Document Type

Report

Publication Date

January 1972

Abstract

Although it is condeded that an adequate supply of water is essential to economic growth and development, what constitutes an "adequate" supply is often controversial and difficult to determine. The problem can be solved by applying basin economic concepts: determining the value of water be estimating its supply and demand. This report demonstrates one method for doing this. The theory of the demand for irrigation water and its empirical application are discussed. An example problem based on data from one of the sub-regions of the study area (the Jordan River Basin of Utah) is presented to illustrate the method. The example problem is solved under alternative assumptions and constraints to demonstrate the sensitivity of the estimated demand for irrigation water to various assumed parameters. Input-output relationships of the production and other activities in each of four sub-regions are estiamted using agricultural budgets. These are combined in a linear programming (LP) model for easy of computation. Constraints account for rotation possibilities and resource use. Primary resource inputs include land (by productivity blass in each sub-region) and irrigation water. The primal problem is one of resource allocation to utilize the available supplies of water and land to maximize net return. The dual LP problem is one of resource valuation and assigns shadow prices to the resources. Parametric solution of the dual at varying levels of water availability estimate the relationship between the quantity of water and its economic value, or a demand function. The dual of the LP problem representing irrigation possibilities in the Jordan River Basin is solved at each basis change as the availability of water is varied. Diverted water is valued at a maximum of approximately $14 per acre-foot. Consumptively used it has a maximum value of over $36. At present levels of irrigation diversions the shadow price falls to less than $3 for diverted water or $6 for consumptively used water. Supply functions for irrigation and municipal and industrical (M&I) water uses are estimated by using a previously developed LP model. Lower bounds are placed on wetland diversions and basin outflow. Both M&I and irrigation diversions are varied to determine their shadow prices at all feasible levels of water supply without increasing imports. The estimated cost of suplying M&I water varies from under $70 to over $236 per acre-foot. The cost of supplying irrigation water varies from $.52 to over $112 per acre-foot. The optimal allocation of resources is estimated by combining the supply and demand models into a single LP problem. (A graphical solution is also presented.) M & I diversions are set at estimated 1965 levels and parametrically increased. Additional M & I diversions are met through a slight reduction in irrigation diversions and by developing groundwater and recharging groundwater aquifers. The model indicates that more than double current M & I diversions can be supplied in this manner with little or no reduction in irrigation use. It is concluded that there is sufficient water within the Jordan River Basin to satisfy M & I needs through at least 1990 ir not to 1020 (depending on how fast M & I demand grows), even if irrigation diversions were maintained at 1965 levels. Additional inter-basin trasnfers are not an economical source of water now or in the forseeable future. Both transfers from irrigation and development within the basin appear to be more optimum methods of meeting increased M & I demands. This is neither exotic nor technologically difficult (and should be studied in greater detail) but it does appear to be a much cheaper solution to the Jordan River Basin's impending water problem than inter-basin transfers.

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