Managing Systems with Non-convex Positive Feedback

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Managing Systems with Non-convex Positive Feedback

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W.A. Brock
D. Starrett ()

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William A. Brock

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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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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repec:att:wimass:192029 is not listed on IDEAS
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. [Downloadable!] (restricted)
Tahvonen, Olli & Salo, Seppo, 1996. "Nonconvexities in Optimal Pollution Accumulation," Journal of Environmental Economics and Management, Elsevier, vol. 31(2), pages 160-177, September. [Downloadable!] (restricted)
Brock, William A, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Blackwell Publishing, vol. 37(2), pages 275-80, April. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May. [Downloadable!] (restricted)

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Mota, Rui Pedro & Domingos, Tiago, 2004. "Optimal ecosystem management with structural dynamics," MPRA Paper 13344, University Library of Munich, Germany. [Downloadable!]
XEPAPADEAS, Anastasios, 2009. "Modeling Complex Systems," MPRA Paper 17498, University Library of Munich, Germany. [Downloadable!]
Anne-Sophie Crépin, 2003. "Multiple Species Boreal Forests – What Faustmann Missed," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 26(4), pages 625-646, December. [Downloadable!] (restricted)
Yacov Tsur & Amos Zemel, 2008. "Regulating environmental threats," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 39(3), pages 297-310, March. [Downloadable!] (restricted)
Anne-Sophie Crépin & Therese Lindahl, 2009. "Grazing Games: Sharing Common Property Resources with Complex Dynamics," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 44(1), pages 29-46, September. [Downloadable!] (restricted)
Guttormsen, Atle G. & Kristofersson, Dadi & Navdal, Eric, 2005. "Managing Genetic Resources for Fun and Profit -- The Role of the Interest Rate in Natural Selection," 2005 Annual meeting, July 24-27, Providence, RI 19354, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]

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