Intertemporal soil management: revisiting the shape of the crop production function

Soil resources play a role in food security and climate change mitigation. Through their practices, farmers impact the physical, biological and chemical quality of their soil. However, farmers face a trade-off between the short-term objectives of production and profitability and the long-term objective of soil resource conservation. In this article, we investigate the conditions under which farmers have a private interest in preserving their soil quality. We use a simplified theoretical soil quality investment model, where farmers maximize their revenues under a soil quality dynamic constraint. Here, soil quality is an endogenous production factor of the crop production function. We show that the existence of an equilibrium depends on the cooperation between soil quality and productive inputs. The results are confronted to a statistical illustration in France. In this case, nitrogen fertilizers are not cooperating with soil organic carbon. Incentives to reduce nitrogen fertilizers would not trigger a negative feedback effect.