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.
Winkler, Ralph, Ulrich Brandt-Pollmann, Ulf Moslener und Johannes Schlöder (2005), On the Transition from Instantaneous to Time-Lagged Capital Accumilation, ZEW Discussion Paper No. 05-30, Mannheim. Download