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