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A NOTE ON THE OPTIMAL CONTROL OF STOCKS ACCUMULATING WITH A DELAY

Published online by Cambridge University Press:  13 July 2010

Ralph Winkler
Ralph Winkler*
Affiliation:
University of Bern
*
Address correspondence to: Ralph Winkler, Department of Economics and Oeschger Centre for Climate Change Research, University of Bern, Schanzeneckstrasse 1, CH-3001 Bern, Switzerland; e-mail: mail@ralph-winkler.de.
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Abstract

We study a generic optimal control problem with a stock that accumulates with constant delay. We show that the optimal system dynamics reduces to a system of ordinary differential equations, implying monotonic optimal paths, if the objective function is additively separable in the stock and the control. This is, however, not true for general objective functions, which may exhibit nonmonotonic and oscillatory optimal paths. The reason is that the impact of the stock on the objective depends on the current level of the control, whereas the control influences the dynamics of the stock with a delay.

Keywords

Additively Separable ObjectiveDelayed Optimal ControlDifferential–Difference EquationsTime to Build
Type
Notes
Information
Macroeconomic Dynamics , Volume 15 , Issue 4 , September 2011 , pp. 565 - 578
Copyright
Copyright © Cambridge University Press 2010

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