-zero-sum games since it is always possible to have an optimal solution. Nevertheless, this cannot fully represent the conflict that actually exists in the real everyday world and there are no simple straight forward solutions to everyday problems of the real world nor are their results straight forward. The Game Theory branch which is a more accurate representative of the dynamics that are present in our world is the theory of non-zero-sum games. The difference between non-zero-sum games and zero-sum games lies in the fact that there does not exist any solution that is universally accepted. This means that there does not exist even one optimal strategy that can be said to be preferred over every other strategy, and there exists not even a predictable outcome. Also, non-zero-sum games are non-strictly competitive as compared to zero-sum games which are completely competitive, since cooperative as well as competitive elements are mostly incorporated in games like these. People who participate in a non-zero sum conflict will have both complementary interests and interests which are totally opposed.

Self-Instructional 142 Material Typical Example of a Non-Zero-Sum Game Game Theoretic Approach to Economics A game that is a typical non-zero-sum game is ‘battle of the sexes’. Though apt, it is still a simple example. In this game, a man and his wife wish to have an evening out. They have two NOTES choices: a boxing match and a ballet. Both of them would prefer to go together and not alone. The man has a preference for the boxing match, his preference would be to visit the ballet with his wife and not go alone to the boxing match. On the same lines, the wife would prefer to go to the ballet but would rather go to the boxing match with her husband than alone to the ballet. Given below is the matrix that represents the game:

Husband Boxing Match Ballet Boxing Match 2, 3 1, 1 Wife Ballet 1, 1 3, 2 While the second element of the ordered pair represents the husband’s payoff matrix, the first element of the ordered pair represents the wife’s payoff matrix. The above matrix is representative of a non-zero-sum, non-strictly competitive conflict. There is a common interest between the man and his wife: they both have a preference of going out together instead of going to separate events alone. Nevertheless, there is also an opposing interest which is that the husband would rather go to the boxing match and the wife to the ballet. Analyzing a Non-Zero-Sum Game

(i) Communication Conventionally, it is believed that the ability to communicate can never be a disadvantage to a player due to the fact that at any time the player can refuse to exercise the right to communicate. It must be remembered that refusal to communicate and being unable to communicate are different things. In various cases, the inability to communicate could be advantageous for a player. In an experiment conducted by R. D. Luce and Howard Raiffa, comparison is made between situations where players cannot communicate and where players can communicate. The game given below was used in their experiment by Luce and Raiffa:

a b A 1, 2 3, 1

B 0, -200 2, -300 If communication cannot happen between Bob and Susan, it is impossible to threaten each other. Therefore, the best that Susan can do is play strategy ‘A’ and the best that Bob can do is play strategy ‘a’. Hence, while Bob gains 2, Susan gains 1. Nevertheless, with communication being allowed, complications occur. Bob can be threatened by Susan into playing strategy ‘b’, or else she will play strategy ‘B’. In case Bob gives in, Bob will lose a point and Susan will gain two.

Self-Instructional Material 143 Game Theoretic (ii) Restricting alternatives Approach to Economics The above mentioned example of battle of the sexes is a dilemma that appears unsolvable. It can only be solved with the wife or the husband restricting the choices available to NOTES their spouses. To take an example, if two tickets are bought by the wife to the ballet, which is indicative of the fact that she will definitely not go to the boxing match, the husband would have to go to the ballet along with his wife for his self-interest maximization. Since two tickets have been bought by the wife, hence the husband’s optimal payoff is going with his wife. In case he visits the boxing match alone, his interests would not be maximized. (iii) Number of times the game is ‘played’ When the game is played just one time, there is no fear to either of the players of retaliation from the other player. Hence, a onetime game might be played differently than if they were playing the game repeatedly. Typical non-zero-sum games examples The typical non-zero sum games are: • Prisoner’s dilemma • Chicken and volunteer’s dilemma • Deadlock and stag hunt

5.3 PURE STRATEGY, MAXIMIN AND MINIMAX

A pure strategy game can be solved according to minimax decision criterion. When each player in a game adopts a single strategy as an optimal strategy, the game is a pure strategy game. Abraham Wald’s maximin decision criterion says that the decision- makers should first specify the worst possible outcome of each strategy and accept a strategy that gives best out of the worst outcomes. The application of maximim criterion can be illustrated by applying it to our example given in Table 5.1 reproduced below. To apply the maximin criterion, the decision makers need to find the worst (minimum) outcome of each strategy. This can be done by reading Table 5.1 row-wise. The maximin column presents the worst outcome of each strategy. The best or the highest outcome

out of the worst outcomes is 5 of strategy S1. Going by the maximim criterion, the Check Your Progress decision-makers would accept strategy S1. 1. What are the two Table 5.1 Application of Maximin Criterion types of zero-sum games? States of Nature 2. Name some games Strategy N1 N2 N3 N4 Maximin

that fall in the S1 20 12 6 5 5 category of games S2 15 16 4 – 2 – 2 played with perfect S 16 8 6 – 1 – 1 information. 3 S 5 12 3 2 2 3. Why is a onetime 4 played game If you look closely at the maximin decision rule, it implies a pessimistic approach different from a game played to investment decision-making. It gives a conservative decision rule for risk avoidance. repeatedly? However, this decision rule can be applied by those investors who fall in the category of

Self-Instructional 144 Material risk averters. This investment rule can also be applied by firms whose very survival Game Theoretic depends on avoiding losses. Approach to Economics Minimax Regret Criterion: The Savage Decision Criterion Minimax regret criterion is another decision rule under uncertainty. This criterion suggests NOTES that the decision-makers should select a strategy that minimizes the maximum regret of a wrong decision. What is regret? Regret is measured by the difference between the pay-off of a given strategy and the pay-off of the best strategy under the same state of nature. Thus, regret is the opportunity cost of a decision. Suppose an investor has three strategies for investment, S1, S2 and S3, giving returns of ` 10,000, ` 8000 and ` 6000, respectively. If the investor opts for strategy S1, he gets the maximum possible return.

He has no regret. But, if he opts for S2 by way of an incorrect decision, then his regret or opportunity cost equals ` 10,000 – ` 8000 = ` 2000. Similarly, if he opts for S3, his regret equals ` 10,000 – ` 6000 = ` 4000. Going by the minimax regret criterion, the investor should opt for strategy S2 because it minimizes the regret. The application of minimax regret criterion can be illustrated with the help of the example we have used in Table 5.1. By using the pay-off matrix, we can construct a regret matrix. The method is simple. Select a column (the state of nature), find the maximum pay-off and subtract from it the pay-offs of all strategies. This process gives a pay-off column. For example, under column N1, strategy S1 has the maximum pay-off

(20). When we subtract 20 from 20, we get 0. It means that if S1 is chosen under the state of nature N1, the regret is zero. Next, strategy S2 has a pay-off 15. When we subtract 15 from 20, we get regret which equals 5. By repeating this process for all the strategies (S1, S2, ... Sn) and all the states of nature (N1, N2, ... Nn), we get a regret matrix as shown in Table 5.2. From the regret matrix, we can find ‘maximin regret’ by listing the maximum regret for each strategy, as shown in the last column. The column

‘maximin regret’ shows that maximum regret is minimum (3) in case of strategy S4.

According to maximin criterion, therefore, strategy S4 should be selected for investment. Table 5.2 Pay-off Matrix and Regret Matrix

States of Nature Regret Matrix Maximin

Strategy N1 N2 N3 N4 N1 N2 N3 N4 Regret

S1 20 12 6 5 0 0 0 0 0

S2 15 10 4 – 2 5 2 2 7 7

S3 16 8 6 – 1 4 4 0 6 6

S4 5 12 3 2 15 0 3 3 3*

5.3.1 Saddle Point and Minimax This is used in a game without a dominant strategy and is a strictly determined game. In a game, a saddle point will be a payoff which is at the same time a column maximum and a row minimum. To locate the saddle points, one needs to box the column maxima and circle the row minima. Entries that are boxed as well as circled are saddle points. A game with a minimum of one saddle point is a game that is strictly determined.

Self-Instructional Material 145 Game Theoretic In case of games that are strictly determined, the following statements will be true: Approach to Economics • The payoff value of each saddle point in the game will be the same. • Choosing the row and column through any saddle point gives the minimax strategies NOTES for both players. In other words, the game is solved via the use of these (pure) strategies. The value of the saddle point entry will be the value of a strictly determined game. The value of a fair game is zero, else it will be biased or unfair. Minimax Minimax is a strategy always used to minimize the maximum possible loss that can be caused by an opponent. Minimax for one-person games The principle known as the minimax regret principle has its basis in the minimax theorem that was put forth by John von Neumann, and is geared for single person games. It uses the concept of regret matrices. Let us suppose that there is a company that needs to decide if it should or should not support a research project. Suppose that the project will cost ‘A’ units. If the project fails, nothing will accrue from it, but if it succeeds then its returns will be ‘B’ units. The matrix given below represents the payoff matrix for the company.

Research Succeeds Fails Company Supports research B - A -A Neglect research 0 0

Using the maximax principle, it is beneficial for a company to always support research, in case its cost is less than the return expected from it. By using the maximin principle, research should never be supported by the company as the cost of the research is at risk. The Minimax principle is a bit more complicated than these two principles. There must be a matrix to reveal the player’s ‘opportunity cost’, or regret, based on all the possible decisions. To take an example, in case a company supports a research work and the research work fails, the regret of the company will be ‘A’, and the price that it had paid for the research project will be ‘B’. If a research work is supported by a company and the research is successful, there will be no regrets for the company. If the research is neglected by a company and the research is successful, the company will regret the same and the regret value will be ‘B-A’ which is the return on the research. The below given matrix is what the minimax regret matrix will look like.

Research Succeeds Fails Supports research 0 c Company Neglect research r-c 0

Self-Instructional 146 Material The purpose is minimization of the maximum possible regret. The above matrix Game Theoretic does not make it clear what the maximum value is. That is, is ‘A’ more than ‘B-A’? in Approach to Economics case (B-A) > A, the research should be supported by the company. In case of (B-A) < A, the research should not be supported by the company. NOTES Minimax for two-person games In case of a two-person, zero-sum game, a player has to lose for the other to win. There cannot be any cooperation.

5.4 MIXED STRATEGY AND RANDOMIZATION

There are some cases that do not have a saddle point. In such cases, the players are forced to select their strategies based on some amount of randomness. Pure strategies are those strategies where the participants make a specific choice or take a specific action in a game. There are certain games where pure strategies are not the best way to play. Herein, mixed strategies play a role. Mixed strategies are strategies in which players make random choices among two or more possible actions, based on sets of chosen probabilities. Here is a simple game played with coins. Two players simultaneously place a single coin each on the table, either tails or heads up. If the coins have the same face up, player 1 gets both the coins else player 2 gets them. Following is the payoff matrix for player 1:

Player 2 Heads Tails Heads 1 -1 Player 1 Tails -1 1

For either of the players, there will be no clear defined strategies. Random selection of the face of the coin will be the best playing strategy. In case either of the players play with this strategy, then there will be a payoff of zero for both players in the long-run. Now, if 50/50 strategy is employed by player 1, and heads is played by the player 75 per cent times, the payoffs for both players will be zero in the long-run. But if 75/25 strategy is followed by player 2, then it becomes easy for player 1 to take advantage of the situation by playing heads more frequently, hence winning more often. It becomes imperative that each player follows a strategy and also analyze the strategy being used by the opponent. 5.4.1 Two-Person Cooperative and Non-cooperative Game Check Your Progress The economic games that firms play can be either cooperative or non-cooperative. In 4. What is a pure a cooperative game, players can negotiate binding contracts that allow them to plan strategy game? joint strategies. In a non-cooperative game, negotiation and enforcement of binding 5. What are saddle contracts are possible. points? 6. Who put forward An example of a cooperative game is the bargaining between a buyer and a seller the Minimax over the price of a rug. If the rug costs $100 to produce and the buyer values the rug at theorem ? $200, a cooperative solution to the game is possible. An agreement to sell the rug at any Self-Instructional Material 147 Game Theoretic price between $101 and $199 will maximize the sum of the buyer’s consumer surplus Approach to Economics and the seller’s profit, while making both parties better off. Another cooperative game would involve two firms negotiating a joint investment to develop a new technology (assuming that neither firm would have enough know-how to succeed on its own). If the NOTES firms can sign a binding contract to divide the profits from their joint investment, a cooperative outcome that makes both parties better off is possible. An example of a non-cooperative game is a situation in which two competing firms take each other’s likely behaviour into account when independently setting their prices. Each firm knows that by undercutting its competitor it can capture more market share, but doing so risks setting off a price war. Another non-cooperative game is the auction mentioned above; each bidder must take the likely behaviour of the other bidders into account when determining an optimal bidding strategy. Note that the fundamental difference between cooperative and non-cooperative games lies in the contracting possibilities. In cooperative games, binding contracts are possible; in non-cooperative games, they are not. We will be concerned mostly with non-cooperative games. In any game, however, the most important aspect of strategic decision making is understanding your opponent’s point of view, and (assuming your opponent is rational) deducing his or her likely responses to your actions. This may seem obvious—of course, one must understand an opponent’s point of view. Yet even in simple gaming situations, people often ignore or misjudge opponents positions and the rational responses those positions imply. 5.4.2 Dominant Strategy A dominant strategy is the firm’s best strategy no matter what strategy its rival selects. A strategy is said to be dominant when a player, irrespective of the rival’s strategy gains a larger payoff than the other players. Therefore, a strategy is dominant when it is said to be better than any other plan or strategy of the opposite player or rival. If one strategy is a dominant strategy, then all the other strategies are dominated. For instance, in the prisoner’s dilemma, each player possesses a dominant strategy. Iterated Deletion of Dominated Strategies Let us consider a game which does not have dominant pure strategies, but can be solved using iterated deletion of dominated strategies. Simply put, strategies that are dominated can be eliminated till a conclusion is reached:

2 Left Middle Right Up 1,0 1,2 0,1 1 Down 0,3 0,1 2,0

Let us locate the dominant strategies. The first dominated strategy is ‘right’. playing the ‘middle’ strategy is the best and most fruitful choice for player 2, hence ‘right’ is dominated by ‘middle’. Therefore, we can eliminate the column under ‘right’ as ‘right’ no longer remains an option. This will be shown by crossing out the column:

Self-Instructional 148 Material Game Theoretic 2 Approach to Economics Left Middle Right Up 1,0 1,2 0,1 1 Down 0,3 0,1 2,0 NOTES

It must be kept in mind that both the players have full knowledge that there is no reason for player 2 to play the ‘right’ strategy—player 1 knows that player 2 is looking for an optimum, hence he too no longer considers the payoffs in the ‘right’ column. As the ‘right’ column has been removed, the ‘down’ column is dominated by ‘up’ for player 1. Whether player 2 plays the ‘middle’ or ‘left’, player 1 will get a payoff of 1 as long as he chooses ‘up’. Therefore, ‘down’ need not be considered now:

2 Left Middle Right Up 1,0 1,2 0,1 1 Down 0,3 0,1 2,0

Now, player 1 will choose ‘up’, and player 2 will choose ‘middle’ or ‘left’. As ‘middle’ is better than ‘left’ (a payoff of 2 vs. 0), ‘middle’ will be chosen by player 2 and the game is solved for the Nash equilibrium:

2 Left Middle Right Up 1,0 1,2 0,1 1 Down 0,3 0,1 2,0

To ensure that the answer arrived at (up, middle) is a Nash equilibrium, check if player 1 or player 2 would wish to make a different choice. So far as player 1 has chosen ‘up’, player 2 will choose ‘middle’. Then again, till player 2 selects ‘middle’, player 1 will go for ‘up’.

5.5 PRISONER’S DILEMMA AND ITS REPETITION

The nature of the problem faced by the oligopoly firms is best explained by the prisoners’ dilemma game. To illustrate prisoners’ dilemma, let us suppose that there are two persons, A and B, who are partners in an illegal activity of match fixing. On a tip-off, the CBI arrests A and B, on suspicion of their involvement in fixing cricket matches. They are arrested and lodged in separate jails with no possibility of communication between them. They are being interrogated separately by the CBI officials with following conditions disclosed to each of them in isolation. • If you confess your involvement in match fixing, you will get a 5-year imprisonment. • If you deny your involvement and your partner denies too, you will be set free for lack of evidence. • If one of you confesses and turns approver, and the other does not, then one who confesses gets a 2-year imprisonment, and one who does not confess gets 10 year imprisonment. Self-Instructional Material 149 Game Theoretic Given these conditions, each suspect has two options open to him: (i) to confess Approach to Economics or (ii) not to confess. Now, both A and B face a dilemma on how to decide whether or not to confess. While taking a decision, both have a common objective, i.e., to minimize the period of imprisonment. Given this objective, the option is quite simple that both of NOTES them deny their involvement in match-fixing. But, there is no certainty that if one denies his involvement, the other will also deny—the other one may confess and turn approver. With this uncertainty, the dilemma in making a choice still remains. For example, if A denies his involvement, and B confesses (settles for a 2-year imprisonment), then A gets a 10 year jail term. So is the case with B. If they both confess, then they get a 5-year jail term each. Then what to do? That is the dilemma. The nature of their problem of decision-making is illustrated in the following Table 5.3 in the form of a ‘pay-off matrix’. The pay-off matrix shows the pay-offs of their different options in terms of the number of years in jail. Table 5.3 Prisoners’ Dilemma: The Pay-off Matrix B’s Options Confess Deny A BA B Confess 5 5 2 10 A’s Options A BA B Deny 10 2 0 0

Given the conditions, it is quite likely that both the suspects may opt for ‘confession’, because neither A knows what B will do, nor B knows what A will do. When they both confess, each gets a 5-year jail term. This is the second best option. For his decision to confess, A might formulate his strategy in the following manner. He reasons: if I confess (though I am innocent), I will get a maximum of 5 years’ imprisonment. But, if I deny (which I must) and B confesses and turns approver then I will get 10 years’ imprisonment. That will be the worst scenario. It is quite likely that suspect B also reasons out his case in the same manner, even if he too is innocent. If they both confess, they would avoid 10 years’ imprisonment, the maximum possible jail sentence under the law. This is the best they could achieve under the given conditions. 5.5.1 Relevance of Prisoners’ Dilemma to Oligopoly The prisoners’ dilemma illustrates the nature of problems oligopoly firms are confronted with in the formulation of their business strategy with respect to such problems as strategic advertising, price cutting or cheating the cartel if there is one. Look at the nature of problems an oligopoly firm is confronted with when it plans to increase its advertisement expenditure (ad-expenditure for short). The basic issue is whether or not to increase the ad-expenditure. If the answer is ‘do not increase’, then the following questions arise. Will the rival firms increase ad-expenditure or will they not? If they do, what will be the consequences for the firm under consideration? And, if the answer is ‘increase’, then the following questions arise. What will be the reaction of the rival firms? Will they increase or will they not increase their ad-expenditure? What will be the pay-off if they do not and what if they do? If the rival firms do increase their advertising, what will be the pay-off to the firm? Will the firm be a net gainer or a net loser? The firm planning to increase ad-spending will have to find the answer to these queries under the conditions of uncertainty. To find a reasonable answer, the firm will have to anticipate actions, reactions and counter-actions by the rival firms and chalk out its own strategy. It is in Self-Instructional case of such problems that the case of prisoners’ dilemma becomes an illustrative example. 150 Material Game Theoretic 5.6 APPLICATION OF GAME THEORY TO OLIGOPOLY Approach to Economics

Let us now apply the game theory to our example of ‘whether or not to increase ad- expenditure’, assuming that there are only two firms, A and B, i.e., the case of a duopoly. NOTES We know that in all games, the players have to anticipate the moves of the opposite player(s) and formulate their own strategy to counter them. To apply the game theory to the case of ‘whether or not to increase ad-expenditure’, the firm needs to know or anticipate the following: • Counter moves by the rival firm in response to increase in ad-expenditure by this firm • The pay-offs of this strategy under two conditions: (a) when the rival firm does not react and (b) the rival firm does make a counter move by increasing its ad- expenditure After this data is obtained, the firm will have to decide on the best possible strategy for playing the game and achieving its objective of, say, increasing sales and capturing a larger share of the market. The best possible strategy in game theory is called the ‘dominant strategy’. A dominant strategy is one that gives optimum pay-off, no matter what the opponent does. Thus, the basic objective of applying the game theory is to arrive at the dominant strategy. Suppose that the possible outcomes of the ad-game under the alternative moves are given in the pay-off matrix presented in Table 5.4. Table 5.4 Pay-off Matrix of the Ad-Game (Increase in sales in million `)

B’s Options Increase Ad Dont’t increase A BA B Increase Ad 20 10 30 0 A’s Strategy A BA B Don’t increase 10 15 25 5

As the matrix shows, if Firm A decides to increase its ad-expenditure, and Firm B counters A’s move by increasing its own ad-expenditure, A’s sales go up by ` 20 million and those of Firm B by ` 10 million. And, if Firm A increases its advertisement and B does not, then A’s sales increase by ` 30 million and there are no sales gain for Firm B. One can similarly find the pay-offs of the strategy ‘Don’t increase’ in case of both firms. Given the pay-off matrix, the question arises, what strategy should Firm A choose to optimize its gain from extra ad-expenditure, irrespective of counter-action by the rival Firm B. It is clear from the pay-off matrix that Firm A will choose the strategy of increasing the ad-expenditure because, no matter what Firm B does, its sales increase by at least ` 20 million. This is, therefore, the dominant strategy for Firm A. A better situation could be that when Firm A increases its expenditure on advertisement, Firm B does not. In that case, sales of Firm A could increase by Rs 30 million and sales of Firm B do not increase. But there is a greater possibility that Firm B will go for counter-advertising in anticiption of losing a part of its market to Firm A in future. Therefore, a strategy based on the assumption that Firm B will not increase its ad-expenditure involves a great deal of uncertainty.

Self-Instructional Material 151 Game Theoretic 5.6.1 Nash Equilibrium Approach to Economics In the preceding section, we have used a very simple example to illustrate the application of game theory to an oligopolistic market setting, with the simplifying assumptions: NOTES • That strategy formulation is a one-time affair • That one firm initiates the competitive warfare and other firms only react to action taken by one firm • That there exists a dominant strategy—a strategy which gives an optimum solution The real-life situation is, however, much more complex. There is a continuous one-to-one and tit-for-tat kind of warfare. Actions, reactions and counter-actions are regular phenomena. Under these conditions, a dominant strategy is often non-existent. To analyse this kind of situation, John Nash, an American mathematician, developed a technique, which is known as Nash equilibrium. Nash equilibrium technique seeks to establish that each firm does the best it can, given the strategy of its competitors and a Nash equilibrium is one in which none of the players can improve their pay-off given the strategy of the other players. In case of our example, Nash equilibrium can be defined as one in which none of the firms can increase its pay-off (sales) given the strategy of the rival firm. Nash equilibrium can be illustrated by making some modifications in the pay-off matrix given in Table 5.4. Now we assume that action and counter-action between Firms A and B is a regular phenomenon and the pay-off matrix that appears finally is given in Table 5.5. The only change in the modified pay-off matrix is that if neither firm A nor firm B increases its ad-expenditure, then pay-offs change from (15, 5) to (25, 5). Table 5.5 Nash Equilibrium: Pay-off Matrix of the Ad-Game (Increase in sales in million `) B’s Options Increase AD Dont’t increase A BA B Increase Ad 20 10 30 0 A’s Strategy A BA B Don’t increase 10 15 25 5 It can be seen from the pay-off matrix (Table 5.5) that Firm A no longer has a dominant strategy. Its optimum decision depends now on what Firm B does. If Firm B increases its ad-expenditure, Firm A has no option but to increase its advertisement expenditure. And, if Firm A reinforces its advertisement expenditure, Firm B will have to follow suit. On the other hand, if Firm B does not increase its ad-expenditure, Firm A does the best by increasing its ad-expenditure. Under these conditions, the conclusion that both the firms arrive at is to increase ad-expenditure if the other firm does so, and ‘don’t increase’, if the competitor ‘does not increase’. In the ultimate analysis, however, both the firms will decide to increase the ad-expenditure. The reason is that if none of the firms increases its ad-outlay, Firm A gains more in terms of increase in its sales (` 25 million) and the gain of Firm B is much less (` 5 million only). And, if Firm B increases advertisement expenditure, its sales increase by ` 10 million. Therefore, Firm B would do best to increase its ad-expenditure. In that case, Firm A will have no option but to do likewise. Thus, the final conclusion that emerges is that both the firms will go for

Self-Instructional 152 Material advertisement war. In that case, each firm finds that it is doing the best given what the Game Theoretic rival firm is doing. This is the Nash equilibrium. Approach to Economics However, there are situations in which there can be more than one Nash equilibrium. For example, if we change the pay-off in the south-east corner from (25, 5) to (22, 8); each firm may find it worthless to wage advertisement war and may settle for ‘don’t NOTES increase’ situation. Thus, there are two possible Nash equilibria.

5.7 SUMMARY

In this unit, you have learnt that,

• A key objective of game theory is to determine the optimal strategy for each player. A strategy is a rule or plan of action for playing the game. • In a zero-sum game, there is no destruction or creation of wealth. Therefore, if the game is a two-person zero-sum game, the loss of one player is gain to the other, hence, that which is won by one player has been lost by the other player. This leads to the player sharing no common interests. • Zero-sum games are of two general types: those games where there is perfect information and those games where there is no perfect information. • The difference between non-zero-sum games and zero-sum games lies in the fact that there does not exist any solution that is universally accepted. This means that there does not exist even one optimal strategy that can be said to be preferred over every other strategy, and there exists not even a predictable outcome. • When each player in a game adopts a single strategy as an optimal strategy, the game is a pure strategy game. • Wald’s maximin decision criterion says that the decision-makers should first specify the worst possible outcome of each strategy and accept a strategy that gives best out of the worst outcomes. • In a game, a saddle point will be a payoff which is at the same time a column maximum and a row minimum. To locate the saddle points, one needs to box the column maxima and circle the row minima. Entries that are boxed as well as circled are saddle points. • Minimax is a strategy always used to minimize the maximum possible loss that can be caused by an opponent. • The principle known as the Minimax Regret Principle has its basis in the Minimax Theorem that was put forth by John von Neumann, and is geared for single person games. It uses the concept of regret matrices. • In case of a two-person, zero-sum game, a player has to lose for the other to win. Check Your Progress There cannot be any cooperation. 7. Define a mixed • There are some cases that do not have a saddle point. In such cases, the players strategy. are forced to select their strategies based on some amount of randomness. Pure 8. What happens in a strategies are those strategies where the participants make a specific choice or cooperative and take a specific action in a game. non-cooperative game? • Mixed strategies are strategies in which players make random choices among 9. When is a strategy two or more possible actions, based on sets of chosen probabilities. said to be dominant?

Self-Instructional Material 153 Game Theoretic • The economic games that firms play can be either cooperative or non-cooperative. Approach to Economics In a cooperative game, players can negotiate binding contracts that allow them to plan joint strategies. In a non-cooperative game, negotiation and enforcement of binding contracts are possible. NOTES • The fundamental difference between cooperative and non-cooperative games lies in the contracting possibilities. In cooperative games, binding contracts are possible; in non-cooperative games, they are not. • A dominant strategy is the firm’s best strategy no matter what strategy its rival selects. A strategy is said to be dominant when a player irrespective of the rival’s strategy gains a larger payoff than the other players. • The nature of the problem faced by the oligopoly firms is best explained by the prisoners’ dilemma game. • The prisoners’ dilemma illustrates the nature of problems oligopoly firms are confronted with in the formulation of their business strategy with respect to such problems as strategic advertising, price cutting or cheating the cartel if there is one. • A dominant strategy is one that gives optimum pay-off, no matter what the opponent does. Thus, the basic objective of applying the game theory is to arrive at the dominant strategy. • John Nash, an American mathematician, developed a technique, which is known as Nash equilibrium. Nash equilibrium technique seeks to establish that each firm does the best it can, given the strategy of its competitors and a Nash equilibrium is one in which none of the players can improve their pay-off given the strategy of the other players. • Nash equilibrium can be defined as one in which none of the firms can increase its pay-off (sales) given the strategy of the rival firm.

5.8 KEY TERMS

• Zero-sum game: It is a mathematical representation of a situation in which each participant’s gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). • Pure strategy game: When each player in a game adopts a single strategy as an optimal strategy, the game is a pure strategy game. • Mixed strategies: Strategies in which players make random choices among two or more possible actions, based on sets of chosen probabilities. • Dominant strategy: A dominant strategy is one that gives optimum pay-off, no matter what the opponent does. • Nash equilibrium: It can be defined as one in which none of the firms can increase its pay-off (sales) given the strategy of the rival firm.

5.9 ANSWERS TO ‘CHECK YOUR PROGRESS’

1. Zero-sum games are of two general types: those games where there is perfect information and those games where there is no perfect information. Self-Instructional 154 Material 2. Some games that fall in the category of games played with perfect information Game Theoretic are noughts and crosses, and chess. Approach to Economics 3. When the game is played just one time, there is no fear to either of the players of retaliation from the other player. Hence, a onetime game might be played differently than if they were playing the game repeatedly. NOTES 4. When each player in a game adopts a single strategy as an optimal strategy, the game is a pure strategy game. 5. In a game, a saddle point will be a payoff which is at the same time a column maximum and a row minimum. To locate the saddle points, one needs to box the column maxima and circle the row minima. Entries that are boxed as well as circled are saddle points. 6. The minimax theorem was put forth by John von Neumann and is geared for single person games. 7. Mixed strategies are strategies in which players make random choices among two or more possible actions, based on sets of chosen probabilities. 8. The economic games that firms play can be either cooperative or non-cooperative. In a cooperative game, players can negotiate binding contracts that allow them to plan joint strategies. In a non-cooperative game, negotiation and enforcement of binding contracts are possible. 9. A dominant strategy is the firm’s best strategy no matter what strategy its rival selects. A strategy is said to be dominant when a player irrespective of the rival’s strategy gains a larger payoff than the other players.

5.10 QUESTIONS AND EXERCISES

Short-Answer Questions 1. What is the key objective of game theory? 2. Differentiate between a zero-sum game and a non-zero-sum game. 3. What is a two-person zero-sum game? 4. How can a pure strategy game be solved? What does Wald’s maximin decision criterion propose? 5. What is a saddle point of a matrix? 6. What is the key feature of minimax decision making? 7. ‘Mixed strategies provide solutions to games when pure strategies fail.’ Give reasons. 8. State the fundamental difference between cooperative and non-cooperative games. 9. Write a note on dominant strategy and Nash equilibrium. Long-Answer Questions 1. Describe the two-person zero-sum and non-zero sum game. 2. Discuss the concept of pure strategy, maximin and minimax in the game theory. 3. Evaluate the minimax theorem and the saddle point in the game theory. Self-Instructional Material 155 Game Theoretic 4. What is a mixed strategy? How is it different from a pure strategy? Approach to Economics 5. Assess the concept of a dominant strategy. 6. ‘The nature of the problem faced by the oligopoly firms is best explained by the NOTES Prisoners’ Dilemma Game.’ Describe. 7. Explain the application of the game theory to oligopolistic market. 8. Critically analyse Nash equilibrium as a strategy used by firms.

5.11 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional 156 Material Alternative Theories UNIT 6 ALTERNATIVE THEORIES OF of Firm FIRM NOTES Structure 6.0 Introduction 6.1 Unit Objectives 6.2 Traditional Theory of Firm and its Critical Evaluation 6.3 Baumol’s Revenue Maximization Model 6.3.1 Baumol’s Model without Advertising 6.3.2 Baumol’s Model with Advertising 6.3.3 Criticism of Baumol’s Model 6.4 Williamson’s Model of Managerial Discretion 6.4.1 Simple Version of Williamson’s Model 6.4.2 Firm’s Equilibrium: Graphical Presentation 6.5 Managerial Firm vs Entrepreneurial Firm 6.5.1 Entrepreneurial Firms 6.5.2 Cyert-March Model of Firms 6.6 Marris’ Model of Managerial Enterprise 6.6.1 Financial Policy for Balanced Growth 6.6.2 Shortcomings of Marris Theory 6.7 Limit Pricing Theory 6.7.1 Bain’s Model of Limit Pricing 6.8 Summary 6.9 Key Terms 6.10 Answers to ‘Check Your Progress’ 6.11 Questions and Exercises 6.12 Further Reading

6.0 INTRODUCTION

This unit will discuss only those alternative theories of firm which have gained considerable ground in economic literature and have a greater relevance to business decision making on empirical grounds. The theories of this category include: (i) Baumol’s theory of sales revenue maximization (ii) Marris’s theory of maximization of firm’s growth rate (iii) Williamson’s theory of maximization of managerial utility function This unit will deal with the basic elements of these alternative theories of firm. The objective here is to make the readers aware of the recent developments in the theory of firm rather than dealing with the alternative theories at length.

6.1 UNIT OBJECTIVES

After going through this unit, you will be able to: • Discuss the traditional theory of firm • Explain Baumol’s theory of sales revenue maximization • Evaluate Williamson’s model of managerial utility maximization Self-Instructional Material 157 Alternative Theories • Analyse the differences between managerial and entrepreneurial firm of Firm • Explain Marris’ model of managerial enterprise • Describe the limit pricing theory with special reference to Bain’s model of limit NOTES pricing 6.2 TRADITIONAL THEORY OF FIRM AND ITS CRITICAL EVALUATION

Although the conventional theory of firm still holds its ground firmly, several alternative theories of firm were proposed during the early 1960s by economists, notably by Simon, Baumol, Marris, Williamson, Berle and Means, Galbraith, and Cyert and March. These economists have questioned the validity of the profit maximization hypothesis and the relevance of the conventional theory to modern business, mainly on empirical grounds. Another major drawback of the conventional theory is that it does not recognize the dichotomy between the ownership and management and its role in setting the goal for the firm. Berle and Means were first to point out in 1932, the separation of management from ownership. The proponents of the recent theories of firm argue that the dichotomy between the ownership and management and the shift in decision-making powers from the owners (of the firm) to its managers give the latter an opportunity to exercise their discretion in setting the goals for the firm, especially in case of large business corporations. The managers of large business corporations set the goals for the firm which in their judgment are feasible and desirable for the firm’s survival and growth. Based on this argument, some economists formulated their own hypotheses and studied extensively the objectives, motivations and behaviour of firms afresh and developed their own theory of firm. As a result, there are now a number of alternative theories of firm postulating different objectives of business firms. The alternative theories of the business firms are sometimes classified under the following categories. • Managerial theories of firm • Growth maximization theories of firm • Maximization of managerial utility theories • Behavioural theories of firm Conventional vs Alternative Theories of Firm A question that may be asked is: Do the alternative theories replace the conventional theory of firm? Or to what extent do the alternative theories really offer an alternative and more appropriate explanation to firms’ behaviour? There are no simple answers to these questions. One thing is clear that the conventional theory of firm based on profit maximization hypothesis is not the only theory applicable to a multitude of firms—large and small, owner-managed and manager-managed, single-product and multi-product, local and multinational, private and public undertakings, and alternative theories do provide alternative explanations to the firm’s behaviour. As regards the validity and plausibility of the alternative theories, this issue can be examined on both theoretical and empirical grounds. The theoretical plausibility of a theory depends on its power to predict. There is a general consensus that the conventional theory has greater explanatory and predictive power than the alternative theories of firm. As regards the empirical validity, the empirical evidence in support of the alternative Self-Instructional 158 Material theories is not unambiguous. In fact, the multitude of alternative theories is in itself an Alternative Theories evidence against them. On the contrary, the empirical evidence against the conventional of Firm theory is not clear and strong. Hance, it can be said that the alternative theories of firm are still in a state of testable hypotheses and they do not offer a replacement to the conventional theory of firm. NOTES

6.3 BAUMOL’S REVENUE MAXIMIZATION MODEL

Baumols’s theory of sales maximization is one of the most important alternative theories of firm’s behaviour. The basic premise of Baumol’s theory is that sales maximization, rather than profit maximization, is the plausible goal of the business firms. He argues that there is no reason to believe that all firms seek to maximize their profits. Business firms, in fact, pursue a number of incompatible objectives and it is not easy to single out one as the most common objective pursued by the firms. However, from his experience as a consultant to many big business houses, Baumol finds that most managers seek to maximize sales revenue rather than profits. He argues that, in modern business, management is separated from ownership, and managers enjoy the discretion to pursue goals other than profit maximization. Their discretion eventually falls in favour of sales maximization. According to Baumol, business managers pursue the goal of sales maximization for the following reasons. First, financial institutions consider sales as an index of performance of the firm and are willing to finance the firm with growing sales. Second, while profit figures are available only annually at the end of the final accounting year, sales figures can be obtained easily and more frequently to assess the performance of the management. Maximization of sales is more satisfying for the managers than the maximization of profits that go into the pockets of the shareholders. Third, salaries and slack earnings of the top managers are linked more closely to sales than to profit. Therefore, managers aim at maximizing sales revenue. Fourth, the routine personnel problems are more easily handled with growing sales. Higher payments may be offered to employees if sales figures indicate better performance. Profits are generally known after a year. To rely on profit figures means, therefore, a longer waiting period for both the employees and the management for resolving labour problems. Fifth, where profit maximization is the goal and it rises in one period to an unusually high level, this becomes the standard profit target for the shareholders that managers find very difficult to maintain in the long run. Therefore, managers tend to aim at sales maximization rather than profit maximization. Check Your Progress 1. Name the Finally sales growing at a rate higher than the rate of market expansion indicate economists who growing market share, a greater competitive strength and better bargaining power of a proposed the firm in a collusive oligopoly. In a competitive market, therefore, sales maximization is alternative theories found to be a more reasonable target. of firm during the early 1960s. To formulate his theory of sales maximization, Baumol has developed two basic 2. How can the models: (i) static model and (ii) dynamic model—each with and without advertising. His alternative theories static models with and without advertising are discussed next. of the business firms be classified?

