Book contents
- Frontmatter
- Contents
- Foreword by Eugene Silberberg
- Preface
- 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
- Index
- References
9 - The Dynamic Envelope Theorem and Economic Interpretations
Published online by Cambridge University Press: 05 June 2012
Book contents
- Frontmatter
- Contents
- Foreword by Eugene Silberberg
- Preface
- 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
- Index
- References
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- Foundations of Dynamic Economic AnalysisOptimal Control Theory and Applications, pp. 231 - 260Publisher: Cambridge University PressPrint publication year: 2005
References
(1990a), “Comparative Dynamics via Envelope Methods in Variational Calculus,” Review of Economics Studies, 57, 689–697CrossRefGoogle Scholar
(1990b), “How to Do Comparative Dynamics on the Back of an Envelope in Optimal Control Theory,” Journal of Economic Dynamics and Control, 14, 655–683CrossRefGoogle Scholar
Eisner, R. and Strotz, R. H. (1963), “Determinants of Business Investment,” Research Study Two in Impacts of Monetary Policy (Englewood Cliffs, N. J.: Prentice-Hall)
Kamien, M. I. and Schwartz, N. L. (1991, 2nd Ed.), Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management (New York: Elsevier Science Publishing Co., Inc.)
and (1991), “The Envelope Theorem in Dynamic Optimization,” Journal of Economic Dynamics and Control, 15, 355–385CrossRefGoogle Scholar
(1987), “Costate Variables Correctly Value Stocks at Each Instant: A Proof,” Journal of Economic Dynamics and Control, 11, 117–122CrossRefGoogle Scholar
(1982), “Differentiability Properties of the Optimal Value Function in Control Theory,” Journal of Economic Dynamics and Control, 4, 303–310CrossRefGoogle Scholar
Seierstad, A. and Sydsæter, K. (1987), Optimal Control Theory with Economic Applications (New York: Elsevier Science Publishing Co., Inc.)
(1974), “A Revision of Comparative Statics Methodology in Economics, or, How to Do Comparative Statics on the Back of an Envelope,” Journal of Economic Theory, 7, 159–172CrossRefGoogle Scholar
Silberberg, E. and Suen, W. (2001, 3rd Ed.), The Structure of Economics: A Mathematical Analysis (New York: Irwin McGraw-Hill)
(1970), “Adjustment Costs and Variable Inputs in the Theory of the Competitive Firm,” Journal of Economic Theory, 2, 329–347CrossRefGoogle Scholar