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Supplemental Colorado River water for a developed groundwater agriculture: A problem of quantities, qualities and conjunctive use
A d v a n c e s in Water R e s o u r c e s
Vol. 1 No. 2 1977
Supplemental Colorado River Water for a Developed Groundwater Agriculture: A Problem of Quantities, Qualities and Conjunctive Use
MARK A. B o f f r E R
Office of Biological Services U.S. Fish and Wildlife Servi~e, Washington, D.C. 20240 (This article was developed while Dr. B o s t e r was at the University of Arizona, Tucson, Arizona.)
WILLIAM E. MARTIN Department of Agricultural Economics, University of Arizona, Tucson, A r i z o n a 85721
Upon completion o f the Central A r i z o n a P r o j e c t (CAP), Colorado R i v e r water will be d e l i v e r e d s o m e 200 m i l e s inland f o r agricultural, domestic, and industrial use. Any new importation o f w a t e r to an area implies adjustments in the organization o f the economy o f the area. F o r irrigated agriculture, a d j u s t m e n t s will o c c u r in input mix, output mix, acreage f a m e d , and in g r o s s and net incomes. A complicating f a c t o r associated with importation of Colorado R i v e r w a t e r is that the imported water will contain different d i s s o l v e d salt concentrations than the groundwater and surface w a t e r currently being used. Mathematical p r o g r a m m i n g models of r e p r e s e n t a t i v e irrigated f a r m s in Pinal County, Arizona, are used to p r o j e c t a d j u s t m e n t s implied under s e v e r a l assumptions as to the availability, cost and salinity o f the various s o u r c e s o f irrigation water. Conclusions are drawn as to the potential winners and l o s e r s f r o m project development. Conclusions include the f o l l o w i n g : I n c r e a s e d salinity should not be o f concern to the f a r m e r s in the county and Indian f a r m s will reap the g r e a t e s t share o f benefits f r o m the Project.
Several interacting events make this r e p o r t relevant-both as a case study of an important i r r i g a t e d agricultural area, Pinal County, Arizona, and as a model for examining other irrigated agricultural a r e a s . Most of A r i z o n a ' s d e s e r t valley soils are suitable for crop production, but receive less than 10 inches of precipitation annually. Thus, farming in the a r e a is almost completely dependent upon irrigation s y s t e m s to meet crop water demands. Pinal County may generally be considered r e p r e s e n t a t i v e in climate and agricultural p r a c t i c e s of the irrigated a r e a s in the Southwestern United States, including the Imperial Valley of southern California. The events are: (1) The Central Arizona P r o j e c t (CAP) is under construction. 1 This project will deliver Colorado River water some 200 miles into central Arizona, including Pinal County, where a fifth of the s t a t e ' s cropland is irrigated mostly with groundwater. (2) In the a r e a s currently using pumped groundwater for irrigation, the groundwater table is falling because of continued groundwater mining. (3) The quality of the Colorado R i v e r water, in t e r m s of dissolved solid content, is d e c r e a s i n g over time. (4) The CAP water will be used in conjunction with already available water supplies of differing quality and cost, which in most a r e a s is groundwater available on demand from the f a r m e r ' s private wells. Thus, the overall objective is to make an economic evaluation of the adjustment p r o b l e m s and alternatives open to irrigated agriculture when faced with a second
1 The Central A r i z o n a P r o j e c t was one of the water r e s o u r c e p r o j e c t s recently reviewed for economic feasibility by P r e s i d e n t C a r t e r ' s administration.
or third water supply of differing quality and cost. However, evaluation of these issues provide insights into s e v e r a l related questions. These include: (I) What is the cost of increased salinity in the Colorado River to the prospective u s e r s of that w a t e r ? (2) What will delivery of that water mean in t e r m s of groundwater conservation in the study a r e a ? (3) Who will reap the benefits from the additional water supply? And finally, (4) Who may find that they do not want the new water supply after all ? To accomplish the general economic evaluation, the following specific evaluations are required. They are: (I)
To project the economic position of r e p r e s e n t a tive individual f a r m e r s and of the county as a whole in 1986 (the projected date of project completion) if no Central Arizona P r o j e c t water is available;
(2)
To project the economic impact of CAP water in the study a r e a in 1986 if CAP water is available to f a r m e r s on a free choice basis. Physical changes expected include changes in the input mix for each crop, the level of physical output for each crop, and the output mix for each f a r m and for the county;
(3) To investigate the economic effects of requiring each farm in the county to use at least 90 p e r cent of its annual CAP water allotment in o r d e r to meet the i r r i g a t i o n d i s t r i c t s ' contractual agreements; (4) To m e a s u r e the loss in net f a r m returns resulting from i n c r e a s e d salinity of Colorado River water --the s o u r c e for Central A r i z o n a P r o j e c t - - o v e r time. 103
Supplemental Colorado R i v e r Water f o r a Developed Groundwater Agriculture Mark A. B o s t e r and William E. Martin (5)
Because the Indian f a r m e r s and the non-Indian f a r m e r s of the a r e a will be subject to different water use rules and water costs, one must d e t e r mine the m a x i m u m quantity of CAP water that could be used effectively by Indian f a r m e r s in the area.
Evaluations 2 through 5 are partial analyses showing changes from the base s i t u a t i o n - n u m b e r 1. They involve only changes in variable costs. The final evaluation (6) investigates the ability of the f a r m e r s to absorb the n e c e s s a r y fixed costs in each situation. Method of Analysis Detailed r e p r e s e n t a t i v e - f a r m organizations, costs and r e t u r n s data are used to develop the linear p r o g r a m ming models used as the tool for analysis. Sixty-nine of these r e p r e s e n t a t i v e - f a r m l i n e a r - p r o g r a m m i n g models are needed to describe adequately the i r r i gated farming activities in Pinal County. Each model includes alternative crop production activities using various quantities of Central A r i z o n a P r o j e c t water, groundwater, and other s u r f a c e water (in the San Carlos P r o j e c t s area) under alternative conditions of use. Each water source, and thus the resulting water mixes, is available in various quantities over time, at different p r i c e s and salinities. The linear p r o g r a m ming models are designed to maximize net farm r e t u r n s above variable production costs subject to the r e s o u r c e constraints faced by the r e p r e s e n t a t i v e f a r m e r s . Individual r e p r e s e n t a t i v e - f a r m r e s u l t s are aggregated into r e s u l t s for each of the seven i r r i g a tion d i s t r i c t s and for the whole county. All irrigated farmland in the county is included within these d i s t r i c t s . A mathematical statement of the generalized r e p r e s e n t a t i v e - f a r m linear p r o g r a m m i n g model is given in the Appendix. THE MODEL AS A DESCRIPTION OF THE PINAL COUNTY PROBLEM The Economic D e c i s i o n s The individual firm employs r e s o u r c e s (factors of production) to produce a product. Although not all f i r m s are interested in profit maximization, agricultural f i r m s (farms) operate in a competitive m a r k e t and t h e r e f o r e only profit maximization a s s u r e s their long run existence. Each firm interested in profit maximization must make three simultaneous decisions: (1) What combination of products to produce, (2) how to combine inputs in the production of a given level of output for a given product, and (3) what level of output to produce (e.g., what yield per a c r e for each product). E c o n o m i s t s t e r m these decisions the product-product, f a c t o r - f a c t o r , and f a c t o r - p r o d u c t decisions, r e s p e c tively. If the firm has profit maximization as its goal, if it knows the costs of inputs and p r i c e s of outputs, the simultaneous solution to the three questions provides the firm with its profit maximizing position. In this study, the f a c t o r - f a c t o r question involves the optimal mix of imported CAP water with local water. How much yield per a c r e of each crop to produce, relative to the variable inputs of water quantity and quality, is handled by the f a c t o r - p r o d u c t decisions. The optimal crop mix is determined by the productproduct relationships. 104
Thus, an objective function is developed for each r e p r e s e n t a t i v e farm. A r e p r e s e n t a t i v e f a r m is defined for four s i z e s (so as to e x p r e s s economies of size), for three depths to water (to e x p r e s s alternative water costs), and for seven i r r i g a t i o n districts (to e x p r e s s differing groundwater qualities). These functions contain net revenue coefficients for each possible production activity on each farm. A production activity is a method of producing a crop on one acre of land. Each crop has s e v e r a l production activities, i.e., each crop is repeated s e v e r a l times in each model to allow for alternative mixes of water sources, each of which has a different cost and salinity. F o r example, one cotton activity uses all pump water, another uses all CAP water, another uses four a c r e - f e e t of pumped water in combination with one a c r e - f o o t of CAP water, another three a c r e - f e e t of pumped water along with two a c r e - f e e t of CAP water, etc. Different costs, different yields, and this different net return coefficients are a s s o c i a t e d with each way of producing an acre of each type of crop. The net r e t u r n above variable cost values for each production activity includes that r e t u r n which must pay for the variable cost of water. Because each water source has a different unit cost, the total water cost a s s o c i ated with each w a t e r mix is different. Unit water costs for each available s o u r c e are included in the objective function in water purchase activities so that the total water cost can be computed within the model.
W a t e r Quantity, W a t e r Quality, ~nd Crop Yield In developing net r e t u r n estimates for each activity, yield estimates as related to water quantity and water quality are crucial. The effects of water quantity on crop output and water quality (salinity) on crop output are each c o n t r o v e r s i a l and complex subjects. However, Stults (1968) has presented estimates of yield r e s p o n s e as related to water quantity in the study area. Bernstein (1964) estimated relative yield as a function of water salinity. Specific l i t e r a t u r e on the joint effects of water quantity and salinity on crop yield does not exist. Dregne (1969) a s s u m e s that the effects of each are additive. Sun (1972), in an innovative economic analysis, makes the same assumption. A thorough review of both the agronomic and economic considerations n e c e s s a r y to a s s e s s i n g the effects of salinity on i r r i g a t e d agriculture is given by Young et al. (1973). They also review the empirical economic studies completed up to that time. However, at the time of their review, the r e c e n t theory on crop sensitivity to irrigation water salinity by Bernstein and F r a n c o i s (1973) was unpublished and not included. This theory essentially states that in a r e a s of p r o p e r soil condition and good drainage, yield r e s p o n s e s appear to be related to the calculated mean salinity against which w a t e r is absorbed, which is influenced m o r e by the salinity of the irrigation water as m e a s u r e d at the surface, than by the mean salinity in the root zone as assumed by the older theory. The older theory consistently o v e r e s t i m a t e d actual crop damage from salinity. Because the models in this study i n c o r p o r a t e the newly developed relationships, estimated economic loss in Pinal County resulting from i n c r e a s e d water salinity turns out to be r e l a tively minor.
