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Foundations of Dynamic Economic Analysis : Optimal Control Theory and Applications - Michael R. Caputo

Foundations of Dynamic Economic Analysis

Optimal Control Theory and Applications

Hardcover

Published: 10th January 2005
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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.

"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

Forewordp. vii
Prefacep. ix
Essential Elements of Continuous Time Dynamic Optimizationp. 1
Necessary Conditions for a Simplified Control Problemp. 24
Concavity and Sufficiency in Optimal Control Problemsp. 52
The Maximum Principle and Economic Interpretationsp. 77
Linear Optimal Control Problemsp. 122
Necessary and Sufficient Conditions for a General Class of Control Problemsp. 149
Necessary and Sufficient Conditions for Isoperimetric Problemsp. 174
Economic Characterization of Reciprocal Isoperimetric Problemsp. 211
The Dynamic Envelope Theorem and Economic Interpretationsp. 231
The Dynamic Envelope Theorem and Transversality Conditionsp. 261
Comparative Dynamics via Envelope Methodsp. 287
Discounting, Current Values, and Time Consistencyp. 312
Local Stability and Phase Portraits of Autonomous Differential Equationsp. 337
Necessary and Sufficient Conditions for Infinite Horizon Control Problemsp. 381
The Neoclassical Optimal Economic Growth Modelp. 412
A Dynamic Limit Pricing Model of the Firmp. 437
The Adjustment Cost Model of the Firmp. 460
Qualitative Properties of Infinite Horizon Optimal Control Problems with One State Variable and One Control Variablep. 481
Dynamic Programming and the Hamilton-Jacobi-Bellman Equationp. 511
Intertemporal Duality in the Adjustment Cost Model of the Firmp. 537
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780521842723
ISBN-10: 0521842727
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 592
Published: 10th January 2005
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 23.5 x 15.88  x 3.81
Weight (kg): 0.95