OF IRRIGATION A CASE FOR FINAL

OF IRRIGATION A CASE FOR FINAL

EVALUATION OF AGRICULTURAL ADJUSTMENT TO

IRRIGATION WATER SALINITY: A CASE STUDY

FOR FINAL

COUNTY,

ARIZONA by

Mark Alan Boster

A Dissertation Submitted to the

Faculty of the

DEPARTMENT

OF

HYDROLOGY

AND

WATER RESOURCES

In Partial Fulfillment of the

Requirements

For the Degree of

DOCTOR

OF PHILOSOPHY

WITH A MAJOR IN WATER RESOURCES

ADMINISTRATION

In the Graduate College

THE UNIVERSITY OF ARIZONA

1976

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

I hereby recommend that this dissertation prepared under my direction by Mark Alan

Boster entitled Evaluation of Agricultural Adjustment to Irrigation

Water Salinity: A Case Study for

Pinal

County, Arizona be accepted as fulfilling the dissertation requirement of the degree of

Doctor of Philosophy

After inspection of the final copy of the dissertation, the

following members of the Final Examination Committee concur in

its approval and recommend its acceptance:*

This approval and acceptance is contingent on the candidate's adequate performance and defense of this dissertation at the final oral examination. The inclusion of this sheet bound into the library copy of the dissertation is evidence of satisfactory performance at the final examination.

STATEMENT BY AUTHOR

This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.

Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission mist be obtained from the author.

SIGNED:

Wet-Li

D7

ACKNOWLEDGMENTS

I wish to express my sincere thanks to my dissertation director,

Professor William E. Martin of the Department of Agricultural Economics, for his professional guidance and thoughtful criticism throughout this project. Dr. Martin has taught me much about research and about myself for which I am very grateful.

Special thanks go to Professor Daniel D. Evans, Department of

Hydrology and Water Resources, who served as chairman of my graduate committee, and to Professors Sol Resnick, Director of the Water Resources

Research Center; Roger Fox, Department of Agricultural Economics; and

Robert Phillips, Department of Civil Engineering, who were also members of my committee and whose comments about the dissertation were very helpful.

Information and ideas shared with me by many persons have materially contributed to this research. I would like to express my appreciation for their assistance and interest in this project. Professor Gordon

Dutt, Department of Soils, Water and Engineering, provided much advice during the initial phases of this project. Dr. Leon Bernstein of the

U. S. Salinity Laboratory met with me and contributed to the formulation of the crop yield-salinity model. Mr. Gene Wright and Dr. Gayle Willett, both of the Department of Agricultural Economics, spent numerous hours helping me develop the calendars of operations for the farms in the study.

Professor Theodore Roefs, formerly with the Department of Hydrology and

Water Resources and currently with the U. S. Office of Water Research and

Technology, provided an extensive critical appraisal of the linear programming models. Staff of the Arizona Water Commission, especially

Mr. Thomas Clark, were most helpful throughout the project.

Thanks also go to Donna Moore who typed innumerable drafts of this dissertation and to Paula Tripp who typed the final copy.

The work upon which this dissertation is based was supported in part by funds provided by the United States Department of the Interior,

Office of Water Research and Technology, as authorized under the Water

Research Act of 1964. Thanks also go to Dr. Jimmye S. Hillman, Head of the Department of Agricultural Economics for additional support and encouragement throughout this effort.

Finally, I thank The University of Arizona Computer Center for the use of their facilities and especially to Mr. Richard Anderson, a consultant at the center, for showing me how to make the computer do things that "could not be done." iv

TABLE OF CONTENTS

LIST OF TABLES

Page vii ix

LIST OF ILLUSTRATIONS

ABSTRACT

CHAPTER

I.

INTRODUCTION

Research Objectives of this Study

Method of Analysis

Description of Thesis

IL THEORETICAL FRAMEWORK AND RELATED RESEARCH

III. THE LINEAR PROGRAMMING MODELS

7

Water Quantity, Water Quality, and Crop Yield

Water Quantity and Crop Yield

Water Quality and Crop Yield

12

Water Quantity, Water Quality, and Crop Yield

. . 17

7

7

Economic Decisions

The Factor-Product Relationship

Factor-Factor Relationships

Product-Product Relationships

21

21

24

25

Enterprise Equilibrium

Related Research

27

29

33

Components of the Model

The Objective Function

Constraints

1 and

2

Constraint

3 (a and b)

Constraint

4 (a and b)

Constraint

5

Constraint

6 (a and b)

Constraint

7

Constraint

8

(a, b, and c)

Constraint

9

Constraint 10

Alternative Analyses

No CAP Water Available in

Pinal County

CAP Water Introduced and Freely Chosen

42

42

43

43

43

44

44

44

39

40

41

41

41

41

1

4

6

6

vi

TABLE OF CONTENTS--Continued

Page

Minimum Level of CAP Water Use Required

All Indian Demands for CAP Water are Satisfied

.

Impact of Increasing Salinity

IV.

THE DATA

Stratification of Representative Farms

Irrigation Districts and Groundwater Quality

.

Farm Sizes

Depth to Water

Yield-Water Quantity-Salinity Combinations Used in the Analyses

Costs and Returns

Net Returns Over Variable Costs

Fixed Costs

Cost and Availability of Local Water Sources

Cost of Pumped Water

Monthly Pumping Restrictions

Water Allocations in Surface Water Areas

Central Arizona Project Water

Land Resources

Cotton Acreage Restrictions

V.

RESULTS OF THE ANALYSES

No CAP Versus CAP Freely Purchased

CAP Freely Purchased Versus Minimum Required

Purchase

Impact of Increased CAP Salinity

All Indian Demands for CAP Water Satisfied

The Value of Additional Water

The Effects of Fixed Costs

Summary

96

96

104

105

109

111

114

123

67

67

71

76

80

55

63

63

65

87

91

47

47

50

53

45

45

46

47

APPENDIX A: YIELD-WATER QUANTITY-SALINITY POINTS ON THE

PRODUCTION SURFACE FOR CROPS TYPICALLY GROWN

IN PINAL

COUNTY, ARIZONA

APPENDIX

B: BUDGETS AND CALENDARS OF OPERATIONS

APPENDIX C: NET RETURNS ABOVE VARIABLE COSTS WITHOUT

CENTRAL ARIZONA PROJECT WATER MIXING

127

146

153

APPENDIX D: DETAILED RESULTS FOR EACH OF THE FIVE ANALYSES

CLASSIFIED BY IRRIGATION DISTRICT

LIST OF REFERENCES

170

176

LIST OF TABLES

Table

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

Area-Weighted Average Salinity of Pumped Water by

Irrigation District

Breakdown of Pinal

County Farms into Four Size Groups

.

Average Pumping Lift for "Shallow," "Middle," and

"Deep" Lifts in the Seven Irrigation Districts,

1986

Average Yield per Acre for "Middle"

Pumpage Lift

Area

Yield-Water Use Relationships for Various Crops by

Pumping Lift and Irrigation District

Comparison of

1965 and

1974 Variable Costs of Production, Excluding the Variable Cost of Water, in the

"Middle" Pumping Lift Areas of

Pinal County, Arizona

Fixed Costs per Farm Excluding Costs of Land and

Management for Typical

Pinal County Farms

Cost of One Acre-Foot of Water per Foot of Lift in

Pinal

County, Arizona,

1986

Average Cost of Pumping Water in

Pinal County, by

Pumping Depth and Irrigation District,

1986

Maximum Thirty Day Pumping Capacity,

1986

Relative Proportion of Pumped Water Available by Months

Annual Allocation of San Carlos Project Surface Water

. .

Initial Allocation of Central Arizona Project Water

Based on Relative Acreage

Ten-Year Average

Pumpage by Non-Indian Irrigation

Districts

Allocation of Winter and Summer Acres,

1986 vii

Page

51

52

54

56

59

66

68

72

73

75

77

79

84

86

89

viii

LIST OF TABLES--Continued

Table

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

Page

90

Allocation of Conserving Base Acreage, 1986

Approximate Number of Farms in Each Irrigation

District by Farm Size and Pumping Depth Class

American-Pima (Long Staple) Cotton Restrictions, 1986 .

Upland (Short Staple) Cotton Restrictions, 1986

Comparison of 1970 Projections and 1975 Projections of Net Revenue Above Variable Costs, Water Use, and

Acreage of Field Crops in Pinal County, Arizona for

1986 98

Projected Net Returns Above Variable Costs, and Projected Water Use in Pinal County, Arizona, 1986

Projected Acreage of Field Crops in Pinal County,

Arizona, 1986

100

102

Comparison of Effects of Three Different Quantities of Central Arizona Project Water on Indian Farmers in Pinal County, Arizona, 1986

110

Projected Aggregate Net Returns Above Variable Costs for Pinal County Farms in 1986 Without CAP Water . • • •

117

Projected Aggregate Net Economic Returns to Pinal

. County Farms in 1986 Without CAP Water

Projected Aggregate Economic Returns Including the

Fixed Cost of a Distribution System to Pinal County

Farms in 1986 With CAP Water Available and Freely

Chosen

Aggregate Willingness to Pay for Fixed Costs of a

Distribution System for CAP Water

118

120

121

92

94

95

LIST OF ILLUSTRATIONS

Figure

1.

2.

3.

4.

5.

6.

Total Physical Product Curve for Total Crop Yield as a Function of Water Quantity (Hypothetical)

Relationship Between Total Crop Yield and Water

Quality (Hypothetical)

Production Surface Relating Total Crop Yield to

Water Quantity and Water Quality (Hypothetical)

Solution to the Factor-Product Decision Using a

Total Physical Product Curve and a Break-Even

Line (Hypothetical)

Solution to the Factor-Factor Decision Using Isoquants and Iso-costs (Hypothetical)

Solution to the Product-Product Decision Using a

Production-Possibility Curve and an Iso-revenue

Curve (Hypothetical)

7.

8.

A Generalized Map of the Seven Irrigation Districts in Final County, Arizona

Salt Tolerance of Selected Crops

Page

11

18

20

22

26

28

49

58 i x

ABSTRACT

The Central Arizona Project (CAP) is a billion-dollar-plus project to construct an aqueduct to transport water from Lake Havasu on the

Colorado River into the Maricopa County-Phoenix area and then through

Pinal County to Tucson. Upon completion of CAP in 1986, some of the

Colorado River water will be delivered to Pinal County for agricultural use. Water available to Pinal County farmers in the initial years of the project is estimated at 659,000 acre-feet annually. Any new importation of water to an established irrigated agricultural area implies adjustments in the organization of the economy of the area. For irrigated agriculture, adjustments will occur in input mix, output mix, acreage farmed, and in gross and net incomes.

A complicating factor associated with importation of Colorado

River water is that the imported water will contain different dissolvedsalt concentrations than will the groundwater and surface water currently being used. Dissolved salts in irrigation water (salinity) decrease crop yields, i.e., as the salinity of water applied to a crop increases, yield per acre decreases. The magnitude of yield reduction due to salinity is dependent on the level of salinity of the irrigation water and on the crop's salt sensitivity. In areas of Pinal County where local water supplies have a lower average salinity than CAP water, average crop yields will decrease if CAP water is added to the crop-water mix. On the other hand, in those areas where the salinity of local water is higher than that of CAP water, higher crop yields will be realized by using CAP water

x i in the crop-water mix. Thus, the optimal CAP-local water mix is determined in order to evaluate the economic adjustments of

Pinal County farmers to the new water source.

Pinal

County is divided into seven irrigation districts, each of which has filed a letter of intent to purchase CAP water. Representative farm data for each district are stratified by farm size and pumping depth. Farms are divided into four size classes in order to reflect economies due to farm size. Because the cost of local pumped water varies with the pumping lift, the farms are also stratified by three depth-to-water classes. Thus, a total of

12 representative farms are necessary to describe the agricultural activities in each irrigation district, and

84 representative farms are needed for the county.

Mathematical programming models of representative irrigated farms in Final County project adjustments implied under several assumptions as to the availability, cost and salinity of irrigation water from various sources. Results show that

(1) most monetary benefits of the project will be captured by the Indian farmers of the county,

(2) groundwater conservation will be minimal unless farmers are forced to purchase large quantities of CAP water,

(3) provision of CAP water will not affect cotton acreage but will significantly increase the acreage of small grains and alfalfa,

(4) the possibility of increased salinity from CAP water should not concern farmers in the county since projected decreases in net income occurring because of increased salinity average only

61 cents per acre per year, and

(5) increased income to non-Indian farmers resulting from provision of CAP water at the currently proposed price will not be sufficient to pay the additional fixed costs for distribution systems.

CHAPTER I

INTRODUCTION

The availability and cost of water are the most limiting factors to agricultural activity in Arizona. Most of the state's desert valley soils are suitable for crop production, but receive less than 10 inches of precipitation annually. Thus, farming in Arizona is almost completely dependent upon irrigation systems to meet crop water demands.

Pinal County, Arizona, located midway between Tucson and Phoenix, contains some of the largest farms and highest income farms in Arizona.

Agriculture in the area is completely dependent upon irrigation systems with nearly all the water for crop irrigation pumped from the underlying groundwater reservoirs. The only surface flow diverted in the area is from the Gila River by the San Carlos Irrigation Project. The continued mining of groundwater over the years for agricultural irrigation in Pinel

County at a rate greater than the recharge rate has lowered the water table in most irrigated areas; in a few areas it has dropped as much as

20 feet in a single year. Declining groundwater levels mean farmers must pump from increasing depths, using more energy and thus, incurring a higher cost per acre-foot of water.

Several kinds of adjustments are being made on the farms in the county in response to the increasing cost of water. First, there is a tendency for farmers to shift from marginally productive crops to those with higher net returns. Further, as the water table declines and water

1

2 costs increase relative to other factors of production, farmers decrease the total per acre water application to a crop during its growing season.

Finally, in some areas farm land has been abandoned, although total farmed acreage in the county has actually increased since its most recent low in 1966 (Arizona Crop and Livestock Reporting Service, 1974).

Many Arizonans have long desired to augment their existing groundwater and surface water supplies with imported water. In 1968, the Central Arizona Project (CAP) was authorized under the Colorado River Basin

Project Act (PL 90-537). This billion-dollar-plus project includes construction of an aqueduct from Lake Havasu on the Colorado River into the

Maricopa County-Phoenix area and then through Pinal County to Tucson

(Bureau of Reclamation, 1972). It will carry as much as 1.6 million acre-feet of Colorado River water into the State in its early years, declining to about 1.1 million acre-feet by 2020. Initially, the water's principal use will be for crop irrigation, but agricultural water use will decrease over a 50-year period as municipal and industrial demands increase and the total volume of water delivered declines. The project construction schedule calls for agricultural water deliveries to begin about 1986.

Proponents suggest several benefits accruing from the project.