A d v a n c e s in W a t e r R e s o u r c e s
The P h y s i c a l and L e g a l C o n s t r a i n t s W a t e r a v a i l a b i l i t y is the only i m p o r t a n t r e s t r i c t i o n c u r r e n t l y faced by P i n a l County f a r m e r s . T y p i c a l l y , f a r m e r s run t h e i r i r r i g a t i o n pumps 24 hours a day f r o m late June until e a r l y August to e x t r a c t the m a x i mum quantity of w a t e r p h y s i c a l l y p o s s i b l e . A second c r i t i c a l w a t e r u s e o c c u r s f r o m J a n u a r y 15 to the end of F e b r u a r y . During this p e r i o d , b a r l e y and wheat a r e i r r i g a t e d and cotton is p r e i r r i g a t e d . However, f a r m e r s t y p i c a l l y only u s e 70 p e r cent of t h e i r pumping c a p a city in the w i n t e r so as to avoid drawdown p r o b l e m s in the s u m m e r . P u m p a g e l i m i t s a r e a s s u m e d to i n c r e a s e l i n e a r l y f r o m the w i n t e r to the s u m m e r and then d e c r e a s e l i n e a r l y f r o m the s u m m e r through the fall. Although no w a t e r c o n t r a c t s for C e n t r a l A r i z o n a w a t e r have as y e t been signed, and exact a l l o c a t i o n s to the county and d i s t r i c t s have not been made, c e r t a i n b a s i c a s s u m p t i o n s about the P r o j e c t a r e n e c e s s a r y if m o d e l s a r e to be c o n s t r u c t e d . A f t e r d i s c u s s i o n s with m e m b e r s of the A r i z o n a W a t e r C o m m i s s i o n , r e a s o n a b l e a s s u m p t i o n s about the total quantity of CAP w a t e r i n i t i a l l y a v a i l a b l e for a g r i c u l t u r a l u s e in P i n a l County and the a l l o c a t i o n of that w a t e r to each i r r i g a t i o n d i s t r i c t was m a d e . P i n a l County w i l l r e c e i v e about 659, 000 a c r e - f e e t of CAP w a t e r in 1986 for a g r i c u l t u r a l u s e . Indian lands a r e to be a l l o c a t e d about o n e - t h i r d of the total a g r i c u l t u r a l CAP w a t e r a v a i l a b l e to the county in 1986. Under the enabling l e g i s l a t i o n , non-Indian lands can use CAP w a t e r only on those lands with a h i s t o r y of i r r i g a t i o n d u r i n g the ten y e a r s p r e c e d i n g e n a c t m e n t of the P r o j e c t l e g i s l a t i o n , i,e., lands r e c e i v i n g i r r i g a t i o n w a t e r m u s t have been under i r r i g a t i o n at s o m e t i m e d u r i n g the p e r i o d S e p t e m b e r , 1958 to S e p t e m b e r , 1968. Thus a land c o n s t r a i n t is c r e a t e d . B e c a u s e of planned canal capacity, no i r r i g a t i o n d i s t r i c t can r e c e i v e m o r e than 13.5 p e r cent of its annual a l l o t m e n t in any month. But, within that l i m i t a t i o n , an individual f a r m can r e c e i v e as much w a t e r as can be p r o f i t a b l y used. C u r r e n t e s t i m a t e s p l a c e the cost of CAP w a t e r for nonIndians at $ 1 5 . 0 0 p e r a c r e - f o o t at the m a i n canal s i d e . This cost t r a n s l a t e s into a cost of $ 1 6 . 6 7 at the f a r m headgate, given a ten p e r cent conveyance l o s s . Indian f a r m e r s will r e c e i v e s u b s i d i z e d CAP w a t e r f r o m the F e d e r a l G o v e r n m e n t at no d i r e c t cost to them. A c c o r d i n g to CAP l e g i s l a t i o n , each non-Indian i r r i g a tion d i s t r i c t m u s t r e d u c e g r o u n d w a t e r pumpage by one a c r e - f o o t for each a c r e - f o o t of P r o j e c t w a t e r p u r chased [43 U.S.C. Sec. 1524 (d)]. This study a s s u m e s that the a v e r a g e y e a r l y pumpage for the p e r i o d 1959 through 1968 is the b a s e a g a i n s t which w a t e r m u s t be t r a d e d . This p e r i o d is chosen since it is the 10 y e a r p e r i o d p r i o r to the p a s s a g e of the CAP b i l l . Total 10 y e a r a v e r a g e annual pumpage for the study a r e a is e s t i m a t e d as 1 , 0 2 4 , 0 0 0 a c r e - f e e t . P r o j e c t e d s a l i n i t y l e v e l s in the C o l o r a d o R i v e r for 1985 r a n g e f r o m a low of 1.2 m m h o s / c m 2 t o a high of 1.5 m m h o s / c m . In the CAP e n v i r o n m e n t a l i m p a c t s t a t e m e n t , the B u r e a u of R e c l a m a t i o n (1972) s t a t e s that e v a p o r a t i o n of Colorado R i v e r w a t e r d u r i n g t r a n s i t to P i n a l County will have a m i n o r effect on concent r a t i o n s of total d i s s o l v e d s o l i d s in the i m p o r t e d w a t e r . A m a x i m u m d e g r a d a t i o n of about six p e r cent between the r i v e r and Pinal County is e s t i m a t e d . Using the
Vol. 1 No. 2 1977
a v e r a g e value f o r s a l i n i t y p r o j e c t i o n s f o r C o l o r a d o R i v e r w a t e r at the point of intake in 1986, with a s i x p e r cent i n c r e a s e in t r a n s i t , an e s t i m a t e of w a t e r quality of about 1.4 m m h o s / c m s a l i n i t y in Pinal County is p r o d u c e d . Land h a s not been a r e s t r a i n t on output in Pinal County in r e c e n t y e a r s , However, to account for double c r o p ping, to a s s u r e that CAP w a t e r is not used to expand a c r e a g e on n o n - I n d i a n f a r m s , and to define the total i r r i g a b l e land in Indian a r e a s , both w i n t e r and s u m m e r land c o n s t r a i n t s a r e included in the m o d e l s . Land is also r e s t r i c t e d b e c a u s e of a r e q u i r e m e n t for a • ' c o n s e r v a t i o n b a s e ' . Cotton a c r e a g e is r e s t r i c t e d to r e f l e c t the f a r m e r s ' t y p i c a l a v e r s i o n to r i s k .
R E S U L T S O F T H E ANALYSES No CAP V e r s u s CAP F r e e l y P u r c h a s e d The i n i t i a l s o l u t i o n s of the r e p r e s e n t a t i v e f a r m m o d e l s a s s u m e no C e n t r a l A r i z o n a P r o j e c t w a t e r is a v a i l a b l e in 1986. This a n a l y s i s e s t a b l i s h e s a b a s e f r o m which to m e a s u r e the e c o n o m i c i m p a c t of i n t r o d u c i n g the new w a t e r into the a r e a . With C e n t r a l A r i z o n a P r o j e c t w a t e r introduced into the 1986 r e p r e s e n t a t i v e f a r m m o d e l s , net r e t u r n s above v a r i a b l e c o s t s for the whole county i n c r e a s e d by 4 . 7 m i l l i o n d o l l a r s or 35 p e r cent above net r e t u r n s if no CAP w a t e r is a v a i l a b l e . S i m i l a r l y , cropped a c r e a g e i n c r e a s e d by n e a r l y 83,200 a c r e s with CAP w a t e r i n t r o d u c e d and f r e e l y p u r c h a s e d . However, 3.9 m i l l i o n d o l l a r s of the 4 . 7 m i l l i o n d o l l a r i n c r e a s e and n e a r l y 55, 300 a c r e s of the 83,200 c r o p p e d a c r e a g e i n c r e a s e o c c u r s on the two Indian R e s e r v a t i o n s w h e r e CAP w a t e r is f r e e and can be u s e d to d e v e l o p new c r o p l a n d s . B e c a u s e total a c r e s of cotton a r e r e s t r i c ted in the model, the r i s e in net r e t u r n s r e s u l t s f r o m a c r e a g e i n c r e a s e s in the other c r o p s . The i n c r e a s e in net income to Indian lands will be a r e a l i n c r e a s e in total net i n c o m e to the Indians s i n c e a l m o s t all c o s t s of the new w a t e r a r e s u b s i d i z e d . However, c e r t a i n fixed c o s t s , such as the c o s t of the d i s t r i b u t i o n s y s t e m f r o m the m a i n canal to the f a r m h e a d g a t e s m u s t be s u b t r a c t e d f r o m the 0 . 8 m i l l i o n d o l l a r i n c r e a s e in income to n o n - I n d i a n s . These c o s t s are discussed later. A 21 p e r cent d e c r e a s e (about 154,000 a c r e - f e e t ) o c c u r s in pumped w a t e r used in the a r e a r e c e i v i n g CAP w a t e r . Other s u r f a c e w a t e r u s e is e s s e n t i a l l y constant. However, t~he total w a t e r applied to c r o p s i n c r e a s e s by 325, 700 a c r e - f e e t - - a 37 p e r cent inc r e a s e in total w a t e r u s e . Why is total w a t e r u s e with CAP higher than total w a t e r use without CAP, if the one for one p u m p - C A P t r a d e - o f f r u l e i s in e f f e c t ? T h e r e a r e two r e a s o n s . F i r s t , the r u l e d o e s not apply on Indian lands where
M i l l i m h o s p e r c e n t i m e t e r ( m m h o s / c m ) is a m e a s u r e of e l e c t r i c a l conductivity of w a t e r and r e f l e c t s the r e l a t i v e s a l i n i t y . The c o n v e r s i o n between s a l i n i t y e x p r e s s e d in p a r t s p e r m i l l i o n (ppm) and in m i l l i m h o s p e r c e n t i m e t e r v a r i e s depending on the w a t e r ' s c h e m i c a l c o m p o s i t i o n . The c o n v e r s i o n r a t e of 670 ppm p e r m m h o / c m used h e r e is r e p r e s e n t a t i v e of P i n a l County. 105
Supplemental Colorado R i v e r Water f o r a Developed Groundwater Agriculture Mark A. B o s t e r and William E. Martin 64 p e r cent of the i n c r e a s e o c c u r s . The Indians have a net i n c r e a s e of 180, 600 a c r e - f e e t of w a t e r use, while d e c r e a s i n g pumpage by only 3,000 a c r e - f e e t . Second, the i n c r e a s e of 145,000 a c r e - f e e t of w a t e r use on non-Indian lands is p o s s i b l e b e c a u s e f a r m e r s a r e t r a d i n g w a t e r a g a i n s t an h i s t o r i c a l a v e r a g e pumpage r a t h e r than what pumpage would have been in that y e a r without CAP. The h i s t o r i c a l a v e r a g e to which the o n e - t o - o n e t r a d e - o f f r u l e a p p l i e s is h i g h e r than e s t i m a t e d pumpage in 1986, b e c a u s e f a r m e r s in the deep pumpage a r e a s would have cut back on pumpage as the w a t e r table fell. Thus, p r o v i s i o n of CAP w a t e r will tend to slow the g r o u n d w a t e r o v e r d r a f t , but not on an acre-foot per acre-foot basis.
