General Equilibrium Notation Pareto Optimality Core

Total Page:16

File Type:pdf, Size:1020Kb

General Equilibrium Notation Pareto Optimality Core General Equilibrium Notation Pareto Optimality Core Econ 2100, Fall 2020 Lecture 1, 8 October Outline 1 Logistics 2 General Equilibrium notation 3 Pareto Optimality 4 The Core Logistics Instructor: Luca Rigotti Offi ce: WWPH ????, email: luca at pitt.edu Offi ce Hours: Wednesday 1:30pm-3pm, or by appointment (send me an email) Teaching Assistant: Morag Dor Offi ce: WWPH ???, email: [email protected] Offi ce Hours: Thursday 2:30-4pm. Class Time and Location Tuesday & Thursday, 9am to 10:15am on Zoom (please leave your camera on if you can) Recitation Times Friday , 8:30am to 10:15am, on Zoom Class Webpages: http://www.pitt.edu/~luca/ECON3030/ and Canvas Announcements None Today Logistics Handouts: For each class, I will post an handout that you can use to take notes (either print and bring to class, or use computer). Useful textbooks: Kreps, Microeconomic Foundations I: Choice and Competitive Markets, Princeton University Press Mas-Collel, Whinston and Green: Microeconomic Theory. Other useful textbooks by Varian, Jehle and Reny, older Kreps. The best book: Gerard Debreu: Theory of Value. Grading Luca’sHalf: Problem sets 90%, Exam 10% Exam, 2 hours long, November 24th at 8:15 Problem Sets Weekly, some questions appear during class. DO NOT look for answers... These are for you to learn what you can and cannot do; we can help you get better only if we know your limits. Working in teams strongly encouraged, but turn in problem sets individually. Start working on exercises on your own, and then get together to discuss. Typically, a Problem Set will be due at the beginning of each Tuesday class (inlcuding the exam class). Goals for This Half Learn and understand the general equilibrium theory every academic economist needs to know. Stimulate interest in theory as a field (some of you may want to become theorists). Enable you to read papers that use general equilibrium theory, and understand seminars. We will cover the following standard topics: general equilibrium theory: economy of consumers and firms, welfare, Pareto optimality, competitive markets, Walrasian equilibrium, First and Second Welfare Theorems, existence of equilibrium, uniqueness of equilibrium, markets with uncertainty and time, Arrow-Debreu economies. In the Spring, Professor Svetlana Kosterina will cover game theory and information economics. Questions? This will be fun: let’sgo! General Equilibrium General Equilibrium Theory Models interactions between all agents in an economy; GE considers tastes, technology, and resources as the only exogenous items. The name general (as opposed to partial) equilibirum refers to the fact that all outcomes are determined endogenously. 1 How would a social planner allocate resources? 1 The main concept is Pareto effi ciency: outcomes cannot be redistributed to improve welfare. 2 How do competitive markets allocate resources? 1 The main concept is competitive equilibrium: all agents make optimal choices, and prices are such that demand and supply are equal in all markets. 1 The crucial assumption is that agents are price-taking optimizers. 3 Questions one can ask in general equilibrium: 1 when is a competitive equilibirum Pareto effi cient? First Welfare Theorem; 2 when is a Pareto effi cient outcome an equilibirum? Second Welfare Theorem; 3 when does a competitive equilibirum exist? Arrow-Debreu-McKenzie Theorem; 4 when is a competitive equilibrium unique? 5 is a competitive equilibrium robust to small perturbations of the parameters? 6 how do we get to a competitive equilibrium and what happens away from it? 7 what is different with time or uncertainty? The Economy An economy consists of I individuals and J firms who consume and produce L perfectly divisible commodities. L Each firm j = 1, ..., J is described by a production set Yj R . Each consumer i = 1, ..., I is described by four objects: L a consumption set Xi R ; preferences %i ; an individual endowment given by a vector of commodities !i Xi ; and J 2 a non-negative share i [0, 1] of the profits of each firm j. 2 Definition An economy with private ownership is a tuple I J Xi , i ,!i , i , Yj f % gi=1 f gj=1 n o If we do not need to track who owns what, we can define an economy as I J Xi , i , Yj ,! f % gi=1 f gj=1 I L n o where ! = !i R is the aggregate endowment. i=1 2 The aggregateP endowment describes the resources available to the economy. Allocations First, we define a possible outcome for the economy. Definition An allocation specifies a consumption vector xi Xi for each consumer i = 1, ..., I , 2 and a production vector yj Yj for each firm j = 1, ..., J; an allocation is 2 I J L(I +J) (x, y) i=1Xi j=1 Yj R 2 This is a long lists of what everyone consumes and what every firm produces: (x1, ..., xI , y1, ..., yJ ) X1 ... XI Y1 ... YJ 2 Notice that, by definition, consumption must be considered by each consumer (xi Xi ) and production must be possible for each firm (yj Yj ). 