Self-Instructional Material 159 Alternative Theories 6.3.1 Baumol’s Model without Advertising of Firm Baumol assumes cost and revenue curves to be given as in conventional theory of pricing. Suppose that the total cost (TC) and the total revenue (TR) curves are given as NOTES in Figure 6.1. The total profit curve, TP, is obtained by plotting the difference between the TR and TC curves. Profits are zero where TR = TC. Given the TR and TC curves, there is a unique level of output at which total sales revenue is maximum. The total sales revenue is maximum at the highest point of the TR curve. At this point, slope of the TR curve (i.e., MR = ∂TR/∂Q) is equal to zero. The highest point on the TR curve can be obtained easily by drawing a line parallel to the horizontal axis and tangent to the TR curve. The point H on the TR curve in Figure 6.1 represents the total maximum sales revenue. A line drawn from point H to output axis

shows that sales revenue is maximized at output OQ3. It implies that a sales revenue

maximizing firm will produce output OQ3 and its price equals HQ3/OQ3.

Fig. 6.1 Sales Revenue Maximization

Profit Constraint and Revenue Maximization

At output OQ3, the firm maximizes its total revenue. At this output, the firm makes a

total profit equal to HQ3 – MQ3 = HM. Since total TP curve gives the measure of total

profit at different levels of output, profit HM = TQ3. If this profit is enough or more than

enough to satisfy the stockholders, the firm will produce output OQ3 and charge a price

= HQ/OQ3. But, if profit at output OQ3 is not enough to satisfy the stockholders, then the firm’s output must be changed to a level at which it makes a satisfactory profit, say

OQ2, which yields a profit LQ2 > TQ3. Thus, there are two types of probable equilibrium: one, in which the profit constraint does not provide an effective barrier to sales maximization, and second, in which profit constraint does provide an effective barrier to sales maximization. In the second type of equilibrium, the firm will produce an output that yields a satisfactory or target profit. It

may be any output between OQ1 and OQ2. For example, if minimum required profit is

OP1, then the firm will stick to its sales maximization goal and produce output OQ3

which yields a profit much greater than the required minimum. Since actual profit (TQ3) is much greater than the minimum required, the minimum profit constraint is not operative.

However, if required minimum profit level is OP2, OQ3 will not yield sufficient profit to meet the profit target. The firm will, therefore, produce an output which yields Self-Instructional 160 Material the required minimum level of profit OP (= LQ ). Given the profit target OP , the firm Alternative Theories 2 2 2 of Firm will produce OQ2 where its profit is just sufficient to meet requirement of minimum profit. As can be seen in Figure 6.1, output (OQ2) is less than the sales maximization output OQ3. Evidently, the profit maximization output, OQ1 is less than the sales maximization output OQ2 (with profit constraint). NOTES 6.3.2 Baumol’s Model with Advertising We have shown above how price and output are determined in a static single period model without advertising. In an oligopolistic market structure, however, price and output are subject to non-price competition. Baumol considers in his model with advertising as the typical form of non-price competition and suggests that the various forms of non- price competition may be analysed on similar lines. In his analysis of advertising, Baumol makes the following assumptions. • Firm’s objective is to maximize sales, subject to a minimum profit constraint. • Advertising causes a shift in the demand curve and hence the total sales revenue (TR) rises with an increase in advertisement expenditure (A) i.e., ∂TR/∂A > 0. • Price remains constant — a simplifying assumption. • Production costs are independent of advertising. This is rather an unrealistic assumption since increase in sales may put output at a different cost structure. Baumol’s model with advertising is presented in Figure 6.2. The TR and TC are measured on the Y-axis and total advertisement outlay on the X-axis. The TR curve is drawn on the assumption that advertising increases total sales in the same manner as price reduction.

Check Your Progress 3. What is the basic Fig. 6.2 Sales Revenue Maximisation premise of Baumol’s theory? The TC curve includes both production and advertisement costs. The total profit 4. Name the two basic curve is drawn by subtracting TC from TR. The profit so estimated is shown by the models formulated by Baumol for his curve PT. As shown in Figure 6.2 profit maximizing advertisement expenditure is OAp theory of sales maximization. which maximizes profit at MAp. Note that MAp = RC. Assuming that minimum profit 5. Give one reason for required is OB, the sales maximizing advertisement outlay would be OAc. This implies that a firm increases its advertisement outlay until it reaches the target profit level the criticism received by the which is lower than the maximum profit. This also means that sales maximizers advertise Baumol’s model. not less but more than the profit maximizers.

Self-Instructional Material 161 Alternative Theories 6.3.3 Criticism of Baumol’s Model of Firm Although Baumol’s sales maximization model is found to be theoretically sound and empirically practicable, economists have pointed out the following shortcomings in his NOTES model. First, it has been argued that in the long-run, Baumol’s sales maximization hypothesis and the conventional hypothesis would yield identical results, because the minimum required level of profits would coincide with the normal level of profits. Second, Baumol’s theory does not distinguish between firm’s equilibrium and industry equilibrium. Nor does it establish industry’s equilibrium when all the firms are sales maximizers. Third, it does not clearly bring out the implications of interdependence of the firm’s price and output decisions. Thus, Baumol’s theory ignores not only actual competition between the firms but also the threat of potential competition in an oligopolistic market. Fourth, Baumol’s claim that his solution is preferable to the solutions offered by the conventional theory, from a social welfare point of view, is not necessarily valid.

6.4 WILLIAMSON’S MODEL OF MANAGERIAL DISCRETION

Williamson’s model of maximization of managerial utility function is a culmination of the managerial utility models. A. A. Berle and G. C. Means were the first business economists to point out, in 1932, that management is separated from ownership in the large multi- product business corporations and this influences the role of business managers in setting the goals of the large corporations. They argued that owners (the shareholders) look for high dividends and, therefore, they might be interested in profit maximization. But, for lack of corporate democracy, the owners have little or no role to play in policy decisions. On the other hand, managers have different motives, desires and aspirations which they seek to maximize rather than maximizing profit. Besides, since corporate managers can generate the necessary capital internally by means of retained earnings and they do not need to venture into the capital market for debt capital, their decisions and actions are not subject to scrutiny. The managers, therefore, feel free to pursue their own interest in the corporate firms. J. K. Galbraith developed Berle-Means hypothesis further and examined the issue extensively which is known as the Berle-Means-Galbriath hypothesis. It claims (i) that manager-controlled firms have lower profits than owner-controlled firms and (ii) that professional managers have no interest in maximizing profits. While some empirical studies support these claims, some others do not. The issue remains controversial. However, Williamson made further improvements in the Berle-Means hypothesis. We discuss Williamson’s hypothesis in some detail. Williamson’s model of maximization of managerial utility function is regarded as another important contribution to the managerial theory of firms’ behaviour. Williamson argues that: • Management is divorced from ownership • Managers enjoy discretionary powers to set the goals of the firm they manage • Managers maximize their own utility function rather than maximizing profit Self-Instructional 162 Material Williamson’s managerial utility function includes both quantifiable and Alternative Theories unquantifiable variables. Quantifiable variables are also called pecuniary variables of Firm which include managers’ salary, slack earnings and perks, and unquantifiable variables include power, prestige, job security, status, professional excellence and discretionary powers to spend money. NOTES

Williamson’s model of managerial utility function (Um) can be expressed as follows.

Maximize Um = f (S, M, ID) ...(6.1) subject to a minimum profit where S = staff salary (management and administration), M = managerial monetary emoluments (including perks, etc.), and ID = discretionary investment.

In Eq. (6.1), S, M and ID are important decision variables in the managerial utility function and, therefore, need some elaboration. The variable S includes all payments to managerial and administrative staff on account of salary. It increases with expansion and promotion of the supporting staff for the top managers. It reflects the power, prestige, status and professional success of the management. Also, it enhances the market value of the managers. Variable M includes managers’ gross emoluments which comprises salary and slack earnings in the form of luxurious residence, office, car, travel grants and entertainment. Variable ID refers to the investment that managers make on their own discretion in addition to routine investment meant for the operation of the business to make a certain minimum profit.

ID reflects manager’s powers, a sense of fulfillment and satisfaction. Assumptions: Williamson makes the following assumptions in his model of managerial utility maximization. (i) Demand function: Q = f(P, S, e) where Q = output, P = price, S = staff expenses, and e = environmental factors causing an upward shift in the demand curve; (ii) Cost function: C = f(Q) where dC/dQ > 0; (iii) Profit measures: (a) Actual profit = P = R – C – S where R = revenue, C = cost of production, and S = staff salary,

(b) Reported profit = R = – M where M = managerial emoluments,

(c) Minimum profit = 0 = R – T

where T = tax and ( 0 + T)  R, and

(d ) Discretionary profit = D = = 0 – T 6.4.1 Simple Version of Williamson’s Model Given the assumptions and the parameters, we present here only the simple version of Williamson’s model. The simple version of the model assumes that ‘managerial emoluments’ equal zero, i.e., M = 0. With this assumption, the managerial utility function (6.1) can be written as:

Maximize Um = f(S, ID) ...(6.2)

Subject to > 0 + T

Self-Instructional Material 163 Alternative Theories The term I in Eq. (6.2) is defined as – ( + T). That is, of Firm D 0 ID = Π – Π0 – T ...(6.3) Equation (6.3) implies that managers set aside a part of actual profit ( ) as NOTES owners’ ‘minimum profit’ ( 0) and a part for tax payment (T). The balance of the actual profit is available to the managers for the purpose of ‘discretionary investment’

(ID).

Note that ID in Eq. (6.3) is the same as discretionary profit ( D) given in (d) above. It means that:

ID = ΠD By substitution, the managerial utility function (6.2) can be rewritten as:

Maximize Um = f(S, ΠD) ...(6.4)

where D = – 0 – T Equation (6.4) gives the final form of the managerial utility function in the simple version of the model. It must, however, be noted here that there is

substitutability between S and D. That is, given the actual profit ( ), S can be increased only by reducing D, and vice versa. Therefore, in their attempt to maximize their utility function (6.4), the managers find an optimum combination of S

and D. This is the point of firm’s equilibrium. The firm’s point of equilibrium is shown below graphically. 6.4.2 Firm’s Equilibrium: Graphical Presentation Williamson’s simple model of firm’s equilibrium is presented graphically in Figure 6.3. To begin with, let us recall that there is substitutability between S and ΠD. This implies that managers can attain a certain level of utility (U) from the various combinations of S and ΠD. This possibility can be shown by an indifference curve as depicted by U1 in Figure 6.3. The indifference curve U1 presents the various combinations of S and ΠD that yield the same level of managerial satisfaction. By the same logic, an indifference map can be constructed assuming different levels of actual profits (Π) and the associated level of managerial utility, as shown by the indifference curves U2, U3 and U4 in Figure 6.3. The higher the indifference curve, the higher the level of managerial satisfaction at different levels of actual profit. The problem now is how to find the optimum point on the indifference map.

This task is accomplished by finding the relationship between S and D and the total actual profit ( ). We know that = TR – TC and TR = P × Q. Therefore, by assuming usual demand and cost functions, we can imagine that increases over some level of output and then it begins to decline. This behaviour of actual profit ( ) is shown by the curve marked in Figure 6.3. By combining manager's indifference

map and the profit function, one can obtain the optimum combination of S and D, i.e., the point of firm's equilibrium. The equilibrium of the firm lies at the point at which the highest indifference curve is tangent to the -curve. As shown in the figure, point E is the point of firm’s equilibrium. Point E denotes a situation in which

managerial utility function (Um) is maximized subject to a minimum profit of EM.

Self-Instructional 164 Material Alternative Theories of Firm

NOTES

Fig. 6.3 Equilibrium of the Firm: Willamson’s Model

Criticism: Williamson’s model, like other models of this category, suffers from certain weaknesses of its own. This model does not deal satisfactorily with the problem of interdependence of firms under oligopolistic competition. Williamson’s model is said to hold only where rivalry is not strong. In the case of strong rivalry, profit maximization hypothesis has been found to be more appropriate.

6.5 MANAGERIAL FIRM vs ENTREPRENEURIAL FIRM

A thin line exists between a manager and an entrepreneur. An entrepreneur is often asked to perform his duties like a manager whereas a manager is always asked to perform his duties like an entrepreneur. A manager is advised to have the opportunism and drive like that of an entrepreneur whereas an entrepreneur is advised to discipline himself in a methodical manner similar to that of a manager (Heller, 2006). In the management literature, the two terms are sometimes used synonymously as both are associated with leadership. There are few researchers who have tried to merge both the terms in their findings of leadership and entrepreneurship (Gupta et al., 2004; Tarabishy et al., 2005), while there are others who have found connections between the concepts of leadership and entrepreneurship (for instance, Cogliser and Brigham, 2004; Vecchio, 2003). However, management and leadership are not necessarily corresponding, but they may be interconnected (Davidson and Griffin, 2000). There are many differences between a manager and an entrepreneur: while a Check Your Progress manager is appointed by a higher authority, an entrepreneur emerges out of the people. 6. Name the first While managers have colleagues, entrepreneurs have helpers to assist them. Managers business economists usually depend on their positional powers whereas entrepreneurs use their natural inherent to point out, in 1932, that powers like charisma, wisdom, cleverness and intuition. Mangers usually influence others management is on the basis of their authority whereas entrepreneurs influence others beyond formal separated from authority. ownership in the large multi-product Structuring on irrational decision-making models from behavioural decision theory, business Busenitz and Barney (1997) proclaim that entrepreneurs are more vulnerable to decision- corporations. making prejudices and heuristics in comparison to managers. Thus, ‘entrepreneurs are 7. Why is the the people who notice opportunities and take risk and responsibility for mobilising the Williamson’s model of managerial resources necessary to produce new and improved goods and services’ (Jones and discretion criticized? George, 2007, p. 42). Whereas, managers are more often responsible to make use of human resources and administering work to accomplish organizational goals effectually Self-Instructional Material 165 Alternative Theories and proficiently (Jones and George, 2007). However, Griffin and Davidson (2000) are of of Firm the view that when performing of roles and duties are concerned, the differences between the duties and roles are more often that of degrees rather than of kind. Organizations require both managers and entrepreneurs or leaders as far as the lifecycle theory of NOTES organizational leadership is concerned (Baliga and Hunt, 1987). Furthermore, to achieve the best out of the two skill sets, both should supplement each other and their ability and talent should overlap (Davidson and Griffin, 2000). Therefore, when an organization is being set-up or is laying its foundation, entrepreneurial leadership is very important in fashioning a goal or idea that helps the organization in taking its first steps. Managerial or entrepreneurial leadership becomes significant in the collectivity and formalization stages in order to speed up growth of the organization. A heavy emphasis on entrepreneurial leadership is needed again at the amplification of the structural stage. 6.5.1 Entrepreneurial Firms The term ‘entrepreneur’ is often used interchangeably with ‘entrepreneurship’. But conceptually it typically means to undertake. It owes its origin to Western societies. But even in the West, the meaning has undergone changes from time to time. In the early sixteenth century they were different. An entrepreneur is a creator whereas entrepreneurship is the creation. Entrepreneurship is the tendency of a person to organize his own business and run it profitably, exploiting the qualities of leadership, decision making, managerial calibre, etc. Entrepreneurship is a role played by or the task performed by an entrepreneur. The central task of the entrepreneur is to take moderate risks and invest money to earn profits by exploiting an opportunity. The word ‘entrepreneurship’ was used to refer to army leaders. In the eighteenth century, it represented a dealer who bought and sold goods at uncertain prices. In 1961, Schumpeter used the term ‘innovator’ for entrepreneur. Entrepreneurship is recognized all over the world in countries such as USA, Germany, and Japan and in developing countries like India. Hans Schollhammer provides a classification of entrepreneurial firms describing them to be of five types. These are described as follows: • Administrative entrepreneurship: In the administrative model, the firm moves beyond formal R&D projects to encourage greater innovation through a philosophy of corporate support to innovators by systematically providing resources for making new ideas commercial realities. An entrepreneurial team led by a champion is supported by contributions from all departments in implementation of these projects. • Opportunistic entrepreneurship: Champions are given the freedom to pursue opportunities both for the organization and through external markets by the loosening of formal structural ties. For instance, Quad/Graphics Inc., the company that prints Newsweek, when printing technology began to change rapidly with computers, challenged its engineers to design state-of-the-art equipment for printing. Quad/ Graphics then created a separate subsidiary, QuadTech, and gave its engineers executive control and the autonomy to sell technology openly to anyone. • Acquisitive entrepreneurship: It is when corporate managers search for external opportunities, such as other firms and entrepreneurial start-ups that can enhance profits. This may be through mergers, acquisitions, joint ventures and licensing agreements. Rather than developing ideas internally, firms actively court other firms that have proprietary knowledge or promising products.

Self-Instructional 166 Material • Imitative entrepreneurship: Imitative entrepreneurship uses the ideas of other Alternative Theories firms and then applies weight or corporate muscle to control markets. The of Firm Japanese, for example, during their initial period of growth, copied American products and produced them at lower costs, and exported them to American markets. Imitation shakes out less efficient producers and more capable firms NOTES who are able to provide consumers with value for their products or services take the initiative. • Incubative entrepreneurship: The ‘incubative’ process is necessary for new ideas to be developed for commercialization. Project teams are created and are expected to put an innovation through its paces, and if warranted to push the implementation. The teams are often established as semi-autonomous new venture development units that often have seed capital, access to corporate resources, freedom of independent action, and responsibility for implementation from inception to commercialization. Corporate endeavour is to support these ideas so that they are successful. This process is reflective of risk-oriented entrepreneurship. Each of these types has a different strategy and a distinct role for the innovator. Each classification implies a supportive environment that benefits not only the corporation, but also the innovative manager. This is easier to accomplish in small companies than in large ones, in part, because large companies have greater geographic differences and bureaucracies. Intrapreneurs embody the same characteristics as the entrepreneur— conviction, passion and drive. Characteristics of a successful entrepreneurial firm The National Business Incubation Association (NBIA) has identified the following characteristics of a successful entrepreneurial firm: • An effective management team that works cooperatively and consists of members selected to provide a range of knowledge and skills • Sound financing, the earlier the better; funding is directly related to a firm’s success, and in some cases can be the deciding factor between a business venture’s success and failure • Principals who make business decisions based on a clear understanding of the market and the competition, rather than their own enchantment with their product or service • Principals who keep on top of best business practices by surrounding themselves with knowledgeable people, remaining open to advice and ideas and being willing and ready to make changes based on new information • A well-researched business plan that provides clear direction and focus • Principals who are good money managers and remain in control of the venture’s books • Entrepreneurs who are passionate about their ventures and communicate that excitement to potential investors, customers and mentors 6.5.2 Cyert-March Model of Firms The behavioural model of Cyert and March is an extension and modified version of Simon’s ‘satisficing behaviour’ model of corporate firms. The Cyert-March model can be appreciated better in contrast to other alternative theories of firm. Traditional theory Self-Instructional Material 167 Alternative Theories of firm assumes ‘profit maximization’ as the sole goal of business firms. Managerial of Firm utility models emphasize the role of the dichotomy between the ownership and the management in setting business goals and claim that managers maximize their utility function. They argue that managers use their discretion to set goals for themselves NOTES different from profit maximization. They set such goals for themselves as maximization of sales revenue, maximization of firm’s growth rate, maximization of manager’s own utility function, and so on. In contrast, Cyert and March look at large multiproduct corporations not as an ordinary firm, but as a coalition of different but related interest groups including owners, managers, workers, input suppliers, customers, bankers, and tax authorities. All these groups have their own interest in the corporations and their interests are often in conflict with one another. • Owners (the stockholders) are interested in maximum profit possible; • managers aim at high salary, power and perks; • workers are interested in high pay packets, bonus, safe working conditions, insurance and other facilities; • customers are interested in high quality goods and lower prices; • input suppliers are interested in continuity and growth in demand for their supplies at higher prices; • bankers expect and want their loans and advances to be secure and repaid on time; and • tax authorities expect honest and regular tax payments. Obviously there is a conflict—more or less—between the interests of the different interest groups. One of the important managerial tasks is the goal formation for the firm reconciling these conflicting interests. Let us now look at the aspiration levels of different interest groups and the process of goal formation. Aspiration Levels and Process of Goal Formulation Goal formulation by reconciling conflicting interests is a complicated task. Cyert and March argue that managers have a crucial task in formulating a goal for the firm that reconciles the conflicting and competing interests of the different interest groups so as to ensure a smooth functioning of the corporation. In reconciling conflicting and competing interests, managers look at the factors that determine the demands of the various interest groups from the corporation. The demands of the various interest groups are determined largely by their ‘aspiration levels’, past performance of the firm, and information available to the interest groups. For example, managers’ demand for a higher salary depends on the level of their aspirations, and their aspirations depend on their experience about the achievements of their aspirations. In a dynamic society, business environment and conditions continue to change. Environmental changes alter the achievements and, therefore, the level of their aspirations and their demands. That is, in a dynamic society— aspirations, achievements and goals of the corporations keep changing continuously. Setting goals: The satisficing behaviour Now the question arises: How are the goals set? The goals of large multiproduct corporations are set by the top management. Since interest groups are many and their aspirations and expectations are many and competing, a single goal cannot be set as it

Self-Instructional 168 Material will not satisfy all concerned. Therefore, the top management sets a set of diversified Alternative Theories goals. As mentioned already, according to Cyert and March, the top management sets of Firm the following five main goals: (i) Production goal (ii) Inventory goal NOTES (iii) Sales goal (iv) Market share (v) Profit goal These goals are determined through a process of continuous bargaining between the coalition groups. The top management attempts in the process of bargaining to bring about a reconciliation between the conflicting goals. However, so long as the firm is able to achieve the above goals, top management finds it helpful in reconciling the ‘aspirations’ of the interest groups. How the achievement of these goals satisfies the different coalition groups is described here briefly. • Production goal aims at continuity in production irrespective of any seasonal variability of demand. This goal is achieved by preventing (a) underutilization of capacity in one period and its overutilization in another period and (b) lay-off of labour in one period and ‘rush recruitment’ in another. This helps in preventing undue variation in the cost of production and the problem of labour unrest and dissatisfaction. As a result, owners, managers and workers are satisfied.\ • Inventory goal aims at maintaining a balanced inventory of both raw materials and finished goods. A balanced inventory of inputs and raw materials ensures continuity of production and supply of goods to the customers and also keeps the suppliers of inputs satisfied. • Sales and market share goals aim at promotion and enhancing the market share of the firm. Sales are promoted through competitive advertising and a pricing strategy. Sales promotion and increase in market shares keep top management and owners satisfied. • Profit goal is so determined that it satisfies the owners (the shareholders), the bankers and other financiers of the firm. Besides, the profit goal aims at making adequate financial provision for future projects. However, setting the goals is an extremely complicated and difficult task. What the top management aims at, in practice, is to achieve an overall satisfactory performance. This, they call the firms’ ‘satisficing behaviour’. This is, according to Simon, a bounded rational behaviour. The practical methods of the ‘satisficing behaviour’ are to bring a reconciliation between the conflicting and competing aspirations. The methods that are generally used include: • Budget allocation and delegation of authority • Regular payment of dues to related interest groups • Allocation of funds for R&D as ‘side payment’ • ‘Slack payments’ to deserving groups • Allocation of priorities to demand from different groups and meeting them in the same sequence • Decentralization of decision-making powers at different levels of managerial functions Self-Instructional Material 169 Alternative Theories Shortcomings of the Cyert-March Model of Firm The behavioural model of Cyert and March has been criticized on the following grounds. (i) It provides only a simulation of managerial technique rather than providing a NOTES behavioural model. (ii) It does not analyze and reveal how a firm reaches its equilibrium level in its ‘satisficing behaviour’. (iii) More importantly, it does not deal with the interdependence in the case of oligopolist firms. (iv) This model has no predictive power whatsoever. (v) At its best, it presents managerial behaviour rather than economic behaviour of the firms.

6.6 MARRIS’ MODEL OF MANAGERIAL ENTERPRISE

Robin Marris’ theory of firm assumes that the goal that managers of a corporate firm set for themselves is to maximize the firm’s balanced growth rate subject to managerial and financial constraints. To prove his point of view, he developed a model of firm’s growth rate maximization. Marris defines firm’s growth rate (Gr) as:

Gr = GD = Gc ...(6.5)

where GD = growth rate of demand for firm’s product and

Gc = growth rate of capital supply to the firm. Equation (6.5) implies that a firm achieves a balanced growth rate when the growth rate of demand for its product equals the growth rate of capital supply to the firm. In maximizing firm’s growth rate, managers are faced with two constraints: (i) managerial constraints and (ii) financial constraints. Managerial constraints arise due to: (a) limits to managers’ ability to manage and to achieve optimum efficiency and (b) managers’ own job security. Financial constraints arise due to conflict between managers’ own utility function which they attempt to maximize and owners’ utility function. Marris defines managerial utility

(Um) and owners’ utility (Uo) functions as follows.

Manager’s utility function: Um = f (salary, power, status, job security)

Check Your Progress Owners utility function: Uo = f (profit, capital, output, market share, 8. State two public reputation) differences between Apparently, there is a divergence and, to some extent, a conflict between the a manager and an entrepreneur. manager’s and owner’s utility functions. However, Marris argues that the divergence 9. List two between Uo and Um is not so wide as it is made out in managerial theories of firm. characteristics of He claims that the two utility functions converge into one variable, i.e., a steady entrepreneurial firms growth in the size of the firm, however defined. Nevertheless, Marris defines steady as identified by National Business growth rate of the firm for managers and owners in terms of two different Incubation variables—for managers in terms of Gd, i.e., growth in demand for firm’s product, Association and for owners in terms of Gc, i.e., the growth of firm’s capital (Gc). Thus, he (NBIA). redefines manager’s and owner’s utility functions as follows.

Self-Instructional 170 Material U = f(G ) ...(6.6) Alternative Theories m d of Firm and Uo = f(Gc) ...(6.7) According to Marris, managers try to maximize utility functions (6.6) and (6.7) in such a way that Gd = Gc. This is what Marris calls the ‘balanced growth rate’. NOTES The firm reaches its equilibrium when ‘balanced growth rate’ is achieved. This is what Eq. (6.5) implies. The manager’s objective is to maximize balanced growth rate (Gr) such that Gd = Gc. Thus, the firm is in equilibrium where:

Gr(max) = Gd = Gc ...(6.8)

Marris redefines Gd and Gc in Eq. (6.8) in operational terms as given below:

Gd = f(d, k) ...(6.9) where d = diversification of product, and k = success rate of new products,

and Gc = r (P) ...(6.10) where r = financial security ratio assumed to be a constant proportion of profit (Π). In Marris’s model, r is assumed to be determined subjectively by the managers. To elaborate on his theory, Marris has developed an elaborate model. We now turn to another aspect of Marris’ theory of firm, i.e., the manager’s financial policy. 6.6.1 Financial Policy for Balanced Growth In their effort to strike a balance between their own and the owner's utility functions, managers adopt a prudent financial policy. In formulating a prudent financial policy, managers use the following three critical ratios. Value of debts (i) Debt ratio or Leverage (r ) = 1 Total assets

Liquid assets (ii) Liquidity ratio (r ) = 2 Total assets Retained profits (iii) Profit retention ratio (r ) = 3 Total profit

Managers keep debt ratio (r1) within a manageable limit by avoiding high debt liabilities including interest and debt repayment. The reason for this strategy is that a high debt ratio might lead to bankruptcy or insolvency and a low debt ratio means relying heavily on own resources which imposes a limit on capital growth. Likewise, high and low liquidity ratios (r2) are avoided. The reason is a high liquidity ratio invites the risk of takeover by the dominant group of owners who could use the liquidity for their other ventures. Low liquidity ratio is avoided because it implies low financial leverage and low ability to meet payment obligations which often leads to loss of prestige and sometimes even to insolvency. The retention ratio is maintained at a level which prevents the change of top management (i.e., job security aspect) and keeps share prices reasonably high. Low retention ratio is avoided because it means high distribution of profits which may attract takeover by raiders. High retention ratio is avoided because it involves the risk of replacement of the top management.

Self-Instructional Material 171 Alternative Theories In brief, a prudent financial policy is devised by constructing ‘a financial of Firm security ratio’ r , which is a weighted average of the three financial ratios. 6.6.2 Shortcomings of Marris Theory NOTES Marris’s theory is regarded as an important contribution to the theory of firm in so far as it introduces financial ratios as decision variables in determining the firm’s goal. Besides, his theory provides a reconciliation between the conflicting utility functions of the managers and owners. However, Marris’s theory has its own shortcomings. One, Marris assumes cost structure and price to be given. Therefore, he assumes implicitly that profit is given too. This assumption is not realistic. If fact, price determination has been the major point of contention in the theory of firms whereas Marris ignores this aspect completely. This is one of the serious drawbacks of his theory. Two, most industries are oligopolistic and hence firms’ business decisions are interdependent. Marris’s theory does not account for this interdependence in firms’ decisions. This implies that product differentiation by rival firms goes unnoticed or is ignored in the firm’s decision-making. His theory has, therefore, a limited applicability. Three, in an oligopolistic industry, if all the firms seek simultaneously to maximize their growth rate, it imposes a serious limitation on the growth in demand for firms’ product and the supply of capital. Marris’s theory does not account for this factor.

6.7 LIMIT PRICING THEORY

Limit price can be defined as the maximum price that existing firms charge with the objective of limiting the number of firms and preventing the entry of new firms to the industry. Limit pricing is a practice of charging a price lower than the profit maximising one. The objective behind this practice is to prevent the entry of new firms to the industry. Limit pricing is thus an entry-preventing-pricing policy. Over time, many economists have developed the limit pricing models. Bain was the first to formulate limit pricing theory in 1949. Later Sylos-Labini (1957), Franco Modigliani (1958), Pashigian (1968), and J. N. Bhagwati (1970) formulated their own theories of limit pricing. In this section, we will briefly describe only Bain’s model of limit pricing—the most famous model. 6.7.1 Bain’s Model of Limit Pricing Bain has attempted, in his model, to explain why oligopoly firms maintain their prices over a long period of time at a level which is lower than the price that would maximize their profits. This price lies somewhere between the long-run competitive price (i.e., P = LAC) and monopoly price (determined where MR = MC). He calls the price so determined Check Your Progress as limit price, i.e., the highest price which the established firms believe they can charge 10. What are the two without inducing entry of new firms. We present here the simplest form of his model. constraints faced by managers in In his model, Bain assumes: (a) that long-run AR, MR and LAC curves are maximizing a firm’s determinate and known; (b) that existing firms are in effective collusions; (c) that there growth rate? exists a limit-price of which existing firms are aware; and (d) that existing firms seek to 11. Why do managers maximize their long-run profits. adopt a prudent financial policy?

Self-Instructional 172 Material The model which Bain has developed on the basis of these assumptions is presented Alternative Theories in Figure 6.4. of Firm

NOTES

Fig. 6.4 Determination of Limit Price

The long-run average and marginal revenue conditions are given by AD and A- MR curves, respectively, and long-run average and marginal cost conditions are given by the horizontal line LAC2 = LMC2. Given the revenue and cost conditions, profit- maximizing monopoly price is OP5 (= JQ1) which is given by intersection of MR and

LMC2 at point B. Since LMC2 and AD intersect at point M, competitive price is OP2.

Thus, the existing firms have monopoly price OP5 at point J on the demand curve and competitive price OP2 determined by point M. The limit price lies between these two prices. By assumption, existing firms can estimate the limit-price. They will therefore determine the limit price a little below the monopoly price, say at OP4 at point K on the demand curve. Limit price OP4 prevents the entry of new firms and existing firms maximize their long-run profits. Any price above OP4 makes profit uncertain because it will attract new firms whose behaviour is uncertain. Therefore, AK part of the demand curve is the uncertain range of demand curve.

In case firms are able to decrease their cost of production and their LAC2 = MC2 shift downward to LAC1 = MC1, competitive price will be OP1 and monopoly price will be OP3 as determined by point T where LAC1 = MC1 intersects the MR curve. In that case, the limit price will be determined somewhere between OP1 and OP3. For example, limit price may be determined at OP2 = MQ4. This explains how limit price is determined.

6.8 SUMMARY

In this unit, you have learnt that, • Although the conventional theory of firm still holds its ground firmly, several alternative theories of firm were proposed during the early 1960s by economists, notably by Simon, Baumol, Marris, Williamson, Berle and Means, Galbraith, and Check Your Progress Cyert and March. 12. Define limit price. • Another major drawback of the conventional theory is that it does not recognize 13. What has Bain the dichotomy between the ownership and management and its role in setting the attempted to explain in his model of limit goal for the firm. pricing?

