DOCSLIB.ORG

Models in Microeconomic Theory Covers Basic Models in Current Microeconomic Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

4&5"+)$'0)#'785()&1$() !"#$%&'()'!(*+"$*")",(*'-.$"+/ Models in !0+1()'23'4&5"+)$'0)#'6+($%'785()&1$()' Microeconomic Theory Models in Microeconomic Theory covers basic models in current microeconomic theory. Part I (Chapters 1–7) presents models of an economic agent, discussing abstract models of preferences, choice, and decision making under uncertainty, before turning to models of the consumer, the producer, and monopoly. Part II (Chapters 8–14) introduces the concept of equilibrium, beginning, unconven� onally, with the models of the jungle and an economy with indivisible goods, and con� nuing with models of an exchange economy, equilibrium with ra� onal expecta� ons, and an economy with asymmetric informa� on. Part III (Chapters Martin J. Osborne 15–16) provides an introduc� on to game theory, covering strategic and extensive games and the concepts of Nash equilibrium and subgame perfect equilibrium. Part IV (Chapters '''''''''''!"#$%&'()'!(*+"$*")",(*'-.$"+/'''' Ariel Rubinstein 17–20) gives a taste of the topics of mechanism design, matching, the axioma� c analysis of economic systems, and social choice. The book focuses on the concepts of model and equilibrium. It states models and results precisely, and provides proofs for all results. It uses only elementary mathema� cs (with almost no calculus), although many of the proofs involve sustained logical arguments. It includes about 150 exercises. With its formal but accessible style, this textbook is designed for undergraduate students of microeconomics at intermediate and advanced levels. As with all Open Book publica� ons, this en� re book is available to read for free on the publisher’s website. Printed and digital edi� ons, together with supplementary digital material, can also be found at www.openbookpublishers.com Cover design by Mar� n J. Osborne book '''' ebooke and OA edi� ons also available OPEN ACCESS www.openbookpublishers.com OBP h To access digital resources including: blog posts videos online appendices and to purchase copies of this book in: hardback paperback ebook editions Go to: htps://www.openbookpublishers.com/product/1159 Open Book Publishers is a non-proft independent initiative. We rely on sales and donations to continue publishing high-quality academic works. MODELS IN MICROECONOMIC THEORY MODELS IN MICROECONOMIC THEORY Martin J. Osborne University of Toronto Ariel Rubinstein Tel Aviv University New York University https://www.openbookpublishers.com c 2020 Martin J. Osborne and Ariel Rubinstein ⃝ This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute, and trans- mit the work providing you do not modify the work, you do not use the work for com- mercial purposes, you attribute the work to the authors, and you provide a link to the license. Attribution should not in any way suggest that the authors endorse you or your use of the work and should include the following information. Martin J. Osborne and Ariel Rubinstein, Models in Microeconomic Theory.Cambridge, UK: Open Book Publishers, 2020, https://doi.org/10.11647/OBP.0204. To access detailed and updated information on the license, please visit https://www. openbookpublishers.com/product/1159#copyright. Further details about CC BY licenses are available at https://creativecommons.org/ licenses/by-nc-nd/4.0/.Allexternallinkswereactiveatthetimeofpublicationun- less otherwise stated and have been archived via the Internet Archive Wayback Machine at https://archive.org/web. Updated digital material and resources associated with this book are available at https: //www.openbookpublishers.com/product/1159#resources. Every effort has been made to identify and contact copyright holders and any omission or error will be corrected if notification is made to the publisher. ISBN Paperback: 978-1-78374-920-1 ISBN Hardback: 978-1-78374-921-8 ISBN Digital (PDF): 978-1-78374-922-5 DOI: 10.11647/OBP.0204 This book is available in two versions, one that uses feminine pronouns and one that uses masculine pronouns. This version uses masculine pronouns. Version: 2020.12.21 (h) Contents Personal note xi Preface xiii Part I Individual behavior 1 1Preferencesandutility3 1.1 Preferences 3 1.2 Preference formation 7 1.3 An experiment 8 1.4 Utility functions 9 Problems 13 Notes 15 2Choice17 2.1 Choice and rational choice 17 2.2 Rationalizing choice 18 2.3 Property α 21 2.4 Satisficing 22 2.5 The money pump argument 23 2.6 Evidence of choices inconsistent with rationality 24 Problems 27 Notes 29 3Preferencesunderuncertainty31 3.1 Lotteries 31 3.2 Preferences over lotteries 31 3.3 Expected utility 35 3.4 Theory and experiments 38 3.5 Risk aversion 39 Problems 41 Notes 43 v vi Contents 4Consumerpreferences45 4.1 Bundles of goods 45 4.2 Preferences over bundles 46 4.3 Monotonicity 