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Bifurcations of optimal vector fields in the shallow lake model

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  • Kiseleva, Tatiana
  • Wagener, F.O.O.

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.

Suggested Citation

  • Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
  • Handle: RePEc:eee:dyncon:v:34:y:2010:i:5:p:825-843
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    References listed on IDEAS

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    1. 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.
    2. Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003. "The Economics of Shallow Lakes," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 603-624, December.
    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. 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.
    5. 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.
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    Citations

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    Cited by:

    1. Hinloopen, J. & Smrkolj, G. & Wagener, F.O.O., 2013. "In Defense of Trusts: R&D Cooperation in Global Perspective," CeNDEF Working Papers 13-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    2. Tatiana Kiseleva, 2016. "Heterogeneous Beliefs and Climate Catastrophes," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(3), pages 599-622, November.
    3. Hinloopen, Jeroen & Smrkolj, Grega & Wagener, Florian, 2013. "From mind to market: A global, dynamic analysis of R&D," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2729-2754.
    4. Engelbert Dockner & Florian Wagener, 2014. "Markov perfect Nash equilibria in models with a single capital stock," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 585-625, August.
    5. Elke Moser & Dieter Grass & Gernot Tragler, 2016. "A non-autonomous optimal control model of renewable energy production under the aspect of fluctuating supply and learning by doing," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 545-575, July.
    6. repec:spr:joptap:v:168:y:2016:i:1:d:10.1007_s10957-015-0747-3 is not listed on IDEAS
    7. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.
    8. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M., 2011. "Two state capital accumulation with heterogenous products: Disruptive vs. non-disruptive goods," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 462-478, April.
    9. Jeroen Hinloopen & Grega Smrkolj & Florian Wagener, 2016. "R&D Cooperatives and Market Collusion: A Global Dynamic Approach," Tinbergen Institute Discussion Papers 16-048/II, Tinbergen Institute.
    10. Caulkins, Jonathan P. & Feichtinger, Gustav & Grass, Dieter & Hartl, Richard F. & Kort, Peter M. & Seidl, Andrea, 2015. "Skiba points in free end-time problems," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 404-419.
    11. Ken-Ichi Akao & Takashi Kamihigashi & Kazuo Nishimura, 2015. "Critical Capital Stock in a Continuous-Time Growth Model with a Convex-Concave Production Function," Discussion Paper Series DP2015-39, Research Institute for Economics & Business Administration, Kobe University.
    12. Matthew A. Cole & Andrea Lucchesi, 2014. "Economic growth and the environment," Chapters,in: Handbook of Sustainable Development, chapter 16, pages 252-266 Edward Elgar Publishing.
    13. Kari Hyytiäinen & Lassi Ahlvik & Heini Ahtiainen & Janne Artell & Anni Huhtala & Kim Dahlbo, 2015. "Policy Goals for Improved Water Quality in the Baltic Sea: When do the Benefits Outweigh the Costs?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 61(2), pages 217-241, June.

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