They argue that the CAP will provide a much needed new water source for

Central Arizona. Project water will temporarily slow the area's groundwater overdraft problem while establishing an additional water supply for the future to meet the rapidly growing population demands. Agriculture will use the water during the initial years, until increased municipal and industrial uses demand the water. In order to insure that importation

3 of the additional water will in fact slow down the groundwater level decline, agricultural users of project water must decrease groundwater pumpage by one acre-foot for each acre-foot of CAP water they accept [43

U.S.C. Sec. 1524(d)]. Proponents believe this rule will slow, if not eliminate, the present groundwater overdraft, and prolong marginal agricultural activity. A reasonable estimate of water initially available from CAP for agricultural use in Pinal County is 659,000 acre-feet per year. An estimate of the mean groundwater pumpage in the county in the

1959 through 1968 period, a reasonable base period on which to compute the volume of water for which CAP water must be traded is 900,000 acre-feet.

1

A complicating factor to the use of CAP water in the established irrigation area is the difference in water quality (salinity) between the CAP water and that found in the area. The estimated salinity of the

CAP water when delivered to Pinal County in 1986 is 1.4 millimhos per centimeter (mmhos/cm) or approximately 940 parts per million (ppm).

2

The area-weighted average salinity of groundwater in the irrigated study is

1.0 mmhos/cm (about 670 ppm). Surface water delivered by the San Carlos

Project averages 1.3 mmhos/cm (870 ppm). Values for individual irrigation districts vary from a low of 0.6 mmhos/cm to a high of 1.8 mmhos/cm.

1.

CAP water delivered to Indian Reservations will not be under the pump-CAP trade-off rule. The estimate of 900,000 acre-feet excludes

Indian pumpage.

2.

Millimhos per centimeter (mmhos/cm) is a measure of electrical conductivity of water and reflects the relative salinity. The conversion between salinity expressed in parts per million (ppm) and in millimhos per centimeter varies depending on the water's chemical composition. The conversion rate of 670 ppm per mmho/cm used here is representative of Pinal County.

4

Crop yields are a function of irrigation water salinity, among other things. Thus, districts with lower salinities than the 1.0 county average currently show higher crop yields than the county average, whereas those with higher average salinities have lower crop yields than the county average. Introduction of CAP water of a different salinity could either raise or lower yields, depending on the area.

Research Objectives of this Study

The overall objective of this study is to make an economic evaluation of the adjustment alternatives open to irrigated agriculture in the proposed service area of the CAP in Pinal County, Arizona. The problem involves projecting the adjustments in response to differing water qualities (CAP vs. groundwater vs. surface water from the San Carlos Project) as well as response to differing water prices from each source. Projections are made for several representative size farms, overlying different pumping depths, within each of the seven irrigation and drainage districts in the county.

3

There are a number of questions related to the overall objective that must be investigated. First, in order to provide base data with which to compare alternative models, one needs to know the projected farming pattern in 1986 if no CAP water were available. Second, one would like to know how farmers would react if CAP water were introduced into

3. The Indian and District components of the San Carlos Project are considered as separate districts in this study. These two districts currently are the only districts actively involved in delivering water.

Other districts which would receive CAP water are the Ak-Chin Indian

Reservation, Central Arizona Irrigation and Drainage District, Hohokam

Irrigation and Drainage District, Maricopa-Stanfield Irrigation and

Drainage District, and New Magma Irrigation District.

5

Pinal

County on a free-choice basis, i.e., farmers could choose CAP water in quantities and at times that maximize their net farm incomes. A third question is how farmers would react and what would be the economic impact if each representative farm were required to use a minimum quantity of their CAP water in order to meet the irrigation district's contractual agreement. Because the Colorado River, the source of CAP water, may increase its salinity over time, a fourth analysis is needed to measure the costs of higher salinity levels in project water. Finally, because Indian farms will receive federally subsidized CAP water at no direct cost to the Indians, the maximum quantity of project water the Indians would desire is in question.

Thus, specific objectives of this study are to:

(1) Project the economic position of representative individual farmers and for the county as a whole in

1986 if no CAP water is available;

(2) project the economic impact of CAP water in the study area in

1986 if CAT water is available to farmers 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 farm and for the county;

(3) investigate the economic effects of requiring each farm in the county to use at least

90 percent of its annual CAP water allotment;

(4) measure the loss in net farm returns that would result from increased salinity of Colorado River water over time

-- the source for the CAP water; and

(5) determine the maximum quantity of CAP water that would be desired by Indian farmers in the area.

6

Method of Analysis

Detailed representative-farm organizations, costs and returns data are used to develop the linear programming models used as the tool for analysis. Sixty-nine of these representative-farm linear-programming models are needed to describe adequately the irrigated farming activities in Final County. Each model includes alternative crop production activities using various quantities of CAP water, groundwater, and other surface water (in the San Carlos Project area) under alternative conditions of use. Each water source, and thus the resulting water mixes, is available in various quantities over time, at different prices and salinities.

The linear programming models are designed to maximize net farm returns above variable production costs subject to the resource constraints faced by the representative farmers. Individual representative-farm results are aggregated into results for each irrigation district and for the whole county.

Description of Thesis

Chapter II develops the theoretical foundation of this study.

The representative-farm linear-programming models are developed and explained in Chapter III. Since data are of prime importance in any empirical research, Chapter IV is devoted to a description of the necessary data. The results and policy implications are given in Chapter V.

CHAPTER II

THEORETICAL FRAMEWORK AND RELATED RESEARCH

The physical relationships of concern to this study, between water quantity and crop yield, between water quality (salinity) and crop yield, and between the combined effects of water quantity and quality on crop yield, along with the theoretical basis of the economic models are presented in this chapter. A discussion of relevant related research is included in the last section.

Water Quantity, Water Quality, and

Crop Yield

Water Quantity and Crop Yield

Water has many functions in plant life. Water is the solvent and transportation medium for all foods, hormones, vitamins, and compounds supplying essential elements; it combines with carbon dioxide in the formation of the initial substances in photosynthesis; it combines with starch and related compounds in the formation of glucose in respiration; and more particularly, it maintains turgor in living cells (Edmond, Senn, and Andrews, 1964, p. 55). Without adequate water, plants do not develop.

Likewise, too much water may "drown" or kill the plant. Between these limits, i.e., too much and too little water, yield varies. Thus, an understanding of the relationship between water quantity and crop yield

7

enables farmers to apply the quantity of irrigation water that maximize his returns.

1

The quantity of water required to produce a crop, other than that retained in the plant, has two components: water los,t from the soil surface and water transpired by the plant. Evapotranspiration is the total water loss by these two processes. The quantity of water lost by evapo-

8 transpiration in the production of a crop is termed consumptive use.

Moisture from the soil enters plant roots by the process of osmosis. Soil moisture tension is a measure of the strength by which water is held to the soil particles and is primarily dependent upon the amount of moisture in the soil. As the quantity of moisture in the soil becomes less, the force by which it is retained increases. Not all of the retained water is available to plants because the mutual attraction between soil and water is so great that a certain portion of moisture is held with a force greater than the absorptive power of the plant. Thus, a point is reached at which the adhesion between soil and water equals the absorptive power of the plant roots, and hence no more moisture can be utilized by the plant.

When the quantity of water absorbed by the roots is less than the quantity lost by transpiration, a negative moisture balance is established in the plant, and very shortly the cells cease to be turgid and the plant starts to wilt. When a plant has wilted to such an extent that it will not revive when placed in a saturated atmosphere, it is said to be

1. The actual quantity of water a farmer should apply to a crop to maximize his returns is an economic question discussed later in this chapter. This section only establishes the physical relationship between water quantity and crop yield.

9 permanently wilted, and the percentage of moisture in the soil when permanent wilting occurs is the wilting coefficient or permanent wilting point (P.W.P.) of the soil.

The maximum soil moisture content is called saturation and occurs when the pore space of the soil is filled with water. However, due to gravity, an adequately drained soil will not remain saturated. If a saturated soil is permitted to drain until no more water yields to the pull of gravity, the quantity of water remaining in the soil is called field capacity. The difference between field capacity and the permanent wilting point is the range of available moisture to the plant.

The complete biophysical effect on crop yield for different levels of soil saturation within the range of available moisture during the growing season is complex and beyond the scope of this study.

2

Rather a simplified water quantity-crop yield model showing yield as a function of gross water quantity applied to the crop is necessary. For economic analysis one must be able to express the relationship between the quantities of inputs and the quantity of outputs in the form of a production function.

A production function is a schedule (or table, or mathematical equation) showing the maximum amount of output that can be produced from any specified set of inputs, given the existing technology or "state of the art." In short, the production function is a catalogue of output possibilities. The general concept of a production function is expressed mathematically as:

2. A detailed discussion can be found in Hagan, 1955; Hendrickson and Veihmeyer, 1950; Hagan, Vaadia and Russell, 1959; Fischer and

Hagan, 1965.

10

Y = f(Xl , X2 , . .

Xn),

(1) where

Y is the output realized from employing the inputs

X1 , X2 , . • .,

X n

(e.g., water, seed, fertilizer, etc.) in the production process.

In order to evaluate the productivity of a specific resource in the production process, for example water, it is necessary to hold the level of other resources constant while the quantity of water is permitted to vary.

If all other inputs to the production process except water are held constant, the functional relationship between output and water quantity is stated:

Y

= f(W1X1 , X2 , . . •X),

(2) where

Y is the total crop yield, W is the quantity of water applied during the growing season, and

X1 , X2 , . . Xn...1 are the other resources (inputs) excluding water necessary to the production process.

When the production function is expressed in this form

-- with only one variable input

-- the resulting curve is termed the total physical product

(TPP) curve. Given at least one input held constant, the shape of the total physical product curve is described by the

Law of

Diminishing Returns.

The Law states that holding at least one input constant while applying increasing quantities of the variable input(s), output may at first increase at an increasing rate, but eventually reaches a point where it increases at a decreasing rate.

Eventually the curve reaches a point where it can either decrease, remain constant at the maximum level, or become asymptotic to a maximum value.

Figure

1 shows a hypothetical

TPP curve for total crop yield

(output) as a function of water quantity (all other inputs held constant).

The function shows that no output is realized until a minimum quantity of

T5 o

F-

-

-

t

Y

o

6;

.5:. Y a. o o"

1

I

I

I

I

1

I i i

I

1

I

I

I i

i

I

I

Total physical product

W

I

W

2

W

3

Water quantity

--->--

Figure

1.

Total Physical Product Curve for Total Crop Yield as a

Function of Water Quantity (Hypothetical).

11

12 water is applied to the crop. As more water is applied, output increases

(at a decreasing rate) until a maximum is reached. Additional water inhibits plant growth and output begins to fall. Three different levels of water application, W

1

,

W

2' and W 3,

are shown with their resulting total yields,

Y

1

, Y

2

, and

Y 3

, respectively.

Water Quality and Crop Yield

Without proper management, dissolved salts in irrigation water can accumulate in the root zone of the receiving soil.

At low concentrations, accumulations cause only small reductions in crop yield, however, at extreme concentrations, the soil's inherent ability to support crops may be destroyed. Thus, an understanding of the relationships between irrigation water quality, soils, and crop responses is necessary if management practices are to be adopted to minimize adverse consequences.

Dissolved salts carried in irrigation water are concentrated in the soil by evaporation from the soil surface and by transpiration due to plant growth. Salt accumulation in the root zone affects plant growth causing smaller yields.

For example, when the electrical conductivity of the saturation extract of soil (EC) 3 reaches a sufficient level to cause crop yield reduction, plant parts

(leaves, stems and fruit) are usually smaller than normal, and leaves often display a characteristically deeper blue-green color. In alfalfa, the decreased yield is roughly proportional to the plant size decrease, however, cotton, barley, and wheat

3. Soil saturation extract electrical conductivity (EC ) is defined as the

EC of the solution separated from a saturated soilepaste.

13 may show little if any reduction in seed or fiber with a

50 percent plant size (Bernstein,

1964).

Bernstein (1964) suggests three reasons for plant growth retardation due to root zone salinity: (1) osmotic effects,

(2) nutritional effects, and (3) toxic effects. Root zone salinity may indirectly affect plant growth through changes in soil structure, permeability and aeration

(Sun, 1972). Also, some plants exhibit salinity sensitivity at various stages of growth (Ayres and Hayward, 1948). Detailed discussions for each of these effects of salinity on crop yield are readily available in the soil science and plant physiology literature. The most comprehensive summary discussion is found in Young, Franklin, and

Nobe (1973).

In order to counteract the adverse effects of salinity, farmers have traditionally applied irrigation water in excess of the plants' consumptive use requirements to prevent salt accumulation in the root zone. The excess water is called leaching water, and the fraction of the irrigation water that must be leached through the root zone to keep the soil salinity within the limit a given crop can tolerate is termed the leaching requirement

(LR).

The calculation of the

LR is based on the conservation of salts, i.e., if the amount of salt entering the soil in the irrigation water equals the amount of salt carried below the root zone in the drainage water, the soil salinity will remain constant. If less water than the amount specified by the

LR is applied, salts accumulate in the root zone, whereas if more water than that specified by the

LR is used the

EC e may decrease. Mathematically this is expressed as:

C i Q i = C d Q d

(3)

14 where C measures the salt concentration of the irrigation or drainage waters in terms of Electrical Conductivity (EC);

Q is the quantity of irrigation or drainage water; and

C.Q and C i d

Q d measure the total amount of salt applied to the soil and drained below the root zone, respectively.

Equation 3 can be rewritten:

C i /C d = Q d

/Q i

.

(4)

The quantity C i /C d

= Q d /Q i is defined as the leaching fraction

(LF).

Thus, when the maximum permissible

C d is specified for a specific case, the minimum permissible

LF is defined. The minimum leaching fraction is termed the leaching requirement (U. S. Salinity Laboratory Staff,

1954).

The

LF is the fraction of total water applied or the excess water that must pass through the root zone to keep the soil salinity less than or equal to the concentrations of the drainage water. The U. S. Salinity

Laboratory Staff (1954) recommend as a general rule of thumb that the saturation extract (EC e

) at which a 50 percent decrease in yield is obtained in uniformly saline soil be substituted for the C d in the LF equation. The resulting yield decrease is about 10 percent.

4

Thus, the additional water necessary for leaching salts from the root zone is determined by a simple calculation.

4.

Leaching requirement was a relatively new concept twenty years ago when the U. S. Salinity Laboratory Staff (1954) compiled Agricultural Handbook Number

60. At that time, there was considerable interest in compiling and comparing the salt tolerance of various crops.

The EC e for a uniformly saline soil giving a

50 percent decrease in yield was thought to approximate the maximum permissible salinity level for the soil water of a crop. The actual decrease in crop yield is less than 50 percent because

C d is at the bottom of the root zone making the average root zone salinity (presumably the determinate of yield reduction) much lower. Only a

10 percent decrease in yield should occur. One should note that this general rule of thumb is void of any economic content.

For example, Erie, French and Harris

(1968) report a seasonal consumptive use of

41.2 inches of water for cotton grown in Mesa and

Tempe, Arizona.

5

Irrigating with 2 mmho/cm water means a leaching requirement of 12.5 percent.

6

In order to assure a 12.5 percent leaching

15 fraction, a farmer would need to apply a total of

47.1 inches of water, or an additional

5.9 inches above the consumptive use requirement, so as to restrict salt accumulation in the root zone

[41.2 / (1.0 - 0.125) =

47.1].

If his irrigation system operated at a 75 percent efficiency rate, the farmer would need to apply a total of 62.8 inches or about

5-1/4 feet of water to the crop during the growing season

(47.1 / 0.75 =

62.8).

