the structure of economics a mathematical analysis third edition2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1 Comparative Statics and the Paradigm of Economics1

1.1 Introduction1

1.2 The Marginalist Paradigm3

1.3 Theories and Refutable Propositions9

The Structure of Theories10

Refutable Propositions12

1.4 Theories Versus Models； Comparative Statics14

1.5 Examples of Comparative Statics16

Problems23

Selected References24

Bibliography24

2 Review of Calculus （One Variable）25

2.1 Functions， Slopes， and Elasticity25

2.2 Maxima and Minima27

2.3 Continuous Compounding28

2.4 The Mean Value Theorem31

2.5 Taylor’s Series32

Applications of Taylor’s Series： Derivation of the First- and Second- Order Conditions for a Maximum； Concavity and Convexity34

3 Functions of Several Variables37

3.1 Functions of Several Variables37

3.2 Level Curves： I37

3.3 Partial Derivatives39

3.4 The Chain Rule45

Second Derivatives by the Chain Rule47

3.5 Level Curves： Ⅱ49

Convexity of the Level Curves51

Monotonic Transformations and Diminishing Marginal Utility53

Problems55

3.6 Homogeneous Functions and Euler’s Theorem56

Problems65

Selected References65

4 Profit Maximization66

4.1 Unconstrained Maxima and Minima： First-Order Necessary Conditions66

4.2 Sufficient Conditions for Maxima and Minima： Two Variables68

Problems72

4.3 An Extended Footnote73

4.4 An Application of Maximizing Behavior： The Profit-Maximizing Firm74

The Supply Function81

4.5 Homogeneity of the Demand and Supply Functions； Elasticities82

Elasticities83

4.6 The Long Run and the Short Run： An Example of the Le Chatelier Principle84

A More Fundamental Look at the Le Chatelier Principle86

Problems87

4.7 Analysis of Finite Changes： A Digression91

Appendix92

Taylor Series for Functions of Several Variables92

Concavity and the Maximum Conditions93

Selected References95

5 Matrices and Determinants96

5.1 Matrices96

5.2 Determinants， Cramer’s Rule98

5.3 The Implicit Function Theorem105

Problems109

Appendix110

Simple Matrix Operations110

The Rank of a Matrix112

The Inverse of a Matrix113

Orthogonality115

Problems116

Selected References116

6 Comparative Statics： The Traditional Methodology117

6.1 Introduction； Profit Maximization Once More117

6.2 Generalization to n Variables121

First-Order Necessary Conditions121

Second-Order Sufficient Conditions121

Profit Maximization： n Factors124

6.3 The Theory of Constrained Maxima and Minima： First-Order Necessary Conditions128

6.4 Constrained Maximization with More than One Constraint： A Digression132

6.5 Second-Order Conditions134

The Geometry of Constrained Maximization138

6.6 General Methodology141

Problems148

Selected References150

7 The Envelope Theorem and Duality151

7.1 History of the Problem151

7.2 The Profit Function152

7.3 General Comparative Statics Analysis： Unconstrained Models156

7.4 Models with Constraints159

Comparative Statics： Primal-Dual Analysis161

An Important Special Case165

Interpretation of the Lagrange Multiplier166

Le Chatelier Effects169

Problems172

Bibliography174

8 The Derivation of Cost Functions175

8.1 The Cost Function175

8.2 Marginal Cost179

8.3 Average Cost180

8.4 A General Relationship Between Average and Marginal Costs181

8.5 The Cost Minimization Problem183

8.6 The Factor Demand Curves189

Interpretation of the Lagrange Multiplier189

8.7 Comparative Statics Relations： The Traditional Methodology193

8.8 Comparative Statics Relations Using Duality Theory202

Reciprocity Conditions202

Cost Curves in the Short and Long Run205

Factor Demands in the Short and Long Run207

Relation to Profit Maximization209

8.9 Elasticities； Further Properties of the Factor Demand Curves211

Homogeneity212

Output Elasticities216

8.10 The Average Cost Curve216

8.11 Analysis of Firms in Long-Run Competitive Equilibrium218

Analysis of Factor Demands in the Long Run220

Problems222

Selected References224

9 Cost and Production Functions： Special Topics225

9.1 Homogeneous and Homothetic Production Functions225

9.2 The Cost Function： Further Properties228

Homothetic Functions232

9.3 The Duality of Cost and Production Functions234

The Importance of Duality237

9.4 Elasticity of Substitution； the Constant-Elasticity-of-Substitution （CES） Production Function238

Generalizations to n Factors248

The Generalized Leontief Cost Function249

Problems250

Bibliography250

10 The Derivation of Consumer Demand Functions252

10.1 Introductory Remarks： The Behavioral Postulates252

10.2 Utility Maximization261

Interpretation of the Lagrange Multiplier266

Roy’s Identity268

10.3 The Relationship Between the Utility Maximization Model and the Cost Minimization Model272

10.4 The Comparative Statics of the Utility Maximization Model； the Traditional Derivation of the Slutsky Equation276

10.5 The Modern Derivation of the Slutsky Equation282

