Modeling regional agricultural production and salinity control alternatives for water quality...

The Colorado River Basin drains 242,000 square miles of land in Wyoming, Utah, New Mexico, Arizona, Nevada, and California. Beneath basin soils lie vast deposits of salt left behind by prehistoric seas. Water development projects and irrigated agriculture have accelerated the rate at which these

naturally occurring salts are leached from the soil. Groundwater flows from irrigated agriculture and natural springs transport nine million tons of salt each year from basin soils to the Colorado River. River salinity is further concentrated by Upper Basin diversions, basin exports, and evaporation. Colorado River water is diverted many times for irrigation, municipal, and industrial uses, and becomes progressively more saline as it moves downstream. As a result of salt loading and salt concentrating, more than half of the basin's 3.1 million irrigated acres are classified as saline.(1) In the Lower Basin, river salinity is responsible for millions of dollars in annual crop losses, nonreclaimable soils, and added costs to municipal and industrial uses.

Water salinity reduces returns to irrigated production by lowering crop yields and increasing farm production costs. Applying more irrigation water, installing drainage systems, and planting salt-tolerant crops are among the alternatives available to farmers for mitigating the effects of rising water salinity levels, but when all the feasible alternatives are exhausted cropland can and has gone out of production. In municipal uses, salinity accelerates the deterioration rate of pipes, plumbing fixtures, and home appliances, and increases household expenditures for drinking water, soaps, detergents, and water treatment. In the industrial sector, water is used in food processing, chemical manufacturing, and as a coolant. The demand for water quality varies widely. In food processing, for example, the tolerance level ranges from 500 to 1,000 mg/l. As a coolant for a coal-fired power plant, salinity levels up to 10,000 mg/1 are tolerable. More frequent equipment replacement and outlays for water treatment are the primary costs to industries supplied by salty water.

Water quality in the Colorado River Basin exhibits the classic case of the downstream externality problem. Salinity impairs 63% of the irrigated acreage in the Lower Basin, yet 72% of the salt in Lower Basin river water originates in the Upper Basin. Legally, Lower Basin water users have no recourse. Although they are entitled to a specific quantity of water, their quality rights are poorly defined. As a result, approximately three million tons of salt from agricultural return flows are loaded into the river each year, affecting hundreds of thousands of irrigated acreage and millions of households. The extent of the affected acreage, the absence of markets for transferring costs, and the conflicting goals between agricultural, and municipal and industrial uses rank salinity as the most important water quality problem in the Colorado River Basin. To assure Lower Basin users of a clean and reliable supply of water, Congress established water quality standards at three locations along the Colorado River. At Hoover Dam in Arizona, Parker Dam in Arizona, and Imperial Dam in California, the maximum allowable salinity levels are 723, 747, and 879 mg/l, respectively.(2) Average observed salinity at Imperial Dam was 753 mg/l in 1991. At the present level of development, with no additional salinity control through the year 2010, water quality at Imperial Dam is expected to vary between 639 and 1,095 mg/l (U.S. Department of the Interior 1993). Although water conservation practices could stem the load of salt from the Upper Basin, the economic incentive to use less water simply does not exist. In the Upper Basin, water is plentiful, and at $8 per acre-foot, water-intensive farming is a common practice. To assure compliance with the standards, federal funds have been allocated through the year 2015 to stem annual salt loads. To date, federal salinity control projects have reduced total annual salt loading by 270,000 tons. An additional 1.26 million tons removal is proposed at a cost of approximately $700 million (U.S. Department of the Interior 1993).

This research develops a model to evaluate the efficiency of current water quality policy in the Colorado River Basin based on the value of water and water quality in agricultural, municipal, and industrial water uses and to determine the level of water quality that maximizes aggregate net returns to the river basin. For evaluating and comparing a wide range of water quality control alternatives, the model developed is the most comprehensive to date.

