Fuel, crop, and water substitution in irrigated agriculture

RESOURCE

and ENERGY

ELSEVIER

Resource and Energy Economics 18 (I 996) 311-33 i

ECONOMICS

Fuel, crop, and water substitution in irrigated agriculture Brian K. Edwards

a, * ,

Richard E. Howitt b, Silvio J. Flaim c

a The Law and Economics Consulting Group, lna, One Rotary Center, 1560 Sherman Avenue, Suite 1260, Evanston. IL 60201. USA b Department of Agricultural Economics, Universi~ of California at Davis, Daris. CA 95616, USA c International Energy Agency, Organisationfor Economic Cooperation and Development, 2 rue Andre-Pascal; 75775 Paris Cedex 16, France

Received 15 February 1995; accepted 6 June 1996

Abstract

This paper examines how changes in electricity costs can alter input use in farming and the resulting composition of output. The agricultural sectors of ,wo states, Arizona and Colorado, are modeled using nonlinear optimization methods to estimate responses to changing relative fuel costs. Simulation results suggest that farmers respond systematically to increases in electricity costs, and do so in ways that involve three areas of change: (1) the substitution between water and other inputs; (2) the crop allocation on irrigated land; and (3) changes in the total irrigated area. For both states, higher electricily prices lead to reductions in water use, with most of these reductions accounted for by reductions in electrically pumped groundwater use, with own-price own-price elasticities on the order of --0.64 and - 0 . 6 8 for Arizona and Colorado, respectively, a result comperable to estimates obtained econometrically elsewhere. The results also confirm complementarity between energy and irrigated land and substitutability between energy and dryland acreage. JEL classification: Q I I; Q4 Keywords: Energy costs; Irrigated agriculture; Input substitution; Calibrated regional model

* Co~: . . . . Jding author.

0928-7655/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0928-7655(96)0001 1-5

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1. Introduction

Much of the agricultural activity in the western United States depends on irrigation supplies. Virtually all agriculture in Arizona and Nevada is irrigated while in other western states, such as Colorado and New Mexico, irrigation methods are combined with dryland cropping practices. In the seven southwestern states, irrigated agriculture accounts for 31 percent of the cropped area and over 40 percent of the gross value of production. The water used for irrigation comes mainly from surface water and groundwater. Most surface water is purchased outright from off-farm sources, but some farms have ponds and lakes to store water for irrigation. ~ Groundwater sources require pumping from wells and about 80 percent of the irrigation pumps are electrically powered, while diesel fuel and natural gas power most of me rest. 2 This suggests that electricity is an important input in irrigated farming, and that changing electricity costs can affect input use and crop output in bo~h irrigated and dryland agriculture. The purpose of this paper is to take a closer look at the roie played by fuel costs in agricultural production. In particular, this paper examines how changes in electricity costs can alter input use in farming and the resulting composition of output. The agricultural sectors of two states, Arizona and Colorado, are modeled using nonlinear optimization methods to estimate how the fanning sector responds to changing relative fuel costs. The results of these simulations suggest that farmers respond systematically to increases in electricity costs, and do so in ways that involve three areas for change: (1) the substitution between water and other inputs; (2) the crop allocation on irrigated land; and (3) changes in the total irrigated area. Moreover, the results of these simulations suggest that economic and environmental policies that change relative fuel prices can have significant regional impacts that extend beyond the residential and commercial sectors to the agricultural sector. Section 2 discusses the motivation for examining electricity use in irrigated agriculture and describes previous research in this area. Section 3 presents the CES production functions (Sato, 1967) for dryland and irrigated -agriculture. Section 4 follows with a discussion of the constrained optimization farming sector model. Section 5 lays out the empirical specification of the model, Section 6 presents the results of the analysis, and Section 7 presents some conclusions and suggestions for future research. Finally, an appendix to this paper describes the first stage of our approach in more detail.

I Such dams are one example of on-farm sources of surface water. According to Agricultural Statistics and Water Use (1992), of 247,189 irrigated farms in the United States, 41,753 (16.9) percent used on-farm sources in 1988. 2 The Farm and Ranch Irrigation Survey indicates that of the 19,032 irrigation pumps used in Arizona and Colorado, 15,605 were electrically powered, 985 were diesel powered, and !,443 were powered by natural gas (United States Department of Agriculture, 1988).

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2. Motivation, previous work, and overview of method Many factors can cause prices for individual fuels to change, or cause prices for all fuels to change together, including unanticipated reductions in the availability of particular fuels, extended periods of unusuaUy warm or cold weather, and deregulation of electricity and natural gas markets. More stringent environmental policies can also change relative fuel prices. Some state utility commissions require energy utilities to incorporate environmental externalities into utility capacity planning decisions. The intention of such requirements is to alter relative energy prices in a way that discourages use of more polluting fuels. The discussion of policy responses to the potential global warming effects of CO 2 emissions has included carbon taxes that increase the cost of coal-generated electricity by a greater proportion than other fuels, such as oil and natural gas. Stabilizing emissions of CO 2 could require carbon taxes as high as $300 per ton, leading to significant increases in electricity prices. 3 Along different lines, policies designed to mitigate the environmental effects of operating dams may ultimately increase the cost of hydroelectric power. 4 To the extent that such cost increases encourage consumption of thermally generated electricity, policy initiatives designed to address the negative downstream environmental effects of hydroelectric power generation will have their own environmental impacts~ namely increased emissions of SO 2 (an acid rain precursor) and NO,, (an ozone precursor). Finally, deregulation of bulk power markets could reduce electricity prices to all sectors, including agriculture. Such reductions could affect the envirom~ent by encouraging electrical irrigation in place of surface water use and result in faster depletion of groundwater aquifers. While the emphasis of this paper is on electricity price increases, it must be pointed out that systematic decreases in electricity prices are also possible in the near future which could, if large enough, have profound effects on irrigated agriculture and groundwater use. For irrigated agriculture, higher electricity costs can affect farming activities through at least four levels of substitution. First, higher electricity costs increase the cost of irrigated tanning, ~¢lative to dryland farming. As such, higher electricity costs can lead to movement of less water-intensive crops to dryland acreage. Second, the distribution of planted acreage between different parcels of land will depend on their relative returns to water on irrigated l~d. Third, higher

3 For example, the IEA's World Energy Outlook found it necessary to increase carbon taxes by $300 per ton of carbon just to stabilize energy-related greenhouse gas emissions at 1990 levels by the year 2000 (Organisation for Economic Co-operation and Development, 1994). Dower and Zinmlerman (199i) discuss the economic consequences of ca,~on taxes. 4 Much of the electricity provided to the irrigation districts in Arizona, for example, comes from hydroelectric power generated by dams operated by the Western Area Power Administration, United States Department of Energy. This power is typically sold to Western's customers at rates that are far below current market prices for electricity.

