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This paper extends Turing analysis to standard recursive op- timal 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 cre- ates (or destroys) spatial heterogeneity. We show how our ap- proach reduces the analysis to a tractable extension of lineariza- tion 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 prob- lem. 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 op- timal control settings is new. JEL Classification Q2, C6

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