- Preface
- Symbols Used
- I. The Recursive Approach

- 1. Introduction
- 2. An Overview

- 2.1 A Deterministic Model of Optimal Growth
- 2.2 A Stochastic Model of Optimal Growth
- 2.3 Competitive Equilibrium Growth
- 2.4 Conclusions and Plans

- II. Deterministic Models

- 3. Mathematical Preliminaries

- 3.1 Metric Spaces and Normed Vector Spaces
- 3.2 The Contraction Mapping Theorem
- 3.3 The Theorem of the Maximum

- 4. Dynamic Programming under Certainty

- 4.1 The Principle of Optimality
- 4.2 Bounded Returns
- 4.3 Constant Returns to Scale
- 4.4 Unbounded Returns
- 4.5 Euler Equations

- 5. Applications of Dynamic Programming under Certainty

- 5.1 The One-Sector Model of Optimal Growth
- 5.2 A “Cake-Eating” Problem
- 5.3 Optimal Growth with Linear Utility
- 5.4 Growth with Technical Progress
- 5.5 A Tree-Cutting Problem
- 5.6 Learning by Doing
- 5.7 Human Capital Accumulation
- 5.8 Growth with Human Capital
- 5.9 Investment with Convex Costs
- 5.10 Investment with Constant Returns
- 5.11 Recursive Preferences
- 5.12 Theory of the Consumer with Recursive Preferences
- 5.13 A Pareto Problem with Recursive Preferences
- 5.14 An (
*s*,*S*) Inventory Problem - 5.15 The Inventory Problem in Continuous Time
- 5.16 A Seller with Unknown Demand
- 5.17 A Consumption-Savings Problem

- 6. Deterministic Dynamics

- 6.1 One-Dimensional Examples
- 6.2 Global Stability: Liapounov Functions
- 6.3 Linear Systems and Linear Approximations
- 6.4 Euler Equations
- 6.5 Applications

- 3. Mathematical Preliminaries
- III. Stochastic Models

- 7. Measure Theory and Integration

- 7.1 Measurable Spaces
- 7.2 Measures
- 7.3 Measurable Functions
- 7.4 Integration
- 7.5 Product Spaces
- 7.6 The Monotone Class Lemma
- 7.7 Conditional Expectation

- 8. Markov Processes

- 8.1 Transition Functions
- 8.2 Probability Measures on Spaces of Sequences
- 8.3 Iterated Integrals
- 8.4 Transitions Defined by Stochastic Difference Equations

- 9. Stochastic Dynamic Programming

- 9.1 The Principle of Optimality
- 9.2 Bounded Returns
- 9.3 Constant Returns to Scale
- 9.4 Unbounded Returns
- 9.5 Stochastic Euler Equations
- 9.6 Policy Functions and Transition Functions

- 10. Applications of Stochastic Dynamic Programming

- 10.1 The One-Sector Model of Optimal Growth
- 10.2 Optimal Growth with Two Capital Goods
- 10.3 Optimal Growth with Many Goods
- 10.4 Industry Investment under Uncertainty
- 10.5 Production and Inventory Accumulation
- 10.6 Asset Prices in an Exchange Economy
- 10.7 A Model of Search Unemployment
- 10.8 The Dynamics of the Search Model
- 10.9 Variations on the Search Model
- 10.10 A Model of Job Matching
- 10.11 Job Matching and Unemployment

- 11. Strong Convergence of Markov Processes

- 11.1 Markov Chains
- 11.2 Convergence Concepts for Measures
- 11.3 Characterizations of Strong Convergence
- 11.4 Sufficient Conditions

- 12. Weak Convergence of Markov Processes

- 12.1 Characterizations of Weak Convergence
- 12.2 Distribution Functions
- 12.3 Weak Convergence of Distribution Functions
- 12.4 Monotone Markov Processes
- 12.5 Dependence of the Invariant Measure on a Parameter
- 12.6 A Loose End

- 13. Applications of Convergence Results for Markov Processes

- 13.1 A Discrete-Space (
*s*,*S*) Inventory Problem - 13.2 A Continuous-State (
*s*,*S*) Process - 13.3 The One-Sector Model of Optimal Growth
- 13.4 Industry Investment under Uncertainty
- 13.5 Equilibrium in a Pure Currency Economy
- 13.6 A Pure Currency Economy with Linear Utility
- 13.7 A Pure Credit Economy with Linear Utility
- 13.8 An Equilibrium Search Economy

- 13.1 A Discrete-Space (
- 14. Laws of Large Numbers

- 14.1 Definitions and Preliminaries
- 14.2 A Strong Law for Markov Processes

- 7. Measure Theory and Integration
- IV. Competitive Equilibrium

- 15. Pareto Optima and Competitive Equilibria

- 15.1 Dual Spaces
- 15.2 The First and Second Welfare Theorems
- 15.3 Issues in the Choice of a Commodity Space
- 15.4 Inner Product Representations of Prices

- 16. Applications of Equilibrium Theory

- 16.1 A One-Sector Model of Growth under Certainty
- 16.2 A Many-Sector Model of Stochastic Growth
- 16.3 An Economy with Sustained Growth
- 16.4 Industry Investment under Uncertainty
- 16.5 Truncation: A Generalization
- 16.6 A Peculiar Example
- 16.7 An Economy with Many Consumers

- 17. Fixed-Point Arguments

- 17.1 An Overlapping-Generations Model
- 17.2 An Application of the Contraction Mapping Theorem
- 17.3 The Brouwer Fixed-Point Theorem
- 17.4 The Schauder Fixed-Point Theorem
- 17.5 Fixed Points of Monotone Operators
- 17.6 Partially Observed Shocks

- 18. Equilibria in Systems with Distortions

- 18.1 An Indirect Approach
- 18.2 A Local Approach Based on First-Order Conditions
- 18.3 A Global Approach Based on First-Order Conditions

- 15. Pareto Optima and Competitive Equilibria
- References
- Index of Theorems
- General Index

# Recursive Methods in Economic Dynamics

#### Product Details

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$104.50 • £83.95 • €94.00

ISBN 9780674750968

Publication Date: 10/10/1989