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electricity costs can cause electrically pumped irrigation methods to be more expensive than surface water sources. For the same portfolio of planted acreage, this would favor the use of surface water. Along similar lines, higher electricity costs increase the costs of using electrically pumped groundwater, relative to pumping methods that rely on other fuels, thereby encouraging farmers to substitute away from the former to the latter. Finally, the change in electricity costs will lead the farmer to reexamine the optimal balance of irrigated water to other inputs, such as fertilizer, pesticides, and capital inputs. In addition to these short term effects, longer term effects on the level and quality of groundwater are possible, a topic addressed recently by Dinar (1994). It is well documented that changing energy prices can have profound effects on economic behavior, at both the microeconomic and macroeconomic levels. In terms of it~ role in agriculture, many studies have examined energy intensity (e.go, Gopalakrishnan and Yanagida, 1986; Gopalakrishnan, 1987) and substitution between energy and other inputs (e.g., Lopez and, Tung, 1982; Ray, 1982). For example, Gopalakrishnan et al. (1989) estimated ;:~wn- and cross-price elasticities and Allen partial elasticities of substitution between energy, land, labor, and capital, and found that input use falls with higher input prices and that capital and energy ate substitutes while land and capital are complementary, as are labor and capital. Other studies that have addressed the role of energy costs in agriculture include Adams et al. (1977), Edwards et al. (1995), Mapp and Dobbins (1977), Sloggett and Mapp (1984), Whittlesey (1986) and Whittlesey ~nd Herrell (1987). A number of non-econometric approaches to modeling agricultural input substitution have also been used, including those that rely on linear programming methods. 5 Although these methods have proven useful in examining many issues relating to farm opera~iions, these methods can carry the burden of fixed proportionality assumptions on inputs used in production. The approach taken here avoids some of these restrictions by using constant elasticity of substitution (CES) production ftmctions. However, the approach taken in this paper will not dispense with linear programming methods altogether. Instead, we will combine linear and nonlinear programming methods into what is called the Positive Mathematical Programming (PMP) method. This approach uses a two-stage process to solve the constrained optimization problem faced by the farmer. The first stage solves a linear programming problem to calibrate the parameters in the model exactly to actual data on acreage allocations between crops, levels of water and other input use, and the resulting outputs of each crop. In doing so, we obtain enough information about production to construct cost functions that ~ e nonlinear in the land input. The second stage of this approach solves the nonlinear programming problem that includes the nonlinear cost functions constructed from the results of

5 In a study with similar objectives, Majoro (1990) uses linear programming methods to examine the response of irrigated agriculture in the Pacific Northwest to rising electricity prices.

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the first stage. Details of this approach beyond those in the appendix to this paper can be found in Howitt (1995a,b). Despite the emphasis on nonlinear programming methods inherent in the PMP approach, we exploit some of the advantages of linear programming techniques. Linear programming models of agricultural production typically assume that inputs are used in fixed proportions to the acreage allocaticn. However, linear programrning methods, as applied to farm planning problems, assume that the regional data used to specify these models are representative of marginal farm production and cost functions. Under the assumptions used in linear programming, behavioral responses to policy actions which should be based on marginal conditions are in reality based on observations of average cost and average returns.

3. Dryland agricultural production We focus on cropping activities involving seven crops (barley, corn grain, corn silage, cotton, hay, sorghum, and wheat) commonly grown on dryland and irrigated acreage in western states. Dryland farming does not involve the use of any surface water or groundwater while irrigated farming will use either, or both simultaneously. According to our specification, dryland production depends on land, capital, chemical, and other inputs, which we group into two nests. The first nest is land, which is disaggregated by crop but n Jt further subdivided into other components (sub-nests). The second nest is for capital, chemicals (fertilizer and pesticides), and other variable inputs. Aggregatin.,g the variable inputs as xiv, we express the CES production function top nest for crop i as Yi "- Ci[ ~iL X?L "[- BiV X~/ ] 3¢t.

(1)

In Eq. (l), C~ is the top-nest scale parameter, fli~ is the top-nest share parameter for land used to produce crop i, and fliv is the top-nest share parameter for variable inputs applied to produce crop i. These will represent the share of inputs from each top level nest, i.e., land and variable inputs, used to produce each crop. Further, we define r/t = l / ( l - st), where s t is the top-level elasticity of substitution. Finally, we define % = l/rlt, where rl~ equals the elasticity of substitution between the land and variable inputs. The variable inputs for dryland cropping (capital, chemicals, and other) are allocated by their own lower nest CES function, given by

xi v - A,v[ flij x~,i, + fl,j2x~ + fli, x~,; ] ~"

(2)

In Eq. (2), we index the variable factors by Jk, with k = capital, chemicals, and other variable inputs, respectively. We define A~v as the sub-nest scale paramet_er. The /3~j coefficients are analogous to those defined in the first equation, and are the sub-nest share parameters for the variable inputs. We define T/iv = 1/(1 - s w ),

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where s w is the variable input elasticity of substitution and, as before, 7iv = 1/7/~ v. When we substitute this equation into Eq. (1), and apply the appropriate summation over the variable inputs~ we obtain the following nested CES production function for dryland crop i: j

1'1,1 ~''

AivE( [3ijx~'")3"v[ l

Yi -" Ci [

(3)

Farmers are assumed to maximize net revenues subject to the above production function (for dryland farming) and constraints on land and other input availability. The water is not a direct factor input for dryland production. However, one of the results of this study is that dryland output is sensitive to changes in electricity costs through substitution across cropping practices.