7

In areas of water scarcity, the additional water for leaching may not be available or only available at high cost. Thus, inexpensive water saving measures would be welcomed by farmers. New technologies on improving water application efficiencies to reduce the amount of excess water required are being explored, and some very promising work in redefining the

LR is coming from the U. S. Salinity Laboratory.

Bernstein and Francois

(1973), working at the Salinity Laboratory, report that their studies on alfalfa indicate that the traditional concept of leaching requirement overstates the amount of leaching water needed.

The traditional calculation assumes plants respond to the average salinity

5.

Erie et al.

(1968) state that cotton grown in Final County would have a very similar consumptive use requirement.

6.

Cotton shows a

50 percent yield at an EC of 16 mmho/cm.

With

2 mnho/cm irrigation water, the

LR is 12.5 percent

(2/16 x 100 = 12.5).

7. The effects of precipitation are ignored in this calculation, so this figure represents the maximum water necessary.

16 of the root zone. They suggest that yield responses appear to be related to the calculated mean salinity against which water is absorbed, which is influenced more by the salinity of the irrigation water than by the salinity of the drainage water. Data indicate that leaching requirements may be reduced by as much as

75 percent of the level previously thought essential for crops of low to moderate tolerance and reduced by as much as

60 percent of the previously recommended levels for highly salt tolerant crops, without further reducing crop yield. Bernstein

(1974) believes that yield responses to salinity for the other field crops are also related to the calculated mean salinity against which water is absorbed by the plant.

Application of Bernstein and Francois's findings requires high irrigation efficiencies and is a trade-off between water use and management intensity. Plants withdraw water from the root zone areas containing the highest quality (lowest salinity) water before extracting water from areas of lower quality. Near the soil surface, water has the lowest salinity, so if water is available to the plant in this area it will be used. Increased management is necessary to assure that the soil near the surface always has sufficient water to meet plant needs. Soil type is not a determining factor if the soil permeability is high enough to permit this type of management.

Again, the physical interactions and theories explaining yield reductions from irrigation water salinity are too complex to be included directly in this study. A simplified water quality-crop yield model obviously is needed for the economic analyses.

The generalized functional relationship between total crop yield and different levels of irrigation water salinity (all other inputs are held constant) may also be expressed in the form of a total physical product function. The relationship is:

Y = f(SIW, X1 , X2 , . .

Xi),

(5) where Y is the total crop yield, S is the salinity of the irrigation

17 water,

W is the quantity of irrigation water, and X1 , X2 , . . Xn_2 are the other factors of production excluding the quantity and quality of water. Because total crop yield is inversely proportional to the level of salinity, the hypothetical shape of the curve is given as in Figure

2.

8

Figure

2 represents the generalized functional relationship between yield and irrigation water salinity. Curves for specific crops maintain the same general relationship but have different slopes. For example, a salt tolerant crop would have a flatter curve whereas a salt sensitive crop would have a steeper curve.

Three different salinity levels are shown in Figure 2: S

1

(low salinity),

S 2 (middle salinity), and

S 3 (high salinity). The output (Y1 ) associated with the low salinity level

(S 1 ) is high and shows little degradation because of the salinity. The outputs for the middle and high salinities are progressively lower.

Water Quantity, Water Quality, and Crop Yield

The effects of water quantity on crop output and water quality

(salinity) on crop output are each controversial and complex subjects.

8. The curve in Figure

2 is not drawn for very low and very high salinities because of disagreement among experts as to the actual shape in these areas.

S i

S 2

S3

Salinity of irrigation water

Figure

2.

Relationship Between Total Crop Yield and Water Quality

(Hypothetical).

18

19

Specific literature on the joint effects of water quantity and salinity on crop yield does not exist. Dregne (1969) assumes that the effects of each are additive. Sun (1972), in an innovative economic analysis, makes the same assumption.

Using the assumption of additivity, it is possible to combine the crop yield-water quantity model and the crop yield-salinity model to develop a model relating crop yield to both water quantity and salinity.

The three dimensional production surface is expressed mathematically as:

Y = f(W, SIX X2 , • • ., Xn 2 ).

(6)

Equation 6 states that crop yield (Y) is a function of both the quantity of irrigation water applied and the salinity of the irrigation water, all other inputs held constant. With some slight modification, Figures 1 and

2 are combined to depict the three dimensional production surface expressed by Equation 6.

Figure 3 illustrates the crop yield-water quantity-salinity model.

With three different possible water quantities

(W

1 , W2' and W

3

) and three different levels of salinity (S

1 , S 2' and S

3

), nine possible combinations of water quantity and quality exist to give nine different levels of yield. For example, Y 1,3 is the resulting yield from applying a low quantity of high salinity water, Y 2,2 is the yield from a medium quantity of middle salinity water, Y 3,1 is the yield from a large quantity of low salinity water, etc. An infinite number of water quantity-water quality input combinations exist over the entire production surface.

It is now possible to evaluate the joint effects of both water quantity and salinity on crop yield in economic models.

20

WI

W

2

Water quantity

Figure

3. Production Surface Relating Total Crop Yield to Water Quantity and Water Quality (Hypothetical).

21

Economic Decisions

The individual firm employs resources (factors of production) to produce a product. Although not all firms are interested in profit maximization, agricultural firms (farms) operate in a competitive market and therefore must maximize profits in order to assure 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 acre) for each product). Economists term these decisions the product-product, factor-factor, and factor-product decisions, respectively. If the firm has profit maximization as its goal, if it knows its production processes, and if it knows the costs of inputs and prices of outputs, the simultaneous solution to the three questions provides the firm with its profit maximizing position.

The Factor-Product Relationship

The solution to the factor-product relationship for a given product on a given farm tells the firm what is the optimal yield per acre to produce. The solution is dependent on the production function, the prices of variable inputs, and the price of a unit of output.

Figure 4 is a graph of the generalized TPP function Y = “WIS, X

1

, X

2

,

X

3'

. . .' X 2

) where Y is the yield per acre, W (water) is the variable factor of production, given the other inputs S (Salinity) and

X

1'

X

2'

• . •, X n-2 are held constant. The variable factor could be any factor of production, e. g., salinity, fertilizer, machinery, etc. Water is

f Y2

10

Y1

-

a;

--5,

a_

1._ o

-E5

1E3

H

A

Break-even li

n

e

sv

W

I

I i

I

I

I i

I

I

I i

Input

W -->"-

\

Total

I

physical product

Figure

4. Solution to the Factor-Product Decision Using a Total

Physical Product Curve and a Break-Even Line (Hypothetical).

22

23 chosen as the variable factor of production for demonstration purposes only.

Point A of Figure 4 represents the maximum level of output per acre obtainable from the variable input

W, given all other inputs held constant. Generally, one's first impression is to produce at the point of maximum output to maximize profit. However, point A on the TPP curve is not the profit maximizing position of the firm unless the variable input, water, is free. The price of the variable input and the price of the product are introduced in order to determine the firm's profit maximizing position.

With both of the prices of

W and Y known, the firm's break-even line (BEL) can be computed. The BEL is the locus of all points where the value of the output produced exactly equals the cost of the variable input under consideration. The BEL is expressed as:

PY=PW,

Y w

(7) where

P is the price of the output, Y is the quantity of output,

P

Y w is the cost of the variable input, and

W is the quantity of the variable input employed. The BEL is shown in Figure

4.

The slope of the BEL is given by the inverse ratio of the prices, i.e., the ratio of the price of the variable input to the price of the product. The solution to the factor-product relationship is:

DY w

TTAT

P

Y

(8) where

-5

DY

-1,71

-

is the marginal product of

W

(the addition to total product attributable to the addition of one unit of variable input

W to the production process),

P w is the price of one unit of the variable input, and

24

P

Y is the price of one unit of output. Thus, the optimal yield per acre for a particular crop is given by the tangency of a line drawn parallel to the BEL with the total physical product curve (point

B).

At that point, the quantity of output in excess of the break-even quantity is the greatest.

Equation

8 can be rewritten as:

, 3Y r - =

P y

BW w

.

(9)

The left hand side of equation

9 defines the marginal value product (MVP) or the value of the additional product resulting from the addition of one unit of the variable input to the production process. Thus, the solution to the factor-product relationship can also be stated as that point on the total physical product curve where the value of the additional output obtained from increasing the variable input by one unit equals the price of the additional unit of input.

Factor-Factor Relationships

The quantity of each input required in some production activities is closely regulated, e.g., pharmaceutical companies mix precise amounts of each ingredient needed for a particular pill or capsule. However, resource substitution is possible in many production activities; especially in agricultural production. Typical factor-factor substitutions in agriculture occur between labor and machinery, capital and labor, and water quantity and salinity. There generally exist various combinations of two inputs that result in the same output level, i.e., one resource can be substituted for the other without changing the output level. The locus of points representing all the combinations of factor substitutions

which yields the same level of total product is termed an iso-quant

(equal quantity) line. Figure 5 illustrates the iso-quants for two inputs, W and S (could be any two factors of production), used to produce various levels of output Y 1 , Y 2 , . .

Y. If the price of each input is known, then for any given level of output the solution (the optimal mix of inputs) to the factor-factor relationship is: aW =

- P s •

P w

(10)

In equation 10

,

DW

is the marginal rate of technical substitution of W

25 for S, or the reduction in the number of units of W per unit of S added so as to maintain a constant output level; Pw is the price of input W;

P s

-2 s is the price of input S; and

is slope of the iso-cost (equal cost) line which shows various combinations of inputs that may be purchased for a stipulated amount of expenditure. Thus, the optimal solution to the factor-factor relationship for any given level of output is the point of tangency of the iso-quant curve for a specific output level and the iso-cost line. This point gives the highest level of output achievable for a given level of cost.

Product-Product Relationships

The product-product decision involves the allocation of given resources between competing commodities. Product-product problems are important to farm operators who must decide what combination of crops to grow with limited resources, e.g., land, water, labor, and capital.

Under the factor-factor relationship, output of product is held constant in quantity and variety while the product mix is varied.

Input

S ---->-

Figure 5. Solution to the Factor-Factor Decision Using Iso-quants and Iso-costs (Hypothetical).

26

Given two competing products, a production-possibility frontier or transformation curve can be developed to show the maximum attainable output of one commodity for every possible volume of output of the other commodity, given the fixed resource base, e.g., the farm and its associated resources (Figure 6). Given the price of each commodity, P and

3

7

1

P , Equation 11 defines the equilibirum solution.

Y

2

_Y 2

1

— ay

2

PY1

27

The left hand side of Equation 11 is the rate of product transformation

(substitution) between the two commodities, and the right hand side is the slope of the iso-revenue (equal revenue) curve. Thus, the optimal mix of product outputs is at the tangency of the product transformation curve and the iso-revenue curve. At this point, the highest revenue is achieved, given the fixed set of resources available. (See Henderson and

Quant, 1971; Ferguson, 1969, or Heady, 1952 for additional discussion.)

Enterprise Equilibrium

The profit maximizing position of a firm is found by the simultaneous solution to all of the independent factor-factor, factorproduct, and product-product decisions, given that firm's production functions for each product. In this study, the factor-factor question involves the optimal mix of imported CAP water with local water. How much yield per acre of each crop to produce, relative to the variable inputs of water quantity and quality, is handled by the factor-product decisions. The optimal crop mix is determined by the product-product relationships.

f

Output

Y

1

Figure 6. Solution to the Product-Product Decision Using a Production-

Possibility Curve and an Iso-revenue Curve (Hypothetical).

28

29

If all of the functional relationships were known, the optimal solution for the farm could be found using calculus as shown in the above discussion. However, empirical data giving continuous functions are not available, precluding the use of calculus to arrive at optimal solutions to the models. Instead, because individual points on the production surface can be estimated, one may assume that the functional relationships between points are linear and use linear programming techniques to solve for the optimal solution. A detailed description of the representativefarm linear-programming models is presented in Chapter III.

Related Research

The literature is voluminous on the physical relationships between crop growth and soil water salinity, but sparse on the economic assessment of direct farm damage from reduced crop yield resulting from the soil water salinity. A thorough review of both the agronomic and economic considerations necessary to assessing the effects of salinity on irrigated agriculture is given by Young et al.

(1973) in their report to the

Bureau of Reclamation. They also review the empirical economic studies completed up to that time. However, at the time of their review, the new theory on crop sensitivity to irrigation water salinity by Bernstein and

Francois

(1973) was unpublished and not included. This study is the first to incorporate Bernstein and Francois's theory in an economic analysis.

Research by Sun

(1972) in the Imperial Valley of California is the most comparable large-scale empirical study in the economics of irrigation water quality and quantity. Sun also develops representative farm-linear programming models to investigate the effects of quantity

30 and quality of irrigation water on agricultural production. However, two fundamental differences exist between this study and Sun's. First, Sun used the traditional crop yield-salinity model based on average root zone salinity. The traditional model may exaggerate damages due to irrigation water salinity. Second, the Imperial Valley of California relys entirely on lower basin Colorado River water as the supply of irrigation water.

Because farmers in this area cannot mix this Colorado River water with lower salinity supplies, an advantage held by many Pinel County farmers, crop damages from salinity should be higher in Imperial Valley than in

Pinel County. From a research methodology point of view, Sun did not have to contend with the problem of the conjunctive use of two to three sources of irrigation water.

Howe and Young

(1975) and Brown and Kleinman

(1975) have also recently reported estimates of income loss because of increasing salinity in the Colorado River. The Brown and Kleinman report is preliminary and does not discuss assumptions or methodology. The Howe and Young report, while more complete, is very sketchy in its report on method. As it says, however, "In the absence of a complete linear programming model, the farm management variable is irrigation practice and the major decision is whether or not to shut down certain acreage"

(1975, p. 17).

Thus, alternative cropping patterns are not considered as they are in this representative farm-linear programming study. Neither the Howe and

Young nor the Brown and Kleinman study uses the new theory on crop response to irrigation water salinity. Neither study includes Pinel County in their study area.

Two previous studies in Pinal County are of particular interest to this research. The first, conducted by Stults (1968), investigated farm adjustments and the resulting economic impact to increasing water costs incurred by farmers in the area because of the falling groundwater table. His study treated Pinal County as an entire unit and assumed that the effect of irrigation pumpage on the decline in the groundwater

31 table is directly related to the quantity of water pumped. Stults solved the county representative-farm models for each of the ten year periods between 1966 and 2006. He computed the total water withdrawal for each ten year period from the crop mix results obtained. The water withdrawal data were used in conjunction with the historical rate of water table decline to project the subsequent decrease in the groundwater table. The new depth to water figures were used in the analysis of the next ten year period. Stults obtained his data on representative farms from a personal interview farm survey with one-fourth of the farmers in the county. The results from his survey form the basis of the organizations, costs, and returns data used in this study, although all of his data have been updated.

The second study in Pinal County, by Burdak (1970), refined

Stults' assumptions about groundwater table decline from farming activity.

Burdak divided Pinal County into five separate areas for analysis and coupled his representative farm models with an analog groundwater model by the U. S. Geological Survey (Anderson, 1968). He used the same iterative procedure as Stults. The water withdrawal data computed at the end of each ten year period were input into the analog groundwater model. The analog model projected the resulting decrease in the groundwater table.

