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 the slowly changing variable. New optimal trajectories are found that were hidden in the simplified analysis. Furthermore, it is shown that two Nash equilibria may exist with the one leading to the steady state with a high level of ecological services dominating the other one. For larger initial states, only the Nash equilibrium with a low level of ecological services exists, which implies that the users of the lake can be trapped in the bad Nash equilibrium. Finally, it is shown that implementing the optimal phosphorus loadings from the simplified version into the full lake model can have considerable welfare losses, as the lake can end up in the wrong basin of attraction, but in most cases welfare losses are small because of the fast-slow dynamics.