Spatial Resource Management under Pollution Externalities

Variables describing the state of an environmental system such as resources (renewable or exhaustible), pollutants, greenhouse gases have a profound spatial dimension. This is because resources or pollutants are harvested, extracted, emitted, or abated in a specific location or locations, the impacts of environmental variables, whether beneficial or detrimental, have a strong spatial dimension, and there is transport of environmental state variables across geographical space due to natural processes. In this paper we study dynamic optimization for the joint management of resources and pollution when pollution affects resource growth and when spatial transport phenomena both for the resources and the pollution are present. We present approaches that deal with dynamic optimization in infinite dimensional spaces which can be used as tools in environmental and resource economic. We also present methods which can be used to study the emergence of spatial patterns in dynamic optimization models. Our methods draw on the celebrated Turing diffusion induced instability but are different from Turing’s mechanism since they apply to forward-optimization models. We believe that this approach provides the tools to analyze a wide range of problems with explicit spatial structure which are very often encountered in environmental and resource economics.