2 2 Is any allocation achieveable for the economy? No The definition of allocation does not reflect available resources. Initial endowments constrain what can be achieved. Feasibility Definition An allocation (x, y) is feasible if I I J xi !i + yj ≤ i=1 i=1 j=1 X X X Consumption and production are compatible with the aggregate endowment. Feasibility has nothing to do with choices by consumers or firms; it just states that a particular allocation could be consumed and produced given the economy’sresources. Why the inequality instead of an equality? Definition The set of feasible allocations is denoted by I J I J L(I +J) (x, y) i=1Xi j=1 Yj : xi ! + yj R f 2 ≤ g i=1 j=1 X X Edgeworth Box Economy There is no production. There are two goods, denoted 1 and 2, and two consumers, denoted A and B. An allocation is given by four numbers xA = (x1 A, x2 A) and xB = (x1 B , x2 B ) A feasible allocation is described as 4 2 2 (xA, xB ) R : xA R+, xB R+, and xA + xB !A + !B 2 2 2 ≤ so a feasible allocation must satisfy x1 A + x1 B !1 A + !1 B and x2 A + x2 B !2 A + !2 B ≤ ≤ Since the inequality is important, we can formaly think of the economy as having one firm with the following technology: 2 Y1 = R+ it can destroy some amounts of the goods. We can represent all feasible allocation by means of an Edgeworth Box. Draw it (with all details). Exchange Economy In an exchange economy there is no production; all consumers can do is trade with each other. This is like an Edgeworth Box economy, but there are I consumers and L goods. In an exchange economy there is a single firm that has the ability to dispose freely of any amount of any of the goods. L Formally, J = 1, and Yj = R+. Example In an exchange economy the set of feasible allocations is I LI x X1 ... XI : xi ! R f 2 ≤ g i=1 X This is a simple environment in which many results are easier to prove, and that most of the time has the same intuition as an economy with production. Edgeworth Box An Edgeworth Box is an exchange economy with two consumers and two goods. 2 2 Formally L = 2, I = 2, X1 = X2 = R+, J = 1, and Yj = R+. Representative Agent Economy There are two goods, food F and labor L, one firm, and one consumer (both are Agent). The Agent’sendowment is ! = (1, 0) (one unit of labor and no food). The Agent’stechnology transforms labor into food: 2 Y = (yL, yF ) R : yL 0, and yF f ( yL) 2 ≤ ≤ The function f ( ) is a standard production function. · The technology has the free disposal property: if y Y and y 0 y then y 0 is also an element of Y . 2 ≤ A feasible allocation is described as 4 2 (x, y) R : x R+, y Y , and x ! + y 2 2 2 ≤ Because of free disposal, one can think of the inequality as an equality without loss. Draw the production possibility set and the set of feasible consumption bundles. Feasible Allocations: Conditions Proposition If the following conditions are satisfied, the set of feasible allocations is closed and bounded.a b 1 Xi is closed and bounded below for each i = 1, ..., I. 2 Yj is closed for each j = 1, ..., J. 3 Y = j Yj is convex and satisfies 1 0L Y (inaction), P2 L 2 Y R 0L (no free-lunch), and \ + f g 3 if y Y and y = 0L then y / Y (irreversibility). 2 6 2 L Moreover, if R+ Yj (free-disposal) and there are xi Xi for each i such that 2 xi !, then the set of feasible allocations is also non empty. i ≤ P aClosed and bounded means there exists an r > 0 such that for each l = 1, ..., L, i = 1, ..., I , and j = 1, ..., J, we have xl,i < r and yl,j < r for each (x, y ) A. b 2 Bounded below means there exists an r > 0 such that xl,i > r for each l = 1, ..., L. When these conditions are not satisfied, the latter in particular, we may have nothing to talk about. So we take them for granted. Pareto Optimality (Effi ciency) A minimal effi ciency requirement is that there is no waste of resources. Definition An allocation (x, y) Pareto dominates the allocation (x, y) if x x x x i %i i and i i i for all i = 1, ..., I for some i Definition A feasible allocation (x, y) is Pareto optimal if there is no other feasible allocation (x 0, y 0) such that x x x x i0 %i i and i0 i i for all i = 1, ..., I for some i A feasible allocation is Pareto optimal if no feasible allocation Pareto dominates it.