The procedure used by

Burdak improved the projections of the groundwater table decline over time and thus, improved the linear programming model

32 results. Neither Stults nor Burdak addressed the question of irrigation water salinity in their studies. Both studies examined agricultural adjustment in the absence of new surface water supplies from the Central

Arizona Project.

CHAPTER III

THE LINEAR PROGRAMMING MODELS

Linear programming is a mathematical technique used to solve a system of simultaneous equations given an objective to be maximized or minimized within the limits of certain given constraints. The particular computational linear programming algorithm used in this analysis was developed by Dallenbach and Bell (1970) and is called "LPGOGO." The original FORTRAN IV code was modified and the capabilities expanded by this author. The linear programming models were solved on the DECsysteral0 digital computer located at The University of Arizona.

Any linear programming problem has three common components: (1) an objective that is to be optimized (such as maximization of profit or minimization of cost), (2) a set of alternative courses of action, or decision variables, to achieve the desired objective, and (3) restrictions on the extent of obtaining the objective, that are expressed in the form of constraints on the values of the decision variables (Dallenbach and

Bell, 1970).

The objective of an individual farm enterprise operating in a competitive market environment is profit maximization. Linear programming models of farm enterprises in Pinal County are designed to maximize net returns above variable production costs. Consideration of fixed costs is not included directly in the linear programming models because

33

34 fixed costs for a particular farm are constant in the short run and occur regardless of the level of farming activity.

Farmers vary their crop mix and their input mix as the means of attaining their objective of profit maximization. Crops typically grown in Pinal County, and those used as alternatives in this study, include

American-Pima cotton, upland cotton, barley, grain sorghum, alfalfa (with and without summer water) and wheat.

1

Thus, in the models, a farmer may adjust the total number of acres of each crop grown, the way any crop is grown, or eliminate certain crops from his crop mix. The linear programming models choose the optimal mix of crops and the optimal mix of inputs that will maximize farm net returns above variable costs.

Farms are limited in the quantity of resources available to use for production. The limited resources restrict the farm in the amount and extent of obtaining its objective of profit maximization. Some of the restrictions included in the linear programming models for

Pinal

County include: maximum quantity of water available during the year and during each month, monthly crop water demands, and land availability.

Individual representative farms are the basis for constructing the models. Representative farms are defined for each of the irrigation districts, stratified by farm size and depth to water, in order to reflect the variety of production situations occurring in the area.

1.

Other crops are grown in

Pinal

County but are excluded from this study because of their minor importance. For example, in

1974,

6,800 acres of safflower and

4,380 acres of vegetables were harvested in the County. Individually, these crops are small relative to total harvested acreage in the County

-- 277,670 acres in 1974.

35

Seven different irrigation districts exist in Pinal County, each of which has filed a latter of intent to purchase Central Arizona Project water. The quality of groundwater and its depths below the surface are the primary differences between each district in the models. Two of the irrigation districts currently receive surface water diverted from the

Gila River.

The size of farms in Pinal County is varied. Therefore, in this study, farms are divided into four different farm size classes in order to reflect production economies due to size. Further, because the depth to water varies throughout the county, three different classes of pumping depth -- shallow, medium, and deep -- are defined. The average pumping lift within each pumping depth class within each irrigation district is calculated and used to compute the cost of pumping water. Thus, three different groundwater costs exist for each irrigation district -- one for each pumping depth class.

With seven irrigation districts, four farm size classes, and three pumping depth classes, a possible 84 different representative farm combinations would exist in Final County. However, because certain irrigation districts do not have farms in a particular size class and/or pumping depth class, only sixty-nine individual farm models are necessary to describe the agricultural activity in the study area.

Each representative farm uses the same basic production functions for each of the crops typically grown in the county. However, economies due to size exist and are reflected by the farm size classes. Large farms are more efficient in the use of inputs than smaller farms and thus, the cost of production on a large farm is less than that for a small farm.

Economies due to size also exist relative to the quantity of irrigation

36 water it is necessary to pump. Farms within the same pumping depth class apply the same quantity of water to a specific crop. However, larger farms within the pumping depth class have more efficient delivery systems

(less water loss) and thus, pump less water than do smaller farms to achieve the same level of application to the crop.

The linear programming models reflect one crop season. Water is assumed to be optimally allocated during the season, i.e., plant water demands are always met and water applications are such that soil near the surface always has sufficient water to meet the plant needs.

The following is a mathematical statement of the generalized representative-farm linear-programming computer model. Specific models vary slightly from this mathematical statement as noted in the later discussion.

The objective of this model is to:

J K

S T

Maximize Z =

E E NR. •

X j j=1 k=1 jk

- E k s=1 t=1

C• W st st

Subject to:

K J

Constraint

1: E E Pump.

X

- PSLK = 0 jk jk k=1 j=1

K J

Constraint

2: E E CAP

4

, k=1 j=1 --"s" jk

=0 s = 1

Constraint

3a: PSLK - E W t=1 st

3b: CSLK -

E W st t=1

=0 s = 2

37

Constraint 4a:

4b:

CSLK

CSLK

< CMAX

> CMIN

Constraint

5:

E W st t=1

< SMAX

K J

Constraint 6a: E E W. •

X.

- jkt jk k=1 j=1

W s=1 st

= 0

6b:

Constraint 7: PSLK + CSLK s=3 t = 1, 2, . • .,8

W st

<WMAX st s = 1, 2, 3 t = 1, 2, . . .,8

< TOTWA

4 J

Constraint

8a: E E

X.

k=1 j=1

31(

5 J

8b: E

E k=3 j=1

J

' s

"

7 J

8c: E

E k=6 j=1

Jx

`

K J

Constraint

9: E E X

- TOTAC k=1 j=1

< WINAC

< SUMAC

< CONBA

=0

Constraint

10:

E

X.

j=1

< MAXCOT k k = 4,5

Where the variables, listed in alphabetical order, are:

C st

=

Cost per acre-foot of water from source s applied in time period t.

CAP jk

= Acre-feet of Central Arizona Project water applied to each acre of crop k grown with water mix j.

CMAX =

Maximum amount of CAP water available to the irrigation district.

CMIN =

Minimum amount of water the irrigation district must use.

CONBA =

Number of conserving base acres available.

38 j =

Water mix index to account for various mixes of pumped and

CAP water.

J =

Number of water mixes for each crop and farm size-pumping depth class.

k =

Type of crop.

1 =

Barley

2 =

Wheat

3 =

Long staple cotton (American-Pima)

4 =

Short staple cotton (Upland)

5 =

Grain sorghum

6 =

Alfalfa (without summer water)

7 = Alfalfa (with summer water)

MAXCOT k

=

Maximum acreage of cotton.

NRjk =

Net returns above all variable production cost except the cost of water for crop k grown with water mix j.

PSLK = Pumping slack

= total water pumped per year.

PUNT jk

=

Acre-feet of pumped water applied to each acre of crop k grown with water mix j.

s = Sources of water.

1 = Pumped water

2 = Central Arizona Project water

3 = Surface water from the San Carlos Project

S = Number of water sources

SMAX =

Maximum amount of surface water available in San Carlos

Project areas.

SUMAC

= Number of crop acres available during the summer (excluding conserving base).

39 t =

Time period.

1 =

January, February

2 =

March, April

3 =

May

4 = June

5 = July

6 = August

7 =

September

8 =

October,

November,

December

TOTAC =

Total acres cropped (counts double cropped acres twice).

TOTWA =

Ten year average pumpage in the area.

W st

=

Total amount of water (acre-feet) from source s applied in time period t.

W jkt

=

Acre-feet of water need in time period t, for each acre of crop k grown with water mix j.

WINAC = Number of crop acres available during the winter.

WMAX st

=

Maximum amount of water available from source s in time period t.

X.,

• 3K

= Acres of land assigned to crop k that is grown with water mix j.

Z =

Total net returns over variable costs for the farm.

Components of the

Model

In the following discussion, the generalized representative-farm linear-programming model is described one mathematical relationship at a time.

40

The Objective Function

The objective of each representative-farm linear-programming model is to maximize net returns above variable costs given the physical restraints on production for the individual farm. An objective function is developed for each representative farm. These functions contain net revenue coefficients derived from data in Appendix A for each production activity on each farm. A production activity is a method of producing a crop on one acre of land. Each crop has several production activities, i.e., each crop is repeated several times in each model to allow for alternative mixes of water sources, each of which has a different cost and salinity. For example, one cotton activity uses all pump water, another uses all CAP water, another uses four acre-feet of pumped water in combination with one acre-foot of CAP, another three acre-feet of pumped water along with two acre-feet of CAP water, etc. Different costs, different yields, and thus different net return coefficients are associated with each way of producing an acre of each type of crop. The net return above variable cost values for each production activity includes that return which must pay for the variable cost of water. Because each water source has a different unit cost, the total water cost associated with each water mix is different. Unit water costs for each available source are included in the objective function as negative quantities in the water purchase activities so that the total water cost can be computed within the model.

Solutions of the models give the maximum net return that could be obtained given the limited resources for production and using the

41 optimum combination of various available water sources of differing prices and qualities.

Constraints

1 and 2

Constraint 1 totals the annual quantity of pumped water used by each production activity in the optimal solution. In the two areas receiving surface water from the Gila River, the average salinity of both surface and pumped water is equal and both sources have the same cost.

Thus, in order to simplify the model in these two areas,

PSLK is the sum of both pumped water and Gila River surface water.

The second constraint operates in the same manner as the first constraint. The resulting variable CSLK is the total quantity of Central

Arizona Project water used by each activity in the optimal solution.

Constraint 3 (a and b)

Linkage enabling the models to subtract water costs from net revenue above other variable cost coefficients is provided in constraints

3a and 3b. Each says that the annual quantity of water used equals the sum of the water used during each time period.

Constraint 4 (a and b)

The maximum annual quantity of CAP water available to a farm is regulated by constraint

4(a).

Constraint 4(h) enables one to require a minimum quantity of CAP water to be used in the optimal solution.

Constraint

5

The sum of other surface water used in each time period must be less than the annual surface water available for delivery to the farm.

42

This constraint is used only in representative farm models with available surface water other than from the CAP, i.e., the San Carlos Project-

Indian Lands and the San Carlos Irrigation and Drainage District.

Constraint 6

(a and b)

Monthly crop water demands are balanced with monthly water sources by constraint

6(a).

Specifically, the irrigation demand for each crop activity during a time period can be satisfied by any combination of the available water sources

-- pumped, CAP, and/or other surface water in the San Carlos Project areas. However, the quantity of water available from each source during the same time period is limited by constraint

6(b). Pumped water is restricted because of the physical well capacity for the farm; CAP deliveries during the period are limited to

13.5 percent of the total annual farm allotment because of canal capacity; and other surface water availability must be less than twenty percent of the annual quantity of surface water available to the farm because of canal capacity.

Constraint

7

The trade-off between pumped water and CAP water is controlled by constraint seven. This constraint states that the total amount of pumped water

(PSLK) and CAP water

(CSLK) must be less than or equal to the ten year average pump water use for the farm. Water is traded against the ten year average rather than on a one for one basis.

43

Constraint 8 (a, b, and c)

Land resources are restricted by constraint 8. Two restrictions

(8a and 8b) are used to allow double cropped acres. Number 8(a) states that the number of acres available for winter crops (wheat, barley, and cotton) is limited by the total acreage with a history of irrigation, exclusive of conserving base acres. Likewise, 8(b) accounts for the crops grown during the summer (sorghum and cotton). Cotton is both a winter and summer crop because its long growing season prevents the planting of a winter crop on land that is planted with cotton. The number of winter acres always equals the number of summer acres. Alfalfa is limited by the available conserving base acreage [constraint 8(c)]. The conserving base acres is the land farmers maintain in non-depleting uses (fallow or idle, pasture, legumes, etc.).

Constraint 9

Total cropped acres are calculated by constraint 9. This constraint is included only for accounting convenience, and has no effect on the optimal solution.

Constraint 10

Because cotton is the most profitable crop grown in Pinal County, constraint 10 is included to limit the number of cotton acres on each representative farm to prevent all-cotton solutions to the models. Cotton restrictions are based on allotments under the 1966 Federal Cotton

Program. Only those farmers with cotton allotments from the program can participate in current price support programs. Thus, because of the risk

44 involved in growing cotton, it is unlikely that farmers not eligible for the cotton price supports will grow a significant amount of cotton.

Alternative Analyses

The sixty-nine representative-farm linear-programming models describing Pinal County farming are developed from the generalized mathematical statement described above. Using the basic models with various changes, several assumptions about CAP water quantities and qualities are investigated. The following discusses the five different analyses performed.

No CAP Water Available in Pinal County

The first analysis assumes no CAP water deliveries and thus provides the basic data for measuring the impact of CAP water. The basic farm models are solved using the 1986 data developed and discussed in

Chapter IV. In this analysis, the annual quantity of Central Arizona

Project water available to each farm (constraint 4a) is set to zero.

Total pumpage by farms (constraint 7) is not restricted. The salinity of irrigation water is the average salinity of local water in each irrigation district.

CAP Water Introduced and Freely Chosen

The second analysis introduces CAP water to the area with farmers purchasing the water freely as needed. The pump-CAP water trade-off rule along with the rule controlling the maximum quantity of CAP delivered during any month are enforced. Because irrigation districts contract for

CAP water rather than individual farms, the trade-off between pumped and

45

CAP water is considered at the district level rather than at the farm level. An iterative process is necessary to assure that all demands for

CAP water by individual representative farms within an irrigation district are met. After the first computer run of all the representative farms within an irrigation district, water is shifted from farms with a surplus to those with greater demands and the models solved again. This process is continued until all the demands for CAP water by individual representative farms are satisfied. The salinity of the CAP water is

1.4 minhos/cm -- the projected level in 1986.

Minimum Level of CAP Water Use Required

When CAP water is freely chosen as described above, many farmers use no project water and most use far less than available. In order to study the implications of requiring farmers to take a minimum amount of

CAP water to satisfy the district's contractual agreement, another computer run is made requiring farms to use at least 90 percent of their annual allotment (constraint 4b is set to the appropriate minimum quantity). The salinity of CAP water is 1.4 mmhos/cm in this analysis.

All Indian Demands for CAP Water are Satisfied

Because Indian farmers receive free CAP water that can be used to expand acreage, they could provide an outlet for unwanted agricultural

CAP water. Thus, the Indian Reservation farm models are run to find the maximum quantity that they would like to use, given their total irrigable acreage available.

46

Impact of Increasing Salinity

Damage to irrigated agriculture resulting from increased salinity levels of the Colorado River is of concern to the Federal Government and to the seven Colorado River Basin states. Studies are being conducted to assess current damages and to project expected damages in order to establish viable salinity control management for the River. Because the source of the Central Arizona Project is the Colorado River, an assessment of expected damages to irrigated agriculture in Pinal County would contribute to the overall analysis. The damage is measured by the loss in net farm income occurring because of higher salinity values for CAP water. The models are run assuming that the CAP water salinity increased to 1.8 mmhos/cm. This is the estimated salinity of Colorado River water delivered to Pinal County in the year 2020 if salinity control programs are not instituted on the River. The difference in results between the runs at 1.4 mmhos/cm (940 ppm) and 1.8 mnhos/cm (1200 ppm) enables one to calculate the cost per acre per unit increase in salinity to farmers in

Pinal County. It is assumed that CAP water is freely chosen.