Self-Instructional Material 173 Alternative Theories • The alternative theories of the business firms are sometimes classified under the of Firm following categories: o Managerial theories of firm o Growth maximization theories of firm NOTES o Maximization of managerial utility theories o Behavioural theories of firm • One thing is clear that the conventional theory of firm based on profit maximization hypothesis is not the only theory applicable to a multitude of firms—large and small, owner-managed and manager-managed, single-product and multi-product, local and multinational, private and public undertakings, and alternative theories do provide alternative explanations to the firm’s behaviour. • There is a general consensus that the conventional theory has greater explanatory and predictive power than the alternative theories of firm. As regards the empirical validity, the empirical evidence in support of the alternative theories is not unambiguous. • Baumols’s theory of sales maximization is one of the most important alternative theories of firm’s behaviour. The basic premise of Baumol’s theory is that sales maximization, rather than profit maximization, is the plausible goal of the business firms. • To formulate his theory of sales maximization, Baumol has developed two basic models: (i) Static Model and (ii) Dynamic Model—each with and without advertising. • There are two types of probable equilibrium: one in which the profit constraint does not provide an effective barrier to sales maximization, and second in which profit constraint does provide an effective barrier to sales maximization. • In an oligopolistic market structure, however, price and output are subject to non- price competition. Baumol considers in his model with advertising as the typical form of non-price competition and suggests that the various forms of non-price competition may be analysed on similar lines. • Baumol’s theory does not distinguish between firm’s equilibrium and industry equilibrium. Nor does it establish industry’s equilibrium when all the firms are sales maximizers. • Williamson’s model of maximization of managerial utility function is a culmination of the managerial utility models. A. A. Berle and G. C. Means were the first business economists to point out, in 1932, that management is separated from ownership in the large multi-product business corporations and this influences the role of business managers in setting the goals of the large corporations. • Williamson’s model does not deal satisfactorily with the problem of interdependence of firms under oligopolistic competition. Williamson’s model is said to hold only where rivalry is not strong. In the case of strong rivalry, profit maximization hypothesis has been found to be more appropriate. • A thin line exists between a manager and an entrepreneur. An entrepreneur is often asked to perform his duties like a manager whereas a manager is always asked to perform his duties like an entrepreneur. • There are many differences between a manager and an entrepreneur: while a manager is appointed by a higher authority, an entrepreneur emerges out of the Self-Instructional 174 Material people. While managers have colleagues, entrepreneurs have helpers to assist Alternative Theories them. of Firm • Structuring on irrational decision-making models from behavioural decision theory, Busenitz and Barney (1997) proclaim that entrepreneurs are more vulnerable to decision-making prejudices and heuristics in comparison to managers. NOTES • The term ‘entrepreneur’ is often used interchangeably with ‘entrepreneurship’. But conceptually it typically means to undertake. It owes its origin to Western societies. • In the administrative model, the firm moves beyond formal R&D projects to encourage greater innovation through a philosophy of corporate support to innovators by systematically providing resources for making new ideas commercial realities. • The behavioural model of Cyert and March is an extension and modified version of Simon’s ‘satisficing behaviour’ model of corporate firms. The Cyert-March model can be appreciated better in contrast to other alternative theories of firm. • Goal formulation by reconciling conflicting interests is a complicated task. Cyert and March argue that managers have a crucial task in formulating a goal for the firm that reconciles the conflicting and competing interests of the different interest groups so as to ensure a smooth functioning of the corporation. • Robin Marris’s theory of firm assumes that the goal that managers of a corporate firm set for themselves is to maximize the firm’s balanced growth rate subject to managerial and financial constraints. • In maximizing firm’s growth rate, managers are faced with two constraints: (i) managerial constraints and (ii) financial constraints. • In their effort to strike a balance between their own and the owner’s utility functions, managers adopt a prudent financial policy. • Marris’s theory is regarded as an important contribution to the theory of firm in so far as it introduces financial ratios as decision variables in determining the firm’s goal. Besides, his theory provides a reconciliation between the conflicting utility functions of the managers and owners. • Limit price can be defined as the maximum price that existing firms charge with the objective of limiting the number of firms and preventing the entry of new firms to the industry. Limit pricing is a practice of charging a price lower than the profit maximising one. • Bain has attempted, in his model, to explain why oligopoly firms maintain their prices over a long period of time at a level which is lower than the price that would maximize their profits.

6.9 KEY TERMS

• Limit price: It can be defined as the maximum price that existing firms charge with the objective of limiting the number of firms and preventing the entry of new firms to the industry. • Limit pricing: It is a practice of charging a price lower than the profit maximising one. Self-Instructional Material 175 Alternative Theories of Firm 6.10 ANSWERS TO ‘CHECK YOUR PROGRESS’

1. Although the conventional theory of firm still holds its ground firmly, several NOTES alternative theories of firm were proposed during the early 1960s by economists, notably by Simon, Baumol, Marris, Williamson, Berle and Means, Galbraith, and Cyert and March. 2. The alternative theories of the business firms are sometimes classified under the following categories: o Managerial theories of firm o Growth maximization theories of firm o Maximization of managerial utility theories o Behavioural theories of firm 3. The basic premise of Baumol’s theory is that sales maximization, rather than profit maximization, is the plausible goal of the business firms. 4. To formulate his theory of sales maximization, Baumol has developed two basic models: (i) static model and (ii) dynamic model—each with and without advertising. 5. Baumol’s theory does not distinguish between firm’s equilibrium and industry equilibrium. Nor does it establish industry’s equilibrium when all the firms are sales maximizers. 6. A. A. Berle and G. C. Means were the first business economists to point out, in 1932, that management is separated from ownership in the large multi-product business corporations and this influences the role of business managers in setting the goals of the large corporations. 7. Williamson’s model does not deal satisfactorily with the problem of interdependence of firms under oligopolistic competition. Williamson’s model is said to hold only where rivalry is not strong. In the case of strong rivalry, profit maximization hypothesis has been found to be more appropriate. 8. There are many differences between a manager and an entrepreneur: while a manager is appointed by a higher authority, an entrepreneur emerges out of the people. While managers have colleagues, entrepreneurs have helpers to assist them. 9. The National Business Incubation Association (NBIA) has identified the following characteristics of a successful entrepreneurial firm: • An effective management team that works cooperatively and consists of members selected to provide a range of knowledge and skills • Sound financing, the earlier the better; funding is directly related to a firm’s success, and in some cases can be the deciding factor between a business venture’s success and failure 10. In maximizing firm’s growth rate, managers are faced with two constraints: (i) managerial constraints and (ii) financial constraints. 11. In their effort to strike a balance between their own and the owner’s utility functions, managers adopt a prudent financial policy. 12. Limit price can be defined as the maximum price that existing firms charge with the objective of limiting the number of firms and preventing the entry of new firms to the industry.

Self-Instructional 176 Material Alternative Theories 13. Bain has attempted, in his model, to explain why oligopoly firms maintain their of Firm prices over a long period of time at a level which is lower than the price that would maximize their profits. NOTES 6.11 QUESTIONS AND EXERCISES

Short-Answer Questions 1. What lies at the foundation of the alternative theories of business firms? Do the alternative theories really offer an alternative explanation to firms’ behaviour? 2. What was the conventional theory of firm based on? 3. According to Baumol, why do business managers pursue the goal of sales maximization? 4. In what way is Baumol’s theory superior to the conventional theory based on profit maximization hypothesis? 5. Does Baumol’s model offer a more appropriate explanation to price and output determination than the conventional theory? 6. How does Williamson’s model of managerial utility maximization explain the equilibrium of the firm? 7. How does Marris define the balanced growth of the firm? How do managers arrive at the balanced growth? What kind of financial policy do the managers adopt to secure their stake in the firm? 8. Write a short note on limit pricing theory. Long-Answer Questions 1. Discuss the traditional theory of firm. 2. Explain Baumol’s theory of sales revenue maximization. 3. Assess Baumol’s model of price and output determination with and without advertisement. 4. Evaluate Williamson’s model of managerial utility maximization. 5. Critically analyse the differences between managerial and entrepreneurial firm. 6. Explain Marris’ model of managerial enterprise. 7. Describe the limit pricing theory with special reference to Bain’s model of limit pricing.

6.12 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra.

Self-Instructional Material 177 Alternative Theories Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: of Firm Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. NOTES Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional 178 Material Theory of General UNIT 7 THEORY OF GENERAL Equilibrium EQUILIBRIUM NOTES Structure 7.0 Introduction 7.1 Unit Objectives 7.2 Principles of General Equilibrium 7.3 Existence, Uniqueness and Stability 7.3.1 Existence 7.3.2 Uniqueness 7.3.3 Stability 7.3.4 Evaluation 7.4 Walrasian Approach to General Equilibrium 7.4.1 Walrasian General Equilibrium Model 7.4.2 Process of Automatic Adjustment 7.5 Computable General Equilibrium 7.5.1 Arrow-Debreu Model and Polynomial Time Algorithm 7.5.2 Arrow-Debreu Pricing: Equilibrium 7.5.3 General Equilibrium under Uncertainty 7.6 Summary 7.7 Key Terms 7.8 Answers to ‘Check Your Progress’ 7.9 Questions and Exercises 7.10 Further Reading

7.0 INTRODUCTION

General equilibrium approach recognises the interdependence of constituent parts of the economic system. It recognises the interrelations and interdependence of economic variables and seek to answer the question how all the segments of the economy reach an equilibrium position simultaneously. General equilibrium shows, by using the tools of partial equilibrium analysis, how prices and outputs are simultaneously determined in all segments of the economy. Basically, general equilibrium is concerned with three questions: (i) Is there really any equilibrium? (ii) Does the equilibrium meet certain optimal criteria? (iii) Is the equilibrium stable? This unit discusses general equilibrium and their various approaches.

7.1 UNIT OBJECTIVES

After going through this unit, you will be able to: • Assess the principles of general equilibrium • Discuss existence, uniqueness and stability of a general equilibrium • Analyse the Walrasian approach to general equilibrium • Discuss Walrasian approach to general equilibrium assuming a two-commodity- Self-Instructional two-consumer-two firms-two inputs model Material 179 Theory of General • Illustrate graphically how economic system reaches the general equilibrium position Equilibrium • Explain the Arrow-Debreu model and the computable general equilibrium

NOTES 7.2 PRINCIPLES OF GENERAL EQUILIBRIUM

A fundamental feature of an economic system is the interdependence and interrelatedness of economic activities—production and consumption—of its various constituents— individuals, households, firms, banks and other kinds of financial institutions. The working mechanism of economic system is unimaginably complex. It is not possible to trace the behaviour of each economic element and its interaction with the rest of the economy and trace equilibrium of each and every element of the economy. The economists, therefore, adopt two kinds of approaches to economic analysis: (i) Partial equilibrium approach, and (ii) General equilibrium approach. Partial equilibrium approach ignores the interdependence of the various segments of the economy. It isolates the segment or the phenomenon of the study from the other segments and assumes non-existence of influences of the changes occurring outside the area delimited for the study. For example, in the analysis of utility-maximization behaviour of the households, their incomes are assumed to remain constant even if incomes change due to change in factor prices in factor markets; prices of related goods (substitutes and complements) are assumed to remain constant even if they change due to change in demand and supply conditions; and the consumer’s taste and performance are assumed to be given even if they are not. Similarly, in the analysis of profit maximizing behaviour of the firms, the factor prices, technology, and commodity-prices are assumed to remain constant even if these variables continue to change. The general equilibrium approach, on the other hand, recognizes the interdependence of constituent parts of the economic system. It recognizes the interrelations and interdependence of economic variables and seeks to answer the question how all the segments of the economy reach an equilibrium position simultaneously. General equilibrium shows, by using the tools of partial equilibrium analysis, how prices and outputs are simultaneously determined in all segments of the economy. We have noted that various parts of the economy are mutually interdependent and function in close relationship with each other. In fact, in an economy everything depends on everything else. In such a system, price of a single commodity or factor cannot, in principal, be determined unless all other prices are known. Furthermore, prices are not determined one by one. If at all, they are determined simultaneously. The general equilibrium approach seeks to answer such questions as: Does the market mechanism produce a general equilibrium solution wherein each market or segment of the economy is in equilibrium? Is the equilibrium in product markets necessarily consistent with the equilibrium in factor markets? Is the behaviour of each consumer consistent with that of every other consumer, with that of every producer, and with that of each factor supplier? If so, is this solution unique, or are there several other set of prices that will satisfy an equilibrium solution? In other words, does there exist a unique equilibrium solution? Even if it exists, will it be stable in the sense that a disturbance which causes a departure from equilibrium sets up automatic forces that bring the system back again to equilibrium? Thus, the task of general equilibrium theory is to find out whether there exists a general equilibrium in an economy. A general equilibrium is defined as a state in which all economic units maximize their respective objective function and all prices are simultaneously in equilibrium, and all markets are cleared. General equilibrium theory Self-Instructional 180 Material explains how this state can, if ever, be attained. If attained, whether it remains stable. Leon Walras (1834–1910), a French economist, was the first to attempt to answer Theory of General these questions in his book Elements of Pure Economics (1874). Although long before Equilibrium Walras, Cournot had realized that ‘for a complete and precise solution of the partial problems of the economic system, it is inevitable that one must consider the system as a whole.’ In their opinion, the problem of general equilibrium was beyond the resources of NOTES mathematical analysis. However, Walras showed, by using a system of simultaneous equations, that all prices and quantities in all markets are simultaneously determined through their interaction with each other.

7.3 EXISTENCE, UNIQUENESS AND STABILITY

In this section, we answer the questions (i) does there exist a general equilibrium solution? (ii) if it does, is it unique? (iii) is the solution stable? 7.3.1 Existence If number of equations and the number of ‘unknowns’ are equal, it may sometimes make one think that there exists a general equilibrium solution. But, the equality of number of equations with that of unknowns is neither a sufficient nor a necessary condition for the existence of a general equilibrium solution. That it is not a sufficient condition is easy to prove. It is possible to find a system of two equations with two unknowns that has no solution in the realm of real numbers, for only real numbers have economic meaning. For instance, suppose we have two equations. x2 + y2 = 0 x2 – y2 = 1

Solving for x and y, we get x = and y = where the imaginary number i satisfies i2 = – 1. It can also be shown that equality of equations and unknowns is not a necessary condition. Consider the equation: x2 + y2 = 0

This single equation with two unknowns offers a unique solution for x and y in the domain of real number, i.e., x = 0 and y = 0.

Check Your Progress 1. Why have economists adopted the two kinds of approaches to economic analysis? What are they? 2. What is the task of general equilibrium theory?

Fig. 7.1 Unique and Stable Equilibrium Self-Instructional Material 181 Theory of General The example suggests that a unique general equilibrium may exist at zero prices Equilibrium and even at negative prices. These may be the cases of certain ‘free goods’ or ‘nuisance goods’. The problems of zero or negative price could be solved by eliminating free goods or nuisance goods. But, as Car Menger pointed out, there may be a tendency of free NOTES goods to decrease as economic development takes place. Therefore, all kinds of goods must be included in Walrasian system. This is something which Walras did not realize. Hence, his demonstration of existence of general equilibrium solution is unsatisfactory. Furthermore, it is mathematically possible to show the existence of general equilibrium solution involving zero and negative prices. But, while negative prices and quantities of consumer goods is understandable, it is difficult to imagine zero or negative factor prices and quantities. One can hardly imagine a worker paying for his employment. 7.3.2 Uniqueness The uniqueness of general equilibrium solution requires that, at all partial equilibrium levels, demand and supply schedules intersect at only one point giving a positive price. At any other price higher than the price so determined, S > D, and at any lower price D > S, as shown in Figure 7.1. But if demand schedule of a commodity is backward bending, as in case of inferior goods, there will be no unique equilibrium. Instead there will

be multiple equilibria. As shown in Figure 7.2, there are two equilibrium points, e1 and e2.

Fig. 7.2 Multiple Equilibria

However, Wald and, later, Arrow and Debreu have shown that ‘the Walrasian system does possess a unique and economically meaningful solution, provided returns to scale are constant or diminishing and there are no joint products or external effects either in production or in consumption.’ Obviously, the unique solution exists under restrictive assumptions. 7.3.3 Stability Walras also tried to show that general equilibrium is stable. ‘Walras’ stability analysis was based on the assumption that the rate of price changes varies directly with the amount of excess demand. Walras, like Marshall, treated instability in the context of multiple equilibria; the unstable position is invariably found between two stable positions. But unstable equilibria in Walras arise from the intersection of a backward bending supply curve of a productive service with a more steeply falling demand curve. This implies the possibility but certainly not the necessity of multiple equilibria because the supply curve may never bend back again no matter how high factor price rise.’ Self-Instructional 182 Material Walras attempted to show not only stability in a single market but also a multimarket Theory of General stability. Hicks has also attempted to show, in his Value and Capital, that the multimarket Equilibrium does not exist provided there are no strong income effects. It is however difficult to establish that the general equilibrium solution is determinate and stable. NOTES 7.3.4 Evaluation Walrasian general equilibrium model has many shortcomings. Many of its assumptions are highly restrictive and unrealistic. The uniqueness and stability of solution that it offers are doubtful. It is also alleged sometimes that the Walrasian general equilibrium model has little economic content. Despite its shortcomings, the Walrasian general equilibrium model has its own merits. First, Walras was the first to recognize and formalize the mutual interdependence of various prices and quantities in an economic system. Although it is widely known that in economics every-thing depends on everything else, the full implications of this generalisation were not grasped before Walras. Second, general equilibrium approach has a wide applicability to the analysis of various economic phenomena. Modern theories of money, international trade, employment, and economic growth are general equilibrium theories in a simplified form. Also, the ‘new’ welfare economics is an outgrowth of general equilibrium theory. The modern macroeconomics and micro-economics can be viewed as different ways of giving operational relevance to general equilibrium analysis.

7.4 WALRASIAN APPROACH TO GENERAL EQUILIBRIUM

In the Walrasian system of general equilibrium, the behaviour of each decision-maker is presented by a set of equations. Since each decision-maker functions simultaneously in two different capacities—as a buyer and as a seller, his behavioural equations consists of two subsets of equations. One subset describes his demand for different commodities (or factors); it contains as many equations as the number of commodities (or factors) supplied. Thus, demand side of the commodity market is described by as many equations as the number of commodities multiplied by the number of consumers demanding the commodities. Similarly, supply side of the market is described by as many equations as the number of commodities multiplied by the number of firms supplying the commodities. Factor market is similarly described, in Walrasian model, by two sets of equations—one each on demand and supply sides. In this system of describing working of an economy through equations, there are as many ‘unknown’ variables to be determined as independent equations. The ‘unknowns’ are the quantities of all commodities and factors purchased and sold by each individual, and prices of all commodities and factors. To illustrate Walrasian system, let us consider a simple two-consumer-two- Check Your Progress commodity-two-factor model for general equilibrium analysis. Assume that there are 3. What does the only two consumers, A and B; only two commodities, X and Y and only two factors, K uniqueness of and L. Assume also that factors K and L are owned by the consumers, and commodities general equilibrium solution require? X and Y are produced by the two firms. Let us now specify the number of equations and 4. State one merit of of ‘unknowns’, assuming the existence of perfect competition in both commodity and Walrasian general factor markets. equilibrium.

Self-Instructional Material 183 Theory of General Note that the number of equations (20) is the same as the number of unknowns Equilibrium (20). It is necessary, though not sufficient, condition for the general equilibrium solution that the number of independent equations must be the same as the number of unknowns. Another requirement of general equilibrium solution is that all equations must be NOTES simultaneously solved. The above example satisfies this condition of general equilibrium solution.

No. of equations No. of unkowns

1. Demand functions of two goods by two 1. Quantities of 2 goods demanded by 2 consumers, 2 × 2 = 4 consumers 2 × 2 = 4 2. Supply functions of two goods by two firms 2. Quantities of 2 goods supplied by 2 2 × 2 = 4 firms 2 × 2 = 4 3. Demand functions of two factors by two 3. Quantities of 2 factors demanded firms 2 × 2 = 4 by 2 firms 2 × 2 = 4 4. Supply functions of two factors by 2 4. Quantities of 2 factors supplied suppliers (A and B) 2 × 2 = 4 by 2 firms 2 × 2 = 4 5. Market clearing equations of commodities 2 5. Prices of 2 commodities 2 6. Market clearing equation of factors 2 6. Price of 2 factors 2 Total No. of Equations 20 Total no. of unknowns 20

The fulfillment of this condition however does not necessarily guarantee the existence of a general equilibrium solution. First, let us formally describe the Walrasian general equilibrium model. 7.4.1 Walrasian General Equilibrium Model Let us suppose that an economy has n commodities, h households (or individuals) and m inputs (or factors) and describe the commodity and input sectors. Commodity sector: The demand for each commodity is expressed by a demand

function which depends on prices of all commodities, P1, P2, …, Pn, and on the level and

distribution of consumer incomes M1, M2, …, Mn, which consumers earn by supplying their factor services. Thus, the demand function for each commodity may be expressed as: d Qi = Di (P1, P2, …, Pn, M1, M2, …, Mn) …(7.1) There are n × h demand functions in the general system. The supply of each commodity is similarly expressed through supply functions. The quantity supplied of a commodity

depends on the prices of all commodities, P1, P2, …, Pn, and prices of all inputs V1, V2,

…, V3. Thus, supply function is given as: s Qi = Si (P1, P2, …, Pn, V1,V2, …, V3) …(7.2) There are n × f supply functions of n commodities for f firms. Input sector: Resources (or inputs) are owned and supplied by the households and demanded by firms. Let R represent the amount of resource K owned by an individual

i. The actual amount supplied Rk of a resource K will depend on all input prices and the level and distribution of ownership. Thus supply function of a resource is given as: s Rk = Sk (V1, V2, …, Vn; Rk1 Rk2, …, Rkn) …(7.3) There will be m × h equations. d The actual amount demanded (Rk ) of each resource will depend on output levels, output prices, and input prices. Thus, d Rk = Dk (Q1, Q2, …, Qn; P1, P2, …, Pn; Self-Instructional 184 Material V , V ... V ) …(7.4) Theory of General 1 2 n Equilibrium where Q1, Q2, …, Qn represent output levels. There will be n × m equations. Besides, resource constraints should also be incorporated into the model. It may NOTES be expressed as:

∑ ≤ ...(7.5) =

Identities: An important identity which emerges from the circular flows of incomes is that values of all outputs, i.e., PiQi must equal the total income of the society, i.e., M1

+ M2, …, Mh. That is,

∑ = ∑ ...(7.6) = =

Secondly, the total expenditure equals total income. Income of each individual is calculated by multiplying the amount of resource K supplied by an individual j, which equals time the resource price Vk. That is,

= ∑ ...(7.7) =

Finally, the fundamental identity for the economy as a whole can thus be expressed as:

∑= ∑∑ ...(7.8) = = =

Equation (7.8) shows that the prices of resources are directly linked to the prices of output. Prices and quantities of resources supplied cannot be determined without determining the price of commodities. The Walrasian model therefore requires that all the equations must be solved simultaneously. A general equilibrium occurs at n + m prices when all the equations are simultaneously solved. Graphical Illustration of Tendency Towards General Equilibrium Assuming a 2 × 2 × 2 model, we show in this unit that the model economy has a tendency towards general equilibrium under the following assumptions. Assumptions • There exists perfect competition in both commodity and factor markets. • There are only two commodities, X and Y, which are substitutes for each other, and two firms produce one commodity each. • Consumers’ utility functions are given and they maximize their utility subject to income constraint. • There are only two factors of production, L and K, which are available in fixed supply. Factors are homogeneous and perfectly divisible.

Self-Instructional Material 185 Theory of General • Production functions show diminishing marginal rate of technical substitution Equilibrium (MRTS) and decreasing returns. • Firms maximize their profits subject to resource constraint. NOTES To begin with, let us assume that both commodity and factor markets are in equilibrium. Prices in both the markets are in equilibrium. Demands for commodities, X and Y, are equal to their respective supplies. Similarly, demand for each factor is equal to its supply.

Fig. 7.3 Market for Commodity X

The equilibrium in commodity X market is illustrated in Figure 7.3. The initial

demand and supply curves for commodity X are represented by Dx1 and Sx1 respectively.

The demand and supply curves intersect at point E1 determining price of X at OPx1. At

this price, demand for X (i.e., OX1) equals its supply. The market for commodity X being in equilibrium, the one-firm industry X would also be in equilibrium. The equilibrium of

firm X is illustrated in Figure 7.4. The firm (or industry) produces OX1 at which AC = MC = Price = MR.

Fig. 7.4 Industry X

Similarly, the initial equilibrium positions of commodity market Y and of the firm producing Y are illustrated in Figs. 7.5 and 7.6, respectively. The commodity market Y is

in equilibrium at price OPy1 at which demand for Y equals its supply, OY1. Industry Y is

in equilibrium at output OY1. At this output, AC = MC = Price = MR in industry Y. Self-Instructional 186 Material Theory of General Equilibrium

NOTES

Fig. 7.5 Market for Commodity Y

Let us now suppose that, due to some exogenous factor, consumers’ taste changes in favour of commodity X. As a result, demand curve for X, i.e., Dx1 shifts upward to the position of Dx2 (see Figure 7.3). Consequently, price of X rises from Px1 to Px2. The output of X rises to OX2 and the industry makes an abnormal profit of ab per unit of output (see Figure 7.4). The supernormal profits attracts firms from industry Y to industry X and the existing ones increase their output. As a result, demand for factors increases. This causes a rise in demand for factors L and K, in industry X. Since factors are fully employed, where do the factors come from? To find an answer to this question, let us examine what is happening in industry Y.

Fig. 7.6 Industry Y

Since we have assumed a shift in consumer’s taste other things remaining the same, the additional demand for X comes only from a shift in demand from Y to X. This shift occurs because X and Y are substitutes for each other. Due to shift in demand from

Y to X, the initial demand curve for Y, i.e., Dy1 shifts downward to the position of Dy2.

Output of Y falls to OY2 and price falls from OPy1 to OPy2. (Figure 7.5). As a result, the equilibrium of industry Y shifts from E1 to E2 and firms incur a loss of ee2 per unit (Figure 7.6). Effect of Change in Factor Demand Let us now examine the effect of change in consumer demand on factor demand and changes in factor market. In order to analyse the effects in a somewhat wider framework,

Self-Instructional Material 187 Theory of General let us drop the assumption that there is only one firm in each industry and assume, Equilibrium instead, that there are several firms in each industry. Recall that the firms in industry X are making supernormal profits while firms is industry Y are incurring losses. Some firms in industry Y are therefore forced to quit the industry and some are induced to NOTES transfer their resources to industry X. Besides, the demand factors in industry X would increase. This tendency in the commodity markets affects the factor markets with respect to each industry. Consider first the increase on demand for factors in industry X and its effect on factor prices. The entry of new firms to industry X and expansion of production by the existing firms increases demand for labour and capital in this industry. The effect of increase in demand for labour is illustrated in Figures 7.7 and 7.8. Suppose that the labour market

for industry X was initially in equilibrium at point E1. Due to the increase in demand for

labour, the demand curve DL1 shifts to DL2 causing increase in the employment of labour

in industry X from OL1 to OL2 and increase in wage rate for the industry from OW1 to

OW2. The increase in demand for labour by an individual firm of the industry is illustrated in Figure 7.8. It shows that the demand curve for labour by an individual firm shifts

rightward from dl1 to dl2. At new wage rate OW2, an individual firm employs Ol2 workers

or l1 l2 additional workers at the ruling wage rate (Note that l1 l2 multiplied by the

number of firms in the industry equals L1 L2 in Figure 7.7).

Fig. 7.7 Labour Market for Industry X

Let us now see what happens in the capital market. The changes in the capital market for industry X is illustrated in Figures 7.9 and 7.10. Demand for capital increases

in this industry, and the initial capital demand curve Dk1 shifts upward to the position of

Dk2 causing equilibrium point of capital market to shift to E2 and return on capital to rise

to Or2 (Figure 7.9). The capital-demand curve for an individual firm in industry X shifts

from dk1 to dk2 as return on capital increases and the employment of capital by an

individual firm increases from Ok1 to Ok2 (Figure 7.10). The total demand for capital in

industry X increases by K1K2 (Figure 7.9) which equals k1k2 multiplied by the of firms in the industry.

Self-Instructional 188 Material Theory of General Equilibrium

NOTES

Fig. 7.8 Demand for Labour by a Firm in Industry X

Let us now see what has happened in the factor markets in respect of industry Y. First let us consider the labour market. The changes in the labour market in respect of industry Y are illustrated in Figures 7.11 and 7.12. Let the labour market for industry Y to be in equilibrium at point E1. Recall from Figure 7.6 that firms in industry Y incur losses. Therefore, the demand for labour decreases and labour demand curve shifts downward from its initial position DL2 to DL1. Consequently, the wage rate decreases from OW2 to

OW1 and employment of labour in the industry decreases from OL3 to OL1. The decrease in demand for labour by an individual firm of industry Y is shown in Figure 7.12 by a downward shift in labour demand curve from dl2 to dll. Each firm employs less of labour even though wage rate has gone down from OW2 to OW1.

Fig. 7.9 Capital Market for Industry X

Let us now turn to the capital market for industry Y. A condition similar to the labour market for the industry Y takes place in the capital market too for industry Y. Demand for capital decreases as shown by the downward shifts of capital demand curve of both individual firms (Figure 7.14) and industry (Figure 7.13) because return on capital in the industry decreases.

Self-Instructional Material 189 Theory of General Equilibrium

NOTES

Fig. 7.10 Demand for Capital by a Firm in Industry X

Fig. 7.11 Labour Market for Industry Y

Fig. 7.12 Demand for Labour by a Firm in Industry Y

To sum up, due to the change in consumer’s preference in favour of commodity X caused by an exogenous factor, demand for commodity X has increased and for commodity Y decreased. As a result, price of X increases and that of Y decreases. Factor price remaining the same, profitability of industry X increases while that of industry Y decreases. This leads to increase in demand for L and K in industry X and to decrease in demand for L and K in industry Y. These changes in demand for factors have led to disequilibrium in the system since firms in industry X are earning supernormal profits

Self-Instructional 190 Material which is in consistent with perfect competition. In a perfectly competitive system, however, Theory of General the disequilibrium is self-correcting. Let us now see how the process of automatic Equilibrium adjustment begins and where it ends.

NOTES

Fig. 7.13 Capital Market for Industry Y

7.4.2 Process of Automatic Adjustment We have noted that both wages and returns on capital increase in industry X and decrease in industry Y. This will cause factors (labour and capital) to move from industry Y to industry X. Consequently, in the long-run, factor supply to industry X would increase and to industry Y, it would decrease. The increase in supply of labour and capital to industry

X is shown by a rightward shift in the labour supply curve from SL1 to SL2 (Figure 7.7) and in capital supply curve from Sk1 to Sk2 (Figure 7.9). With increased supply of labour and capital to industry X, the supply of commodity

X increase causing supply curve to shift to Sx2 and new equilibrium is reached at point E3

(Figure 7.3). As shown in Figure 7.3, new equilibrium is gained at the original price OPx1 but at a greater output of X. In industry Y reverse happens. Since factors move out of industry Y, the factor supply to the industry is reduced as shown by downward shift in factor supply curves in Figures 7.11 and 7.13. Besides, since firms of this industry have a tendency to move out, industry’s production declines. Consequently, the market supply curve of commodity Y shifts backwards to Sy1. A new equilibrium is reached at point E2 at original price OPy1 (Figure 7.5) and level of output (OY3) falls much below the original output OY1.

Fig. 7.14 Demand for Capital by a Firm in Industry Y

Self-Instructional Material 191 Theory of General Thus, in the long-run, markets of both the commodities, X and Y, return to a stable Equilibrium equilibrium at the original price level, though at different levels of output: while output of X increases, that of Y decreases. An important point to be borne in mind is that new equilibrium is not necessarily gained at the original price. Whether new equilibrium is NOTES gained at original price or not depends on the extent of increase (decrease) in the supply of the commodity, i.e., the extent to which supply curve shifts forward (backward). The original equilibrium is regained only if supply of commodity increases (decreases) and supply curve shifts forward (backward) exactly to the extent of excess (shortfall) in demand. If shifts in the supply curve are greater or smaller than excess of deficit in demand, the new equilibrium price will be different from the original price. Once the commodity markets reach new equilibrium and stabilize, the inward and outward flows of factors ends. For example, as shown in Figures 7.3 and 7.4, industry X

and its firms are in equilibrium. Price is refixed at OPx1 at which all firms are earning only normal profits, since price = AC = MC = MR (Figure 7.4). There is no incentive for the existing firms to expand their output. Nor is there any incentive for new firms to enter the industry. Under these conditions, there is no incentive for the factors to move to this industry. This leads to saturation in the factor markets for industry X. It simultaneously stops the flow of resources out of industry Y. This leads to saturation in factor markets for both the industries. The new equilibria in labour and capital markets for industry X are presented in Figures 7.7 and 7.9. The labour supply curve for industry X finally shifts to and a

new equilibrium is set at point E3 (Figure 7.7). Similarly, the capital supply curve for

industry X shifts to Sk2 (Figure 7.9) and a new equilibrium is set in capital market for

industry X at original wage rate Or1. Thus, both labour and capital markets reach a new equilibrium. The new equilibria in labour and capital markets are presented in Figures 7.11 and 7.13. The labour supply curve for industry Y shifts backward to and a new equilibrium

is set at point E3 (Figure 7.11). As to capital market for industry Y, capital supply curve

shifts backward to Sk1 and new equilibrium is set at E3 at original rate of return, Or1. Thus, both factor markets for industry Y reach a new equilibrium, though at a much lower level of employment of both labour and capital. In industry Y labour employment

decreases from to and capital employment decreases from to . As in case of commodity markets, whether factor markets reach new equilibrium at the original level of factor prices or not depends on the extent to which factor supply curve shift forward (or backward). We may now sum up the above discussion. We started by assuming the whole system to be in equilibrium. The system was then assumed to be disturbed by an exogenous factor, i.e., change in consumer’s taste. This led to a chain of actions and reactions in commodity and factor markets. These actions and reactions led the system to stabilize at a new equilibrium. The attainment of new equilibrium is however certain only under Check Your Progress perfect competition and continuous production function with diminishing returns to scale. 5. How is the factor market described in The above illustration does not provide a formal proof of existence of a stable the Walrasian general equilibrium solution. It simply describes the tendency towards a general equilibrium model? under perfectly competitive conditions. 6. When is the original equilibrium regained?

Self-Instructional 192 Material Theory of General 7.5 COMPUTABLE GENERAL EQUILIBRIUM Equilibrium

Computable general equilibrium (CGE) models are a class of economic models that use real economic data to evaluate how an economy might react to changes in policy, NOTES technology or other external factors. CGE models are also referred to as AGE (applied general equilibrium) models. In mathematical economics, applied general equilibrium (AGE) models were established by Herbert Scarf at Yale University in 1967, in two papers, and a follow-up book with Terje Hansen in 1973, with the object of empirically assessing the Arrow– Debreu model of general equilibrium theory with empirical data, to provide ‘a general method for the explicit numerical solution of the neoclassical model’ (Scarf with Hansen 1973: 1). The model developed by Arrow-Debreu is a basic and fundamental model of general equilibrium in economics and finance. The model developed by Arrow-Debreu model has generalized the notion of commodity by differentiating the commodities on the basis of time and place of delivery. For example, ‘apples in Singapore in the month of June’ and ‘apples in Malaysia in the month of July’ are considered as two different commodities rather than one. Under given set of assumptions, the first thorough evidence of the subsistence of a market clearing equilibrium was propounded by Kenneth J. Arrow and Gerad Debreu (1951). The impact and significance of the model developed by Arrow and Debreu cannot be separated from that of mathematical economics. They both developed a chain of extraordinary papers (of which two papers were produced by Arrow and Debreu individually in 1951 and third one by Arrow-Debreu in 1954). The research done by both of them has great significance not only in the field of economic science but also for the financial markets, institutions and business across the world. Their model is frequently used in microeconomics as a model of general reference. The revolutionary work of Arrow and Debreu has had a continuing effect on the study of financial facets of the economy in a general equilibrium framework. The relevance of the model can be understood from the fact that fifteen years later since the birth of the model in 1969, it was still applicable and reinterpreted to yield new economic insights. And twenty years later, i.e., Debreu 1970, 1974, the same model was still competent in yielding fresh and fundamental properties in mathematics. The relevance of the model increased with the introduction of time and uncertainty in the general equilibrium models. Since 1950s, many researchers have extended the model developed by Arrow-Debreu in the field of economics in general and also in the field of financial economics. Despite the significance and relevance of their model in economics and finance, many eminent researchers have criticized their model. But the contribution of Arrow-Debreu model is everlasting in the history of economics. The Arrow-Debreu model is also known as Arrow-Debreu-McKenzie model (ADM model). This model is a fundamental model used in general (economic) equilibrium theory. The ADM model is named after Kenneth J. Arrow (b. 1921) and Gerard Debreu (1921-2004) on ‘existence of an equilibrium for a competitive economy’ as well as Lionel W. McKenzie (b. 1919) who are the originators of this model. As per Farlex Financial Dictionary (2009), this model is one of the most general models of competitive economy and is a crucial part of general equilibrium theory, as it can be used to prove the existence of general equilibrium (or Walrasian equilibrium) of an economy. Once we Self-Instructional Material 193 Theory of General can prove the existence of such an equilibrium, it is possible to show that it is unique Equilibrium under certain conditions, but not in general. Further, the model was extended by Arrow to deal with the issues relating to stability of equilibrium, uncertainty and efficiency of competitive equilibrium. NOTES 7.5.1 Arrow-Debreu Model and Polynomial Time Algorithm Given linear markets with a bounded number of divisible goods, there, in fact, is a polynomial time algorithm for finding equilibrium. There is a poly-time algorithm for computing a Є-Pareto curve in linear markets with indivisible commodities and a fixed number of agents. With a bounded number of goods, there is a poly-time algorithm which, for any linear indivisible market for which a price equilibrium exists, and for any Є>0, finds a Є- approximate equilibrium. The Arrow-Debreu model has great impact on economics and financial economics. The key applications of this model can be narrated as under: • It resolves the long-standing dilemma of proving the existence of equilibrium in a Walrasian (competitive) system. Their model has analyzed the exact situations of the most competitive markets. The model has suggested that under certain assumptions in economic conditions (like perfect competition and independence of demand), a given set of prices such as aggregate supplies will be equal to aggregate demand of every commodity. • If discussed on purely mathematical logics, the Arrow-Debreu model can be simply tailored into spatial or inter-temporal models with appropriate definition of the commodities based on the commodity’s location or time of delivery. • The Arrow-Debreu model can easily implement the conditions of expectations and uncertainty in itself to analyse commodities specific to the conditions of various states of the world. • Theoretically, the model can be applied and extended to the models used in financial economics, money markets, international trade and related subjects. • In general equilibrium structure, the Arrow-Debreu model can be applied in evaluating the overall effect on resource allocation of policy changes in areas such as taxation, tariff and price control. • In general, the model can be applied to all general equilibrium models which are dependent on mathematical accuracy and evidences. • In case of financial economics, this model represents a particular type of securities product which is known as Arrow-Debreu security. This tool is effectively used to understand the pricing and hedging related aspects in derivative analysis. • This model is also used in financial engineering. • But the model has limited application in multi-period or continuous markets. Despite the above implications of the model, it has been criticized for the assumptions on which it is based. Critics of the view that the model is not fit for the real economy. But economists in favour of this model say that the Arrow-Debreu framework is significant for derivative industry and can help in rapid growth of this industry.