3.1. Irrigated agricultural production The first and second nests for irrigated farming are identical to those for dryland farming, namely land and variable inputs. The third nest is for water, which contains three water inputs (surface water, electrically pumped groundwater, and non-electrically pumped groundwater). The third water nest is as follows: ~ '1'1. -~. Pir2X~r~ /') Xi W ---Ai W i [JirlXi,~[ ~, 1"1r3t'4"''r3Y~']ir"Yi,,

(4)

In Eq. (4), we index the water inputs (surface water, electrically pumped groundwater, and non-electrically pumped groundwater) with r k. We define the parameters for the variable inputs analogously to those defined for dryland production. Substituting this additional nest into the irrigated agriculture analog of Eq. (1) yields the following nested CES production function for irrigated agriculture:

Yi=q[#i, xTL+#iv

J

Air E ( flijx~ "')v''' j=l

-]" [3i W A i w E ([3irX?~') ~/ir

.

(5)

r=l

To complete our specification of irrigated production, define fliw as the top-nest share parameter for water inputs and Aiw as the sub-nest scale parameter for water inputs for crop i. Finally, define r/i r equal to 1 / ( 1 - s i r ) (with sir = water input substitution elasticity), and 7ir equal to 1/rlir.

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4. The op.timization problem for irrigated and dry land agriculture We make the usual assumptions of optimizing behavior for farmers, in that they choose the crop mix and input combinations for each crop that maximize profits. In addition, we assume that the individual regions modeled are smell enough that changes in their purchases or sales will not influence the market price for products or inputs. If these considerations did not hold the model could be mc~iifie.d by addition of the appropriate supply and demand functions. The production function specified in Eq. (5) gives four margins of adjustment to the farmer faced with increased costs of one source of energy. First, the balance between irrigated and dryland production is determined by the marginal profitability of irrigated production. Second, within the irrigated production acreage, the ratios of irrigated crops grown will depend on their marginal returns to water or irrigated land, whichever is the scarcer. Third, the nested production function specification allows us to consider two additional margins of adjustment within the irrigated production nest. As the marginal cost of one source of water, say electrically pumped supplies, changes there is a trade off between water from different sources or water pumped using different energy sources. Finally, the optimizing farmer will reexamine the optimal balance of irrigated water to other inputs given the change in costs. One practical avenue of adjustment would be to increase the capital investment in irrigation technology or management, thus 6 allowing the same production per acre from a smaller amount of applied water. The case of fuel switching from electrical power to diesel or natural gas within the irrigated crop production sector is modeled by the elasticity of substitution in the 'water' nest and depends on the nature of power contracts and the capital requirements needed to switch. Likewise, the potential for substituting other variable inputs for water depends on farmer expectations on the duration of the electricity cost increases. Data on the baseline values for most variable inputs were not available on a regional and crop basis, consequently the initial crop specific variable input "allocations were determined in proportion to the crop land allocation. It should be noted that the production function in Eq. (5) is characterized by consent :eturns to scale for a constant quality of land. The basis for the increasing cost of production as regional land allocation to a given crop increases is primarily in the changing quality of the available land. 7 Farmers know which are the most suitable fields for a given crop and allocate production to them on that basis. Other

6 We can also take a portfolio management view of the farmer, iN which case they would divide a portfolio of land between alternative crops A dynamic analysis that adopted this view would then allow us to consider crop rotation, including leaving plots fallow, as part of a long run maximization problem. 7 This was first formalized by Ricardo (1971, first published in 1817), but has long been recognized by farmers, agronomists, and soil scientists. See Peach (1993) for a more recent discussion.

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factors such as risk and timing and machinery constraints may also contribute to the increasing costs of production. In this specification, the land cost functions are quadratic in land, and yields are held constant at the average base data level. An empirical policy model should reflect the current farm production decisions, the constraints on land and water, the varying quality of land and the ability to substitute input and output combinations. A full multi-output econometric specification is the traditional empirical approach, however given the meager data base usually available on a regional basis, we use a calibration method that uses prior estimates of elasticities of substitution, and a single cross section data set to derive model parameters that precisely calibrate to the aggregate production technology. The difference in calibrating partial equilibrium resource based models is that due to constraints on the resource base and other regional economic factors, the nominal input or rental prices cannot be assumed to clear the markets for the base year situation. For instance, the use of subsidized electric power for irrigation or surface water from a federal project is limited by the contracts and institutions for that project. Allocation of these inputs does not proceed as if the subsidized cost is the market clearing price, but rather, considers the opportunity cost of the subsidized inputs. Recovery of the correct technology from observed allocations requires that the nominal price and the opportunity cost are summed before being used to calibrate the production and cost functions. An empirical method that calculates these factor opportunity costs and uses them to calibrate regional agricultural production models using sequential models of constrained profit maximizing behavior are detailed in Howitt (1995a,b). This paper extends this calibration approach to a nested CES production function specification that enables the fuel switching elasticity of substitution to be differentiated from that of other inputs in the crop production process as shown in Eqs. (4) and (5). Calibration of the effect of differing land quality anti-other cost increasing factors is achieved by using the dual values on crop lana aUocations calculated in the initial linear model stage to derive a quadratic cost function. The cost function is nonlinear in land allocated to a particular cropping activity and is contained in Eq. (6). The calibrated CES model that is used to simulate the effects of higher electricity cost on both irrigated and dryland agriculture is presented in Eqs. (6)-(8). The objective function in Eq. (6) maximizes net returns to the farmer's land and management, taking into account the nested production function. The nonlinear land allocation costs and the fixed nominal prices of other inputs and resource constraints: H-. Epici, il I

yi, + EP,2Ci2 Yi 2 i2 I J

-- E [ OliXiL "Jr"0.5"YiX2L] -- E E C j X i j i i j

ii R - EECrXilr il r

(6)

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The first line of Eq. (6) is gross revenues to irrigated and dryland farming and reflects the production from Eq. (5) for irrigated areas and from Eq. (3) for dryland production. We have indexed irrigated crops by ij and dryland crops by i 2. T h e first term in the second line is the cost function for the land input which use the a i and yi that we calculated from the results of the first stage linear programming problem. The second term in this line represents the variable input costs where the prices of each variable inputs are cj. The variable inputs are the same under both cropping practices; hence the same j index is used for both. The final term is for water costs, which are divided between surface, electrically pumped groundwater, and nonelectrically pumped groundwater. The unit costs of each type of water are given by c r. The simulations that form the basis of our analysis will be driven by electricity rate increases that increase the cost of electrically pumped groundwater to the farmer. Since we assume that outputs are identical under both cropping practices, e.g., a bushel of irrigated wheat is identical to a bushel of dryland wheat, crops receive the same price p~, regardless of cropping practice. The individual crop prices were indexed by cropping practice to maintain notational consistency, so that Pi~ = Pi2 for each i. The discussion of Eqs. (1)-(5) above describes the remaining parameters of Eq. (6). Eq. (6) is maximized subject to J constraints for each variable input, each of which is expressed as !