Previous Work

Three previous works estimated the marginal value of water quality to uses in the Imperial Valley. Moore, Snyder, and Sun developed farm-level models for nine crops grown on three soil types to quantify the value of clean water in irrigated production. The selected crops, soil types, and farm sizes were representative of the Imperial Valley Irrigation District. Inputs to production were irrigation treatment, water quality, and leaching fraction. Four water-quality levels between 490 and 1,950 mg/l(3) were simulated. Their results showed that the value of Imperial Dam water quality to Imperial Valley agriculture was between $2,000 and $4,300 per mg/l.(4) The value of water quality was quantified by Kleinman and Brown in a study to analyze the effects of salinity at Imperial Dam on agricultural, municipal, and industrial water uses. For salinity levels between 875 and 1,225 mg/l, they estimated that a 1 mg/l increase in salinity would result in $418,500 worth of damages to municipal uses, $17,200 in lost productivity to agricultural uses, and $89,400 in indirect costs to regional uses. The value of water quality at the margin was estimated to be $525,100 per 1 mg/l change in salinity.(5) Using linear programming, Gardner and Young compared the cost of salt load reduction in the Grand Valley with the benefits to Imperial Valley agriculture. They found that a rise in input water salinity from 800 mg/l to 1,100 mg/l would cost Imperial Valley producers $13.88 million. Allowing for fluctuations in crop prices, the marginal value of water quality to Imperial Valley growers was estimated to be $39,000 per 1 mg/l salinity.(6)

This research expands the scope of previous work by evaluating agricultural production in five Upper Basin regions responsible for 80% of the annual agriculturally induced salinity and assessing the downstream effects on agricultural, municipal, and industrial uses at both Grand Junction and Imperial Dam. A set of regional production models were estimated which allowed us to (a) capture the cost of managerial alternatives to salinity control (e.g., input use reduction, shifting to less water-intensive crops) and (b) determine the effect of changes in water quality on downstream productivity. All six of the estimated production models were evaluated simultaneously within a basin-wide model that included production activities in multiple regions, a physical model of river basin hydrology, and a benefit function to account for agricultural returns, salinity control costs, and municipal and industrial water quality values.

Regional Production Models

Nonlinear regional production functions in land, capital, water, and water quality for Colorado River Basin crops have not been estimated in previous work, and the limitations of existing data precluded estimation by econometric methods. Traditional calibration approaches require calibration constraints that restrict the range of alternative scenarios and for that reason are limiting in policy analysis. For this work, a new procedure was employed. Flexible agricultural production models were calibrated using a new two-step procedure developed by Howitt. The calibrated models were augmented in a third step to include the effects of water quality on crop productivity.

Step 1: Obtain Resource Shadow Values

In the first step, we used linear programming to estimate the shadow value of resource inputs in regional production. We assumed efficient allocation of regional resource inputs and then obtained the shadow value of each resource in production as revealed by its marginal contribution to production and net returns.

The shadow value [[Lambda].sub.j] for each resource input j [element of] J was defined to be the marginal profitability of the input in the lowest valued crop i = 1, ...., I. In equation (1), p is crop price, Q is total production, X is input quantity, r is input cost, and a is the linear rate of input use.

(1) [[Lambda].sub.j] = min

[Mathematical Expression Omitted]

We estimated the shadow value of each input in each region.

Step 2: Calibrate Nonlinear Production Parameters

Using the estimated resource shadow values from step 1, the production parameters were calibrated to satisfy the first- and second-order conditions for profit maximization, observed output levels, existing cropping patterns, and constant returns to scale in the least profitable crops.

A total of I + IJ Cobb-Douglas production parameters were obtained by minimizing the sum of squared errors (E), where I is the number of crops and J is the number of inputs. The objective was to choose the parameters ([Alpha]) that minimize E,

[Mathematical Expression Omitted]

subject to the definition of the error terms in equations (3), (5), (6), and (7), and the inequality constraint in equation (4). The error vector, [Epsilon], is defined as [Epsilon] = [[Epsilon]1[prime] [Epsilon]2[prime] [Epsilon]3[prime] [Epsilon]4[prime]][prime] and is of dimension (1 + 21 + IJ x 1).(7)

Equations (3) and (4) constrain the parameters to satisfy the first- and second-order conditions for profit maximization. In equation (3), [Mathematical Expression Omitted] is the estimated resource shadow value from step 1.

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

Equation (5) requires that the calibrated functions Q([Mathematical Expression Omitted], X) reproduce observed output levels [Q.sup.0] at the base level of resource allocation [X.sup.0]:

(5) [Q.sup.0] + Q([Alpha], [X.sup.0]) + [Epsilon]2.

Equation (6) requires the difference in value between average and marginal yields to equal the shadow value of land [Mathematical Expression Omitted], where [Mathematical Expression Omitted] is the observed allocation of land:

[Mathematical Expression Omitted].

Equation (7) imposes constant returns to scale on the lowest-valued crop in the region. For Cobb-Douglas production the constraint is

(7) [summation over i] [[Alpha].sub.j] = 1 + [Epsilon]4.

