| Abstract: |
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
optimizations 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. |
| Keywords: |
spatial transport, renewable resource, pollution, optimization, in
finite dimensional spaces, Turing instability, pattern formation, policy design |