Advanced Search
MyIDEAS: Login

Bifurcations of optimal vector fields in the shallow lake model

Contents:

Author Info

  • Kiseleva, T.

    ()
    (University of Amsterdam)

  • Wagener, F.O.O.

    ()
    (University of Amsterdam)

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www1.fee.uva.nl/cendef/publications/papers/Kiseleva_Wagener_working_paper_2009.pdf
Download Restriction: no

Bibliographic Info

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

as in new window
Length:
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
Email:
Web page: http://www.fee.uva.nl/cendef/
More information through EDIRC

Related research

Keywords:

Other versions of this item:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Mäler, K-G. & Xepapadeas, A. & Zeeuw, A.J. de, 2000. "The Economics of Shallow Lakes," Discussion Paper 2000-69, Tilburg University, Center for Economic Research.
  2. 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.
  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, European Association of Environmental and Resource Economists, vol. 26(4), pages 575-602, December.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Jeroen Hinloopen & Grega Smrkolj & Florian Wagener, 2011. "From Mind to Market: A Global, Dynamic Analysis of R&D," Tinbergen Institute Discussion Papers 11-139/1, Tinbergen Institute.
  2. 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.
  3. 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.
  4. 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.
  5. Jeroen Hinloopen & Grega Smrkolj & Florian Wagener, 2013. "In Defense of Trusts: R&D Cooperation in Global Perspective," Tinbergen Institute Discussion Papers 13-045/II, Tinbergen Institute, revised 04 Mar 2014.
  6. Jeroen Hinloopen & Grega Smrkolj & Florian Wagener, 2011. "From Mind to Market: A Global, Dynamic Analysis of R&D," Tinbergen Institute Discussion Papers 11-139/1, Tinbergen Institute.
  7. Kiseleva, T. & Wagener, F.O.O., 2011. "Bifurcations of Optimal Vector Fields," CeNDEF Working Papers 11-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:ams:ndfwpp:09-12. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Cees C.G. Diks).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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