Microeconomic Foundations I (ebook)

Chapter One. Choice, Preference, and Utility 1

• 1.1. Consumer Choice: The Basics 1
  
• 1.2. Proving Most of Proposition 1.2, and More 5
  
• 1.3. The No-Better-Than Sets and Utility Representations 7
  
• 1.4. Strict Preference and Indifference 9
  
• 1.5. Infinite Sets and Utility Representations 10
  
• 1.6. Choice from Infinite Sets 15
  
• 1.7. Equivalent Utility Representations 17
  
• 1.8. Commentary 18
  
• Bibliographic Notes 23
  
• Problems 23

Chapter Two. Structural Properties of Preferences and Utility Functions 30

• 2.1. Monotonicity 31
  
• 2.2. Convexity 32
  
• 2.3. Continuity 35
  
• 2.4. Indifference Curve Diagrams 38
  
• 2.5. Weak and Additive Separability 39
  
• 2.6. Quasi-linearity 43
  
• 2.7. Homotheticity 44
  
• Bibliographic Notes 45
  
• Problems 45

Chapter Three. Basics of Consumer Demand 50

• 3.1. The Consumer's Problem 50
  
• 3.2. Basic Facts about the CP 52
  
• 3.3. The Marshallian Demand Correspondence and Indirect Utility Function 54
  
• 3.4. Solving the CP with Calculus 56
  
• Bibliographic Notes 63
  
• Problems 64

Chapter Four. Revealed Preference and Afriat's Theorem 67

• 4.1. An Example and Basic Ideas 67
  
• 4.2. GARP and Afriat's Theorem 70
  
• 4.3. Comparative Statics and the Own-Price Effect 74
  
• Bibliographic Notes 77
  
• Problems 78

Chapter Five. Choice under Uncertainty 79

• 5.1. Two Models and Three Representations 79
  
• 5.2. The Mixture-Space Theorem 89
  
• 5.3. States of Nature and Subjective Expected Utility 101
  
• 5.4. Subjective and Objective Probability and the Harsanyi Doctrine 108
  
• 5.5. Empirical and Theoretical Critiques 110
  
• Bibliographic Notes 116
  
• Problems 116

Chapter Six. Utility for Money 123

• 6.1. Properties of Utility Functions for Money 123
  
• 6.2. Induced Preferences for Income 134
  
• 6.3. Demand for Insurance and Risky Assets 138
  
• Bibliographic Notes 140
  
• Problems 140

Chapter Seven. Dynamic Choice 148

• 7.1. The Standard Strategic Approach 149
  
• 7.2. Dynamic Programming 152
  
• 7.3. Testable Restrictions of the Standard Model 153
  
• 7.4. Three Alternatives to the Standard Model 156
  
• Bibliographic Notes 161
  
• Problems 161

Chapter Eight. Social Choice and Efficiency 166

• 8.1. Arrow's Theorem 166
  
• 8.2. What Do We Give Up? 172
  
• 8.3. Efficiency 175
  
• 8.4. Identifying the Pareto Frontier: Utility Imputations and Bergsonian Social Utility Functionals 176
  
• 8.5. Syndicate Theory and Efficient Risk Sharing: Applying Proposition 8.10 184
  