Recommended publications
  • Preview Guide
    ContentsNOT FOR SALE Preface xiii CHAPTER 3 The Behavior of Consumers 45 3.1 Tastes 45 CHAPTER 1 Indifference Curves 45 Supply, Demand, Marginal Values 48 and Equilibrium 1 More on Indifference Curves 53 1.1 Demand 1 3.2 The Budget Line and the Demand versus Quantity Consumer’s Choice 53 Demanded 1 The Budget Line 54 Demand Curves 2 The Consumer’s Choice 56 Changes in Demand 3 Market Demand 7 3.3 Applications of Indifference The Shape of the Demand Curve 7 Curves 59 The Wide Scope of Economics 10 Standards of Living 59 The Least Bad Tax 64 1.2 Supply 10 Summary 69 Supply versus Quantity Supplied 10 Author Commentary 69 1.3 Equilibrium 13 Review Questions 70 The Equilibrium Point 13 Numerical Exercises 70 Changes in the Equilibrium Point 15 Problem Set 71 Summary 23 Appendix to Chapter 3 77 Author Commentary 24 Cardinal Utility 77 Review Questions 25 The Consumer’s Optimum 79 Numerical Exercises 25 Problem Set 26 CHAPTER 4 Consumers in the Marketplace 81 CHAPTER 2 4.1 Changes in Income 81 Prices, Costs, and the Gains Changes in Income and Changes in the from Trade 31 Budget Line 81 Changes in Income and Changes in the 2.1 Prices 31 Optimum Point 82 Absolute versus Relative Prices 32 The Engel Curve 84 Some Applications 34 4.2 Changes in Price 85 2.2 Costs, Efficiency, and Gains from Changes in Price and Changes in the Trade 35 Budget Line 85 Costs and Efficiency 35 Changes in Price and Changes in the Optimum Point 86 Specialization and the Gains from Trade 37 The Demand Curve 88 Why People Trade 39 4.3 Income and Substitution Summary 41
    [Show full text]
  • Coasean Fictions: Law and Economics Revisited
    Seattle Journal for Social Justice Volume 5 Issue 2 Article 28 May 2007 Coasean Fictions: Law and Economics Revisited Alejandro Nadal Follow this and additional works at: https://digitalcommons.law.seattleu.edu/sjsj Recommended Citation Nadal, Alejandro (2007) "Coasean Fictions: Law and Economics Revisited," Seattle Journal for Social Justice: Vol. 5 : Iss. 2 , Article 28. Available at: https://digitalcommons.law.seattleu.edu/sjsj/vol5/iss2/28 This Article is brought to you for free and open access by the Student Publications and Programs at Seattle University School of Law Digital Commons. It has been accepted for inclusion in Seattle Journal for Social Justice by an authorized editor of Seattle University School of Law Digital Commons. For more information, please contact [email protected]. 569 Coasean Fictions: Law and Economics Revisited Alejandro Nadal1 After the 1960s, a strong academic movement developed in the United States around the idea that the study of the law, as well as legal practice, could be strengthened through economic analysis.2 This trend was started through the works of R.H. Coase and Guido Calabresi, and grew with later developments introduced by Richard Posner and Robert D. Cooter, as well as Gary Becker.3 Law and Economics (L&E) is the name given to the application of modern economics to legal analysis and practice. Proponents of L&E have portrayed the movement as improving clarity and logic in legal analysis, and even as a tool to modify the conceptual categories used by lawyers and courts to think about
    [Show full text]
  • Francis Ysidro Edgeworth
    Francis Ysidro Edgeworth Previous (Francis Xavier) (/entry/Francis_Xavier) Next (Francis of Assisi) (/entry/Francis_of_Assisi) Francis Ysidro Edgeworth (February 8, 1845 – February 13, 1926) was an Irish (/entry/Ireland) polymath, a highly influential figure in the development of neo­ classical economics, and contributor to the development of statistical theory. He was the first to apply certain formal mathematical techniques to individual decision making in economics. Edgeworth developed utility theory, introducing the indifference curve and the famous "Edgeworth box," which have become standards in economic theory. He is also known for the "Edgeworth conjecture" which states that the core of an economy shrinks to the set of competitive equilibria as the number of agents in the economy gets large. The high degree of originality demonstrated in his