Welfare Economics and Social Choice Theory (eBook)

Allan M. Feldman has taught economics at Brown University for 34 years. He has written and published articles in the areas of general equilibrium theory, fairness and equity, Arrow’s theorem, strategy-proofness, majority voting theory, compensation criteria, the value of life, and law and economics. He has taught thousands of Brown undergraduates in a wide variety of courses, and has served for many years as the director of undergraduate studies in economics at Brown. He has also worked as an economics consultant in litigation. Roberto Serrano is a Professor of Economics at Brown University, where he has worked since 1992 when he got his PhD from Harvard University. His fields of research are economic theory and game theory. He has been an Associate Editor of several journals, including Economic Theory, Mathematical Social Sciences and Research in Economics. He has published over thirty articles in refereed journals, and his research has been supported through fellowships and awards from prestigious institutions, including The Sloan Foundation, the U.S.-Israel Binational Science Foundation, the U.S. National Science Foundation and Spain’s Fundacion Banco Herrero.

Contents 6
Preface 12
Introduction 14
1. The Concerns of Welfare Economics 14
2. The Concerns of Social Choice Theory 17
3. Practical Concerns of Welfare Economics and Social Choice Theory 20
Chapter 1 PREFERENCES AND UTILITY 24
1. Fundamental Assumptions 24
2. Best Alternatives and Utility Functions 26
3. The Formal Model of Preferences 27
4. Decisions under Uncertainty and Expected Utility 32
5. Introduction to Social Preferences 37
6. Exercises 41
7. Appendix 42
8. Selected References 43
Chapter 2 BARTER EXCHANGE 46
1. Introduction 46
2. Allocations 47
3. The Edgeworth Box Diagram 49
4. Pareto Optimal Allocations and the Core 50
5. Algebraic Examples 53
6. Final Notes on the Core: The Number of Coahtions 59
7. Exercises 59
8. Selected References 60
Chapter 3 WELFARE PROPERTIES OF MARKET EXCHANGE 64
1. Introduction 64
2. The Two-Person, Two-Goods Model 65
3. Competitive Equilibrium in an Exchange Economy: Formal Preliminaries 69
4. The First Fundamental Theorem of Welfare Economics 72
5. The Second Fundamental Theorem of Welfare Economics 76
6. An Algebraic Example 83
7. Exercises 86
8. Selected References 88
Chapter 4 WELFARE PROPERTIES OF ^'JUNGLE" EXCHANGE 92
1. Power as a Basis for Exchange 92
2. A Model of Indivisible Objects 93
3. A 4-Person 4-Houses Example 95
4. Finding a Market Equilibrium with Top Cycles 98
5. Fundamental Theorems of Welfare Economics and Jungle Economics 100
6. Exercises 104
7. Selected References 104
Chapter 5 ECONOMIES WITH PRODUCTION 106
1. Introduction 106
2. Optimal Production Plans 109
3. Competitive Equilibrium Production Plans 112
4. The First Fundamental Theorem of Welfare Economics, Production Version 115
5. The Second Fundamental Theorem of Welfare Economics, Production Version 117
6. Extending the Production Model, and Combining Production and Exchange 120
7. An Algebraic Example in a Simple Production Model 124
8. Exercises 126
9. Appendix 127
10. Selected References 128
Chapter 6 UNCERTAINTY IN EXCHANGE 132
1. Introduction 132
2. States of the World 133
3. Symmetric Uncertainty 134
4. Examples 141
5. Asymmetric Information 143
6. Exercises 152
7. Selected References 152
Chapter 7 EXTERNALITIES 156
1. Introduction 156
2. Externalities in an Exchange Economy: An Example 159
3. Pigouvian Taxes and Subsidies: The Exchange Example Continued 163
4. Pigouvian Taxes and Subsidies: A Production Example 166
5. Exercises 170
6. Selected References 171
Chapter 8 PUBLIC GOODS 174
1. Introduction 174
2. The Public Goods Model 175
3. The Samuelson Public Good Optimality Condition 177
4. Private Financing of the Public Good and the Free Rider Problem 180
5. The Wicksell-Lindahl Tax Scheme 182
6. Fixed Tax Shares and Majority Voting 187
7. The Demand-Revealing Tax Scheme 189
8. The Groves-Ledyard Tax Scheme 197
9. Exercises 201
10. Selected References 202
Chapter 9 COMPENSATION CRITERIA 208
1. Introduction 208
2. Notational Preliminaries 209
3. The Pareto Criterion 210
4. The Kaldor Criterion 212
5. The Scitovsky Criterion 214
6. The Samuelson Criterion 215
7. Compensation Criteria in Exchange Economies 217
8. Consumer's Surplus — Money Metrics 219
9. Consumers' Surplus - Boadway Paradox 221
10. Quasilinear Utility 223
11. Cost Benefit Analysis with One Good 226
12. Exercises 227
13. Selected References 228
Chapter 10 FAIRNESS AND THE RAWLS CRITERION 230
1. Introduction 230
2. Fairness 231
3. The Rawls Criterion 234
4. Exercises 238
5. Selected References 239
Chapter 11 LIFE AND DEATH CHOICES 242
1. Introduction 242
2. Economic Model — The Money Value of a Life 243
3. A Formal Version of the Economic Model 244
4. The Broome Paradox 247
5. Ex-Ante and Ex-Post 248
6. Problems with Utilitarian Measures of Life/Death Choices 251
7. The Pareto Principle and Extended Pareto Principles 256
8. What's Repugnant About the Repugnant Conclusion? 259
9. Conclusions About Life and Death Choices 260
10. Exercises 261
11. Selected References 261
Chapter 12 MAJORITY VOTING 266
1. Introduction 266
2. The Majority Voting Criterion 267
3. Majority Voting and Single-Peakedness 269
4. Majority Voting and Single-Peakedness: The Multidimensional Case 276
5. Multidimensional Voting — Are the Cycles That Bad? 281
6. Exercises 283
7. Selected References 284
Chapter 13 ARROW'S IMPOSSIBILITY THEOREM 288
1. Introduction 288
2. A Simple Model for Arrow's Impossibility Theorem 289
3. Requirements on the Arrow Social Welfare Function 290
4. Applying the Requirements 293
5. Arrow's Impossibility Theorem 295
6. Relaxing the Universality Requirement 300
7. Reactions to Arrow's Impossibility Theorem 301
8. Another Version of Arrow's Theorem 304
9. Exercises 307
10. Selected References 308
Chapter 14 DOMINANT-STRATEGY IMPLEMENTATION 312
1. Introduction 312
2. Examples of Strategic Manipulation 314
3. The Gibbard-Satterthwaite Impossibility Theorem 318
4. Significance of the Gibbard-Satterthwaite Theorem 325
5. Exercises 327
6. Appendix 329
7. Selected References 330
Chapter 15 NASH IMPLEMENTATION 334
1. Introduction 334
2. An Example 335
3. Maskin Monotonicity 337
4. Maskin's Theorem 339
5. Comments on Maskin's Theorem 345
6. Limitations of Maskin Monotonicity and Approximate Implementation 346
7. Exercises 350
8. Appendix 352
9. Selected References 354
Chapter 16 BAYESIAN IMPLEMENTATION 358
1. Introduction 358
2. Asymmetric Information in the Model of Types 359
3. Incentive Compatibility 363
4. From Truthful to Full Implementability 366
5. Bayesian Implement ability: Example 3 Continued 369
6. Bayesian Implementability: Theory 370
7. Exercises 372
8. Selected References 372
Chapter 17 EPILOGUE 376
Solutions to Exercises 384
Index 412