48 4.4 Continuity 49 4.5 Convexity 50 4.6 Differentiability 53 Problems 54 Notes 56 5Consumerbehavior57 5.1 Budget sets 57 5.2 Demand functions 58 5.3 Rational consumer 59 5.4 Differentiable preferences 61 5.5 Rationalizing a demand function 64 5.6 Properties of demand functions 68 Problems 71 Notes 74 6Producerbehavior75 6.1 The producer 75 6.2 Output maximization 77 6.3 Profit maximization 79 6.4 Cost function 81 6.5 Producers’ preferences 84 Problems 85 Notes 87 7Monopoly89 7.1 Basic model 89 7.2 Uniform-price monopolistic market 90 7.3 Discriminatory monopoly 94 7.4 Implicit discrimination 96 Problems 99 Notes 102 Contents vii Part II Equilibrium 103 8Ajungle105 8.1 Model 105 8.2 Equilibrium 108 8.3 Pareto stability 110 8.4 Equilibrium and Pareto stability in a jungle 112 8.5 Which allocations can be obtained by a social planner who controls the power relation? 113 8.6 Externalities 116 Problems 118 Notes 120 9Amarket121 9.1 Model 121 9.2 Existence and construction of a market equilibrium 127 9.3 Equilibrium and Pareto stability 131 9.4 Uniqueness of market equilibrium 132 Problems 134 Notes 135 10 An exchange economy 137 10.1 Model 137 10.2 Competitive equilibrium 139 10.3 Existence of a competitive equilibrium 144 10.4 Reopening trade 145 10.5 Equilibrium and Pareto stability 146 10.6 The core 148 10.7 Competitive equilibrium based on demand functions 149 10.8 Manipulability 150 10.9 Edgeworth box 150 Problems 152 Notes 155 11 Variants of an exchange economy 157 11.1 Market with indivisible good and money 157 11.2 Exchange economy with uncertainty 164 Problems 171 Notes 173 viii Contents 12 A market with consumers and producers 175 12.1 Production economy 175 12.2 An economy with capital and labor 180 Problems 183 13 Equilibrium with prices and expectations 187 13.1 Distributing customers among bank branches 187 13.2 Asymmetric information and adverse selection 192 13.3 A fishing economy 196 Problems 199 Notes 201 14 A market with asymmetric information 203 14.1 Introductory model 203 14.2 Labor market with education 204 Problems 211 Notes 213 Part III Game theory 215 15 Strategic games 217 15.1 Strategic games and Nash equilibrium 217 15.2 Basic examples 218 15.3 Economic examples 223 15.4 Existence of Nash equilibrium 229 15.5 Strictly competitive games 232 15.6 Kantian equilibrium 234 15.7 Mixed strategies 235 15.8 Interpreting Nash equilibrium 241 Problems 241 Notes 246 16 Extensive games 249 16.1 Extensive games and subgame perfect equilibrium 250 16.2 What is a strategy? 256 16.3 Backward induction 257 16.4 Bargaining 263 Problems 275 Notes 278 Contents ix Part IV Topics 279 17 Mechanism design 281 17.1 Deciding on a public project 281 17.2 Strategy-proof mechanisms 282 17.3 The Vickrey-Clarke-Groves mechanism 284 Problems 287 Notes 288 18 Matching 289 18.1 The matching problem 289 18.2 The Gale-Shapley algorithm 290 18.3 The Gale-Shapley algorithm and stability 295 Problems 298 Notes 299 19 Socialism 301 19.1 Model 301 19.2 Properties of economic systems 304 19.3 Characterization of socialism 307 Problems 310 Notes 311 20 Aggregating preferences 313 20.1 Social preferences 313 20.2 Preference aggregation functions 314 20.3 Properties of preference aggregation functions 316 20.4 Arrow’s impossibility theorem 319 20.5 Gibbard-Satterthwaite theorem 323 Problems 326 Notes 328 References 329 Personal note In 1981 I joined the Department of Economics at the Hebrew University of Jerusalem and started teaching a course in “Price Theory”. In those days, I battled colleagues to bring some game theory into the course — a step that was frowned upon. In 1986, I stopped teaching undergraduate microeconomics (with excep- tions in one or two years). But, as my retirement from my Israeli university ap- proached, I felt an urge to return to the subject. For five years (2012–2017), I taught a course in intermediate microeconomics at Tel Aviv University. This time Itriedtoputlessgametheoryinthecourseandfocusmoreonconceptsofmar- ket equilibrium. One can view this trajectory as part of a cycle of life. But a prin- ciple also links my strivings during these two periods: I don’t see anything holy in economic models. I don’t view a model as right or wrong. I find some models interesting and others less so. I prefer to teach a course that contains a vari- ety of models and not to be dogmatic regarding one particular approach. And I don’t have any respect for what is considered to be fashionable by the academic community. The lecture notes (in Hebrew) from my course in Tel Aviv were the basis of this book. I thank my Teaching Assistants in that course for their help. In 2016, I joined forces with my old friend and coauthor Martin Osborne. The collaboration reshaped my original sloppy lecture notes in both style and degree of precision.
Recommended publications
  • Approximate Nash Equilibria in Large Nonconvex Aggregative Games

