Economic development on a finite planet with stochastic soil degradation

World economic development is associated with growing food consumption. Agricultural land, however, suffers from over-exploitation and is subject to environmental shocks which are projected to become more severe due to climate change. We present a stochastic model of a dynamic economy where soil is an essential input and natural disasters are sizeable, multiple, and random. Expansion of economic activities raises effective soil units but contributes to an aggregate loss of soil-protective ecosystem services, which exacerbates soil degradation at the time of a shock. We provide closed-form analytical solutions and show that optimal development is characterized by a constant growth rate of stocks and consumption until an environmental shock arrives causing all variables to jump downwards. Optimal soil management consists of spending a constant fraction of output on preservation measures, which is an increasing function of the shocks hazard rate, degradation intensity of agricultural practices, and the damage intensity of environmental impact. We derive the optimal propensity to save and discuss the impact of human pressure and risk exposure on soil and output. We also discuss quantitative impacts of climate change on optimal soil management.