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Optimal control and spatial heterogeneity : pattern formation in economic-ecological models

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  • Brock,W.A.
  • Xepapadeas,A.

    (University of Wisconsin-Madison, Social Systems Research Institute)

Abstract

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.

(This abstract was borrowed from another version of this item.)

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File URL: http://www.ssc.wisc.edu/econ/archive/wp2005-11.pdf
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Bibliographic Info

Paper provided by Wisconsin Madison - Social Systems in its series Working papers with number 11.

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Date of creation: 2005
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Handle: RePEc:att:wimass:200511

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Postal: UNIVERSITY OF WISCONSIN MADISON, SOCIAL SYSTEMS RESEARCH INSTITUTE(S.S.R.I.), MADISON WISCONSIN 53706 U.S.A.

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References

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  1. 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.
  2. Michel, P., 1980. "On the Transversality Condition in Infinite Horizon Optimal Problems," Cahiers de recherche 8024, Universite de Montreal, Departement de sciences economiques.
  3. 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.
  4. 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.
  5. 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.
  6. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  7. Cees Diks & Roy van der Weide, 2003. "Heterogeneity as a Natural Source of Randomness," Tinbergen Institute Discussion Papers 03-073/1, Tinbergen Institute.
  8. 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.
  9. 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.
  10. 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.
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Cited by:
  1. Rauscher, Michael & Barbier, Edward B., 2010. "Biodiversity and geography," Resource and Energy Economics, Elsevier, vol. 32(2), pages 241-260, April.

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