    Approximate Nash Equilibria in Large Nonconvex Aggregative Games

    Approximate Nash equilibria in large nonconvex aggregative games Kang Liu,∗ Nadia Oudjane,† Cheng Wan‡ November 26, 2020 Abstract 1 This paper shows the existence of O( nγ )-Nash equilibria in n-player noncooperative aggregative games where the players' cost functions depend only on their own action and the average of all the players' actions, and is lower semicontinuous in the former while γ-H¨oldercontinuous in the latter. Neither the action sets nor the cost functions need to be convex. For an important class of aggregative games which includes con- gestion games with γ being 1, a proximal best-reply algorithm is used to construct an 1 3 O( n )-Nash equilibria with at most O(n ) iterations. These results are applied in a nu- merical example of demand-side management of the electricity system. The asymptotic performance of the algorithm is illustrated when n tends to infinity. Keywords. Shapley-Folkman lemma, aggregative games, nonconvex game, large finite game, -Nash equilibrium, proximal best-reply algorithm, congestion game MSC Class Primary: 91A06; secondary: 90C26 1 Introduction In this paper, players minimize their costs so that the definition of equilibria and equilibrium conditions are in the opposite sense of the usual usage where players maximize their payoffs. Players have actions in Euclidean spaces. If it is not precised, then \Nash equilibrium" means a pure-strategy Nash equilibrium. This paper studies the approximation of pure-strategy Nash equilibria (PNE for short) in a specific class of finite-player noncooperative games, referred to as large nonconvex aggregative games. Recall that the cost functions of players in an aggregative game depend on their own action (i.e.
  • Lecture 4 " Theory of Choice and Individual Demand

    Lecture 4 " Theory of Choice and Individual Demand

    Lecture 4 - Theory of Choice and Individual Demand David Autor 14.03 Fall 2004 Agenda 1. Utility maximization 2. Indirect Utility function 3. Application: Gift giving –Waldfogel paper 4. Expenditure function 5. Relationship between Expenditure function and Indirect utility function 6. Demand functions 7. Application: Food stamps –Whitmore paper 8. Income and substitution e¤ects 9. Normal and inferior goods 10. Compensated and uncompensated demand (Hicksian, Marshallian) 11. Application: Gi¤en goods –Jensen and Miller paper Roadmap: 1 Axioms of consumer preference Primal Dual Max U(x,y) Min pxx+ pyy s.t. pxx+ pyy < I s.t. U(x,y) > U Indirect Utility function Expenditure function E*= E(p , p , U) U*= V(px, py, I) x y Marshallian demand Hicksian demand X = d (p , p , I) = x x y X = hx(px, py, U) = (by Roy’s identity) (by Shepard’s lemma) ¶V / ¶p ¶ E - x - ¶V / ¶I Slutsky equation ¶p x 1 Theory of consumer choice 1.1 Utility maximization subject to budget constraint Ingredients: Utility function (preferences) Budget constraint Price vector Consumer’sproblem Maximize utility subjet to budget constraint Characteristics of solution: Budget exhaustion (non-satiation) For most solutions: psychic tradeo¤ = monetary payo¤ Psychic tradeo¤ is MRS Monetary tradeo¤ is the price ratio 2 From a visual point of view utility maximization corresponds to the following point: (Note that the slope of the budget set is equal to px ) py Graph 35 y IC3 IC2 IC1 B C A D x What’swrong with some of these points? We can see that A P B, A I D, C P A.
  • A Stated Preference Case Study on Traffic Noise in Lisbon