Self-Instructional 194 Material 7.5.2 Arrow-Debreu Pricing: Equilibrium Theory of General Equilibrium The Arrow-Debreu pricing and equilibrium has been discussed in the following six sections: • Arrow-Debreu vs CAPM NOTES • Arrow-Debreu economy • Optimal risk sharing • Competitive equilibrium and Pareto optimum • Euler equations • Equilibrium and no-arbitrage 1. Arrow-Debreu equilibrium The modern portfolio theory and (MPT) and capital asset pricing model (CAPM) are considered the two basic models for asset pricing and analysis. These models are generally accepted the way the pricing of risk and cash flows are considered under it. Markowitz, Lintner, Sharpe and Mossin considered σ2 on horizontal axis and µ on vertical axis. By considering these two parameters, the results obtained in portfolio management and asset pricing were found more progressive. But the generalization of these results became a complicated task. For this, the returns must show a quadratic utility of normal distribution pattern.

T=M P *

CML rf e t a t S

d a B

e h t

n i

n o i t p m u s n o C

Consumption in the Good State

Fig. 7.15 Arrow-Debreu Equilibrium Self-Instructional Material 195 Theory of General Arrow and Debreu considered the consumption of good state on horizontal axis and Equilibrium consumption in bad state on vertical axis. Arrow-Debreu model does not require a restrictive assumption of capital asset pricing model. But their model is considered for the generalized results provided by it. The benefits of considering Arrow-Debreu model NOTES of asset pricing are: • There is no need of returns to be normally distributed. • The investors need not have a quadratic utility function. • Their model also draws explicit linkage between asset pricing and rest of the economy. But both the models are considered significant in asset pricing. 2. Arrow-Debreu economy The key features of Arrow-Debreu economy are: (i) There are two dates: t = 0 (today, when assets are purchases) and t =1 (the future, when payoffs are received). This can be generalized. π (ii) There are N possible states at t =1, with probability i, where I = 1, 2, …..N. (iii) There is one perishable good at each date. The more goods can be added and the possibility of storage can be introduced at the cost of more notional complexity. (iv) At the initial stage, individuals receive goods as endowments. Again at a cost of notational complexity, production can be introduced. (v) Different investors (K investors, j = 1,2,…K) may have different preferences and endowments. Let 0 w j = agent j ‘s endowment at t = 0 i w j = agent j ‘s endowment in state i at t = 1 0 c j = agent j ‘s consumption at t = 0 i c j = agent j ‘s consumption in state i at t = 1 The consumption at t = 0 is used as the ‘numeraire,’ that is, the good in terms of which all other prices are quoted. Let qi be the price at t = 0, measured in units of t = 0 consumption, of a contingent claim that pays off one unit of consumption in a particular state i at t = 1 and zero otherwise. For further simplicity, let’s assume that each investor first uses the contingent claims market to sell off his or her endowments at t = 0 and in each state at t = 1, then uses the same markets to buy back consumption at t = 0 and in each state at t = 1. Then we would not need additional notation to keep track of purchases and sales of contingent claims: purchases coincide with consumption and sales with endowments. Therefore, investor j in A-D economy faces the constraint of budget. NN 00i i ii wj+∑∑ q w jj ≥+ c qc j ii=11= Note that in Arrow-Debreu economy one can always go back and compute net sales:

00 ii wcjj− and wcjj− for all i = 1, 2, ..., N

Self-Instructional 196 Material or purchases Theory of General Equilibrium 00 ii cwjj− and cwjj− for all i = 1, 2, ..., N of contingent claims if these turn out to be of interest. But if the assumption of investors having different utility functions is withdrawn NOTES from the model, then more sharper results can be obtained. In that case, the investors will be assumed to have a utility function of maximizing vN-M expected utility. But they are allowed to have a different Bernoulli utility function which says that possibly different investors have different attitude towards risk. 0 i So, the investor j opts c j and c j for all i = 1; 2; : : : ; N in order to maximize:

N 00i ucjj()+β Euc [()] jj = uc jj () +β∑ π ijj uc () i=1 In the above, the discount factor β is a measure of patience subject to constraint of budget.

NN 00i i ii wj+∑∑ qw jj ≥+ c qc j ii=11= It is worth noting that the mathematical structure of the investors’ problem is identical to the problem faced by consumers who must divide their income into amounts to be spent on oranges, apples and banana. If the model is expanded and more than two periods are included, then obviously more notions are required. But conceptually and mathematically this expansion will include only the inclusion of more goods, i.e., mangoes and pears. In Arrow-Debreu economy the investors take the prices because of existence of perfectly competitive market. And the investor is able to purchase as little of each good at the prevailing competitive prices. But in microeconomics, in a more general way, all markets must clear that the quantity demanded for a good is equal to quantity supplies. Therefore, in Arrow-Debreu economy, market clearing calls for:

KK 00 ∑∑wcjj= jj=11= And

KK ii ∑∑wcjj= jj=11 = For all i = 1, 2, …. N. These conditions simultaneously explain the equilibrium in the market for goods and contingent claims as well. Thus, a competitive equilibrium in an Arrow-Debreu economy consists of a set of 0 i consumptions c j for all j = 1; 2; : : : ; K and c j for all i = 1; 2; : : : ; N and j = 1; 2; : : : ; K and a set of prices qi i = 1; 2; : : : ; N such that, all markets are clear and at given prices; each investor’s consumption maximizes the utility considering the budget constraints. 3. Optimal risk sharing This approach is used to understand how investors can share risk optimally while keeping in mind that the competitive-equilibrium model of Arrow-Debreu economy will use financial markets to do this. Imagine that the economy consists of two types of investors

Self-Instructional Material 197 Theory of General (type 1 and type 2, in equal numbers). Suppose, there are only two possible states at t=1: Equilibrium state 1 which occurs with probability π1, and state 2 which occurs with a probability of

π2 = 1– π1 The aggregate endowments are w0 at t = 0 , w1 in state 1 at t = 1, and w2 in state NOTES 2 at t = 1. The two agent types have expected utility but they may differ in their Bernoulli utility functions and hence in terms of risk aversion:

0 12 ucjj()+β [ π12 uc jj () +π uc jj ()]

0011 2 2 The social planner chooses ccccc121,,,, 21 and c2 to maximize

θ0 +β π 12 +π {uc11( )  111 uc( ) 211 uc( ) } + −θ0 +β π 12 +π ()1 {}uc22() 122 uc () 222 uc ()

Subject to the aggregate resource constraints

000 wcc≥+12 111 wcc≥+12 222 wcc≥+12

4. Competitive equilibrium and pareto optimum

0 i The first requirement for a competitive equilibrium is investor j opts c j and c j for all i = 1, 2, 3…….N to maximize,

N 0 i ucj() j +β∑ πij u () c j i=1 Subject to constraints of budget,

NN 0ii 01i wj+∑∑ qw jj ≥+ c qc j ii=11= The Lagrangian for the investor’s problem,

N NB 0 i 00i i ii ucj() j +β∑ πij uc () j +λ j w j + ∑∑ qwcj − j − qcj i=1 ii=11= It leads to the first order conditions, ′ 0 ucjj( ) −λ j =0

′ ii βπijuc( j) − λ j q = 0 for all i =1, 2, ..., N

′ 0 ucjj( ) −λ j =0

′ ii βπijuc( j) − λ j q = 0 for all i =1, 2, ..., N It implies,

′′ii0 βπijjuc( ) = ucq jj( ) for all i = 1, 2, ..., N

Self-Instructional 198 Material Or Theory of General Equilibrium ′ i βπijuc( j) qi = ′ 0 for all i = 1, 2, ..., N ucjj() NOTES As an actor of the economy, the investor takes the price qi as given and uses it to 0 i choose c j and c j optimally. But as an observer, this condition of optimality can be used 0 i to see what the investors’ choices of c j and c j explain about the contingent claim price qi and by extension regarding asset prices in a broader sense.

′ i βπijuc( j) qi = ′ 0 for all i = 1, 2, ..., N ucjj() The price qi tends to be higher when: 1. β is larger, indicating that investors are more patient π 2. i is larger, indicating that state i is more likely

′ i ′ 0 3. ucjj()is larger or ucjj() is smaller

′ i βπijuc( j) qi = ′ 0 for all i = 1, 2, ..., N ucjj() tends to be higher when N is larger or is smaller.

If uj is concave, that is, if investor j is risk averse, then a larger value of it i corresponds to a smaller value of c j and a smaller value of corresponds to a larger value 0 of c j .

′ i βπijuc( j) qi = ′ 0 for all i = 1, 2, ..., N ucjj()

′ i ′ 0 i tends to be higher when ucjj()is larger or ucjj()is smaller. That is q is higher if investor j′s consumption falls between t = 0 and state i at t = 1. The same condition must be taken as it is for all investors in the economy. Hence, qi is higher if everyone expects consumption to fall in state i .

′ i βπijuc( j) qi = ′ 0 for all i = 1, 2, ..., N ucjj() During recession when consumption by all is expected to fall. Hence, the A-D model associates a high contingent claim price qi with a recession, drawing an explicit link between asset prices and the rest of the economy that is, at best, implicit in the CAPM. 5. Euler equations Before moving on, it will be useful to use a no-arbitrage argument to derive an equation that will lie at the heart of the CCAPM. Consider an asset that, unlike a contingent claim, delivers payoffs in all N states of the world at t = 1. Let  denote the random pay-offs as it appears to investors at t = 0, and let Xi denote more specifically the payoffs made in each state i = 1; 2; : : : ; N at t = 1.

Self-Instructional Material 199 Theory of General X1 Equilibrium

X2 NOTES

X3

PA = ?

X4

X5 t =0 t = 1  The random payoffs equals Xi in each state i = 1; 2; 3; 4; 5. The payoffs from this asset can be replicated by purchasing a bundle of contingent claims:

X1 contingent claims for state 1

X2 contingent claims for state 2 : : :

XN contingent claims for state N The payoffs from this asset can be replicated by purchasing a bundle of contingent claims: 1 X1 contingent claims for state 1 at cost q X1 2 X2 contingent claims for state 2 at cost q X2 : : : N XN contingent claims for state N at cost q XN A no-arbitrage argument implies that the price of the asset must equal the price of all the contingent claims in the equivalent bundle. • If the price of the asset was less than the price of the bundle of contingent claims, investors could profit by buying the asset and selling the bundle of claims. • If the price of the bundle of contingent claims was less than the price of the asset, investors could profit by buying the bundle of claims and selling the asset. Hence, the asset price must be:

N A12 Ni P=++ q X12 qX... q XNi =∑ qX i=1 In an A-D equilibrium, however,

′ i βπijuc( j) qi = ′ 0 for all i = 1, 2, ..., N ucjj()

Self-Instructional 200 Material must hold for all j = 1; 2; : : : ;K Theory of General Equilibrium Substitute the A-D equilibrium conditions:

′ i βπijuc( j) qi = ′ 0 for all i = 1, 2, ..., N NOTES ucjj()

into the no-arbitrage pricing condition:

N Ai P= ∑ qXi i=1

N βπ uc′ ()i = ij j ∑′ 0 X i i=1 ucjj()

N βπ uc′ ()i = ij j PXAi∑′ o i=1 ucjj() Implies,

N ′′0 i ucPjjA()=βπ∑ ijj uc () X i i=1 Or, using definition of expected value:

′′0 = β  ucPjjA() EucX jj () 6. Equilibrium and No-arbitrage The Arrow-Debreu model is known as an explicit equilibrium model of asset prices. Through the equilibrium condition:

βπ uc′ ()i i = ij j q ′ 0 ucjj() Which must hold for all states I =1, 2, ……, N and all investors j = 1, 2, …..K. The Arrow-Debreu model links asset prices to aggregate, undiversifiable risk in the economy as a whole. The generality of Arrow-Debreu model is both a strength as well as a weakness. The strength of this is that it makes no specific assumptions about the preferences or distribution of asset returns. The weakness is that it seems difficult to apply in on the products of financial markets, viz., stocks, bond, and options. 7.5.3 General Equilibrium under Uncertainty In general equilibrium theory, the ‘allocation’ of a given quantity of each commodity implies its final consumption with its corresponding utility score under uncertainty. The final consumption of a given allocation will depend on the state of nature in such a way that equal quantities of the same commodity could produce different utility scores. Consider an economy with 2 consumers and 1 consumption good. There are 2 periods, t = 0 (today) and t = 1 (tomorrow). The agents do not know the state of the

Self-Instructional Material 201 Theory of General world at t = 1. To simplify, we will assume that there are two possible states (alternatives), Equilibrium e = e1, e2. The probabilities of each state are:

p(e1) = , p(e2) = 1 – NOTES We consider that there is a unique good in the economy that may be consumed only at t = 1 (that is, there is no consumption at t = 0.) Let us use the following notation: s s X i is the amount of the good that agent i consumes in state e . s s w i are the initial endowments that agent i has in state e .

sss wwws=12 =, = 1, 2. The utility functions of agents are as follows:

12 1 2 uj( x i, x i) =π ux ii ( ) + (1 −π ) uxii ( ) i = 1, 2 i.e., the agents maximizes the utility

t =1

Agent 1 Agent 2 Agent 1 Agent 2

1 1 1 1 w2 e1 w1 x1 x2 t = 0 2 2 2 2 e2 w1 w2 x1 x2

1 1 = 1 = 1 1 w1 + w2 w x1 + x2

2 2 w2 2 x 2 w1 + w2 ==x1 + 2 This situation can also be presented using Edgeworth’s Box. In economics, an Edgeworth box is named after Francis Ysidro Edgeworth, who was an Anglo-Irish philosopher and political economist. It is a way of representing various distributions of resources.

2 x 1

( 1 1 w2 + 2 w 1 + w 2, 1 w 2 )

2 x 2

2 x 1

1 x 1 1 1 x 1 x 2

Self-Instructional Fig. 7.16 Edgeworth Box 202 Material Criticisms of General Equilibrium Theory Theory of General Equilibrium The general equilibrium theory of economic welfare has been criticized on the following grounds: • It is less applicable to real world problems. This is the reason that it has been NOTES called as the celestial mechanics of a non-existent world. • The major limitation of multiple equlibria of general equilibrium theory has been resolved only by Arrow and Debreu. • The use of the concept of ‘tatonnment’ is also another limitation of general equilibrium theory. According to it an auctioneer: (i) Processes all bids and offers (ii) Determines which prices that clear all markets (iii) Then allows trades • No empirical evidences are provided by this theory.

7.6 SUMMARY

In this unit, you have learnt that: • A fundamental feature of an economic system is the interdependence and interrelatedness of economic activities—production and consumption—of its various constituents—individuals, households, firms, banks and other kinds of financial institutions. • Partial equilibrium approach ignores the interdependence of the various segments of the economy. It isolates the segment or the phenomenon of the study from the other segments and assumes non-existence of influences of the changes occurring outside the area delimited for the study. • The general equilibrium approach, on the other hand, recognizes the interdependence of constituent parts of the economic system. It recognizes the Check Your Progress interrelations and interdependence of economic variables and seeks to answer the question how all the segments of the economy reach an equilibrium position 7. Fill in the blanks with appropriate simultaneously. words. • The task of general equilibrium theory is to find out whether there exists a general (i) The Arrow- equilibrium in an economy. Debreu model has great impact • A general equilibrium is defined as a state in which all economic units maximize on economics their respective objective function and all prices are simultaneously in equilibrium, and and all markets are cleared. ______. (ii) The Arrow- • If number of equations and the number of ‘unknowns’ are equal, it may sometimes Debreu model is make one think that there exists a general equilibrium solution. But, the equality of known as an number of equations with that of unknowns is neither a sufficient nor a necessary ______model of asset condition for the existence of a general equilibrium solution. prices. • The uniqueness of general equilibrium solution requires that, at all partial equilibrium 8. Mention one levels, demand and supply schedules intersect at only one point giving a positive limitation of general equilibrium theory. price. 9. What is an • Walras was the first to recognize and formalize the mutual interdependence of Edgeworth’s box? various prices and quantities in an economic system. Although it is widely known Self-Instructional Material 203 Theory of General that in economics, everything depends on everything else, the full implications of Equilibrium this generalisation were not grasped before Walras. • In the Walrasian system of general equilibrium, the behaviour of each decision- maker is presented by a set of equations. Since each decision-maker functions NOTES simultaneously in two different capacities—as a buyer and as a seller, his behavioural equations consists of two subsets of equations. • Factor market is described, in Walrasian model, by two sets of equations—one each on demand and supply sides. • An important point to be borne in mind is that new equilibrium is not necessarily gained at the original price. Whether new equilibrium is gained at original price or not depends on the extent of increase (decrease) in the supply of the commodity, i.e., the extent to which supply curve shifts forward (backward). • The original equilibrium is regained only if supply of commodity increases (decreases) and supply curve shifts forward (backward) exactly to the extent of excess (shortfall) in demand. • As in case of commodity markets, whether factor markets reach new equilibrium at the original level of factor prices or not depends on the extent to which factor supply curve shift forward (or backward). • Given linear markets with a bounded number of divisible goods, there, in fact, is a polynomial time algorithm for finding equilibrium. • The Arrow-Debreu model has great impact on economics and financial economics. • The Arrow-Debreu model can easily implement the conditions of expectations and uncertainty in itself to analyse commodities specific to the conditions of various states of the world. • In general equilibrium structure, the Arrow-Debreu model can be applied in evaluating the overall effect on resource allocation of policy changes in areas such as taxation, tariff and price control. • The modern portfolio theory and (MPT) and Capital Asset Pricing Model (CAPM) are considered two basic models for asset pricing and analysis. These models are generally accepted the way the pricing of risk and cash flows are considered under it. • The Arrow-Debreu model is known as an explicit equilibrium model of asset prices. • In general equilibrium theory, the ‘allocation’ of a given quantity of each commodity implies its final consumption with its corresponding utility score under uncertainty. The final consumption of a given allocation will depend on the state of nature in such a way that equal quantities of the same commodity could produce different utility scores.

7.7 KEY TERMS

• General equilibrium: It is defined as a state in which all economic units maximize their respective objective function and all prices are simultaneously in equilibrium, and all markets are cleared.

Self-Instructional 204 Material • Numeraire: It is an item or commodity acting as a measure of value or as a Theory of General standard for currency exchange. Equilibrium

7.8 ANSWERS TO ‘CHECK YOUR PROGRESS’ NOTES

1. The working mechanism of economic system is unimaginably complex. It is not possible to trace the behaviour of each economic element and its interaction with the rest of the economy and trace equilibrium of each and every element of the economy. The economists, therefore, adopt two kinds of approaches to economic analysis: (i) partial equilibrium approach, and (ii) general equilibrium approach. 2. The task of general equilibrium theory is to find out whether there exists a general equilibrium in an economy. 3. The uniqueness of general equilibrium solution requires that at all partial equilibrium levels, demand and supply schedules intersect at only one point giving a positive price. 4. Walras was the first to recognize and formalize the mutual interdependence of various prices and quantities in an economic system. Although it is widely known that in economics or every-thing depends on everything else, the full implications of this generalisation were not grasped before Walras. 5. Factor market is described in Walrasian model by two sets of equations—one each on demand and supply sides. 6. The original equilibrium is regained only if supply of commodity increases (decreases) and supply curve shifts forward (backward) exactly to the extent of excess (shortfall) in demand. 7. (i) Financial economics (ii) Explicit equilibrium 8. The use of the concept of ‘tatonnment’ is a limitation of general equilibrium theory. 9. The Edgeworth’s box is a way of representing various distributions of resources.

7.9 QUESTIONS AND EXERCISES

Short-Answer Questions 1. What are the limitations of partial equilibrium analysis? 2. Distinguish between general and partial equilibrium analysis. 3. Define general equilibrium. 4. Does general equilibrium analysis offer a unique solution of price and output determination? 5. What are the conditions for the stable general equilibrium solution? 6. Outline the general equilibrium approach to economic studies. 7. State the conditions for the existence, stability and uniqueness of a general equilibrium in an economy with two factors, two commodities and two consumers. 8. What are the conditions for the stability of the Walrasian general equilibrium? Do such conditions exist in reality? Self-Instructional Material 205 Theory of General 9. What is the process of automatic adjustment? Equilibrium 10. What are the key features of Arrow-Debreu economy? 11. Briefly state the Arrow-Debreu economy. NOTES 12. State some of the criticisms of general equilibrium theory. Long-Answer Questions 1. Assess the principles of general equilibrium. 2. Discuss the existence, uniqueness and stability of a general equilibrium. 3. Critically analyse the Walrasian approach to general equilibrium. 4. Discuss Walrasian approach to general equilibrium assuming a two-commodity- two-consumer-two firms-two inputs model. Illustrate graphically how economic system reaches the general equilibrium position. 5. Evaluate the process of automatic adjustment. 6. Explain the Arrow-Debreu model. 7. Discuss the impacts of Arrow-Debreu model on economics and financial economics. 8. What does the theory of general equilibrium under uncertainty state?

7.10 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional 206 Material Welfare Economics UNIT 8 WELFARE ECONOMICS

Structure NOTES 8.0 Introduction 8.1 Unit Objectives 8.2 Meaning and Nature of Welfare Economics 8.2.1 Nature of Welfare Economics 8.3 Pareto Optimality 8.3.1 Pareto’s Welfare Economics 8.3.2 Criticism of Pareto Optimality 8.4 Pareto Optimality Conditions: Consumption, Production and Exchange 8.4.1 Pareto Optimality under Perfect Competition 8.4.2 Externalities and Pareto Optimality 8.4.3 Indivisibilities and Pareto Optimality 8.5 Compensation Tests 8.5.1 Kaldor-Hicks’ Compensation Criterion 8.5.2 Scitovsky’s Double-Criterion 8.5.3 Little’s Criterion 8.6 Social Welfare Function 8.7 Arrow’s Impossibility Theorem 8.8 Summary 8.9 Key Terms 8.10 Answers to ‘Check Your Progress’ 8.11 Questions and Exercises 8.12 Further Reading

8.0 INTRODUCTION

Economics has both positive and normative character. We have so far been concerned with the positive aspects of economies, especially microeconomics. Our main concern was optimum allocation of resources at micro levels, i.e., how individual consumers and firms maximize their objective functions—consumers their utility function and firms their profit function. From the analysis of these aspects of economic theory, it may appear that if all individual firms optimize their resource allocation with a view to maximizing their profit function, the total output of goods and services available to the society will be maximum. And, when all individual consumers optimize their resource allocation to maximize their utility function, the total utility enjoyed by the society as a whole will be maximum. In other words, if both firms and consumers maximize their respective objective functions, the total economic welfare of the society will be maximum. This, however, may not be true because private and public interests can and do conflict. Therefore, optimization of resource allocation from an individual’s point of view may not conform to the tests of optimum allocation of resources from society’s point of view. Positive microeconomics leaves unanswered many economic problems regarding maximization of social welfare. Nor does it suggest appropriate policy measures that can maximize the economic well-being of the society as a whole. The branch of economic analysis which is concerned with these problems is called welfare economics. In this unit, we will discuss analytical apparatus of welfare economics including concept of welfare economics, Pareto optimality, compensation tests, social welfare function and Arrow’s impossibility theorem. Self-Instructional Material 207 Welfare Economics 8.1 UNIT OBJECTIVES

After going through this unit, you will be able to: NOTES • Discuss the meaning and nature of welfare economics • Explain the concept of Pareto optimality • Assess the Pareto optimality conditions • Evaluate the Pareto optimality under perfect competition • Describe Kaldor, Hicks, Scitovsky and Little’s compensation tests for ordering states • Analyse Bergson’s social welfare function • Discuss Arrow’s impossibility theorem

8.2 MEANING AND NATURE OF WELFARE ECONOMICS

As regards the origin of welfare economics, it is very difficult to point out the period in the history of economic thoughts which marks the beginning of welfare economics. Nor is it reasonable to associate the emergence of welfare economics with any particular economist, because E. J. Mishan points out that ‘welfare economics does not appear at any time to have wholly engaged the labours of any one economist’. Some believe that Pigou’s Wealth and Welfare and his later work Economics of Welfare mark the emergence of welfare economics as a separate branch of economics. But Hla Myint has pointed out, in his Theories of Welfare Economics, that the classical economist had a great deal to say on a subject which could reasonably be brought within the compass of welfare economics. Many textbooks, however, commence discussion on welfare economics with Pareto. Welfare economics is the study of economic welfare of the members of a society as a group. In the words of Oscar Lange, ‘Welfare economics is concerned with the conditions which determine the total economic welfare of a community.’ Reder defines ‘welfare economics’ as that ‘branch of economics science that attempts to establish and apply the criteria of propriety to economic policies.’ In his survey of welfare economics, Mishan defines ‘theoretical welfare economics’ as ‘that branch of study which endeavours to formulate propositions by which we may rank on the scale of better and worse, alternative economic situations open to society’. The function of welfare economics is to evaluate the alternative economic situations and determine whether one economic situation yields greater economic welfare than others. Welfare economics may also be defined as that branch of economic science which evaluates alternative economic situations (i.e., alternative patterns of resource allocations) from the viewpoint of economic well-being of the society as a whole. 8.2.1 Nature of Welfare Economics Economists hold different views on the question whether welfare economics is a positive (pure) or normative (applied) science. Although welfare economics has been closely associated with positive economics from the inception of economic thinking, ‘at one point in economic thought, it was felt that welfare economics was unscientific; that it Self-Instructional 208 Material was normative and was hence a branch of ethics. . . .’ (M. W. Reder, Studies in the Welfare Economics Theory of Welfare Economics). It was also argued that welfare economics is concerned with ‘what ought to be’ and, hence, it is ‘normative’ in character. This view, however, has not been universally held. Pigou, for example, was concerned, in his Economics of Welfare, with the causes of economic welfare and did not make any policy NOTES recommendation. Pigou’s Economics of Welfare is, therefore, a positive study. A widely held view on this issue is that welfare economics is both a positive and a normative science. Positive economics is primarily concerned with understanding, explaining and predicting the working of the economic system. Welfare economics is a positive science insofar as it attempts to explain and predict the outcome of the functioning of the economic system. Welfare propositions ‘may be subjected to test in the same way as those of positive economics,’ though testing welfare propositions is much more difficult than the propositions of general positive economics. The information gained through positive analysis is useful in devising appropriate policy measures to maximize the welfare of the society. The task of normative economics is to determine ‘what ought to be’. Welfare economics is a normative science in that it provides guidelines for policy formulations to maximize social welfare. Maximization of economic welfare presumes a welfare function which consists essentially of value judgements. Given the welfare function, welfare economics, as a normative science, provides guidelines for appropriate policy measures.

8.3 PARETO OPTIMALITY

It was Vilfred Pareto, an Italian economist, who broke away from the cardinal utility tradition and gave a new orientation to welfare economics. He rejected cardinal utility concept and additive utility function on the ground of their limitations mentioned above. With the rejection of cardinal utility thesis, the attempts to quantify the social welfare ended, at least temporarily, perhaps because welfare is not an observable quantity like a market price or an item of personal consumption. Pareto introduced a new concept, i.e., the concept of social optimum. This concept is central to Paretian welfare economics. The basic idea behind this concept is that while it is not possible to add up utilities of individuals to arrive at the total social welfare, it is possible to determine whether social welfare is optimum. Conceptually, social welfare is said to be optimum when nobody can be made better-off without making somebody worse-off. In the words of Boulding, ‘A social optimum is defined as a situation in which nobody can move to a position which he prefer without moving somebody else to a position which is less preferred.’ The basic point in regard to the concept of social optimum which need to be noted is that social optimum does not define (or determine) a quantity or magnitude of welfare. It is rather associated with the question whether the magnitude of social welfare from a given economic situation can be or cannot be increased by changing the economic situation. Check Your Progress The test of increase in social welfare is that at least one person should be made better- 1. Define welfare off without making anybody else worse-off. economics. 2. Why is welfare However, it is difficult to conceive economic policies which can improve the economics welfare of an individual without injuring another. To overcome this problem, the considered to be a economists, viz., Kaldor, Hicks and Scitovsky, have evolved the compensation principle. positive science?

Self-Instructional Material 209 Welfare Economics This principle states that the person who benefits from an economic policy or reorganization must be able to compensate the person who becomes worse-off due to this policy and yet remain better-off. Modern welfare economics does not attempt to quantify the total social welfare. NOTES It concerns itself with only the indicators of change in welfare. It analyses whether total welfare increases or decreases when there is a change in economic situation. This approach is based on the premise that while cardinal measurement of utility is not possible, expression of utility in ordinal sense is possible and it is an adequate guide to change in the welfare of an individual. It is this principle on which the modern welfare criteria are based. Having introduced the welfare economics and the concept of economic welfare, let us now discuss various theories of welfare and welfare criteria devised by welfare economists. 8.3.1 Pareto’s Welfare Economics Pareto’s Manual of Political Economy (1906) represents a decisive watershed in the history of subjective welfare economics. Pareto broke away from the traditional utilitarian economics. He rejected the hypothesis based on cardinal utility and also the additive utility function, and arrived at his welfare conclusions which do not require any interpersonal comparison whatever. Some have, therefore, called Pareto’s welfare economics as new welfare economics. Pareto Optimum Pareto optimum is also called as Pareto efficiency, Pareto unanimity rule, Pareto criteria, and Social optimum. Pareto optimum is defined as a position from which it is not possible to improve welfare of any one by any reallocation of factors or of goods and services without impairing the welfare of someone else. In other words, a Paretian optimum position is attained when it is not possible, through any reallocation of resources or reorganization of economy, to make anyone better-off in the sense of putting him on a higher indifference curve without making someone worse-off in the sense of making him go down on a lower indifference curve on the scale of his preference. From the concept of Pareto optimum, is derived Pareto Criterion of welfare. According to Pareto criterion, any change that makes at least one person better-off without making someone else worse-off definitely causes an improvement in social welfare. Conversely, any change that makes at least one person worse-off and no one better-off causes decrease in social welfare. 8.3.2 Criticism of Pareto Optimality The Paretian concept of ‘social optimum’ is definitely an improvement over cardinal utility approach, in that it is, as is claimed, free from the problems of additive utility function and interpersonal comparison of utility. The concept has however been criticized on the following grounds. First, Pareto’s optimum does not define a unique optimum economic situation. As Winch has pointed out, ‘There are three aspects of optimum performance of an economic system, associated respectively with the three basic functions—the transformation function, the utility function and the welfare function. The unique optimum economic situation requires perfect performance in all the three respects, but the term Paretian

Self-Instructional 210 Material Optimum has come to mean the simultaneous fulfillment of the first two functions Welfare Economics regardless of the third.’ There are therefore an infinite number of Paretian optima that satisfy the optimality conditions. The Paretian optimum, however, does not determine the optimum optimorum—the best of the best. In fact, each Paretian optimum (as defined above) is sub-optimum. It is, therefore, quite likely that an optimum situation NOTES which corresponds to a bad distribution of income may be worse than a sub-optimum position corresponding to a good distribution of income. That is, a situation in which Pareto optimality conditions are fulfilled may well be inferior to a number of other situations in which they are not fulfilled. Second, it follows from the above that Pareto optimum does not guarantee the maximization of social welfare. Any point on production possibility curve, given the factor prices and technology, may satisfy Paretian efficiency in production. But, as we will show later, all points do not represent the maximum social welfare. Thus, Pereto optimum, as it is defined, offers only necessary but, not sufficient condition of welfare maximization. Third, Pareto optimum raises the question of payment of compensation because it is difficult to imagine an economic change that benefits at least one person without harming another. If interpersonal comparisons are rejected, then we cannot say whether gains of the person who benefit from the change is greater than or equal to or less than the loss of the person who suffers from the change. It may thus be said that Pareto optimum does not offer a measure to evaluate the change that makes some persons better-off and some others worse-off.