is $199,400 p e r y e a r as of 2020, or 1.1 p e r cent of the b a s e of $18, 306, 629. This d e c r e a s e a v e r a g e s only 61 cents p e r i r r i g a t e d a c r e , in 2020 ( l e s s in the p r e c e d ing y e a r s ) o r 0.23 cents p e r y e a r p e r i r r i g a t e d a c r e p e r p a r t m i l l i o n i n c r e a s e in s a l i n i t y . 3 Total w a t e r use in the County d e c r e a s e s by only 32, 400 a c r e feet when CAP w a t e r s a l i n i t y i n c r e a s e s to 1.8 m m h o s / c m . The d e c r e a s e d total w a t e r u s e r e s u l t s a l m o s t e n t i r e l y f r o m cutbacks in CAP w a t e r p u r c h a s e s . Total c r o p p e d a c r e s also d e c l i n e , but only by 2,000 a c r e s . Sixty p e r cent of the d e c r e a s e is f r o m b a r l e y , the m o s t e c o n o m i c a l l y m a r g i n a l crop, dropping out of the County's c r o p m i x . All Indian D e m a n d s f o r CAP W a t e r S a t i s f i e d
CAP F r e e l y P u r c h a s e d V e r s u s "Minimum R e q u i r e d Purchase Since n o n - i n d i a n s m u s t r e p a y the c o s t s of the C e n t r a l A r i z o n a P r o j e c t through w a t e r p u r c h a s e s , it is p o s s i b l e that a m i n i m u m w a t e r p u r c h a s e m a y be r e q u i r e d . In this p a r t of the a n a l y s i s , individual f a r m s a r e r e q u i r e d to u s e at l e a s t ninety p e r c e n t of t h e i r annual CAP a l l o t m e n t r a t h e r than a f r e e l y s e l e c t e d quantity. As expected, net r e t u r n s above v a r i a b l e c o s t s d e c r e a s e when this additional c o n s t r a i n t is added, but only by about $465, 000. However, the d e c r e a s e in net r e t u r n s all o c c u r s within the five n o n - I n d i a n d i s t r i c t s (the Indian R e s e r v a t i o n s f r e e l y use all the CAP w a t e r a v a i l a b l e to them) and so b a l a n c e s out m o r e than half of the 0 . 8 m i l l i o n d o l l a r gain to non-Indian f a r m e r s m a d e when CAP w a t e r was f u r n i s h e d on a f r e e choice basis. With a CAP w a t e r u s e of 619, 000 a c r e - f e e t out of the 659, 000 a c r e - f e e t total CAP allocation, (139, 000 a c r e feet of which was not f r e e l y chosen) the t r a d e - o f f r a t i o between CAP and pump w a t e r r i s e s to about 2.3 a c r e feet of CAP u s e d for each 1 a c r e - f o o t of pump w a t e r no l o n g e r used. The r a t i o was only 3.1 a c r e - f e e t of CAP to 1 a c r e - f o o t of pump w a t e r when CAP was f r e e l y chosen. A l m o s t no shift in the c o u n t y ' s c r o p mix is o b s e r v e d . In o r d e r to u s e all of the r e q u i r e d CAP w a t e r , however, the n u m b e r of double c r o p p e d a c r e s i n c r e a s e d slightly and the C A P - l o c a l w a t e r m i x shifted to m i x e s with h i g h e r q u a n t i t i e s of CAP w a t e r . Most of the r e q u i r e m e n t to u s e m o r e CAP w a t e r was s i m p l y r e f l e c t e d in d e c r e a s e d net i n c o m e . Most of the d e c r e a s e in net i n c o m e is f r o m the h i g h e r p r i c e of CAP w a t e r r a t h e r than f r o m d e c r e a s e s in y i e l d due to use of p o o r e r quality w a t e r . In fact, in one D i s t r i c t , the quality of the w a t e r m i x i m p r o v e d .
I m p a c t of I n c r e a s e d C A P Salinity It is e s t i m a t e d that C o l o r a d o R i v e r w a t e r d e l i v e r e d to P i n a l County w i l l have a m e a n s a l i n i t y of 1.4 m m h o s / cm in 1986 and a m e a n s a l i n i t y of 1 . 8 m m h o s / c m in 2020 if no a d d i t i o n a l s a l i n i t y c o n t r o l p r o g r a m s a r e i n s t i t u t e d . F o r any s a l i n i t y c o n t r o l p r o g r a m to be e c o n o m i c a l l y efficient, the cost of the c o n t r o l p r o g r a m should be l e s s than the value of the d e c r e a s e in a g r i c u l t u r a l p r o d u c t i o n if no c o n t r o l s a r e e s t a b l i s h e d . The m o d e l s c o m p a r e the value of net r e t u r n s above v a r i a b l e c o s t s at the two s a l i n i t y l e v e l s when CAP w a t e r is f r e e l y chosen. The t o t a l d e c r e a s e in net r e t u r n s above v a r i a b l e c o s t s f o r P i n a l County f a r m e r s 106
F a r m e r s on the two Indian R e s e r v a t i o n s in P i n a l County will r e c e i v e F e d e r a l l y s u b s i d i z e d CAP w a t e r at no d i r e c t v a r i a b l e cost to them, and the w a t e r can be used to expand i r r i g a t e d a c r e a g e . Thus, the Indian R e s e r v a t i o n s could p r o v i d e an outlet f o r e x c e s s a g r i c u l t u r a l CAP w a t e r . F u r t h e r , a m e a s u r e of economic b e n e f i t s a c c r u i n g to Indian f a r m e r s r e c e i v i n g the f r e e CAP w a t e r is of i n t e r e s t to d e c i s i o n - m a k e r s a l l o c a t i n g the p r o j e c t w a t e r . The r e p r e s e n t a t i v e - f a r m m o d e l s for both the Indian D i s t r i c t lands a r e m o d i f i e d to d e t e r m i n e the m a x i m u m quantity of CAP w a t e r that could be u s e d e f f e c t i v e l y by each if i r r i g a t e d a c r e age w e r e expanded to include all of the i r r i g a b l e lands on the r e s e r v a t i o n . With an u n l i m i t e d quantity of f r e e CAP a v a i l a b l e , the two r e s e r v a t i o n s would u s e n e a r l y twice as much w a t e r as the i n i t i a l annual allotment, and net r e t u r n s above v a r i a b l e c o s t s would i n c r e a s e 4 . 7 t i m e s .
The E f f e c t s of F i x e d C o s t s In o r d e r to d e t e r m i n e the net e c o n o m i c p o s i t i o n of f a r m e r s in P i n a l County, fixed f a r m c o s t s a l s o m u s t be c o n s i d e r e d . F i x e d c o s t s a r e those c o s t s i n c u r r e d by the f a r m o p e r a t i o n r e g a r d l e s s of the f a r m ' s l e v e l of production, for e x a m p l e , d e p r e c i a t i o n of buildings, m a c h i n e r y , w e l l s , and d i t c h e s ; i n t e r e s t on the i n v e s t ment; and t a x e s . D e t a i l e d fixed cost v a l u e s for f a r m s in P i n a l County a r e d e v e l o p e d in B o s t e r (1976). However, these fixed c o s t s e s t i m a t e s do not include the fixed c o s t of CAP d e l i v e r y s y s t e m s , that is, the l a t e r a l c a n a l s which the f a r m e r m u s t p r o v i d e to t r a n s p o r t the CAP w a t e r f r o m the main canal to the f a r m h e a d g a t e . D e t a i l e d fixed cost d a t a for the CAP d i s t r i b u t i o n s y s t e m a r e not a v a i l a b l e , and t h e i r c o m putation is beyond the s c o p e of this study, although c o n s u l t a n t s ' r e p o r t s (Beck, 1971a, b, c) show that the c o s t s could e a s i l y be ten or m o r e d o l l a r s p e r a c r e foot p e r y e a r . Although the p r e c i s e c o s t of c o n s t r u c t i n g l a t e r a l d i s t r i b u t i o n s y s t e m s for the CAP w a t e r cannot be
The value of 0.23 cents p e r y e a r p e r i r r i g a t e d a c r e p e r p a r t p e r m i l l i o n i n c r e a s e in s a l i n i t y is computed by dividing 61 cents by 268 p a r t s p e r m i l l i o n i n c r e a s e in s a l i n i t y (0.4 m m h o s / c m x 670 p p m / m m h o s / c m = 268 ppm).
A d v a n c e s in W a t e r R e s o u r c e s
made, it is p o s s i b l e to c a l c u l a t e the f a r m e r s ' m a x i mum w i l l i n g n e s s to pay for the d i s t r i b u t i o n s y s t e m s . This c a l c u l a t i o n is made by e s t i m a t i n g the d i f f e r e n c e in net f a r m i n c o m e s with and without using CAP w a t e r . The d i f f e r e n c e would be the m a x i m u m amount that f a r m e r s ' could afford to pay annually in o r d e r to d e l i v e r the w a t e r f r o m the m a i n canal to t h e i r h e a d gates.
Vol. 1 No. 2 1977
studied, the question of s i g n i f i c a n t c r o p l o s s f r o m i n c r e a s e d s a l i n i t y in the o t h e r a r e a s is r a i s e d . It a p p e a r s that b e n e f i t s of w a t e r d e v e l o p m e n t a r e not all that they may at f i r s t s e e m , even in this v e r y a r i d a g r i c u l t u r a l a r e a with a g r o u n d w a t e r o v e r d r a f t p r o b l e m .
Appendix Obviously, numerous assumptions are necessary for It is shown in B o s t e r (1976) that although net r e t u r n s the analyses. S o m e of the major assumptions include: above v a r i a b l e c o s t s i n c r e a s e in m o s t i r r i g a t i o n (1) Yield reduction due to irrigation water salinity is d i s t r i c t s when C e n t r a l A r i z o n a P r o j e c t w a t e r is i n t r o related to the calculated m e a n salinity against which duced into P i n a l County, v e r y l i t t l e of the i n c r e a s e water is absorbed, which is influenced m o r e by the o c c u r s on non-Indian l a n d s . B e c a u s e non-Indian "salinity of the irrigation water than by the salinity of f a r m e r s m u s t i n c u r the c o n s t r u c t i o n cost of a d i s t r i b u - the drainage water; (2) yield reductions from water tion s y s t e m (Indian f a r m e r s l i k e l y will r e c e i v e t h e i r s free), it is unlikely that the i n c r e a s e in net r e t u r n s above v a r i a b l e c o s t s will in fact exceed the a s s o c i a t e d fixed c o s t s .