CHAPTER IV

THE DATA

This chapter discusses the derivation of data necessary for the linear programming models. The first section is a discussion of those data necessary to define individual representative farms, including definition of the seven irrigation districts, four farm size classes, and three pumping depth classes. The second section develops those points on the production surface used in the analysis. Net returns data necessary for each production activity are given in the third section.

Pumped water and Gila River surface water availability and cost are discussed in the fourth section. The fifth section discusses the quantity of CAP water available in

1986, its cost, and restrictions in its use. The last section considers land restrictions to farmers in the area.

Stratification of

Representative Farms

Irrigation Districts and Groundwater Quality

Although it is possible for farmers to contract independently for

CAP water, individual contracts by farmers are unlikely because of the large expense of a distribution system. Rather, contractual agreements will be made by groups of farmers (irrigation districts) who share the cost of the distribution system.

47

48

Six irrigation districts, incorporating nearly all of the farming activity in Pinal County, have filed letters of intent to purchase CAP water. One of the six, the San Carlos Project, contains both an Indian and non-Indian component, each of which is considered a separate irrigation district in this study. Thus, a total of seven irrigation districts are included in the analysis. The seven districts are the San Carlos

Project Indian Lands, San Carlos Irrigation and Drainage District, Ak-

Chin Indian Reservation, Central Arizona Irrigation and Drainage District,

Hohokam Irrigation and Drainage District, Maricopa-Stanfield Irrigation and Drainage District, and the New Magma Irrigation and Drainage District.

A generalized map of Pinal County showing the seven irrigation districts is presented as Figure 7. One of the primary differences in the quality of resources among irrigation districts is the average salinity of groundwater.

Groundwater salinity data in Pinal County are limited. The U. S.

Geological Survey (Hardt, Cattany, and Kister, 1964) and The University of Arizona (Smith et al., 1963; Smith, Draper and Fuller, 1964; and Dutt and McCreary, 1970) are the sources of published groundwater quality data for the area. The Bureau of Indian Affairs Office in Sacaton monitors a few wells on Indian lands and is an additional source of data (McMakin,

1974). Individual sources do not provide adequate well sampling coverage of the area, so data from all sources are aggregated into a larger data set. Multiple data values for a specific well are averaged. According to the Arizona Water Commission (Boyer, 1971), the combining of data from different sources and years is justified because the average groundwater quality in Arizona has changed only slightly in the last 30 years.

MARICOPA COUNTY

COCI

7

ITY

4

EXPLANATION

..

I

AU Chin (Maricopa) Indian Reservation Irrigation

Maricopa-Stanfield Irrigation and Drainage nistrint

New Magma Irrigation and Drainage District

Hohokam Irrigation and Drainage District

San Carlos

'

Project Irrigation and Drainage District

San Carlos Project-Indian Lands

EZZZI

Central Arizona Irrigation and Drainage District

Figure 7. A Generalized Map of the Seven Irrigation Districts in

Pinal County, Arizona.

49

50

The Thiessen Polygon Method (Thiessen, 1911) is used to determine the average salinity for the entire study area and for each irrigation district. The acreage-weighted average groundwater salinity for Pinal

County is 1.0 mmho/cm and is the value associated with the county's average crop yields. Therefore, areas with less saline irrigation water than the county average show higher yields per acre than the county average and those with more saline water have lower yields. Individual irrigation district average salinity values are given in Table 1. Historical water quality records of surface flow in the Gila River show an average salinity of 1.3 mmhos/cm at the turnout for the San Carlos Project. Because pumped water in the San Carlos Project has an average salinity of 1.3

mmhos/cm, surface water delivered by the Project, a mix of pumped and

Gila River water, is assumed to have an average salinity of 1.3 mmhos/cm.

Farm Sizes

Stults (1968) found that economies due to farm size exist in

Final County. In order to reflect these economies in the costs and returns data, the farms in Final County are divided into four size classes -- Farm Sizes I, II, III, and IV. The range of cropped acres for each farm size class is given in Table 2.

Stults also found large differences in the efficiency of water use among the four farm size classes. Specifically, small farms tend to pump more water per acre than large farms in order to deliver the same quantity of water to the crop and thus to produce the same yield. He found that water use per cropped acre by farm size as a percent of the mean water used is as follows:

Table 1. Area-Weighted Average Salinity of Pumped Water by Irrigation

District.

Area

Salinity (mmhos/cm)

Ak-Chin Indian Reservation

0.6

Central Arizona Irrigation and Drainage

District

Hohokam Irrigation and Drainage District

1.1

1.8

Maricopa-Stanfield Irrigation and

Drainage District

New Magma Irrigation and Drainage District

San Carlos Project Indian Lands

San Carlos Irrigation and Drainage

District

0.9

0.9

1.3

1.3

51

Table 2. Breakdown of Final

County Farms into

Four

Size Groups.

Size Group

Range of

Cropped Acres

Average

Cropped

Acres

Farm Size I

Farm Size

II

Farm Size III

Farm Size

IV

Source: Stults (1968).

0 - 220

221 - 520

521 - 960

961 and above

106

341

675

1,705

52

53

Farm Size I -- 114 percent; Farm Size II -- 108.5 percent;

Farm Size III -- 104 percent; Farm Size IV -- 95.5 percent.

Stults suggests three possible reasons for this variation in efficiency of water use:

(1) Large farms tend to have a larger proportion of their ditches lined with concrete.

(2) The quality of management may increase as farm size increases.

(3) Larger farms are usually leveled to a more optimum grade, thereby increasing irrigation efficiency.

Monthly crop water requirements are multiplied by the appropriate irrigation efficiency. The result provides the amount of water the farmer starts at his headgate to assure adequate crop watering. The total cost of water to the farmer is figured at the farm headgate.

Depth to Water

The variable cost of water is central to this study. The price of water to most Final County farmers is the variable cost of pumping groundwater. Because the cost of water varies with pumping lift, and because the depth to water varies throughout the county, pumping lifts are divided into three depth-to-water categories: "Shallow" (less than

349 feet), "Middle" (350-499 feet), and "Deep" (greater than 500 feet).

The weighted average pumping depth for "shallow," "middle," and

"deep" lifts in each irrigation district is defined in Table 3 and is based on Burdak's (1970) 1986 projections. Values shown for irrigation districts that overlap Burdak's subareas are computed from an area weighted average.

Table 3. Average Pumping Lift for "Shallow," "Middle," and "Deep" Lifts in the Seven Irrigation Districts,

1986.

54

Subarea

Percent of Wells in Each Depth

Weighted Average

Depth (feet)

Ak-Chin Indian Reservation

"Shallow" Lift

"Middle" Lift

"Deep" Lift

Central Arizona Irrigation and

Drainage District

"Shallow" Lift

"Middle" Lift

"Deep" Lift

Hohokam Irrigation and

Drainage District

"Shallow" Lift

"Middle" Lift

"Deep" Lift

Maricopa-Stanfield Irrigation and

Drainage District

"Shallow" Lift

"Middle" Lift

"Deep" Lift

New Magma Irrigation and

Drainage District

"Shallow" Lift

"Middle" Lift

"Deep" Lift

San Carlos Project Indian Lands

"Shallow" Lift

"Middle" Lift

"Deep" Lift

San Carlos Irrigation and

Drainage District

"Shallow" Lift

"Middle" Lift

"Deep" Lift

21

19

60

0

40

60

27

40

33

10

35

55

9

17

74

33

56

11

28

43

29

302

448

599

436

571

264

413

564

286

462

580

337 .

462

524

287

326

537

269

365

552

55

Because the cost per acre-foot of water pumped from underlying aquifers is directly related to the pumping lift, the cost of water in

"shallow" lift areas is less than the cost in "middle" lift areas which in turn is less than the cost in "deep" lift areas. Because water is less expensive in "shallow" areas, farmers in these areas apply more water to crops than farmers in the other lift areas. The additional water enables the farmer to move farther out on the total physical product curve increasing his output per acre. Similarly, farmers in "middle" pumping lift areas apply more water than those in "deep" areas, but less than farmers in "shallow" areas. Yields per acre in the "middle" areas are lower than those in the "shallow" areas but higher than those in the

"deep" areas. The highest water cost and thus the lowest quantity of water application per acre to a crop occurs in the "deep" areas. Correspondingly, yields per acre in "deep" pumping lift areas are the lowest.

Yield-Water Quantity-Salinity

Combinations Used in the Analyses

Average yield per acre values used in this study are approximately the average yields realized in

Pinal County from

1965 through

1973 (Table

4).

An exception is the higher yield Mexican wheat recently introduced into

Pinal

County. Thus, wheat average yield is based on

1970 through

1973 data.

Water quantity and quality (salinity) are both factors of production which, when varied, result in different crop yields. The average salinity of pumped water varies by irrigation district resulting in crop yield differentials between irrigation districts. Yield differentials

Table 4. Average Yield per Acre for "Middle"

Pumpage Lift Area.

Crop

Yield

Upland Cotton

1,065 lbs.

American-Pima Cotton

574 lbs.

Barley

Wheat

3,400 lbs.

4,000 lbs.

Alfalfa (with summer water)

6 tons

4 tons

Alfalfa (without summer water)

Grain sorghum (short season)

3,400 lbs.

(average)

3,300 lbs.

Farm Size I and II

Farm Size III and IV

3,500 lbs.

Source: 'Arizona Crop and Livestock Reporting Service

(1974).

56

57 also occur between farms within an irrigation district if CAP water is mixed with local water sources. Mixing CAP water with the local supplies may either increase or decrease crop yield, because the salinity of CAP water is different than the salinity of local water sources. For example, if the local water has a higher salinity than CAP water, blending the two sources improves the overall quality of irrigation water and increases yield. If the salinity of local water supplies is lower than the salinity of CAP water, the resulting overall water quality from blending is reduced which in turn decreases yield. Relative reductions from 100 percent yield for selected crops when irrigated with water of various salinities are found in Figure 8. The salinity of Pinal County water is less than 2.0 mmhos/cm, so only a small portion of Figure 8 applies.

As previously discussed, the yield per acre of a crop also varies with the quantity of irrigation water applied during the growing season, which is related to the farm's pumping lift. This study assumes that yield reductions from 100 percent because of water shortage do not occur on farms in "shallow" pumping lift areas. Thus, 100 percent yield is defined as that yield occurring in shallow pump areas with "perfect" water quality. The base data on yield-quantity relationships, assuming average county water quality, are given in Stults (1968). Then, assuming additivity of the adverse effect of water quantity and quality, Table 5 was developed. Table 5 shows the expected yield for each crop grown in each irrigation district with three different quantities of water. The water quantity values used in this study are the same ones used by both

Stults (1968) and Burdak (1970), and represent typical water applications in each pumping depth class as reported in the farm interviews conducted

100

90

-

a

80

7)

-

5,

Barley-_

)

,

Q)70

>

:;:: o

--ii; 60

CC

50

o

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/

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Cotton

/

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i

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i

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1

6

i

8

I

10

I

12

14

1

16

EC

e

in millimhos per centimetre at

25°

Celsius

1

18

Figure 8. Salt Tolerance of Selected Crops

Source: Bernstein, 1964.

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63 by Stults. Table 5 demonstrates yield differentials within each district from different water quantities, along with yield differentials between irrigation districts because of differences in the salinity of local water.

In order to define points on the yield-water quantity-salinity production surface used in this analysis, Table 5 is expanded to include various mixes of CAP and local water (Appendix A). For each water mix, the quantity-weighted average salinity is computed. For example,

American-Pima cotton grown on a farm in the Ak-Chin area with a "middle" pumping lift requires 5 acre-feet of water annually. If the crop is irrigated with two acre-feet of CAP water with a salinity of 1.4 mhos/cm, and three acre-feet of local water with a salinity of 0.6 mmhos/cm, the quantity-weighted average salinity of all the water applied during the year is 0.9 mmhos/cm [

(2x1.4) + (3x0.6)

5

= 0.9 1.

The reduction from salinity is found in Figure 8 using the quantity-weighted average salinity computed. Values obtained from Figure

8 used with data on yield reduction because of water shortage from Table

5 define the yield-water quantity-salinity points on the production surface.

Costs and

Returns

Net Returns Over Variable Costs

The linear programming models require data on the net returns over variable costs for each production activity. A production activity in the models is one acre of a crop grown by a specified process. For example, cotton is repeated several times to allow for alternative mixes

64 of CAP and local water sources of differing costs and salinities. Each repetition is a separate production activity. Each production activity is associated with a different yield and total water cost, resulting in a different net income. Net returns above variable costs coefficients for each activity in the models include that return which must pay for the cost of water. Thus, net returns above variable cost coefficients for each production activity are the difference between gross income and the calendar variable costs other than the variable cost of water. The total cost of water is different for each possible mix of CAP and local water. The models are designed to calculate the water cost and subtract the total from the sum of the net returns above other variable costs.

Gross income is the product of yield and product price. Product prices assumed in this study are: long staple (American-Pima) cotton,

69ç per pound; short staple (Upland) cotton,

40ç per pound; barley, $79.20

per ton; grain sorghum,

$102.10 per ton; alfalfa,

$41.50 per ton; and wheat, $86.70 per ton. These prices are the

1973 seasonal average prices for each crop, with the exception of American-Pima cotton. The seasonal average price for American-Pima cotton in

1973 was unusually high because of short supplies. Therefore, the estimated

1974 seasonal average price was selected for the analysis. All prices are considered representative of long term trends in product prices in relationship to production costs.

Further, it is assumed that the relative prices of crops are constant overtime.

Calendars of operations for each crop were developed to provide necessary technical coefficients and variable production cost estimates.

Stults' budgets, used both in his and

Burdak's studies, were developed

65 from the farm interview questionnaires. These basic budgets were updated to 1974 conditions to reflect subsequent changes in farming techniques, crop varieties, and costs. Consultations with farm management personnel

(Wright, 1974; Robertson, 1974; and Willett, 1974) along with published field crop budgets for Yuma County (Hathorn et al., 1974) provide the basis for updating the Stults budgets.

A calendar of operations for each crop grown in a "middle" pumping depth was developed for the largest farm size (Farm Size IV) using Spring, 1974 cost data (see Appendix B). The increased variable cost of production on Stults' 1965 Farm Size IV budgets (1967) to updated

1974 budgets is used to update the calendar of operations for Farm Sizes

I, II, and III. The dollar increase in variable costs per acre computed for Farm Size IV is added to the smaller farm size costs per acre developed by Stults for each crop. A comparison of the variable costs of production other than the variable cost of water overlying "middle" pumping depths, as developed by Stults and as adjusted for this study are given in Table 6.

Net returns above variable costs without CAP water mixing are presented in Appendix C. Values for net returns over variable costs for different mixes of CAP and local water are derived from data in Appendix A.