• 8.6. Efficiency? 192
  
• Bibliographic Notes 194
  
• Problems 194

Chapter Nine. Competitive and Profit-Maximizing Firms 197

• 9.1. The Production-Possibility Set 198
  
• 9.2. Profit Maximization 199
  
• 9.3. Basics of the Firm's Profit-Maximization Problem 201
  
• 9.4. Afriat's Theorem for Firms 207
  
• 9.5. From Profit Functions to Production-Possibility Sets 211
  
• 9.6. How Many Production-Possibility Sets Give the Same Profit Function? 213
  
• 9.7. What Is Going On Here, Mathematically? 216
  
• 9.8. Differentiability of the Profit Function 219
  
• 9.9. Cost Minimization and Input-Requirement Sets 222
  
• 9.10. Why DoWe Care? 228
  
• Bibilographic Notes 229
  
• Problems 229

Chapter Ten. The Expenditure-Minimization Problem 233

• 10.1. Defining the EMP 233
  
• 10.2. Basic Analysis of the EMP 235
  
• 10.3. Hicksian Demand and the Expenditure Function 236
  
• 10.4. Properties of the Expenditure Function 238
  
• 10.5. How Many Continuous Utility Functions
  
• Give the Same Expenditure Function? 240
  
• 10.6. Recovering Continuous Utility Functions from Expenditure Functions 247
  
• 10.7. Is an Alleged Expenditure Function Really an Expenditure Function? 248
  
• 10.8. Connecting the CP and the EMP 254
  
• Bibliographic Notes 255
  
• Problems 255

Chapter Eleven. Classic Demand Theory 258

• 11.1. Roy's Identity and the Slutsky Equation 258
  
• 11.2. Differentiability of Indirect Utility 262
  
• 11.3. Duality of Utility and Indirect Utility 269
  
• 11.4. Differentiability of Marshallian Demand 274
  
• 11.5. Integrability 279
  
• 11.6. Complements and Substitutes 283
  
• 11.7. Integrability and Revealed Preference 284
  
• Bibliographic Notes 286
  
• Problems 287

Chapter Twelve. Producer and Consumer Surplus 289

• 12.1. Producer Surplus 289
  
• 12.2. Consumer Surplus 296
  
• Bibliographic Notes 304
  
• Problems 304

Chapter Thirteen. Aggregating Firms and Consumers 306

• 13.1. Aggregating Firms 307
  
• 13.2. Aggregating Consumers 310
  
• 13.3. Convexification through Aggregation 318
  
• Bibliographic Notes 326
  
• Problems 326

Chapter Fourteen. General Equilibrium 329

• 14.1. Definitions 329
  
• 14.2. Basic Properties ofWalrasian Equilibrium 333
  
• 14.3. The Edgeworth Box 335
  
• 14.4. Existence ofWalrasian Equilibria 338
  
• 14.5. The Set of Equilibria for a Fixed Economy 351
  
• 14.6. The Equilibrium Correspondence 354
  
• Bibliographic Notes 354
  
• Problems 355

Chapter Fifteen. General Equilibrium, Efficiency, and the Core 358

• 15.1. The First Theorem ofWelfare Economics 359
  
• 15.2. The Second Theorem ofWelfare Economics 362
  
• 15.3. Walrasian Equilibria Are in the Core 366
  
• 15.4. In a Large Enough Economy, Every Core Allocation Is a Walrasian-Equilibrium Allocation 370
  
• 15.5. Externalities and Lindahl Equilibrium 380
  
• Bibliographic Notes 383
  
• Problems 383

Chapter Sixteen. General Equilibrium, Time, and Uncertainty 386

• 16.1. A Framework for Time and Uncertainty 386
  
• 16.2. General Equilibrium with Time and Uncertainty 389
  
• 16.3. Equilibria of Plans, Prices, and Price Expectations: I. Pure Exchange with Contingent Claims 392
  
• 16.4. EPPPE: II. Complex Financial Securities and Complete Markets 402
  
• 16.5. EPPPE: III. Complex Securities with Real Dividends and Complete Markets 418
  
• 16.6. Incomplete Markets 419
  
• 16.7. Firms 424
  
• Bibliographic Notes 431
  
• Problems 432

About the Appendices 437

Appendix One: Mathematical Induction 439

Appendix Two: Some Simple Real Analysis 441

• A2.1. The Setting 441
  
• A2.2. Distance, Neighborhoods, and Open and Closed Sets 441
  
• A2.3. Sequences and Limits 445
  
• A2.4. Boundedness, (Completeness), and Compactness 446
  
• A2.5. Continuous Functions 447
  
• A2.6. Simply Connected Sets and the Intermediate-Value Theorem 448
  
• A2.7. Suprema and Infima; Maxes and Mins 448
  
• A2.8. The Maximum of a Continuous Function on a Compact Set 449
  
• A2.9. Lims Sup and Inf 450
  
• A2.10. Upper and Lower Semi-continuous Functions 451

Appendix Three: Convexity 452

• A3.1. Convex Sets 452
  
• A3.2. The Separating- and Supporting-Hyperplane Theorems 457
  
• A3.3. The Support-Function Theorem 459
  
• A3.4. Concave and Convex Functions 461
  
• A3.5. Quasi-concavity and Quasi-convexity 463
  
• A3.6. Supergradients and Subgradients 466
  
• A3.7. Concave and Convex Functions and Calculus 468

Appendix Four: Correspondences 469

• A4.1. Functions and Correspondences 470
  
• A4.2. Continuity of Correspondences 471
  
• A4.3. Singleton-Valued Correspondences and Continuity 474
  
• A4.4. Parametric Constrained Optimization Problems and Berge's Theorem 475
  
• A4.5. Why this Terminology? 477

Appendix Five: Constrained Optimization 479

Appendix Six: Dynamic Programming 485

• A6.1. Several Examples 485
  
• A6.2. A General Formulation 489
  
• A6.3. Bellman's Equation 494
  
• A6.4. Conserving and Unimprovable Strategies 496
  
• A6.5. Additive Rewards 501
  
• A6.6. States of the System 504
  
• A6.7. Solving Finite-Horizon Problems 506
  
• A6.8. Infinite-Horizon Problems and Stationarity 509
  
• A6.9. Solving Infinite-Horizon (Stationary) Problems with Unimprovability 512
  
• A6.10. Policy Iteration (and Transience) 516
  
• A6.11. Value Iteration 518
  
• A6.12. Examples 521
  
• A6.13. Things Not Covered Here: Other Optimality Criteria; Continuous Time and Control Theory 527
  
• A6.14. Multi-armed Bandits and Complexity 528
  
• A6.15. Four More Problems You Can Solve 530

Appendix Seven: The Implicit Function Theorem 534

Appendix Eight: Fixed-Point Theory 535

References 543
Index 551