The structure of economics : a mathematical analysis

Başlık:

Yazar:

Silberberg, Eugene.

ISBN:

9780070575509

9780071009300

Ek Yazar:

Silberberg, Eugene.

Edition:

2nd ed.

Yayım Bilgisi:

Fiziksel Tanım:

xvi, 686 pages : illustrations ; 24 cm

Konu Terimleri:

Economics, Mathematical.

Ekonomi, Matemetiksel.

Mevcut:*

Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... İktisadi İdari Bilimler Fakültesi	Kitap	0111899	HB135 .S54 1990	Searching... Unknown

This text combines mathematical economics with microeconomic theory and can be required or recommended as part of a course in graduate microeconomic theory, advanced undergraduate or graduate-level mathematical economics, or any advanced topics course. It also has reference value for international, library, professional and reference markets. This revision addresses significant new topics--the theory of contracts and markets with imperfect information--that have recently become prominent in the microeconomics literature.

Author Notes

Eugene Silberberg is Professor of Economics at the University of Washington in Seattle. He received his B.S. from the City College of New York and his Ph.D. from Purdue. His publications contributed to the development of modern duality theory in economics. He has specialized in teaching the application of these techniques to important economic models.

Preface	p. xv
1 Comparative Statics and the Paradigm of Economics	p. 1
1.1 Introduction	p. 1
1.2 The Marginalist Paradigm	p. 3
1.3 Theories and Refutable Propositions	p. 9
The Structure of Theories	p. 10
Refutable Propositions	p. 12
1.4 Theories versus Models; Comparative Statics	p. 14
1.5 Examples of Comparative Statics	p. 16
Problems	p. 23
Bibliography	p. 25
2 Review of Calculus (One Variable)	p. 26
2.1 Functions, Limits, Continuity	p. 26
Limits, Continuity	p. 28
Problems	p. 30
2.2 Derivatives	p. 31
Differentiation of Polynomials	p. 32
Problems	p. 34
2.3 Differentials	p. 34
Problems	p. 36
2.4 The Chain Rule	p. 36
2.5 The Product and Quotient Rules	p. 38
The Product Rule	p. 38
The Quotient Rule	p. 39
2.6 Implicit Functions	p. 39
2.7 Elasticity	p. 40
2.8 Maxima and Minima	p. 41
Problems	p. 45
2.9 Two Important Functions: y = ex; y = logex	p. 46
1. The Function y = ex	p. 46
2. The Function y = logex	p. 50
Problems	p. 52
2.10 The Mean Value Theorem	p. 53
2.11 Taylor's Series	p. 54
Applications of Taylor's Series: Derivation of the First- and Second-Order Conditions for a Maximum; Concavity and Convexity	p. 56
2.12 Integration	p. 58
Indefinite Integrals	p. 58
The Integral as the Area under a Curve	p. 60
Problems	p. 64
2.13 Differential Equations	p. 65
Problems	p. 67
Selected References	p. 67
3 Functions of Several Variables	p. 68
3.1 Functions of Several Variables	p. 68
3.2 Level Curves: I	p. 69
3.3 Partial Derivatives	p. 70
3.4 The Total Differential of a Function of Several Variables	p. 76
Problems	p. 78
3.5 The Chain Rule	p. 79
Monotonic Transformations	p. 82
Second Derivatives by the Chain Rule	p. 84
3.6 Level Curves: II	p. 86
Convexity of the Level Curves	p. 89
Problems	p. 91
3.7 Homogeneous Functions and Euler's Theorem	p. 92
Problems	p. 101
Appendix	p. 101
Selected References	p. 106
4 Profit Maximization	p. 107
4.1 Unconstrained Maxima and Minima: First-Order Necessary Conditions	p. 107
4.2 Sufficient Conditions for Maxima and Minima: Two Variables	p. 109
Problems	p. 112
4.3 An Extended Footnote	p. 113
4.4 An Application of Maximizing Behavior: The Profit-Maximizing Firm	p. 114
The Supply Function	p. 121
4.5 Homogeneity of the Demand and Supply Functions; Elasticities	p. 122
Elasticities	p. 123
4.6 The Long Run and the Short Run: An Example of the Le Chatelier Principle	p. 124
A More Fundamental Look at the Le Chatelier Principle	p. 126
Problems	p. 128
4.7 Analysis of Finite Changes: A Digression	p. 130
Appendix	p. 131
Taylor Series for Functions of Several Variables	p. 131
Concavity and the Maximum Conditions	p. 132
Selected References	p. 133
5 Matrices and Determinants	p. 135
5.1 Matrices	p. 135
5.2 Determinants, Cramer's Rule	p. 137
5.3 The Implicit Function Theorem	p. 144
Problems	p. 149
