WATER RESOURCES RESEARCH, VOL. 25, NO. 7, PAGES 1461-1468, JULY 1989 Some Further Evidence on the Derived Demand for Irrigation Electricity' A Dual Cost Function Approach JEFFERY D. CONNOR, J. DAVID GLYER, AND RICHARD M. ADAMS Departmentof Agricultural and Resource Economics, OregonState University,Corvallis Most cropproduction in the western UnitedStates is dependent on waterfrom irrigation, oftenusing substantial amounts of energyto obtain and apply suchwater. The sensitivity of crop production to rising energy costs is an issue of concern to producers, input suppliers, and others.In this paperthe effects of increasing electricity prices on electricity consumption and other production inputs are assessed usinga dual cost estimationprocedure.The empirical focus is on selectedregionsof the western United States where electricity is the primary source of irrigation energy. Demand for irrigation electricity varies across regions but is found to be price elastic. INTRODUCTION Information on the demand for and value of water in agriculturalproduction is important in addressing a range of policy issues. The provisionof water at priceswhich are less than full social costs in most water development schemes necessitatesallocation rules to distribute limited supplies. Rules, however, typically do not reflect actual demand. The use of water markets therefore frequently is proposed as an alternative to other allocation mechanisms. There is one componentof irrigated agricultural production that already reflects market forces. This involves the 40 million acres of land dependant on groundwater or other subsurface sources for irrigation. Farmers "produce" water for irrigation through expenditureson pumps, maintenance, and energy. Increasesin real energy prices, as occurred in the 1970s and 1980s, have a significant impact on producer profitabilityand hence usage of water in such a setting [Frederick and Gibbons, 1986]. Electricity is the energy source most commonly used to pump and distribute irrigation water. In the West, over two thirdsof the energyusedin irrigationis electricity;this figure approaches 100% in some regions of the Northwest [Torg- erson et al., 1987]. While the real prices of other energy sources decreased in the mid-1980s, in some regions the price of electricity continued to rise. Reasonsfor the con- tinued increasein electricity prices include growing internal- ization of environmental costs associated with electricity generation, the high cost of additions to capacity and the distribution of fixed costs over fewer units when demand for additional capacity proved more price elastic than was forecast. The present study focuses on electricity demands in a sampleof 16 countieslocated in eight western stateswhere producersrely on electricity to pump and distribute irriga- tion water. The overall objective is to measure variations in electricity demanded by these producers as a result of difference in prices, adjusting for acreage,irrigation capital, and well depth. A secondary objective is to explore the efficacy of a dual cost approachfor the analysisof irrigation demand. Results from this approach provide a benchmark for comparison with earlier demand studies that use alterna- Copyright 1989 by the American Geophysical Union. Paper number 89WR00462. 0043-1397/89/89 WR-00462505.00 tive techniques. This analysis is also useful in drawing implications aboutthe effects of changes in electricityprices on the welfare of producers, regional economies, and elec- tric utilities. For example, the responseof agricultural pro- ducers to increasing irrigation prices, as manifested in the estimated price elasticity of demand for electricity, has implicationsfor rate structures and revenues of electric utilities. BACKGROUND This study differs from past studies of irrigation demand by employing a dual cost function to measure producer response. While not previously applied in this setting, the dual cost approachhas been used widely in the analysisof derived demand for energy [Berndt and Wood, 1975; Lopez and Tung, 1982]and for water by water utilities [Teeples and Glyer, 1987].The techniquehas someadvantages over other approaches commonlyusedin studies of irrigation demand, such as linear programmingor "primal" econometric esti- mation. Unlike linear programming techniques applied to electricity demand [Whittlesey et al., 1986; Gardener and Young, 1984], dual cost methods do not require an a priori description of the matrix of feasible production technologies. This is an important consideration because substantial infor- mation is required to capture a realistic range of adjustments to risinginput prices within programming models. Consider- ation of an incompleterange of production activities has, in some instances, unrealistically constrained elasticity esti- mates [Chancellor and Johnston, 1986]. More importantly, by specifying fixed coefficients for production, programming models ignore the flexibility in production which may be capturedin actual observations of producerbehavior. This has been demonstrated by Despotakis and Fisher [1988], who compare simulations based on fixed-coefficient models with those obtained from duality-based estimates. Econometric techniques allow estimation of input de- mandsas functions of exogenously determined input prices, as well as levels of outputs and fixed factors. A full primal specification involves a series of steps, initiating with the direct estimationof a profit or cost function for the firm and subsequent solutionof optimal factor demand relationships. Typically, however, ad hoc primal applications are used; theseestimatedirectly the factor demand relationships with- out explicit linkage to optimizing behavior. In either case, primal-based econometric studies of the demandfor irriga- 1461