Conclusions
The o s t e n s i b l e b e n e f i t s of t r a n s p o r t i n g s u r f a c e w a t e r into C e n t r a l A r i z o n a , a m a j o r c r o p p r o d u c i n g a r e a , a r e to (1) be of e c o n o m i c benefit to the non-Indian a g r i c u l t u r a l economy and (2) to s i g n i f i c a n t l y r e d u c e the p h y s i c a l d e c l i n e in the u n d e r g r o u n d w a t e r table. B e c a u s e of the p r o j e c t e d i n c r e a s e in s a l i n i t y in the C o l o r a d o R i v e r , a m a j o r w o r r y is that s i g n i f i c a n t a g r i c u l t u r a l l o s s will o c c u r with u s e of C o l o r a d o R i v e r w a t e r in this and o t h e r a g r i c u l t u r a l a r e a s . The r e s u l t s of this study do not s u p p o r t t h e s e widely held b e l i e f s for e i t h e r the o s t e n s i b l e b e n e f i t s or l o s s e s .
s h o r t a g e and f r o m s a l i n i t y a r e additive; (3) w a t e r is o p t i m a l l y a l l o c a t e d d u r i n g the c r o p s e a s o n ; (4) the c r o p s s e l e c t e d for this study will continue to be the m o s t i m p o r t a n t ones grown in the a r e a ; (5) the r a t i o of p r o d u c t p r i c e s to input c o s t s is constant over time; and (6) the r e l a t i v e p r i c e s of c r o p s a r e constant over t i m e . A d e t a i l e d e x p l a n a t i o n of the a s s u m p t i o n s in the m o d e l s is found in B o s t e r (1976). The following is a m a t h e m a t i c a l s t a t e m e n t of the generalized representative-farm linear-programming c o m p u t e r model. Specific m o d e l s v a r y slightly f r o m this s t a t e m e n t . The o b j e c t i v e of this model is to:
J Maximize Z =
K
~,
NRjk.
j : l k-----i
(2)
(3)
D e l i v e r y of CAP w a t e r under the p r o p o s e d l e g i s l a t i v e r e s t r i c t i o n s will not a s s u r e groundw a t e r c o n s e r v a t i o n at anywhere n e a r a o n e - t o - o n e t r a d e - o f f and thus w i l l not s i g n i f i c a n t l y r e d u c e groundwater decline.
Subject to:
N e a r l y all of the m o n e t a r y b e n e f i t s f r o m the P r o j e c t to a g r i c u l t u r e in P i n a l County will be c a p t u r e d by Indian r a t h e r than by non-Indian f a r m e r s . (Original b e n e f i t - c o s t e s t i m a t e s w e r e made on the b a s i s of the non-Indian c o m m e r c i a l farms.)
Constraint 2:
Indian f a r m e r s will have the f a r m land c a p a c i t y to u s e any e x c e s s CAP w a t e r f r o m non-Indian f a r m e r s if t h e r e is no d i r e c t c o s t to the Indians for the w a t e r and they a r e allowed to u s e the CAP w a t e r to expand a c r e a g e .
(4) R e q u i r i n g n o n - i n d i a n f a r m e r s to u s e a m i n i m u m quantity of CAP w a t e r in t h e i r c r o p w a t e r m i x would r e d u c e c o n s i d e r a b l y the m o n e t a r y gains to be r e a l i z e d if CAP w a t e r w e r e m a d e a v a i l a b l e with the quantity u s e d to be f r e e l y chosen by the farmers. (5) While p r o v i s i o n of CAP w a t e r to the f a r m h e a d gate at a p r i c e of $ 1 6 . 6 7 p e r a c r e - f o o t would i n c r e a s e s o m e non-Indian f a r m e r ' s net income, the a g g r e g a t e i n c r e a s e in net i n c o m e in non-Indian d i s t r i c t s w i l l not likely be enough to pay for the n e c e s s a r y CAP d i s t r i b u t i o n s y s t e m s within P i n a l County. (6)
The p o s s i b i l i t y of i n c r e a s e d s a l i n i t y f r o m CAP w a t e r should not be of c o n c e r n to f a r m e r s in the county. Since other a r e a s using C o l o r a d o R i v e r w a t e r a r e quite s i m i l a r to the s p e c i f i c a r e a
T
~ ~ C s t . Wst s=lt--1
Specific r e s u l t s of t h i s study a r e as follows: (1)
S
Xjk--
K
Constraint 1:
J
~
P U M P j k . Xj k -
k=~
PSLK = 0
j=l
K
J
~
~
k=l
j=l
C A P j k . Xjk-- C S L K = 0 T
Constraint 3a: P S L K - - ~,
Wst = 0
s = 1
Wst : 0
S : 2
t~- 1 T
3b: C S L K t----I
Constraint 4a: CSLK-< CMAX
4b: C S L K _> C M I N T
C o n s t r a i n t 5:
~, W s t _< S M A X
s=3
t=1 K
J
Z Wjkt. XjR- Wst= 0
C o n s t r a i n t 6a:
k---1 j=1 = 1,2,3 ~ = 1,2, ...,8
s
6b: W
st
_< WMAX
st
s : 1, 2,3
t----- 1,2, . . . , 8
C o n s t r a i n t 7: PSLK + CSLK _< TOTWA 4
C o n s t r a i n t 8a:
j
~ ~, k=l j = 1
Xjk -< WINAC
107
Supplemental Colorado River Water for a Developed Groundwater Agriculture Mark A. Boster and William E. Martin 5
SUMAC = N u m b e r of c r o p a c r e s a v a i l a b l e d u r i n g the s u m m e r (excluding conserving base).
J
8b: ~ ~ k=3 j = 1 7
J
8C: ~
•
Xjk <
SUMAC
Xjk
C o n s t r a i n t 9:
TOTAC
~ ~ Xjk-- TOTAC = 0 k=1 J = 1
TOTWA =
Wjk t
W h e r e t h e v a r i a b l e s , l i s t e d in a l p h a b e t i c a l o r d e r , a r e : = C o s t p e r a c r e - f o o t of w a t e r f r o m s o u r c e s a p p l i e d in t i m e p e r i o d t. =
CAPjk
M a x i m u m a m o u n t of C A P w a t e r a v a i l a b l e to t h e f a r m t h r o u g h the i r r i g a t i o n d i s t r i c t .
Xjk
CM~
=
M i n i m u m a m o u n t of w a t e r the irrigation district must use.
Z
=
N u m b e r of c o n s e r v i n g b a s e acres available.
=
W a t e r m i x index to a c c o u n t for v a r i o u s m i x e s of p u m p e d and C A P w a t e r .
J
=
k
=
N u m b e r of w a t e r m i x e s f o r e a c h c r o p and f a r m s i z e pumping depth class. T y p e of c r o p . k = 1,2, ....,7
CSLK =
CAP water slack which equals total CAP water used per year.
MAXCOT k
=
M a x i m u m a c r e a g e of cotton.
NRjk
=
Net r e t u r n s a b o v e a l l v a r i a b l e p r o d u c t i o n c o s t e x c e p t the c o s t of w a t e r f o r c r o p k g r o w n w i t h w a t e r m i x j.
PSLK
=
Pumping slack which equals total water pumped per year.
PUMPjk
=
A c r e - f e e t of p u m p e d w a t e r a p p l i e d to e a c h a c r e of c r o p k g r o w n with w a t e r m i x j.
s = S o u r c e of w a t e r . Pumped water 2=
Central Arizona Project water
3=
S u r f a c e w a t e r f r o m the San Carlos Project
S
N u m b e r of w a t e r s o u r c e s
SMAX = M a x i m u m a m o u n t of s u r f a c e w a t e r a v a i l a b l e in San C a r l o s Project areas.
"~- A c r e - f e e t of w a t e r n e e d
in t i m e p e r i o d t, f o r e a c h a c r e of c r o p k g r o w n with water mix j.
W M A X s t = M a x i m u m a m o u n t of w a t e r a v a i l a b l e f r o m s o u r c e s in t i m e p e r i o d t.
=
j
T o t a l a m o u n t of w a t e r ( a c r e feet) f r o m s o u r c e s a p p l i e d in t i m e p e r i o d t.
WINAC = N u m b e r of c r o p a c r e s a v a i l able during the winter.
A c r e - f e e t of C e n t r a l A r i z o n a P r o j e c t w a t e r a p p l i e d to e a c h a c r e of c r o p k g r o w n with water mix j.
CMAX
CONBA
Ten year average pumpage in the a r e a .
Wst =
J
C o n s t r a i n t 10: ~, Xj k _< MAXCOT k k = 4, 5 k=l
108
T o t a l a c r e s c r o p p e d (counts double cropped acres twice).
=
J
Cst
t = 1, 2, o...,8
-< CONBA
k=6 3 = I K
Time period,
t=
= A c r e s of l a n d a s s i g n e d to crop k that is grown with w a t e r m i x j. =
T o t a l net r e t u r n s o v e r v a r i a b l e c o s t s f o r the f a r m .
REFERENCES
Central Arizona Project Engineering and Planning Study: Central Arizona Irrigation and Drainage District. P h o e n i x .
B e c k , R. W. a n d A s s o c i a t e s .
M a r c h , 1971a.
Central Arizona Project Engineering and Planning Study: New Magma Irrigation and Drainage District. P h o e n i x . M a r c h , 19"llb. Central Arizona Project Engineering and Planning Study: Maricopa-Stanfield Irrigation and Drainage District. P h o e n i x . M a r c h , 1971c. B e r n s t e i n , L . Salt Tolerance of Plants. U . S . D e p a r t m e n t of A g r i c u l t u r e , A g r i c u l t u r a l i n f o r m a t i o n B u l l e t i n 283, W a s h i n g t o n , 1964. __, and L. E . F r a n c o i s . ' L e a c h i n g R e q u i r e m e n t S t u d i e s : S e n s i t i v i t y of A l f a l f a to S a l i n i t y of I r r i g a tion and D r a i n a g e W a t e r s . 'Soil Science Society of America Proceedings, v o l . 37, no. 6, N o v . - D e c . , 1973. B o s t e r , M a r k A l a n . ' E v a l u a t i o n of A g r i c u l t u r a l A d j u s t m e n t to I r r i g a t i o n W a t e r S a l i n i t y : A C a s e Study f o r P i n a l County, A r i z o n a . ' U n p u b l i s h e d P h . D . D i s s e r t a t i o n . U n i v e r s i t y of A r i z o n a , T u c s o n . 1976. B u r e a u of R e c l a m a t i o n . P r o p o s e d C e n t r a l A r i z o n a Project. Final Environmental Statement, Washington. S e p t e m b e r , 1972. D r e g n e , H . E . Prediction of Crop Yields from Quantity and Salinity o/Irrigation Water. A g r i c u l t u r a l E x p e r i m e n t S t a t i o n B u l l e t i n 543, New M e x i c o S t a t e U n i v e r s i t y , L a s C r u c e s . M a r c h , 1969. S t u l t s , H a r o l d M. ' P r e d i c t i n g F a r m e r R e s t ) o n s e to a F a l l i n g W a t e r T a b l e : A n A r i z o n a C a s e Study. ' U n p u b l i s h e d P h . D . d i s s e r t a t i o n . The U n i v e r s i t y of A r i z o n a , T u c s o n . 1968.
A d v a n c e s in Water R e s o u r c e s Sun, Po-chaun. 'An Economic Analysis on the Effects of Quantity and Quality of I r r i g a t i o n W a t e r on A g r i c u l t u r a l Production in I m p e r i a l Valley, California. ' Unpublished Ph.D. d i s s e r t a t i o n , The University of California, Davis. 1972. Young, R. A., W. T. Franklin, and K. C. Nobe. A s s e s s i n g Economic E f f e c t s of Salinity on Irrigated Agricul-
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ture in the Colorado R i v e r B a s i n : A g r o n o m i c and Economic Considerations. Report to the Bureau of Reclamation, U.S. D e p a r t m e n t of the Interior, Contract no. 14-06-D-7341, D e p a r t m e n t s of Econom i e s and Agronomy, Colorado State University, F o r t Collins. August, 1973.
