THE STRUCTURE OF ECONOMICS:A MATHEMATICAL ANALYSISPDF电子书下载

1 Comparative Statics and the Paradigm of Economics 1

1.1 Introduction 1

1.2 The Marginalist Paradigm 3

1.3 Theories and Refutable Propositions 9

The Structure of Theories 10

Refutable Propositions 12

1.4 Theories Versus Models；Comparative Statics 14

1.5 Examples of Comparative Statics 16

Problems 23

Selected References 24

Bibliography 24

2 Review of Calculus（One Variable） 25

2.1 Functions，Slopes，and Elasticity 25

2.2 Maxima and Minima 27

2.3 Continuous Compounding 28

2.4 The Mean Value Theorem 31

2.5 Taylor’s Series 32

Applications of Taylor’s Series：Derivation of the First-and Second-Order Conditions for a Maximum；Concavity and Convexity 34

3 Functions of Several Variables 37

3.1 Functions of Several Variables 37

3.2 Level Curves：Ⅰ 37

3.3 Partial Derivatives 39

3.4 The Chain Rule 45

Second Derivatives by the Chain Rule 47

3.5 Level Curves：Ⅱ 49

Convexity of the Level Curves 51

Monotonic Transformations and Diminishing Marginal Utility 53

Problems 55

3.6 Homogeneous Functions and Euler’s Theorem 56

Problems 65

Selected References 65

4 Profit Maximization 66

4.1 Unconstrained Maxima and Minima：First-Order Necessary Conditions 66

4.2 Sufficient Conditions for Maxima and Minima：Two Variables 68 Problems 72

4.3 An Extended Footnote 73

4.4 An Application of Maximizing Behavior：The Profit-Maximizing Firm 74

The Supply Function 81

4.5 Homogeneity of the Demand and Supply Functions；Elasticities 82

Elasticities 83

4.6 The Long Run and the Short Run：An Example of the Le Chatelier Principle 84

A More Fundamental Look at the Le Chatelier Principle 86

Problems 87

4.7 Analysis of Finite Changes：A Digression 91

Appendix 92

Taylor Series for Functions of Several Variables 92

Concavity and the Maximum Conditions 93

Selected References 95

5 Matrices and Determinants 96

5.1 Matrices 96

5.2 Determinants，Cramer’s Rule 98

5.3 The Implicit Function Theorem 105

Problems 109

Appendix 110

Simple Matrix Operations 110

The Rank of a Matrix 112

The Inverse of a Matrix 113

Orthogonality 115

Problems 116

Selected References 116

6 Comparative Statics：The Traditional Methodology 117

6.1 Introduction；Profit Maximization Once More 117

6.2 Generalization to n Variables 121

First-Order Necessary Conditions 121

Second-Order Sufficient Conditions 121

Profit Maximization：n Factors 124

6.3 The Theory of Constrained Maxima and Minima：First-Order Necessary Conditions 128

6.4 Constrained Maximization with More than One Constraint：A Digression 132

6.5 Second-Order Conditions 134

The Geometry of Constrained Maximization 138

6.6 General Methodology 141

Problems 148

Selected References 150

7 The Envelope Theorem and Duality 151

7.1 History of the Problem 151

7.2 The Profit Function 152

7.3 General Comparative Statics Analysis：Unconstrained Models 156

7.4 Models with Constraints 159

Comparative Statics：Primal-Dual Analysis 161

An Important Special Case 165

Interpretation of the Lagrange Multiplier 166

Le Chatelier Effects 169

Problems 172

Bibliography 174

8 The Derivation of Cost Functions 175

8.1 The Cost Function 175

8.2 Marginal Cost 179

8.3 Average Cost 180

8.4 A General Relationship Between Average and Marginal Costs 181

8.5 The Cost Minimization Problem 183

8.6 The Factor Demand Curves 189

Interpretation of the Lagrange Multiplier 189

8.7 Comparative Statics Relations：The Traditional Methodology 193

8.8 Comparative Statics Relations Using Duality Theory 202

Reciprocity Conditions 202

Cost Curves in the Short and Long Run 205

Factor Demands in the Short and Long Run 207

Relation to Profit Maximization 209

8.9 Elasticities；Further Properties of the Factor Demand Curves 211

Homogeneity 212

Output Elasticities 216

8.10 The Average Cost Curve 216

8.11 Analysis of Firms in Long-Run Competitive Equilibrium 218

Analysis of Factor Demands in the Long Run 220

Problems 222

Selected References 224

9 Cost and Production Functions：Special Topics 225

9.1 Homogeneous and Homothetic Production Functions 225

9.2 The Cost Function：Further Properties 228

Homothetic Functions 232

9.3 The Duality of Cost and Production Functions 234

The Importance of Duality 237

9.4 Elasticity of Substitution；the Constant-Elasticity-of-Substitution（CES）Production Function 238

Generalizations to n Factors 248

The Generalized Leontief Cost Function 249

Problems 250

Bibliography 250

10 The Derivation of Consumer Demand Functions 252

10.1 Introductory Remarks：The Behavioral Postulates 252

10.2 Utility Maximization 261

Interpretation of the Lagrange Multiplier 266

Roy’s Identity 268

10.3 The Relationship Between the Utility Maximization Model and the Cost Minimization Model 272

10.4 The Comparative Statics of the Utility Maximization Model；the Traditional Derivation of the Slutsky Equation 276

10.5 The Modern Derivation of the Slutsky Equation 282

Conditional Demands 286

The Addition of a New Commodity 288

