State Water Resources Research Institute Program

Project ID: 2008ID132B
Title: Regional Economic Demand for Irrigation Water in Idaho's Eastern Snake River Plain
Project Type: Information Transfer
Start Date: 3/01/2008
End Date: 2/28/2009
Congressional District: 1st and 2nd
Focus Categories: Economics, Water Supply, Irrigation
Keywords: Irrigation water demand functions, water production functions, evapotranspiration production functions, water economics
Principal Investigators: Taylor, Garth; Elbakidze, Levan
Federal Funds: $ 18,120
Non-Federal Matching Funds: $ 36,240
Abstract: Demands for water throughout the west are exploding. Agricultural, municipal and industrial, energy, and environmental water demand are all increasing. Western water supplies are fully, if not over allocated, and new water supply for new demands (including potable water supplies) must come from reallocation of existing supplies. Irrigation in the United States accounts for 42 percent of fresh water withdrawals and 83 percent of consumptive use (table 2.1). In the 12 most western contiguous states, 82 percent of withdrawals and 92 percent of consumptive use is for agriculture. Economic studies of potential reallocation mechanisms and the economic impact of reallocation require knowledge of the economic demand for irrigation water.

Estimation of agricultural demand functions are costly and data intensive. To obtain the degrees of freedom, data needs to be obtained from a cross section of farms or a time series for many years from numerous farms. And given these data limitations the estimates may not be particularly accurate. Time series data are usually discarded because the assumption of a stable demand function over 20 or 30 years is obviously not reasonable. The cross section data are most often estimated by farm or irrigation district. In lieu of conducting a costly survey of Idaho farms, that may not yield the required data to estimate demand functions, this study will formulate the agricultural water demand functions from the basic building block of crop water use, easily accessible crop price data, agronomic requirement for crop rotations etc., and other farmer constraints and risk environment.

To avoid the survey costs and inaccuracies of an econometric research, a mathematical programming approach will be used in this research. The mathematical program will provide a demand data (price/quantity relationship) from which demand elasticities, calibration prices and quantities, and demand shift parameters can be estimated.

Traditional optimization models such as linear programming rely on data based on observed average conditions (e.g., average production costs, yields, and prices), which are expressed as fixed coefficients. As a result, these models tend to select crops with the highest average returns until resources (land, water, capital) are exhausted. The predicted crop mix is therefore less diverse than we observe in reality. The most widespread reason for diversity of crop mix is the underlying diversity in growing conditions and market conditions. Simply put, any crop-producing region includes a broad range of production conditions. All farms and plots of land do not produce under the same, average set of conditions; therefore, the marginal cost and revenue curves do not coincide with average cost and revenue curves.

Economic theory suggests that economic decisions are based on marginal (incremental) conditions, and that these differ from the average conditions. Positive Mathematical Programming (PMP) is a technique developed to incorporate both marginal and average conditions into an optimization model (Howitt 1995). In the conventional case of diminishing economic returns, productivity declines as output increases. Therefore, the marginal cost of producing another unit of crop increases as production increases and the marginal cost exceeds the average cost. The PMP technique uses this idea to reproduce the variety of crops observed in the data.

Two alterative mathematical approaches will be explored:


Progress/Completion Report, PDF

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