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.
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Bibliographic InfoPaper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2005.96.
Date of creation: Jul 2005
Date of revision:
Spatial analysis; Pattern formation; Turing mechanism; Turing space; Pontryagin’s principle; Bioeconomics;
Other versions of this item:
- Brock,W.A. & Xepapadeas,A., 2005. "Optimal control and spatial heterogeneity : pattern formation in economic-ecological models," Working papers 11, Wisconsin Madison - Social Systems.
- 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-2005-12-09 (All new papers)
- NEP-ENV-2005-12-09 (Environmental Economics)
- NEP-GEO-2005-12-09 (Economic Geography)
- NEP-RES-2005-12-09 (Resource Economics)
- NEP-URE-2005-12-09 (Urban & Real Estate Economics)
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