!

]~,xij < ]~.,x~ i=i

(7)

i=1

and R constraints for each water input, each of which is expressed as i

i

Ex,;. i=1

(8)

t=!

The x 0 and x~r correspond to the constraints on each variable and water input. The parameters used to convert the linear cost function used in the first stage to a nonlinear cost function, namely a i and T~, are calculated from the first stage linear programming problem. The details of the first stage of the PMP approach are presented in Appendix A.

5. Empirical specification To exami Je the role of changing electricity costs in agriculture, we examine agriculture in Arizona and Colorado as our case studies. Arizona relies on irrigation for virtually all of its agricultural crop production. As a result, the impacts of higher electricity costs there will be restricted to substitution between surface and groundwater methods, substitution between electricity and other energy sources for pumping groundwater, and resulting impacts on irrigated crop

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production. By way of contrast, the vast majority of wheat and most sorghum in Colorado are grown on dryland acreage. Including Colorado in our analysis allows us to capture substitution across cropping practices. The possibility of switching between irrigated and dryland cropping practices allows for the examination of an additional hypothesis, albeit superficially, about the relative impacts of higher electricity costs on agriculture. Moving crops from irrigated to dryland agriculture, as is possible in Colorado, leaves farmers with an additional means of responding to liigher electricity costs. Increases in electricity costs can lead farmers to move less water-intensive crops to dryland acreage. As a result, some of the loss due to increased pumping costs will be offset somewhat by additional revenues from increased dryland farming. However, one cannot expect farmers to be able Lo i-ecover all losses to irrigated farming. On the contrary, full recovery of losses could be interpreted as evidence that their decisions before the increase in electricity costs were less than optimal. As a result, we exFect net losses to Colorado agriculture, despite opportunities to offset some of these Josses. In contrast, farmers in Arizona will have to rely on substitution between g~ound and surface water at one level, between electricity and non-electricity energy inputs on another level, and between land, water, and other inputs on still another level when facing higher electricity costs. No dryland substitution possibility exists at prevailing prices, so we might expect net profits to be more sensitive to a given increase in electricity costs in Arizona than in Colorado. The effect of higher electricity costs in either state will depend on additional factors omitted from the model, however. The results of this analysis provide some tests of the sensitivity, but are not exhaustive. This analysis examines three magnitudes of electricity cost changes. The first is a low electricity cost increase of 2.5 percent, the second is a medium cost increase of 5 percent, and we consider high electricity costs changes of 10 percent. This range of cost changes allows us to examine the extent to which marginal impacts increase with larger increases in electricity costs. Since the analysis is not dynamic, the long term response to higher electricity costs is not examined in this paper. Moreover, the extent of, and the means through, which agriculture could partially absorb electricity cost increases over time is not addressed. We confine the analysis to short term impacts of a one time increase in the cost of electricity. Finally, the combination of static and state-level analysis precludes consideration of how increases in electricity costs would result in regional differences in crop or the quantity and quality of groundwater. The analysis is performed for 1990, since acreage, yield, and input data for this year are relatively complete. 8 The base year data includes acreage allocations for

s The model could be extended to analyze how impacts charJge over time, given projections of baseline values for inputs, outputs, and prices for both inputs and outputs, but this analysis is clearly beyond the scope of this paper.

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each crop and cropping practice. !rrigated acreage is further divided by water source, i.e., between surface water and ~oundwater. Groundwater acreage is further divided between electrically pumped groundwater and water pumped using other energy sources. The other energy sources include natural gas, diesel, gasoline and gasohol, and propane and butane. For the analysis, we aggregated pumped acreage that used these other energy sources into one other category. To determine how much of each type of water was used, we first converted acreage into water use, using information on the water required for each crop (United States Department of Agriculture, 1988). Multiplying harvested acreage for each crop by this water requirement results in the acre-feet of water used by each irrigated crop. The next step was to divide water use for each crop into three water source categories. The split between ground and surface water was determined from the Farm and Ranch irrigation Survey which divided total irrigated acreage for each state into two categories,~ pumped and off-farm (surface water). These shares were used to divide water use between surface and groundwater. Since this survey also divides pumped acreage by energy source, we were able to estimate the shares of total pump irrigated acreage for each energy source. These shares were then applied to the acre-feet water requirements of each crop to determine the baseline quantities of each type of water applied to each crop. Implicit in this approach are two caveats. The first is that water requirements for each crop are independent of the source of water used. The second is that the water requirement of each crop remains relatively constant throughout each state, despite intra-state differences in climate and soil quality. Primary cropping data was obtained from the individual state agriculture departments and annual state agricultural statistics reports. 9 These publications typically contain data on acreage for each crop (by cropping practice), yields per acre, and output of each crop, as well as other economic and financial information on farm activities at the state and county !evels. In addition, these publications included prices for each crop (usually, an average of monthly prices for the year). Cost data was obtained from the United States Department of Agriculture that included unit costs for land, capital, chemistry, and other inputs.

6. Simulations and simulation results The results of this analysis are based on comparing the results of the baseline simulation described in the previous section with results of simulations with higher electricity prices. The tirst stage linear programming problem is used to generate the baseline simulation, and assumes no change in electricity prices. This stage also calibrates the model t~ the observed base year values of inputs and outputs.

