Is the Irrigation Water Demand Really Convex?*
Christophe BONTEMPS#
Stéphane COUTURE%
Pascal FAVARD§
July 4th, 2001
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Abstract: 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 farmer's 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
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 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.
Keywords: Seasonal irrigation water demand, uncertainty,
regulation policy.
JEL Classification: Q15, D81.
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