    A Stated Preference Case Study on Traffic Noise in Lisbon

    The Valuation of Environmental Externalities: A stated preference case study on traffic noise in Lisbon by Elisabete M. M. Arsenio Submitted in accordance with the requirements for the degree of Doctor of Philosophy University of Leeds Institute for Transport Studies August 2002 The candidate confirms that the work submitted is his own and that appropriate credit has been given where reference has been made to the work of others. Acknowledgments To pursue a PhD under a part-time scheme is only possible through a strong will and effective support. I thank my supervisors at the ITS, Dr. Abigail Bristow and Dr. Mark Wardman for all the support and useful comments throughout this challenging topic. I would also like to thank the ITS Directors during my research study Prof. Chris Nash and Prof A. D. May for having supported my attendance in useful Courses and Conferences. I would like to thank Mr. Stephen Clark for the invaluable help on the computer survey, as well as to Dr. John Preston for the earlier research motivation. I would like to thank Dr. Hazel Briggs, Ms Anna Kruk, Ms Julie Whitham, Mr. F. Saremi, Mr. T. Horrobin and Dr. R. Batley for the facilities’ support. Thanks also due to Prof. P. Mackie, Prof. P. Bonsall, Mr. F. Montgomery, Ms. Frances Hodgson and Dr. J. Toner. Thanks for all joy and friendship to Bill Lythgoe, Eric Moreno, Jiao Wang, Shojiro and Mauricio. Special thanks are also due to Dr. Paul Firmin for the friendship and precious comments towards the presentation of this thesis. Without Dr.
  • Lecture Notes General Equilibrium Theory: Ss205

    Lecture Notes General Equilibrium Theory: Ss205

    LECTURE NOTES GENERAL EQUILIBRIUM THEORY: SS205 FEDERICO ECHENIQUE CALTECH 1 2 Contents 0. Disclaimer 4 1. Preliminary definitions 5 1.1. Binary relations 5 1.2. Preferences in Euclidean space 5 2. Consumer Theory 6 2.1. Digression: upper hemi continuity 7 2.2. Properties of demand 7 3. Economies 8 3.1. Exchange economies 8 3.2. Economies with production 11 4. Welfare Theorems 13 4.1. First Welfare Theorem 13 4.2. Second Welfare Theorem 14 5. Scitovsky Contours and cost-benefit analysis 20 6. Excess demand functions 22 6.1. Notation 22 6.2. Aggregate excess demand in an exchange economy 22 6.3. Aggregate excess demand 25 7. Existence of competitive equilibria 26 7.1. The Negishi approach 28 8. Uniqueness 32 9. Representative Consumer 34 9.1. Samuelsonian Aggregation 37 9.2. Eisenberg's Theorem 39 10. Determinacy 39 GENERAL EQUILIBRIUM THEORY 3 10.1. Digression: Implicit Function Theorem 40 10.2. Regular and Critical Economies 41 10.3. Digression: Measure Zero Sets and Transversality 44 10.4. Genericity of regular economies 45 11. Observable Consequences of Competitive Equilibrium 46 11.1. Digression on Afriat's Theorem 46 11.2. Sonnenschein-Mantel-Debreu Theorem: Anything goes 47 11.3. Brown and Matzkin: Testable Restrictions On Competitve Equilibrium 48 12. The Core 49 12.1. Pareto Optimality, The Core and Walrasian Equiilbria 51 12.2. Debreu-Scarf Core Convergence Theorem 51 13. Partial equilibrium 58 13.1. Aggregate demand and welfare 60 13.2. Production 61 13.3. Public goods 62 13.4. Lindahl equilibrium 63 14.
  • 2. Budget Constraint.Pdf

