Capital Theory Equilibrum Analysis and

In Capital Theory and Equilibrium Analysis and Recursive Utility, Robert Becker and John Boyd have synthesized their previously unpublished work on recursive models.

Robert Becker is the author of Capital Theory Equilibrum Analysis and Recursive Utility, published by Wiley. John Boyd is the author of Capital Theory Equilibrum Analysis and Recursive Utility, published by Wiley.

List of Examples

xi

(4)

Preface

xv

1 The Recursive Utility Approach

1

(28)

1.1 Introduction

1

(1)

1.2 What Is a Recursive Utility Function?

2

(7)

1.3 Why Study Recursive Utility?

9

(9)

1.3.1 The Long-Run Incidence of Capital Taxation

9

(7)

The Tax Model

9

(3)

Tax Incidence with TAS Utility

12

(1)

Tax Incidence with Epstein-Hynes Utility

13

(3)

1.3.2 The Impatience Problem

16

(2)

The Impatience Problem with Epstein-Hynes Utility

18

(1)

1.4 Recursive Utility and Commodity Spaces

18

(9)

1.4.1 Diminishing Returns and Bounded Growth

19

(2)

1.4.2 Non-Decreasing Returns and Sustained Growth

21

(4)

Growth and Exogenous Technical Progress

21

(1)

Endogenous Growth Models

22

(3)

1.4.3 Order Structures

25

(2)

Weak Separability of the Future from the Present

25

(1)

Partial Orders on the Commodity Space

26

(1)

1.5 Conclusion

27

(2)

2 Commodity and Price Spaces

29

(34)

2.1 Introduction

29

(1)

2.2 Commodity Spaces

29

(20)

2.2.1 Order Properties Free Disposal

32

(1)

2.2.2 Topological Properties

33

(9)

Metric Spaces

35

(3)

Continuity

38

(1)

Compactness and Product Spaces

39

(2)

Connectedness

41

(1)

2.2.3 Linear Topologies

42

(7)

Order Convergence

44

(2)

Semicontinuity

46

(1)

Contraction Mapping Theorems

47

(2)

2.3 Commodity Price Dualities

49

(13)

2.3.1 Duals and Hyperplanes

52

(1)

2.3.2 Hahn-Banach Theorems

53

(2)

2.3.3 Dual Pairs and Weak Topologies

55

(3)

2.3.4 Order Duals

58

(2)

2.3.5 The Dual of XXX

60

(2)

2.4 Conclusion

62

(1)

3 Representation of Recursive Preferences

63

(47)

3.1 Introduction

63

(1)

3.2 Preference Orders and Utility Theory

64

(7)

3.3 Recursive Utility: the Koopmans Axioms

71

(13)

3.3.1 The Axioms

72

(3)

3.3.2 Biconvergence

75

(3)

3.3.3 Recursive Preferences and Additivity

78

(6)

3.4 Impatience, Discounting, and Myopia

84

(12)

3.4.1 Impatience and Time Perspective

85

(1)

3.4.2 Myopia and the Continuity Axiom

86

(6)

3.4.3 The Norm of Marginal Impatience Conditions

92

(4)

3.5 Recursive Utility: the Aggregator

96

(12)

3.5.1 Basic Properties of the Aggregator

97

(3)

3.5.2 The Existence of Recursive Utility

100

(1)

3.5.3 Aggregators Bounded from Below

101

(2)

3.5.4 Unbounded Aggregators

103

(5)

3.6 Conclusion

108

(2)

4 Existence and Characterization of Optimal Paths

110

(45)

4.1 Introduction

110

(2)

4.2 Fundamentals of Existence Theory

112

(9)

4.2.1 A Simple Capital Accumulation Model

112

(2)

4.2.2 The Weierstrass Theorem

114

(1)

4.2.3 One-Sector TAS Existence Theory

115

(3)

4.2.4 Extended Utilitarianism

118

(3)

4.3 Multisector Capital Accumulation Models

121

(7)

4.3.1 The von Neumann and Malinvaud Models

123

(4)

4.3.2 The Feasible Correspondence

127

(1)

4.4 The Existence and Sensitivity of Optimal Paths

128

(7)

4.4.1 The Maximum Theorem

129

(1)

4.4.2 Optimal Paths

130

(5)

4.5 Recursive Dynamic Programming

135

(8)

4.5.1 Dynamic Programming with TAS Utility

135

(3)

4.5.2 Recursive Utility and Multisector Models

138

(3)

4.5.3 Dynamic Programming and Extended Utilitarianism

141

(2)

4.6 Characterization of Optimal Paths

143

(11)

4.6.1 No-Arbitrage Conditions

143

(6)

4.6.2 Complete Characterization of Optimal Paths

149

(5)

