Bifurcations of optimal vector fields in the shallow lake model
The solution structure of the set of optimal solutions of the shallow lake problem, a problem of optimal pollution management, is studied as we vary the values of the system parameters: the natural resilience, the relative importance of the resource for social welfare and the future discount rate. We find parameter values at which qualitative changes occur. Using theoretical results on the bifurcations of the solution structure to infinite horizon optimization problems obtained earlier, we give a fairly complete bifurcation analysis of the shallow lake problem. In particular, we show how the increase of the discount rate affects the parameter regions where an oligotrophic steady state, corresponding to low pollution level, is globally stable or locally stable under optimal dynamics. Asymptotically, an increase of the discount rate can be offset with a proportional increase of the relative social weight of the resource.
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- F.O.O. Wagener, 2009.
"Shallow Lake Economics Run Deep: Nonlinear Aspects of an Economic-Ecological Interest Conflict,"
Tinbergen Institute Discussion Papers
09-033/1, Tinbergen Institute.
- Florian Wagener, 2013. "Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict," Computational Management Science, Springer, vol. 10(4), pages 423-450, December.
- Wagener, F.O.O., 2009. "Shallow lake economics run deep: Nonlinear aspects of an economic-ecological interest conflict," CeNDEF Working Papers 09-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- W.A. Brock & D. Starrett, 2003. "Managing Systems with Non-convex Positive Feedback," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 575-602, December.
- Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
- Mäler, K-G. & Xepapadeas, A. & de Zeeuw, A.J., 2000.
"The Economics of Shallow Lakes,"
2000-69, Tilburg University, Center for Economic Research.
- Wagener, F.O.O., 2003. "Structural analysis of optimal investment for firms with non-concave production," CeNDEF Working Papers 03-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
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