New Economic Model of Eutrophication of Shallow Lakes and the Existence of Equivalent Policies

Abstract

The search for Skiba points in infinite-time optimal control problems with several steady states is an active research area. In this paper, we apply the backward integration method and show its power and relative simplicity as a tool for this task. We apply the method for the classical model of the economy shallow lake based on the phosphorous dynamics and explicitly compute the optimal trajectories and the Skiba points. We also suggest a more natural welfare function, which takes into account the finite value of any economic resource, and show, again in an explicit manner, that it also possesses Skiba points.