8.4 PARETO OPTIMALITY CONDITIONS: CONSUMPTION, PRODUCTION AND EXCHANGE

Having described the concept by Pareto optimum and its weaknesses, we discuss, in this section, the first order conditions that must be satisfied to attain the maximum social welfare in accordance with Pareto optimality. Hicks calls these conditions marginal conditions of maximum welfare. The marginal conditions of Pareto optimality or Pareto efficiency have been set out by Hicks, Lerner and Lange. The marginal conditions of maximum welfare have been derived directly from the definition of maximum welfare. As mentioned above, maximum social welfare is achieved when it is impossible to make any one better-off, by reallocating resources, without making someone else worse-off. Achieving maximum social welfare in this Check Your Progress sense is possible only when allocation of productive factors between the various 3. Name the economist commodities, allocation of commodities between the consumers, and allocation of who broke away productive factors between the different firms are all optimum. Pareto optimality is, from the cardinal therefore, also called as allocative efficiency. utility tradition and gave a new First order conditions: We now turn to explain the marginal conditions or the first orientation to order conditions of Pareto optimality in welfare maximization under the following welfare economics. categories: 4. What is the basic idea behind the • Pareto optimality in exchange, i.e., optimum allocation of products among the concept of social consumers optimum? 5. Define Pareto • Pareto optimality in production, i.e., optimum allocation of input and output optimum. among the firms

Self-Instructional Material 211 Welfare Economics • General optimality of production and exchange, i.e., simultaneous fulfillment of production and exchange optimality conditions • Other optimality conditions of welfare maximization NOTES Assumption of Paretian Model Before we explain the marginal conditions of welfare maximization, let us set out the necessary assumptions which are usually made for the fulfilment of marginal conditions. 1. We assume a model of two commodities (X and Y), two consumers (A and B),

two inputs (capital, K and labour, L) and two firms (F1 and F2), respectively. 2. Consumers maximize their respective utility functions which are independent of each other. 3. Inputs, K and L, are homogeneous, perfectly divisible, and available in fixed quantities which are exogenously determined. Both inputs are used in the production function of both the goods. 4. Production functions for both goods are given. 5. There is perfect competition in both product and factors markets. 1. Pareto optimality condition of exchange Pareto optimality in exchange is achieved when allocation of commodities among the consumers is such that it is not possible to increase the satisfaction of any person without reducing the satisfaction of someone else. The marginal condition that must be fulfilled to achieve Pareto optimality (or efficiency) in exchange requires that marginal rate of substitution between any two products must be the same for every consumer of both the products. This marginality condition, with reference to two-commodity and two-consumer model, may be expressed as: A B MRS x,y = MRS x,y It means that the ratio of the marginal utilities of any two products must be the same for every consumer. In a situation in which this condition is not fulfilled, it will always be possible to increase the total welfare by transferring some units of a good from a person who derives a lower utility to the person who derives a greater utility. The Pareto optimum allocation of goods among the consumers is illustrated by using Edgeworth box diagram, as presented in Figure 8.1 assuming that there are only

two consumers, A and B, and only two commodities X and Y. In Figure 8.1, OA is the point

of origin for consumer A and point OB for consumer B. The length of the horizontal axis

of the diagram, OAM = OBN represents the total quantity of commodity X available to

consumers A and B, and the length of the vertical axis, OAN = OBM shows the total

quantity of commodity Y. Indifference curves A1 to A5 represent A’s scale of preference ′ and B1 to B5 represent B’s scale of preference. The Edgeworth contract curve CC , represents the points on indifference map that satisfy the Pareto optimality condition of exchange. Every point on the CC′ curve satisfies the marginality condition, that is, A B MRS x,y = MRS x,y Distribution of goods, X and Y, between consumers A and B represented by any other point is inefficient. Therefore, movement towards a point on contract curve improves the satisfaction level of either both the consumers or of at least one consumer without

Self-Instructional 212 Material affecting the satisfaction of the other. For example, suppose both the consumers are at Welfare Economics point J. Movement along the curve JK increases the satisfaction of A as he moves to an upper indifference curve from A2 to A3 while B remains on the same indifference curve,

B3. Similarly, movement from point J towards L increases the satisfaction of B, without affecting A’s satisfaction. Any point in the shaded area, say H, indicates the increase in NOTES the satisfaction of both, A and B, as both move onto their upper indifference curves. Thus, movement towards the contract curve from any other point shows the improvement in the total welfare. Since contract curve is formed by joining the points of tangency of indifference curves of consumers A and B, and at each point of tangency marginal rates of substitution (MRSx,y) between the two goods, X and Y, is the same for both the consumers, each point on the contract curve satisfies the Pareto optimality condition of exchange.

Fig. 8.1 Edgeworth Box Diagram: Efficiency in Exchange

The following inferences can be drawn from the information contained in Figure 8.1. 1. Since there are infinite points on the contract curve CC′ that satisfy the optimality condition, there are infinite Pareto optima. 2. It is not possible to conclude that every Pareto optimum solution indicates greater social welfare than that indicated by every non-optimal point. For example, we cannot compare optimal point K with non-optimal point H because while A will prefer optimal point K, B will prefer a non-optimal point, H. Thus without an explicit interpersonal comparison of utilities it will not be possible to judge which of the two points (K or H) is socially optimal. 3. An upward movement on the contract curve makes A better off and B worse off. Similarly, a downward movement makes B better off and makes A worse off. Therefore, it cannot be said that every point on the CC′ curve represents optimum optimorum. 2. Pareto optimality in production: Optimum allocation of productive factors The second marginal condition of Pareto optimality is related to optimal allocation of factors (L and K) between the products (X and Y). Pareto optimality in factor allocation requires that factors are so allocated between goods X and Y that it is not possible to increase the output of any commodity by reallocating the factors, without causing decrease in the production of another. The marginal condition that must be fulfilled to achieve Pareto optimality in resource allocation is that marginal rate of technical substitution

Self-Instructional Material 213 Welfare Economics (MRTS) between L and K is the same for both the goods, X and Y2, produced by F1 and

F2. Technically, optimum allocation of inputs between X and Y requires that: X Y MRTS L,K = MRTS L,K NOTES Pareto optimality in the allocation of factors between the two products and also between the two firms has been presented in Edgeworth box diagram given in Figure 8.2. The analysis is analogous to one developed to present the marginal condition of optimum allocation of goods between the consumers.

In Figure 8.2, horizontal axis measures the total amount of labour (Ox W) and

vertical axis represents the total quantity of capital (Qx M) available for production of

commodities X and Y. Isoquant map for commodity X is given by X1, X2, X3, X4 and X5

with origin Ox. And isoquant map of commodity Y, with origin at Oy is inverted and

superimposed on the isoquant map of X. Isoquants for Y are given by Y1, Y2, Y3, Y4 and

Y5. The curve joining the two points of origin, Ox and Oy is obtained by connecting tangential points of isoquants for X and Y. This curve, called contract curve of

production, is the locus of tangency points of the isoquants of the two firms F1 and F2 both producing goods X and Y. At each point of tangency, the MRTS for both goods is the same, that is, X Y MRTS L,K = MRTS L,K

Fig. 8.2 Edgeworth Box of Production

Therefore, only those points which lie on the contract curve of production represent the Pareto optimality or Pareto efficiency in production. Any other point that satisfies

the above condition is inefficient. For example, let us consider point P, where OxQ

(= MN) of labour is allocated to the production of X and QW (= OyN) of labour to the production of Y. And, PQ of capital is allocated to X while PN of capital goes to the X production of Y. Note that isoquant X3 and Y2 intersect at point P. Therefore, MRTS L,K Y = MRTS L,K. Yet Point P marks Pareto inefficient allocation of L and K between X and Y. For, any movement towards the contract curve, through the shaded area will improve the efficiency in resource allocation for both the goods. For example, factor allocation represented by point H will increase the production of both, X and Y, as both products move onto higher isoquants. Movements along the ridge lines of the shaded area improves the output of one of the commodities without reducing the production of the other. Therefore, any point on the ridge lines indicates a more efficient allocation of L and K, than point P. For Example, Self-Instructional 214 Material movement along PJ indicates reallocation of factors which leads to increase in the Welfare Economics production of X without reducing production of Y. Similarly, movement along PB increases production of Y without affecting output of X. But, once a point on contract curve is reached, it will not be possible to increase the production of any commodity without reducing of the other. Thus, each point on the contract curve QxOy represents optimal NOTES allocation of K and L between X and X in Paretian sense. Again, Pareto optimality condition of production does not offer a unique solution. It can be seen in Figure 8.2 that there are infinite points on the contract curve of production that satisfy the marginal condition of Pareto optimality. But a reasoning analogous to one applied to the optimality condition in Figure 8.1, it is not possible to say which point on the production contract curve represents optimum optimorum. Optimal allocation of resources between firms Another condition that must be satisfied for Pareto optimality of production is optimum degree of specialisation of firms. That is, each firm produces X and Y in such quantities that it is not possible, by reallocation of output among firms, to increase the output of any of these goods without reducing the output of the other. A necessary condition that must be fulfilled is that marginal rates of transformation (MRT) between X and Y must be the same for all firms producing them both. This is however not a sufficient condition. Sufficient condition requires that the equality of MRT be found at the point of tangency of MRT curves—not at the points of intersection. If this condition is not fulfilled it will always be possible to increase the total social product by reallocating goods between firms.

For example, if firm F1 can produce one additional unit of X at the cost of 3 units of Y, and firm F2 can produce 2 units of Y at the cost of one unit of X, then MRT for F1 is 1X = 3Y, and for F2, it is 2Y = 1X. It means that if F1 produces one unit less of X and F2 produces one additional unit of X, then production of Y can be increased by one unit, without reducing the production of X. This point can be represented graphically as follows. Suppose that the marginal rates of transformation (MRT) curves of firms F1 and F2 for products X and Y are, respectively, given as CD and EF in Figure 8.3(a) and (b). If we invert the panel (b) shifting its origin to north-east corner, the position that emerges will be as shown in Figure 8.4. The MRT curves CD and EF intersect each other at two points, P1 and P2.

Fig. 8.3 Marginal Rate of Transformation Curves Self-Instructional Material 215 Welfare Economics At both points P1 and P2, the MRT of firm F1 equals MRT of firm F2. But none of these points optimizes the output of the two firms. Nor does it maximize the output of X

and Y. For example, if two firms settle at point P2, firm F1 will produce MP2 of X and

QP2 of Y, and firm F2 will produce NP2 of X and RP2 of Y. By adding the output of each NOTES commodity produced by each firm, we can obtain the total output of X and Y.

Total output of X = MP2 + NP2 = MN

Total output of Y = QP2 + RP2 = RQ

Thus, if the two firms settle at point P2, the maximum total output of X will be MN and that of Y will be RQ. It may be noted from Figure 8.4 that total output of X and Y will

not change if firms settle at point P1, though output mix of each firm will change.

Fig. 8.4 Optimum Degree of Specialisation

It may, however, be observed from Figure 8.4 that if the firms move from point P2

towards P1 (or from point P1 towards P2) along their respective MRT curves, production of both X and Y will increase to a certain level and then decreases. The maximum output of X and Y can be obtained by shifting the inverted panel (b) further north-eastward until MRT curve EF is tangent to MRT curve CD, while its origin shifts to As shown in Figure 8.4, MRT curves, CD and EF are tangent with each other at point P. This point satisfies both necessary and sufficient conditions of Pareto optimality of specializations

between firms for output mix. At point P, firm F1 produces PH of Y and PB of X and firm

F2 produces PJ of X and GP of Y. Thus, Total output of X = BP + PJ = BJ, and BJ > MN Total output of Y = PH + PG = GH, and GH > RQ The output GH of X and BJ of Y, is maximum that can be produced given the factors. Also, the output-mix at the two firms is optimum. 3. General optimality of production and exchange The third necessary condition that must be fulfilled to optimize the social welfare in the Paretian scheme is that the bundle of factors used and goods produced in the economy be so organized that greater satisfaction of one person is impossible without loss for another. For this, it is necessary that optimality conditions of both production and exchange must be fulfilled simultaneously and at the same level of output of various goods. In

Self-Instructional 216 Material other words, the optimum output-mix must match with the optimum demand mix. This is Welfare Economics called, the ‘Top Level’ optimality condition of welfare maximization. The fulfilment of the top level Pareto optimality condition requires (for our 2 × 2 × 2 model) that the MRT between the two products (X and Y) must be equal to the MRS between the two products for the two consumers (A and B). That is, NOTES A B MRTx,y = MRS x,y = MRS x,y The fulfilment of this condition is graphically illustrated in Figure 8.5. The curve TT′ is the production possibility (or product transformation) curve. The slope of curve TT′ gives the MRT. The indifference curves of consumer A are given by A1, A2, A3, ... and ′ those of consumer B are given by B3, B4, ... (for details see Figure 8.1). Curve CC is the contract curve of exchange. The product transformation curve TT′ is intersected by the contract curve of exchange CC′, at point P. We know that at each point on CC′ curve: A B MRS x,y = MRS x,y The product transformation curve TT′ shows the MRT, the rate at which one commodity can be transformed into the other, given the technology. Although MRT is different at different points of the transformation curve TT′, it is equal to MRS at point P. Point P satisfies therefore the third Pareto optimality condition of welfare maximization.

Fig. 8.5 General Optimality of Production and Exchange

We may now summarise the basic marginal conditions of Pareto optimality. 1. The marginal rate of substitution (MRS) between any pair of goods must be the same for all consumers. 2. The marginal rate of technical substitution (MRTS) between any pair of factors must be equal for all commodities and all firms. 3. The marginal rate of transformation (MRT) between any pair of goods must be equal to the marginal rates of substitution for any pair of goods. 4. Other conditions of pareto optimality In addition to the three optimality conditions explained above, the following marginal condition must also be simultaneously satisfied for social welfare to be maximum.

Self-Instructional Material 217 Welfare Economics First, the owner of a factor is always in a position to use it for personal satisfaction or to rent it out for income, or use it partly for personal use and for earning income. If it is rented out, the reward that is paid to the owner for renting the marginal unit of a factor must be equal to the value of the marginal physical product of the factor unit. This is NOTES what Pareto calls the optimum allocation of factor-units time. Second, the marginal rate of substitution between resource control at any pair of

moments (ti and tj) is the same for every pair of individuals or firms including pairs in which one member is a firm and the other is an individual. This condition relates to optimum control of resources through time by individuals and firms. This is inter-temporal condition of maximum welfare. Third, Boulding has pointed out two other conditions relating to time-preference which have not been explicitly stated in the literature: (i) that owner rates of time preference for any one individual for two commodities must be the same; and (ii) that the rate of time preference for an individual must be equal to the rate of time substitution in production (the marginal own-rate of return) for every commodity. Total Conditions’ of Pareto Optimality Even if first order conditions are satisfied, it does not ensure the maximization of social welfare. There is another ‘set of conditions’, what Hicks calls ‘total conditions’ that must be satisfied in order that social welfare is maximized. The ‘total conditions’ may be stated as ‘it must be impossible to increase welfare by producing a product not otherwise produced (or produced by only one firm); or by using a factor not otherwise used (or used by only one firm)’. Thus, in order that social welfare is maximum, all the conditions first order, second order, and total conditions—must be simultaneously satisfied. But this maximum will not be unique. The reason is that it presupposes a given distribution of income which is not determined by the optimality conditions of welfare maximization. If income distribution (presumed to the given) changes, it will cause a change in welfare maximizing output and factor allocation. 8.4.1 Pareto Optimality under Perfect Competition A necessary condition for Pareto optimality is the existence of perfect competition in both product and factor markets. In this section, we will show how perfect competition leads to Pareto optimality in exchange or consumption and production. (i) Efficiency in exchange under perfect competition: Pareto optimality of exchange requires that marginal rate of substitution between any two goods must be the same for all individuals consuming them both, i.e., A B MRS x,y = MRS x,y Every utility maximizing consumer attains his equilibrium (or the level of maximum satisfaction) where:

MRSx,y =

where Px, Py are prices of commodities, X and Y, respectively.

We know that under perfect competition, Px and Py are given for all the consumers. Therefore,

Self-Instructional 218 Material A B Welfare Economics MRS x,y = MRS x,y = Px/Py Under perfect competition, this condition holds for any pair of goods for all the consumers consuming them both. Perfect competition, therefore, ensures optimality in exchange. NOTES (ii) Efficiency in production under perfect competition: Pareto efficiency (or optimality) in production requires that MRTS between any two factors must be the same for all commodities for whose production both these factors are used. With reference to two-products, X and Y, and two factors, L and K, in our model, this condition may be expressed as: X Y MRTS l,k = MRTS l,k Profit maximizing firms are in equilibrium, with respect to a product (say X), where:

X = MRTS l,k =

where Pl = w = wages, and Pk = r = rate of interest.

When factor market is perfectly competitive, Pl and Pk are the same for all the firms using L and K. Therefore, X Y MRTS l,k = MRTS l,k = Pl/Pk Thus, perfect competition ensures also the optimality of production, i.e., the first order condition of maximum welfare. (iii) Efficiency in production and exchange under prefect competition: The third condition of Pareto optimality requires that MRS must be equal to MRT for all products. We have already shown that:

MRSx,y =

Under perfect competition, a profit maximising firm sets its optimum combination of output where: ∆ MRT = = x,y ∆

Since in a perfectly competitive market, MCx = Px and MCy = Py, therefore,

= MRTx,y =

Since MRSx,y =

therefore, MRSx,y = = MRTx,y

It is then proved that, under perfect competition, all the three Pareto optimality conditions of welfare maximization are satisfied. It is thus established that perfect competition ensures the maximization of social welfare provided second order conditions are simultaneously satisfied.

Self-Instructional Material 219 Welfare Economics Some Exception We have concluded above that perfect competition is a necessary condition for attainment of Pareto optimality in exchange and production. There are, however, certain cases in NOTES which perfect competition is neither a necessary or a sufficient condition for maximising welfare in the Paretian sense. Besides, there are certain other factors which cause non- optimisation of welfare measures even if first order conditions are satisfied under perfect competition. Some important cases of these categories are given below. 1. Pareto optimality in exchange may not be attained under perfect competition if one or more consumers are satiated. A consumer is said to be satiated or has reached the maximum possible level of his satisfaction when his MU = O for all goods that he consumes. If a consumer is satiated, goods may be diverted from him, without reducing his total satisfaction, to those whose MU > O. This results in increase in the total satisfaction of the society. Therefore, one additional condition of Pareto optimality under perfect competition is that no consumer is satiated. 2. Corner solution prevents Pareto optimality. In some cases, under perfect competition, Pareto optimality may be represented by a corner solution, as shown by point C in Figure 8.6. In such cases, marginality condition is not satisfied. Yet in an optimum solution, such a solution represents minimum rather than maximum welfare. In such cases, thus, perfect competition offers a solution which represent only minimum welfare, because only commodity Y will be produced and consumed.

Fig. 8.6 Corner Solution of Pareto-Optimality

8.4.2 Externalities and Pareto Optimality The foregoing conclusion that perfect competition leads to Pareto optimality is based upon the assumption that there are no externalities in consumption and production. This assumption implies: • That production function of each producer is independent of others • Utility function of each individual is independent of others If independence of production and utility functions is not assumed, activity of an individual (firm or consumer) will affect the activities of others (firms or consumers). Such effects are known as externalities. If externalities are present, Pareto optimality may not be attained even under the conditions of perfect competition.

Self-Instructional 220 Material In this section, we will explain externalities of various kinds and how they affect Welfare Economics the realization of Pareto optimality under perfect competition. Meaning of externalities The term externalities refers to the external economies and diseconomies. External NOTES economies are the gains that arise from the activities of an economic unit and accrues to other members of the society for which they cannot be charged through the market price system. Similarly, external diseconomies are the costs that are imposed on the members of the society by the activities of others for which market system does not provide a compensation to those who suffer. External economies and diseconomies arise in both production and consumption. Let us now examine the effects of external economies and diseconomies in production and consumption on welfare maximization. Externalities in Production Externalities in production consist of both external economies and external diseconomies. External economies and diseconomies are discussed below. External economies in production To understand the external economies in production, consider the following examples: 1. When an irrigation facility is extended to non-irrigated areas, productivity of land increases and land values go up. The land owners who gain are not required to bear the cost of irrigation programmes. 2. When new production units of an industry are set up, the demand for inputs increases. This increase in demand for inputs might give an opportunity to the input suppliers to expand their production. The expansion of production might reduce the cost of input production due to economies of scale. As a result, the input-prices for all the users of inputs decrease. This is an external gain to the input users. 3. The education and training programmes of the government increases the supply of skilled labour to the industrial units. But industrial units do not bear the cost of education and training. A part of this gain to the industrial units may percolate down to the consumers in terms of lower price. 4. Construction of roads and railways reduces the cost of transportation in terms of both money and time. The advantage accrues to the industrial units which do not bear the cost of road and railway construction. 5. Afforestation schemes increase rainfalls and oxygen gas in the air; reduce air- pollution; and maintain ecological balance, which benefits the citizens in general and farmers in particular. But none of them bears the cost of afforestation. The external economies in production create a divergence between private and social gains. The divergence between the private and social costs results in non-optimization of production. The case of non-optimization due to externality in production is shown in Figure 8.7. Recall that under perfect competition, a firm producing a commodity (say, X) is in equilibrium when its:

MCx = Px = PB where PB is private benefit.

Self-Instructional Material 221 Welfare Economics As shown in Figure 8.7, the firms produce OQ which maximizes their profits. In the absence of economies in production, the price and output will be Pareto optimum.

NOTES

Fig. 8.7 Private and Social Benefits and Optimum Output

In reality, however, external economies do exist which result in social benefits.

The price, Px, which consumers pay equals only their private benefits (PB) i.e., PBx = Px, which does not include their social gains. If, by some means, social benefits of external

economies are measured and added to Px, the marginal social benefit (MSBx) will exceed ′ Px. The MSBx will then rise to P x. There is thus a divergence between private and social ′ benefits. The difference between Px and P x (or between PBx and MSBx) measures the divergence.

Let us suppose that when social benefits of external economies are added to Px,

it rises to MSBx (Figure 8.7). In that case, equilibrium point E1 shifts to E2 and profit maximising output increases to OQ′ which is greater than OQ. Thus, Pareto optimum (OQ) is less than the socially optimum output (OQ′) when external economies are accounted for in social pricing. That is, exclusion of social benefits (SB), when SB > O output OQ means under-production. It may, therefore, be concluded that, in the presence of external economies in production, Pareto optimality may not be realized even under perfect competition. External diseconomies in production The famous examples of diseconomies of industrial production are the following: • Air-pollution caused by factory smoke and fumes of transport vehicles cause health hazards to the public • Water-pollution caused by discharge of industrial refuse and waste create health hazards for human, animal (particularly fishes) and plant lives • Concentration of industries in an area creates industrial slums which breed various kinds of diseases and crimes Due to health hazards caused by production, medical expenses of the inhabitants of the area go up. This is an external cost to the society resulting from the external diseconomies of production. All such costs incurred by the society, individually or Self-Instructional 222 Material collectively, to prevent the ill-effects of production of a commodity are included in the Welfare Economics external social cost (ESC). The external cost is not included in the private cost of production. The social cost (SC) of a product can be measured as: SC = PC + EC NOTES where PC = private cost and EC = external cost. There is, obviously, a divergence between private cost and social cost. That is, SC > PC, if EC > O. By definition, therefore, marginal social cost (MSC) exceeds the marginal private cost, MC. That is, in production of commodity, say X,

MSCx > MCx Because of the divergence between private and social costs, Pareto-optimality cannot be said to conform to social optimum. This point is illustrated in Figure 8.8. Given the MCx curve and price OPx, the Pareto optimal output will be OX1, determined by equilibrium point E1 because at this level of output:

MCx = Px = MRx

Fig. 8.8 Divergence between Private and Social Costs and Optimum Output

If it were possible to measure the marginal external cost (MECx) and firms were made to pay for the full social costs, their MCx curve will shift to MSCx curve. Note that the vertical distance between MCx and MSCx measures the external cost of production of commodity X. Given the MSCx and Px, a profit maximizing firm will find its equilibrium at point E0 and produce OX0 of X. Obviously, if external costs are included, the Pareto optimal output will decrease from OX1 to OX0. It implies that exclusion of external costs (when EC > O) leads to over production which is socially non-optional. However, in case social benefits and social costs of production cancel out, the Pareto optimality can be realized under perfect competition. The equality of social costs and benefits is however not certain. Externalities in Consumption Like externalities in production, externalities in consumption prevent the realization of Pareto optimality in consumption. Externalities in consumption arise due to interdependence of utility functions. We explain below how external economies and diseconomies in consumption affect optimality under competitive conditions.

Self-Instructional Material 223 Welfare Economics (a) External economies in consumption: When a housewife replaces her traditional charcoal-stove with a gas-stove, her neighbours benefit because air-pollution caused by smoke is reduced. When a household buys a TV set, its neighbours benefit when the TV owner allows them to watch TV programmes. Similarly, if a NOTES person plants trees around his house or decorates his courtyard with flowerpots, his neighbours benefit from the oxygen produced by the trees and also from the beautiful greenery around. A well-maintained car improves the safety of the people on the road and reduces air-pollution. Expenditure on education by some people gives others benefit of an educated society. All such external benefits imply that utility functions of some individuals are dependent on the consumption of others. Interdependence of utility functions violates one of the marginal conditions of Pareto optimality, i.e., MRS between any pair of goods must be the same for all consumers. Since utility of one consumer increases because of increase in the consumption of another consumer, it is always possible to redistribute the goods and increase total social utility. (b) External diseconomies in consumption. Analogous to diseconomies in production, there are diseconomies in consumption too. Diseconomies in consumption arises where increase in the consumption of a commodity by an individual decreases the total utility of others. For example, (i) smoking cigarette in a bus, railway compartment, theatre or restaurant causes disutility to non- smokers; (ii) playing TV and music system loudly causes disutility to neighbours; and (iii) Veblen and snob effects also cause diseconomies in consumption. Such diseconomies of consumption imply interdependence of utility functions, since utility of a commodity for a consumer depends on the consumption of that commodity by others. How interdependence of utility functions affects Pareto optimality is shown graphically in Figure 8.9(a) and (b) assuming (i) that there are only two consumers, A and B, of two commodities X and Y; (ii) that indifference maps of A and B are given as in Figure 8.9(a) and (b), respectively, (iii) that utility level of A is not affected by B’s consumption; and (iv) that utility level of B is affected by A’s consumption of X, but not of Y.

Fig. 8.9 Interdependence of Utility Functions and Pareto-Optimality

Self-Instructional 224 Material To begin the analysis, let us assume that A and B are at points J and R on their Welfare Economics A B respective indifference maps and MRS x,y = MRS x,y. Given this condition, let the commodities X and Y so redistribute between A and B that consumer A moves to point L and his consumption of commodity X decreases by JK. Since A remains on the same indifference curve his total utility remains unchanged. NOTES But since B’s utility is dependent also on A’s consumption of X (which has decreased), his indifference map shifts downward due to fall in consumption of X by consumer A. The downward shifts is denoted by the dotted indifference curves [Figure 8.9(b)]. Let us suppose that consumer B moves from point R on old indifference curve 80 to point T on the new indifference curve 90. Thus, his index of total satisfaction increases from 80 to 90. As a result of this shift, the total satisfaction index increases from 180 (= A’s 100 + B’s 80) to 190 (= A’s 100 + B’s 90), despite the fact that at new A B equilibrium of A and B, MRS x,y = MRS x,y. It may thus be concluded that when externalities exist, equality of MRS between any pair of goods for any two consumers does not ensure realization of Pareto optimality. For, utility level of one consumer (B) can be increased without reducing utility level of the other consumer (A). Externalities of Public Goods We have shown above why Pareto optimality cannot be ensured if there are externalities in the production and consumption of private goods. Here, we discuss optimality conditions in respect of public goods and externalities that arise due to collective consumption of such goods. For our purpose here, a pure public good is one to which exclusion principle of market cannot be applied. Recall the characteristics of pure public good as mentioned earlier: (i) nobody can be excluded from its consumption, nor can consumers be forced to pay for their benefit; (ii) its consumption is collective and all consumers are supplied with it jointly; (iii) satisfaction level of no consumer is reduced by the consumption of others; (iv) its supply to existing consumers is not reduced if number of consumers increases; (v) no individual can appropriate a public good for his personal use; and (vi) its MC = O (though not infinitely) because its opportunity cost is zero. The standard examples of public goods are (a) radio and TV transmission; (b) improved sanitary system of a town; (c) air-pollution control programmes; (d) road safety-measures; (e) tree-plantation on the road sides, and green-belts of a city. Some of these goods may however turn to be a non-public goods beyond a certain number of consumers. Given the characteristics of public goods, the Pareto optimality conditions are not valid to this category of goods. Public goods, therefore, require formulation of new rules. The rule for optimum output of public goods is that the sum of its marginal benefits must equal its marginal cost. The marginal benefit of an individual from a public goods, X, can be measured in terms of money that the individual is willing to pay for his benefit. According to Baumol, the marginal benefit of the individual has to be measured in terms of his marginal rate of substitution between X and money (m). Thus, the marginal benefit of an individual from X,

= =

Self-Instructional Material 225 Welfare Economics The sum of marginal benefits of n individuals from commodity X is expressed as:

+ +⋅⋅⋅+

NOTES The optimum output condition for the public good (X) is then:

+ +⋅⋅⋅+ =

In an economy, however, a public good exists along with many private goods. Under this condition, a Pareto optimum can be realized only by equating the MRT between the public goods and the private goods with the sum of MRS between the same pair of goods for all the individuals. That is, Pareto optimality in case of a public good, X, and a private good Y is realized when:

MRTx,y = MRSx,y There are however problems in discovering individual utility functions. The knowledge of individual utility function is necessary to obtain the sum of MRS of all the individuals. 8.4.3 Indivisibilities and Pareto Optimality One of the assumptions of Pareto optimality conditions is that commodities and inputs are perfectly divisible. In reality, however, it is not unusual to come across indivisibility of production processes. If indivisibilities are introduced, perfect competition may not lead to optimal allocation of resources. Suppose there are two types of technology: one used by small-scale firms and the other used by large-scale firms. The large-scale firms enjoy the economies of scale and, therefore, have lower average cost of production than the small-scale firm. If the technology used by large-scale firms is indivisible, then perfect competition does not lead to optimum allocation of resources; nor does it lead to maximization of welfare. Suppose a large number of firms are in competitive equilibrium and MRT = MRS for all firms and consumers. Assume also that production process is indivisible and that economies of scale that accrue to the large firms are not available to the small firms. On the other hand, a few large firms can produce goods more efficiently. That is, large firms that enjoy the economies of scale can produce large output by using the same quantity of inputs. It means that if all inputs are used only by a small number of large firms, production Check Your Progress possibility curve will shift upward. It may thus be concluded that if indivisibilities exist, 6. When is Pareto production by small firms will be inoptimal, even if marginal conditions are satisfied optimality in under perfectly competitive conditions. exchange achieved? 7. State one condition that must be 8.5 COMPENSATION TESTS satisfied for Pareto’s optimality of According to Pareto criterion social welfare increases if any reorganization or reallocation production. of resources makes at least one individual better off without making any other individual 8. Define external economies. worse off. However, it is difficult to imagine an economic change or implementation of 9. What are the a policy measure that does not affect any individual adversely. In reality, most economic standard examples changes make some people better off at the cost of some others. Pareto criterion does of public goods? not evaluate such economic changes. Some economists, viz., Kaldor, Hicks and Scitovsky,

Self-Instructional 226 Material have however devised compensation criteria that attempt to overcome the limitations of Welfare Economics the Paretian criteria for maximization of social welfare. This has come to be called as New Welfare Economis. In this section, we explain the compensation criteria proposed by Kaldor, Hicks, and Scitovsky. NOTES 8.5.1 Kaldor-Hicks’ Compensation Criterion Although Kaldor and Hicks proposed their compensation criterion in separate articles in 1939. Their criteria are very much alike. Their criteria are, therefore, jointly referred to as Kaldor-Hicks criterion. A minor difference between their criteria is that Kaldor evaluates compensation from gainers’ point of view while Hicks does it from losers’ angle. According to Kaldor, if an economic change makes some people gain and some others lose, and gainers are able to compensate the losers and yet are better off than they were before the change, then the change increases social welfare. According to Hicks, if an economic change makes some people gain and some others lose, and losers are not able to bribe the gainers to prevent them from voting for the change, then the change is socially desirable. Both criteria are essentially the same. The Kaldor-Hicks criterion may be stated as follows. If gainers of a proposed economic change (or reallocation of resources) evaluate their gains at G and losers evaluate their losses at L, and if G > L, then gainers would be able to compensate the losers and yet retain a net gain. The proposed change is, therefore, socially desirable as it increases the social welfare. The Kaldor-Hicks compensation criterion is graphically illustrated in Figure 8.10. Vertical axis measures B’s utility and the horizontal axis measures A’s utility. The curve UP is the utility possiblity curve obtained by graphing combination of utilities of A and B represented by the consumption contract curve in Edgeworth box diagram of exchange (See Figure 8.1). The curve UP shows the various combinations of utility received by A and B, in the utility space, when the economy is in general equilibrium. At each point on UP curve, A B MRS x,y = MRS x,y Given the utility possibility curve, curve UP, let WD represent the alternative utility combinations after an economic change is introduced.

Fig. 8.10 Utility Possibility Curves and Kaldor-Hicks Criterion

Now, consider first the utility possibility curve UP. All points on this curve (e.g., points J and K) represent the alternative distributions of total utility with the existing Self-Instructional Material 227 Welfare Economics distribution of resources. A change from J to K implies that A (the gainer) can compensate B (the loser) without retaining any net gain, since A’s gain equals B’s loss. Pareto optimality condition can evaluate this change. But a movement from J to R, after an economic change is introduced, would make A better off and B worse off. This change cannot be NOTES evaluated by Pareto criterion. On the Kaldor-Hicks criterion, however, movement from J to R is an improvement in welfare, because A can compensate B for his loss and yet be better off than his position at J. The movement from X point J to point R makes B to lose JD utility and A to gain DR utility. Note that DR = DK + KR and DK is just sufficient to compensate B for his loss of utility. After compensating B for his loss of utility, A retains KR utility. Thus, A is better off. This kind of resource reallocation increases total social welfare. The Kaldor- Hicks criterion applies also to movement from point K to Q. Whether compensation is paid or not paid, in Kaldor’s opinion, is a matter of political or ethical decision. In the welfare criterion, compensation is simply a measure of loser’s loss. In formulating his criterion for judging the social desirability of an economic change, Kaldor merely suggests that the gainers must potentially be able to compensate the losers and yet retain some gains to themselves. Kaldor-Hicks criterion is thus considered to be a potentially superior criterion and an improvement in Pareto welfare criteria. Criticism The fundamental problem in compensation criterion is that it refers to only potential rather than the actual compensation. But there is a world of difference between a potential and an actual compensation. If losers are actually compensated for their loss, then there is no problem. It satisfied the Pareto criterion, i.e., at least one person is better off and no person is worse off. But, if the potential compensation is not actually paid, it would imply that the prevailing distribution of income measures the relative strength of feelings of gainers and losers. It follows that the individual preference pattern is also known. This means ‘interpersonal comparison of utility’. But this is an issue that is unresolved. The Kaldor-Hicks criterion, therefore, does not provide a test free from value judgement. Second, another problem with Kaldor-Hicks criterion is that it uses money value of gains and losses in evaluating the economic efficiency of a change. This results in a serious shortcoming in compensation criterion as it ignores the real value of gains and losses. If gainers are highly rich, the real value of their monetary gain (even if it far exceeds the losses of losers) may be insignificant compared to the real loss to the poor (even if monetary loss is much less than gainers monetary gain). Finally, Scitovsky pointed out a contradiction in Kaldor-Hicks criterion. The contradiction is illustrated in Figure 8.11. Suppose a proposed economic change not only affects the utility of each individual (i.e., of A and B) but also simultaneously shifts the utility possibility curve (UP) to the place of WD, as shown in Figure 8.11. That is, a change from J to K not only changes utilities of A and B, but also shifts the utility possibility curve from UP to WD. Note that WD intersects UP. There is no reason why it should not. To demonstrate the contradiction, let us begin by considering point J which represents a combination of utilities of A and B.

Self-Instructional 228 Material Welfare Economics

NOTES

Fig. 8.11 Contradiction in Kaldor-Hicks Criterion

Any policy change that makes A and B to move to point L or M or to any point like Q between L and M, satisfies Pareto criterion. However, Pareto criterion cannot evaluate a situation that results due to a move from point J to R, because, in this case, A gains at the cost of B. This situation can, however, be evaluated on the basis of Kaldor-Hicks criterion, simply by asking A how much he would like to pay to have the change and by asking B how much he would pay to prevent the change. Suppose A puts his amount Ma and B puts Mb. If Ma > Mb, the policy change makes an improvement in welfare. In the same way, a move from J to K satisfied the Kaldor-Hicks criterion. But the same argument cannot be applied to the change from point K back to J. The reason is that in the change from J to K, K is a superior point as it is on a higher utility probability curve. But a change from K to J, makes J a superior point and K an inferior point. Thus, Kaldor-Hicks criterion is self-contradictory. 8.5.2 Scitovsky’s Double-Criterion As already mentioned, Scitovsky pointed out a contradiction in Kaldor-Hicks criterion. He then proposed his double-criterion. His criterion may be stated as follows. A change in economic situation of individual would increase welfare only if: (a) the change improves welfare on Kaldor-Hicks criterion; and (b) those who lose from the change are not capable of bribing those who gain for voting against the change, i.e., reversal of change does not improve the welfare. Obviously Scitovsky’s criterion is rather stringent. Scitovsky’s criterion is based on the premise of Kaldor-Hicks criterion. Rather, one of his double-criterion is Kaldor-Hicks criterion itself. Therefore, most criticism against Kaldor-Hicks criterion is applied to Scitovsky’s double-criterion. In addition, there are only a few changes in real life that would meet the Scitovsky double-criterion. In fact, if the double-criterion is to be satisfied for an increase in welfare, the general welfare should not be affected by change in expenditure pattern and in income distribution. 8.5.3 Little’s Criterion The Little criterion was developed by Ian M. D. Little in his paper ‘A Critique of Welfare Economics’, 1949, and it establishes an advance step for compensation principle theory. Little disapproves the separation between efficiency and distribution and he demands as in Scitovsky’s criterion, for the Kaldor’s and Hicks’ criteria to hold. Furthermore, this criterion also requires that the income distribution is not degraded by the change of states. Self-Instructional Material 229 Welfare Economics This criterion, however, brings some precincts, as a result of its contained value judgement. The criterion will be met, if by a change of states the positively affected individual (winner) is poorer than the negatively affected individual (loser). As an example, let’s analyse the following graph, where we consider the utility of two individuals (A on NOTES the x-axis and B on the y-axis), which we will compare using the utility possibility frontier of two different moments.