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Supplemental Colorado River Water for a Developed Groundwater Agriculture: A Problem of Quantities, Qualities and Conjunctive Use
MARK A. B o f f r E R
Office of Biological Services U.S. Fish and Wildlife Servi~e, Washington, D.C. 20240 (This article was developed while Dr. B o s t e r was at the University of Arizona, Tucson, Arizona.)
WILLIAM E. MARTIN Department of Agricultural Economics, University of Arizona, Tucson, A r i z o n a 85721
Upon completion o f the Central A r i z o n a P r o j e c t (CAP), Colorado R i v e r water will be d e l i v e r e d s o m e 200 m i l e s inland f o r agricultural, domestic, and industrial use. Any new importation o f w a t e r to an area implies adjustments in the organization o f the economy o f the area. F o r irrigated agriculture, a d j u s t m e n t s will o c c u r in input mix, output mix, acreage f a m e d , and in g r o s s and net incomes. A complicating f a c t o r associated with importation of Colorado R i v e r w a t e r is that the imported water will contain different d i s s o l v e d salt concentrations than the groundwater and surface w a t e r currently being used. Mathematical p r o g r a m m i n g models of r e p r e s e n t a t i v e irrigated f a r m s in Pinal County, Arizona, are used to p r o j e c t a d j u s t m e n t s implied under s e v e r a l assumptions as to the availability, cost and salinity o f the various s o u r c e s o f irrigation water. Conclusions are drawn as to the potential winners and l o s e r s f r o m project development. Conclusions include the f o l l o w i n g : I n c r e a s e d salinity should not be o f concern to the f a r m e r s in the county and Indian f a r m s will reap the g r e a t e s t share o f benefits f r o m the Project.
Several interacting events make this r e p o r t relevant-both as a case study of an important i r r i g a t e d agricultural area, Pinal County, Arizona, and as a model for examining other irrigated agricultural a r e a s . Most of A r i z o n a ' s d e s e r t valley soils are suitable for crop production, but receive less than 10 inches of precipitation annually. Thus, farming in the a r e a is almost completely dependent upon irrigation s y s t e m s to meet crop water demands. Pinal County may generally be considered r e p r e s e n t a t i v e in climate and agricultural p r a c t i c e s of the irrigated a r e a s in the Southwestern United States, including the Imperial Valley of southern California. The events are: (1) The Central Arizona P r o j e c t (CAP) is under construction. 1 This project will deliver Colorado River water some 200 miles into central Arizona, including Pinal County, where a fifth of the s t a t e ' s cropland is irrigated mostly with groundwater. (2) In the a r e a s currently using pumped groundwater for irrigation, the groundwater table is falling because of continued groundwater mining. (3) The quality of the Colorado R i v e r water, in t e r m s of dissolved solid content, is d e c r e a s i n g over time. (4) The CAP water will be used in conjunction with already available water supplies of differing quality and cost, which in most a r e a s is groundwater available on demand from the f a r m e r ' s private wells. Thus, the overall objective is to make an economic evaluation of the adjustment p r o b l e m s and alternatives open to irrigated agriculture when faced with a second
1 The Central A r i z o n a P r o j e c t was one of the water r e s o u r c e p r o j e c t s recently reviewed for economic feasibility by P r e s i d e n t C a r t e r ' s administration.
or third water supply of differing quality and cost. However, evaluation of these issues provide insights into s e v e r a l related questions. These include: (I) What is the cost of increased salinity in the Colorado River to the prospective u s e r s of that w a t e r ? (2) What will delivery of that water mean in t e r m s of groundwater conservation in the study a r e a ? (3) Who will reap the benefits from the additional water supply? And finally, (4) Who may find that they do not want the new water supply after all ? To accomplish the general economic evaluation, the following specific evaluations are required. They are: (I)
To project the economic position of r e p r e s e n t a tive individual f a r m e r s and of the county as a whole in 1986 (the projected date of project completion) if no Central Arizona P r o j e c t water is available;
(2)
To project the economic impact of CAP water in the study a r e a in 1986 if CAP water is available to f a r m e r s on a free choice basis. Physical changes expected include changes in the input mix for each crop, the level of physical output for each crop, and the output mix for each f a r m and for the county;
(3) To investigate the economic effects of requiring each farm in the county to use at least 90 p e r cent of its annual CAP water allotment in o r d e r to meet the i r r i g a t i o n d i s t r i c t s ' contractual agreements; (4) To m e a s u r e the loss in net f a r m returns resulting from i n c r e a s e d salinity of Colorado River water --the s o u r c e for Central A r i z o n a P r o j e c t - - o v e r time. 103
Supplemental Colorado R i v e r Water f o r a Developed Groundwater Agriculture Mark A. B o s t e r and William E. Martin (5)
Because the Indian f a r m e r s and the non-Indian f a r m e r s of the a r e a will be subject to different water use rules and water costs, one must d e t e r mine the m a x i m u m quantity of CAP water that could be used effectively by Indian f a r m e r s in the area.
Evaluations 2 through 5 are partial analyses showing changes from the base s i t u a t i o n - n u m b e r 1. They involve only changes in variable costs. The final evaluation (6) investigates the ability of the f a r m e r s to absorb the n e c e s s a r y fixed costs in each situation. Method of Analysis Detailed r e p r e s e n t a t i v e - f a r m organizations, costs and r e t u r n s data are used to develop the linear p r o g r a m ming models used as the tool for analysis. Sixty-nine of these r e p r e s e n t a t i v e - f a r m l i n e a r - p r o g r a m m i n g models are needed to describe adequately the i r r i gated farming activities in Pinal County. Each model includes alternative crop production activities using various quantities of Central A r i z o n a P r o j e c t water, groundwater, and other s u r f a c e water (in the San Carlos P r o j e c t s area) under alternative conditions of use. Each water source, and thus the resulting water mixes, is available in various quantities over time, at different p r i c e s and salinities. The linear p r o g r a m ming models are designed to maximize net farm r e t u r n s above variable production costs subject to the r e s o u r c e constraints faced by the r e p r e s e n t a t i v e f a r m e r s . Individual r e p r e s e n t a t i v e - f a r m r e s u l t s are aggregated into r e s u l t s for each of the seven i r r i g a tion d i s t r i c t s and for the whole county. All irrigated farmland in the county is included within these d i s t r i c t s . A mathematical statement of the generalized r e p r e s e n t a t i v e - f a r m linear p r o g r a m m i n g model is given in the Appendix. THE MODEL AS A DESCRIPTION OF THE PINAL COUNTY PROBLEM The Economic D e c i s i o n s The individual firm employs r e s o u r c e s (factors of production) to produce a product. Although not all f i r m s are interested in profit maximization, agricultural f i r m s (farms) operate in a competitive m a r k e t and t h e r e f o r e only profit maximization a s s u r e s their long run existence. Each firm interested in profit maximization must make three simultaneous decisions: (1) What combination of products to produce, (2) how to combine inputs in the production of a given level of output for a given product, and (3) what level of output to produce (e.g., what yield per a c r e for each product). E c o n o m i s t s t e r m these decisions the product-product, f a c t o r - f a c t o r , and f a c t o r - p r o d u c t decisions, r e s p e c tively. If the firm has profit maximization as its goal, if it knows the costs of inputs and p r i c e s of outputs, the simultaneous solution to the three questions provides the firm with its profit maximizing position. In this study, the f a c t o r - f a c t o r question involves the optimal mix of imported CAP water with local water. How much yield per a c r e of each crop to produce, relative to the variable inputs of water quantity and quality, is handled by the f a c t o r - p r o d u c t decisions. The optimal crop mix is determined by the productproduct relationships. 104
Thus, an objective function is developed for each r e p r e s e n t a t i v e farm. A r e p r e s e n t a t i v e f a r m is defined for four s i z e s (so as to e x p r e s s economies of size), for three depths to water (to e x p r e s s alternative water costs), and for seven i r r i g a t i o n districts (to e x p r e s s differing groundwater qualities). These functions contain net revenue coefficients for each possible production activity on each farm. A production activity is a method of producing a crop on one acre of land. Each crop has s e v e r a l production activities, i.e., each crop is repeated s e v e r a l times in each model to allow for alternative mixes of water sources, each of which has a different cost and salinity. F o r example, one cotton activity uses all pump water, another uses all CAP water, another uses four a c r e - f e e t of pumped water in combination with one a c r e - f o o t of CAP water, another three a c r e - f e e t of pumped water along with two a c r e - f e e t of CAP water, etc. Different costs, different yields, and this different net return coefficients are a s s o c i a t e d with each way of producing an acre of each type of crop. The net r e t u r n above variable cost values for each production activity includes that r e t u r n which must pay for the variable cost of water. Because each water source has a different unit cost, the total water cost a s s o c i ated with each w a t e r mix is different. Unit water costs for each available s o u r c e are included in the objective function in water purchase activities so that the total water cost can be computed within the model.
W a t e r Quantity, W a t e r Quality, ~nd Crop Yield In developing net r e t u r n estimates for each activity, yield estimates as related to water quantity and water quality are crucial. The effects of water quantity on crop output and water quality (salinity) on crop output are each c o n t r o v e r s i a l and complex subjects. However, Stults (1968) has presented estimates of yield r e s p o n s e as related to water quantity in the study area. Bernstein (1964) estimated relative yield as a function of water salinity. Specific l i t e r a t u r e on the joint effects of water quantity and salinity on crop yield does not exist. Dregne (1969) a s s u m e s that the effects of each are additive. Sun (1972), in an innovative economic analysis, makes the same assumption. A thorough review of both the agronomic and economic considerations n e c e s s a r y to a s s e s s i n g the effects of salinity on i r r i g a t e d agriculture is given by Young et al. (1973). They also review the empirical economic studies completed up to that time. However, at the time of their review, the r e c e n t theory on crop sensitivity to irrigation water salinity by Bernstein and F r a n c o i s (1973) was unpublished and not included. This theory essentially states that in a r e a s of p r o p e r soil condition and good drainage, yield r e s p o n s e s appear to be related to the calculated mean salinity against which w a t e r is absorbed, which is influenced m o r e by the salinity of the irrigation water as m e a s u r e d at the surface, than by the mean salinity in the root zone as assumed by the older theory. The older theory consistently o v e r e s t i m a t e d actual crop damage from salinity. Because the models in this study i n c o r p o r a t e the newly developed relationships, estimated economic loss in Pinal County resulting from i n c r e a s e d water salinity turns out to be r e l a tively minor.
