On the Transition from Instantaneous to Time-Lagged Capital Accumilation

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 beween investment and capital accumulation, the more likely and more pronounced becomes cyclical behavior of the optimal paths.

Ulf Moslener und Johannes Schlöder (2005), On the Transition from Instantaneous to Time-Lagged Capital Accumilation, ZEW Discussion Paper Nr. 05-30, Mannheim.