9 Arizona Agricultural Statistics Service (1991) and Colorado Agricultural Statistics Service (1991).

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The baseline electricity prices are transformed by the percentage changes under each scenario to determine the electricity prices used in the second stage. The impacts of higher electricity prices on irrigated and dryland agriculture are measured by differences in the results between the baseline and simulations. Generally, the results indicate that crop and acreage substitution occurs even for fairly small increases in electricity prices and the extent of substitution between inputs increases in proportion to the electricity cost increases. Moreover, a given increase in electricity costs appears to have a larger impact on net revenues in Arizona than in Colorado, suggesting that the presence of dryland acreage allows farmers flexibility in responding to higher electricity costs. For both states, higher electricity prices lead to reductions in water use, with most of these reductions coming from reductions in electrically pumped groundwater use. A 10 percent increase in electricity costs reduces overall water use by 2.7 percent in Arizona and by 3.3 percent in Colorado, as shown in Tables 1 and 2, respectively. Use of electrically pumped groundwater falls by 6.4 percent in Arizona and by 6.8 percent in Colorado, implying own-price elasticities on the order of - 0 . 6 4 and -0.68 for Arizona and Colorado, respectively. This is comparable to estimates ranging from -0.6335 obtained by Gopalakrishnan et al. (198 q) to - 0.8481 obtained by Gopalakrishnan (1987) for the own-price elasticity of energy. In terms of acre-feet, electrically pualped groundwater use falls by 99,815 acre-feet in Arizona and by 142,367 acre-feet in Colorado. A 10 percent increase in energy costs actually increases barley acreage by 18.2 percent, or by about 2,729 acres. This increase in barley acreage is offset by reductions in acreage to the other crops, with reductions in cotton acreage accounting for 1,260 acres and hay accounting for a reduction of 1,193 acres. Most of the remaining reduction in acreage comes from corn silage, which loses 190 acres. While the water requirements of cotton are clearly the highest of all the crops considered in this study, suggesting that farmers might substantially reduce cotton acreage, the higher net return to water used on cotton ensures that large amounts of acreage remain in cotton. Statewide reductions in net revenues to these crops are small in percentage terms under all three scenarios. Even when electricity costs increase by 10 percent, net revenues fall by 1.95 percent, which amounts to about $3.3 million. Reductions in net revenues to cotton and hay account for nearly $3.0 million of this loss, while losses to wheat account for most of the remainder. The results for Arizona are presented in Table 1. For Colorado, reductions in total irrigated acreage will be exactly offset by increases in dryland acreage, leaving the total amount of land allocated to farming (the sum of irrigated and dryland acreage) unchanged. As can be inferred from Table 3, a 10 percent increase in electricity costs causes 16,557 irrigated acres to be moved into dryland acreage. This amounts to 0.67 percent of irrigated acreage, implying a cross-price elasticity of -0.067, which suggests some degree of complementarity between energy and irrigated land. The 0.56 percent increase in dryland acreage implies a cross-price elasticity of 0.056, suggesting substitutability

472,000 19Y.000 1,000 98,000

3,720,100 1,863,063 1,550,475 306,562

Water use (acre-feet) Surface water G r o u n d w a t e r electric Ground,~v~;ter other

555,146,237 4,411,260 3,305,344 4,536,000 366,825,000 i 37, ! 26,500 6,891,039 32.051,094

167,020,876 581,744 626,439 532,001 124,179,854 27,564,451 120,536 13~415,851

Output (Dollars) B,',,rley Corn grain Corn silage Cotton Hay Sorghum ~'heat

Net revenues (dollars) Barley Corn grain Corn silage Cotton Hay Sorghum Wheat

7,000 8,000

796,000 ! 5,000

Irrigated acreage (acres) Barley Corn grain Corn silage Cotton Hay Sorghum Wheat

Baseline

166,184,642 599,923 619,037 520,729 123,644,040 27,33 I, 184 119,796 13,349,933

553,499,727 4,627,254 3,281,837 4,474,592 365,863,827 136,427,5 i i 6,865,282 31,959,423

3,694.342 1,863,545 1,524,180 306,617

796,000 15,698 6,985 7,951 471,679 ! 94,694 1,000 97,994

L o w (2.5%)

-- 0.50 3. i 2 - 1.18 - 2.12 - 0.43 - 0.85 - 0.61 - 0.49

- 0.30 4.90 - 0.7 i - 1.35 - 0.26 - 0.5 i - 0.37 - 0.29

- 0.69 0.03 - 1.70 0.02

-

0.00 4.66 0.21 0.62 0.07 0.16 0.03 0.01

% Deviation

! 65,362,999 616,886 611,810 509,826 123,117,489 27,102,776 119,070 13,285,143

55 !,932,869 4,796,333 3,259,867 4,415,897 364,970,745 135,763,293 6,843,969 31,882,764

3,669,088 1,863,736 1,498,726 306,626

796,000 16,382 6,971 7,903 47 ! ,364 194,394 999 97,988

M e d i u m (5%)

Table 1 Selected inputs, outputs, and percentage deviations from baseline for Arizona: Irrigated crops

- 0.99 6.04 -2.34 - 4.17 - 0.86 - 1.67 - 1.22 - 0.97

- 0.58 8.73 - 1.38 - 2.65 - 0.51 - 0.99 - 0.68 - 0.53

- 1.37 0.04 - 3.34 0.02

-

0.00 9.21 0.42 1.22 0.13 0.31 0.06 0.01

% Deviation

163,758,3555 648,375 597,790 488,958 122,088,5800 26,658,697 1 i7,650 13,158,306

548,860,5644 5,121,939 3,216,974 4,302,617 363,219,5566 134,465,6822 6,802,072 31,731,723

3,621,223 1,863,948 1,450,659 306,616

796,000 17,729 6,942 7,810 470,740 193,807 999 97,973

High (10%)

- 1.95 I l.a5 -4.57 - 8.09 - 1.68 - 3.29 - 2.39 - 1.92

- 1.13 16.11 - 2.67 - 5.15 - 0.98 - 1.94 - !.29 - ~,.00

- 2.66 0.05 - 6.44 0.02

0.00 18.19 - 0.82 - 2.37 - 0.27 - 0.61 - O. 12 - 0.03

% Deviation

I

oo

,,,,.

4,912,894 66,244,531 7,660,168 195,072,334 8,419,764

27,633,486

Wheat

309,943,179

27,048,000

9,894,000

694,656,689 35,185,000 298,802,500 56,209,689 267,517,500

Barley Corn grain Corn silage Hay Sorghum

Net revenues (dollars)

Wheat

Sorghum

Output (dollars) Barley Corn grain Corn silage Hay

354,889

2,140,098

G r o u n d w a t e r electric

G r o u n d w a t e r other

2,105,284

Surface water

4,600,271

113,335 1,200,000 64,000 181,500

Corn silage Hay Sorghum Wheat

W a t e r use (acre-feet)

126,000 804,000

2,488,835

Barley Corn grain

Irrigated acreage (acres)

Baseline

27,582,891

4,850,371 65,629,241 7,567,932 194,505,332 8,392,970

308,528,736

27,000,388

9,867°876

691,283,582 34,897,782 296,905,490 55,761,253 266,850,792

354,535

2,101,329

2,104,596

4,560,460

112,903 1,199,061 63,947 181,428

125,509 801,695

2,484,543

L o w (2.5%)