A d v a n c e s in W a t e r R e s o u r c e s
The P h y s i c a l and L e g a l C o n s t r a i n t s W a t e r a v a i l a b i l i t y is the only i m p o r t a n t r e s t r i c t i o n c u r r e n t l y faced by P i n a l County f a r m e r s . T y p i c a l l y , f a r m e r s run t h e i r i r r i g a t i o n pumps 24 hours a day f r o m late June until e a r l y August to e x t r a c t the m a x i mum quantity of w a t e r p h y s i c a l l y p o s s i b l e . A second c r i t i c a l w a t e r u s e o c c u r s f r o m J a n u a r y 15 to the end of F e b r u a r y . During this p e r i o d , b a r l e y and wheat a r e i r r i g a t e d and cotton is p r e i r r i g a t e d . However, f a r m e r s t y p i c a l l y only u s e 70 p e r cent of t h e i r pumping c a p a city in the w i n t e r so as to avoid drawdown p r o b l e m s in the s u m m e r . P u m p a g e l i m i t s a r e a s s u m e d to i n c r e a s e l i n e a r l y f r o m the w i n t e r to the s u m m e r and then d e c r e a s e l i n e a r l y f r o m the s u m m e r through the fall. Although no w a t e r c o n t r a c t s for C e n t r a l A r i z o n a w a t e r have as y e t been signed, and exact a l l o c a t i o n s to the county and d i s t r i c t s have not been made, c e r t a i n b a s i c a s s u m p t i o n s about the P r o j e c t a r e n e c e s s a r y if m o d e l s a r e to be c o n s t r u c t e d . A f t e r d i s c u s s i o n s with m e m b e r s of the A r i z o n a W a t e r C o m m i s s i o n , r e a s o n a b l e a s s u m p t i o n s about the total quantity of CAP w a t e r i n i t i a l l y a v a i l a b l e for a g r i c u l t u r a l u s e in P i n a l County and the a l l o c a t i o n of that w a t e r to each i r r i g a t i o n d i s t r i c t was m a d e . P i n a l County w i l l r e c e i v e about 659, 000 a c r e - f e e t of CAP w a t e r in 1986 for a g r i c u l t u r a l u s e . Indian lands a r e to be a l l o c a t e d about o n e - t h i r d of the total a g r i c u l t u r a l CAP w a t e r a v a i l a b l e to the county in 1986. Under the enabling l e g i s l a t i o n , non-Indian lands can use CAP w a t e r only on those lands with a h i s t o r y of i r r i g a t i o n d u r i n g the ten y e a r s p r e c e d i n g e n a c t m e n t of the P r o j e c t l e g i s l a t i o n , i,e., lands r e c e i v i n g i r r i g a t i o n w a t e r m u s t have been under i r r i g a t i o n at s o m e t i m e d u r i n g the p e r i o d S e p t e m b e r , 1958 to S e p t e m b e r , 1968. Thus a land c o n s t r a i n t is c r e a t e d . B e c a u s e of planned canal capacity, no i r r i g a t i o n d i s t r i c t can r e c e i v e m o r e than 13.5 p e r cent of its annual a l l o t m e n t in any month. But, within that l i m i t a t i o n , an individual f a r m can r e c e i v e as much w a t e r as can be p r o f i t a b l y used. C u r r e n t e s t i m a t e s p l a c e the cost of CAP w a t e r for nonIndians at $ 1 5 . 0 0 p e r a c r e - f o o t at the m a i n canal s i d e . This cost t r a n s l a t e s into a cost of $ 1 6 . 6 7 at the f a r m headgate, given a ten p e r cent conveyance l o s s . Indian f a r m e r s will r e c e i v e s u b s i d i z e d CAP w a t e r f r o m the F e d e r a l G o v e r n m e n t at no d i r e c t cost to them. A c c o r d i n g to CAP l e g i s l a t i o n , each non-Indian i r r i g a tion d i s t r i c t m u s t r e d u c e g r o u n d w a t e r pumpage by one a c r e - f o o t for each a c r e - f o o t of P r o j e c t w a t e r p u r chased [43 U.S.C. Sec. 1524 (d)]. This study a s s u m e s that the a v e r a g e y e a r l y pumpage for the p e r i o d 1959 through 1968 is the b a s e a g a i n s t which w a t e r m u s t be t r a d e d . This p e r i o d is chosen since it is the 10 y e a r p e r i o d p r i o r to the p a s s a g e of the CAP b i l l . Total 10 y e a r a v e r a g e annual pumpage for the study a r e a is e s t i m a t e d as 1 , 0 2 4 , 0 0 0 a c r e - f e e t . P r o j e c t e d s a l i n i t y l e v e l s in the C o l o r a d o R i v e r for 1985 r a n g e f r o m a low of 1.2 m m h o s / c m 2 t o a high of 1.5 m m h o s / c m . In the CAP e n v i r o n m e n t a l i m p a c t s t a t e m e n t , the B u r e a u of R e c l a m a t i o n (1972) s t a t e s that e v a p o r a t i o n of Colorado R i v e r w a t e r d u r i n g t r a n s i t to P i n a l County will have a m i n o r effect on concent r a t i o n s of total d i s s o l v e d s o l i d s in the i m p o r t e d w a t e r . A m a x i m u m d e g r a d a t i o n of about six p e r cent between the r i v e r and Pinal County is e s t i m a t e d . Using the
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a v e r a g e value f o r s a l i n i t y p r o j e c t i o n s f o r C o l o r a d o R i v e r w a t e r at the point of intake in 1986, with a s i x p e r cent i n c r e a s e in t r a n s i t , an e s t i m a t e of w a t e r quality of about 1.4 m m h o s / c m s a l i n i t y in Pinal County is p r o d u c e d . Land h a s not been a r e s t r a i n t on output in Pinal County in r e c e n t y e a r s , However, to account for double c r o p ping, to a s s u r e that CAP w a t e r is not used to expand a c r e a g e on n o n - I n d i a n f a r m s , and to define the total i r r i g a b l e land in Indian a r e a s , both w i n t e r and s u m m e r land c o n s t r a i n t s a r e included in the m o d e l s . Land is also r e s t r i c t e d b e c a u s e of a r e q u i r e m e n t for a • ' c o n s e r v a t i o n b a s e ' . Cotton a c r e a g e is r e s t r i c t e d to r e f l e c t the f a r m e r s ' t y p i c a l a v e r s i o n to r i s k .
R E S U L T S O F T H E ANALYSES No CAP V e r s u s CAP F r e e l y P u r c h a s e d The i n i t i a l s o l u t i o n s of the r e p r e s e n t a t i v e f a r m m o d e l s a s s u m e no C e n t r a l A r i z o n a P r o j e c t w a t e r is a v a i l a b l e in 1986. This a n a l y s i s e s t a b l i s h e s a b a s e f r o m which to m e a s u r e the e c o n o m i c i m p a c t of i n t r o d u c i n g the new w a t e r into the a r e a . With C e n t r a l A r i z o n a P r o j e c t w a t e r introduced into the 1986 r e p r e s e n t a t i v e f a r m m o d e l s , net r e t u r n s above v a r i a b l e c o s t s for the whole county i n c r e a s e d by 4 . 7 m i l l i o n d o l l a r s or 35 p e r cent above net r e t u r n s if no CAP w a t e r is a v a i l a b l e . S i m i l a r l y , cropped a c r e a g e i n c r e a s e d by n e a r l y 83,200 a c r e s with CAP w a t e r i n t r o d u c e d and f r e e l y p u r c h a s e d . However, 3.9 m i l l i o n d o l l a r s of the 4 . 7 m i l l i o n d o l l a r i n c r e a s e and n e a r l y 55, 300 a c r e s of the 83,200 c r o p p e d a c r e a g e i n c r e a s e o c c u r s on the two Indian R e s e r v a t i o n s w h e r e CAP w a t e r is f r e e and can be u s e d to d e v e l o p new c r o p l a n d s . B e c a u s e total a c r e s of cotton a r e r e s t r i c ted in the model, the r i s e in net r e t u r n s r e s u l t s f r o m a c r e a g e i n c r e a s e s in the other c r o p s . The i n c r e a s e in net income to Indian lands will be a r e a l i n c r e a s e in total net i n c o m e to the Indians s i n c e a l m o s t all c o s t s of the new w a t e r a r e s u b s i d i z e d . However, c e r t a i n fixed c o s t s , such as the c o s t of the d i s t r i b u t i o n s y s t e m f r o m the m a i n canal to the f a r m h e a d g a t e s m u s t be s u b t r a c t e d f r o m the 0 . 8 m i l l i o n d o l l a r i n c r e a s e in income to n o n - I n d i a n s . These c o s t s are discussed later. A 21 p e r cent d e c r e a s e (about 154,000 a c r e - f e e t ) o c c u r s in pumped w a t e r used in the a r e a r e c e i v i n g CAP w a t e r . Other s u r f a c e w a t e r u s e is e s s e n t i a l l y constant. However, t~he total w a t e r applied to c r o p s i n c r e a s e s by 325, 700 a c r e - f e e t - - a 37 p e r cent inc r e a s e in total w a t e r u s e . Why is total w a t e r u s e with CAP higher than total w a t e r use without CAP, if the one for one p u m p - C A P t r a d e - o f f r u l e i s in e f f e c t ? T h e r e a r e two r e a s o n s . F i r s t , the r u l e d o e s not apply on Indian lands where
M i l l i m h o s p e r c e n t i m e t e r ( m m h o s / c m ) is a m e a s u r e of e l e c t r i c a l conductivity of w a t e r and r e f l e c t s the r e l a t i v e s a l i n i t y . The c o n v e r s i o n between s a l i n i t y e x p r e s s e d in p a r t s p e r m i l l i o n (ppm) and in m i l l i m h o s p e r c e n t i m e t e r v a r i e s depending on the w a t e r ' s c h e m i c a l c o m p o s i t i o n . The c o n v e r s i o n r a t e of 670 ppm p e r m m h o / c m used h e r e is r e p r e s e n t a t i v e of P i n a l County. 105
Supplemental Colorado R i v e r Water f o r a Developed Groundwater Agriculture Mark A. B o s t e r and William E. Martin 64 p e r cent of the i n c r e a s e o c c u r s . The Indians have a net i n c r e a s e of 180, 600 a c r e - f e e t of w a t e r use, while d e c r e a s i n g pumpage by only 3,000 a c r e - f e e t . Second, the i n c r e a s e of 145,000 a c r e - f e e t of w a t e r use on non-Indian lands is p o s s i b l e b e c a u s e f a r m e r s a r e t r a d i n g w a t e r a g a i n s t an h i s t o r i c a l a v e r a g e pumpage r a t h e r than what pumpage would have been in that y e a r without CAP. The h i s t o r i c a l a v e r a g e to which the o n e - t o - o n e t r a d e - o f f r u l e a p p l i e s is h i g h e r than e s t i m a t e d pumpage in 1986, b e c a u s e f a r m e r s in the deep pumpage a r e a s would have cut back on pumpage as the w a t e r table fell. Thus, p r o v i s i o n of CAP w a t e r will tend to slow the g r o u n d w a t e r o v e r d r a f t , but not on an acre-foot per acre-foot basis.