4.7 Conclusion

154

(1)

5 Statics and Dynamics of Optimal Paths

155

(58)

5.1 Introduction

155

(2)

5.2 One-Sector Models

157

(16)

5.2.1 The Inada Conditions

157

(2)

5.2.2 Stationary States in One-Sector Models

159

(3)

5.2.3 Monotonicity and Turnpikes in TAS Models

162

(5)

Differential Approach

163

(1)

Nonclassical Models

164

(3)

5.2.4 Monotonicity and Turnpikes in Recursive Models

167

(3)

5.2.5 Growing Economies

170

(3)

5.3 Steady States in Multisectoral Models

173

(13)

5.3.1 Stationary Optimal Programs for Additive Utility

173

(3)

5.3.2 Stationary Optimal Programs for Recursive Utility

176

(10)

5.4 Stability of Multisectoral Models

186

(16)

5.4.1 The Undiscounted Model

186

(4)

5.4.2 The Visit Lemma

190

(1)

5.4.3 Uniqueness of Steady States

191

(3)

5.4.4 Local Analysis of Steady States

194

(4)

5.4.5 Local and Global Stability

198

(4)

5.5 Cycles and Chaos in Optimal Growth

202

(9)

5.5.1 The Existence of Cycles

203

(5)

5.5.2 Chaotic Dynamics

208

(3)

5.6 Conclusion

211

(2)

6 Equivalence Principles and Dynamic Equilibria

213

(29)

6.1 Introduction

213

(3)

6.2 Equivalence Principles for One-Sector Models

216

(12)

6.2.1 The Perfect Foresight Equivalence Theorem

217

(3)

Perfect Foresight Competitive Equilibrium

217

(2)

The PFCE Equivalence Principle

219

(1)

6.2.2 The Fisher Equivalence Theorem

220

(2)

6.2.3 The Equivalence Theorem and Transversality

222

(3)

6.2.4 Recursive Competitive Equilibrium and Equivalence

225

(3)

6.3 Multisector Equivalence Principles

228

(9)

6.3.1 The Portfolio Equilibrium Condition

228

(1)

6.3.2 The Two-Sector Equivalence Theorem

229

(7)

The Household Sector

230

(1)

The Production Sector

231

(1)

The Transformation Function

232

(1)

Perfect Foresight Equilibrium

233

(1)

The Optimal Growth Problem

234

(1)

The Equivalence Theorem

235

(1)

6.3.3 Dynamics and the Two-Sector Equivalence Theorem

236

(1)

6.4 Transversality and the Hahn problem

237

(4)

6.5 Transversality and Decentralization

241

(1)

7 Comparative Dynamics

242

(43)

7.1 Introduction

242

(4)

7.2 The Reduced-Form TAS Model

246

(14)

7.2.1 Comparative Dynamics for Monotonic Programs

247

(7)

7.2.2 Comparative Dynamics for Oscillating Programs

254

(3)

7.2.3 Comparative Dynamics and Capital Income Tax Reform

257

(3)

7.3 A Primer of Lattice Programming

260

(11)

7.3.1 More about Lattices

261

(3)

7.3.2 An Introduction to Monotone Comparative Statics

264

(2)

7.3.3 Topkis's Theorems

266

(5)

7.4 Lattice Programming and the TAS Model

271

(6)

7.4.1 Monotonicity of Optimal Capital Policy Functions

272

(2)

7.4.2 The Capital Deepening Theorem

274

(3)

7.5 Recursive Utility Models

277

(7)

7.5.1 Recursive Utility, Monotonicity, and Lattice Programming

277

(1)

7.5.2 Increasing Impatience and Recursive Utility

277

(2)

7.5.3 Capital Deepening and Recursive Utility

279

(5)

7.6 Conclusion

284

(1)

8 Dynamic Competitive Equilibrium

285

(31)

8.1 Introduction

285

(1)

8.2 Dynamic Economies

286

(12)

8.2.1 Infinite Horizon Economies

288

(9)

8.2.2 Existence of Pareto Optima

297

(1)

8.3 The Core and Edgeworth Equilibria

298

(3)

8.3.1 Existence of Core Allocations

298

(1)

8.3.2 Replicas and Edgeworth Equilibria

299

(2)

8.4 The Core and Competitive Equilibrium

301

(10)

8.4.1 Core Equivalence

301

(7)

8.4.2 The Welfare Theorems

308

(1)

8.4.3 Representation of Equilibrium as Welfare Maximum

309

(2)

8.5 Models with Very Heterogeneous Discounting

311

(4)

8.6 Conclusion

315

(1)

References

316

(18)

Index

334

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Capital Theory Equilibrum Analysis and Recursive Utility

Summary

Author Biography

Table of Contents

Supplemental Materials