U 2 Kaldor Hicks y x K No x y K No z z y y K z H No No y

x

UPFA UPFB

U1

Fig. 8.12 Little’s Criterion

Kaldor’s criterion is met when going from X to Y, Y to X or Y to Z, but not when going from Z to Y. However, Hicks’ criterion is only met when going from Y to Z. Therefore, when comparing state Y to Z, winners can compensate the loss of the losers, but losers cannot compensate the other part in order to avoid the change. This is the only case in our example where the Scitovsky criterion is met, making Z preferred to Y. However, Little’s criterion is only met if individual B is poorer than individual A.

8.6 SOCIAL WELFARE FUNCTION

It should be understood that attempts to device value-free welfare criteria have not yielded satisfactory results. It is not possible to evaluate a change which makes some persons better-off and some worse-off without making some implicit value judgement about the deservingness of an individual or a group. Recognizing the inevitability of value judgement, Bergson suggested that the only way out to resolve this problem is to formulate a set of explicit value judgments which enable the analyst to evaluate the situation. The value judgements may be set up by the analyst himself, government authorities, legislators, social reformers, or an individual or a group of the society. Check Your Progress Bergson suggested that value judgements may be explicitly formulated in the 10. State the difference form of a social welfare function. A social welfare function is an indifference map between Kaldor- which ranks different combinations of individual utilities according to a set of explicit Hicks criteria. value judgements about the distribution of income. It is analogous to the utility function 11. State the of a consumer. More precisely, a social welfare function is an ordinal index of welfare of fundamental problem in the society and is a function of the utility levels of all individual members. It may be compensation expressed as criterion. W = f (u , u , ..., u ) 12. How can the 1 2 n Scitovsky criterion where W denotes social welfare and u1, is utility index of the ith individual. be stated?

Self-Instructional 230 Material Assuming a simple economy of two persons, A and B, the social welfare function Welfare Economics may be written as:

W = F (UA, UB) This function may be represented by a set of social indifference curves, as shown NOTES in Figure 8.13. Each social indifference curve in the utility space (such as W1,W2..., Wn) is the locus of combination of utilities of individuals A and B, which yields the same level of social welfare. The social welfare function as mapped in Figure 8.13 permits as analyst to judge unambiguously whether a proposed policy change is or is not an improvement in welfare. For example, a change from P to R or M improves social welfare since these points are on higher social indifference curves. But a change from P to Q does not improve social welfare as Q lies on the same social indifference curve.

Fig. 8.13 Bergson’s Social Welfare Function

Limitations of Bergson’s Criterion Although Bergson’s criterion has been well received by economists, it has its own weaknesses. First, Bergson’s criterion requires explicit value judgements. Value judgements of different categories of judges are bound to be different. Economists’ value judgement may be different from those of the legislators, electorates or a Commission assigned with the task of policy making. Bergson does not offer a solution to resolve such differences in value judgement. Second, there is no easy method of constructing social welfare function. Bergson’s criterion does not come out with necessary instructions for drafting welfare judgements which are required in the formulation of welfare function. It implies that the most difficult problem of this criterion remains unsolved. As Mishan has pointed out, ‘Although the social welfare function had received continual mention since Bergson’s 1938 formulation, no instruction in the drafting of this grandiose design had been hazarded.’ In simple Check Your Progress words, although usefulness of social welfare function is widely recognized, no attempt has been made to provide guidelines for constructing a reasonable social welfare function. 13. What is a social welfare function? Third, construction of social welfare function on the basis of ordinal preferences 14. State one limitation of the individuals leads to contradictions if majority rule is applied. If majority votes for a of Bergson’s social non-essential commodity, the essential ones may not be adequately produced. welfare function.

Self-Instructional Material 231 Welfare Economics 8.7 ARROW’S IMPOSSIBILITY THEOREM

The theory of social choice was invented by Kenneth J. Arrow. The theory emerged out NOTES from the failed efforts of Arrow to arrange the Bergson-Samuelson approach. It developed into an enormous literature, with lots of consequences to a range of subfields and topics. The social choice structure is, potentially, so common that one may mistakenly combine it with normative economics. In a restraining definition, nonetheless, social choice is measured in agreement with the dilemma of creating heterogeneous individual preferences into a reliable ranking. Occasionally, an even more restraining concept of ‘Arrovian social choice’ is used to forename works which authentically accept Arrow’s particular saying. In an effort to build a dependable social ranking of a set of choices on the foundation of individual preferences above this set, Arrow (1951) obtained an impossibility theorem. A generalization of the structure of welfare economics, covering all communal decisions from political democratic system and group decisions to market distribution it is a self- evident technique which positions a standard of severity for any potential attempt. The impossibility theorem generally says that there is no universal technique to order a given set of (more than two) substitutes on the basis of (at least two) individual preferences, if one desires to value three conditions: • Weak Pareto: Common and agreed preferences are constantly appreciated (if every person prefers A to B, then A is superior to B). • Independence of irrelevant alternatives: Any detachment of two substitutes must be graded on the exclusive basis of individual preferences above this subset. • No-dictatorship: No individual is a ruler in the common sense that his stringent preferences are constantly observed by the ranking, no matter what they and the other individuals’ inclinations are. The unfeasibility holds when one desires to envelop an immense diversity of likely profiles of individual preferences. When there is adequate homogeneity among preferences, for example when alternatives fluctuate only in one aspect and individual preferences are based on the aloofness of alternatives to their favoured option beside this aspect (imagine, for example, of political choices on the left-right variety), then dependable methods subsist (Black 1958). Arrow’s outcome evidently expands the range of analysis ahead of the traditional spotlight of welfare economics, and satisfactorily elucidates the difficulties of autonomous voting procedures such as the Condorcet paradox (consisting of the information that popular rule may be intransitive). The examination of voting procedures is an extensive field. This examination discloses a profound worry between rules supported on the mass principle and rules which defend minorities by taking description of liking in a more comprehensive way. Experts of welfare economics formerly argued that Arrow’s outcomes had no bearing on economic allocation (e.g. Samuelson 1967), and there is some uncertainty in Arrow (1951) about whether, in an economic framework, the finest relevance of the theorem is regarding individual self-centred experiences over individual consumptions, in which case it is certainly applicable to welfare economics, or regarding individual moral values about universal allocations. It is now commonly considered that the formal structure of social option can wisely be functional to the Bergson-Samuelson problem of ranking allocation on the bases of individual tastes. Applications of Arrow’s theorem to different economic situations have been made. Self-Instructional 232 Material Amartya Sen (1970s), an Indian economist, suggests an additional simplification of the Welfare Economics social choice structure, by authorizing deliberation of information concerning individual utility functions, not merely preferences. This improvement is provoked by the impossibility theorem, but also by the moral relevance of diverse kinds of data. Distributional concerns perceptibly want interpersonal comparisons of well-being. For example, a democratic NOTES assessment of allocations requires willpower of who the worst-off are. It is alluring to imagine such comparisons in terms of utilities. This has activated a significant body of literature which has significantly elucidated the meaning of diverse kinds of interpersonal utility comparisons (of levels, differences, etc.) and the association between them and diverse social criteria (egalitarianism and utilitarianism). This literature has also presented significant formal analysis of the theory of welfarism, showing that it includes two subcomponents. The primary one is the Paretian condition where the option is corresponding to another when all individuals are indifferent among them. This eliminates using non-welfarist information regarding alternatives, but does not eliminate using non-welfarist information regarding individuals. The next one is freedom, a condition prepared in terms of utilities. It may be entitled independence of unrelated utilities and speaks that the social position of any couple of alternatives must depend only on usefulness levels at these two alternatives, so that alteration in the outline of utility functions which would depart the usefulness levels unaffected at the two options should not change how they are positioned. This ruled out non-welfarist information concerning individuals, but does not prohibit using non-welfarist information concerning alternatives (one may be favoured because it has more liberty). The mixture of the two conditions eliminates all non-welfare information. Despite the vital explanation made, the opening of utility functions basically amounts to going back to elderly welfare economics, after the malfunctions of novel welfare economics, Bergson, Samuelson and Arrow to give attractive solutions with data on consumer tastes only. A linked issue is how the assessment of individual welfare must be completed, or, consistently, how interpersonal comparisons must be executed. Welfare economics conventionally relied on ‘utility’, and the extensive informational base of social alternative is generally devised with utilities. But, utility functions may be agreed upon a diversity of significant explanations, so that similar formalism may be used to converse interpersonal evaluation of resources, opportunities, abilities and the like. In other words, one may split two the subjects: • One requires extra information than individual preference sorting in order to execute interpersonal comparisons • What type of extra information is morally pertinent (subjective utility or objective ideas of opportunities)? The second issue is straightway connected to philosophical deliberations concerning how well-being should be considered and to the ‘equality of what’ debate. The previous issue is still debated. Expanding the informational foundation by introducing arithmetical indices of well-being is not the only believable addition. Arrow’s impracticality is attained with the stipulation of self-governance of irrelevant alternatives, which may be rationally examined, when the theorem is reformulated with utility functions as primitive data, as the variation of independence of irrelevant utilities with a situation of ordinal non-comparability, saying that the position of two alternatives must depend merely on individuals’ ordinal non-comparable preferences. Arrow’s unfeasibility may be evaded by soothing the ordinal non-comparability condition, and this is the above- described expansion of the informational foundation by relying on utility functions. Self-Instructional Material 233 Welfare Economics However, Arrow’s impracticality may also be evaded by soothing self-government of unrelated utilities only. In particular, it formulates logic to order alternatives on the foundation of how these alternatives are measured by individuals in comparison to other alternatives. The notion of informational basis itself must not be restricted to issues of NOTES interpersonal comparisons.

8.8 SUMMARY

In this unit, you have learnt that: • Economics has both positive and normative character. We have so far been concerned with the positive aspects of economies, especially microeconomics. Our main concern was optimum allocation of resources at micro levels, i.e., how individual consumers and firms maximize their objective functions—consumers their utility function and firms their profit function. • As regards the origin of welfare economics, it is very difficult to point out the period in the history of economic thoughts which marks the beginning of welfare economics. • Welfare economics may also be defined as that branch of economic science which evaluates alternative economic situations (i.e., alternative patterns of resource allocations) from the viewpoint of economic well-being of the society as a whole. • Welfare economics is a positive science insofar as it attempts to explain and predict the outcome of the functioning of the economic system. • It was Vilfred Pareto, an Italian economist, who broke away from the cardinal utility tradition and gave a new orientation to welfare economics. He rejected cardinal utility concept and additive utility function on the ground of their limitations mentioned above. • Pareto introduced a new concept, i.e., the concept of social optimum. This concept is central to Paretian welfare economics. The basic idea behind this concept is Check Your Progress that while it is not possible to add up utilities of individuals to arrive at the total 15. Fill in the blanks social welfare, it is possible to determine whether social welfare is optimum. with appropriate • Modern welfare economics does not attempt to quantify the total social welfare. terms. It concerns itself with only the indicators of change in welfare. It analyses whether (i) The theory of social choice was total welfare increases or decreases when there is a change in economic situation. invented by • Pareto’s Manual of Political Economy (1906) represents a decisive watershed ______. in the history of subjective welfare economics. Pareto broke away from the (ii) Arrow’s unfeasibility may traditional utilitarian economics. be evaded by • Pareto optimum is also called as Pareto Efficiency, Pareto Unanimity Rule, Pareto soothing the Criteria, and Social Optimum. Pareto optimum is defined as a position from which ______condition. it is not possible to improve welfare of any one by any reallocation of factors or of (iii) The notion of goods and services without impairing the welfare of someone else. informational basis • The Paretian concept of ‘social optimum’ is definitely an improvement over cardinal itself must not be restricted to issues utility approach, in that it is, as is claimed, free from the problems of additive utility of ______. function and interpersonal comparison of utility.

Self-Instructional 234 Material • Pareto optimum raises the question of payment of compensation because it is Welfare Economics difficult to imagine an economic change that benefits at least one person without harming another. • The marginal conditions of maximum welfare have been derived directly from the definition of maximum welfare. NOTES • Pareto optimality in exchange is achieved when allocation of commodities among the consumers is such that it is not possible to increase the satisfaction of any person without reducing the satisfaction of someone else. • A condition that must be satisfied for Pareto optimality of production is optimum degree of specialization of firms. • Even if first order conditions are satisfied, it does not ensure the maximization of social welfare. There is another ‘set of conditions’, what Hicks calls ‘total conditions’ that must be satisfied in order that social welfare is maximized. • A necessary condition for Pareto optimality is the existence of perfect competition in both product and factor markets. • The term externalities refers to the external economies and diseconomies. External economies are the gains that arise from the activities of an economic unit and accrues to other members of the society for which they cannot be charged through the market price system. • Similarly, external diseconomies are the costs that are imposed on the members of the society by the activities of others for which market system does not provide a compensation to those who suffer. • Like externalities in production, externalities in consumption prevent the realisation of Pareto optimality in consumption. External in consumption arise due to interdependence of utility functions. • The standard examples of public goods are: (a) Radio and TV transmission; (b) improved sanitary system of a town; (c) air-pollution control programmes; (d) road safety-measures; (e) tree-plantation on the road sides, and green-belts of a city. • One of the assumptions of Pareto optimality conditions is that commodities and inputs are perfectly divisible. In reality, however, it is not unusual to come across indivisibility of production processes. If indivisibilities are introduced, perfect competition may not lead to optimal allocation of resources. • A minor difference between Kaldor-Hicks criteria is that Kaldor evaluates compensation from gainers’ point of view while Hicks does it from losers’ angle. • The fundamental problem in compensation criterion is that it refers to only potential rather than the actual compensation. But there is a world of difference between a potential and an actual compensation. • Scitovsky pointed out a contradiction in Kaldor-Hicks criterion. He then proposed his double-criterion. • Scitovsky criterion may be stated as follows. A change in economic situation of individual would increase welfare only if (a) the change improves welfare on Kaldor-Hicks criterion; and (b) those who lose from the change are not capable

Self-Instructional Material 235 Welfare Economics of bribing those who gain for voting against the change, i.e., reversal of change does not improve the welfare. • The Little criterion was developed by Ian M. D. Little in his paper ‘A Critique of Welfare Economics’, 1949, and it establishes an advance step for compensation NOTES principle theory. Little disapproves the separation between efficiency and distribution and he demands as in Scitovsky’s criterion, for the Kaldor’s and Hicks’ criteria to hold. • Bergson suggested that value judgements may be explicitly formulated in the form of a social welfare function. A social welfare function is an indifference map which ranks different combinations of individual utilities according to a set of explicit value judgements about the distribution of income. • Bergson’s criterion requires explicit value judgements. Value judgements of different categories of judges are bound to be different. Economists’ value judgement may be different from those of the legislators, electorates or a Commission assigned with the task of policy making. Bergson does not offer a solution to resolve such differences in value judgement. • The theory of social choice was invented by Kenneth J. Arrow. The theory emerged out from the failed efforts of Arrow to arrange the Bergson-Samuelson approach. It developed into an enormous literature, with lots of consequences to a range of subfields and topics. • In an effort to build a dependable social ranking of a set of choices on the foundation of individual preferences above this set, Arrow (1951) obtained an impossibility theorem. • Amartya Sen (1970s), an Indian economist, suggests an additional simplification of the social choice structure, by authorizing deliberation of information concerning individual utility functions, not merely preferences. • The notion of informational basis itself must not be restricted to issues of interpersonal comparisons.

8.9 KEY TERMS

• Welfare economics: It may be defined as that branch of economic science which evaluates alternative economic situations (i.e., alternative patterns of resource allocations) from the viewpoint of economic well-being of the society as a whole. • Pareto optimum: It is defined as a position from which it is not possible to improve welfare of any one by any reallocation of factors or of goods and services without impairing the welfare of someone else. • Externalities: The term externalities refers to the external economies and diseconomies. • External economies: They are the gains that arise from the activities of an economic unit and accrues to other members of the society for which they cannot be charged through the market price system. • External diseconomies: They are the costs that are imposed on the members of the society by the activities of others for which market system does not provide a compensation to those who suffer. Self-Instructional 236 Material • Social welfare function: It is an indifference map which ranks different Welfare Economics combinations of individual utilities according to a set of explicit value judgements about the distribution of income.

8.10 ANSWERS TO ‘CHECK YOUR PROGRESS’ NOTES

1. Welfare economics may be defined as that branch of economic science which evaluates alternative economic situations (i.e., alternative patterns of resource allocations) from the viewpoint of economic well-being of the society as a whole. 2. Welfare economics is a positive science insofar as it attempts to explain and predict the outcome of the functioning of the economic system. 3. Vilfred Pareto, an Italian economist, broke away from the cardinal utility tradition and gave a new orientation to welfare economics. 4. The basic idea behind the concept of social optimum is that while it is not possible to add up utilities of individuals to arrive at the total social welfare, it is possible to determine whether social welfare is optimum. 5. Pareto optimum is defined as a position from which it is not possible to improve welfare of any one by any reallocation of factors or of goods and services without impairing the welfare of someone else. 6. Pareto optimality in exchange is achieved when allocation of commodities among consumers is such that it is not possible to increase the satisfaction of any person without reducing the satisfaction of someone else. 7. A condition that must be satisfied for Pareto optimality of production is optimum degree of specialization of firms. 8. External economies are the gains that arise from the activities of an economic unit and accrues to other members of the society for which they cannot be charged through the market price system. 9. The standard examples of public goods are (a) radio and TV transmission; (b) improved sanitary system of a town; (c) air-pollution control programmes; (d) road safety-measures; (e) tree-plantation on the road sides, and green-belts of a city. 10. A minor difference between Kaldor-Hicks criteria is that Kaldor evaluates compensation from gainers’ point of view while Hicks does it from losers’ angle. 11. The fundamental problem in compensation criterion is that it refers to only potential rather than the actual compensation. But there is a world of difference between a potential and an actual compensation. 12. Scitovsky criterion may be stated as follows. A change in economic situation of individual would increase welfare only if (a) the change improves welfare on Kaldor-Hicks criterion; and (b) those who lose from the change are not capable of bribing those who gain for voting against the change, i.e., reversal of change does not improve the welfare. 13. A social welfare function is an indifference map which ranks different combinations of individual utilities according to a set of explicit value judgements about the distribution of income.

Self-Instructional Material 237 Welfare Economics 14. Bergson’s criterion requires explicit value judgements. Value judgements of different categories of judges are bound to be different. Economists’ value judgement may be different from those of the legislators, electorates or a Commission assigned with the task of policy making. Bergson does not offer a NOTES solution to resolve such differences in value judgement. 15. (i) Kenneth J. Arrow (ii) Ordinal non-comparability (iii) Interpersonal comparisons

8.11 QUESTIONS AND EXERCISES

Short-Answer Questions 1. What is welfare economics? Is it positive or normative in character? 2. ‘Pareto introduced a new concept, i.e., the concept of social optimum.’ State briefly. 3. Why is Pareto’s welfare economics called new welfare wconomics? 4. State marginal conditions of Pareto optimum in consumption and production under perfect conditions. 5. What are the conditions that must be fulfilled to achieve Pareto optimality in exchange and production under perfect conditions? 6. How are the conditions affected by the presence of: (i) Externalities in production and consumption, and (ii) Public goods? 7. How far can the Kaldor-Hicks-Scitovsky criteria be considered as an improvement over the Pareto criterion? 8. What is social welfare function? Does it solve the problem of Pareto’s value-free criterion of social welfare? 9. What does Arrow’s impossibility theorem state? 10. How and why did Amartya Sen simplify Arrow’s social choice theory? Long-Answer Questions 1. Discuss the meaning and nature of welfare economics. 2. Explain the concept of Pareto optimality. 3. How has Pareto’s optimality theory been criticized? Discuss. 4. Assess the Pareto optimality conditions in detail. 5. Evaluate Pareto’s optimality theory under perfect competition. 6. ‘Externalities in production consist of both external economies and external diseconomies.’ Discuss. 7. ‘The Pareto criterion does not give us a sufficient basis for ordering states. The Kaldor-Hicks-Scitovsky criteria do not carry us much farther.’ Examine critically. 8. Critically analyse Bergson’s social welfare function. 9. Discuss Arrow’s impossibility theorem. Self-Instructional 238 Material Welfare Economics 8.12 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. NOTES Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional Material 239

Choice under Uncertainty UNIT 9 CHOICE UNDER and Risk UNCERTAINTY AND RISK NOTES Structure 9.0 Introduction 9.1 Unit Objectives 9.2 Difference between Uncertainty and Risk 9.3 Classes of Measures: Ordinal and Cardinal Measures 9.3.1 Axioms of Neumann-Morgenstern (N-M) Utility 9.4 Relationship between Shape of Utility Function and Behaviour towards Risk 9.4.1 Elasticity of Marginal Utility and Risk Aversion 9.4.2 Absolute and Relative Risk Aversion 9.5 Summary 9.6 Key Terms 9.7 Answers to ‘Check Your Progress’ 9.8 Questions and Exercises 9.9 Further Reading

9.0 INTRODUCTION

Most market conditions are known to the investor or can be predicted in investment decisions under the condition of certainty. In reality, however, a large area of investment decisions fall in the realm of risk and uncertainty. It is important to note that risk and uncertainty go hand in hand. Wherever there is uncertainty, there is risk. The probability of some kinds of risk is calculable whereas that of some other kinds of risk is not. The calculable risk like accident, fire and theft are insurable. Therefore, decision-making in case of insurable risks is a relatively easier task. But, incalculable risks are not insurable. Therefore, investment decisions are greatly complicated where the probability of an outcome is not estimable. However, some useful techniques have been devised and developed by economists, statisticians and management experts to facilitate investment decision-making under the conditions of risk and uncertainty. Also, there are several techniques and methods that are applied under different business conditions and for evaluating investment projects. In this unit, however, we concentrate on the popular methods of investment decision-making. Let us begin with the concepts of and distinction between risk and uncertainty as applied to business decision-making.

9.1 UNIT OBJECTIVES

After going through this unit, you will be able to: • Differentiate between uncertainty and risk • Discuss the cardinal and ordinal measures of utility • Evaluate the axioms and characteristics of Neumann-Morgenstern (N-M) utility • Assess the relationship between shape of utility function and behaviour towards

risk Self-Instructional Material 241 Choice under Uncertainty • Explain the concept of elasticity of marginal utility and risk aversion and Risk • Analyse absolute and relative risk aversion

NOTES 9.2 DIFFERENCE BETWEEN UNCERTAINTY AND RISK

The concept of risk and uncertainty can be better explained and understood in contrast to the concept of certainty. Therefore, let us first have a closer look at the concept of certainty and then proceed to explain the concepts of risk and uncertainty. Certainty is the state of perfect knowledge about the market conditions. In the state of certainty, there is only one rate of return on the investment and that rate is known to the investors. That is, in the state of certainty, the investors are fully aware of the outcome of their investment decisions. For example, if you deposit your savings in ‘fixed deposit’ bearing 10 per cent interest, you know for certain that the return on your investment in time deposit is 10 per cent, and FDR can be converted into cash any day. Or, if you buy government bonds or treasury bills, etc. bearing an interest of 11 per cent, you know for sure that the return on your investment is 11 per cent per annum, your principal remaining safe. In either case, you are sure that there is little or no possibility of the bank or the government defaulting on interest payment or on refunding the money. This is called the state of certainty. However, there is a vast area of investment avenues in which the outcome of investment decisions is not precisely known. The investors do not know precisely or cannot predict accurately the possible return on their investment. Some examples will make the point clear. Suppose a firm invests in R&D to innovate a new product and spends money on its production and sale. The success of the product in a competitive market and the return on investment in R&D and in production and sale of the product can hardly be predicted accurately. There is, therefore, an element of uncertainty. Consider another example. Suppose a company doubles its expenditure on advertisement of its product with a view to increasing its sales. Whether sales will definitely increase proportionately can hardly be forecast with a high degree of certainty, for it depends on a number of unpredictable conditions. Consider yet another example. Maruti Udyog Limited (MUL) decided in July 2014 to invest money in financing the sale of its own cars with a view to preventing the downslide in its sales which it had experienced over the past two years. However, the managers of MUL could hardly claim the knowledge of or predict the outcome of this decision accurately. Hence, this decision involves risk and uncertainty. In real life situations, in fact, a large number of business decisions are taken under the conditions of risk and uncertainty, i.e., the lack of precise knowledge about the outcome of the business decisions. Let us now look into the precise meaning of the terms risk and uncertainty in business decisions. Meaning of Risk In common parlance, risk means a low probability of an expected outcome. From business decision-making point of view, risk refers to a situation in which a business decision is expected to yield more than one outcome and the probability of each outcome is known to the decision makers or it can be reliably estimated. For example, if a company doubles its advertisement expenditure, there are four probable outcomes: (i) its sales may more- than-double, (ii) they may just double, (iii) increase in sales may be less than double and (iv) sales do not increase at all. The company has the knowledge of these probabilities Self-Instructional 242 Material or has estimated the probabilities of the four outcomes on the basis of its past experience Choice under Uncertainty as: (i) more-than double: — 20 per cent (or 0.2), (ii) almost double — 40 per cent and Risk (or 0.4), (iii) less-than double — 50 per cent (or 0.5) and (iv) no increase — 10 per cent (or 0.1). It means that there is 80 per cent risk in expecting more-than-doubling of sales, and 60 per cent risk in expecting doubling of sale, and so on. NOTES There are two approaches to estimating probabilities of outcomes of a business decision, viz., (i) a priori approach, i.e., the approach based on deductive logic or intuition and (ii) posteriori approach, i.e., estimating the probability statistically on the basis of the past data. In case of a priori probability, we know that when a coin is tossed, the probabilities of ‘head’ or ‘tail’ are 50:50, and when a dice is thrown, each side has 1/6 chance to be on the top. The posteriori assumes that the probability of an event in the past will hold in future also. The probability of outcomes of a decision can be estimated statistically by way of ‘standard deviation’ and ‘coefficient of variation’. Meaning of Uncertainty Uncertainty refers to a situation in which there are more than one outcome of a business decision and the probability of no outcome is not known nor can it be meaningfully estimated. The unpredictability of outcome may be due to the lack of reliable market information, inadequate past experience, and high volatility of the market conditions. For example, if an Indian firm, highly concerned with population burden on the country, invents an irreversible sterility drug, the outcome regarding its success is completely unpredictable. Consider the case of insurance companies. It is possible for them to predict fairly accurately the probability of death rate of insured people, accident rate of cars and other automobiles, rate of buildings catching fire, and so on, but it is not possible to predict the death of a particular insured individual, a particular car meeting an accident or a particular house catching fire, etc. The long-term investment decisions involve a great deal of uncertainty with unpredictable outcomes. But, in reality, investment decisions involving uncertainty have to be taken on the basis of whatever information can be collected, generated and ‘guesstimated’. For the purpose of decision-making, uncertainty is classified as: • Complete ignorance • Partial ignorance In case of complete ignorance, investment decisions are taken by the investor using their own judgement or using any of the rational criteria. What criterion he chooses depends on his attitude towards risk. The investor’s attitude towards risk may be that of: • A risk averter • A risk neutral • A risk seeker or risk lover In simple words, a risk averter avoids investment in high-risk business. A risk- neutral investor takes the best possible decision on the basis of his judgement, understanding of the situation and his past experience. He does his best and leaves the rest to the market. A risk lover is one who goes by the dictum that ‘the higher the risk, the higher the gain’. Unlike other categories of investors, he prefers investment in risky business with high expected gains. In case of partial ignorance, on the other hand, there is some knowledge about the future market conditions; some information can be obtained from the experts in the Self-Instructional Material 243 Choice under Uncertainty field, and some probability estimates can be made. The available information may be and Risk incomplete and unreliable. Under this condition, the decision-makers use their subjective judgement to assign an a priori probability to the outcome or the pay-off of each possible action such that the sum of such probability distribution is always equal to NOTES one. This is called subjective probability distribution. The investment decisions are taken in this case on the basis of the subjective probability distribution.

9.3 CLASSES OF MEASURES: ORDINAL AND CARDINAL MEASURES

We have learnt about the concept of utility in unit 1. Here, we deal with the measurability of utility. Utility is a psychological phenomenon. It is a feeling of satisfaction, pleasure or happiness. Is utility measurable quantitatively? Measurability of utility has, however, been a contentious issue. The classical economists, viz., Jeremy Bentham, Leon Walrus, Carl Menger, etc. and the neo-classical economist, notably Alfred Marshall, believed that utility is cardinally or quantitatively measurable like height, weight, length, temperature and air pressure. This belief resulted in the Cardinal Utility concept. The modern economists, most notably J. R. Hicks and R. G. D. Allen, however, hold the view that utility is not quantitatively measurable—it is not measurable in absolute terms. Utility can be expressed only ordinally comparatively or in terms of ‘less than’ or ‘more than’. It is, therefore, possible to list the goods and services in order of their preferability or desirability. This is known as the ordinal concept of utility. Let us now look into the origin of the two concepts of utility and their use in the analysis of demand. (i) Cardinal measurement of utility: Some early psychological experiments on an individual’s responses to various stimuli led classical and neo-classical economists to believe that utility is measurable and cardinally quantifiable. This belief gave rise to the concept of cardinal utility. It implies that utility can be assigned a cardinal number like 1, 2 and 3. The neo-classical economists, especially Marshall, devised a method of measuring utility. According to Marshall, utility of a commodity for a person equals the amount of money he/she is willing to pay for a unit of the commodity. In other words, price one is prepared to pay for a unit of a commodity equals the utility he expects to derive from the commodity. They formulated the theory of consumption on the assumption that utility is cardinally measurable. They coined and used a term ‘util’ meaning ‘units of utility’. In their economic analysis, they assumed: (i) that one ‘util’ equals one unit of money, and (ii) that utility of money remains constant. Check Your Progress It has, however, been realized over time that absolute or cardinal measurement 1. How can the of utility is not possible. Difficulties in measuring utility have proved to be concept of risk and insurmountable. Neither economists nor scientists have succeeded in devising a uncertainty be technique or an instrument for measuring the feeling of satisfaction, i.e., the utility. understood? Numerous factors affect the state of consumer’s mood, which are impossible to 2. Define risk. determine and quantify. Utility is, therefore, immeasurable in cardinal terms. 3. How can the probability of (ii) Ordinal measurement of utility: The modern economists have discarded the outcomes of a concept of cardinal utility and have instead employed the concept of ordinal decision be utility for analysing consumer behaviour. The concept of ordinal utility is based estimated statistically? on the fact that it may not be possible for consumers to express the utility of a commodity in numerical terms, but it is always possible for them to tell

Self-Instructional 244 Material introspectively whether a commodity is more or less or equally useful as compared Choice under Uncertainty to another. For example, a consumer may not be able to tell that a bottle of Pepsi and Risk gives 5 utils and a glass of fruit juice gives 10 utils. But he or she can always tell whether a glass of fruit juice gives more or less utility than a bottle of Pepsi. This assumption forms the basis of the ordinal theory of consumer behaviour. NOTES To sum up, the neo-classical economists maintained that cardinal measurement of utility is practically possible and is meaningful in consumer analysis. The modern economists, on the other hand, maintain that utility being a psychological phenomenon is inherently immeasurable quantitatively. They also maintain that the concept of ordinal utility is a feasible concept and it meets the conceptual requirement of analysing the consumer behaviour. However, both the concepts of utility are used in analysing consumer behaviour. Two Approaches to Consumer Demand Analysis Based on cardinal and ordinal concepts of utility, there are two approaches to the analysis of consumer behaviour. (i) Cardinal utility approach, attributed to Alfred Marshall and his followers, is also called the neo-classical approach or Marshallian approach. (ii) Ordinal utility approach, pioneered by J. R. Hicks, a Nobel laureate and R. G. D. Allen, is also called Hicks-Allen approach or the indifference curve analysis. The two approaches are not in conflict with one another. In fact, they represent two levels of sophistication in the analysis of consumer behaviour. Both the approaches are important for managerial decisions depending on the level of sophistication required. It is important to note in this regard that in spite of tremendous developments in consumption theory based on ordinal utility, the neo-classical demand theory based on cardinal utility has retained its appeal and applicability to the analysis of market behaviour. Besides, the study of neo-classical demand theory serves as a foundation for understanding the advanced theories of consumer behaviour. The study of neo-classical theory of demand is of particular importance and contributes a great deal in managerial decisions. 9.3.1 Axioms of Neumann-Morgenstern (N-M) Utility A major contribution to the utility theory was made by a famous mathematician, John von Neumann, and a well-known economist Oskar Morgenstern in their famous book Theory of Games and Economic Behaviour. Their theory is also known as Modern Utility Theory and Neumann-Morgenstern Hypothesis (N-M hypothesis). It is important to note that N-M hypothesis is concerned with the measurement of utility concept, particularly of money, rather than explaining the utility maximizing behaviour of the consumer. In other words, the prime objective of N-M hypothesis is to provide a measure (or an index) of utility and to show that marginal utility of money decreases. To appreciate the contribution of modern utility theory, we need to look at its point of deviation from the cardinal and ordinal utility theories of consumer behaviour. Recall that the cardinal utility assumes measurability of utility in terms of constant utility of money. The ordinal utility theory considers cardinal measurement of utility neither possible nor necessary in consumer analysis, and relies on ordinal concept of utility. An important aspect of these theories is that they presume all consumer choices to be made under certain and riskless conditions. That is, these theories ignore the possibility of

Self-Instructional Material 245 Choice under Uncertainty uncertainty and risk involved in consumer’s alternative choices. Neumann and and Risk Morgenstern have gone, without disputing the ordinal utility approach, one step forward to suggest a measure of utility where risk is involved in choice-making. In this section, we will briefly describe the basic idea of N-M hypothesis, its NOTES approach towards construction of utility index, and also look into its drawbacks. Characteristics of N-M Utility Index The N-M hypothesis suggests that if an individual behaves consistently, it is possible to construct his ‘utility index’ and express his preferences numerically. For example, consider an individual who makes a choice between: (i) witnessing a test cricket-match (M) being played in the city, and (ii) going around for sight-seeing (S). Suppose his preference is given as M > S. Let us now introduce the element of uncertainty in his choice for, under N-M hypothesis, the consumer is required to make choice under the conditions of uncertainty. In order to introduce uncertainty (or a risk element), let us suppose that the cricket-match (M) is likely to be interrupted by rainfall. Therefore, if the individual goes

to witness the match he may either enjoy a good cricket (Mg) or a bad cricket (Mb) due to interruptions by rainfall. Assuming certain probability rates of rainfall, individual’s preferences for the alternative probability rates may be hypothetically ranked as follows. (i) If probability of clear weather is rated at 80 per cent (or 0.8) the individual expects

to enjoy a good cricket (Mg) and he prefers Mg to S. (ii) If probability of clear weather is 60 per cent (or 0.6) and of rainfall 40 per cent (or 0.4), the individual becomes indifferent between the alternatives, M and S. Given the first set of probability rates and ranking of individual’s preferences, his preferences may be arranged, assuming consistency in his behaviour, as follows.

