Cover: Recursive Methods in Economic Dynamics in HARDCOVER

Recursive Methods in Economic Dynamics

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HARDCOVER

$104.50 • £83.95 • €94.00

ISBN 9780674750968

Publication Date: 10/10/1989

Short

608 pages

6-1/8 x 9-1/4 inches

27 line illustrations

World

  • 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
  • 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
    • 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 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
  • References
  • Index of Theorems
  • General Index

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