Fixed Costs

Fixed costs are those costs which are incurred regardless of the farm's level of production, for example, depreciation of buildings, machinery, wells, and ditches; interest on loans; and taxes. Total farm

66

Table 6. Comparison of

1965 and 1974

Variable Costs of Production,

Excluding the Variable Cost of Water, in the "Middle"

Pumping Lift Areas of Pinal

County, Arizona.

Crop

American-Pima Cotton

Upland Cotton

Alfalfa (with summer water)

Alfalfa (without summer water)

Grain Sorghum

Barley

Wheat

Farm Size I

1965a

138.23

81.14

1974 1965 a

1974 dollars per acre

- - - -

235.52

117.79

Farm Size

II

121.62

121.62

79.19

218.91

218.91

115.84

61.14

42.10

34.04

33.67

88.02

93.39

70.64

84.17

59.39

39.71

32.86

32.99

86.27

91.90

68.76

83.41

Crop

American-Pima Cotton

Upland Cotton

Alfalfa (with summer water)

Alfalfa (without summer water)

Grain Sorghum

Barley

Wheat

Farm Size III

Farm Size IV

1965 a

1974

1965 a

1974 dollars per acre

- - -

115.34

115.34

77.46

57.96

39.69

32.97

33.10

212.63

212.63

114.11

83.87

91.90

68.76

83.41

113.46

113.46

75.99

56.99

40.61

32.16

32.91

210.75

210.75

112.64

83.87

91.90

68.76

83.41

report.

a.

1965 variable cost data are from the

Stults (1967) file

67 fixed costs of production are not included directly in the linear programning models, but must be subtracted from the linear programming model results in order to evaluate the farm's short run and potential long run economic position.

Stults (1968, p. 51) developed fixed cost budgets for each farm size-pumping depth class in Pinal County for 1966. As with his variable costs of production, his fixed cost budgets are updated to reflect 1973 conditions. Farm machinery fixed costs increased 51 percent from 1966 to

1973 (U. S. Department of Agriculture, 1973, p. 13). An index to represent the increase fixed costs associated with irrigation wells is not available. Therefore, it is assumed that irrigation well fixed costs increase by the same percentage as machinery fixed costs. During the same time period, 1966 to 1973, farm property taxes increased by 59 percent (Economic Research Service, 1974, p. 57). Stults' fixed cost values for buildings and concrete ditches are inflated by 28 percent, which is the change in the wholesale price index for all industrial commodities from 1966 to 1973 (Bureau of Labor Statistics, 1975). Fixed costs for each farm size-pumping depth class are given in Table 7. Values in

Table 7 do not include the fixed cost of CAP delivery systems, that is, the lateral canals which the farmers must provide to bring the CAP water from the main canal to their farm headgates.

Cost and Availability of Local Water Sources

Cost of Pumped Water

Using the average depth to water data in Table 3 in combination with 1974 power costs in the various subareas, approximate pumping costs

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70 are computed for each irrigation district. The method of estimation is given by Nelson and Busch (1967).

Costs of pumping water are divided into fixed, added capital, and variable costs. Only the latter two costs are included directly in the linear programming models. Costs directly related to the operation of the well are variable costs and include fuel, repair and maintenance, lubrication, and attendance. Added capital costs are those costs related to the declining groundwater table, for example, adding column and bowls, and increasing the size of the power unit to accommodate the greater lift.

Equations for both electric and natural gas powered wells are given by Nelson and Busch.

Stults and

Burdak included natural gas powered wells in their analysis. However, in these projections for the year

1986, all natural gas powered wells are assumed to be replaced with electric powered wells because of dwindling natural gas supplies for agriculture and thus increasing costs. Thus, the equations for variable and added capital cost of pumping per acre-foot per foot of lift

(AFF) used in this study are:

Variable costs per

AFF

1,024 P e

+ 0.00752

E e

(12) and

Added capital cost per

AFF =

(92.20)

(decline in ft.)

(lift, ft.)

(AF pumped per year) (13)

In equation

12, P e is the price of electricity per

KWH, E e is the overall efficiency of the pumping plant (Nelson and Busch give

51.7 percent as the average in

Pinal

County), and

0.00752 represents the total cost of repairs, lubrication and attendance. In equation

13, 92.20 is the current cost per foot of well deepening. Other values used in equation

13

71 are the average values found by Nelson and Busch for Final County. Using equations 12 and 13, the costs of one acre-foot of water per foot of lift is determined for the seven irrigation districts (Table 8).

The cost of an acre-foot of pumped water to a particular farm size-pumping depth class within an irrigation district is computed by multiplying the appropriate pumping cost (dollars per acre-foot per foot of lift) for the district by the weighted average pumping depth for the farm (Table 3). Table 9 shows the average cost of pumped water in each irrigation district by pumping depth.

Monthly Pumping Restrictions

Water availability is probably the most important restriction faced by Pinal County farmers. Typically, farmers run their irrigation pumps 24 hours a day from late June until early August to extract the maximum quantity of water physically possible. Because irrigation cycles are typically two-week periods, both Stults and Burdak used the amount of water used by farmers during the July 1 through 15 period (typical summer irrigation period) as the principal summer water restriction.

A second critical water use period is defined by Stults and occurs from January 15 to the end of February. During this period, barley and wheat are irrigated and cotton is preirrigated. Unless limited by land availability, barley and wheat acreage are determined by the available water during this period. Stults and Burdak used the amount of water typically pumped from January 15 through February 28 as the winter water availability restriction.

Table

8.

Cost of One Acre-Foot of Water per Foot of Lift in Pinal

County, Arizona, 1986.

a

Irrigation District

Pumping Costs b

(dollars per acre-foot per foot of lift)

Ak-Chin

Central Arizona

Hohokam

Maricopa-Stanfield

New Magma

San Carlos Project Indian Lands

San Carlos Irrigation District

0.038764

0.031039

0.033812

0.032822

0.031831

0.029851

0.029851

a.

Values are the sum of added capital and variable cost of pumping. Fixed cost of pumping are not included in the values.

b.

These figures include

$0.002524 per acre-foot of lift added capital cost.

72

73

Table

9.

Average Cost of Pumping Water in Pinal County, by Pumping Depth and Irrigation District, 1986.

a

Irrigation District

Ak-Chin

Central Arizona

Hohokam

Maricopa-Stanfield

New Magma

San Carlos Project Indian

Lands

San Carlos Irrigation

District

Pumping Depth

Shallow

Middle

Deep

- - - dollars per acre-foot

- - -

11.71

17.37

23.22

13.53

17.72

8.93

13.96

19.07

9.39

15.16

19.04

10.73

14.71

16.68

8.57

8.03

9.73

10.90

16.03

16.48

a. Values are the sum of added capital and variable cost of pumping. Fixed cost of pumping are not included in the values.

74

While the summer water restriction represents the maximum quantity of water available during any given time period, the winter water restriction is less than total water availability. Most farms choose not to expand wheat and barley acreage, even though they could do so by increasing pumping to the well's physical capacity, for several reasons.

First, the net return from barley and wheat is typically low, especially in the deep pumping areas. Thus, most farmers choose to curtail winter pumpage to minimize water table drawdown in the summer when maximum pumpage is desirable for higher valued crops. Further, by conserving water in the winter, the farmer is less likely to have surging (pump cavitation) during summer withdrawals. Lateral movement of groundwater in Final County is generally slow enough to permit individual farmers to conserve water early in the season for use later in the season, but fast enough so that conservation of groundwater over longer time periods is ineffective.

While winter and summer water restrictions are sufficient if only pumped water is available, the trade-off between pumped and CAP water mixes in this analysis necessitates that monthly crop water demands and monthly water supplies be used in the models. Thus, the Stults and Burdak

15 day summer water values for 1986 are doubled to provide thirty day or monthly pumping capacities. Values for maximum thirty day pumpage used in this study are shown in Table 10.

In order to define monthly pumping restrictions, the relative amount of water available during each month is needed. Stults' and

Burdak's summer restriction was for June,

July, and August. This maximum pumpage (100 percent of the 30 day maximum) is assigned to these three

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75

76 months. Their winter restriction was

70 percent of their summer restriction. Seventy percent is the value used in this study for January and

February.

Pumpage limits are assumed to increase linearly from the winter to the summer and then decrease linearly from the summer through the fall. The relative amount of available monthly water is defined in Table

11.

Thus, the maximum quantity of pumped water available during any month is computed by multiplying the maximum thirty day pumping value from Table

10 by the relative quantity value for the month found in

Table

11.

Water Allocations in Surface Water Areas

Two irrigation districts in the study area receive surface water other than CAP water in addition to pumpage -- the San Carlos Irrigation and Drainage District and the San Carlos Project Indian Lands. Water diversions from the Gila River, groundwater withdrawals, and deliveries to project lands holding water "rights," are controlled by the San Carlos

Irrigation Project Joint Works Office. The Joint Works Office annually assesses the available water in storage reservoirs and determines the safe amount of groundwater that can be pumped to augment the surface flow. Each farmer holding water "rights" is notified of the quantity of water to expect during the coming year. Water deliveries by the San

Carlos Project, whether surface or pumped, are treated as surface water in this study since the groundwater is pumped by the Project and delivered at the same price as the surface water. Farmers receiving San

Carlos Project water pay an annual assessment covering the project's cost.

The assessment entitles them to receive their annual allotment of Project

January

February

March

April

May

June

July

August

September

October

November

December

Table

11.

Relative Proportion of Pumped Water Available by Months.

Month

Pumped Water Available as a Percent of Availability in July

90

100

100

100

70

70

80

80

90

70

70

70

77

78 water at no extra cost. The cost of pumping groundwater is included in the annual assessment. The annual assessment is considered a fixed cost, and thus, the surface water delivered by the Project has no variable cost to the farmers. Some farmers holding land with rights to Project water also own adjacent non-Project land. Many of these farmers, especially in the District part, actively pump wells on their adjacent land for use on

Project lands. This water is termed pumped water in this study.

The San Carlos Project Indian Lands received an average of 62,969 acre-feet of water delivered to the land by the Joint Works between 1963 and 1972. During the same ten-year period, the District part received an average of 90,143 acre-feet. This water is allocated to farm size classes and pumping depth classes according to the relative proportion of summer water that Burdak found in each class. The results are found in Table 12.

Discussions with officials of the San Carlos Project indicate that the irrigation system can deliver to a farm, during any month, twenty percent of its annual allotment. Thus, San Carlos project lands are restricted in the model to a maximum surface water delivery during any month of twenty percent of their annual allotment.

Pumped water data for the San Carlos Project are included in Burdak's Casa Grande and Coolidge subareas. These subareas are not contiguous with the Irrigation Districts of this study. It is necessary to distribute the data to the overlapping areas of this study, i.e., the San

Carlos Project Indian Lands, the San Carlos Irrigation District, and the

Hohokam Irrigation District. Most of the wells in Burdak's Casa Grande and Coolidge areas are located in the Hohokam Irrigation and Drainage

District. According to the Bureau of Reclamation's "Well Location Map:

79

Table

12.

Annual Allocation of San Carlos Project Surface Water.

Farm Size

Pumping Depth

San Carlos Irrigation

Project

Indian Lands

(acre-feet)

District Lands

(acre-feet)

Shallow

Middle

Deep

504

630

126

901

901

1,803

II

Shallow

Middle

Deep

2,519

5,038

630

4,056

5,409

4,056

III

I

V

Shallow

Middle

Deep

Shallow

Middle

Deep

6,927

11,964

2,519

10,705

17,631

3,778

8,113

11,719

7,211

13,521

19,831

12,620

80

San Carlos Area" (1960), there are approximately 279 non-Project wells

(wells not controlled by the San Carlos Project Joint Works) in the area.

Some non-Project wells deliver water to Project lands, but are located in the Hohokam area. Under the CAP authorization, groundwater from districts contracting for CAP water may not transfer water outside their district

[43 U.S.C. Sec. 1524 (c) (3)]. This rule precludes further transfers when the CAP comes on-line, and thus, these wells are allocated to Hohokam.

Of the 279 non-Project wells in the area, 204 are in Hohokam, 72 are on District Lands, and three are on Indian Lands. The matrix showing the distribution between the two subareas in Burdak's study and the three in this study is:

Coolidge

76

Casa Grande

128

Total

204

Hohokam

San Carlos District

53

3

19

72

3

San Carlos Indian

The pumped water is distributed to the three irrigation districts according to the relative proportion of wells in each area. The results are included in Table 10.

Central Arizona

Project Water

The major objective of this study is to investigate the impact of

Central Arizona Project water on irrigated agriculture in Pinal

County,

Arizona. Although no water contracts have as yet been signed, and exact allocations to the county and districts have not been made, certain basic assumptions about the Project are necessary if models are to be constructed.

81

After discussions with members of the Arizona Water Commission, a reasonable assumption about the quantity of CAP water initially available for agricultural use in Pinal County in 1986 is 659,000 acre-feet. The method used to distribute the County's CAP water allocation to each irrigation district is discussed below.

The Ak-Chin Indian Reservation has requested 50,000 acre-feet of water delivered to the farm headgates for 10,800 acres (4.63 acre-feet/ acre). From discussions with the Arizona Water Commission, it appears that 58,000 acre-feet measured at the main canai side is a reasonable quantity they should expect. With a 15 percent conveyance loss, this translates to 49,300 acre-feet at the farm headgate. Thus, the Ak-Chin reservation should receive about 58,000 acre-feet of water at the main canal.

The Gila River Indian Community has 62,000 developed agricultural acres, of which about 39,000 acres are in the San Carlos Project. A total of about 50,000 developed and nondeveloped acres are within the

Project. Non-Project lands of the Gila River Indian community are not included in this study because most of the non-Project land is in Maricopa County. Further, it is likely that CAP water will be used on Project lands rather than non-Project lands because a distribution system already exists on the Project lands. Because Indians can develope new lands under the CAP legislation, it is reasonable to assume that they will develop the full 50,000 acres in the San Carlos

Project area. The average annual quantity of other surface water delivered to the Indian part by the San Carlos Project Joint

Works is 111,000 acre-feet and is subtracted from computed total water needs to obtain the CAP water

82 allocation. Thus, based on a value of 5.4 acre-feet of water per acre measured at the main canal (the same value used for the Ak-Chin Indian

Reservation), the Gila River Indian Reservation should receive about

159,000 acre-feet of CAP water at the main canal side [(5.4 acre-feet per acre x 50,000 acres) - 111,000 acre-feet]. Using the above calculations, Indian lands receive one-third of the total agricultural CAP water available to Pinal County in 1986.

Non-Indian lands can use CAP water only on those lands with a history of irrigation during the ten years preceding enactment of the

Central Arizona Project legislation, i.e., lands receiving irrigation water must have been under irrigation at some time during the period

September, 1958 to September, 1968. The remaining 442,000 acre-feet of

CAP water is allocated to the five non-Indian districts according to their relative number of average irrigated acres. Thus, Central Arizona should receive 128,180 acre-feet (29 percent); Hohokam, 79,560 acre-feet

(18 percent); Maricopa-Stanfield, 145,860 acre-feet (33 percen0; New

Magma, 30,940 acre-feet (7 percent), and San Carlos Project-District

Lands, 57,460 acre-feet (13 percent).

