Optimal control and spatial heterogeneity : pattern formation in economic-ecological models
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Wisconsin Madison - Social Systems in its series Working papers with number 11.
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.
Other versions of this item:
- Anastasios Xepapadeas & William Brock, 2005. "Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models," Working Papers 2005.96, Fondazione Eni Enrico Mattei.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-10-15 (All new papers)
- NEP-GEO-2005-10-15 (Economic Geography)
- NEP-URE-2005-10-15 (Urban & Real Estate Economics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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, 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.
- Brock,W. & Xepapadeas,A., 2000. "Optimal ecosystem management when species compete for limiting resources," Working papers 27, Wisconsin Madison - Social Systems.
- 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.
- 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.
- 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.
- 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.
- Edward B. Barbier & Michael Rauscher, 2007.
"Biodiversity and Geography,"
CESifo Working Paper Series
2022, CESifo Group Munich.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ailsenne Sumwalt).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.