most important book on economics, Mathematical Psychics, was matched only by the difficulty in reading it. A deep thinker, his contributions were far ahead of his time and continue to inform the fields of (/entry/File:Edgeworth.jpeg) microeconomics (/entry/Microeconomics) and areas such as welfare economics. Francis Y. Edgeworth Thus, Edgeworth's work has advanced our understanding of economic relationships among traders, and thus contributes to the establishment of a better society for all. Life Contents Ysidro Francis Edgeworth (the order of his given names was later reversed) 1 Life was born on February 8, 1845 in Edgeworthstown, Ireland (/entry/Ireland), into 2 Work a large and wealthy landowning family. His aunt was the famous novelist Maria 2.1 Edgeworth conjecture Edgeworth, who wrote the Castle Rackrent. He was educated by private tutors 2.2 Edgeworth Box until 1862, when he went on to study classics and languages at Trinity College, 2.3 Edgeworth limit theorem Dublin.
    [Show full text]
  • Econ 337901 Financial Economics
    ECON 337901 FINANCIAL ECONOMICS Peter Ireland Boston College Spring 2021 These lecture notes by Peter Ireland are licensed under a Creative Commons Attribution-NonCommerical-ShareAlike 4.0 International (CC BY-NC-SA 4.0) License. http://creativecommons.org/licenses/by-nc-sa/4.0/. 1 Mathematical and Economic Foundations A Mathematical Preliminaries 1 Unconstrained Optimization 2 Constrained Optimization B Consumer Optimization 1 Graphical Analysis 2 Algebraic Analysis 3 The Time Dimension 4 The Risk Dimension C General Equilibrium 1 Optimal Allocations 2 Equilibrium Allocations Mathematical Preliminaries Unconstrained Optimization max F (x) x Constrained Optimization max F (x) subject to c ≥ G(x) x Unconstrained Optimization To find the value of x that solves max F (x) x you can: 1. Try out every possible value of x. 2. Use calculus. Since search could take forever, let's use calculus instead. Unconstrained Optimization Theorem If x ∗ solves max F (x); x then x ∗ is a critical point of F , that is, F 0(x ∗) = 0: Unconstrained Optimization F (x) maximized at x ∗ = 5 Unconstrained Optimization F 0(x) > 0 when x < 5. F (x) can be increased by increasing x. Unconstrained Optimization F 0(x) < 0 when x > 5. F (x) can be increased by decreasing x. Unconstrained Optimization F 0(x) = 0 when x = 5. F (x) is maximized. Unconstrained Optimization Theorem If x ∗ solves max F (x); x then x ∗ is a critical point of F , that is, F 0(x ∗) = 0: Note that the same first-order necessary condition F 0(x ∗) = 0 also characterizes a value of x ∗ that minimizes F (x).
    [Show full text]
  • A Sparsity-Based Model of Bounded Rationality
    NBER WORKING PAPER SERIES A SPARSITY-BASED MODEL OF BOUNDED RATIONALITY Xavier Gabaix Working Paper 16911 http://www.nber.org/papers/w16911 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 March 2011 I thank David Laibson for a great many enlightening conversations about behavioral economics over the years. For very helpful comments, I thank the editor and the referees, and Andrew Abel, Nick Barberis, Daniel Benjamin, Douglas Bernheim, Andrew Caplin, Pierre-André Chiappori, Vincent Crawford, Stefano DellaVigna, Alex Edmans, Ed Glaeser, Oliver Hart, David Hirshleifer, Harrison Hong, Daniel Kahneman, Paul Klemperer, Botond Kőszegi, Sendhil Mullainathan, Matthew Rabin, Antonio Rangel, Larry Samuelson, Yuliy Sannikov, Thomas Sargent, Josh Schwartzstein, and participants at various seminars and conferences. I am grateful to Jonathan Libgober, Elliot Lipnowski, Farzad Saidi, and Jerome Williams for very good research assistance, and to the NYU CGEB, INET, the NSF (grant SES-1325181) for financial support. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2011 by Xavier Gabaix. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. A Sparsity-Based Model of Bounded Rationality Xavier Gabaix NBER Working Paper No. 16911 March 2011, Revised May 2014 JEL No. D03,D42,D8,D83,E31,G1 ABSTRACT This paper defines and analyzes a “sparse max” operator, which is a less than fully attentive and rational version of the traditional max operator.