The Arizona Water Commission recommended using a conveyance loss factor of 15 percent from the main canal to the farm headgate for Indian

Lands. Beck and Associates (1971a, b, c) used a 10 percent conveyance loss for Maricopa-Stanfield, Central Arizona, and New Magma. The loss factor for San Carlos District Lands and Hohokam is also assumed to be

10 percent.

CAP water is allocated to the different farm size-pumping depth classes according to the relative number of irrigated acreage in each

83

(see

Table

13). The values in Table 13 are the initial values used in the computer models. After the initial model solutions, in order to meet all demands for Central Arizona Project water by individual representative farms, water in the models is shifted within each district from farms with surplus CAP water to those with greater demands. Thus, all demands for additional CAP water are satisfied. No irrigation district can receive more than 13.5 percent of its annual allotment in any month because of canal capacity, but an individual farm can receive as much as can be profitably used.

Current estimates place the cost of CAP water for non-Indians at

$15.00 per acre-foot at the main canal side. This cost translates into a cost of $16.67 at the farm headgate, given the ten percent conveyance loss factor for non-Indian farmers. Indian farmers will receive subsidized CAP water from the Federal Government at no direct cost to them.

According to CAP legislation, each non-Indian irrigation district must reduce groundwater pumpage by one acre-foot for each acre-foot of

Project water purchased [43 U.S.C. Sec. 1524(d)]. This study assumes that the average yearly pumpage for the period 1959 through 1968 is the base against which water must be traded. This period is chosen since it is the 10 year period prior to the passage of the CAP bill. The ten year average pumpage rate in the Lower Santa Cruz River Basin (pumpage in New

Magma is not included) for this period was 1,079,500 acre-feet

(Arizona

Water Commission, 1973). Domestic consumption in the basin is included in the estimate.

According to the Pinal County Supervisor's

Office, 45,000 people live in the area. With a 108 gallon per day per person use rate, total

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84

domestic water use is estimated at 5,441 acre-feet per year. Thus, the annual irrigation pumpage in the Lower Santa Cruz River Basin is

1,074,059 acre-feet. Pumpage in areas outside Pinal County but within the Santa Cruz River Basin totals about 110,000 acre-feet, which places

85 the ten year average pumpage rate for Pinal County (New Magma is not included) at about 964,000 acre-feet.

Allocation of the ten-year average pumping rate among the irrigation districts was made after discussions with Arizona Water Commission personnel. However, their data did not include a value for pumping of non-Project wells in the San Carlos Project area, and their value for pumpage in the Maricopa-Stanfield area appears high when compared to other areas. The ten year average non-Project pumping in the

San Carlos District area is estimated at 102,000 acre-feet. The

Maricopa-Stanfield figure suggested by the Arizona Water Commission is reduced by 102,000 to account for non-Project pumping in the San Carlos

District area. Pumpage in New Magma during the ten year period is estimated as 60,000 acre-feet. Table 14 summarizes the ten year average pumpage for non-Indian lands.

Projected salinity levels in the Colorado River for 1985 range from a low of 1.2 mmhos/cm to a high of 1.5 mmhos/cm. In the CAP

Environmental Impact Statement, the Bureau of Reclamation (1972) states that evaporation of Colorado River water during transit to Pinal County will have a minor effect on concentrations of total dissolved solids in the imported water. A maximum degredation of about six percent between

Lake Havasu and Final County is estimated. Using the average value for salinity projections for Colorado River water in Lake Havasu in 1986,

Table 14. Ten

-

Year Average Pumpage by Non-Indian Irrigation Districts.

Irrigation District

Pumpage to Nearest

1,000 acre-feet

Hohokam

Central Arizona

Maricopa-Stanfield

New Magma

San Carlos Irrigation District

190,000

250,000

298,000

60,000

102,000

86

with a six percent increase in transit, an estimate of water quality of about 1.4 mmhos/cm salinity in Pinal County is produced.

87

Land

Resources

Land has not been a restraint on output in Pinal County in recent years. However, to account for double cropping, to assure that CAP water is not used to expand acreage on non-Indian farms, and to define the total irrigable land in Indian areas, land constraints are included in the models. Two land restrictions are required, and are called Winter

Acres and Summer Acres. Two restrictions rather than one are used because barley and wheat require only winter acres, while grain sorghum only requires summer acreage. Cotton requires both winter and summer acreage. Summer Acres always equals Winter Acres.

Burdak's 1986 acreage values for his five subareas are redistributed to the seven irrigation districts in this study. His Eloy and Queen

Creek subareas correspond to the Central Arizona and New Magma irrigation districts, respectively, and can be used without modification.

However, geographic boundaries for the other irrigation districts of this study do not agree with the subarea of his study, requiring some modification of the values.

Ak-Chin is contained in Burdak's Maricopa subarea and represents about eleven percent of the irrigated land. Assuming a random distribution of farms across the area, Ak-Chin is separated from the Maricopa subarea by multiplying each farm size-pumping depth class by eleven percent. With Ak-Chin separated, the remaining land in Maricopa is added to

88 the acreage values in Burdak's Stanfield subarea to produce the Maricopa-

Stanfield Irrigation District.

The Casa Grande and Coolidge areas are divided into Hohokam, San

Carlos Project Indian Lands, and San Carlos Irrigation District. Necessary data are lacking for a division based on the relative number of irrigated acreage. Thus, the two subareas are divided into the three irrigation districts according to relative physical size (square miles). This division resulted in San Carlos Project Lands receiving slightly more land than their historical average acreage, and consequently, Hohokam received slightly less than its historical average. Thus, San Carlos

Project Indian Land values are reduced by 23 percent and the District

Lands by 12 percent to conform to historical averages. Hohokam received the land removed from the two districts. Table 15 shows the final allocation of Winter and Summer Acres.

Conserving base is land which is kept in non-depleting uses

(fallow or idle, pasture, green manure crops or legumes) if farmers are to participate in Federal government cotton price support programs. Alfalfa is the only non-depleting crop grown in Pinal

County. It is not likely that the conserving base acreage will ever become a restriction in the linear programming models because of the large amount of land in this category relative to available water.

However, because alfalfa can use this land rather than the more restrictive

Winter and Summer Acres, it is included in the models. Conserving base acreage is distributed in exactly the same manner as Winter and Summer

Acres. The distribution is shown in

Table 16.

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Kelso, Martin, and Mack

(1973) report a total of

256,976 cropland acres in

Pinal

County. The cropland acreage includes the 178,283 Winter and Summer Acres reported in Table 15 plus 78,693 acres of the conserving base (Table 16) typically used for alfalfa. Because the acreage typically used for alfalfa is distributed over the farm size-pumping depth classes in the same proportion as conserving base acreage, total cropland acreage for each farm size-pumping depth class can be computed. By dividing cropland acreage by the appropriate value for average acres per farm from Table 2, one can estimate the number of farms in each representative farm class. Table

17 displays the approximate number of farms in each irrigation district by farm size and pumping depth class.

Cotton Acreage Restrictions

Cotton is the most profitable crop grown in

Pinal County, and therefore, must be restricted to prevent all cotton solutions by the models, an unreasonable result in view of farmers' perception of the relation between total supply and price, and their perception of risk.

Both Stults and

Burdak based their cotton restrictions on the

1966

Federal

Cotton Program.

Only those farmers with cotton allotments from the program can participate in the current price support programs. Thus, it is unlikely that farmers not eligible for cotton price supports will grow a significant amount of cotton.

The restrictions used in this study are

Burdak's 1986 values, which are based on the 1966 Cotton

Program.

Cotton restrictions are distributed to each irrigation district according to the procedures discussed in the acreage section above.

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19

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95

CHAPTER V

RESULTS

OF THE ANALYSES

The major objective of this study, as stated in

Chapter

I, is to investigate the economic impact of Central Arizona Project water on irrigated agriculture in Pinal County,

Arizona. The projected adjustments in optimum enterprise combinations for representative farms under several alternative management schemes, when

CAP water is delivered to the

County, are presented in this chapter.

Changes in water use, land use, crop mix, and net revenue above variable costs are the principal focal points.

Results of the five alternative management schemes (discussed in detail in Chapter

III) are discussed individually and jointly. Specifically, the five schemes are: (1) with no CAP water available in Pinal

County,

(2) where

CAP water is introduced and freely chosen,

(3) with a minimum level of CAP water use required,

(4) where all Indian demands for

CAP water are satisfied, and (5) where the salinity of CAP water is allowed to increase.

In most cases, only aggregated results for the county as a whole are given in this chapter. Detailed results for each of the five analyses, classified by irrigation district, are given in

Appendix D.

A supplement to this dissertation contains the individual representative farm results for each analysis

(Boster, 1975).

No CAP Versus CAP Freely Purchased

The initial solutions of the representative farm models assume no

Central Arizona

Project water is available in 1986. This analysis

96

97 establishes a base from which to measure the economic impact of introducing CAP water into the area.

The initial analysis also enables comparison of

Burdak's projections, made in

1970, with those of this study. The basic representativefarm linear-programming models of this study contain modifications and conceptual improvements over Burdak's models. However, much of the basic representative farm data used in this study were originally developed by

Stults and used by Burdak. Thus, the results of the initial analysis without CAP water introduced into Pinal County should be similar to

Burdak's 1986 projections for the county. Table

20 presents the projections made in

1970 by Burdak, and the

1975 projections of this study for net revenue above variable costs, water use, and acreage of field crops in

Pinal County,

Arizona, for

1986. Considerable agreement exists between the two projections. Agreements and disagreements are discussed below.

Although net returns above variable costs projected in this study are nearly

14.8 million dollars less than those projected in the 1970 study, total water use and the crop mix are similar.

American-Pima cotton and upland cotton acreage are virtually identical as expected (both studies use the same cotton acreage restrictions). Total projected acres of alfalfa are about

19 percent less in the

1975 study than the

1970 study. Barley and wheat are winter crops historically grown in the area.

Burdak's models project that farmers will grow all barley rather than all wheat or some combination of the two as the winter crop. However, since his work, new higher yield wheat varieties have been introduced into

Pinal County and are used in the

1975 projection models. As expected, a shift by farmers from barley to the higher yield wheat is projected for

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1986 by the 1975 models. Total winter crop acreage (wheat) is 47 percent

(25,800 acres) higher than that projected by

Burdak's models, whereas the number of double cropped acres increases by only 25,600 acres.

Thus, there is also a slight shift from alfalfa to wheat. Total water use is

25,000 acre-feet more in the 1975 study, explainable by the increase in wheat acreage.

Why are projected net returns above variable costs so much lower in the 1975 study if the projected crop mixes are similar and if the projected total cropped acreage is slightly higher in the

1975 study? First, the similarity in crop mixes in each study suggests that the productivity ratios between the crops are similar; noting the exception for barley and wheat. Secondly, the value of net returns above variable costs is the result of subtracting total variable costs from gross returns (gross returns is the product of yield and product price). Both product prices and variable production costs in this study are updated versions of those used by

Burdak.

1

The lower net returns above variable costs projected for 1986 by the

1975 models simply reflects a proportionately larger increase in production costs than in product prices for each crop.

With

Central Arizona Project water introduced into the 1986 representative farm models, net returns above variable costs for the whole county increase by

4.7 million dollars or

35 percent above net returns if no CAP water is available (see

Table

21, rows

1 and 2).

Similarly, cropped acreage increases by nearly

83,200 acres with CAP water introduced and freely purchased. However,

3.9 million dollars of the 4.7

1. A complete discussion of the method used to update product prices and variable production costs is given in

Chapter

IV.

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2 the rise in net returns results from acreage increases in the other crops (see Table 22, rows 1 and 2).

The increase in net income to Indian lands will be a real increase in total net income to the Indians since almost all costs of the new water are subsidized. However, certain fixed costs, such as the cost of the distribution system from the main canal to the farm headgates must be subtracted from the 0.8 million dollar increase in income to non-Indians.

These costs are discussed later in this chapter.

Table 21 (rows 1 and 2) also shows a 21 percent decrease (about

154,000 acre-feet) of pumped water used in the area receiving CAP water.

Other surface water use is essentially constant. However, the total water applied to crops increases by 325,700 acre-feet -- a 37 percent increase in total water use.

Why is total water use with CAP higher than total water use without CAP, if the one for one pump-CAP trade-off rule is in effect? There are two reasons. First, the rule does not apply on

Indian lands where

64 percent of the increase occurs. The Indians have a net increase of

180,600 acre-feet of water use, while decreasing pumpage by only 3,000 acre-feet. Second, the increase of 145,000 acre-feet of water use on non-Indian lands is possible because farmers are trading water against an

2. Cotton is the most profitable crop grown in Pinal County, and therefore, must be restricted to prevent all cotton solutions by the models, an unreasonable result in view of farmers' perception of the relation between total supply and price, and their perception of risk.

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102

historical average pumpage rather than what pumpage would have been in

103 that year without CAP. The historical average is higher than what pumpage would have been, because farmers in the deep pumpage areas would have cut back on pumpage as the water table fell. Thus, provision of CAP water will tend to slow the groundwater overdraft, but not on an acrefoot per acre-foot basis.

The CAP-local water mix applied to crops varies throughout the county. In the Ak-Chin area where CAP water is free but of a lower quality than local supplies, farmers mostly ignore the quality question by growing their crops with all CAP water. The exception is for grain sorghum. Nearly all the local water used in the Ak-Chin area is mixed with CAP water and applied to grain sorghum, a salt sensitive crop. However, on the San Carlos Indian Reservation no clear pattern to the CAPlocal water mix is apparent. San Carlos Indian farmers have a large supply of free water available because they receive both CAP and San

Carlos Project water at no direct cost. Further, the salinity of local and CAP water is so similar that one water source is no more preferable than the other. The water mix on San Carlos Project Indian lands is thus based on water availability rather than on salinity levels.

New Magma uses no CAP water because of relatively low cost good quality local supplies. The CAP water used on San Carlos District lands is mixed in small quantities (usually one acre-foot of CAF water per acre) with local supplies. In the remaining three irrigation districts,

Central Arizona, Hohokam, and Maricopa-Stanfield, CAP-local water mixes at all different levels, with the greatest use on farms in deep pumping lifts where CAP water is less expensive than local supplies.

104

CAP

Freely Purchased Versus

Minimum Required Purchase

Several adjustments occur when individual farms are required to use at least ninety percent of their annual

CAP allotment rather than a freely selected quantity.

As expected, net returns above variable costs decrease when this additional constraint is added, but only by about

$465,000 or less than three percent (Table 21, rows 2 and 3). However, the decrease in net returns all occurs within the five non-Indian districts (the Indian Reservations freely use all the

CAP water available to them) and so balances out more than half of the 0.8 million dollar gain to non-Indian farmers made when

CAP water was furnished on a free choice basis.

Now, with a CAP water use of 619,000 acre-feet out of the 659,000 acre-feet total

CAP allocation, (139,000 acre-feet of which was not freely chosen) the trade-off ratio between CAP and pump water rises to about 2.3 acre-feet of

CAP used for each one acre-foot of pump water no longer used. The ratio was only 3.1 acre-feet of

CAP to one acre-foot of pump water when

CAP was freely chosen.