Conditional Demands286

The Addition of a New Commodity288

10.6 Elasticity Formulas for Money-Income-Held-Constant and Real-Income-Held-Constant Demand Curves291

The Slutsky Equation in Elasticity Form291

Compensated Demand Curves294

10.7 Special Topics297

Separable Utility Functions297

The Labor-Leisure Choice299

Slutsky Versus Hicks Compensations304

The Division of Labor Is Limited by the Extent of the Market306

Problems310

Selected References313

11 Special Topics in Consumer Theory314

11.1 Revealed Preference and Exchange314

11.2 The Strong Axiom of Revealed Preference and Integrabity322

Integrability325

11.3 The Composite Commodity Theorem332

Shipping the Good Apples Out335

11.4 Household Production Functions341

Comparative Statics345

11.5 Consumer’s Surplus347

Example354

Empirical Approximations355

11.6 Empirical Estimation and Functional Forms357

Linear Expenditure System357

CES Utility Function359

Indirect Addilog Utility Function360

Translog Specifications361

Almost Ideal Demand System362

Problems363

References on Theory366

References on Functional Forms366

12 Intertemporal Choice368

12.1 n-Period Utility Maximization368

Time Preference371

Fisherian Investment378

The Fisher Separation Theorem380

Real Versus Nominal Interest Rates382

12.2 The Determination of the Interest Rate384

12.3 Stocks and Flows387

Problems391

Selected References392

13 Behavior Under Uncertainty394

13.1 Uncertainty and Probability394

Random Variables and Probability Distributions395

Mean and Variance396

13.2 Specification of Preferences399

State Preference Approach399

The Expected Utility Hypothesis400

Cardinal and Ordinal Utility401

13.3 Risk Aversion403

Measures of Risk Aversion405

Mean-Variance Utility Function406

Gambling， Insurance， and Diversification409

13.4 Comparative Statics411

Allocation of Wealth to Risky Assets411

Output Decisions Under Price Uncertainty412

Increases in Riskiness413

Problems416

Selected References416

14 Maximization with Inequality and Nonnegativity Constraints418

14.1 Nonnegativity418

Functions of Two or More Variables423

14.2 Inequality Constraints427

14.3 The Saddle Point Theorem432

14.4 Nonlinear Programming437

14.5 An “Adding-Up” Theorem440

Problems442

Appendix443

Bibliography446

15 Contracts and Incentives448

15.1 The Organization of Production448

15.2 Principal-Agent Models449

Comparative Statics452

Multitask Agency454

15.3 Performance Measurement457

Choosing the Performance Measure460

15.4 Costly Monitoring and Efficiency Wages461

15.5 Team Production463

15.6 Incomplete Contracts466

Factors Affecting Ownership Structure469

Problems471

Selected References471

16 Markets with Imperfect Information473

16.1 The Value of Information in Decision Making473

16.2 Search474

Sequential Search476

Equilibrium Price Dispersion478

16.3 Adverse Selection482

Favorable Selection485

16.4 Signaling487

A More General Analysis490

16.5 Monopolistic Screening491

Problems496

Selected References497

17 General Equilibrium Ⅰ： Linear Models498

17.1 Introduction： Fixed-Coefficient Technology498

17.2 The Linear Activity Analysis Model： A Specific Example507

17.3 The Rybczynski Theorem513

17.4 The Stolper-Samuelson Theorem515

17.5 The Dual Problem517

17.6 The Simplex Algorithm526

Mathematical Prerequisites526

The Simplex Algorithm： Example530

Problems534

Bibliography536

18 General Equilibrium Ⅱ： Nonlinear Models537

18.1 Tangency Conditions537

18.2 General Comparative Statics Results545

18.3 The Factor Price Equalization and Related Theorems550

The Four-Equation Model556

The Factor Price Equalization Theorem558

The Stolper-Samuelson Theorems559

The Rybczynski Theorem566

18.4 Applications of the Two-Good， Two-Factor Model568

18.5 Summary and Conclusions572

Problems574

Bibliography576

19 Welfare Economics577

19.1 Social Welfare Functions577

19.2 The Pareto Conditions581

Pure Exchange581

Production584

19.3 The Classical “Theorems” of Welfare Economics591

19.4 A “Nontheorem” About Taxation594

19.5 The Theory of the Second Best595

19.6 Public Goods597

19.7 Consumer’s Surplus as a Measure of Welfare Gains and Losses600

19.8 Property Rights and Transactions Costs604

The Coase Theorem608

The Theory of Share Tenancy： An Application of the Coase Theorem611

Problems615

Bibliography616

20 Resource Allocation over Time： Optimal Control Theory617

20.1 The Meaning of Dynamics617

Brief History621

20.2 Solution to the Problem621

The Calculus of Variations627

Endpoint （Transversality） Conditions629

Autonomous Problems630

Sufficient Conditions632

20.3 Solutions to Di633

erential Equations633

Simultaneous Differential Equations636

20.4 Interpretations and Solutions637

Intertemporal Choice637

Harvesting a Renewable Resource640

Capital Utilization644

Problems649

Selected References650

Hints and Answers652

Index661