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
Problems250
Bibliography250
10 The Derivation of Consumer Demand Functions '
252
1.41 Introductory Remarks: The Behavioral Postulates
252
1.42 Utility Maximization
261
Interpretation of the Lagrange Multiplier
266
Roy's Identity
268
1.43 The Relationship Between the Utility Maximization Model and
the Cost
Minimization Model
272
1.44 The Comparative Statics of the Utility Maximization Model;
the Traditional
Derivation of the Slutsky Equation
276
1.45 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
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
Problems310
Selected References313
11 Special Topics in Consumer Theory
1.46 Revealed Preference and Exchange
1.47 The Strong Axiom of Revealed Preference and Integrability
Integrability
325
11.3 The Composite Commodity Theorem
Shipping the Good Apples Out
335
11.4 Household Production Functions
Comparative Statics
345
11.5 Consumer's Surplus
Example
354
Empirical Approximations
355
11.6 Empirical Estimation and Functional Forms
Linear Expenditure System
357
CES Utility Function
359
Indirect Addilog Utility Function
360
Translog Specifications361
Almost Ideal Demand System 362
Problems363
References on Theory366
References on Functional Forms 366
12 Intertemporal Choice368
12.1 n-Period Utility Maximization368
Time Preference371
Fisherian Investment378
The Fisher Separation Theorem 380
Real Versus Nominal Interest Rates 382
1.48 The Determination of the Interest Rate 384
1.49 Stocks and Flows387
Problems391
Selected References392
13 Behavior Under Uncertainty394
13.1 Uncertainty and Probability394
Random Variables and Probability Distributions 395
Mean and Variance396
13.2 Specification of Preferences399
State Preference Approach399
The Expected Utility Hypothesis 400
Cardinal and Ordinal Utility 401
13.3 Risk Aversion403
Measures of Risk Aversion405
Mean-Variance Utility Function 406
Gambling, Insurance, and Diversification 409
13.4 Comparative Statics411
Allocation of Wealth to Risky Assets 411
Output Decisions Under Price Uncertainty 412
Increases in Riskiness413
Problems416
Selected References416
14 Maximization with Inequality and
Nonnegativity Constraints418
14.1 Nonnegativity418
Functions of Two or More Variables 423
1.50 Inequality Constraints427
1.51 The Saddle Point Theorem 432
1.52 Nonlinear Programming437
1.53 An "Adding-Up" Theorem 440
Problems442
Appendix443
Bibliography446
15 Contracts and Incentives448
1.54 The Organization of Production448
1.55 Principal-Agent Models449
Comparative Statics452
Multitask Agency454
15.3 Performance Measurement457
Choosing the Performance Measure 460
1.56 Costly Monitoring and Efficiency Wages 461
1.57 Team Production463
1.58 Incomplete Contracts466
Factors Affecting Ownership Structure 469
Problems471
Selected References471
16 Markets with Imperfect Information 473
1.59 The Value of Information in Decision Making 473
1.60 Search474
Sequential Search476
Equilibrium Price Dispersion 478
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 Models 498
1.61 Introduction: Fixed-Coefficient Technology 498
1.62 The Linear Activity Analysis Model: A Specific Example 507
1.63 The Rybczynski Theorem 513
1.64 The Stolper-Samuelson Theorem 515
1.65 The Dual Problem 517
1.66 The Simplex Algorithm 526
Mathematical Prerequisites526
The Simplex Algorithm: Example 530
Problems534
Bibliography536
18 General Equilibrium II: Nonlinear Models 537
1.67 Tangency Conditions537
1.68 General Comparative Statics Results 545
1.69 The Factor Price Equalization and Related Theorems 550
The Four-Equation Model556
The Factor Price Equalization Theorem 558
The Stolper-Samuelson Theorems 559
The Rybczynski Theorem 566
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