Time-lagged accumulation of stock pollutants

In this paper I study the optimal control path for a (capital or pollution) stock which accumulates time with a lag to its control. It is shown that the optimal control path is non-monotonic and cyclical in general, but it is monotonic if the objective function is additively separable in the control and the stock variables. On the one hand, this result generalizes the existing time-to-build literature, where time lagged capital accumulation is supposed to be sufficient for cyclical optimal paths. On the other hand, this result challenges the use of additively separable welfare functions as a good approximation to the "real world" in environmental economic problems and raises questions about the design of optimal environmental policies.