Foundations of Dynamic Economic Analysis: Optimal Control Theory and Applications

ISBN-13: 9780521842723 / Angielski / Twarda / 2005 / 592 str.

Michael Ralph Caputo

Opis

Presenting a thorough introductory exposition of optimal control theory, this work differs from the existing textbooks on the subject due to its emphasis on the economic interpretation of the mathematics and the qualitative properties of the solutions. Moreover, it is a modern exposition of optimal control theory in that it presents numerous complementary methods. It is aimed at first-year and second-year PhD students in economics, agricultural and resource economics, operations research, management science, and applied mathematics.

Recenzje

"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

Spis treści

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.