Recursive Methods in Economic Dynamics » (1st Edition)

Robert E. Lucas, Jr., is the John Dewey Distinguished Service Professor of Economics at the University of Chicago. In 1995, he was awarded the Nobel Prize in Economics.

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.

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: LiapounovFunctions


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