Foundations of Dynamic Economic Analysis: Optimal Control Theory and Applications

by Michael R. Caputo

• ISBN13: 9780521603683
• ISBN10: 0521603684
• Format: Paperback
• Copyright: 2005-01-17
• Publisher: Cambridge University Press

Summary

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.

Author Biography

Michael R. Caputo is Professor of Economics in the College of Business Administration, University of Central Florida, in Orlando.

Table of Contents

Foreword by Eugene Silberberg	vii
Preface	ix
1 Essential Elements of Continuous Time Dynamic Optimization	1	(23)
2 Necessary Conditions for a Simplified Control Problem	24	(28)
3 Concavity and Sufficiency in Optimal Control Problems	52	(25)
4 The Maximum Principle and Economic Interpretations	77	(45)
5 Linear Optimal Control Problems	122	(27)
6 Necessary and Sufficient Conditions for a General Class of Control Problems	149	(25)
7 Necessary and Sufficient Conditions for Isoperimetric Problems	174	(37)
8 Economic Characterization of Reciprocal Isoperimetric Problems	211	(20)
9 The Dynamic Envelope Theorem and Economic Interpretations	231	(30)
10 The Dynamic Envelope Theorem and Transversality Conditions	261	(26)
11 Comparative Dynamics via Envelope Methods	287	(25)
12 Discounting, Current Values, and Time Consistency	312	(25)
13 Local Stability and Phase Portraits of Autonomous Differential Equations	337	(44)
14 Necessary and Sufficient Conditions for Infinite Horizon Control Problems	381	(31)
15 The Neoclassical Optimal Economic Growth Model	412	(25)
16 A Dynamic Limit Pricing Model of the Firm	437	(23)
17 The Adjustment Cost Model of the Firm	460	(21)
18 Qualitative Properties of Infinite Horizon Optimal Control Problems with One State Variable and One Control Variable	481	(30)
19 Dynamic Programming and the Hamilton-Jacobi-Bellman Equation	511	(26)
20 Intertemporal Duality in the Adjustment Cost Model of the Firm	537	(30)
Index	567