Is the irrigation water demand really convex?

We estimate the irrigation water demand for a season under uncertainty using a dynamic programming model and a crop-growth simulation model (EPIC-PHASE) linked to a CRRA utility function representing the farmer's objective function. This model is used to generate the data allowing the estimation of irrigation water demand by a nonparametric procedure. An application shows that demand functions present four main areas: for very small quantities, the demand is inelastic. In the second area, where water is no more an essential input and is not yet a risk reducing input, the demand is elastic. But, we find a third, non-intuitive, area for larger quantities where the water is a risk reducing input and the demand becomes inelastic again. In the last area the water demand is obviously elastic for important total water quantities. This result is of great importance to analyse a regulation policy.