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Bifurcations of optimal vector fields in the shallow lake model

  • Kiseleva, T.


    (University of Amsterdam)

  • Wagener, F.O.O.


    (University of Amsterdam)

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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Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 09-12.

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Date of creation: 2009
Date of revision:
Handle: RePEc:ams:ndfwpp:09-12
Contact details of provider: Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
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  1. 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.
  2. 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.
  3. 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.
  4. Mäler, K-G. & Xepapadeas, A. & de Zeeuw, A.J., 2000. "The Economics of Shallow Lakes," Discussion Paper 2000-69, Tilburg University, Center for Economic Research.
  5. W.A. Brock & D. Starrett, 2003. "Managing Systems with Non-convex Positive Feedback," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 26(4), pages 575-602, December.
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