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# Microeconomic Foundations I: Choice and Competitive Markets

## byDavid M. Kreps

### Hardcover | October 28, 2012

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*Microeconomic Foundations I* develops the choice, price, and general equilibrium theory topics typically found in first-year theory sequences, but in deeper and more complete mathematical form than most standard texts provide. The objective is to take the reader from acquaintance with these foundational topics to something closer to mastery of the models and results connected to them.

- Provides a rigorous treatment of some of the basic tools of economic modeling and reasoning, along with an assessment of the strengths and weaknesses of these tools
- Complements standard texts
- Covers choice, preference, and utility; structural properties of preferences and utility functions; basics of consumer demand; revealed preference and Afriat's Theorem; choice under uncertainty; dynamic choice; social choice and efficiency; competitive and profit-maximizing firms; expenditure minimization; demand theory (duality methods); producer and consumer surplus; aggregation; general equilibrium; efficiency and the core; GET, time, and uncertainty; and other topics
- Features a free web-based student's guide, which gives solutions to approximately half the problems, and a limited-access instructor's manual, which provides solutions to the rest of the problems
- Contains appendixes that review most of the specific mathematics employed in the book, including a from-first-principles treatment of dynamic programming

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The following ISBNs are associated with this title:

ISBN - 10:0691155836

ISBN - 13:9780691155838

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Table of Contents

*Preface*xiii

**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

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