Optimal harvesting of a spatially distributed renewable resource with endogenous pricing

In this paper, we focus on the exploitation of a renewable resource in a spatial setting. Building upon the spatial harvesting model of [Behringer and Upmann, J. Econ. Dyn. Control 42 (2014) 105–120], we endogenize the price for the resource assuming that after harvesting the good is non-durable, i.e. the harvesting yield must be supplied on the market instantaneously. We find necessary optimality conditions and use them to derive an iterative algorithm to improve at each step the harvesting effort. We find that with endogenous prices the full exploitation result of [Behringer and Upmann, J. Econ. Dyn. Control 42 (2014) 105–120] may cease to hold.