    2. Budget Constraint.Pdf

    Engineering Economic Analysis 2019 SPRING Prof. D. J. LEE, SNU Chap. 2 BUDGET CONSTRAINT Consumption Choice Sets . A consumption choice set, X, is the collection of all consumption choices available to the consumer. n X = R+ . A consumption bundle, x, containing x1 units of commodity 1, x2 units of commodity 2 and so on up to xn units of commodity n is denoted by the vector xx =(1 ,..., xn ) ∈ X n . Commodity price vector pp =(1 ,..., pn ) ∈R+ 1 Budget Constraints . Q: When is a bundle (x1, … , xn) affordable at prices p1, … , pn? • A: When p1x1 + … + pnxn ≤ m where m is the consumer’s (disposable) income. The consumer’s budget set is the set of all affordable bundles; B(p1, … , pn, m) = { (x1, … , xn) | x1 ≥ 0, … , xn ≥ 0 and p1x1 + … + pnxn ≤ m } . The budget constraint is the upper boundary of the budget set. p1x1 + … + pnxn = m 2 Budget Set and Constraint for Two Commodities x2 Budget constraint is m /p2 p1x1 + p2x2 = m. m /p1 x1 3 Budget Set and Constraint for Two Commodities x2 Budget constraint is m /p2 p1x1 + p2x2 = m. the collection of all affordable bundles. Budget p1x1 + p2x2 ≤ m. Set m /p1 x1 4 Budget Constraint for Three Commodities • If n = 3 x2 p1x1 + p2x2 + p3x3 = m m /p2 m /p3 x3 m /p1 x1 5 Budget Set for Three Commodities x 2 { (x1,x2,x3) | x1 ≥ 0, x2 ≥ 0, x3 ≥ 0 and m /p2 p1x1 + p2x2 + p3x3 ≤ m} m /p3 x3 m /p1 x1 6 Opportunity cost in Budget Constraints x2 p1x1 + p2x2 = m Slope is -p1/p2 a2 Opp.
  • Game Theory: Preferences and Expected Utility

    Game Theory: Preferences and Expected Utility

    Game Theory: Preferences and Expected Utility Branislav L. Slantchev Department of Political Science, University of California – San Diego April 19, 2005 Contents. 1 Preferences 2 2 Utility Representation 4 3 Choice Under Uncertainty 5 3.1Lotteries............................................. 5 3.2PreferencesOverLotteries.................................. 7 3.3vNMExpectedUtilityFunctions............................... 9 3.4TheExpectedUtilityTheorem................................ 11 4 Risk Aversion 16 1 Preferences We want to examine the behavior of an individual, called a player, who must choose from among a set of outcomes. Begin by formalizing the set of outcomes from which this choice is to be made. Let X be the (finite) set of outcomes with common elements x,y,z. The elements of this set are mutually exclusive (choice of one implies rejection of the others). For example, X can represent the set of candidates in an election and the player needs to chose for whom to vote. Or it can represent a set of diplomatic and military actions—bombing, land invasion, sanctions—among which a player must choose one for implementation. The standard way to model the player is with his preference relation, sometimes called a binary relation. The relation on X represents the relative merits of any two outcomes for the player with respect to some criterion. For example, in mathematics the familiar weak inequality relation, ’≥’, defined on the set of integers, is interpreted as “integer x is at least as big as integer y” whenever we write x ≥ y. Similarly, a relation “is more liberal than,” denoted by ’P’, can be defined on the set of candidates, and interpreted as “candidate x is more liberal than candidate y” whenever we write xPy.
  • Nine Lives of Neoliberalism

    Nine Lives of Neoliberalism

    A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Plehwe, Dieter (Ed.); Slobodian, Quinn (Ed.); Mirowski, Philip (Ed.) Book — Published Version Nine Lives of Neoliberalism Provided in Cooperation with: WZB Berlin Social Science Center Suggested Citation: Plehwe, Dieter (Ed.); Slobodian, Quinn (Ed.); Mirowski, Philip (Ed.) (2020) : Nine Lives of Neoliberalism, ISBN 978-1-78873-255-0, Verso, London, New York, NY, https://www.versobooks.com/books/3075-nine-lives-of-neoliberalism This Version is available at: http://hdl.handle.net/10419/215796 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative
  • 3 Lecture 3: Choices from Budget Sets