Empirical Results

To calibrate the production functions, yield, price, cost, and resource use data were obtained from various sources, including the Colorado Department of Agriculture, the U.S. Department of Commerce (1984, 1986), and the Utah Department of Agriculture. For yields and output price by crop and region, county-level prices received by farmers were used. Yield and price data are published annually. Unit costs of resource inputs for each crop are available by state (USDA-ERS 1985). The production parameters were calibrated using data representing 70% of the irrigated acreage in the Lower Gunnison Basin and the Grand Valley, approximately 80% of the irrigated acreage in Uinta, Price, and San Rafael, and 69% of the harvested irrigated acreage in the Imperial Valley.

Results show that output elasticities in land are large relative to the elasticities of water and capital. The output elasticity of land is largest for alfalfa production in the Grand Valley (0.888) and in Lower Gunnison (0.884); it is lowest for corn silage production in Price-San Rafael (0.214). The estimated output elasticity of water ranges from 0.368 in Imperial Valley alfalfa production to 0.039 in Price-San Rafael and Uinta corn silage production. The elasticity of capital is small, ranging from 0.007 for cotton and wheat grown in the Imperial Valley up to 0.033 for alfalfa in Lower Gunnison and other hay in Price-San Rafael and Uinta. Calibrated parameters are displayed in table 1.

The calibrated results compare favorably to econometric results obtained by Just, Zilberman, and Hochman. For vegetable crops in Israel, output elasticities for water ranged from 0.004 to 0.0788. The output elasticities of water from the calibrated model for field crops ranged from 0.039 to 0.368. Dinar and Knapp estimated output elasticities of water for cotton and alfalfa in California to be 0.335 and 1.005. The calibrated elasticity of water was 0.258 for cotton and 0.368 for alfalfa grown in the Imperial Valley.

Step 3: Determine Production Response to a Change in Irrigation Water Salinity

The third step introduces crop yield response information in the calibrated Cobb-Douglas models to predict the effect of a change in irrigation water salinity on agricultural production. To this end the Cobb-Douglas production models were augmented with agronomically derived salinity response coefficients. Agronomic estimates from Letey and Dinar were obtained for this purpose and used to derive a production shift function which when multiplied by the calibrated Cobb-Douglas functions yielded regional production estimates in land, capital, water, and water quality.

Letey and Dinar brought together linear yield response to applied water (from various sources), yield response to soil salinity (from Maas and Hoffman 1977), and functions representing the relationship between soil and applied water salinity, plant consumptive use of water, leaching fraction, and root zone depth in order to generate relative yield(8) data for a range of applied water and water salinity levels. The generated data were estimated using linear, log-log, and quadratic functional forms. The best fit for explaining yield decline with increasing salinity and decreasing water application was the quadratic function

(8) y = [[Beta].sub.0] + [[Beta].sub.1]C + [[Beta].sub.2][C.sup.2] + [[Beta].sub.3]CW + [[Beta].sub.4]W + [[Beta].sub.5][W.sup.2].

From equation (8), a change in relative crop yield due to a small change in water salinity can be expressed as

(9) [Delta]y/[Delta]C = [[Beta].sub.1] + 2[[Beta].sub.2]C + [[Beta].sub.3]W.

Empirical estimates of the coefficients from equation (9), using data from Letey and Dinar, are shown in table 2.

Table 1. Calibrated Cobb-Douglas Production Parameters

                Intercept     Land      Water     Capital

                               Grand Valley

Alfalfa            3.62       0.888     0.080      0.032
Barley           145.53       0.734     0.058      0.018
Corn grain       327.0        0.539     0.042      0.015
Corn silage       44.4        0.516     0.054      0.027
Wheat             66.3        0.651     0.050      0.014

                              Imperial Valley

Alfalfa            5.32       0.580     0.368      0.020
Cotton             4.23       0.421     0.258      0.007
Wheat             80.2        0.784     0.209      0.007

                              Lower Gunnison

Alfalfa            3.36       0.884     0.083      0.033
Barley           105.0        0.806     0.066      0.020
Corn grain       431.0        0.535     0.043      0.029
Corn silage       35.3        0.687     0.074      0.019
Wheat            148.0        0.705     0.056      0.015

                           Price and San Rafael

Alfalfa           16.1        0.357     0.076      0.023
Other hay          4.6        0.403     0.087      0.033
Wheat             63.8        0.357     0.097      0.020
Corn grain        66.8        0.275     0.051      0.013
Corn silage       24.2        0.214     0.039      0.021
Barley            61.9        0.513     0.127      0.024
Oats              93.7        0.282     0.096      0.029
Pasture            3.8        0.586     0.295      0.119