Appendix	p. 149
Simple Matrix Operations	p. 149
The Rank of a Matrix	p. 151
The Inverse of a Matrix	p. 153
Orthogonality	p. 154
Problems	p. 155
Selected References	p. 155
6 Comparative Statics: The Traditional Methodology	p. 156
6.1 Introduction; Profit Maximization Once More	p. 156
6.2 Generalizations to n Variables	p. 160
First-Order Necessary Conditions	p. 160
Second-Order Sufficient Conditions	p. 160
Profit Maximization: n Factors	p. 163
6.3 The Theory of Constrained Maxima and Minima: First-Order Necessary Conditions	p. 166
6.4 Constrained Maximization with More than One Constraint: A Digression	p. 171
6.5 Second-Order Conditions	p. 173
The Geometry of Constrained Maximization	p. 176
6.6 General Methodology	p. 180
Problems	p. 187
Selected References	p. 189
7 The Envelope Theorem and Duality	p. 190
7.1 History of the Problem	p. 190
7.2 The Profit Function	p. 192
7.3 General Comparative Statics Analysis: Unconstrained Models	p. 195
7.4 Models with Constraints	p. 198
Comparative Statics: Primal-Dual Analysis	p. 200
An Important Special Case	p. 203
Interpretation of the Lagrange Multiplier	p. 204
Problems	p. 207
7.5 The Comparative Statics of Maximization Systems	p. 210
Reciprocity Relations	p. 214
Qualitative Results	p. 215
Le Chatelier Effects	p. 216
Bibliography	p. 222
8 The Derivation of Cost Functions	p. 223
8.1 The Cost Function	p. 223
8.2 Marginal Cost	p. 226
8.3 Average Cost	p. 227
8.4 A General Relationship between Average and Marginal Costs	p. 229
8.5 The Cost Minimization Problem	p. 230
8.6 The Factor Demand Curves	p. 236
Interpretation of the Lagrange Multiplier	p. 237
8.7 Comparative Statics Relations: The Traditional Methodology	p. 241
8.8 Comparative Statics Relations Using Duality Theory	p. 249
Reciprocity Conditions	p. 250
Cost Curves in the Short and Long Run	p. 252
Factor Demands in the Short and Long Run	p. 254
Relation to Profit Maximization	p. 256
8.9 Elasticities; Further Properties of the Factor-Demand Curves	p. 258
Homogeneity	p. 259
Output Elasticities	p. 262
8.10 The Average Cost Curve	p. 263
8.11 Analysis of Firms in Long-Run Competitive Equilibrium	p. 265
Analysis of Factor Demands in the Long Run	p. 267
Problems	p. 269
Selected References	p. 271
9 Cost and Production Functions: Special Topics	p. 272
9.1 Homogeneous and Homothetic Production Functions	p. 272
9.2 The Cost Function: Further Properties	p. 275
Homothetic Functions	p. 279
9.3 The Duality of Cost and Production Functions	p. 281
The Importance of Duality	p. 285
9.4 Elasticity of Substitution; the Constant-Elasticity-of-Substitution (CES) Production Function	p. 285
Generalization to n Factors	p. 296
The Generalized Leontief Cost Function	p. 297
Problems	p. 297
Bibliography	p. 298
10 The Derivation of Consumer Demand Functions	p. 299
10.1 Introductory Remarks: The Behavioral Postulates	p. 299
10.2 Utility Maximization	p. 308
Interpretation of the Lagrange Multiplier	p. 313
Roy's Identity	p. 315
10.3 The Relationship between the Utility Maximization Model and the Cost Minimization Model	p. 319
10.4 The Comparative Statics of the Utility Maximization Model; the Traditional Derivation of the Slutsky Equation	p. 323
10.5 The Modern Derivation of the Slutsky Equation	p. 329
Conditional Demands	p. 333
The Addition of a New Commodity	p. 335
10.6 Elasticity Formulas for Money-Income-Held-Constant and Real-Income-Held-Constant Demand Curves	p. 338
The Slutsky Equation in Elasticity Form	p. 338
Compensated Demand Curves	p. 341
10.7 Special Topics	p. 344
Separable Utility Functions	p. 344
The Labor-Leisure Choice	p. 346
Slutsky versus Hicks Compensations	p. 351
The Division of Labor Is Limited by the Extent of the Market	p. 353
Problems	p. 357
Selected References	p. 360
11 Special Topics in Consumer Theory	p. 362
11.1 Revealed Preference and Exchange	p. 362
11.2 The Strong Axiom of Revealed Preference and Integrability	p. 370
Integrability	p. 373
11.3 The Composite Commodity Theorem	p. 381
Shipping the Good Apples Out	p. 384
11.4 Household Production Functions	p. 389
Comparative Statics	p. 393
11.5 Consumer's Surplus	p. 396
Example	p. 402
Empirical Approximation	p. 403
