A simple bio-economic model of soil natural capital

Considering soil as an ecosystem, we build a simple bio-economic model with two interelated stocks. One is the soil organic matter, basis of several ecosystem services, and the other one is the stock of nutrients directly contributing to the plant's biomass elaboration. Humification process of the crops residues contributes to the SOM, while mineralisation process contributes to the stock of nutrients. The production function is a Linear Liebig with plateau. The economic part of the model relies on the long term profit maximisation in the context of private management. We retained two controls: the mineral fertilization adding to the stock of nutrients, and the rate of biomass given back to soil. By combining both controls, we identified management regimes and defined the set of stationaries states. Going beyong that standard step of analysis, we simulated optimal time path for differents initial conditions and different set of parameter values. We specifically focused on the role of the price of fertilizers relative to the price of the agricultural products. Results show that private management of soil natural capital drives to the quasi depeletion of SOM. As a consequence, there is a need for public incentives to promote ecosystems services non supported by market