                                Uinta Basin

Alfalfa           19.0        0.522     0.065      0.020
Other hay          2.19       0.877     0.090      0.033
Wheat             86.5        0.583     0.082      0.017
Corn grain       149.0        0.440     0.050      0.013
Corn silage       47.5        0.354     0.039      0.021
Barley          105.0         0.716     0.093      0.018
Oats             79.3         0.797     0.100      0.031

Using Letey and Dinar's coefficient estimates, observed regional yields, and existing regional irrigation water quality, a "yield shift" function, [Psi]([center dot]), was derived. In equation (10), [y.sup.0] is proportion of maximum yields under base-year irrigation salinity and [C.sup.0] is base-year salinity:

[Mathematical Expression Omitted].

When salinity is constant, [Psi]([center dot]) = 0. Regional production as a function of salinity is

[Mathematical Expression Omitted].

From equation (11), the marginal product of water is

[Mathematical Expression Omitted].

The augmented production function, [Mathematical Expression Omitted], in equation (11) allows both total product and marginal product of water to vary with water salinity. Total production decreases with increasing water salinity for all crops. In table 2, [[Beta].sub.3] [less than] 0 for both alfalfa and corn, revealing from equation (12) that the marginal product of water decreases as water salinity rises. For barley, cotton, and wheat, [[Beta].sub.3] [greater than] 0, indicating that for those crops the marginal product of irrigation water increases as irrigation water becomes more saline.

Optimization Model

To determine the level of water salinity that maximizes net returns to the river basin, an optimization model was specified. The optimization model includes three components: the downstream benefits of improved water quality, the cost of upstream salinity reduction, and the hydrologic relationship between upstream salinity reduction and downstream water quality.

Table 2. Quadratic Crop Yield Coefficients

                               Coefficient(a)
Crop(b)     [[Beta].sub.1]     [[Beta].sub.2]     [[Beta].sub.3]

                   C              [C.sup.2]            C W
Alfalfa         -0.022            0.000068            -0.018
Barley          -0.002           -0.001                0.008
Corn            -0.035           -0.001               -0.015
Cotton          -0.020           -0.009                0.020
Wheat           -0.002           -0.001                0.008

Source: Letey and Dinar.

a Coefficients that appear in the partial derivative of the
quadratic crop response function [equation (9)].

b Crop yield in percent of maximum, salinity (C) in ds/m, and water
(W) in cm-ha.

Downstream Benefits

Within the model context, the beneficiaries of a reduction in Upper Basin salt loads are the agricultural users in the Grand Valley, and the agricultural, municipal, and industrial users at Imperial Dam.

Agricultural profit. Agricultural profits vary by region and crop. Under existing salinity conditions, profits for field crop production in Grand Valley range from $100 to $249/ac, and in Imperial Valley from $249 to $567/ac. As salinity levels fall, yields and hence profits improve, input use shifts, and cropping patterns change.

Agricultural profit is defined as

[Mathematical Expression Omitted]

where [[Pi].sub.g] is agricultural profit for regions g, [p.sub.g] is the (I x l) vector of crop prices, [Q.sub.g] is the (I x l) vector of crop production, [r.sub.jg] is the (I x 1) vector of costs, and [L.sub.g], [W.sub.g], and [K.sub.g] are the (I x l) vectors of input use for land, water, and capital. Production for crop i in region g is Cobb-Douglas in land, water, and capital, and concave in increasing water salinity, as defined in equation (11). Vector [Mathematical Expression Omitted] in equations (13) and (14) is a (I x 1) vector of crop production in region g, and [[Psi].sub.ig]([center dot]) [equations (14) and (10)] is the proportionate change in crop yield due to a change in irrigation water salinity:

[Mathematical Expression Omitted],

[Mathematical Expression Omitted].

Resource use in each region is limited to [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [Mathematical Expression Omitted], and water use is additionally constrained by W[D.sub.g], the volume of water withdrawn from the river and [R.sub.idg] return flows from sources indexed by d, which includes deep percolation from fields, and on-farm and off-farm conveyance systems. These restrictions are expressed as follows:

[Mathematical Expression Omitted],

[Mathematical Expression Omitted]

Municipal and industrial benefits. The values of municipal and industrial water uses in region 6 (Imperial Dam) were modeled as a linear function of the change in water salinity (dC). Defining m to be the average combined municipal and industrial value of water quality per mg/l, total municipal and industrial benefits from a change in salinity are

(16) [B.sub.g] = [m.sub.g]d[C.sub.g] for g = 6.