is $199,400 p e r y e a r as of 2020, or 1.1 p e r cent of the b a s e of $18, 306, 629. This d e c r e a s e a v e r a g e s only 61 cents p e r i r r i g a t e d a c r e , in 2020 ( l e s s in the p r e c e d ing y e a r s ) o r 0.23 cents p e r y e a r p e r i r r i g a t e d a c r e p e r p a r t m i l l i o n i n c r e a s e in s a l i n i t y . 3 Total w a t e r use in the County d e c r e a s e s by only 32, 400 a c r e feet when CAP w a t e r s a l i n i t y i n c r e a s e s to 1.8 m m h o s / c m . The d e c r e a s e d total w a t e r u s e r e s u l t s a l m o s t e n t i r e l y f r o m cutbacks in CAP w a t e r p u r c h a s e s . Total c r o p p e d a c r e s also d e c l i n e , but only by 2,000 a c r e s . Sixty p e r cent of the d e c r e a s e is f r o m b a r l e y , the m o s t e c o n o m i c a l l y m a r g i n a l crop, dropping out of the County's c r o p m i x . All Indian D e m a n d s f o r CAP W a t e r S a t i s f i e d
CAP F r e e l y P u r c h a s e d V e r s u s "Minimum R e q u i r e d Purchase Since n o n - i n d i a n s m u s t r e p a y the c o s t s of the C e n t r a l A r i z o n a P r o j e c t through w a t e r p u r c h a s e s , it is p o s s i b l e that a m i n i m u m w a t e r p u r c h a s e m a y be r e q u i r e d . In this p a r t of the a n a l y s i s , individual f a r m s a r e r e q u i r e d to u s e at l e a s t ninety p e r c e n t of t h e i r annual CAP a l l o t m e n t r a t h e r than a f r e e l y s e l e c t e d quantity. As expected, net r e t u r n s above v a r i a b l e c o s t s d e c r e a s e when this additional c o n s t r a i n t is added, but only by about $465, 000. However, the d e c r e a s e in net r e t u r n s all o c c u r s within the five n o n - I n d i a n d i s t r i c t s (the Indian R e s e r v a t i o n s f r e e l y use all the CAP w a t e r a v a i l a b l e to them) and so b a l a n c e s out m o r e than half of the 0 . 8 m i l l i o n d o l l a r gain to non-Indian f a r m e r s m a d e when CAP w a t e r was f u r n i s h e d on a f r e e choice basis. With a CAP w a t e r u s e of 619, 000 a c r e - f e e t out of the 659, 000 a c r e - f e e t total CAP allocation, (139, 000 a c r e feet of which was not f r e e l y chosen) the t r a d e - o f f r a t i o between CAP and pump w a t e r r i s e s to about 2.3 a c r e feet of CAP u s e d for each 1 a c r e - f o o t of pump w a t e r no l o n g e r used. The r a t i o was only 3.1 a c r e - f e e t of CAP to 1 a c r e - f o o t of pump w a t e r when CAP was f r e e l y chosen. A l m o s t no shift in the c o u n t y ' s c r o p mix is o b s e r v e d . In o r d e r to u s e all of the r e q u i r e d CAP w a t e r , however, the n u m b e r of double c r o p p e d a c r e s i n c r e a s e d slightly and the C A P - l o c a l w a t e r m i x shifted to m i x e s with h i g h e r q u a n t i t i e s of CAP w a t e r . Most of the r e q u i r e m e n t to u s e m o r e CAP w a t e r was s i m p l y r e f l e c t e d in d e c r e a s e d net i n c o m e . Most of the d e c r e a s e in net i n c o m e is f r o m the h i g h e r p r i c e of CAP w a t e r r a t h e r than f r o m d e c r e a s e s in y i e l d due to use of p o o r e r quality w a t e r . In fact, in one D i s t r i c t , the quality of the w a t e r m i x i m p r o v e d .
I m p a c t of I n c r e a s e d C A P Salinity It is e s t i m a t e d that C o l o r a d o R i v e r w a t e r d e l i v e r e d to P i n a l County w i l l have a m e a n s a l i n i t y of 1.4 m m h o s / cm in 1986 and a m e a n s a l i n i t y of 1 . 8 m m h o s / c m in 2020 if no a d d i t i o n a l s a l i n i t y c o n t r o l p r o g r a m s a r e i n s t i t u t e d . F o r any s a l i n i t y c o n t r o l p r o g r a m to be e c o n o m i c a l l y efficient, the cost of the c o n t r o l p r o g r a m should be l e s s than the value of the d e c r e a s e in a g r i c u l t u r a l p r o d u c t i o n if no c o n t r o l s a r e e s t a b l i s h e d . The m o d e l s c o m p a r e the value of net r e t u r n s above v a r i a b l e c o s t s at the two s a l i n i t y l e v e l s when CAP w a t e r is f r e e l y chosen. The t o t a l d e c r e a s e in net r e t u r n s above v a r i a b l e c o s t s f o r P i n a l County f a r m e r s 106
F a r m e r s on the two Indian R e s e r v a t i o n s in P i n a l County will r e c e i v e F e d e r a l l y s u b s i d i z e d CAP w a t e r at no d i r e c t v a r i a b l e cost to them, and the w a t e r can be used to expand i r r i g a t e d a c r e a g e . Thus, the Indian R e s e r v a t i o n s could p r o v i d e an outlet f o r e x c e s s a g r i c u l t u r a l CAP w a t e r . F u r t h e r , a m e a s u r e of economic b e n e f i t s a c c r u i n g to Indian f a r m e r s r e c e i v i n g the f r e e CAP w a t e r is of i n t e r e s t to d e c i s i o n - m a k e r s a l l o c a t i n g the p r o j e c t w a t e r . The r e p r e s e n t a t i v e - f a r m m o d e l s for both the Indian D i s t r i c t lands a r e m o d i f i e d to d e t e r m i n e the m a x i m u m quantity of CAP w a t e r that could be u s e d e f f e c t i v e l y by each if i r r i g a t e d a c r e age w e r e expanded to include all of the i r r i g a b l e lands on the r e s e r v a t i o n . With an u n l i m i t e d quantity of f r e e CAP a v a i l a b l e , the two r e s e r v a t i o n s would u s e n e a r l y twice as much w a t e r as the i n i t i a l annual allotment, and net r e t u r n s above v a r i a b l e c o s t s would i n c r e a s e 4 . 7 t i m e s .
The E f f e c t s of F i x e d C o s t s In o r d e r to d e t e r m i n e the net e c o n o m i c p o s i t i o n of f a r m e r s in P i n a l County, fixed f a r m c o s t s a l s o m u s t be c o n s i d e r e d . F i x e d c o s t s a r e those c o s t s i n c u r r e d by the f a r m o p e r a t i o n r e g a r d l e s s of the f a r m ' s l e v e l of production, for e x a m p l e , d e p r e c i a t i o n of buildings, m a c h i n e r y , w e l l s , and d i t c h e s ; i n t e r e s t on the i n v e s t ment; and t a x e s . D e t a i l e d fixed cost v a l u e s for f a r m s in P i n a l County a r e d e v e l o p e d in B o s t e r (1976). However, these fixed c o s t s e s t i m a t e s do not include the fixed c o s t of CAP d e l i v e r y s y s t e m s , that is, the l a t e r a l c a n a l s which the f a r m e r m u s t p r o v i d e to t r a n s p o r t the CAP w a t e r f r o m the main canal to the f a r m h e a d g a t e . D e t a i l e d fixed cost d a t a for the CAP d i s t r i b u t i o n s y s t e m a r e not a v a i l a b l e , and t h e i r c o m putation is beyond the s c o p e of this study, although c o n s u l t a n t s ' r e p o r t s (Beck, 1971a, b, c) show that the c o s t s could e a s i l y be ten or m o r e d o l l a r s p e r a c r e foot p e r y e a r . Although the p r e c i s e c o s t of c o n s t r u c t i n g l a t e r a l d i s t r i b u t i o n s y s t e m s for the CAP w a t e r cannot be
The value of 0.23 cents p e r y e a r p e r i r r i g a t e d a c r e p e r p a r t p e r m i l l i o n i n c r e a s e in s a l i n i t y is computed by dividing 61 cents by 268 p a r t s p e r m i l l i o n i n c r e a s e in s a l i n i t y (0.4 m m h o s / c m x 670 p p m / m m h o s / c m = 268 ppm).
A d v a n c e s in W a t e r R e s o u r c e s
made, it is p o s s i b l e to c a l c u l a t e the f a r m e r s ' m a x i mum w i l l i n g n e s s to pay for the d i s t r i b u t i o n s y s t e m s . This c a l c u l a t i o n is made by e s t i m a t i n g the d i f f e r e n c e in net f a r m i n c o m e s with and without using CAP w a t e r . The d i f f e r e n c e would be the m a x i m u m amount that f a r m e r s ' could afford to pay annually in o r d e r to d e l i v e r the w a t e r f r o m the m a i n canal to t h e i r h e a d gates.
Vol. 1 No. 2 1977
studied, the question of s i g n i f i c a n t c r o p l o s s f r o m i n c r e a s e d s a l i n i t y in the o t h e r a r e a s is r a i s e d . It a p p e a r s that b e n e f i t s of w a t e r d e v e l o p m e n t a r e not all that they may at f i r s t s e e m , even in this v e r y a r i d a g r i c u l t u r a l a r e a with a g r o u n d w a t e r o v e r d r a f t p r o b l e m .
Appendix Obviously, numerous assumptions are necessary for It is shown in B o s t e r (1976) that although net r e t u r n s the analyses. S o m e of the major assumptions include: above v a r i a b l e c o s t s i n c r e a s e in m o s t i r r i g a t i o n (1) Yield reduction due to irrigation water salinity is d i s t r i c t s when C e n t r a l A r i z o n a P r o j e c t w a t e r is i n t r o related to the calculated m e a n salinity against which duced into P i n a l County, v e r y l i t t l e of the i n c r e a s e water is absorbed, which is influenced m o r e by the o c c u r s on non-Indian l a n d s . B e c a u s e non-Indian "salinity of the irrigation water than by the salinity of f a r m e r s m u s t i n c u r the c o n s t r u c t i o n cost of a d i s t r i b u - the drainage water; (2) yield reductions from water tion s y s t e m (Indian f a r m e r s l i k e l y will r e c e i v e t h e i r s free), it is unlikely that the i n c r e a s e in net r e t u r n s above v a r i a b l e c o s t s will in fact exceed the a s s o c i a t e d fixed c o s t s .
