Christophe Bontemps

Irrigation water demand for the decision maker

This paper deals with the problems of estimating irrigation water demand. We propose an original method of estimation in two steps. First, we develop a dynamic programming model in order to explain the optimal irrigation management plan. Based on a microeconomic approach describing the farmers behavior, this economic model, introducing an agronomic model, and an algorithm of solution search, is used to compute a realistic database. Second, these data are used to estimate profit functions by a non-parametric method. The irrigation water demand function is estimated using a non-parametric derivation procedure.An application to irrigation water demand is proposed in the southwestern area of France where conflicts appear frequently. The same results appear for different climates: for small quantities of water available, irrigation water demand seems to be quite inelastic. If one increases the total quantity of water available, the shape of the curve changes and the demand appears more elastic. The threshold price at which the changes in price-responsiveness appears, depends on weather conditions and range from 0.30 F/m3 in a wet year to 1.60 F/m3 in a dry year. These results are crucial information for the regulator in order to analyze the effects of a water regulation policy, based on prices. The impact of an increase in the water price will depend not only on the climate but also on the location of the initial and final prices on the demand function.JEL classification: C14, C16, Q15

Is the Irrigation Water Demand Really Convex

The seasonal irrigation water demand under uncertainty, which lies at the core of this paper, is still very roughly known. We know, however, that irrigated agriculture accounts for a large proportion of water use, especially in many water-scarce areas. In this paper, we estimate the irrigation water demand, for various climatic conditions characterizing the distribution of the necessarily stochastic, demand functions under uncertainty. We use a dynamic programming model to represent the farmers decision program under uncertainty. A crop-growth simulation model (EPIC-PHASE), provides the response function to the decisions taken and climatic events and is linked to a CRRA utility function representing the farmers objective function. This model is used to generate the data allowing the estimation of irrigation water demand by a nonparametric procedure. An application to irrigation water demand is proposed in the South-West of France. We show that the estimated demand functions present four main areas: For very small quantities, where the farmer considers water as an essential input to crop growth, the demand is inelastic. The second area corresponds to mean quantities where the plant has reached a satisfactory level of growth; water is no more an essential input and is not yet a risk reducing input. The farmer is more responsive to change in water price. 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. The last area is classic, the water demand is obviously elastic for important total water quantities. This result is of great importance to analyze a regulation policy.