Foundations of Dynamic Economic Analysis
Optimal Control Theory and Applications

Foundations of Dynamic Economic Analysis presents an introductory but thorough exposition of optimal control theory.

Michael R. Caputo (Author)

9780521603683, Cambridge University Press

Paperback, published 17 January 2005

592 pages, 47 b/w illus. 1 table
23.5 x 15.4 x 3.1 cm, 0.811 kg

"Michael Caputo's Foundations of Dynamic Economic Analysis presents a well-written, complete, up to date exposition of the theory and techniques of dynamic optimization applied to a variety of economics problems. Of special interest is the presentation of Caputo's generalization of Silberberg's primal-dual approach to comparative statics and comparative dynamics." -Morton Kamien, Northwestern University

Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.

1. Essential elements of continuous time dynamic optimization
2. Necessary conditions for a simplified control problem
3. Concavity and sufficiency in optimal control problems
4. The maximum principle and economic interpretations
5. Linear optimal control problems
6. Necessary and sufficient conditions for a general class of control problems
7. Necessary and sufficient conditions for isoperimetric problems
8. Economic characterization of reciprocal isoperimetric problems
9. The dynamic envelope theorem and economic interpretations
10. The dynamic envelope theorem and transversality conditions
11. Comparative dynamics via envelope methods
12. Discounting, current values, and time consistency
13. Local stability and phase portraits of autonomous differential equations
14. Necessary and sufficient conditions for infinite horizon control problems
15. The neoclassical optimal economic growth model
16. A dynamic limit pricing model of the firm
17. The adjustment cost model of the firm
18. Qualitative properties of infinite horizon optimal control problems with one state variable and one control variable
19. Dynamic programming and the Hamilton-Jacobi-Bellman equation
20. Intertemporal duality in the adjustment cost model of the firm.

Subject Areas: Economic statistics [KCHS]