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
Athens University of Economics and Business
FEEM Working Paper No. 96.2005
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
Date posted: August 9, 2005
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