Divergent Time Scales in a Coupled Ecological-Economic Model of Regional Growth

This paper establishes a coupled human-ecological model where slow-varying migration is interacting with fast-varying nutrient dynamics in lake ecology. The nonlinearity and fast-slow dynamics built in the model can generate regime shifts (that is, shifts between different equilibrium states) and slowly-reversible ecological changes. Because ecological conditions do affect and are affected by uncoordinated individual decisions on migration and land-use, the policy challenge does not only lie in the optimal use of ecological service but also in the provision of the right incentives that regulates individual behavior. The possibility of regime shifts and slowly-reversible changes in this coupled model makes policy analysis more interesting and technically challenging. Within this framework, this paper shows that specification of relative time scale between the fast and slow dynamic processes is crucial for the analysis of the system dynamics with/without policy intervention. The calculated solutions show that specification of relative time scale can significantly change the cost, magnitude and length of active intervention in optimal policy. This paper shows that optimal policy (even when resilience does not enter into optimization problem) will always increase the resilience of the desirable equilibrium in the coupled system. The extent of this improvement in resilience depends crucially on the relative time scale. It also shows that simplifying assumptions on the relative time scale can lead to incorrect predictions for both the short-and long-run dynamics.