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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

Suggested Citation

  • 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.
    • Handle: RePEc:kap:enreec:v:26:y:2003:i:4:p:575-602
    DOI: 10.1023/B:EARE.0000007350.11040.e3
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    References listed on IDEAS

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    1. W. A. Brock & A. Haurie, 1976. "On Existence of Overtaking Optimal Trajectories Over an Infinite Time Horizon," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 337-346, November.
    2. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 275-280.
    3. Ivar Ekeland & José Alexandre Scheinkman, 1986. "Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 216-229, May.
    4. 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.
    5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, 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.
    7. 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.
    8. Ludwig,D. & Carpenter,S. & Brock,W., 2002. "Optimal phosphorus loading for a potentially eutrophic lake," Working papers 9, Wisconsin Madison - Social Systems.
    9. Brock, W. A. & Dochert, W. D., 1983. "The Generalized Maximum Principle," SSRI Workshop Series 292592, University of Wisconsin-Madison, Social Systems Research Institute.
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