Contents

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 Spaced

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

5.1: The One-Sector Model of Optimal Growth

5.4: Growth with Technical Progress

5.5: A Tree-Cutting Problem

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

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

10.1: The One-Sector Model of Optimal Growth

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 Stong 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 Measures on a Parameter

12.6: A Loose End

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

14. Laws of Large Numbers

14.1: Definitions and Preliminaries

14.2: A Strong Law for Markov Processes

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 Ecomony 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 Indrect Approach

18.2: A Local Approach Based on First-Order Conditions

18.3: A Global Approach Based on First-Order Conditions

References

Index of Theorems

General Index