0.49 0.82 0.63 0.80 0.25

1.27 0.93 1.20 0.29 0.32 - 0.18

-

- 0.46

- 0.18

- 0.26

-

- 0.10

- 1.81

-0.03

- 0.87

- 0.38 -0.08 - 0.08 -0.04

- 0.39 - 0.29

- 0.17

% Deviation

27,533,509

4,789,728 65,028,719 7,478,097 193,950,049 8,366,777

307,146,878

26,971,645

9,849,168

688,374,686 34,639,323 295,194,016 55,344,536 266,375,998

354,187

2,064,153

2,103,924

4,522,265

112,484 1,198,155 63,896 181,360

125,038 799,456

2,480,389

M e d i u m (5%)

Table 2 Selected inputs, outputs, and percentage deviations f r o m baseline for Colorado: Irrigated crops

0.90 1.55 1.21 1.54 0.43

2.51 1.84 2.38 0.58 0.63 - 0.36

-

- 0.90

- 0.28

- 0.45

-

- 0.20

- 3.55

-0.06

- 1.70

- 0.75 -0.15 - 0.16 -0.08

- 0.76 - ~.57

- 0.34

% Deviation

27,436,932

4,672,554 63,862,921 7,304,238 192,865,698 8,315,638

304,457,981

26,915,371

9,812,588

682,706,223 34,137,545 291,858,967 54,534,177 265,447,575

353,480

1,994,029

2,102,480

4,449,988

111,666 1,196,382 63,796 181,227

124,122 795.085

2,472,278

High (10%)

1.72 2.98 2.32 2.98 0.77

4.89 3.60 4.65 1.13 ! .24 - 0.71

-

- 1.77

- 0.49

- 0.82

-

- 0.40

-6,83

-0.13

- 3.27

- 1.47 -0.30 - 0.32 -0.15

- 1.49 - 1.11

- 0.67

% Deviation

I

oe

q~

e~

238,362,211 2,015,000 3,525,000 663,111 34,980,000 11,199,600 185,979,500

158,290,715 236,951 928,171 92,984 20,852,675 6,704,938 ~29A74,996

Net revenues (dollars) Barley Corn grain Corn silage Hay Sorghum Wheat

2,968,165 24,000 26,000 3,665 350,000 156,000 2,408,500

Output (dollars) Barley Corn grain Corn silage Hay Sorghum Wheat

Dryland acreage (acres) Barley Corn grain Corn silage Hay Sorghum Wheat

Baseline

! 58,481,207 247, ! 13 929,907 93,257 20,873,8 ! 7 6,714,9 i I 129,622,201

238,495,742 2, !90,894 3,526,926 664,382 34,962,595 11,199,328 185,951,617

2,972,457 24,918 26,049 3,676 350,353 ! 56,231 2,411,230

Low (2.5%)

0. i 2 4.29 0.19 0.29 0. I 0 0.15 0. ! 1

0.06 8.73 0.05 0. ! 9 - 0.05 -0.00 -0.01

0.14 3.83 0. ! 9 0.30 0. ! 0 0.15 0. i !

% Deviation

158,672,546 253,736 931,702 93,543 20,895,493 6,725,183 129,773,889

238,834,354 2,249,615 3,533,733 666,423 34,998,901 11,216,459 186,169,223

2,976,611 25,586 26,099 3,687 350,716 156,470 2,414,052

Medium (5%)

Table 3 Selected inputs, outputs, and percentage deviations from baseline for Colorado: Dryland crops 0,56 12.04 0:76 1.21 0.4! 0,60 0,46 0.48 17.33 0.62 1.10 0.26 0.45 0.33 0.48 12.54 0.76 1.20 0.41 0.60 0.46

239.495,537 2,364,274 3,5~17,026 670,407 35,069.793 11,24~9,910 186.,594327 ~59,049,114 266,669 935,207 94,102 20,937,818 6,745,239 130,070,079

0.20 I 1 .~4 0.25 0.50 0.05 0.15 0.10 0.24 7.08 0.38 0.60, 0.21 '4',.30 0.23

% Deviation

2,984,722 26,890 26,197 3,709 351,427 156,937 2,419,562

High (10% )

0.28 6.61 0.38 0.60 0.20 0.30 0.23

% Deviation

b2

i too

OO

933,018,900 3Z200,000 302,327,500 56,872,800 302,497,500 21,093,600 213,027,500

468,233,893 5,149,845 67,172,703 7,753,152 215,925,009 15,124,702 157,1. 08,482

Net revenues (dollar~s'Y' Barley Corn grain Corn silage Hay Sorghum Wheat

4,600,271 2,105,284 2,140,098 354,889

Water use (acre-feet) Surface water Groundwater electric Groundwater other

Output (dollars) Barley Corn grain Corn silage Hay Sorghum Wheat

5,457,000 150,000 830,000 117,000 1,550,000 220,000 2,590,000

Total acreage (acres) Barley Corn grain Corn silage Hay Sorghum Wheat

Baseline

467,009,943 5,097,484 66,559,149 7,661,188 215,379,149 15,107,881 157,205,092

929,779,324 37,088,676 300,432,416 56,425,636 301,813,387 21,067,204 212,952,004

4,560,460 2,104,596 2,101,329 354,535

5,457,000 150,427 827,744 116,579 '. ,549,414 220,178 2,592,658

Low (2.5%)

-0.26 - 1.02 -- 0.91 - 1.19 -0.25 - 0.11 0.06

- 0.35 - 0.31) - 0.63 - 0.79 -0.23 - 0.13 - 0.04

- 0.87 -0.03 - 1.81 - 0.10

0.00 0.28 - 0.27 -0.36 - 0.04 0.08 0.10

% Deviation

465,820,425 5,043,464 65,960,422 7,571,640 214,845,542 15,091,960 157,307,398

927,209,040 36,888,938 298,727,749 56,010,959 301,374,899 21,065,627 213,140,868

4,522,265 2,103,924 2,064,153 354,187

5,457,000 150,624 825,555 116,171 1,548,872 220,366 2,595,412

Medium (5%)

Table 4 Selected inputs, outputs, and percentage deviations from baseline for Colorado: All crops