10.6 Elasticity Formulas for Money-Income-Held-Constant and Real-Income-Held-Constant Demand Curves 291

The Slutsky Equation in Elasticity Form 291

Compensated Demand Curves 294

10.7 Special Topics 297

Separable Utility Functions 297

The Labor-Leisure Choice 299

Slutsky Versus Hicks Compensations 304

The Division of Labor Is Limited by the Extent of the Market 306

Problems 310

Selected References 313

11 Special Topics in Consumer Theory 314

11.1 Revealed Preference and Exchange 314

11.2 The Strong Axiom of Revealed Preference and Integrability 322

Integrability 325

11.3 The Composite Commodity Theorem 332

Shipping the Good Apples Out 335

11.4 Household Production Functions 341

Comparative Statics 345

11.5 Consumer’s Surplus 347

Example 354

Empirical Approximations 355

11.6 Empirical Estimation and Functional Forms 357

Linear Expenditure System 357

CES Utility Function 359

Indirect Addilog Utility Function 360

Translog Specifications 361

Almost Ideal Demand System 362

Problems 363

References on Theory 366

References on Functional Forms 366

12 Intertemporal Choice 368

12.1 n-Period Utility Maximization 368

Time Preference 371

Fisherian Investment 378

The Fisher Separation Theorem 380

Real Versus Nominal Interest Rates 382

12.2 The Determination of the Interest Rate 384

12.3 Stocks and Flows 387

Problems 391

Selected References 392

13 Behavior Under Uncertainty 394

13.1 Uncertainty and Probability 394

Random Variables and Probability Distributions 395

Mean and Variance 396

13.2 Specification of Preferences 399

State Preference Approach 399

The Expected Utility Hypothesis 400

Cardinal and Ordinal Utility 401

13.3 Risk Aversion 403

Measures of Risk Aversion 405

Mean-Variance Utility Function 406

Gambling，Insurance，and Diversification 409

13.4 Comparative Statics 411

Allocation of Wealth to Risky Assets 411

Output Decisions Under Price Uncertainty 412

Increases in Riskiness 413

Problems 416

Selected References 416

14 Maximization with Inequality and Nonnegativity Constraints 418

14.1 Nonnegativity 418

Functions of Two or More Variables 423

14.2 Inequality Constraints 427

14.3 The Saddle Point Theorem 432

14.4 Nonlinear Programming 437

14.5 An “Adding-Up” Theorem 440

Problems 442

Appendix 443

Bibliography 446

15 Contracts and Incentives 448

15.1 The Organization of Production 448

15.2 Principal-Agent Models 449

Comparative Statics 452

Multitask Agency 454

15.3 Performance Measurement 457

Choosing the Performance Measure 460

15.4 Costly Monitoring and Efficiency Wages 461

15.5 Team Production 463

15.6 Incomplete Contracts 466

Factors Affecting Ownership Structure 469

Problems 471

Selected References 471

16 Markets with Imperfect Information 473

16.1 The Value of Information in Decision Making 473

16.2 Search 474

Sequential Search 476

Equilibrium Price Dispersion 478

16.3 Adverse Selection 482

Favorable Selection 485

16.4 Signaling 487

A More General Analysis 490

16.5 Monopolistic Screening 491

Problems 496

Selected References 497

17 General Equilibrium Ⅰ：Linear Models 498

17.1 Introduction：Fixed-Coefficient Technology 498

17.2 The Linear Activity Analysis Model：A Specific Example 507

17.3 The Rybczynski Theorem 513

17.4 The Stolper-Samuelson Theorem 515

17.5 The Dual Problem 517

17.6 The Simplex Algorithm 526

Mathematical Prerequisites 526

The Simplex Algorithm：Example 530

Problems 534

Bibliography 536

18 General Equilibrium Ⅱ：Nonlinear Models 537

18.1 Tangency Conditions 537

18.2 General Comparative Statics Results 545

18.3 The Factor Price Equalization and Related Theorems 550

The Four-Equation Model 556

The Factor Price Equalization Theorem 558

The Stolper-Samuelson Theorems 559

The Rybczynski Theorem 566

18.4 Applications of the Two-Good，Two-Factor Model 568

18.5 Summary and Conclusions 572

Problems 574

Bibliography 576

19 Welfare Economics 577

19.1 Social Welfare Functions 577

19.2 The Pareto Conditions 581

Pure Exchange 581

Production 584

19.3 The Classical “Theorems” of Welfare Economics 591

19.4 A “Nontheorem” About Taxation 594

19.5 The Theory of the Second Best 595

19.6 Public Goods 597

19.7 Consumer’s Surplus as a Measure of Welfare Gains and Losses 600

19.8 Property Rights and Transactions Costs 604

The Coase Theorem 608

The Theory of Share Tenancy：An Application of the Coase Theorem 611

Problems 615

Bibliography 616

20 Resource Allocation over Time：Optimal Control Theory 617

20.1 The Meaning of Dynamics 617

Brief History 621

20.2 Solution to the Problem 621

The Calculus of Variations 627

Endpoint（Transversality）Conditions 629

Autonomous Problems 630

Sufficient Conditions 632

20.3 Solutions to Differential Equations 633

Simultaneous Differential Equations 636

20.4 Interpretations and Solutions 637

Intertemporal Choice 637

Harvesting a Renewable Resource 640

Capital Utilization 644

Problems 649

Selected References 650

Hints and Answers 652

Index 661