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Managing Systems with Non-convex Positive Feedback

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  • W.A. Brock
  • D. Starrett

    ()

Abstract

We study here optimal management of dynamic ecological systemsthat exhibit a destabilizing positive feedback. The prototypeexample is that of a shallow lake in which phosphorous loadingplaced by anthropogenic activities (fertilizers for farmingand gardening) is stored in sediments until a critical levelis reached after which there is a destabilizing return to thewater – the tradeoff between farming interests and lake qualitygenerates an optimal control problem. We show that in such systems, there may be a variety of local optima and associatedbasins of attraction wherein the optimal path may depend onstarting state (phosphorous stock). We characterize the variouspossible optimal behaviors and identify the ambiguities thatcan only be resolved by choice of functional form. Copyright Kluwer Academic Publishers 2003

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File URL: http://hdl.handle.net/10.1023/B:EARE.0000007350.11040.e3
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Bibliographic Info

Article provided by European Association of Environmental and Resource Economists in its journal Environmental and Resource Economics.

Volume (Year): 26 (2003)
Issue (Month): 4 (December)
Pages: 575-602

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Handle: RePEc:kap:enreec:v:26:y:2003:i:4:p:575-602

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Web page: http://www.springerlink.com/link.asp?id=100263

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Keywords: basins of attraction; dynamic optimization; lake ecology; non-convex dynamics; positive feedback;

References

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  1. Keller, Klaus & Bolker, Benjamin M. & Bradford, D.F.David F., 2004. "Uncertain climate thresholds and optimal economic growth," Journal of Environmental Economics and Management, Elsevier, vol. 48(1), pages 723-741, July.
  2. Ludwig,D. & Carpenter,S. & Brock,W., 2002. "Optimal phosphorus loading for a potentially eutrophic lake," Working papers 9, Wisconsin Madison - Social Systems.
  3. Spence, A Michael & Starrett, David, 1975. "Most Rapid Approach Paths in Accumulation Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 388-403, June.
  4. Brock, William A, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Wiley Blackwell, vol. 37(2), pages 275-80, April.
  5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May.
  6. Tahvonen, Olli & Salo, Seppo, 1996. "Nonconvexities in Optimal Pollution Accumulation," Journal of Environmental Economics and Management, Elsevier, vol. 31(2), pages 160-177, September.
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