Optimal policies aimed at stabilization of populations with logistic growth under human intervention

Abstract

This work examines both positive and negative impacts that economic growth may have on the ecological dynamics and stability of a single biological species. Local extinction of the species may force the social planner to implement defensive expenditures aimed at conservation of the species population by means of habitat protection. The latter may lead to an ecological equilibrium that will be different from the natural equilibrium that would have arisen in the absence of human intervention. Moreover, the existence of such equilibrium is formally demonstrated and its stability properties are revised. Additionally, optimal-choice decision policies are constructed on the basis of Pontryagin's maximum principle. Under such policies together with initial abundance of the species, the growth trajectories will move the system towards the fixed point of maximum species abundance.