    [Show full text]
  • Exchange Economy in Two-User Multiple-Input Single-Output
    1 Exchange Economy in Two-User Multiple-Input Single-Output Interference Channels Rami Mochaourab, Student Member, IEEE, and Eduard Jorswieck, Senior Member, IEEE Abstract—We study the conflict between two links in a Pareto optimal point is an achievable utility tuple from which it multiple-input single-output interference channel. This setting is is impossible to increase the performance of one link without strictly competitive and can be related to perfectly competitive degrading the performance of another. Consequently, Pareto market models. In such models, general equilibrium theory is used to determine equilibrium measures that are Pareto optimal. optimality ensures efficient exploitation of the wireless channel First, we consider the links to be consumers that can trade resources. For this purpose, there has been several work on goods within themselves. The goods in our setting correspond to characterizing the set of beamforming vectors that are relevant beamforming vectors. We utilize the conflict representation of the for Pareto optimal operation in the MISO IFC [4]–[8]. Next, consumers in the Edgeworth box, a graphical tool that depicts we will discuss these approaches. the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. Afterwards, we model the situation between the links as a competitive market A. Characterization of Pareto Optimal Points which additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices Designing a Pareto optimal mechanism requires finding the that equate the demand to the supply of goods. We calculate joint beamforming vectors used at the transmitters that lead the unique Walrasian equilibrium and propose a coordination process that is realized by an arbitrator which distributes the to the Pareto optimal point.
    [Show full text]
  • Econ 4365 Syllabus
    Fall 2018 Prof. Janet Kohlhase University of Houston ECON 7341– Section 16322 MICROECONOMIC THEORY I Meets TTh 1-2:30 in M212 (McElhinney Building) Office: 201B McElhinney (M) hours: TTh 5:00-6:00pm or by appointment 713-743-3799 email: [email protected] web pages: http://www.uh.edu/~kohlhase (general information) http://www.uh.edu/blackboard (class website, use Blackboard Learn; password access) TA: Jose Mota, a second year Ph.D. student in economics, office 207 McElhinney Hall, email [email protected], office hours by appointment. Overview: This course is the first in a sequence of two advanced microeconomic theory courses offered in the graduate economics curriculum at the University of Houston. This course provides an in-depth coverage of the modern microeconomic theory of economic choices made by individual consumers and firms. The course also examines non-strategic markets such as perfect competition (both partial and general equilibrium versions) and monopoly. Topics covered include special classes of preferences and production functions, choice under uncertainty, measures of welfare at various levels—consumer, one market, and many markets in general equilibrium. The course uses mathematical methods typically used in microeconomic theory such as optimization, constrained optimization (including the Kuhn-Tucker Theorem), the envelope theorem, and comparative statics. The second micro course (Econ 7342) will develop models of asymmetric information, strategic behavior and interactions among agents and groups of agents. Logistics: Class time consists of two parts, lectures and labs. The lectures are held TTh 1- 2:30 and are taught by me. The lab is held on Fridays from 10:30am-noon in the economics conference room, room 212M, and is taught by the teaching assistant (TA).
