Pattern formation, spatial externalities and regulation in coupled economic–ecological systems

We study the management of ecosystems in which interacting state variables that are affected by management decisions diffuse in space. We study pattern formation first in a setting where economic agents maximize myopic profits and ignore spillovers onto agents at other sites, and second in the context of a social planner who internalizes these spillovers. We compare patterns under these two institutions and study how the differences in the patterns generated by these two institutions impact the design of regulatory schemes to internalize the externalities. At the same time we introduce new methods based on Fourier series type decompositions that enable us to turn an intractable infinite dimensional optimal control problem into a countable number of finite dimensional optimal control problems. As far as we know these methods are new to the economics literature. Our theory is applied to the management and regulation of a semi-arid system.