Conclusions
The o s t e n s i b l e b e n e f i t s of t r a n s p o r t i n g s u r f a c e w a t e r into C e n t r a l A r i z o n a , a m a j o r c r o p p r o d u c i n g a r e a , a r e to (1) be of e c o n o m i c benefit to the non-Indian a g r i c u l t u r a l economy and (2) to s i g n i f i c a n t l y r e d u c e the p h y s i c a l d e c l i n e in the u n d e r g r o u n d w a t e r table. B e c a u s e of the p r o j e c t e d i n c r e a s e in s a l i n i t y in the C o l o r a d o R i v e r , a m a j o r w o r r y is that s i g n i f i c a n t a g r i c u l t u r a l l o s s will o c c u r with u s e of C o l o r a d o R i v e r w a t e r in this and o t h e r a g r i c u l t u r a l a r e a s . The r e s u l t s of this study do not s u p p o r t t h e s e widely held b e l i e f s for e i t h e r the o s t e n s i b l e b e n e f i t s or l o s s e s .
s h o r t a g e and f r o m s a l i n i t y a r e additive; (3) w a t e r is o p t i m a l l y a l l o c a t e d d u r i n g the c r o p s e a s o n ; (4) the c r o p s s e l e c t e d for this study will continue to be the m o s t i m p o r t a n t ones grown in the a r e a ; (5) the r a t i o of p r o d u c t p r i c e s to input c o s t s is constant over time; and (6) the r e l a t i v e p r i c e s of c r o p s a r e constant over t i m e . A d e t a i l e d e x p l a n a t i o n of the a s s u m p t i o n s in the m o d e l s is found in B o s t e r (1976). The following is a m a t h e m a t i c a l s t a t e m e n t of the generalized representative-farm linear-programming c o m p u t e r model. Specific m o d e l s v a r y slightly f r o m this s t a t e m e n t . The o b j e c t i v e of this model is to:
J Maximize Z =
K
~,
NRjk.
j : l k-----i
(2)
(3)
D e l i v e r y of CAP w a t e r under the p r o p o s e d l e g i s l a t i v e r e s t r i c t i o n s will not a s s u r e groundw a t e r c o n s e r v a t i o n at anywhere n e a r a o n e - t o - o n e t r a d e - o f f and thus w i l l not s i g n i f i c a n t l y r e d u c e groundwater decline.
Subject to:
N e a r l y all of the m o n e t a r y b e n e f i t s f r o m the P r o j e c t to a g r i c u l t u r e in P i n a l County will be c a p t u r e d by Indian r a t h e r than by non-Indian f a r m e r s . (Original b e n e f i t - c o s t e s t i m a t e s w e r e made on the b a s i s of the non-Indian c o m m e r c i a l farms.)
Constraint 2:
Indian f a r m e r s will have the f a r m land c a p a c i t y to u s e any e x c e s s CAP w a t e r f r o m non-Indian f a r m e r s if t h e r e is no d i r e c t c o s t to the Indians for the w a t e r and they a r e allowed to u s e the CAP w a t e r to expand a c r e a g e .
(4) R e q u i r i n g n o n - i n d i a n f a r m e r s to u s e a m i n i m u m quantity of CAP w a t e r in t h e i r c r o p w a t e r m i x would r e d u c e c o n s i d e r a b l y the m o n e t a r y gains to be r e a l i z e d if CAP w a t e r w e r e m a d e a v a i l a b l e with the quantity u s e d to be f r e e l y chosen by the farmers. (5) While p r o v i s i o n of CAP w a t e r to the f a r m h e a d gate at a p r i c e of $ 1 6 . 6 7 p e r a c r e - f o o t would i n c r e a s e s o m e non-Indian f a r m e r ' s net income, the a g g r e g a t e i n c r e a s e in net i n c o m e in non-Indian d i s t r i c t s w i l l not likely be enough to pay for the n e c e s s a r y CAP d i s t r i b u t i o n s y s t e m s within P i n a l County. (6)
The p o s s i b i l i t y of i n c r e a s e d s a l i n i t y f r o m CAP w a t e r should not be of c o n c e r n to f a r m e r s in the county. Since other a r e a s using C o l o r a d o R i v e r w a t e r a r e quite s i m i l a r to the s p e c i f i c a r e a
T
~ ~ C s t . Wst s=lt--1
Specific r e s u l t s of t h i s study a r e as follows: (1)
S
Xjk--
K
Constraint 1:
J
~
P U M P j k . Xj k -
k=~
PSLK = 0
j=l
K
J
~
~
k=l
j=l
C A P j k . Xjk-- C S L K = 0 T
Constraint 3a: P S L K - - ~,
Wst = 0
s = 1
Wst : 0
S : 2
t~- 1 T
3b: C S L K t----I
Constraint 4a: CSLK-< CMAX
4b: C S L K _> C M I N T
C o n s t r a i n t 5:
~, W s t _< S M A X
s=3
t=1 K
J
Z Wjkt. XjR- Wst= 0
C o n s t r a i n t 6a:
k---1 j=1 = 1,2,3 ~ = 1,2, ...,8
s
6b: W
st
_< WMAX
st
s : 1, 2,3
t----- 1,2, . . . , 8
C o n s t r a i n t 7: PSLK + CSLK _< TOTWA 4
C o n s t r a i n t 8a:
j
~ ~, k=l j = 1
Xjk -< WINAC
107
Supplemental Colorado River Water for a Developed Groundwater Agriculture Mark A. Boster and William E. Martin 5
SUMAC = N u m b e r of c r o p a c r e s a v a i l a b l e d u r i n g the s u m m e r (excluding conserving base).
J
8b: ~ ~ k=3 j = 1 7
J
8C: ~
•
Xjk <
SUMAC
Xjk
C o n s t r a i n t 9:
TOTAC
~ ~ Xjk-- TOTAC = 0 k=1 J = 1
TOTWA =
Wjk t
W h e r e t h e v a r i a b l e s , l i s t e d in a l p h a b e t i c a l o r d e r , a r e : = C o s t p e r a c r e - f o o t of w a t e r f r o m s o u r c e s a p p l i e d in t i m e p e r i o d t. =
CAPjk
M a x i m u m a m o u n t of C A P w a t e r a v a i l a b l e to t h e f a r m t h r o u g h the i r r i g a t i o n d i s t r i c t .
Xjk
CM~
=
M i n i m u m a m o u n t of w a t e r the irrigation district must use.
Z
=
N u m b e r of c o n s e r v i n g b a s e acres available.
=
W a t e r m i x index to a c c o u n t for v a r i o u s m i x e s of p u m p e d and C A P w a t e r .
J
=
k
=
N u m b e r of w a t e r m i x e s f o r e a c h c r o p and f a r m s i z e pumping depth class. T y p e of c r o p . k = 1,2, ....,7
CSLK =
CAP water slack which equals total CAP water used per year.
MAXCOT k
=
M a x i m u m a c r e a g e of cotton.
NRjk
=
Net r e t u r n s a b o v e a l l v a r i a b l e p r o d u c t i o n c o s t e x c e p t the c o s t of w a t e r f o r c r o p k g r o w n w i t h w a t e r m i x j.
PSLK
=
Pumping slack which equals total water pumped per year.
PUMPjk
=
A c r e - f e e t of p u m p e d w a t e r a p p l i e d to e a c h a c r e of c r o p k g r o w n with w a t e r m i x j.
s = S o u r c e of w a t e r . Pumped water 2=
Central Arizona Project water
3=
S u r f a c e w a t e r f r o m the San Carlos Project
S
N u m b e r of w a t e r s o u r c e s
SMAX = M a x i m u m a m o u n t of s u r f a c e w a t e r a v a i l a b l e in San C a r l o s Project areas.
"~- A c r e - f e e t of w a t e r n e e d
in t i m e p e r i o d t, f o r e a c h a c r e of c r o p k g r o w n with water mix j.
W M A X s t = M a x i m u m a m o u n t of w a t e r a v a i l a b l e f r o m s o u r c e s in t i m e p e r i o d t.
=
j
T o t a l a m o u n t of w a t e r ( a c r e feet) f r o m s o u r c e s a p p l i e d in t i m e p e r i o d t.
WINAC = N u m b e r of c r o p a c r e s a v a i l able during the winter.
A c r e - f e e t of C e n t r a l A r i z o n a P r o j e c t w a t e r a p p l i e d to e a c h a c r e of c r o p k g r o w n with water mix j.
CMAX
CONBA
Ten year average pumpage in the a r e a .
Wst =
J
C o n s t r a i n t 10: ~, Xj k _< MAXCOT k k = 4, 5 k=l
108
T o t a l a c r e s c r o p p e d (counts double cropped acres twice).
=
J
Cst
t = 1, 2, o...,8
-< CONBA
k=6 3 = I K
Time period,
t=
= A c r e s of l a n d a s s i g n e d to crop k that is grown with w a t e r m i x j. =
T o t a l net r e t u r n s o v e r v a r i a b l e c o s t s f o r the f a r m .
REFERENCES
Central Arizona Project Engineering and Planning Study: Central Arizona Irrigation and Drainage District. P h o e n i x .
B e c k , R. W. a n d A s s o c i a t e s .
M a r c h , 1971a.
Central Arizona Project Engineering and Planning Study: New Magma Irrigation and Drainage District. P h o e n i x . M a r c h , 19"llb. Central Arizona Project Engineering and Planning Study: Maricopa-Stanfield Irrigation and Drainage District. P h o e n i x . M a r c h , 1971c. B e r n s t e i n , L . Salt Tolerance of Plants. U . S . D e p a r t m e n t of A g r i c u l t u r e , A g r i c u l t u r a l i n f o r m a t i o n B u l l e t i n 283, W a s h i n g t o n , 1964. __, and L. E . F r a n c o i s . ' L e a c h i n g R e q u i r e m e n t S t u d i e s : S e n s i t i v i t y of A l f a l f a to S a l i n i t y of I r r i g a tion and D r a i n a g e W a t e r s . 'Soil Science Society of America Proceedings, v o l . 37, no. 6, N o v . - D e c . , 1973. B o s t e r , M a r k A l a n . ' E v a l u a t i o n of A g r i c u l t u r a l A d j u s t m e n t to I r r i g a t i o n W a t e r S a l i n i t y : A C a s e Study f o r P i n a l County, A r i z o n a . ' U n p u b l i s h e d P h . D . D i s s e r t a t i o n . U n i v e r s i t y of A r i z o n a , T u c s o n . 1976. B u r e a u of R e c l a m a t i o n . P r o p o s e d C e n t r a l A r i z o n a Project. Final Environmental Statement, Washington. S e p t e m b e r , 1972. D r e g n e , H . E . Prediction of Crop Yields from Quantity and Salinity o/Irrigation Water. A g r i c u l t u r a l E x p e r i m e n t S t a t i o n B u l l e t i n 543, New M e x i c o S t a t e U n i v e r s i t y , L a s C r u c e s . M a r c h , 1969. S t u l t s , H a r o l d M. ' P r e d i c t i n g F a r m e r R e s t ) o n s e to a F a l l i n g W a t e r T a b l e : A n A r i z o n a C a s e Study. ' U n p u b l i s h e d P h . D . d i s s e r t a t i o n . The U n i v e r s i t y of A r i z o n a , T u c s o n . 1968.
A d v a n c e s in Water R e s o u r c e s Sun, Po-chaun. 'An Economic Analysis on the Effects of Quantity and Quality of I r r i g a t i o n W a t e r on A g r i c u l t u r a l Production in I m p e r i a l Valley, California. ' Unpublished Ph.D. d i s s e r t a t i o n , The University of California, Davis. 1972. Young, R. A., W. T. Franklin, and K. C. Nobe. A s s e s s i n g Economic E f f e c t s of Salinity on Irrigated Agricul-
Vol. 1 No. 2 1977
ture in the Colorado R i v e r B a s i n : A g r o n o m i c and Economic Considerations. Report to the Bureau of Reclamation, U.S. D e p a r t m e n t of the Interior, Contract no. 14-06-D-7341, D e p a r t m e n t s of Econom i e s and Agronomy, Colorado State University, F o r t Collins. August, 1973.
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