Optimal pollution control with distributed delays

We present a model of optimal stock pollution control with general distributed delays in the stock accumulation dynamics. Using generic functional forms and a distribution structure covering a wide range of distributions, we solve analytically the complex dynamic system that arises from the introduction of these distributed delays. From a theoretical standpoint, our contribution extends the dynamic optimization literature that focused on single discrete delays and develops an original method to address control problems written as mixed type functional differential equations with general kernels. Our results show the qualitative impact of acknowledging these distributed delays on the optimal pollution paths dynamics. We study analytically the properties of the dynamics and we identify the conditions for the occurrence of limit cycles. This theoretical work contributes to the design of efficient environmental policies in the presence of complex delays.

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