Municipal and industrial uses in the Imperial Valley gain $607,000 for each 1 mg/l reduction in water salinity, as estimated by Lohman, Milliken, and Dorn.

Control Costs

Water quality control alternatives included in the model were all proposed federal salinity control projects and an unconstrained reallocation of Upper Basin agricultural resources.

Federal projects. A series of federal projects have been proposed to reduce deep percolation from irrigated fields and on-farm and off-farm water conveyance systems. The projects were represented as a vector of discrete choice variables F (k x 1) whose elements take on values of one if chosen and zero otherwise.(9) Project costs are annualized and represented by [r.sub.F] (k x 1), so total annual investment (Z) in federal salinity control projects (F) is

(17) Z = [r[prime].sub.F]F

Federal projects to reduce salt loading ranged from $4.44/ton to $300.46/ton for improving on-farm and off-farm irrigation water use and water conveyance efficiency.

Managerial alternatives. Salt loading can also be reduced by reallocating agricultural inputs on upstream farms. For example, switching to crops that are less water intensive, reducing water application rates, and removing land from irrigated production can effectively reduce Upper Basin salt loads. The cost of these managerial alternatives is measured in terms of foregone agricultural profits:

(18) ag loss [equivalent to] [[Pi].sub.g]([Q.sup.0], [X.sup.0]) - [[Pi].sub.g] [Q(X), X]

where

[[Pi].sub.g] = [p[prime].sub.g][Q.sub.g] - [r[prime].sub.LG][L.sub.g] - [r[prime].sub.Wg][W.sub.g] - [r[prime].sub.Kg][K.sub.g] for g = 1, ..., 5.

Profits for field crop production in these Upper Basin regions range from $11/ac to $359/ac. In these predominantly agricultural regions the secondary effects of acreage reduction likely would be significant. Due to the nature of this study, however, the secondary economic effects were not included in the analysis.

Hydrology Model

To link upstream agricultural activities with downstream salinity, the Colorado River Basin hydrology model developed by Lee, Howitt, and Marino was used. The change in downstream salinity (d[C.sub.g]) in regions 2 and 6 is modeled as a function of the change in upstream salt loading (AS) and the change in upstream water use ([Delta]U). Region 1 (Lower Gunnison) is located upstream from region 2 (Grand Valley); regions 3 (Price), 4 (San Rafael), and 5 (Uinta) are situated upstream of region 6 (Imperial Dam). So, within the context of the model, water quality in regions 2 and 6 are influenced by activities that reduce salt loading. Regions 1, 3, 4, and 5 are hydraulically "upstream" or parallel to all other regions in the model; so for purposes of this analysis, their irrigation water quality is assumed to be in steady-state.

Let p represent the rate of decay, [Eta] the rate of evaporation, and [T.sub.g] the rate of salt flow at g; [V.sub.g] is river flow volume at g. River water salinity for regions 2 and 6 is represented by equations (19) and (20), as follows:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

Let [R.sub.g] denote the vector of return flow volumes from region g to the river. Return flow volume is defined to be a function of water application rate (W), acreage planted (L), federal salinity control projects implemented (F), water diverted to the region (W[D.sub.g]), and a series of crop- and soil-specific parameters ([Gamma]) (e.g., crop consumptive use, leaching fraction):

(21) [R.sub.g] = R([W.sub.g], [L.sub.g], F, W[D.sub.g], [[Gamma].sub.g]).

In equation(22), [c.sub.g] is the vector of the salinities of the return flows. The change in salt load from region g is expressed as

(22) [Delta][S.sub.g]

for g = 1 ... 5

= -[Delta]W[D.sub.g]/[Delta]t [C.sub.g] + ([V.sub.g] - W[D.sub.g]) [Delta][C.sub.g]/[Delta]t + [c[prime].sub.g] [Delta][R.sub.g]/[Delta]t.

The change in river flow below region g is

(23) [Delta][U.sub.G] = -[Delta]W[D.sub.g]/[Delta]t + [Delta][R.sub.g]/[Delta]t.

for g = 1 ... 5

Objective Function

The objective is to choose land, water application rate, capital, and investment in federal projects (F) to maximize net returns (N) over all uses. Because of the dams and large reservoirs in the river basin, several years will elapse before the effect of a change in Upper Basin water can be detected in Lower Basin water quality. To account for this lag, [Delta], in equation (24) discounts net benefits from an improvement in water quality. In equation (24), [[Pi].sub.g] is regional profit, [Mathematical Expression Omitted] is the gradient of discounted net returns to downstream uses from a small change in salinity, and dC is the total change in salinity.(10)

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted].