11.6 Empirical Estimation and Functional Forms	p. 405
Linear Expenditure System	p. 406
CES Utility Function	p. 407
Indirect Addilog Utility Function	p. 408
Translog Specifications	p. 409
Almost Ideal Demand System	p. 411
Problems	p. 412
References on Theory	p. 414
References on Functional Forms	p. 415
12 Intertemporal Choice	p. 416
12.1 n-Period Utility Maximization	p. 416
Time Preference	p. 419
The Fisher Separation Theorem	p. 426
Real versus Nominal Interest Rates	p. 428
12.2 The Determination of the Interest Rate	p. 430
12.3 Stocks and Flows	p. 433
Problems	p. 437
Selected References	p. 438
13 Behavior under Uncertainty	p. 440
13.1 Uncertainty and Probability	p. 440
Random Variables and Probability Distributions	p. 441
Mean and Variance	p. 442
13.2 Specification of Preferences	p. 445
State Preference Approach	p. 445
The Expected Utility Hypothesis	p. 446
Cardinal and Ordinal Utility	p. 447
13.3 Risk Aversion	p. 449
Measures of Risk Aversion	p. 451
Gambling, Insurance and Diversification	p. 452
Problems	p. 454
13.4 Comparative Statics	p. 455
Allocation of Wealth to Risky Assets	p. 455
Problems	p. 456
Output Decisions under Price Uncertainty	p. 456
Increases in Riskiness	p. 458
References	p. 460
14 Maximization with Inequality and Nonnegativity Constraints	p. 462
14.1 Nonnegativity	p. 462
Functions of Two or More Variables	p. 467
14.2 Inequality Constraints	p. 470
14.3 The Saddlepoint Theorem	p. 476
14.4 Nonlinear Programming	p. 480
14.5 An "Adding-Up" Theorem	p. 483
Problems	p. 485
Appendix	p. 487
Bibliography	p. 490
15 General Equilibrium I: Linear Models	p. 491
15.1 Introduction: Fixed-Coefficient Technology	p. 491
15.2 The Linear Activity Analysis Model: A Specific Example	p. 500
15.3 The Rybczynski Theorem	p. 507
15.4 The Stolper-Samuelson Theorem	p. 509
15.5 The Dual Problem	p. 510
15.6 The Simplex Algorithm	p. 520
Mathematical Prerequisites	p. 520
The Simplex Algorithm: Example	p. 524
Problems	p. 528
Bibliography	p. 530
16 General Equilibrium II: Nonlinear Models	p. 531
16.1 Tangency Conditions	p. 531
16.2 General Comparative Statics Results	p. 539
16.3 The Factor Price Equalization and Related Theorems	p. 544
The Four-Equation Model	p. 550
The Factor Price Equalization Theorem	p. 553
The Stolper-Samuelson Theorems	p. 554
The Rybczynski Theorem	p. 561
16.4 Applications of the Two-Good, Two-Factor Model	p. 563
Summary and Conclusions	p. 567
Problems	p. 570
Bibliography	p. 571
17 Welfare Economics	p. 573
17.1 Social Welfare Functions	p. 573
17.2 The Pareto Conditions	p. 577
Pure Exchange	p. 578
Production	p. 581
17.3 The Classical "Theorems" of Welfare Economics	p. 587
17.4 A "Nontheorem" about Taxation	p. 589
17.5 The Theory of the Second Best	p. 591
17.6 Public Goods	p. 593
17.7 Consumer's Surplus as a Measure of Welfare Gains and Losses	p. 596
17.8 Property Rights and Transactions Costs	p. 600
Private Property	p. 602
Common Property	p. 603
The Coase Theorem	p. 604
The Theory of Share Tenancy: An Application of the Coase Theorem	p. 607
Problems	p. 611
Bibliography	p. 612
18 Resource Allocation over Time: Optimal Control Theory	p. 613
18.1 The Meaning of Dynamics	p. 613
Brief History	p. 617
18.2 Solution to the Problem	p. 617
The Calculus of Variations	p. 622
Endpoint (Transversality) Conditions	p. 624
Autonomous Problems	p. 625
Sufficient Conditions	p. 627
18.3 Solutions to Differential Equations	p. 628
Simultaneous Differential Equations	p. 631
18.4 Interpretations and Solutions	p. 632
Intertemporal Choice	p. 632
Harvesting a Renewable Resource	p. 635
Capital Utilization	p. 639
Problems	p. 644
Selected References	p. 645
19 Equilibrium, Disequilibrium, and the Stability of Markets	p. 647
19.1 Three Sources of Refutable Hypotheses	p. 647
19.2 Equilibrium and Stability	p. 651
Walrasian Stability	p. 652
Marshallian Stability	p. 655
19.3 Multimarket Equilibrium and Stability	p. 656
Open Systems: Stability	p. 657
Closed Economics	p. 661
19.4 Game Theory	p. 662
19.5 Overview and Conclusions	p. 666
Problems	p. 669
Bibliography	p. 669
Hints and Answers	p. 671
Index	p. 681

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