-0.52 - 2.07 - 1.80 -2.34 -0.50 - 0.22 0.13

- 0.62 - 0.84 - 1.19 - 1.52 -0.37 - 0.13 0.05

- 1.70 -0.06 - 3.55 - 0.20

0.00 0.42 - 0.54 -0.71 - 0.07 0.17 0.21

% Deviation

463,507,095 4,939,223 64,798,128 7,398,340 213,803,515 15,060,878 157,507,011

922,201,760 36,501,819 295,405,993 55,204,584 300,517,368 21,062,498 213,509,498

4,449,988 2,102,480 1,994,029 353,480

5,457,000 151,012 821,282 115,375 1,547,809 220,732 2,600,789

High (10%)

- 1.01 - 4.00 - 3.54 -4.58 -0.98 - 0.42 0.25

- 1.16 - 1.88 - 2.29 - 2.93 -0.65 - 0.15 0.23

- 3.27 -0.13 - 6.83 - 0.40

0.00 0.67 - 1.05 - 1.39 - 0.14 0.33 0.42

,

% Deviation

I

?

e~

?

t,J

B.K. Edwards et a l . / Resource and Energy Economics 18 (1996) 311-331

327

between energy and dryland acreage. For purposes of comparison, Gopalakrishnan et al. (1989) obtained a cross-price elasticity of 0.1702, indicating substitutability between energy and land. In terms of crop-specific effects on the land input, a l0 percent increase in the price of electricity causes acreage to all irrigated crops to fall and acreage to all dryland crops to increase, but by different proportions for each crop. The largest absolute reduction in irrigated acres is in corn for grain, which fall by 8,915 acres, or 53.8 percent of the reduction in total irrigated acreage. The next largest reduction in irrigated acreage comes from hay, which loses 3,618 acres, or 21.9 percent of the reduction in total irrigated acreage. Irrigated barley and corn silage together lost 3,547 irrigated acres, which amounts to 21.4 percent of the reduction in total irrigated acreage. The remaining reduction of 477 irrigated acres is accounted for by sorghum ann wheat. Over two-thirds of the acreage taken out of irrigation is moved into dryland wheat, which increases by 11,062 acres (0.46 percen0o Most of the remaining increases in dryland acreage is accounted for by barley (2,890 acres), hay (1,427 acres), and sorghum (937 acres). In contrast to Arizona, where use of less electrically pumped groundwater was associated with slight increases in surface water and non-electrically pumped groundwater use, surface water and non-electrically pumped groundwater use decline under all price change scenarios in Colorado. But these reductions are much smaller in both absolute and relative terms than those that occur for electrically pumped groundwater. This might be accounted for by farmers switching between cropping practices, an option not available to Arizona farmers at prevailing prices and costs. Net profits for all crops fall, but by smaller percentage amounts than the corresponding increases in electricity prices. Net revenues for all crops fall by $984,983 under the low electricity price change case (0.16 percent), and by $4,824,101 in the high electricity price change case (0.79 percent). These results are somewhat lower, in percentage terms, than those that occur in Arizona under all three scenarios, offering initizl evidence that the additional option of moving crops to d~land acreage gives farmers a small safety net against higher groundwater pumping costs. In terms of net revenue, this substitution between cropping practices helps to offset some of the losses that occur to irrigated agriculture, but is not nearly sufficient to offset all of the losses that occur. Net profits to dryland wheat alone increase by $759,888, but this gain is offset by large losses in net revenue from imgated corn grain and hay, which together account for nearly $4.6 million of the total loss of $5.5 million that occurs in irrigated agriculture as a whole. Tables 2-4 summarize tile results for the state of Colorado.

7. Summary and conclusions The results ,of this analysis suggest that energy costs play an important role in determining how farms allocate inputs between crops in arid regions. Although

328

B.K. Edwards ct M. / Resource and Energy Economics 18 (1996) 311-331

this analysis has been based on hypothetical increases in electricity costs, the results illustrate the extent to which substitution is possible and indicate the potential magnitude of input substitution, and the resulting effect on net revenues. These results also suggest that policy options that affect the energy sector can also have impacts on the farming sector, and that these impacts can be large enough to warrant individual consideration when alternative energy policy options are being considered. A case in point is the potential for increased envirt~omental regulation of the energy industry and policy options designed to conserve the use of water. A third poss~b~2"ty involves the future availability of hydroelectric power which, for Arizona, Colorado, and other western states, represents an important source of electricity for the farming s,~,ctor, especially for small utilities and imgation districts. Reductions in the availability of hydroelectric power could induce utilities to rely on other energy sources to satisfy end-user demand, which could have other offsetting environmental impacts. Future research in this area could go in many directions, but three possibilities come to mind. The first relates to the static nature of the analysis presented in this paper. One substitution possibility that has not been considered explicitly is selection of groundwater pumping technology. Consideration of this issue would require separate consideration of capital investment decisions on the part of farms. Presumably, farms would choose to purchase irrigation pumps based on the stream of expected net returns, which would include the cost of energy to operate the pumps. Similarly, improvements in the etticiency of existing electrical irrigation pumps could mitigate these impacts over time, but these improvements would most likely be reflected in the longer term net benefit decision that is made when replacement pumps are purchased. Along similar lines, the static nature of this analysis rules out consideration of other types of technological change, including improvements in fertilizers and pesticides, and the development of more droughtresistant crops. All we can do at this juncture is to speculate that increases in the cost of irrigated farming could provide additional incentives for research and development in these areas. Along different lines, an analysis at the statewide level involves making some strong assumptions about the yields and water requirements for each crop, namely, that statewide averages represent yields and water requirements in every region in the state. A cursory examination of county-level yields suggests that some intra-state variability in yields does occur. A less aggregate analysis would require study of individual regions of each state, and the regional distribution of agricultural activity and cropping practices.

Acknowledgements The authors appreciate comments from two anonymous referees and hereby absolve them of any responsibility for any remaining errors or omissions. The

B.K. Edwards et a l . / Resource and Energy Economics 18 (1996) 311-331

329

views and opinions expressed herein do not necessarily reflect any official position of the Law and Economics Consulting Group, Incorporated or the International Energy Agency, Organisation for Economic Cooperation and Development.

