IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v34y2010i5p825-843.html
   My bibliography  Save this article

Bifurcations of optimal vector fields in the shallow lake model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(09)00217-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, November.
    4. Wagener, F.O.O., 2005. "Structural analysis of optimal investment for firms with non-concave revenue," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 474-489, August.
    5. 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.
    6. J. P. Caulkins & G. Feichtinger & D. Grass & G. Tragler, 2007. "Bifurcating DNS Thresholds in a Model of Organizational Bridge Building," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 19-35, April.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dmitry Gromov & Thorsten Upmann, 2021. "Dynamics and Economics of Shallow Lakes: A Survey," Sustainability, MDPI, vol. 13(24), pages 1-16, December.
    2. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.
    3. Elke Moser & Andrea Seidl & Gustav Feichtinger, 2014. "History-dependence in production-pollution-trade-off models: a multi-stage approach," Annals of Operations Research, Springer, vol. 222(1), pages 457-481, November.
    4. Reddy, P.V. & Schumacher, J.M. & Engwerda, J.C., 2012. "Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model," Discussion Paper 2012-001, Tilburg University, Center for Economic Research.
    5. Moghayer, S. & Wagener, F.O.O., 2009. "Genesis of indifference thresholds and infinitely many indifference points in discrete time infinite horizon optimisation problems," CeNDEF Working Papers 09-14, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    6. Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 60-73, April.
    7. Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 60-73.
    8. Crépin, Anne-Sophie & Biggs, Reinette & Polasky, Stephen & Troell, Max & de Zeeuw, Aart, 2012. "Regime shifts and management," Ecological Economics, Elsevier, vol. 84(C), pages 15-22.
    9. F. O. O. Wagener, 2006. "Skiba Points for Small Discount Rates," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 261-277, February.
    10. Heijnen, P. & Wagener, F.O.O., 2013. "Avoiding an ecological regime shift is sound economic policy," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1322-1341.
    11. I. Zeiler & J.P. Caulkins & G. Tragler, 2011. "Optimal Control of Interacting Systems with DNSS Property: The Case of Illicit Drug Use," Post-Print hal-00978258, HAL.
    12. Dieter Grass, 2015. "From 0D to 1D spatial models using OCMat," Papers 1505.03956, arXiv.org.
    13. Lemoine, Derek M. & Traeger, Christian P., 2010. "Tipping Points and Ambiguity in the Economics of Climate Change," CUDARE Working Papers 98127, University of California, Berkeley, Department of Agricultural and Resource Economics.
    14. 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.
    15. Wagener, Florian & de Zeeuw, Aart, 2021. "Stable partial cooperation in managing systems with tipping points," Journal of Environmental Economics and Management, Elsevier, vol. 109(C).
    16. Polasky, Stephen & de Zeeuw, Aart & Wagener, Florian, 2011. "Optimal management with potential regime shifts," Journal of Environmental Economics and Management, Elsevier, vol. 62(2), pages 229-240, September.
    17. Aart Zeeuw & Chuan-Zhong Li, 2016. "The Economics of Tipping Points," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(3), pages 513-517, November.
    18. Johannus Janmaat, 2012. "Fishing in a Shallow Lake: Exploring a Classic Fishery Model in a Habitat with Shallow Lake Dynamics," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 51(2), pages 215-239, February.
    19. Yuri Yegorov & Dieter Grass & Magda Mirescu & Gustav Feichtinger & Franz Wirl, 2020. "Growth and Collapse of Empires: A Dynamic Optimization Model," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 620-643, August.
    20. Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:34:y:2010:i:5:p:825-843. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.