Recursive Methods in Economic Dynamics
By: Nancy L. Stokey and Robert E. Lucas, Jr., with Edward C. Prescott.
Contributors: Lucas, Robert E.; Prescott, Edward C.
Publisher: Harvard University Press
Published: 1989
Place of publication: Cambridge, MA, USA
Language: eng
Format: Hardcover
Number of pages: 588
ISBN-13: 9780674750968
Copyright date: 1989
Subjects: Economics, Mathematical.; Recursive functions.
Description: This rigorous but brilliantly lucid book presents a self-contained treatment of modern economic dynamics. Stokey, Lucas, and Prescott develop the basic methods of recursive analysis and illustrate the many areas where they can usefully be applied.

After presenting an overview of the recursive approach, the authors develop economic applications for deterministic dynamic programming and the stability theory of first-order difference equations. They then treat stochastic dynamic programming and the convergence theory of discrete-time Markov processes, illustrating each with additional economic applications. They also derive a strong law of large numbers for Markov processes. Finally, they present the two fundamental theorems of welfare economics and show how to apply the methods developed earlier to general equilibrium systems.

The authors go on to apply their methods to many areas of economics. Models of firm and industry investment, household consumption behavior, long-run growth, capital accumulation, job search, job matching, inventory behavior, asset pricing, and money demand are among those they use to show how predictions can he made about individual and social behavior. Researchers and graduate students in economic theory will find this book essential.
--back cover
Notes: Bibliography: p. 563-573.
Includes indexes.
Table of contents: title: Preface; title: Symbols Used; title: I. The Recursive Approach; title: 1. Introduction; title: 2. An Overview; title: 2.1 A Deterministic Model of Optimal Growth; title: 2.2 A Stochastic Model of Optimal Growth; title: 2.3 Competitive Equilibrium Growth; title: 2.4 Conclusions and Plans; title: II. Deterministic Models; title: 3. Mathematical Preliminaries; title: 3.1 Metric Spaces and Normed Vector Spaces; title: 3.2 The Contraction Mapping Theorem; title: 3.3 The Theorem of the Maximum; title: 4. Dynamic Programming under Certainty; title: 4.1 The Principle of Optimality; title: 4.2 Bounded Returns; title: 4.3 Constant Returns to Scale; title: 4.4 Unbounded Returns; title: 4.5 Euler Equations; title: 5. Applications of Dynamic Programming under Certainty; title: 5.1 The One-Sector Model of Optimal Growth; title: 5.2 A “Cake-Eating” Problem; title: 5.3 Optimal Growth with Linear Utility; title: 5.4 Growth with Technical Progress; title: 5.5 A Tree-Cutting Problem; title: 5.6 Learning by Doing; title: 5.7 Human Capital Accumulation; title: 5.8 Growth with Human Capital; title: 5.9 Investment with Convex Costs; title: 5.10 Investment with Constant Returns; title: 5.11 Recursive Preferences; title: 5.12 Theory of the Consumer with Recursive Preferences; title: 5.13 A Pareto Problem with Recursive Preferences; title: 5.14 An (s, S) Inventory Problem; title: 5.15 The Inventory Problem in Continuous Time; title: 5.16 A Seller with Unknown Demand; title: 5.17 A Consumption-Savings Problem; title: 6. Deterministic Dynamics; title: 6.1 One-Dimensional Examples; title: 6.2 Global Stability: Liapounov Functions; title: 6.3 Linear Systems and Linear Approximations; title: 6.4 Euler Equations; title: 6.5 Applications; title: III. Stochastic Models; title: 7. Measure Theory and Integration; title: 7.1 Measurable Spaces; title: 7.2 Measures; title: 7.3 Measurable Functions; title: 7.4 Integration; title: 7.5 Product Spaces; title: 7.6 The Monotone Class Lemma; title: 7.7 Conditional Expectation; title: 8. Markov Processes; title: 8.1 Transition Functions; title: 8.2 Probability Measures on Spaces of Sequences; title: 8.3 Iterated Integrals; title: 8.4 Transitions Defined by Stochastic Difference Equations; title: 9. Stochastic Dynamic Programming; title: 9.1 The Principle of Optimality; title: 9.2 Bounded Returns; title: 9.3 Constant Returns to Scale; title: 9.4 Unbounded Returns; title: 9.5 Stochastic Euler Equations; title: 9.6 Policy Functions and Transition Functions; title: 10. Applications of Stochastic Dynamic Programming; title: 10.1 The One-Sector Model of Optimal Growth; title: 10.2 Optimal Growth with Two Capital Goods; title: 10.3 Optimal Growth with Many Goods; title: 10.4 Industry Investment under Uncertainty; title: 10.5 Production and Inventory Accumulation; title: 10.6 Asset Prices in an Exchange Economy; title: 10.7 A Model of Search Unemployment; title: 10.8 The Dynamics of the Search Model; title: 10.9 Variations on the Search Model; title: 10.10 A Model of Job Matching; title: 10.11 Job Matching and Unemployment; title: 11. Strong Convergence of Markov Processes; title: 11.1 Markov Chains; title: 11.2 Convergence Concepts for Measures; title: 11.3 Characterizations of Strong Convergence; title: 11.4 Sufficient Conditions; title: 12. Weak Convergence of Markov Processes; title: 12.1 Characterizations of Weak Convergence; title: 12.2 Distribution Functions; title: 12.3 Weak Convergence of Distribution Functions; title: 12.4 Monotone Markov Processes; title: 12.5 Dependence of the Invariant Measure on a Parameter; title: 12.6 A Loose End; title: 13. Applications of Convergence Results for Markov Processes; title: 13.1 A Discrete-Space (s, S) Inventory Problem; title: 13.2 A Continuous-State (s, S) Process; title: 13.3 The One-Sector Model of Optimal Growth; title: 13.4 Industry Investment under Uncertainty; title: 13.5 Equilibrium in a Pure Currency Economy; title: 13.6 A Pure Currency Economy with Linear Utility; title: 13.7 A Pure Credit Economy with Linear Utility; title: 13.8 An Equilibrium Search Economy; title: 14. Laws of Large Numbers; title: 14.1 Definitions and Preliminaries; title: 14.2 A Strong Law for Markov Processes; title: IV. Competitive Equilibrium; title: 15. Pareto Optima and Competitive Equilibria; title: 15.1 Dual Spaces; title: 15.2 The First and Second Welfare Theorems; title: 15.3 Issues in the Choice of a Commodity Space; title: 15.4 Inner Product Representations of Prices; title: 16. Applications of Equilibrium Theory; title: 16.1 A One-Sector Model of Growth under Certainty; title: 16.2 A Many-Sector Model of Stochastic Growth; title: 16.3 An Economy with Sustained Growth; title: 16.4 Industry Investment under Uncertainty; title: 16.5 Truncation: A Generalization; title: 16.6 A Peculiar Example; title: 16.7 An Economy with Many Consumers; title: 17. Fixed-Point Arguments; title: 17.1 An Overlapping-Generations Model; title: 17.2 An Application of the Contraction Mapping Theorem; title: 17.3 The Brouwer Fixed-Point Theorem; title: 17.4 The Schauder Fixed-Point Theorem; title: 17.5 Fixed Points of Monotone Operators; title: 17.6 Partially Observed Shocks; title: 18. Equilibria in Systems with Distortions; title: 18.1 An Indirect Approach; title: 18.2 A Local Approach Based on First-Order Conditions; title: 18.3 A Global Approach Based on First-Order Conditions; title: References; title: Index of Theorems; title: General Index