IDEAS home Printed from https://ideas.repec.org/p/att/wimass/200511.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.)

Suggested Citation

  • Brock,W.A. & Xepapadeas,A., 2005. "Optimal control and spatial heterogeneity : pattern formation in economic-ecological models," Working papers 11, Wisconsin Madison - Social Systems.
  • Handle: RePEc:att:wimass:200511
    as

    Download full text from publisher

    File URL: http://www.ssc.wisc.edu/econ/archive/wp2005-11.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
    5. Cees Diks & Roy van der Weide, 2003. "Heterogeneity as a Natural Source of Randomness," Tinbergen Institute Discussion Papers 03-073/1, Tinbergen Institute.
    6. 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.
    7. 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.
    8. 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.
    9. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
    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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rauscher, Michael & Barbier, Edward B., 2010. "Biodiversity and geography," Resource and Energy Economics, Elsevier, vol. 32(2), pages 241-260, April.

    More about this item

    JEL classification:

    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:att:wimass:200511. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ailsenne Sumwalt). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.