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http://ssrn.com/abstract=773925
 
 

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Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models


William A. Brock


University of Wisconsin, Madison - Department of Economics ; University of Missouri at Columbia - Department of Economics

Anastasios Xepapadeas


Athens University of Economics and Business

July 2005

FEEM Working Paper No. 96.2005

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.

Number of Pages in PDF File: 54

Keywords: Spatial analysis, Pattern formation, Turing mechanism, Turing space, Pontryagin's principle, Bioeconomics

JEL Classification: Q2, C6

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Date posted: August 9, 2005  

Suggested Citation

Brock, William A. and Xepapadeas, Anastasios, Optimal Control and Spatial Heterogeneity: Pattern Formation in Economic-Ecological Models (July 2005). FEEM Working Paper No. 96.2005. Available at SSRN: http://ssrn.com/abstract=773925 or http://dx.doi.org/10.2139/ssrn.773925

Contact Information

William A. Brock
University of Wisconsin, Madison - Department of Economics ( email )
1180 Observatory Drive
Madison, WI 53706
United States
608-263-6655 (Phone)
608-263-3876 (Fax)
University of Missouri at Columbia - Department of Economics ( email )
118 Professional Building
Columbia, MO 65211
United States
Anastasios Xepapadeas (Contact Author)
Athens University of Economics and Business ( email )
76 Patission Street
Athens, 104 34
Greece
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