On the Transition from Instantaneous to Time-Lagged Capital Accumilation: The Case of Leontief Type Production Functions - Ralph Winkler; Ulrich Brandt-Pollmann; Ulf Moslener; Johannes Schlöder (Zentrum für Europäische Wirtschaftsforschung (ZEW), 2005)
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: E32; C61; C63; 330; cyclical optimal paths; numerical optimization; time-lagged optimal control; time-to-build; Investition; Kontrolltheorie; Lag-Modell; Input-Output; Konjunkturtheorie; Theorie