Empirical Model

Currently, regional resources are allocated to irrigated agriculture without regard to the quantity of salt loaded in irrigation return flows or the consequences downstream. To determine if an alternative allocation of resources would net a higher level of aggregate returns than currently exists, the model was parameterized with existing published and unpublished data on Colorado River Basin production and hydrology. The values of water quality in downstream municipal and industrial uses were taken from estimates reported in Lohman, Milliken, and Dorn. Federal irrigation projects included on-farm conservation measures (e.g., laser leveling, shortening irrigation runs), water conveyance improvements (e.g., pipe laterals, canal lining), and soil conserving practices (e.g., gully plugging, contour furrowing). Federal projects and costs were obtained from the U.S. Department of Agriculture, Soil Conservation Service (1981) and the U.S. Department of the Interior, Bureau of Reclamation (1982, 1986, 1989). Annual dollars to fund federal projects were assumed to be unconstrained. Nonstructural (managerial) alternatives to salinity control - such as shifting to crops that are less water intensive, reducing water application rate, and removing land from irrigated production - were captured through the nonlinear production functions for the Upper Basin regions [equation (14)], and the cost inferred by the corresponding reduction in farm profits [equation (18)]. Land, water, and capital are constrained regionally for agricultural irrigation, but within the model context, water may be reallocated downstream for purposes of dilution. Data from the U.S. Department of the Interior (1993) were used to update the hydrology model from Lee, Howitt, and Marino. The optimization model was run using GAMS/Minos software (Kendrick and Meeraus).

Optimization Model Results

The optimal reduction of salt from the river was estimated to be 1.268 million tons per year; this would cause river salinity in the Grand Valley to fall 71 mg/l from a base level of 500 mg/1 [TABULAR DATA FOR TABLE 3 OMITTED] salinity to 429 mg/1, and Imperial Dam salinity to drop 153 mg/1 from current levels of 753 mg/l to 600 mg/l, as shown in table 3. To achieve this level of salinity reduction at the lowest cost, Upper Basin agriculture in the Lower Gunnison and the Grand Valley in Colorado shifted largely out of production. In Utah, the Price and San Rafael regions' crops shifted slightly out of alfalfa and pasture and into other crops, and in Uinta, crops shifted out of hay and into alfalfa. Land use results appear in table 4. As a result of the large reduction in acreage, profits in the Upper Basin regions fall and imputed land values drop. The net cost to Upper Basin agriculture from removing land from irrigated production, shifting crops, and reallocating resources was estimated to be $16.27 million. Salt load reduction from investment in proposed federal projects would cost $22.59 million. Gains to Lower Basin agriculture in the Imperial Valley were $1.61 million, and savings to municipal and industrial water uses were estimated to be $92.84 million. The net social benefit of this outcome would be $55.45 million per year. The results are displayed in tables 3 through 5.

Alternatively, we can consider the current situation, in which Upper Basin farmers are expected to continue farming, as usual, and all salinity reduction is expected to come about as a result of federally funded projects. In this scenario, labeled the "status quo," salinity reduction is more costly, so equilibrium water salinity levels at Imperial Dam are higher than the unrestricted optimum, total expenditures for salinity control are greater, and net welfare gains are smaller. Results show that in this second-best scenario "optimal" salt load reduction is 680,000 tons, water salinity at Imperial Dam is 688 mg/l, and annualized expenditures for federal salinity control projects are $37.5 million. Net welfare gain is $4.3 million per year. Results appear in tables 3, 4, and 5.

A slightly less restrictive alternative allows [TABULAR DATA FOR TABLE 4 OMITTED] for some reallocation of Upper Basin resource use to reduce salt loading, provided that Upper Basin agricultural profits are maintained. This scenario, referred to as "constant profits," yields a slight reduction in federal expenses for salinity control than the "status quo," while at the same time achieves a 5 mg/1 lower salinity level at Imperial Dam. In this scenario, equilibrium salt loading is reduced 710,000 tons, water salinity at Imperial Dam is 683 mg/1, federal salinity control expenditures are $36.4 million per year, and net welfare gains are $8.3 million annually. Results are displayed in tables 3, 4, and 5.

Remarks

Due to the high value of water quality to Lower Basin users and the high marginal cost of some federal projects, these results indicate that the [TABULAR DATA FOR TABLE 5 OMITTED] least-cost means of improving Colorado River water quality, mitigating the downstream externality problem, and moving toward a more efficient allocation of basin resources includes a combination of water conservation, acreage reduction, and federal salinity control projects. Although the same level of salinity reduction can be achieved with federal projects alone, the cost would be $700 million (U.S. Department of the Interior 1993), eighteen times more than a policy that includes acreage reduction. These results support the findings of Gardner and Young, Howe and Orr, and Booker and Young.