Appendix A. The linear programming stage of the positive mathematical programming approach The first stage of the PMP approach is to solve the following linear programming problem: 1

M a x / / = ~-,Pi Yi - ci x ;

( A.I )

i

subject to the following series of resource, water, and calibration constraints: Resource constraints (for each input j = l to J):

XiJ x* i=, XiL

~,xij. i=~j=,

(A.2)

Water constraints (for irrigated crops): I i=

R Xi r E ~Xi l r = I XiL

•

I R ~-~ ~ E X i r ° i = ir=

(g.3)

1

PMP calibration constraints (for each crop i = l to I): x/* < XiL + e for net profits > 0,

(A.4)

x/* >_ XiL -- e for net profits < 0.

(A.5)

For the objective function and constraints, define Pi as the price of ,'top i, Yi as the output of crop i, c~ equal to the linearized cost per acre of land, xi* as the acreage allocated to crop i, and e as the perturbation for the land input. In addition, define xij = quantity of input j applied to crop i and XiL = quantity of land applied to crop i. Finally, the per unit costs are aggregated up to a single per acre cost coefficient using the following equation: J

X0

c i = ~., cij ~ j= 1

(A.6)

"~iL

where ci = linearized cost for crop i and c~j = unit cost of input j for crop i. For dryland production, j = land, capital, chemicals, and other inputs. For irrigated production, j = land, capital, chemicals, surface water, electrically pumped groundwater, and non-electrically pumped groundwater. The solution to the above problem yields values for cropland and other inputs that are virtually equal to the baseline values of each input, and generate the outputs of each crop that correspond to actual production.

330

B.K. Edwards et al./ Resource and Energy Economics 18 (1996) 311-331

A linear programming problem specified without the e perturbations, as we have specified in Eqs. (A.4) and (A.5), would result in a degenerate solution and the resulting dual values would not be unique. The perturbation causes the land constraint to bind before the least profitable calibration constraint is binding. The dual values are therefore unique. As demonstrated in Howitt (1995a,b)~ the perturbation decouples the resource constraint set from the calibration constraints. In effect, the dual values on the calibration constraints are functions of the resource constraints, but the resource constraint dual values are not influenced by the calibration constraints. As a result, the opportunity costs of resources are used in the calibration process, but are not changed by it. What the PMP approach does is to tilt the average cost specification to one that is increasing in land, but retains the same average costs and results in the same optimal land allocation for the base year. Referring to the original form of our example, the PMP derivation calculates the a and 3' parameters used in Eq. (6) so that the average cost, objective function, and the dual on the land constraints are unchanged, but the marginal conditions calibrate to the base year land allocations without constraints. The revised cost function that is presented in Eq. (6) which, for crop i, is expressed as a i x i -0.53"ix 2, becomes the quadratic specification derived from the dual values on the binding calibration constraints. The actual problem was solved and simulations carded out with the GAMS/MINOS (Brooke et al., 1992) optimization software package.

References Adams, R.N., G. King and W. Johnston, 1977, Effect of energy cost increases and regional allocation policies on agricultural production, American Journal of Agricultural Economics, 444-455. Arizona Agricultural Statistics Service, 1991, 1990 Arizona agricultural statistics (United States Department of Agriculture, Washington, DC, and the University of Arizona, Tucson, AZ). Brooke, A., D. Kendrick and A. Meeraus, 1992, GAMS: A uers's guide (The Scientific Press, San Francisco, CA). Colorado Agricultural Statistics Service, 1991, Colorado agricultural statistics (United States Department of Agriculture, Washington, DC, and Colorado Department of Agriculture, Denver, CO ). Dinar, A., 1994, Impact of energy cost and water resource availability on agriculture and groundwater quality in California, Resource and Energy Economics 16, 47-66. Dower, R. and M. Zimmerman, 1991, The fight climate for carbon taxes: Creating economic incentives for protecting the atmosphere (World Resources Institute, Washington, DC). Edwards, B., S. Flaim, R. Howitt ~nd S. Palmer, 1995, Impacts on irrigated agriculture of changes in electricity costs resulting from Western Area Power Administratio~?s power marketing alternatives, ANL/DIS/TM-9 (Argonne National Laboratory, Argonne, IL). Gopalakrishnan, C., 1987, Energy-nonenergy input substitution in western U.S. agriculture: Some timings, The Enerby Journal 8, 133-145. Gopalakrishnan, C. and J. Yanagida, 1986, Energy intensity and factor substitution in western United States agriculture, In: N. Whittlesey, ed., Energy and water management in western irrigated agriculture (Westview Press, Boulder, CO). Gopalakrishnan, C., G.H. Khaleghi and R.B. Shrestha, 1989, Energy-non-energy input substitution in US agriculture: Some findings, Applied Economics 21, no. 5, 673-679.

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Howitt, k.E., 19~5a, Positive mathematical programming, American Journal of Agricultural Economics 77, May, 329-342. Howitt, R.E., 1995b, A calibration method for agricultural economic production models, Journal of Agricultural Economics 47, no. 2, 147-159. Lopez, R. and F. Tung, 1982, Energy and non-energy input substitution possibilities and output scale effects in Canadian agriculture, Canadian Journal of Agricultural Economics 30, no. 2, 115-132. Majoro, M., 1990, Response of Pacific northwest irrigated agriculture to rising electricity costs, Doctoral dissertation (Washington State University, Seattle, WA). Mapp, H.P. and C. Dobbins, 1977, The impact of increased energy costs on water use and agricultural output in the Oklahoma panhandle (Agricultural Experiment Station, Oklahoma State University, Stillwater, OK). Organisation for Economic Co-operation and Development, International Energy Agency, 1994, World energy outlook: 1994 Edition (OECD, Paris). Peach, T., 1993, Interpreting Ricardo (Cambridge University Press, Cambridge). Ray, S., 1982, A translog cost function analysis of U.S. agriculture, 1938-77, American Journal of Agricultural Economics 64, no. 3, 490-498. Sato, K., 1967, A two-level constant elasticity of substitution production function, Review of Economic Studies 34, 201-218. Sloggett, G.R. and H.P. Mapp, 1984, An analysis of rising irrigation costs in the great plains, Water Resources Bulletin 20, no. 2, 229-233. United States Department of Agriculture, 1988, Farm and ranch irrigation survey (US Department of Agriculture, Washington, DC). Whittlesey, N.K., ed., 1986, Energy and water management in western irrigated agriculture (Westview Press, Boulder, CO). Whittlesey, N.K. and J. Herrell, 1987, Impacts of energy cost increases on irrigated land values, Western Journal of Agricultural Economics 12, no. 1, !-7.