Dynamics and optimal control for a spatially-structured environmental-economic model

A deterministic model of economic growth and pollution accumulation, in the form of a system of partial differential equations, is designed and analyzed. The model assumes pollution as a by-product of production. The stock of pollution has a negative impact on production. The accumulation of pollution is dampened by a share of the investments, in the form of an environmental tax. We consider a linear region where both capital and pollution can diffuse. This economic-environmental model is described by a pair of partial differential equations whose dynamics and steady state characteristics with respect to time and space are studied. Then we look at this ambient environment from the point of view of a social planner who can act on the consumption and taxation, also functions of time and space, considering the dynamics of capital and pollution as constraints.