Journal
JOURNAL OF ECONOMIC DYNAMICS & CONTROL
Volume 32, Issue 9, Pages 2745-2787Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jedc.2007.08.005
Keywords
spatial analysis; pattern formation; optimal control; optimal diffusion-induced instability
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This paper develops local stability analysis for deterministic optimal control theory for recursive infinite horizon intertemporal optimization problems where there is a continuum of spatial sites and the state variable can diffuse over these sites. We identify sufficient conditions for a type of local instability which emerges from the interaction of the discount rate on the future, the curvature of the Hamiltonian, and the spatial features of the problem. We call this phenomenon optimal diffusion-induced instability (ODI). We illustrate our analytical methods with three stylized applications. The first application is the optimal management of spatially connected human dominated ecosystems. The second and third applications are harvesting of spatially interconnected renewable resources. (C) 2007 Elsevier B.V. All rights reserved.
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