Mg > S > Mb This ordering of his preferences follows the utility expected from these alternatives. Consider now (the second) situation in which probabilities of their clear weather and rainfall are rated as 60:40 (or 0.6:0.4). Under these probability rates, the individual is

indifferent between M and S. It means that the composite expected utility (Ue) of Mg

and Mb is the same as that of S. The expected utility, under the conditions of uncertainty, is obtained by multiplying the riskless utility (U) of an event by its probability rate (P). Thus, individual’s equation of indifference may be expressed as:

U(S) = P · U(Mg) + (1 – P) · U(Mb)

As we have assumed above, the probability (P) of Mg is 0.6 and probability of Mb is 1 – P = 1 – 0.6 = 0.4. Now if the individual is somehow in a position to obtain the

information regarding the utilities which he can assign to Mg and Mb, he is able to assign

a numerical value to U(S). Let us assume that the values Mg at 50 utils and Mb at 25 utils,

i.e., U(Mg) = 50 and U(Mb) = 25. By substituting these values in the above equation, we get: U(S) = 0.6(50) + 0.4(25) U(S) = 30 + 10 = 40 Thus, the individual assigns 40 utils to S. This illustrates the N-M measure of utility index. Having computed the utility index of S, individual’s preferences may be

ranked as Mg > S > Mb and may be numerically expressed as:

Self-Instructional 50 > 40 > 25. 246 Material Assumptions Choice under Uncertainty and Risk The construction of N-M utility index is based on three basic assumptions. 1. Transitivity: The N-M hypothesis, like indifference curve and revealed preference theories, assumes transitivity in consumer’s preferences. That is, if he prefers A NOTES to B and B to C, then he prefers A to C. 2. Consistency: Consistency in consumer’s behaviour implies that if a consumer preferss A to B, A having a probability P and B having a probability 1 – P, then he will not prefer B to A under the same probabilities. 3. Continuity of preferences: The consumer has a ‘system of preferences that is all-embracing and complete.’ His preferences have continuity in the sense that if he prefers event A to B when probability of A equals 1 (i.e., P(A) = 1) and if he prefers B to A when P(A) = 0, there lies a probability between 1 and 0, at which he is indifferent between events A and B. Appraisal of N-M Utility Index The N-M utility index is only a theoretical or conceptual measure of utility. It provides a basis for indexing the expected utility levels under uncertain conditions. It does not measure the intensity of introspective satisfaction or pleasure nor is it the purpose of N-M measure of ‘cardinal’ utility. It is also worth noting that N-M cardinal utility is not identical with neo-classical cardinal utility. While cardinal utility, in the neo-classical sense, means actual, absolute measurement of strength of feeling, the word ‘cardinal’ has been used in N-M measure of utility entirely in the ‘operational’ sense. The N-M measure of utility serves a useful purpose by providing a basis for rational thinking and prediction, particularly where uncertainty and risk are involved, in spite of the fact that there is an arbitrariness in the method of computing utility index.

9.4 RELATIONSHIP BETWEEN SHAPE OF UTILITY FUNCTION AND BEHAVIOUR TOWARDS RISK

Based on the behaviour that people project towards risk, it is possible to place them under one of the three distinct categories. The category under which they will be placed will depend on the respective Bernoulli utility functions that they display with their Check Your Progress behaviours. 4. Name the classical Let us use the example of tossing a coin to explain this. Assume that on heads the economists who amount won is ` 10 and on tails the amount won is ` 20. Hence, the gamble’s expected believed that utility value will be: is cardinally measurable. (0.5 × 10) + (0.5 × 20) = $15. 5. What are the two approaches to the A person who is risk-averse analysis of consumer When an individual’s utility of the gamble’s expected value is higher than the expected behaviour? utility from the gamble itself, the individual is considered to be risk-averse. This is a more 6. What does the N-M precise definition of Bernoulli’s idea. hypothesis suggest?

Self-Instructional Material 247 Choice under Uncertainty A person’s risk-averse behaviour can be captured in the concave Bernoulli utility function, and Risk like a logarithmic function. In the case of the gamble of coin toss as given above, a person who is risk averse and whose Bernoulli utility function was: u(w) = log(w) ; (w representing the outcome) NOTES might have an expected utility over the gamble of: 0.5 × log(10) + 0.5 × log(20) = 1.15, And the utility expected of the value will be: log (15) = 1.176

u(w)

u(w) = log(w)

i

i o w

Fig. 9.1 Bernoulli Utility Function

A person who is risk loving When an individual’s utility of the gamble’s expected value is lower than the expected utility from the gamble itself, they are categorised as being risk-loving. Nevertheless, it is important to note that, this is not how normally gambling behaviour works, for example in a casino. If this definition is to be accepted, then a truly risk-loving person should be ready to put all his assets at stake for just one roll of dice. Risk-loving behaviour is captured in the convex Bernoulli utility function. For example, an exponential function. In case of the gamble given above, a risk-loving person with the Bernoulli utility function as: u(w) = w2 would display an expected utility for the gamble as being: 0.5 × 102 + 0.5 × 202 = 250, When the utility of the gamble’s expected value is: 152 = 225

Self-Instructional 248 Material u(w) Choice under Uncertainty and Risk

u(w) = w2

NOTES

i i o w

Fig. 9.2 Convex Bernoulli Utility Function

A person who is risk neutral When an individual’s utility of the gamble’s expected value is exactly equal to the expected utility from the gamble itself, they are categorised as being risk-neutral. In practice, the best example of risk-neutrality are the majority of the financial institutions that adopt this method in making investments. A linear Bernoulli function is used to capture risk-neutral behaviour. In the case of the gamble that has been discussed above, a risk-neutral person with Bernoulli utility function as: u(w) = 2w would have an expected utility over the gamble of: (0.5 × 2 × 10) + (0.5 × 2 × 20) = 30, While the utility of the expected value of the gamble is: 2 × 15 = 30

u(w)

u(w) = k.w

i i o w

Fig. 9.3 Linear Bernoulli Function Self-Instructional Material 249 Choice under Uncertainty If we take the example of insurance, while the buyers of insurance display and Risk behaviour that is risk-averse, the insurance company itself shows a behaviour of being risk-neutral. The insurance company is earning its profit with the received premiums’ value being greater than the value of the loss that the company expects. NOTES Any gambling ‘g’ will have the certainty equivalent which is an amount of money, say ‘Q’, which will certainly accrue and will provide the consumer the exact same utility as would be provided by the gamble itself. A gamble’s risk premium is the difference of the gamble’s expected value and the gamble’s certainty equivalent. From the above, it can be said that a person who is risk averse will have certainty equivalent lower than the gamble’s expected value, and the person’s risk premium will be positive. This means that a person who is risk averse will require some added incentive to actually participate in the gambling risk. There is a zero risk premium for a person who is risk neutral and the person’s certainty equivalent is exactly the same as the gamble’s expected value. On the other hand, a person who is risk loving has a risk premium in the negative. This is due to the need to accept the expected value for extra incentives, not due to the risky gamble, and the person will have a higher certainty equivalent than the gamble’s expected value. 9.4.1 Elasticity of Marginal Utility and Risk Aversion The money income of an individual is representative of the market basket of goods that can be purchased by him. The assumption that will be made is that the individual is aware of the existing probabilities of gaining or making money income in various situations and the pay-offs/outcomes will be measured not in rupees but as provided utility. As has been seen above, individuals have their own attitudes towards risk. Mostly, individuals opt for situations that are less risky, and that which will have less variability as far as rewards/outcomes are concerned. We could say that mostly individuals aim at keeping their risks at a minimum and these persons are referred to as risk averse or risk averters. People who like to take risks are referred to as risk lovers or risk seekers. There are persons who are referred to as risk neutral also as they are the ones who have an attitude of indifference towards risk. People have different attitude towards risk based on whether the marginal utility of money increases, diminishes or remains constant. A person who is risk averse will have diminishing marginal utility with increase in money. In the case of a risk seeker, there is increase in marginal utility of money with increase in money. For a risk neutral person, marginal utility of money remains constant with increase in the amount of money. Risk Averter Let us look at money income as a single composite commodity to consider risk attitude in the light of marginal utility. The money income of an individual is representative of the basket of goods that he can purchase from the market. We are going with the assumption that the individual is well aware of the probabilities of gaining/making money income in various situations and that the pay-offs or outcomes will be measured in the utility provided rather than in terms of rupees.

Self-Instructional 250 Material Y Choice under Uncertainty and Risk C U 75 65 B y

t NOTES

i 55 l i

t A

U 45

0 10 15 20 30 Mondy income (in Thousands)

Fig. 9.4 Money Income and Utility

In the figure given above, the X axis represents the money income and the Y axis represents utility while the curve OU has been drawn to represent the utility function of money income of a risk-averse individual. Here, OL is the slope of total utility function and with the increase in the individual’s money income, this slope is seen to decrease. As there is an increase in the individual’s money income from ` 10,000 to ` 20,000, there is an increase in his total utility by twenty units as it escalates from 45 units to 65. When there is a rise in money income from ` 20,000 to ` 30,000, the individual’s total utility increases from 65 units to 75 units which is an increase of just 10 units. In the above graph, the concave utility function shows the marginal utility of money of the individual decreasing with a decrease in his money income, showing that the individual is risk averse. Consider that at this point the individual is in a job that provides him with ` 15,000 fixed monthly salary. Since this has no uncertainty as far as income from the job is concerned, there is no risk present. If the individual decides to move to a job of a salesperson whose income is dependent on commission, it will involve risk since the income will not be certain. In case he is successful in his sales job, he might make an income much higher than he is currently making and if he is not that good he might earn just about the same as he is earning in his current job. Let us consider that in the new job that he is considering to take lies a 50-50 probability of getting either ` 30,000 or ` 10,000 (implying that the probability for each is 0.5). Therefore, in case of uncertainty, there is no way for the individual to know what the actual utility is of performing a specific action. Since there are probabilities of alternative outcomes, it is possible to calculate the expected utility. Whether or not the new risky job will be taken up by the individual can be known through comparison of the utility that is expected from the new risky job against the utility from the job the individual is currently holding. In the above graph, the OU, the utility function curve, shows that the money income of ` 15,000 in certainty is 55. In the new risky job, in case the individual is successful and has an income of ` 30,000, the utility gained from ` 30,000 is 75. In case he fails at the new risky job and just gains ` 10,000 as income his utility will be 45. While the utility function of money income shows the individual to be risk-averse, but as the risky job’s expected utility appears greater than the present job’s utility with a certain income, the individual will opt for the risky job.

Self-Instructional Material 251 Choice under Uncertainty Now, consider that in the new risky job, the individual succeeds and earns an and Risk income of ` 30,000, which is twice as the assured income from the present job. If failure at the new job on the part of the individual will decrease the income to zero, then the expected utility of the risky job is given by: NOTES E (U) = 0.5 U (0) + 0.5 U (30,000) = 0 + 0.5 × 75 = 37.5 Hence, the new jobs expected utility is lower than the utility of 55 which the individual gains from the current job which is providing him ` 15,000 as a fixed assured income. Even in the risky job the income that can be expected is ` 15,000: [E(x) = 0.5 × 0 + 0.5 × 30,000 = 15000] In the graph given above, the choice of a risk-averse individual is being represented and for him there is a fall in marginal utility of money with increase in money. We are now in a position to provide a precise definition of a risk-averse individual. A risk lover or risk-preferred person is an individual who likes to opt for an outcome that is risky but comes with the same expected income as a certain income. For an individual who is risk-loving, there is an increase in the marginal utility of income with increase in his money income. This is represented by the convex total utility function curve OU in the graph given below.

U U y t i l

i C t 83 U

M - N 43 B

20 0 10 20 30 x Money Income (in '000)

Fig. 9.5 Convex Total Utility Function

Consider that this individual who is risk-loving is holding a job that earns him ` 20,000 as a certain income. The above graph depicts that 43 units is the utility of ` 20,000 for the individual. In case the individual is offered a risky job with ` 30,000 as income if he proves to be extremely efficient and just ` 10,000 if he is extremely inefficient with equal probability of 0.5 in both the jobs, then the new jobs expected utility will be: E (U) = 0.5 U (10,000) + 0.5 U (30,000) As depicted in the graph above, ` 20 is the utility of ` 10,000 for this individual and for ` 30,000 it is 83. Hence,

Self-Instructional 252 Material E (U) = 0.5 (20) + 0.5 (83) Choice under Uncertainty and Risk = 10 + 41.5 = 51.5 With 51.5 being the new risky job’s expected utility which is more than the present job’s NOTES utility of 43, the new job will be preferred by the risk-loving individual despite the fact that the expected income in the new risky job is also ` 20,000 as: (0.5 × 10,000) + 0.5 (30,000) = ` 20,000). Risk-loving individuals are the ones who gamble, purchase lotteries, take part in criminal activities, and commit big frauds, even at the risk of punishment if caught. A person will be considered to be risk neutral, if he is indifferent either towards a certain given income or an uncertain income with the same expected value. A person is risk neutral if his money income’s marginal utility remains constant with increase in his money income. The graph given below represents a risk neutral individual’s total utility function.

Fig. 9.6 Risk Neutral Individual’s Total Utility Function

The graph in the figure above shows that the utility of a certain income of ` 20,000 is 80. With the new risky job and rise in income on being a successful salesman to ` 30,000, the utility goes up to 120 units. Then again in case the individual is unsuccessful at the new risky job as a salesman, the income falls to ` 10,000 and its utility slips to 40 units. The assumption is that increase in income or decrease in income is equally possible at the new risky job. The expected utility of the new risky job is: E (U) = 0.5 U (10,000) + 0.5 U (30,000) = 0.5 (40) + 0.5 (120) = 20 + 60 = 80

Self-Instructional Material 253 Choice under Uncertainty Risk Aversion and Fair Bets and Risk According to Bernoulli’s hypothesis, an individual whose marginal utility of money declines will not be willing to accept a fair gamble. A fair gamble or game is that where the NOTES gamble’s expected value of income is equal to the same amount of income with certainty. An individual refusing a fair bet will be considered to be risk-averse. This individual will give preference to a ‘given income with certainty to a risky gamble with the same expected value of income’. The commonest attitude found towards risk is of risk aversion. It is because of this attitude that many people take insurance for all kinds of risks like accident, theft, illness, to name a few. The risk-averse individuals are the ones who would rather be in occupations or jobs that get them stable income rather than those that have uncertain income. The Neumann-Morgenstern method of measuring expected utility can be used to explain the risk-averse attitude. For an individual who is risk averse, as his income increases, his marginal utility of income diminishes.

Y H B U(i) 75 C 70 D 62.5 A L 50 G s e c i d n I

y t i l i t U

M0 M1 M2 M3 M4 0 1500 2000 3000 4000 4500 x Income

Fig. 9.7 Neumann-Morgenstern Utility Function Curve

The graph in the figure given above shows the Neumann-Morgenstern utility function curve U (I). The utility curve begins at the origin and continues on a positive slope showing that the individual has preference for more income in comparison to less income. Additionally, a conclave utility curve implies that an individual’s marginal utility of income diminishes with increase in his income. The utility curve in the above graph depicts the risk-averse attitude. Neumann-Morgenstern Concave Utility Curve of a Risk-Averter Assume that the current income of an individual is ` 3,000. The individual is offered a fair gamble where there is a 50-50 chance of losing/winning ` 1,000 which places the probability of winning at 0.5 or 1/2. In case he wins the game, his income will go up to ` 4,000 and on losing it will go down to ` 2,000. In such an uncertain situation, the individual’s expected money value of income is: E (V) = 1/2 × 4000 + 1/2 × 2000 = ` 3000 If the gamble is not accepted by the individual, his income will remain ` 3,000 with certainty. Even ‘though the expected value of his uncertain income prospect is Self-Instructional 254 Material equal to his income with certainty, a risk averter will not accept the gamble’. The reason Choice under Uncertainty being that he will act according to the expected utility of his income in the uncertain and Risk situation. According to the above graph, the utility obtained from ` 4,000 is 75 and just 50 from ` 2,000. NOTES The uncertain prospects expected utility is: E (U) = 1/2 (75) + 1/2 (50) = 37.5 + 25 = 62.5 The individual’s rejection of the gamble is based on his diminishing marginal utility of money income. He perceives the utility gained from ` 1,000 to be lower than the loss he would incur on ` 1000 on losing the gamble. Therefore, if money income’s marginal utility diminishes, an individual will stay away from fair gambles. An individual of this type is known as a risk averter as he would rather go for an income with certainty than for a gamble that provides the same expected value. Here is an example to explain the above situation. Consider that the individual has a certain income of ` 3,000 and is offered 2 fair gambles. • A 50:50 chance to lose or win ` 1000 • A 50:50 chance to lose or win ` 1,500 In the second case, the even chance to lose or win the expected value of income will be: 1/2(1500) + 1/2 (4500) = `. 3000 In the above figure on the utility curve U (I), a straight line segment GH is drawn to join G (corresponding to income of ` 1500) and H (corresponding to income of ` 4500). GH, the straight-line segment shows the expected utility from the expected money value of ` 3,000 from the second gamble which is: M₂L Which is less than M₂D of the first gamble. Hence, the first gamble is preferred by the individual as it has lower variability of outcome compared to the second gamble. In the case where there is certainty of income, there is no risk, as there exists no variability of outcome. 9.4.2 Absolute and Relative Risk Aversion It can be possible that a person is risk averse in some segments while he is risk loving in others and can also change his attitude towards risk in any segment. It is argued by Friedman and Savage that an individual can be at the same time risk averse and risk loving for different choices and for different segments of wealth. Therefore, effectively, we cannot consider it to be irrational when an individual purchases insurance to cover some varieties of risk on a day and them is seen gambling on the same day. They proposed that all individuals are capable of irrational behaviour when they are faced with choices that are risky under some situations.

Self-Instructional Material 255 Choice under Uncertainty It is also possible to make a distinction between an individual’s reaction to absolute and Risk changes in wealth and to proportional changes in wealth, where the former measures an absolute risk aversion and the latter measures a relative risk aversion. The implication of a decreasing absolute risk aversion depends on the amount of NOTES wealth an individual is ready to risk which will increase with increase in wealth. Similarly, the implication of a decreasing relative risk aversion depends on the proportion an individual will be ready to risk which will rise with rise in wealth. In case of constant absolute risk aversion, the amount of wealth which the individual will put to risk will stay constant with increase in wealth, while the proportion of wealth will remain the same with constant relative risk aversion. Individuals will be ready to put increasing smaller amounts of wealth at risk as they grow wealthier, with increasing absolute risk aversion, and decreasing proportions of wealth with increasing relative risk aversion. Using the Arrow-Pratt measure, we can write the relative risk aversion measure in the following manner: Arrow-Pratt relative risk aversion = -W U’’(W)/U’(W) where, W = Level of wealth U’(W) = First derivative of utility to wealth, measuring how utility changes as wealth changes U’’(W) = Second derivative of utility to wealth, measuring how the change in utility itself changes as wealth changes We can use the log utility function to illustrate the concept: U = log (W) U’ = 1/W U’’ = 1/W 2 Absolute risk aversion coefficient = U’’/U’ =W Relative risk aversion coefficient = 1 Therefore, the log utility function shows a decreasing absolute risk aversion in which an individual will be willing to invest more money in risky assets as their wealth Check Your Progress increases. It also shows a constant relative risk aversion in which an individual will be 7. When is an willing to invest the same percentage of wealth in risky assets even when their wealth individual increases. considered to be risk averse? Majority of the risk and return models, are in practice based around certain specific 8. When is an assumptions regarding relative and absolute risk aversion, and also if they decrease, individual increase or remain constant with increase in wealth. categorised as being risk-neutral? 9. On what basis do 9.5 SUMMARY people have different attitude In this unit, you have learnt that, towards risk? 10. What did Friedman • The concept of risk and uncertainty can be better explained and understood in and Savage argue contrast to the concept of certainty. regarding being risk- averse and risk • Certainty is the state of perfect knowledge about the market conditions. In the loving? state of certainty, there is only one rate of return on the investment and that rate is known to the investors.

Self-Instructional 256 Material • In common parlance, risk means a low probability of an expected outcome. From Choice under Uncertainty business decision-making point of view, risk refers to a situation in which a business and Risk decision is expected to yield more than one outcome and the probability of each outcome is known to the decision makers or it can be reliably estimated. • There are two approaches to estimating probabilities of outcomes of a business NOTES decision, viz., (i) a priori approach, i.e., the approach based on deductive logic or intuition and (ii) posteriori approach, i.e., estimating the probability statistically on the basis of the past data. • The probability of outcomes of a decision can be estimated statistically by way of ‘standard deviation’ and ‘coefficient of variation’. • Uncertainty refers to a situation in which there is more than one outcome of a business decision and the probability of no outcome is known nor can it be meaningfully estimated. • For the purpose of decision-making, uncertainty is classified as: o Complete ignorance o Partial ignorance • Utility is a psychological phenomenon. It is a feeling of satisfaction, pleasure or happiness. • Measurability of utility has, however, been a contentious issue. The classical economists, viz., Jeremy Bentham, Leon Walrus, Carl Menger, etc. and the neo- classical economist, notably Alfred Marshall, believed that utility is cardinally or quantitatively measurable like height, weight, length, temperature and air pressure. This belief resulted in the Cardinal Utility concept. • The modern economists, most notably J. R. Hicks and R. G. D. Allen, however, hold the view that utility is not quantitatively measurable—it is not measurable in absolute terms. Utility can be expressed only ordinally comparatively or in terms of ‘less than’ or ‘more than’. It is, therefore, possible to list the goods and services in order of their preferability or desirability. This is known as the ordinal concept of utility. • According to Marshall, utility of a commodity for a person equals the amount of money he/she is willing to pay for a unit of the commodity. In other words, price one is prepared to pay for a unit of a commodity equals the utility he expects to derive from the commodity. They formulated the theory of consumption on the assumption that utility is cardinally measurable. They coined and used a term ‘util’ meaning ‘units of utility’. • The modern economists have discarded the concept of cardinal utility and have instead employed the concept of ordinal utility for analysing consumer behaviour. The concept of ordinal utility is based on the fact that it may not be possible for consumers to express the utility of a commodity in numerical terms, but it is always possible for them to tell introspectively whether a commodity is more or less or equally useful as compared to another. • A major contribution to the utility theory was made by a famous mathematician, John von Neumann, and a well-known economist Oskar Morgenstern in their famous book Theory of Games and Economic Behaviour. • The N-M hypothesis suggests that if an individual behaves consistently, it is possible to construct his ‘utility index’ and express his preferences numerically. • The N-M utility index is only a theoretical or conceptual measure of utility. It provides a basis for indexing the expected utility levels under uncertain conditions. Self-Instructional Material 257 Choice under Uncertainty It does not measure the intensity of introspective satisfaction or pleasure nor is it and Risk the purpose of N-M measure of ‘cardinal’ utility. • It is worth noting that N-M cardinal utility is not identical with neo-classical cardinal utility. While cardinal utility, in the neo-classical sense, means actual, absolute NOTES measurement of strength of feeling, the word ‘cardinal’ has been used in N-M measure of utility entirely in the ‘operational’ sense. • Based on the behaviour that people project towards risk, it is possible to place them under one of the three distinct categories. The category under which they will be placed will depend on the respective Bernoulli utility functions that they display with their behaviours. • When an individual’s utility of the gamble’s expected value is higher than the expected utility from the gamble itself, the individual is considered to be risk- averse. • A person’s risk-averse behaviour can be captured in the concave Bernoulli utility function, like a logarithmic function. • When an individual’s utility of the gamble’s expected value is lower than the expected utility from the gamble itself, they are categorized as being risk-loving. • Risk-loving behaviour is captured in the convex Bernoulli utility function. For example, an exponential function. • When an individual’s utility of the gamble’s expected value is exactly equal to the expected utility from the gamble itself, they are categorized as being risk-neutral. A linear Bernoulli function is used to capture risk-neutral behaviour. • A gamble’s risk premium is the difference of the gamble’s expected value and the gamble’s certainty equivalent. • The money income of an individual is representative of the market basket of goods that can be purchased by him. The assumption that will be made is that the individual is aware of the existing probabilities of gaining or making money income in various situations and the pay-offs/outcomes will be measured not in rupees but as provided utility. • People have different attitude towards risk based on whether the marginal utility of money increases, diminishes or remains constant. • A risk lover or risk-preferred person is an individual who likes to opt for an outcome that is risky but comes with the same expected income as a certain income. • Risk-loving individuals are the ones who gamble, purchase lotteries, take part in criminal activities, and commit big frauds, even at the risk of punishment if caught. • According to Bernoulli’s hypothesis, an individual whose marginal utility of money declines will not be willing to accept a fair gamble. A fair gamble or game is that where the gamble’s expected value of income is equal to the same amount of income with certainty. • The Neumann-Morgenstern method of measuring expected utility can be used to explain the risk-averse attitude. For an individual who is risk-averse, as his income increases, his marginal utility of income diminishes. • It can be possible that a person is risk-averse in some segments while he is risk- loving in others and can also change his attitude towards risk in any segment. It is argued by Friedman and Savage that an individual can be at the same time risk- averse and risk-loving for different choices and for different segments of wealth. Self-Instructional 258 Material • It is also possible to make a distinction between an individual’s reaction to absolute Choice under Uncertainty changes in wealth and to proportional changes in wealth, where the former and Risk measures an absolute risk aversion and the latter measures a relative risk aversion.

9.6 KEY TERMS NOTES

• Certainty: It is the state of perfect knowledge about the market conditions. • Risk: It refers to a situation in which a business decision is expected to yield more than one outcome and the probability of each outcome is known to the decision makers or it can be reliably estimated. • Uncertainty: It refers to a situation in which there are more than one outcome of a business decision and the probability of no outcome is not known nor can it be meaningfully estimated. • Gamble risk premium: A gamble’s risk premium is the difference of the gamble’s expected value and the gamble’s certainty equivalent.

9.7 ANSWERS TO ‘CHECK YOUR PROGRESS’

1. The concept of risk and uncertainty can be better explained and understood in contrast to the concept of certainty. 2. Risk refers to a situation in which a business decision is expected to yield more than one outcome and the probability of each outcome is known to the decision makers or it can be reliably estimated. 3. The probability of outcomes of a decision can be estimated statistically by way of ‘standard deviation’ and ‘coefficient of variation’. 4. Classical economists, like, Jeremy Bentham, Leon Walrus and Carl Menger and the neo-classical economist, notably Alfred Marshall, believed that utility is cardinally or quantitatively measurable. 5. Based on cardinal and ordinal concepts of utility, there are two approaches to the analysis of consumer behaviour: (i) Cardinal utility approach, attributed to Alfred Marshall and his followers, is also called the neo-classical approach or Marshallian approach. (ii) Ordinal utility approach, pioneered by J. R. Hicks, a Nobel laureate and R. G. D. Allen, is also called Hicks-Allen approach or the indifference curve analysis. 6. The N-M hypothesis suggests that if an individual behaves consistently, it is possible to construct his ‘utility index’ and express his preferences numerically. 7. When an individual’s utility of the gamble’s expected value is higher than the expected utility from the gamble itself, the individual is considered to be risk averse. 8. When an individual’s utility of the gamble’s expected value is exactly equal to the expected utility from the gamble itself, they are categorised as being risk neutral. 9. People have different attitude towards risk based on whether the marginal utility of money increases, diminishes or remains constant. 10. It is argued by Friedman and Savage that an individual can be at the same time risk averse and risk loving for different choices and for different segments of

wealth. Self-Instructional Material 259 Choice under Uncertainty and Risk 9.8 QUESTIONS AND EXERCISES

Short-Answer Questions NOTES 1. What is certainty? What are the two approaches to estimate probabilities of outcomes of a business decision? 2. What is uncertainty? How can it be classified? 3. What is subjective probability distribution? 4. What led to the idea of cardinal utility and ordinal utility? Why have the modern economists discarded the concept of cardinal utility? 5. How is N-M cardinal utility different from neo-classical cardinal utility? 6. Who is a risk-averse person? How can his behaviour be captured? 7. Illustrate graphically the attitude of a risk averter towards risk. 8. What does Bernoulli’s hypothesis of fair gamble state? Long-Answer Questions 1. Differentiate between uncertainty and risk in decision making. 2. Discuss the ordinal and cardinal measures of utility. 3. Assess the principle of Neumann-Morgenstern utility and the assumptions of N- M utility index. 4. ‘Based on the behaviour that people project towards risk, it is possible to place them under one of the three distinct categories.’ What are these categories? 5. Evaluate the elasticity of marginal utility and risk aversion. 6. Describe absolute and relative risk aversion.

9.9 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.;W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

Self-Instructional 260 Material Economics of Imperfect UNIT 10 ECONOMICS OF Information IMPERFECT INFORMATION NOTES Structure 10.0 Introduction 10.1 Unit Objectives 10.2 Information and Decision Making under Certainty and Uncertainty 10.2.1 Investment Decisions under Certainty 10.2.2 Investment Decisions under Uncertainty 10.3 Asymmetric Information 10.3.1 Adverse Selection and Signalling 10.3.2 Moral Hazard and its Application to Insurance 10.4 Summary 10.5 Key Terms 10.6 Answers to ‘Check Your Progress’ 10.7 Questions and Exercises 10.8 Further Reading

10.0 INTRODUCTION

Imperfect information can be due to ignorance or uncertainty. If the market participant is aware that better information is available, information becomes another need or want. Information may be acquired through an economic transaction and becomes a commodity that is a cost to the buyer or seller. Useful information is available as a market product in forms of books, media broadcasts, and consulting services. Decision making is an important aspect of imperfect information. Most decision theories are normative or prescriptive, i.e., it is concerned with identifying the best decision making assuming an ideal decision maker who is fully informed, able to compute with perfect accuracy, and fully rational. The practical application of this prescriptive approach (how people ought to make decision) is called decision analysis, and it is aimed at finding tools, methodologies and software to help people make better decisions. The most systematic and comprehensive software tools developed in this way are called decision support systems. In this unit, you will be acquainted with the economics of imperfect information and decision-making under certainty and uncertainty.

10.1 UNIT OBJECTIVES

After going through this unit, you will be able to: • Discuss the concept of risk, certainty and uncertainty • Describe investment decisions under the condition of certainty • Evaluate investment decisions under the condition of uncertainty • Assess the concept of asymmetric information • Analyse the term adverse selection and signalling • Explain moral hazard as a problem • Discuss the applications of moral hazards on insurance Self-Instructional Material 261 Economics of Imperfect Information 10.2 INFORMATION AND DECISION MAKING UNDER CERTAINTY AND UNCERTAINTY

NOTES In recent decades, there has been increasing interest in what is sometimes called ‘behavioural decision theory’ and this has contributed to a re-evaluation of what rational decision-making requires. Uncertainty: Uncertainty is a case when there is more than one possible outcome to a decision and where the probability of each specific outcome occurring is not known. This may be due to the insufficiency in past information or instability in the structure of the variables. In extreme forms of uncertainty, not even the outcomes themselves are known. Many of the choices that people make, involve considerable uncertainty. Most people, for example, borrow to finance large purchases, such as a house or college education, and plan to pay for them out of future income. But for most of us, future incomes are uncertain. Our earnings can go up or down; we can be promoted or demoted, or even lose our jobs. And if we delay buying a house or investing in college education, we risk increasing price rates that could make such purchases less affordable. Certainty: Certainty refers to a situation where there is only one possible outcome to a decision and this outcome is known precisely. For example, investing in treasuring bills leads to only one outcome and this is known with certainty. The reason is that there is virtually no chance that the central government will fail to redeem these treasuring bills. Risk: Risk refers to a situation where there is more than one possible outcome to a decision and the probability of each specific outcome is known or can be estimated. Thus, risk requires that the decision maker knows all the possible outcomes of the decision and have some idea of the probability of each outcome’s occurrence. For example, in tossing a coin, we can get either a head or a tail, and each has an equal chance of occurring. In general, the greater the number of possible outcomes, the greater is the risk associated with the decision. Choice under Uncertainty So far in consumption theory, we have assumed that prices, incomes and other variables are known with certainty. If a consumer purchases a house, he knows the benefits of ownership of the house. But when uncertainty exists, a decision does not lead to a single outcome but to several possible outcomes with different probabilities. If you decide to purchase a house in New Delhi, you are not certain of enjoying all its benefits. You are taking a gamble. One remote but distinct outcome is that your dream home will be damaged extensively by an earthquake. Or, if you have invested in a college education and look forward to a prosperous career, you may not receive the benefits of the education you have worked for so diligently. There is a probability that you will be killed in an automobile accident. Each of these dismal events has only a small probability of occurring, but if it does, it is devastating. In each example an individual makes a decision where multiple outcomes are possible.

Self-Instructional 262 Material Since more than single outcomes are associated with decision, it makes little Economics of Imperfect Information sense to say that the individual maximizes utility, because multiple possible outcomes have multiple possible utilities. To analyse decision making under uncertainty, we must replace utility maximization with some other goal. NOTES 10.2.1 Investment Decisions under Certainty The condition of certainty refers to a state of perfect knowledge. It implies that investors have complete knowledge about the market conditions, especially the investment opportunities, cost of capital and the expected returns on the investment. Of the several criteria proposed for evaluating the profitability of the various kinds of projects, the three most commonly used criteria under certainty are: • Pay-back (or pay-out) period • Net discounted present value • Internal rate of return or marginal efficiency of capital These criteria are equally applicable to a variety of investment decisions regarding new investments and those pertaining to replacement, scrapping, and widening or deepening of capital. Incidentally, from analysis point of view, there is no structural difference between decisions on new investment and those on replacement. Let us now briefly describe the three criteria mentioned above and look into their applicability. We will discuss these criteria under the condition of certainty. Pay-Back Period Method The pay-back period is also known as ‘pay-out’ and ‘pay-off’ period. The pay-back period method is the simplest and one of the most widely used methods of project evaluation. The pay-back period is defined as the time required to recover the total investment outlay from the gross earnings, i.e., gross of capital wastage or depreciation. If a project is expected to generate a constant flow of income over its life-time, the pay- back period may be calculated as given below.

Total Investment outlays Pay-back Period = Gross Return per period For example, if a project costs ` 40,000 million and is expected to yield an annual income of ` 8,000 million, then its pay-off period is computed as follows:

` 40,000 million Pay-off Period = ` 8,000 million = 5 years In case of projects which yield cash in varying amounts, the pay-back period may be obtained through the cumulative total of annual returns until the total equals the investment outlay. The sum of cash inflows gives the pay-back period. For example, suppose that the cost of a project is ` 10,000 million which yields cash flows over 5 years as given in Col. 3 of Table 10.1. The table provides necessary information for the calculation of pay-back period.

