Optimal pollution control with distributed delays

We present a model of optimal stock pollution control with distributed delays in the stock accumulation dynamics. Using generic functional forms and a distribution structure that covers a wide range of distributions, we solve analytically the complex dynamic system that arises from the introduction of these distributed delays. Our contribution extends the dynamic optimization literature that focused on the single discrete delay case and develops an original method to address control problems with mixed type functional differential equations. Our results show the qualitative impact of acknowledging these distributed delays on the optimal pollution paths dynamics and identify the occurrence of limit cycles and the stability conditions of such a model that can be used to design efficient environmental policies.