Optimal Management of Ecosystem Services with Pollution Traps: The Lake Model Revisited

In this paper, optimal management of the lake model and common- property outcomes are reconsidered when the lake model is extended with a slowly changing variable (describing sedimentation and recycling of phosphorus), which is considered xed in the simplied version that has been used in the literature up to now. Some intuitive results are reconrmed but new optimal trajectories are found that were hidden in the simplied analysis. Moreover, it is shown that in the case of common-property, two Nash equilibria exist in a certain area of initial conditions but the one leading to the steady state with a high level of ecological services dominates the other one. However, for an adjacent area of initial conditions, only the Nash equilibrium steady state with a low level of ecological services exists.This implies that users of the lake are trapped in the bad Nash equilibrium as a result of initial conditions, leading to a substantial drop in welfare because the good Nash equilibrium is not reachable from the prevailing initial conditions. Finally, it is shown that the welfare losses of implementing the optimal phosphorus loadings from the simplied version into the full lake model are small, because of the fast-slow dynamics. The analytical tool that is used in this paper is an advanced extension of a Matlab solver for boundary value problems.

Keywords: ecosystem services, fast-slow dynamics, games, lakes, multiple equilibria, optimal control, pollution trap

Grass, D., A. Xepapadeas, and A. de Zeeuw. 2015. Beijer Discussion Paper 255: Optimal Management of Ecosystem Services with Pollution Traps: The Lake Model Revisited. Beijer Discussion Paper Series.