Pollution diffusion, limited production factors, non-monotonic growth and the emergence of spatially heterogeneous steady states

We develop a spatial growth model for an agricultural economy where pollution diffuses in the soil. At each location, the only production factor is fertile soil, which is at the same time naturally bounded by the amount of available land, and eventually exposed to pollution diffused from neighboring locations. We develop a novel technique to obtain the policy maker's optimal solution, which is analytical in the case of an homogeneous economy and covers all cases, for impatience rates ranging from almost zero to extremely high. When agents are very patient, the policy maker starts by making fully fertile all land before allowing for positive consumption. For slightly more impatient agents, the policy maker will allow for some consumption from the beginning, in the cleaning-up stage. With time, abatement stops, consumption raises and land becomes fully polluted in the long-term. We provide with some general results for the general spatially heterogeneous economy and its long-run, completing our study with some numerical exercises. Worth noting, simulations reveal that also in the non-homogeneous economy optimal consumption may transit through four different stages in time, responding to changes in fertile land and not necessarily in a smooth manner.