Optimal control and spatial heterogeneity : pattern formation in economic-ecological models
This paper extends Turing analysis to standard recursive optimal control frameworks in economics and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates (or destroys) spatial heterogeneity. We show how our approach reduces the analysis to a tractable extension of linearization methods applied to the spatial analog of the well known costate/state dynamics. We explicitly show the existence of a non-empty Turing space of diffusive instability by developing a linear-quadratic approximation of the original non-linear problem. We apply our method to a bioeconomic problem, but the method has more general economic applications where spatial considerations and pattern formation are important. We believe that the extension of Turing analysis and the theory associated with the dispersion relationship to recursive infinite horizon optimal control settings is new.
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|Date of creation:||2005|
|Date of revision:|
|Contact details of provider:|| Postal: UNIVERSITY OF WISCONSIN MADISON, SOCIAL SYSTEMS RESEARCH INSTITUTE(S.S.R.I.), MADISON WISCONSIN 53706 U.S.A.|
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- Diks, C.G.H. & Weide, R. van der, 2003. "Heterogeneity as a natural source of randomness," CeNDEF Working Papers 03-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Dixit, Avinash K & Stiglitz, Joseph E, 1977.
"Monopolistic Competition and Optimum Product Diversity,"
American Economic Review,
American Economic Association, vol. 67(3), pages 297-308, June.
- Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
- Brock, William A. & Hommes, Cars H. & Wagener, Florian O. O., 2005.
"Evolutionary dynamics in markets with many trader types,"
Journal of Mathematical Economics,
Elsevier, vol. 41(1-2), pages 7-42, February.
- Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2002. "Evolutionary dynamics in markets with many trader types," CeNDEF Working Papers 02-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Michel, Philippe, 1982.
"On the Transversality Condition in Infinite Horizon Optimal Problems,"
Econometric Society, vol. 50(4), pages 975-85, July.
- Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
- Sanchirico, James N. & Wilen, James E., 2001. "A Bioeconomic Model of Marine Reserve Creation," Journal of Environmental Economics and Management, Elsevier, vol. 42(3), pages 257-276, November.
- Sanchirico, James N. & Wilen, James E., 1999. "Bioeconomics of Spatial Exploitation in a Patchy Environment," Journal of Environmental Economics and Management, Elsevier, vol. 37(2), pages 129-150, March.
- Sanchirico, James N., 2005. "Additivity properties in metapopulation models: implications for the assessment of marine reserves," Journal of Environmental Economics and Management, Elsevier, vol. 49(1), pages 1-25, January.
- Magill, Michael J. P., 1977. "A local analysis of N-sector capital accumulation under uncertainty," Journal of Economic Theory, Elsevier, vol. 15(1), pages 211-219, June.
- Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
- Brock,W. & Xepapadeas,A., 2000.
"Optimal ecosystem management when species compete for limiting resources,"
27, Wisconsin Madison - Social Systems.
- Brock, William & Xepapadeas, Anastasios, 2002. "Optimal Ecosystem Management when Species Compete for Limiting Resources," Journal of Environmental Economics and Management, Elsevier, vol. 44(2), pages 189-220, September.
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