Retention of current Upper Basin agricultural farming practices and agricultural profits would require greater expenditure for more costly federal projects to control salinity. Results indicate that federal expenditures up to $37.5 million are warranted by downstream benefits from improved water quality if Upper Basin farming remains unchanged.

Irrigation projects and resources are allocated based on their relative effectiveness at improving downstream water quality in the absence of transactions costs and equity considerations. The additional costs incurred from water quality monitoring, enforcement, and litigation would likely offset the net benefits, suggesting that when transaction, monitoring, and enforcement costs are considered, a smaller reduction in salt loading may be optimal.

Conclusion

In this paper we present an empirical approach for analyzing the economics of agriculturally induced externalities. Irrigated agriculture for six regions in the Colorado River Basin were modeled with Cobb-Douglas production functions in land, capital, water, and water quality. These nonlinear regional production models serve two purposes: (i) to include input use reduction and cropping pattern shifts as a means of upstream salinity control, and (ii) to assess the downstream agricultural benefits of upstream salinity control. Since the production models were constrained only by fixed resources, a range of policy options beyond the scope of previous studies could be evaluated and compared. The hydrology model provided the physical linkage between Upper Basin water use and salt loading and Lower Basin water salinity, and it allowed the equations of the basin-wide model to be solved simultaneously. Nonlinear programming was used to evaluate the trade-off between upstream production and the value of downstream water quality in the absence of transaction costs and constraints to water transfers. Results showed that on-farm water conservation and acreage reduction offers huge potential savings over more costly structural projects for improving water quality and meeting water quality standards.

To obtain a more comprehensive model of basin agriculture, to control more of the agriculturally induced river salinity, and to fully value the benefits to water quality improvement, additional information on acreage planted, resource use, and cropping patterns is needed. Future studies might also consider evaluating advances in irrigation technology and management to conserve water, dispose of salts, and reuse return flows. New developments to cope with rising water salinity through irrigation scheduling, salt-tolerant crop varieties, and water and soil treatment can be studied in an economic context to better model downstream response, and to quantify the value of water quality improvement.

The authors acknowledge Oscar Burt and Miguel Marifio for their contributions to the development of this research effort. The comments from the two journal reviewers and the senior editor of the AJAE, which helped improve the overall quality of the final manuscript, are appreciated. Initial funding for this research came from the Resource and Technology Division of the Economic Research Service, USDA. Additional support was provided by the Department of Economics, University of Hawaii.

1 Soils with total dissolved solids in excess of 1,300 mg/l (2 mmhos/cm) are considered saline.

2 The concentration of salt in river water is expressed in units of milligrams per liter which is abbreviated mg/l.

3 Results were reported in units of mmhos/cm; 650 mg/l = 1 mmhos/cm.

4 In 1986 dollars. Dollar amounts reported by Moore, Snyder, and Sun were inflated to allow for a 54% increase in crop prices between 1970 and 1986.

5 Kleinman and Brown's agricultural figures were inflated by 4% to account for the increase in crop prices between 1976 and 1986. Similarly, the municipal and industrial figures were increased 74% to capture the rise in GNP between 1976 and 1986.

6 Gardner and Young (GY) attribute the difference in their estimates and those of Kleinman and Brown (KB) to be primarily due to the way crop sensitivity to salinity and soil quality were handled within the region-wide models. GY allowed for higher yields from crops planted on the best soil class. KB used regional average yields to represent yields on the best soils. Further, KB assumed that salt-sensitive crops would only be planted on well-drained soils (where increases in salinity are more easily mitigated). Thus, KB's estimated farm returns were relatively less sensitive to changes in salinity than were GY's, so KB estimated a smaller marginal value of water salinity than did GY.

7 [Epsilon]1 is (IJ x 1), [Epsilon]2 and [Epsilon]3 are (I x l), and [Epsilon]4 is (1 x 1).

8 Relative crop yield (y) as a proportion of maximum yield when salinity is zero, 0 [less than or equal to] y [less than or equal to] 1.

9 To illustrate, let [f.sub.R] represent the vector of proposed federal projects in terms of volume of return flow reduced. Then [f[prime].sub.R]F would indicate total reduction in return flows from federal projects. Multiplying [f.sub.R] by salinity of the return flows [c.sub.R] and then by F would yield ([f.sub.R][c.sub.R])[prime]F or total salt load reduction from federal projects. So [r[prime].sub.F]F is total annualized cost of chosen federal salinity control projects.

