Optimizing Environmental Taxation on Physical Capital for a Spatially Structured Economic Growth Model Including Pollution Diffusion

We present a spatially structured dynamic economic growth model which takes into account the level of pollution induced by production, and a possible taxation based on the amount of produced pollution. Then we analyze an optimal harvesting control problem with an objective function composed of three terms, namely the intertemporal utility of the decision maker, the space-time average of the level of pollution in the habitat, and the disutility due to the imposition of taxation. With respect to our previous works, in this paper, the system is subject to two controls, namely the level of consumption and, in addition, the taxation on physical capital rate. The optimal controls are determined by means of a sweep-type numerical algorithm that allows to solve a system of four backward-forward reaction-diffusion equations.