Models in Microeconomic Theory Martin J. Osborne Ariel Rubinstein h 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: https://www.openbookpublishers.com/product/1159 Open Book Publishers is a non-profit 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). 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Version: 2020.12.21 (h) Contents Personal note xi Preface xiii Part I Individual behavior 1 1 Preferences and utility 3 1.1 Preferences 3 1.2 Preference formation 7 1.3 An experiment 8 1.4 Utility functions 9 Problems 13 Notes 15 2 Choice 17 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 3 Preferences under uncertainty 31 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 4 Consumer preferences 45 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 Di ff erentiability 53 Problems 54 Notes 56 5 Consumer behavior 57 5.1 Budget sets 57 5.2 Demand functions 58 5.3 Rational consumer 59 5.4 Di ff erentiable preferences 61 5.5 Rationalizing a demand function 64 5.6 Properties of demand functions 68 Problems 71 Notes 74 6 Producer behavior 75 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 7 Monopoly 89 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 8 A jungle 105 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 9 A market 121 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 I tried to put less game theory in the course and focus more on concepts of mar- 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. I don’t consider the current version to be the end of the journey. We have made some progress, but, to my mind, some chapters (chiefly 4–7, 11–12, and 15–16) are insufficiently innovative. So I hope we will revise the book signifi- cantly in the coming years. As for all my other books, the electronic version of this book is freely avail- able. I invite you to download my books at http://arielrubinstein.tau.ac. il/books.html Ariel Rubinstein Tel Aviv University and New York University http://arielrubinstein.tau.ac.il xi Preface The book contains material for a year-long undergraduate course in what is of- ten called “Intermediate microeconomics”. It covers basic concepts and models of current microeconomics theory. Our main aim is to give the reader an under- standing of the concepts of model and equilibrium in microeconomic theory. The connection between models in microeconomics and the world is sub- tle, and microeconomic theorists differ in their views about the purpose of their work. Ariel has expressed his views about the meaning of models in economic theory frequently, especially in his book Economic fables (Rubinstein 2012). Al- though we do not discuss applications and implications of the theory for policy, we strongly believe that economic models should be connected to the world; they should concern concepts we use in the real world when thinking about economic interactions. A main principle that guides us is that concepts, models and results should be stated precisely. Nevertheless, the mathematics we use is elementary, and in particular we use almost no calculus. We also have tried to avoid involved computations, both in the text and the exercises. However, many of the proofs involve sustained logical arguments. Contents Part I (Chapters 1–7) presents basic models of an economic agent. We start with an abstract discussion of preferences (Chapter 1), choice (Chapter 2), and de- cision making under uncertainty (Chapter 3) and then discuss the consumer (Chapters 4 and 5), the producer (Chapter 6) and monopoly (Chapter 7). The chapter on the producer is unconventional in not assuming that a producer nec- essarily wants to maximize profit. The core of the book is Part II (Chapters 8–14), which introduces the con- cept of equilibrium in economic models. Chapters 8 and 9 provide an unconven- tional introduction to the topic through the models of the jungle (Chapter 8) and an economy with indivisible goods (Chapter 9). The subsequent chapters cover the more conventional model of an exchange economy (Chapters 10 and 11), introducing production (Chapter 12), rational expectations (Chapter 13), and asymmetric information (Chapter 14). Part III (Chapters 15–16) provide a short introduction to game theory and its applications in economics. We discuss only the concepts of Nash equilibrium xiii xiv Preface Part I: Individual behavior 1: Preferences 2: Choice 3: Uncertainty 4: Consumer preferences 5: Consumer behavior 6: Producer behavior 7: Monopoly Part II: Equilibrium 8: Jungle 9: Market 10: Exchange economy 11: Exchange examples 12: Consumers & producers 13: Prices and expectations 14: Asymmetric information Part III: Game theory 15: Strategic games 16: Extensive games Part IV: Topics 17: Mechanism design 18: Matching 19: Socialism 20: Social choice and subgame perfect equilibrium, and treat equilibria only as steady states; we do not discuss epistemic interpretations of the solution concepts. Part IV (Chapters 17–20) gives the reader a taste of the topics of mechanism design (Chapter 17), matching (Chapter 18), the axiomatic analysis of economic systems (Chapter 19) and social choice (Chapter 20). Some chapters (for example, 8, 9, 13, 14, and 17–20) could be used a basis for advanced undergraduate or graduate courses in microeconomics. We intend to revise the book occasionally. See our personal websites for information about revisions. Exercises The book contains about 150 exercises. A solution manual is available for in- structors. To request it, please visit the page about the book on either of our websites. Hyperlinks Every term with a technical meaning in each definition is hyperlinked to its def- inition. After clicking on such a term, click the “Back” button in your pdf viewer Preface xv to return to the definition; if your viewer does not have such a button, the key combination alt+left arrow may have the same effect. Personal pronouns During our thirty years of collaboration we have often debated the use of gen- dered pronouns in academic material. In our book A course in game theory (1994) we expressed our opinions, which remain unchanged. Martin prefers to use fem- inine pronouns and Ariel insists on using masculine pronouns. We do not repeat our positions in detail here. In one sentence, Ariel argues: “I am a strong believer in the need to repair gender injustice but the cure is in other frontiers, which require much more than language gestures”. Martin’s position is elaborated in his book An introduction to game theory (2004, xv–xvi), where he cites evidence that the use of male-focussed language reinforces sexist stereotypes and ways of thought, and argues that while the use of feminine pronouns is obviously not sex-neutral, it can only help to address the existing bias. In our 1994 book we adopted a compromise that neither of us liked. Here we adopt a different solution: this book has two editions, one that uses feminine pronouns and one that uses masculine pronouns. We leave it to you to make your choice. Acknowledgments We are grateful to Minghao Zou, who read the entire book and alerted us to many errors and confusions. We thank all the members of the Open Book Publishers team for their very efficient handling of the book. Working with them has been a pleasure. Martin J. Osborne University of Toronto https://economics.utoronto.ca/osborne Ariel Rubinstein Tel Aviv University and New York University http://arielrubinstein.tau.ac.il MODELS IN MICROECONOMIC THEORY