Preservation of Agricultural Soils with Endogenous Stochastic Degradation

Soils are often subject to environmental shocks which are caused by negative extern- alities linked to overexploitation. We present a stochastic model of a dynamic agricultural economy where natural disasters are sizeable, multiple, and random. Expansion of agricultural activities raises effective soil units (an index of quality and quantity) but contributes to an aggregate loss of soil-protective ecosystem services, which increases the extent of 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 effective soil units and crop consumption until an environmental shock arrives causing both variables to jump downwards. Optimal policy consists of spending a constant fraction of output on soil preservation. This fraction is an increasing function of the shocks arrival rate, degradation intensity of agricultural practices, and the damage intensity of environmental impact. Implications for the optimal propensity to save are also discussed. An extension of the model provides a solution for the optimal preservation policy when both the hazard rate and damages are endogenous.