Self-Instructional Material 263 Economics of Imperfect Table 10.1 Calculation of Pay-back Period Information Year Total fixed outlay Annual Cash-flows Cumulative (` in million) (` in million) Total of Col. (3) (` in million) NOTES (1) (2) (3) (4) 1st 10,000 4,000 4,000 2nd — 3,500 7,500 3rd — 2,500 10,000 4th — 1,500 11,500 5th — 1,000 12,500 As the table shows, the cumulative total of annual cash flows breaks-even with the total outlay of the project (` 10,000 million) at the end of the 3rd year. Thus, the pay- back period of the project is 3 years In case of projects with different investments yielding different annual returns, the project evaluation procedure can be described as follows. After pay-back period of each project is calculated, projects are ranked in increasing order of their pay-back period. Let us suppose, for example, that a firm has to select one out of four riskless projects, viz., A, B, C and D. The total cost of each project and their respective annual yields are given in columns (2) and (3), respectively, in Table 10.2. The calculation of their respective pay-back period given in column (4) of the table. Project B ranks 1st and projects C, D and A rank 2nd, 3rd, and 4th, respectively. The firm will invest in these project in the same order, if it adopts the pay-back period criterion for project evaluation. In case projects A, B, C and D yield cash flows at different rates in the subsequent years, the cumulative total method can be adopted to calculate their pay-back periods as shown in Table 10.1 and projects ranked accordingly. After projects are ranked, they are selected in order of their ranking depending on the availability of funds. All other things being the same, a project with a shorter pay-off period is preferred to those with longer pay-off period. This method of ranking projects or project selection is considered to be simple, realistic and safe. Its simplicity is obvious in the calculation of the pay-off period. It is realistic in the sense that businessmen want their money back as quickly as possible and this method serves their purpose. It is safe since it avoids incalculable risk in the long run. Table 10.2 Ranking of Projects

Project Total outlay Annual return Pay-back period Rank (` in million) (` in million) (Years) (1) (2) (3) (4) (5) A 36,000 6,000 36,000 ÷ 6,000 = 6 4 B 24,000 8,000 24,000 ÷ 8,000 = 3 1 C 20,000 5,000 20,000 ÷5,000 = 4 2 D 15,000 3,000 15,000 ÷3,000 = 5 3

Self-Instructional 264 Material This method is ‘a crude rule of thumb’ and can hardly be defended except on the Economics of Imperfect ground of avoiding risk associated with long pay-back projects. Besides, this method Information assumes that cash inflows are known with a high degree of certainty. The second and the major drawback of this criterion is that it considers only a short period in which cost of project is recovered. It ignores the period and the subsequent NOTES returns, after the pay-off period. This criterion, if applied, may deprive the investor of additional earning in future. For example, suppose that an investor has to make a choice between two Projects A and B, their costs and returns are given as follows: (i) Project A: Total cost = ` 24,000 Annual returns ` 8,000 over three years Pay-back period = 3 years (ii) Project B: Total cost = ` 20,000 Annual returns ` 5,000 over six years Pay-back period = 20,000/5,000 = 4 years Obviously, according to pay-off period criterion, Project A will be preferred to project B. But this will lead to foregoing an additional expected income of ` 6,000, calculated as follows. Total yield from Project B = ` 5000 × 6 (years) = ` 30,000 Total yield from Project A = ` 8000 × 3 (years) = ` 24,000 Loss of expected additional income = Total earning from Projects B less total earning from Project A. = ` 30,000 – ` 24,000 = ` 6000. The application of pay-back criterion can be justified only if project B involves a high degree of uncertainty and risk. Nevertheless, this criterion can be profitably adopted if terminal year of all projects under consideration is the same. Net Present Value Method Concept of present value: Time value of money—The concept of the present value of money is very well reflected in the proverb ‘a bird in the hand is worth two in the bush’. In general, money received today is valued more than money receivable tomorrow. Cash in hand is valued more because it gives: (i) liquidity and (ii) an opportunity to invest it and earn return (interest) on it. This is called the time value of money. The concept of the time value of money is very often applied to investment decisions. Generally, there is a time-lag between investment and its returns. When an investment is made today, it begins to yield returns at some future date. The time gap between the investment and the first return from the investment is called ‘time lag’. During this time lag, the investor loses interest on the expected incomes. This implies that a rupee received today is worth more than a rupee receivable at some future date. Or conversely, a rupee expected to be received one year hence is worth less than a rupee today. In the context of the time value of money, the present value of a future income is lower than the value of the same amount received today. The concept of present value of money can be better understood through an example. Suppose that a sum of ` 100 held in cash today is deposited in a bank at 10 per cent rate of interest. After one year, ` 100 today will increase to ` 110. The amount (principal + interest) is worked out as follows. Self-Instructional Material 265 Economics of Imperfect Amount = 100 + 100 (10/100) Information = 100 + 100 (0.1) = 100 + 10 = 110 NOTES It follows that ` 110 expected one year hence is worth only ` 100 today. This means that ` 100 is the present value of ` 110 to be earned after a period of one year. The present value (PV) of ` 110 can be obtained as follows.

110 PV of `110 = = 100 (1+ 0.1) The present value of a future income may thus be defined as its value discounted at the current rate of interest. Alternatively, the present value of an amount expected at a future date, say after one year, is the sum of money which must be invested today to get that amount after one year.

The Formula for Computing Present Value: Suppose that an amount X0 is invested for a period of one year at a compounding interest rate. At the end of the year, the total

receipt, say X1 can be expressed as:

X1 = (X0 + r X0) = X0 (1 + r) …(10.1) Equation (10.1) shows that X increases at the rate of (1 + r) to take the value X after 0 1 one year. It implies that if X is discounted at the same rate of interest, it gives its 1 present value (PV). The formula for computing the present value is given below.

X1 1 PV of X = = X  …(10.2) 1­ (1+ r ) 1 1+ r In Eq. (10.2), 1/(1 + r) is the discount rate for one year. Given the rate of interest (i.e., the numerical value for r), any income receivable after one year can be discounted to its present value. For example, the present value of an income of ` 500 expected after one year at 10 per cent interest per annum (where r = 0.10), can be calculated as:

1 PV = 500  = 454.55 1+ 0.10 It means that, at 10 per cent interest rate, the present value of ` 500 expected

after one year is ` 454.55. The discount rate (d2) for an income receivable after 2 years 2 3 will be 1/(1 + r) , and for an income receivable after 3 years, d3 = 1/(1 + r) and so on. The formula for discount rate for the nth year is given as:

1 d = n ...(10.3) n (1+ r ) The formula for calculating present value (PV) of an amount receivable in the nth year is given as:

1 X PV = n n ...(10.4) (1+ r )

X n or PV = (1+ r ) n

Self-Instructional 266 Material Present Value of an Income Stream: The formula for calculating the total present Economics of Imperfect value (TPV) of a stream of annual return (R) over n years is given as: Information

RRRR 12+ +3 ++ n TPV = 23... n ...(10.5a) (1+++rrr ) (1 ) (1 ) (1 + r ) NOTES n 1 R = ∑ n n j=1 (1+ r )

n Rn or = ∑ n ...(10.5b) j =1 (1+ r) Net present value and investment decision—Having noted the concept of present value (PV) and the method of calculating PV of a future income, let us now see how investment decisions are taken on the basis of present value. In fact, present value (PV) adjusted for the cost of investment provides the basis of investment decisions. The PV adjusted for its cost is called ‘net present value’. The investment decision—accepting or rejecting a project—is taken on the basis of net present value. The net present value (NPV) may be defined as the difference between the present value (PV) of an income stream and the cost of investment (C), i.e., NPV = PV – C

n 1 RC− or = ∑ n n ...(10.6) j=1 (1+ r ) where C is the total cost of investment without any recurring expenditure. The investment decision rules can be specified as follows: (i) if NPV > 0, the project is acceptable (ii) if NPV = 0, the project is accepted or rejected on non-economic considerations (iii) if NPV < 0, the project is rejected If investment is a recurring expenditure, the total present cost (TPC) for n years can be calculated in the same manner as present value of an income stream is calculated, i.e.,

n Cn TPC = ∑ n ...(10.7) j =1 (1+ r)

n R n C n − n And then, NPV = ∑∑n n j=11(1+ r) j = (1+ r)

n Rn − Cn = ∑ n ...(10.8) j =1 (1+ r) The investment decision rule in this case is the same as given above. If the NPV is positive (i.e., NPV > 0), the project is profitable and acceptable. The firm can borrow any amount at the existing interest rate (r) and invest in it. When a choice between two projects has to be made, the one with higher NPV would be chosen.

Self-Instructional Material 267 Economics of Imperfect The Internal Rate of Return (IRR) is also called Marginal Efficiency of Investment Information (MEI), Internal Rate of Project (IRP) and Break-even Rate (BER). For example, if a one-year project costing ` 100 million yields ` 120 million at the end the year, then its internal rate of return (r) can be obtained as follows. NOTES 120 million ` (1 +r ) = 100 million = (1 + r) 100 = 120 and r = 0.20 The IRR of this project is 0.20 or 20 per cent. No other value of r can equate the NPV of the project with its cost. The IRR or MEI is defined as ‘the rate of interest or return which renders the discounted present value of its expected future marginal yields exactly equal to the investment cost of project’. In other words, ‘IRR is the rate of return (r) at which the discounted present value of receipts and expenditures are equal’. The IRR of a project yielding a stream of returns over n years and involving different investment costs can be obtained by using the formula given in Eq. (10.9).

n n Rn Cn ∑ n = ∑ n ...(10.9) j =1 (1+ r) j =1 (1+ r)

n n Rn Cn or ∑ n – ∑ n = 0 ...(10.10) j =1 (1+ r) j =1 (1+ r) The IRR criterion is basically the same as Keynes’s Marginal Efficiency of Investment (MEI). This criterion is theoretically superior to other criteria, though it has its own shortcomings. The IRR criterion says that so long as internal rate of return is greater than the market rate of interest, it is always profitable to borrow and invest. However, in a perfectly competitive market, a firm’s internal rate of return always equals the market rate of interest. From Eq. (10.10) it may be inferred that IRR and NPV criteria lead to the same conclusion or yield the same decision. There are situations, however, where the two criteria give conflicting results. For example, suppose that a firm has to make a choice between projects A and project B, each having a productive life of two years. The stream of net income at the end of the year from the two projects and their respective costs are presented in Table 10.3. Table 10.3 Flow of Net Incomes

Cost of project Ist year 2nd year Project A 100 0 140 Project B 100 130 0 Let us now calculate the NPV for both the projects, assuming a 10 per cent expected rate of return, and compare the result with IRR. Remember that NPV = PV – C.

Self-Instructional 268 Material Economics of Imperfect 0 140 +=115.70 Information Project A: PV = (1++ 0.10) (1 0.10)2 and NPV = 115.70 – 100 = 15.70 Since NPV is positive (` 15.70) at the expected rate of return of 10 per cent, NOTES Project A is acceptable. But if we raise the expected rate of return to 20 per cent, Project A will not be acceptable because at this rate of return, NPV is negative (– 2.78), as calculated below:

0 140 +−100 NPV = (1++ 0.20) (1 0.20)2 = 97.22 – 100 = – 2.78

130 0 +=118.18 Project B: PV = (1++ 0.10) (1 0.10)2 and NPV = 118.18 – 100 = 18.18. Project B is acceptable at the rate of 10 per cent return since NPV which equals 18.18 per cent is positive. It will be acceptable even at the expected return or interest rate of 20 per cent since, in that case, NPV will be ` 8.33 calculated as follows.

130 0 +−100 NPV = (1++ 0.20) (1 0.20)2 = 108.33 – 100 = 8.23 Having calculated the NPVs for Projects A and B, let us now calculate the IRR for both projects, for comparing the decisions. By definition, the IRR is the rate of return (r) which renders the net present value (NPV) equal to zero. Using the definition (10.10), r for Project A may be calculated as follows.

140 0+ −= 100 0 NPV = (1+ r ) 2 By solving this equation, we can obtain the value of r as shown below.

140 0+ −= 100 0 NPV = (1+ r ) 2

140 (1 + r)2 = = 1.40 100

(1 + r)= 1.40 = 1.183 r = 0.183 or 18.3 per cent Likewise, in case of Project B, the value of r can be obtained as follows.

130 +=0 100 NPV = (1+ r )

130 (1 + r)= = 1.30 100 r = 0.30 or 30 per cent

Self-Instructional Material 269 Economics of Imperfect We find that IRR of Project A is 18.3 per cent and for Project B it is 30 per cent. Information The NPV at different interest rates and the IRRS of Project A and B can be tabulated as given in Table 10.4. Table 10.4 NPV and IRR of Projects A and B NOTES Project A Project B r NPV r NPV 0.0 40.00 0.00 30.00 10.0 16.70 10.00 18.18 18.3 = IRR 0.00 20.00 8.33 20.0 –2.78 30.00 = IRR 0.00 The conflict between the two criteria may be shown by plotting the information given in Table 10.4 as shown in Fig. 10.2. The lines marked by Project A and Project B show relation between the various rates of return (r) and the corresponding NPV for Projects A and B. The two lines internally intersect at point P. The value of r at point P is 7.7 per cent. It shows that only at 7.7 per cent rate of return, both projects are equally acceptable. Below a rate of 7.7 per cent return, Project A is preferable because its NPV is higher than that of Project B. But above 7.7 per cent return, Project B is preferable because its NPV is higher than that of Project A. It follows that if a firm opts for Project A with higher NPV, it will earn a return less than 7.7 per cent and will have a longer pay- back period. Thus, the choice between the two projects will be based on the pay-off- period. Furthermore, if firms evaluate the two projects on the basis of their IRR, Project B should be preferable since its IRR = r = 30 per cent is greater than that of Project A (with its IRR = 18.3 per cent). Obviously, the two criteria (NPV and IRR) produce conflicting conclusions in regard to the choice of projects. In actual practice, however, the firms are guided by their objective relative to returns. 10.2.2 Investment Decisions under Uncertainty In this sec­tion, we will discuss the techniques of investment decisions under uncertainty. As defined above, uncertainty refers to a situation in which a decision is expected to yield more than one outcome and the probability of none of the possible outcomes is known. Therefore, decisions taken under uncertainty are neces­sarily subjective. However, analysts have devised some decision rules to impart some objectivity to the subjective decisions, provided decision-makers are able to identify the possible ‘states of nature’ and can estimate the outcome of each strategy. Some such important decision rules are discussed below. Hurwicz Decision Criterion Hurwicz has suggested a criterion for investment decisions under uncertainty. In his opinion, full realization of optimistic pay-off or full realization of most pessimistic pay-off is a rare phenomenon. The actual pay-off of a strategy lies somewhere between the two extreme situations. According to Hur­wicz criterion, therefore, the decision-makers need to construct a decision index of most optimistic and most pessimistic pay-offs of each alternative strategy. The decision index is, in fact, a weighted average of maximum possible and minimum possible pay-offs, weight being their subjective probability such

Self-Instructional 270 Material that sum of probabilities of maximum (Max) and minimum (Min) pay-offs equals one. Economics of Imperfect Information Hurwicz formula for decision index (Di) is given below.

Di = a Maxi + (1 – a) Mini where D = decision index of the ith strategy; and a = probability of maximum pay-off. i NOTES The construction of Hurwicz decision index is illustrated in Table 10.5. Column

(2) presents the maximum possible pay-offs of investment strategies, S1, S2, S3 and S4 listed in column (1). Column (3) shows the probability of maximum pay-offs. Column (4) gives the weighted pay-offs of the maximum pay-offs of the four strategies. Weighted pay-off equals the maximum pay-off multiplied by a (where a is subjective probability of pay-off). Note that the same probability applies to all the strategies. Columns (5), (6) and (7) give similar values of minimum pay-offs of the four strat­egies. The last column (8) gives the decision index. Table 10.5 Hurwicz Decision Index

Strategy Max αα Max Min (1 – α) (1 – α) min D (1) (2) (3) (4) (5) (6) (7) (8)

S1 10 0.8 8 6 0.2 1.2 9.2

S2 20 0.8 16 10 0.2 2.0 18.0

S3 15 0.8 12 5 0.2 1.0 13.0

S4 12 0.8 9 – 10 0.2 – 1.0 8.0

As regards the investment decision, as the table (Col. 8) shows, strategy S2 has the highest decision index (18.0). Therefore, strategy S2 is preferable to all other strategies. Laplace Decision Criterion The Laplace criterion uses the Bayesian rule to calculate the expected value of each strategy. Bayesian rule says that where meaningful estimate of probabilities is not available, the outcome of each strategy under each state of nature must be assigned the same probability and that the sum of probabilities of outcome of each strategy must add up to one. For this reason, the Laplace criterion is also called the ‘Bayesian criterion’. By assuming equal probability for all events, the environment of ‘uncertainty’ is converted into an environment of ‘risk’. Once this decision rule is accepted, then decision-makers can apply the decision criteria that are applied under the condition of risk. The most common method used for the purpose is to calculate the ‘expected value’. Once expected value of each strategy is worked out, then the strategy with the highest expected value is selected.

This decision rule avoids the problem that arises due to subjectivity in assuming a Check Your Progress probability of pay-offs. This criterion is, there­fore, regarded as the criterion of rationality 1. What is uncertainty? because it is free from a decision-maker’s attitude towards risk. 2. What does the To sum up, uncertainty is an important factor in investment decisions but there is condition of no unique method of dealing with uncer­tainty. There are several ways of making certainty mean? investment decisions under the condition of uncertainty. None of the methods, as described 3. State one limitation of the pay-back above, lead to a flawless decision. However, they do add some degree of certainty to period method. decision-making. The choice of method depends on the availability of necessary data 4. What is a decision and reliability of a method under different conditions. index?

Self-Instructional Material 271 Economics of Imperfect Information 10.3 ASYMMETRIC INFORMATION

Asymmetric information is a situation where some people have more information about NOTES a thing than others. Asymmetric information is characteristic of many business situations. Usually, a seller of a product knows more about its quality than the buyer does. Workers usually know their own skills and abilities better than employers. And business managers know more about their firm’s costs, competitive position, and investment opportunities than do the firm’s owners. Asymmetric information explains many institutional arrangements in our society. It is one reason why automobile companies offer warranties on parts and service for new cars; why firms and employees sign contracts that include incentives and rewards, and why the shareholders of corporations must monitor the behaviour of managers. Suppose you buy a new car for ` 20,000, drove it 100 miles, and then decided you really did not want it. There was nothing wrong with the car—it performed beautifully and met all your expectations. You simply felt that you could do just as well without it and would be better off saving the money for other things. So you decide to sell the car. How much should you expect to get for it? Probably not more than ` 16,000—even though the car is brand new, has been driven only 100 miles, and has a warranty that is transferable to a new owner. And if you were a prospective buyer, you probably would not pay much more than ` 16,000 yourself. Used cars sell for much less than new cars because there is asymmetric information about their quality: The seller of a used car knows much more about the car than the prospective buyer does. The buyer can hire a mechanic to check the car, but the seller has had experience with it and will know more about it. Furthermore, the very fact that the car is for sale indicates that it may be a ‘lemon’—why sell a reliable car? As a result, the prospective buyer of a used car will always be suspicious of its quality. Asymmetric information is also present in many other markets. Here are just a few examples. • Retail store: Will the store repair or allow you to return a defective product? The store knows more about its policy than you do. • Dealers of rare stamps, coins, books, and paintings: Are the items real or counterfeit? The dealer knows much more about their authenticity than you do. • Roofers, plumbers, and electricians: When a roofer repairs or renovates the roof of your house, do you climb up to check the quality of the work? • Restaurants: How often do you go into the kitchen to check if the chef is using fresh ingredients and obeying the heath laws? In all these cases, the seller knows much more about the quality of the product than the buyer does. Unless sellers can provide information about quality to buyers, low- quality goods and services will drive out high-quality ones. Implications of Asymmetric Information In an ideal world of fully functioning markets, consumers would be able to choose between low-quality and high-quality cars. While some will choose low-quality cars because they cost less, others will prefer to pay more for high-quality cars. Unfortunately, consumers

Self-Instructional 272 Material cannot in fact easily determine the quality of a used car until after they purchase it. As Economics of Imperfect a result, the price of used cars fall, and high-quality cars are driven out of the market. Information Market failure arises because there are owners of high-quality cars who value their cars less than potential buyers of high-quality cars. As a result, both parties can enjoy gains from trade. Unfortunately, the buyers’ lack of information prevents this NOTES mutually beneficial trade from occurring. The implications of asymmetric information about product quality were first analysed by George Akerlof. Akerlof’s analysis goes far beyond the market for used cars. The markets for insurance, financial, credit and even employment are also characterized by asymmetric quality information. To understand the implications of asymmetric information, we take the market for used cars and then see how the same principles apply to other markets. Market for Used Cars Suppose two kinds of used cars are available—high-quality cars and low-quality cars. Also, suppose that sellers and buyers can tell which kind of car is which. There will then be two markets, as illustrated in Figure 10.1. In part (a) SH is the supply curve for high-quality cars, and DH is the demand curve. Similarly SL and DL in part (b) are the supply and demand curves for low-quality cars. For any given price, SH lies to the left of St because owners of high-quality cars are more reluctant to part with them and must receive a higher price to do so. Similarly, DH is higher than DL because buyers are willing to pay more to get a high-quality car. As the figure shows, the market price for high- quality cars is ` 10,000, for low-quality cars ` 5000, and 50,000 cars of each type are sold. In reality, the seller of a used car knows much more about its quality than a buyer does. Buyers discover the quality only after they buy a car and drive it for a while. Consider, what happens, then, if sellers know the quality of cars, but buyers do not. Initially, buyers might think that the odds are 50-50 that a car they have will be high- quality. Why? Because when both sellers and buyers knew the quality, 50,000 cars of each type were sold. When making a purchase, buyers would therefore view all cars as ‘medium’ quality. Of course, after buying the car, they will learn its true quality. The demand for cars perceived to be medium-quality, denoted by DM in Figure 10.1, is below

DH but above DL. As the figure shows, fewer high-quality cars (25,000) and more low-quality cars (75,000) will now be sold.

PH PL

SH $10,000

DH

SL DM $5,000 DM DLM DLM DL DL

25,000 50,000 QH 50,00075,000 QL (a) High-Quality Cars (b) Low-Quality Cars

Fig 10.1 The Market for Used Cars Self-Instructional Material 273 Economics of Imperfect As consumers begin to realize that most cars sold (about three-fourths of the Information total) are low quality, their perceived demand shifts. As Figure 10.1 shows, the new

perceived demand curve might be DLM, which means that, on average, cars are thought to be of low to medium quality. However, the mix of cars then shifts even more heavily NOTES to low quality. As a result, the perceived demand curve shifts further to the left, pushing the mix of cars even further toward low quality. This shifting continues until only low- quality cars are sold. At that point, the market price would be too low to bring forth any high-quality cars for sale, so consumers correctly assume that any car they buy will be

of low quality, and the only relevant demand curve will be DL. The situation in Figure 10.1 is extreme. The market may come into equilibrium at a price that brings forth at least some high-quality cars. But the fraction of high- quality cars will be smaller than it would be if consumers could identify quality before making the purchase. That is why a person should expect to sell his brand new car, which he knows is in perfect condition, for much less than he has paid for it. Because of asymmetric information, low-quality goods drive high-quality goods out of the market. This phenomenon is sometimes referred to as the lemons problem. The English meaning of lemon is ‘no attraction in anything’. A lemon problem may arise when low quality goods drive out high quality goods from market. Asymmetric information exists when one side of a potential transaction has more information than the other side. When asymmetric information exists, the owners of high quality products suffer losses. When they offer high quality products, and sell them in a poor market that includes low quality products, they receive a lower price with adverse selection. The products that appear in the market are different from the products that firms sell when both sides have complete information. When asymmetric information exists, market institutions such as warranties and testing arise, and there is greater reliance on the seller’s reputation. 10.3.1 Adverse Selection and Signalling Adverse selection is a process used in economics in which such results occur which are undesired when the buyers and sellers have access to different or imperfect information. This imperfect knowledge causes a shift in the price and quantity of goods and services. This results into a selection of ‘bad’ products or services. For instance, if a bank sets a fixed or stable price for all its checking account customers, then it runs into the risk of being unfavourably affected by its low-balance and high activity customers. The bank would not profit much due to the individual price. George Akerlof’s ‘The Market for Lemons’ from 1970 is an archetypal paper on adverse selection. This paper brought numerous informational concerns to the forefront of economic theory. This paper also discusses the two principal solutions to this problem, screening and signalling. Signalling The idea of signalling was originally propounded by Michael Spence. He was of the idea that when a situation of information asymmetry comes into being, people can or may signal their type, simultaneously transporting information to the other party and resolving the asymmetry. This technique was usually applied in the context of searching a job wherein an employer wants to hire a new employee who is ‘skilled in learning’. This is true that all

Self-Instructional the employees coming in for an interview will claim to be ‘skilled in learning’, but only 274 Material the employee’s themselves know if they really are ‘skilled in learning’ or not. This is an Economics of Imperfect information asymmetry. Skills are dependent on various factors such as diet, money and Information exercise. Further, Spence proposes that if a person goes to a school or college, this signals as an ability to learn. It is a known fact that a person who is skilled in learning will easily NOTES finish his studies than a person who is unskilled. This skilled person by finishing his education signals to the prospective employers his capacity for learning. It does not matter how varied or how less the student has grasped in college, their finishing the college functions as a signal of their capacity of learning. Moreover, getting done with the college or education may act as a signal of the willingness of the individual to adhere to orthodox views, or the ability to pay for the education or it may signal a willingness to comply with authority. 10.3.2 Moral Hazard and its Application to Insurance A moral hazard problem exists when an agent takes less than the socially optimal care in response to a principal’s action. Moral hazard occurs when an insured party whose actions are unobserved can affect the probability or magnitude of a payment associated with an event. When one party is fully insured and cannot be accurately monitored by an insurance company with limited information, the insured party may take an action that increases the likelihood that an accident or an injury will occur. For example, if a person’s house is fully insured against theft, the person may be less diligent about locking the doors when he leaves, then he may choose not to install an alarm system. The possibility that an individual’s behaviour may change because the individual has an insurance is an example of a problem known as moral hazard. The concept of moral hazard applies not only to problems of insurance but also to problems of workers who perform below their capabilities when employers cannot monitor their behaviour (‘job shirking’). In general, moral hazard occurs when a party whose actions are unobserved affects the probability or magnitude of a payment. For example, if one has a complete medical insurance coverage, he may visit the doctor more often than he would if his coverage were limited. If the insurance provider can monitor its insurees’ behaviour, it can also charge higher fees for those who make more claims. But if the company cannot monitor behaviour, it may find its payments to be larger than expected. Under conditions of moral hazard, insurance companies may be forced to increase premiums for everyone, or even to refuse to sell insurance at all. Consider, for example, the decisions faced by the owners of a warehouse valued at ` 100,000 by their insurance company. Suppose that if the owners run a 50 fire- prevention programme for their employees, the probability of a fire is .005. Without this programme, the probability increases to .01. Knowing this, the insurance company faces a dilemma if it cannot monitor the company’s decision to conduct a fire-prevention programme. The policy that the insurance company offers cannot include a clause stating that payments will be made only if there is a fire-prevention programme. If the programme were in place, the company could insure the warehouse for a premium equal to the expected loss from a fire—an expected loss equal to .005 × 100,000 = 500. Once the insurance policy is purchased, however, the owners no longer have an incentive to run the programme. If there is a fire, they will be fully compensated for their financial loss. Thus, if the insurance company sells a policy for 500, it will incur losses because the expected loss from the fire will be 1000(.01 × 100,000). Self-Instructional Material 275 Economics of Imperfect Moral hazard is not only a problem for insurance companies. It also alters the Information ability of markets to allocate resources efficiently. In Figure 10.2, for example, D gives the demand for automobile driving in miles per week. The demand curve, which measures the marginal benefits of driving, is downward sloping because some people switch to NOTES alternative transportation as the cost of driving increases. Suppose, initially the cost of driving includes the insurance cost and that insurance companies can accurately measure miles driven. In this case, there is no moral hazard and the marginal cost of driving is given by MC. Drivers know that more driving will increase their insurance premium and so increases their total cost of driving (the cost per mile is assumed to be constant). For example, if the cost of driving is 1.50 per mile (50 paisa of which is insurance cost), the driver will go 100 miles per week.

Cost per Mile

()` 2.00

1.50 MC

1.00 MC

0.50 D = MB 0 50 100 140 Miles per Week

Fig. 10.2 The Effects of Moral Hazard

A moral hazard problem arises when insurance companies cannot monitor individual driving habits, so that the insurance premium does not depend on miles driven. In that case, drivers assume that any additional accident costs that they incur will be spread over a large group, with only a negligible portion accruing to each of them individually. Because their insurance premium does not vary with the number of miles that they drive, an additional mile of transportation will cost ` 1.00, as shown by the marginal cost curve MC’, rather than ` 1.50. The number of miles driven will increase from 100 to the socially inefficient level of 140. Moral hazard not only alters behaviour, it also creates economic inefficiency. The inefficiency arises because the insured individual perceives either the cost or the benefit of the activity differently from the true social cost or benefit. In the driving example of Check Your Progress Figure 10.2, the efficient level of driving is given by the intersection of the marginal 5. What is asymmetric benefit (MB) and marginal cost (MC) curves. With moral hazard, however, the individual’s information? perceived marginal cost (MC’) is less than actual cost, and the number of miles driven 6. Why do market per week (140) is higher than the efficient level at which marginal benefit is equal to failures arise? marginal cost (100). 7. Who analysed the first implications of asymmetric 10.4 SUMMARY information about product quality? 8. When does a moral In this unit, you have learnt that: hazard occur? • Most decision theories are normative or prescriptive, i.e., it is concerned with identifying the best decision making assuming an ideal decision maker who is fully Self-Instructional informed, able to compute with perfect accuracy, and fully rational. 276 Material • Uncertainty is a case when there is more than one possible outcome to a decision Economics of Imperfect and where the probability of each specific outcome occurring is not known. Information • Certainty refers to a situation where there is only one possible outcome to a decision and this outcome is known precisely. NOTES • Risk refers to a situation where there is more than one possible outcome to a decision and the probability of each specific outcome is known or can be estimated. • The condition of certainty refers to a state of perfect knowledge. It implies that investors have complete knowledge about the market conditions, especially the investment opportunities, cost of capital and the expected returns on the investment. • The pay-back period is also known as ‘pay-out’ and ‘pay-off’ period. The pay- back period method is the simplest and one of the most widely used methods of project evaluation. • All other things being the same, a project with a shorter pay-off period is preferred to those with longer pay-off period. This method of ranking projects or project selection is considered to be simple, realistic and safe. • The concept of the present value of money is very well reflected in the proverb ‘a bird in the hand is worth two in the bush’. In general, money received today is valued more than money receivable tomorrow. • The Internal Rate of Return (IRR) is also called Marginal Efficiency of Investment (MEI), Internal Rate of Project (IRP) and Break-even Rate (BER). • The IRR or MEI is defined as ‘the rate of interest or return which renders the discounted present value of its expected future marginal yields exactly equal to the investment cost of project’. • Hurwicz has suggested a criterion for investment decisions under uncertainty. In his opinion, full realization of optimistic pay-off or full realization of most pessimistic pay-off is a rare phenomenon. • The Laplace criterion uses the Bayesian rule to calculate the expected value of each strategy. Bayesian rule says that where meaningful estimate of probabilities is not available, the outcome of each strategy under each state of nature must be assigned the same probability and that the sum of probabilities of outcome of each strategy must add up to one. • Asymmetric information is a situation where some people have more information about a thing than others. Asymmetric information is characteristic of many business situations. • Asymmetric information explains many institutional arrangements in our society. It is one reason why automobile companies offer warranties on parts and service for new cars; why firms and employees sign contracts that include incentives and rewards, and why the shareholders of corporations must monitor the behaviour of managers. • In an ideal world of fully functioning markets, consumers would be able to choose between low-quality and high-quality cars. While some will choose low-quality cars because they cost less, others will prefer to pay more for high-quality cars. • The implications of asymmetric information about product quality were first analysed by George Akerlof.

Self-Instructional Material 277 Economics of Imperfect • Adverse selection is a process used in economics in which such results occur Information which are undesired when the buyers and sellers have access to different or imperfect information. • George Akerlof’s ‘The Market for Lemons’ from 1970 is an archetypal paper on NOTES adverse selection. This paper brought numerous informational concerns to the forefront of economic theory. This paper also discusses the two principal solutions to this problem, screening and signalling. • The idea of signalling was originally propounded by Michael Spence. He was of the idea that when a situation of information asymmetry comes into being, people can or may signal their type, simultaneously transporting information to the other party and resolving the asymmetry. • A moral hazard problem exists when an agent takes less than the socially optimal care in response to a principal’s action. • The concept of moral hazard applies not only to problems of insurance but also to problems of workers who perform below their capabilities when employers cannot monitor their behaviour (‘job shirking’). • A moral hazard problem arises when insurance companies cannot monitor individual driving habits, so that the insurance premium does not depend on miles driven. • Moral hazard not only alters behaviour, it also creates economic inefficiency. The inefficiency arises because the insured individual perceives either the cost or the benefit of the activity differently from the true social cost or benefit.

10.5 KEY TERMS

• Uncertainty: It is a case when there is more than one possible outcome to a decision and where the probability of each specific outcome occurring is not known. • Certainty: It refers to a situation where there is only one possible outcome to a decision and this outcome is known precisely. • Risk: It refers to a situation where there is more than one possible outcome to a decision and the probability of each specific outcome is known or can be estimated. • Condition of certainty: It refers to a state of perfect knowledge. • Pay-back period: It is defined as the time required to recover the total investment outlay from the gross earnings, i.e., gross of capital wastage or depreciation. • Time lag: The time gap between the investment and the first return from the investment is called ‘time lag’. • Internal Rate of Return (IRR): The rate of interest or return which renders the discounted present value of its expected future marginal yields exactly equal to the investment cost of project. • Asymmetric information: It is a situation where some people have more information about a thing than others. • Adverse selection: It is a process used in economics in which such results occur which are undesired when the buyers and sellers have access to different or imperfect information. Self-Instructional 278 Material Economics of Imperfect 10.6 ANSWERS TO ‘CHECK YOUR PROGRESS’ Information

1. Uncertainty is a case when there is more than one possible outcome to a decision and where the probability of each specific outcome occurring is not known. NOTES 2. The condition of certainty refers to a state of perfect knowledge. It implies that investors have complete knowledge about the market conditions, especially the investment opportunities, cost of capital and the expected returns on the investment. 3. This method is ‘a crude rule of thumb’ and can hardly be defended except on the ground of avoiding risk associated with long pay-back projects. Besides, this method assumes that cash inflows are known with a high degree of certainty. 4. The decision index is, in fact, a weighted average of maximum possible and minimum possible pay-offs, weight being their subjective probability such that sum of probabilities of maximum (Max) and minimum (Min) pay-offs equals one. 5. Asymmetric information is a situation where some people have more information about a thing than others. Asymmetric information is characteristic of many business situations. 6. Market failure arises because there are owners of high-quality cars who value their cars less than potential buyers of high-quality cars. As a result, both parties can enjoy gains from trade. 7. The implications of asymmetric information about product quality were first analysed by George Akerlof. 8. Moral hazard occurs when an insured party whose actions are unobserved can affect the probability or magnitude of a payment associated with an event.

10.7 QUESTIONS AND EXERCISES

Short-Answer Questions 1. What is decision analysis? 2. Distinguish between certainty and uncertainty. 3. Write a note on the concept of present value. 4. Define internal rate of return (IRR). 5. ‘Hurwicz has suggested a criterion for investment decisions under uncertainty.’ What is this criterion? 6. Why do automobile companies offer warranties on parts and service for new cars? 7. How does the market for used cars describe the idea of asymmetric information? 8. What is the lemon’s problem? 9. Write a note on adverse selection and signalling. 10. What is a moral hazard? Long-Answer Questions 1. Discuss the concept of risk, certainty and uncertainty. Also, discuss choices taken

under uncertainty. Self-Instructional Material 279 Economics of Imperfect 2. Describe investment decisions under the condition of certainty. Information 3. Evaluate investment decisions under the condition of uncertainty. 4. Assess the concept of asymmetric information. Also, discuss the implications of NOTES asymmetric information using the example of market for used cars. 5. Critically evaluate the term ‘adverse selection’ and ‘signalling’. 6. What is moral hazard? Discuss. 7. Discuss the applications of moral hazards on insurance.

10.8 FURTHER READING

Dwivedi, D. N. 2002. Managerial Economics, 6th Edition. New Delhi: Vikas Publishing House. Keat, Paul G. and K.Y. Philip. 2003. Managerial Economics: Economic Tools for Today’s Decision Makers, 4th Edition. Singapore: Pearson Education Inc. Keating, B. and J. H. Wilson. 2003. Managerial Economics: An Economic Foundation for Business Decisions, 2nd Edition. New Delhi: Biztantra. Mansfield, E.; W. B. Allen; N. A. Doherty and K. Weigelt. 2002. Managerial Economics: Theory, Applications and Cases, 5th Edition. NY: W. Orton & Co. Peterson, H. C. and W. C. Lewis. 1999. Managerial Economics, 4th Edition. Singapore: Pearson Education, Inc. Salvantore, Dominick. 2001. Managerial Economics in a Global Economy, 4th Edition. Australia: Thomson-South Western. Thomas, Christopher R. and Maurice S. Charles. 2005. Managerial Economics: Concepts and Applications, 8th Edition. New Delhi: Tata McGraw-Hill.

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