    3 Lecture 3: Choices from Budget Sets

    3 Lecture 3: Choices from Budget Sets Up to now, we have been rather demanding about the data that we need in order to test our models. We have made two important assumptions: that we observe choices from all possible choice sets, and that we observe choice correspondences (i.e. we see all the options that a decision maker would be ‘happy with’). In many cases, we may not be so lucky with our data. Unfortunately, without these two properties, conditions and are no longer necessary or sufficient to guarantee a utility representation. Consider the following example of an incomplete data set. Example 1 Let = and say we observe the following (incomplete) choice correspondence { } ( )= { } { } ( )= { } { } ( )= { } { } This choice correspondence satisfies properties and trivially. is satisfied because we do not observe any choices from sets that are subsets of each other. is satisfied because we never see two objects chosen from the same set. However, there is no way that we can rationalize these choices with a complete preference relation. The first observation implies that ,thesecond  that and the third that 3. Thus, any binary relation that would rationalize these choices   would be intransitive. In fact, in order for theorem 1 to hold, we don’t have to observe choices from all subsets of , but we do have to need at least all subsets of that contain two and three elements (you should go back and look at the proof of theorem 1 and check that you agree with this statement). What about if we drop the assumption that we observe a choice correspondence, and instead observe a choice function? For example, we could ask the following question: Question 1 Let :2 ∅ be a choice function.
  • EC9D3 Advanced Microeconomics, Part I: Lecture 2

    EC9D3 Advanced Microeconomics, Part I: Lecture 2

    EC9D3 Advanced Microeconomics, Part I: Lecture 2 Francesco Squintani August, 2020 Budget Set Up to now we focused on how to represent the consumer's preferences. We shall now consider the sour note of the constraint that is imposed on such preferences. Definition (Budget Set) The consumer's budget set is: B(p; m) = fx j (p x) ≤ m; x 2 X g Francesco Squintani EC9D3 Advanced Microeconomics, Part I August, 2020 2 / 49 Budget Set (2) 6 x1 2 L = 2 X = R+ c c c c c c c c c c c c B(p; m) c c c c c c c - x2 Francesco Squintani EC9D3 Advanced Microeconomics, Part I August, 2020 3 / 49 Income and Prices The two exogenous variables that characterize the consumer's budget set are: the level of income m the vector of prices p = (p1;:::; pL). Often the budget set is characterized by a level of income represented by the value of the consumer's endowment x0 (labour supply): m = (p x0) Francesco Squintani EC9D3 Advanced Microeconomics, Part I August, 2020 4 / 49 Utility Maximization The basic consumer's problem (with rational, continuous and monotonic preferences): max u(x) fxg s:t: x 2 B(p; m) Result If p > 0 and u(·) is continuous, then the utility maximization problem has a solution. Proof: If p > 0 (i.e. pl > 0, 8l = 1;:::; L) the budget set is compact (closed, bounded) hence by Weierstrass theorem the maximization of a continuous function on a compact set has a solution. Francesco Squintani EC9D3 Advanced Microeconomics, Part I August, 2020 5 / 49 First Order Condition Result If u(·) is continuously differentiable, the solution x∗ = x(p; m) to the consumer's problem is characterized by the following necessary conditions.
  • Time Preference and Economic Progress

