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.