PRELIMINARY VERSION - PLEASE DO NOT CITE
year potatoes, four-year grains followed by one-year sugar beets, and grains or beans with
alfalfa.
The per-acre crop yield is assumed to be represented by a quadratic function as:
yij =φ0j +φ1j(αiwij)+φ2j(αiwij)2. (14)
The parameters of the production function for all the crops considered in this study are calculated
from the data representing the crop production in the ESPA. The University of Idaho crop
budgets were used to determine the parameters of the production function (University of Idaho
Crop Budgets, 2003). The information about the irrigation water requirements for various crops
was obtained from the study by Allen and Brockway (1983). We assume that (a) there is no yield
when the consumptive water use is zero for potatoes, sugar beets, corn grain, corn silage, and dry
edible beans (i.e., φ0j = 0), (b) a maximum yield can be obtained with a given effective annual
water use, and (c) the yield curve is a symmetric quadratic function so that the production is zero
at twice the effective water use. Since wheat, barley, and alfalfa can be produced without
irrigation water in some parts of the ESPA, the coefficients φ0j for these crops represent the
yields that can be obtained without applying water.
We assume that the efficiency of water use (αi ) is a function of technology choice and
land quality represented by an index δi . Using the data from NRCS (2005), we generate a soil
quality index and determine the distribution of soil quality for the entire region. The soil quality
index δi is then scaled to correspond to the water use efficiency with the traditional technology
(i.e., α1i = δi) and can assume values from 0 to 1. In the region, the farmers use both the furrow
technology and the sprinkler technology. When the efficiency of water use with the traditional
furrow technology is 0.60, the adoption of a sprinkler irrigation system increases efficiency of
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