References

Booker, J.F., and R.A. Young. "Modelling Intrastate and Interstate Markets for Colorado River Water Resources." JEEM 26(1994):66-87.

Colorado Department of Agriculture, Crop and Livestock Reporting Service. "Colorado Agricultural Statistics," 1985.

Gardner, R., and R.A. Young. "Assessing Strategies for the Control of Irrigation Induced Salinity in the Upper Colorado River Basin." Amer. J. Agr. Econ. 70(February 1988):37-49.

Howe, C.W., and D.V. Orr. "Effects of Agricultural Acreage Reduction on Water Availability and Salinity in the Upper Colorado River Basin." Water Resour. Res. 10(October 1974):893-97.

Howitt, R.E. "Calibration Methods for Agricultural Economic Production Models." J. Agr. Econ., in press, 1995.

Just, R.E., D. Zilberman, and E. Hochman. "Estimation of Multicrop Production Functions." Amer. J. Agr. Econ. 65(November 1983):770-80.

Kendrick, D., and A. Meeraus. GAMS: An Introduction. Washington DC: Development Research Department, The World Bank, 1985.

Kleinman, A.P., and B. Brown. "Colorado River Salinity Economic Impacts on Agricultural, Municipal, and Industrial Users." Colorado River Water Quality Office, Engineering and Research Center, Department of the Interior, December 1980.

Lee, D.J. "A Dynamic Modelling Approach to Policy Analysis: Salinity in the Colorado River Basin." PhD dissertation, University of California, Davis, 1989.

Lee, D.J., R.E. Howitt, and M.A. Marino. "A Stochastic Model of Surface Water Quality: Application to Salinity in the Colorado River Basin." Water Resour. Res. 29(1993):3917-23.

Letey, J., and A. Dinar. "Simulated Crop Water Production Functions for Several Crops when Irrigated with Saline Waters." Hilgardia 54(1986):1-32.

Lohman, L.C., J.G. Milliken, and W.S. Dorn. "Estimating the Economic Impacts of Salinity of the Colorado River Final Report." With K.E. Tuccy. Milliken Chapman Research Group, Inc. Prepared for the U.S. Department of the Interior, Bureau of Reclamation, February 1988.

Maas, E.V., and G.J. Hoffman. "Crop Salt Tolerance - A Current Assessment," J. Irrig. Drain. Div. Amer. Soc. Civil. Eng. 103(June 1977):115-34.

Moore, C.V., J.H. Snyder, and P. Sun. "Effects of Colorado River Quality and Supply on Irrigated Agriculture." Water Resour. Res. 10(April 1974):137-44.

U.S. Department of Agriculture, Economic Research Service, "U.S. Mathematical Programming Agricultural Sector Model." Firm Enterprise Data System, 1985.

U.S. Department of Agriculture (USDA), Soil Conservation Service. "On-Farm Program for Salinity Control." Final Report for the Grand Valley Salinity Study. December 1977.

-----. "Potential On-Farm Irrigation Improvements." Final Report of the Lower Gunnison Salinity Control Study. September 1981.

-----. "Preliminary Cost Figures for the Price-San Rafael Unit." As per phone conversation with Lee Page, SCS economist, December 1988.

U.S. Department of Commerce, Bureau of the Census. "Colorado State and County Data." 1982 Census of Agriculture vol. 6, no. 1, 1984.

-----. 1984 Farm and Ranch Irrigation Survey. June 1986.

U.S. Department of the Interior. "Quality of Water in the Colorado River Basin." Progress Report No. 14, 1989.

U.S. Department of the Interior, Bureau of Reclamation. "Grand Valley Unit Stage Two Development." Supplement to the Definite Plan Report. June 1983, revised (May 1986).

-----. "Lower Gunnison Basin Unit." Feasibility Report/Final Environmental Impact Statement. November 1982.

U.S. D.O.I. "Quality of Water in the Colorado River Basin." Progress Report No. 16, 1993.

-----. "Uinta Basin Unit." Planning Report/Final Environmental Impact Statement. April 1986.

Utah State Department of Agriculture, Agricultural Statistics Service. "Utah Agricultural Statistics" Annual Report, 1988.

Appendix

Variable Definitions

[TABULAR DATA FOR TABLE 1 OMITTED]

Donna J. Lee is an assistant professor in the Food and Resource Economics Department, University of Florida. Richard E. Howitt is a professor in the Department of Agricultural Economics, University of California, Davis.