    [Show full text]
  • Algebraic Theory of Pareto Efficient Exchange
    Algebraic Theory of Pareto Efficient Exchange August 2002 by David A. Hennessy Harvey E. Lapan Professor University Professor Department of Economics & CARD Department of Economics Iowa State University Iowa State University Ames, IA 50011-1070 Ames, IA 50011-1070 Mailing address for correspondence David A. Hennessy Department of Economics & CARD 578 C Heady Hall Iowa State University Ames, IA 50011-1070 Ph: (515) 294-6171 Fax: (515) 294-6336 e-mail: [email protected] Algebraic Theory of Pareto Efficient Exchange Abstract We study pure exchange economies with symmetries on preferences up to taste intensity transformations. In a 2-person, 2-good endowment economy, we show that bilateral symmetry on each utility functional precludes a rectangle in the Edgeworth box as the location of Pareto optimal allocations. Under strictly quasi-concave preferences, a larger set can be ruled out. The inadmissible region is still larger when preferences are homothetic and identical up to taste intensity parameters. Symmetry also places bounds on the relations between terms of trade and efficient allocation. The inferences can be extended to an n-person, m-good endowment economy under generalized permutation group symmetries on preferences. JEL classification: D51, D61, C60 KEYWORDS: bilateral symmetry, general equilibrium, group majorize, homothetic preferences, permutation groups, taste differences, terms of trade. 1. INTRODUCTION SYMMETRY AND MARKET EXCHANGE ARE INTIMATELY related phenomena. Market transactions are motivated by asymmetries in tastes or endowments. Absent transactions costs, these asymmetries are exploited through exchange where the terms of trade are invariant to the parties involved. Consequently, in a pure exchange economy there should be fundamental structural relationships between the nature of heterogeneities among consumers, equilibrium decisions by consumers, and the equilibrium prices that guide these decisions.
    [Show full text]
  • Economic Efficiency in Edgeworth Box Market the Case of Two Goods
    European Journal of Sustainable Development (2013), 2, 4, 355-360 ISSN: 2239-5938 Economic Efficiency in Edgeworth Box Market the Case of Two Goods Prof. As. Dudi SULI1, MSc Eriona DEDA2, MSc Hergys SULI3 ABSRACT: Is very important for our markets, an appreciation for some of benefits of trade and understanding to how prices get established in simple markets. The Edgewrth box serves to orient the markets scientifically and at the same time can be used by decision makers in the planning resources process to meet customer demand. Using a production Edgewrth box , shows that efficiency in production has similar properties to efficiency in distribution. From the optimal choices inside the Edgeworth box, we derive a production possibilities frontier that describes all the efficient combinations of two goods to maximize the benefit of both consumers. The Edgewrth box serves to orient the markets scientifically and at the same time can be used by decision makers in the planning resources process to meet customer demand. To analyze efficiency in production we use Edgeworth box. In the Edgeworth box, we analyze how the market achieves a competitive equilibrium. Keywords: Edgeworth box, the efficient production set, competitive equilibrium, efficiency 1. Introduction Efficiency in production Is very important for our markets, an appreciation for some of benefits of trade and understanding to how prices get established in simple markets. The Edgewrth box serves to orient the markets scientifically and at the same time can be used by decision makers in the planning resources process to meet customer demand decision makers can be: | 1Department of Agricultural Political Economy, 2Department of Economics and Agribusiness of Tirana.
    [Show full text]
  • Public Finance
    EDO UNIVERSITY IYAMHO Department of Economics ECO 313: Public Finance Instructor: Dr. Anthony Imoisi, email: [email protected] Course Code: ECO 313 Course Title: Public Finance Number of Units: 2 units Course Duration: Two hours per week Course Lecturer: Imoisi Anthony Ilegbinosa (Ph.D) Intended Learning Outcomes At the completion of this course, students are expected to: Define clearly the meaning scope and nature of Public Finance. Have a knowledge of various tools of normative analysis Understand various roles of government in the economy Discuss the difference between public and private goods Discuss why government should intervene in economic activities Course Details: Week 1: Public Finance and Ideology Organic view of Government Mechanistic view of Government Government at a Glance Week 2: Tools of Normative Analysis Welfare Economics The First Fundamental Theorem of Welfare Economics Fairness and the Second Fundamental Theorem of Welfare Economics Week 3: Market Failure Market Power Nonexistence of Markets An Overview of Market Failure Week 4 & 5: Public Goods and Privatization Definition of Public Goods Efficient Provision of Public Goods Privatization Public Goods and Public Choice Week 6: Externalities [[ECONOMICS DEPARTMENT, EDO UNIVERSITY, IYAMHO ] ] Page 1 The Nature of Externalities Graphical Analysis Private Responses Week 7 & 8: Public Responses to Externalities Taxes and Subsidies Emission Fee Cap and Trade Emission Fee versus Cap and Trade Command and Control Regulation Implications