    Time Preference and Economic Progress

    Alexandru Pătruți, 45 ISSN 2071-789X Mihai Vladimir Topan RECENT ISSUES IN ECONOMIC DEVELOPMENT Alexandru Pătruți, Mihai Vladimir Topan, Time Preference, Growth and Civilization: Economic Insights into the Workings of Society, Economics & Sociology, Vol. 5, No 2a, 2012, pp. 45-56. Alexandru Pătruti, PhD TIME PREFERENCE, GROWTH AND Candidate Bucharest University of Economic CIVILIZATION: ECONOMIC Science Department of International INSIGHTS INTO THE WORKINGS Business and Economics Faculty of International Business OF SOCIETY and Economics 6, Piata Romana, 1st district, ABSTRACT. Economic concepts are not mere ivory 010374, Romania tower abstractions disconnected from reality. To a +4.021.319.19.00 certain extent they can help interdisciplinary endeavours E-mail: [email protected] at explaining various non-economic realities (the family, education, charity, civilization, etc.). Following the Mihai Vladimir Topan, insights of Hoppe (2001), we argue that the economic PhD Lecturer concept of social time preference can provide insights – Bucharest University of Economic when interpreted in the proper context – into the degree Science Department of International of civilization of a nation/region/city/group of people. Business and Economics More specifically, growth and prosperity backed by the Faculty of International Business proper institutional context lead, ceteris paribus, to a and Economics diminishing of the social rate of time preference, and 6, Piata Romana, 1st district, therefore to more future-oriented behaviours compatible 010374, Romania with a more ambitious, capital intensive structure of +4.021.319.19.00 production, and with the accumulation of sustainable E-mail: [email protected] cultural patterns; on the other hand, improper institutional arrangements which hamper growth and Received: July, 2012 prosperity lead to an increase in the social rate of time 1st Revision: September, 2012 preference, to more present-oriented behaviours and, Accepted: Desember, 2012 ultimately, to the erosion of culture.
  • Revealed Preference with a Subset of Goods

    Revealed Preference with a Subset of Goods

    JOURNAL OF ECONOMIC THEORY 46, 179-185 (1988) Revealed Preference with a Subset of Goods HAL R. VARIAN* Department of Economics, Unioersity of Michigan, Ann Arbor, Michigan 48109 Received November 4. 1985; revised August 14. 1987 Suppose that you observe n choices of k goods and prices when the consumer is actually choosing from a set of k + 1 goods. Then revealed preference theory puts essentially no restrictions on the behavior of the data. This is true even if you also observe the quantity demanded of good k+ 1, or its price. The proofs of these statements are not difficult. Journal cf Economic Literature Classification Number: 022. ii? 1988 Academic Press. Inc. Suppose that we are given n observations on a consumer’s choices of k goods, (p,, x,), where pi and xi are nonnegative k-dimensional vectors. Under what conditions can we find a utility function u: Rk -+ R that rationalizes these observations? That is, when can we find a utility function that achieves its constrained maximum at the observed choices? This is, of course, a classical question of consumer theory. It has been addressed from two distinct viewpoints, the first known as integrabilitv theory and the second known as revealed preference theory. Integrability theory is appropriate when one is given an entire demand function while revealed preference theory is more suited when one is given a finite set of demand observations, the case described above. In the revealed preference case, it is well known that some variant of the Strong Axiom of Revealed Preference (SARP) is a necessary and sufficient condition for the data (pi, xi) to be consistent with utility maximization.
  • Revealed Preference in Game Theory

    Revealed Preference in Game Theory

    Revealed Preference in Game Theory Ad´am´ Galambos 1 Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, IL, 60208 Abstract I characterize joint choice behavior generated by the pure strategy Nash equilib- rium solution concept by an extension of the Congruence Axiom of Richter(1966) to multiple agents. At the same time, I relax the “complete domain” assumption of Yanovskaya(1980) and Sprumont(2000) to “closed domain.” Without any restric- tions on the domain of the choice correspondence, determining pure strategy Nash rationalizability is computationally very complex. Specifically, it is NP–complete even if there are only two players. In contrast, the analogous problem with a single decision maker can be determined in polynomial time. Key words: Nash equilibrium; Revealed preference; Complexity Email address: [email protected] (Ad´am´ Galambos). 1 I am grateful to Professor Marcel K. Richter for many inspiring and stimulating discussions on these topics, as well as many suggestions. I wish to thank Profes- sors Beth Allen, Andrew McLennan and Jan Werner, and participants of the Mi- cro/Finance and Micro/Game theory workshops at the University of Minnesota for their comments. This paper is based on my doctoral dissertation at the University of Minnesota. I gratefully acknowledge the financial support of the NSF through grant SES-0099206 (principal investigator: Professor Jan Werner). 27 September 2005 1 Introduction What are the testable implications of the Nash equilibrium solution? If we observed a group of agents play different games, could we tell, without knowing their preferences, whether they are playing according to Nash equilibrium? Such questions could be of interest to a regulatory agency, wanting to know if some firms they observe in the market are behaving in a competitive or in a collusive way.