Bifurcations of optimal vector fields in the shallow lake model

Tatiana Kiseleva and Florian Wagener

No 09-12, CeNDEF Working Papers from Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance

Abstract: 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.

Date: 2009
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Citations: View citations in EconPapers (1)

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Journal Article: Bifurcations of optimal vector fields in the shallow lake model (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:ams:ndfwpp:09-12

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