    [Show full text]
  • Economic Theory and Social Policy: Where We Are, Where We Are Headed
    ESIC 2018 DOI: 10.26613/esic/2.1.64 Economic Theory and Social Policy: Where We Are, Where We Are Headed Herbert Gintis Abstract Standard economic theory has told us for more than half a century that, to attain a high level of social welfare, there is no viable alternative to a market economy regulated by a powerful state. Critics often represent standard economic theory as a doctrinal defense of the free market. The truth is quite the opposite. Free market ideology is unfounded. Stan- dard economic theory provides the proper framework for analyzing market failure. This theory must of course be supplemented by a theory of state failure, as well as a theory of nonstate solutions to market failures. Standard economic theory offers a poor approach to macroeconomic dynamics, but we complexity and evolutionary theorists are working on correcting this situation. Keywords: neoclassical economic theory, general equilibrium theory, economic policy, evolutionary economics, complex dynamics RADICAL ECONOMICS AND BEYOND In the midst of bloody wars at home and abroad, with my professors either oblivious While studying for my PhD in mathematics to or mildly-to-avidly supporting the war in at Harvard, I became deeply involved in the Vietnam, I was certain that the economic theory anti-Vietnam war and civil rights movements. they espoused must be deeply flawed and began Feeling an uncomfortable gap between the to develop an alternative. How deeply disaf- abstractness of mathematical theory and con- fected was I? Here are the final sentences of a creteness of radical politics, I completed my paper I published in the orthodox American master’s in math, and switched to the PhD pro- Economic Review at that time: gram in economics at Harvard, producing some years later, at the height of the influence of the We [young economists] must be outlaws to radical student movement, a doctoral disserta- preserve our sanity and to seek a decent world tion entitled “Power and Alienation: Towards for our children.
    [Show full text]
  • General Equilibrium
    Hart Notes Matthew Basilico April, 2013 Part I General Equilibrium Chapter 15 - General Equilibrium Theory: Examples • Pure exchange economy with Edgeworth Box • Production with One-Firm, One-Consumer • [Small Open Economy] 15B. Pure Exchange: The Edgeworth Box Denitions and Set Up Pure Exchange Economy • An economy in which there are no production opportunities. Agents possess endowments, eco- nomic activity consists of trading and consumption Edgeworth Box Economy • Preliminaries Assume consumers act as price takers Two consumers i = 1; 2; Two commodities l = 1; 2 • Consumption and Endowment 0 Consumer i s consumption vector is xi = (x1i; x2i) Consumer 0s consumption set is 2 ∗ i R+ Consumer has preference relation over consumption vectors in this set ∗ i %i 0 Consumer i s endowment vector is !i = (!1i;!2i) ∗ Total endowment of good l is !¯l = !l1 + !l2 • Allocation 1 An allocation 4 is an assignment of a nonnegative consumption vector to each con- x 2 R+ sumer ∗ x = (x1; x2) = ((x11; x21) ; (x12; x22)) A feasible allocation is ∗ xl1 + xl2 ≤ !¯l for l = 1; 2 A nonwasteful allocation is ∗ xl1 + xl2 =! ¯l for l = 1; 2 ∗ These can be depicted in Edgeworth Box • Wealth and Budget Sets Wealth: Not given exogenously, only endowments are given. Wealth is determined by by prices. ∗ p · !i = p1!1i + p2!2i Budget Set: Given endowment, budget set is a function of prices 2 ∗ Bi (p) = xi 2 R+ : p · xi ≤ p · !i ∗ Graphically, draw budget line [slope = − p1 ]. Consumer 1's budget set consists of p2 all nonnegative vectors below and to the left; consumer 2's is above and to the right • Graph: Axes: horizontal is good 1, vertial is good 2 Origins: consumer 1 in SW corner (as usual), consumer 2 in NE corner (unique to Edgeworth boxes) • Oer Curve = Demand (as a function of p) (A depiction of preferences of each consumer) %i ∗ Asume strictly convex, continuous, strongly monotone 2 As p varies, budget line pivots around !.
    [Show full text]