A Note on the Optimal Control of Stocks Accumulating with a Delay

16 Pages Posted: 27 Jan 2010 Last revised: 31 Aug 2012

Ralph Winkler

University of Bern - Department of Economics; University of Bern - Oeschger Centre for Climate Change Research

Date Written: January 27, 2010

Abstract

We study a generic optimal control problem with a stock that accumulates with a 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 non-monotonic and oscillatory optimal paths. The reason is that the impact of the stock on the objective depends on the current level of the control, while the control influences the dynamcis of the stock with a delay.

Keywords: additively separable objective, delayed optimal control, differential- difference equations, time-to-build

JEL Classification: C60, O40, D90

Suggested Citation

Winkler, Ralph, A Note on the Optimal Control of Stocks Accumulating with a Delay (January 27, 2010). Macroeconomic Dynamics, Vol. 15, No. 4, pp. 565-578, 2011. Available at SSRN: https://ssrn.com/abstract=1543122

Ralph Winkler (Contact Author)

University of Bern - Department of Economics ( email )

Schanzeneckstrasse 1
Bern, 3001
Switzerland
+41 31 631 4508 (Phone)

HOME PAGE: http://www.ralph-winkler.de

University of Bern - Oeschger Centre for Climate Change Research ( email )

Zähringerstrasse 25
Bern, 3012
Switzerland

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