Water Quantity Management in a Heterogeneous Landscape with Farsighted Farmers

Agricultural production contributes to many environmental problems. In semi-arid areas, agricultural irrigation causes the so-called waterlogging phenomenon. This phenomenon is both spatial and dynamic since percolation depends on soil quality summed up in landscape heterogeneity and evolves along time. Furthermore, farmers can be farsighted with respect to their contribution to percolation. We study regulation schemes to be implemented to restore the socially optimal spatial and temporal production plan of farmers in such a context. We show that both a temporal tax on percolation and a spatio-temporal tax on inputs (both at the extensive and at the intensive margin) are efficient for the restoration of the socially optimal solution. Furthermore, a numerical example demonstrates that the consequences of implementing a fiscal scheme designed for myopic farmers whereas they are farsighted depends on the distribution of soil quality.