On the Transition from Instantaneous to Time-Lagged Capital Accumulation: The Case of Leontief-Type Production Functions

23 Pages Posted: 18 Jan 2005 Last revised: 30 Jul 2008

Ralph Winkler

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

Ullrich Brandt-Pollmann

University of Heidelberg - Interdisciplinary Institute for Environmental Economics

Ulf Moslener

Frankfurt School of Finance & Management gemeinnützige GmbH

Johannes Schloeder

Interdisciplinary Center for Scientific Computing

Date Written: May 2005

Abstract

We formulate an optimal control capital accumulation model with a Leontief-type production function and an exogenously given time-lag between investment and the accumulation of the capital stock, to analyze the qualitative and quantitative influence of time-lags on the system dynamics. As known from the time-to-build literature, optimal investment paths for positive and finite time-lags are in general cyclical, in contrast to the monotonic optimal paths for instantaneous capital accumulation. We show that the transition between instantaneous and time-lagged capital accumulation is continuous, in the sense that the greater is the time-lag between investment and capital accumulation, the more likely and more pronounced becomes cyclical behavior of the optimal paths.

Keywords: Cyclical optimal paths, numerical optimization, time-lagged optimal control, time-to-build

JEL Classification: E32, C63, C61

Suggested Citation

Winkler, Ralph and Brandt-Pollmann, Ullrich and Moslener, Ulf and Schloeder, Johannes, On the Transition from Instantaneous to Time-Lagged Capital Accumulation: The Case of Leontief-Type Production Functions (May 2005). Zentum Fuer Europaeische Wirtschaftsforschung (ZEW) - Center for European Economic Research Discussion Paper No. 05-30. Available at SSRN: https://ssrn.com/abstract=650169 or http://dx.doi.org/10.2139/ssrn.650169

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

Ullrich Brandt-Pollmann

University of Heidelberg - Interdisciplinary Institute for Environmental Economics ( email )

Grabengasse 1
Heidelberg
Germany

Ulf Moslener

Frankfurt School of Finance & Management gemeinnützige GmbH ( email )

Sonnemannstraße 9-11
Frankfurt am Main, 60314
Germany

Johannes Schloeder

Interdisciplinary Center for Scientific Computing ( email )

Im Neuenheimer Feld 368
Heidelberg, D-69120
Germany

HOME PAGE: http://www.iwr.uni-heidelberg.de/

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