Solving ecological management problems using dynamic programming

We study an ecological management problem where the interaction of the maximizing-welfare dynamic decision and the dynamics of the ecosystem admits multiple equilibria. We follow the example of a shallow lake by Brock, etc. Low loading preserves resilience of the ecosystem while high loading may lead to the deterioration of the ecosystem. We consider instruments of a regulatory agency that may help to maintain and enhance resilience by enlarging the domain of attraction of the low-pollution equilibrium. The global dynamics of all our model variants, without and with tax rates, are analytically studied by the Hamilton-Jacobi-Bellman method and numerically solved through dynamic programming.