Almost no shift in the county's crop mix is observed (Table 22, rows 2 and 3). In order to use all of the required CAP water, however, the number of double cropped acres increased slightly and the CAP-local water mix shifted to mixes with higher quantities of

CAP water. Most of the requirement to use more CAP water was simply reflected in decreased net income. Most of the decrease in net income is from the higher price of CAP water rather than from decreases in yield due to use of poorer

105 quality water. In fact, in the Hohokam Irrigation District, the quality of the water mix improved.

Impact of Increased CAP Salinity

Recently there has been much interest in the West in evaluation of the cost of increased salinity to irrigated agriculture, especially in the Colorado River Basin. It is estimated that Colorado River water delivered to Pinal County will have a mean salinity of 1.4 mmhos/cm in

1986 and a mean salinity of 1.8 mmhos/cm in 2020 if no additional salinity control programs are instituted. To be economically efficient programs, the cost of any control programs should be less than the value of the decrease in agricultural production if no controls are established.

The linear programming models compare the value of net returns above variable costs as the two salinity levels when CAP water is freely chosen (Table 21, rows 2 and 4). The total decrease in net returns above variable costs for Pinal County farmers is $199,400, or 1.1 percent of the base of $18,306,629. This decrease averages only 61 cents per year per irrigated acre, or 0.23 cents per year per irrigated acre per part per million increase in salinity.

3

Total water use in the County decreases by only 32,400 acre-feet when CAP water salinity increases to 1.8 mmhos/cm (Table 21, rows 2 and

4). The decreased total water use results almost entirely from cutbacks in CAP water purchases. Total cropped acres also declines, but only by

3. The value 0.23 cents per year per irrigated acre per part per million increase in salinity is computed by dividing 61 cents by 268 parts per million increase in salinity (0.4 mmhos/cm x 670 ppm/mmho/cm =

268 ppm).

106

2,000 acres (Table 22, rows 2 and 4). Sixty percent of the decrease is from barley dropping out of the County's crop mix. Although barley is the most salt tolerant crop grown in Pinal County, it is also the most economically marginal crop grown. Thus, the slight decrease in yield from increasing CAP water salinity from 1.4 to 1.8 mmhos/cm is sufficient to reduce net returns for barley to the point where it is no longer profitable to grow. Slight decreases in both American-Pima Cotton and alfalfa are observed while a very small increase in wheat is noted.

The number of different CAP-local water mixes increases at the higher salinity level. Shifts to both higher and lower concentrations of

CAP water in crop water mixes are observed in each district. Whereas a farmer might use the same CAP-local water mix for an entire crop when the salinity of CAP water is 1.4 mmhos/cm, there is a slight tendency for farmers to shift to two different mixes when the salinity rises to 1.8

mmhos/cm. At the higher salinity value, the quantity of CAP water in the crop water mix is increased by one acre-foot on part of the crop and decreased by one acre-foot in the mix applied to the other part of the crop.

The estimate of losses of 0.23 cents per year per irrigated acre per part per million increase in salinity should be compared to the estimates of Sun (1972), the only other comparable study on the Colorado

River area. Sun did not directly compute the damage from salinity in

Imperial Valley, California in cents per year per irrigated acre per part per million increase in salinity. In an attempt to make such a calculation from Sun's data (see Sun, 1972, Tables 5.2, 5.3, and 5.9) an inconsistency in his results was discovered. Sun's calculation of annual crop damage per acre for an increase in irrigation water salinity from

107

1.5 mmhos/cm to

2.0 mmhos/cm was computed by dividing the decrease in net farm returns by the available crop acres, resulting in a loss value of about

16 dollars per year per acre or

4.83 cents per year per acre per ppm.

4

It appears that Sun should have divided the decrease in net farm returns by total cropped acreage, which counts double cropped acreage twice to obtain the loss value. Using the data in Sun's Tables

5.2 and

5.3, an annual loss value of 2.79 cents per acre per ppm is obtained.

The exact magnitude of the loss due to salinity in Imperial Valley is not critical to this study. Rather, an explanation of why the projected loss value for Imperial Valley is greater than the projected loss value in

Pinal

County is necessary.

The higher salinity damage value projected for Imperial Valley,

California result from two different reasons. Higher valued crops, e.g., lettuce and sugar beets, are typically grown in Imperial Valley, but not in Pinal County. Because these crops have high per acre values and are also relatively salt sensitive, the decreased crop yield resulting from increased irrigation water salinity represents a large loss in total revenue to the area, which in turn is reflected in higher annual cost per acre per ppm values. The second reason for the higher loss value in

Imperial Valley is because of different crop yield-water quality models used in the two studies. Using the traditional approach, Sun based his yield reductions on the average root zone salinity. This study, however, uses the new method postulated by the U. S. Salinity Laboratory which computes crop loss from the salinity of the irrigation water applied to and

4. In a report by the Bureau of Reclamation, Kleinman, Barney,

Titmus (1974) used this value from Sun but rounded it to

5 cents.

108 the crop (see Chapter II). The first method projects higher crop loss than the second and thus results in higher loss values. Assuming that the new method of estimating yield reduction is correct, but recognizing that a crop mix including higher valued crops has traditionally been grown in the Imperial Valley than in Pinal County, one would expect loss values for the Imperial Valley to be higher than for Pinal County, but not nearly as high as the estimate made by Sun.

Two other studies recently reported as part of a regional study on the effects of increasing salinity levels of the Colorado River also estimate agricultural damages. The first, by two Bureau of Reclamation economists, Brown and Kleinman (1975), presents damage estimates but does not explain the method used to calculate the values. Their values range from a low of 0.16 cents per year per acre per ppm increase for the

Coachella Irrigation District in California to a high of 5.55 cents per year per ppm increase for Imperial Valley of California. Their estimates for three areas in Arizona, none of which are in Pinal County, are 0.49

cents for the Wellton-Mohawk area; 1.3 cents for the Yuma Valley; and

1.06 cents for the Lower Gila River area (all values are in cents per year per ppm increase in salinity). All three Arizona estimates are higher than the estimate for Pinal County presented herein.

The second report by Howe and Young (1975) concentrates on regional income effects (secondary impacts) of increasing salinity in the

Colorado River. Although they do not directly present primary impacts comparable to those of this study, one can estimate the impacts from their data. Their value ranges from 1.47 to 6.75 cents per year per ppm increase in salinity. Again, even the lowest figure is higher than the

estimate for Pinal County. As Howe and Young (1975, P. 17) state, because they did not use complete linear programming models in deriving

109 their estimates, "our crop loss estimates represent an upper bound on the actual crop losses."

All Indian Demands for CAP Water Satisfied

Farmers on the two Indian Reservations in Pinal County will receive Federally subsidized CAP water at no direct variable cost to them, and the water can be used to expand irrigated acreage. Thus, the Indian

Reservations could provide an outlet for excess agricultural CAP water.

Further, a measure of economic benefits accruing to Indian farmers receiving the free CAP water is of interest to decision-makers allocating the project water. The representative-farm models for both the Ak-Chin and San Carlos Project Indian lands are modified to determine the maximum quantity of CAP water that would be desired by each if irrigated acreage were expanded to include all of the irrigable lands on the reservation.

5

Table 23 compares three levels of CAP water delivered to Indian farmers.

The crop mix adjustments and the resulting economic impact of introducing a fixed quantity of CAP water to Indian lands is discussed above. With an unlimited quantity of free CAP water available, Ak-Chin farmers apply 114,848 acre-feet and San Carlos Indian farmers apply

246,313 acre-feet. The total quantity, 361,161 acre-feet, is nearly twice as much as the initial annual allotment. In both areas, the

5. Irrigable acreage available for double cropping on San Carlos

Project Indian lands is assumed to be 50,000 acres -- the total acreage with rights to San Carlos Project water. Irrigable land on the Ak-Chin

Reservation is 20,200 acres (Board of Consultants, 1972).

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111 quantity of pumped water used decreases considerably as the amount of CAP water increases.

The most dramatic economic impact occurs on the

Ak-Chin

Reservation where net returns above variable costs vary from a low of

$117,671 without CAP water to a maximum of

$2,479,997 with all demands for CAP water satisfied, an increase of

21 times. The impact of unlimited CAP water is not as great on the San Carlos Indian lands, who already receive free water from the San Carlos Irrigation Project. However, net returns above variable costs increase by three and a half times

-- from 1.8 million dollars to 6.5 million dollars. Because cotton acreage is restricted in the models, the increased available water is used to increase acreage of grain sorghum, alfalfa, and wheat.

6

Total CAP water applied to crops in the county with Indian water unrestricted and non-Indian water freely chosen is 657,500 acre-feet, just 1,500 acre-feet less than the total assumed county allotment of 659,000 acre-feet.

The Value of Additional Water

In economic theory, the value of the additional product resulting from the addition of one unit of the variable input to the production process, all other inputs held constant, is termed the marginal value product (MVP). If a resource is scarce to the production process, its

MVP is positive, whereas the MVP for a resource that is surplus to the production process is zero or negative.

6. Even though large quantities of new water are made available to the Indians, it is unlikely that they would want to increase cotton acreage significantly because of the associated risks. Therefore, it was decided to maintain the acreage restrictions on cotton at their current levels.

112

In addition to providing the optimum combination of crops to be grown and the net income above variable cost that would result, the linear programming models also provide the maximum amount of money that could be paid for an additional acre-foot of water if alternative quantities of water were available. These estimates of what could be paid for an additional acre-foot of water are termed the marginal value products of the additional water. The linear programming MVP's (shadow prices) are larger in value than the classical economic theory MVP's because the quantity of other inputs are not held constant by the linear programming models. The linear programming MVP's measure the value of an additional acre-foot of water, all other profitable complementary adjustments being made.

If CAP water is not available to Pinal County, the MVP for additional water in many of the representative farms is positive during one or two critical water use periods, e.g., the January-February or the July periods. None of the representative farm models project water scarcity in every time period. Thus, water shortages exist because the physical pumping capacity of the irrigation wells on the farm is reached during the critical periods. Although additional well capacity during these high use periods would enable the farmer to expand crop acreage or change his crop mix, or both, the increased revenue generated from using the additional water would probably be much less than the cost of increasing the irrigation well capacity. The additional revenue generated would be small because the values for the marginal acre-foot of water is only for the first relatively small block of additional water supplied to each farm. For larger additions of water, the value per acre-foot for

113 additional acre-feet would decline as the need for additional water decreases. In Pinal County, the MVPs for additional water decrease to zero rapidly.

A reasonable estimate of a single weighted average value for

Pinal County as a whole for the MVP of an additional acre-foot of water during the summer is about $9.00 per acre-foot. A similar estimate for the critical winter time period, January-February, is about $8.00 per acre-foot. The winter MVP is lower than the summer MVP because a higher valued crop mix is grown during the summer than during the winter. Both the winter and summer estimates are of the same general magnitude as that of Kelso et al. (1973) for the MVP of an additional acre-foot of water for Pinal County of $12.00 per acre-foot. Their estimate is based on the older work by Stults (1968) and Burdak (1970).

The highest average estimates for the MVPs of additional water are in irrigation districts where the groundwater table is falling rapidly and the cost of pumped water is rising. The Ak-Chin Indian Reservation has the highest average values in Pinal County for the marginal acrefoot of water in both the winter and summer time periods. Ak-Chin is also the only area in the county where the MVP for an additional acrefoot of winter water ($21.02) is higher than the estimated value for summer water ($14.79). The additional winter water at or lower than a price of $21.02 would enable Ak-Chin farmers to expand wheat and alfalfa acreage. The Maricopa-Stanfield Irrigation District completely surrounds

Ak-Chin and has the second highest average

MVPs for additional winter and summer water. The marginal acre-foot of water to Maricopa-Stanfield farmers during the winter is estimated at $12.13 and $12.46 for the summer.

114

The lowest average estimates for the MVPs of additional water are in areas of relatively abundant water supplies at relatively low costs.

The Central Arizona and Hohokam Irrigation districts have the lowest MVPs for additional water in Pinal County. Surplus supply exists in the winter in both areas so additional winter water has no value. Estimated average MVPs for an additional acre-foot of summer water are about $2.00

and $3.00 per acre-foot for Hohokam and Central Arizona, respectively.

It is for the above reasons that some representative farmers in some districts were projected to purchase CAP water at the price of

$16.67 per acre-foot while some farmers did not wish to do so when water was freely chosen. It is also for the above reasons that net income declined, relative to its maximum when water was freely chosen, when farmers were required to purchase additional water.

The Effects of

Fixed Costs

In order to determine the net economic position of farmers in

Pinal County, fixed farm costs also must be considered. Fixed costs are those costs incurred by the farm operation regardless of the farm's level of production, for example, depreciation of buildings, machinery, wells, and ditches; interest on the investment; and taxes. Fixed cost values for farms in Pinal County are discussed in Chapter

IV and presented in

Table 7.

Values in Table 7 do not include the fixed cost of CAP delivery systems, that is, the lateral canals which the farmer must provide to transport the CAP water from the main canal to the farm headgate. Detailed fixed cost data for the CAP distribution system are not available,

115 and their computation is beyond the scope of this study. However, several observations may be made without additional detailed fixed cost estimates.

First, Indian farmers are not directly responsible for the cost of their distribution system and therefore do not incur the associated fixed costs. Distribution systems on Indian lands will be constructed and financed by the Federal government.

Second, Federal loans for the construction of distribution canals on non-Indian lands will be available to irrigation districts.

Specifically,

$100,000,000 is available through the CAP authorization legislation. Moneys from this source are interest free over the entire

50 year payoff period.

An additional source of funding may be the

Small Reclamation Projects

Act of 1956 (P.L. 84-130).

The Arizona

Water

Commission believes that

80 to

90 percent of the construction cost of distribution systems on non-Indian lands can be secured at no interest with a 50 year repayment period.

The only available estimates of distribution construction costs in Pinal

County are those by R.

W. Beck and Associates

(1971a, b, c) for the Central Arizona, Maricopa-Stanfield, and New Magma Irrigation and

Drainage Districts.

Each irrigation district analysis consists of five different management assumptions for five different annual allotments of

CAP water. Values for the annual costs of the total construction cost

(assuming

90 percent

Federal financing) range from

$352,000 to

$1,113,000 for Central Arizona, $32,000 to

$173,000 for New Magma, and $255,000 to

$1,197,000 for Maricopa-Stanfield. The higher values represent the annual construction cost of a distribution system servicing the entire irrigation district. The smaller value represents a management assumption of less

116 than desired CAP water allocation which is concentrated on a reduced area of the district. This study assumes that CAP water is available to each farm in the irrigation districts and thus Beck's higher values are more reasonable estimates than the lower ones. Beck's values are not used directly in this study because the reports lacked sufficient data to modify the values to a form usable in this analysis.

Although the precise cost of constructing lateral distribution systems for the CAP water cannot be made, it is possible to calculate the farmers' maximum willingness to pay for the distribution system. This is done by estimating the difference in net farm incomes with and without using CAP water. The difference would be the maximum amount that farmers' could afford to pay annually in order to deliver the water from the main canal to their headgates. The computations follow.

Table

24 gives the net returns above variable costs for each farm size and pumping depth class in each irrigation district without CAP water being available and without consideration of any fixed costs.

Naturally all entries in the table are positive, indicating that farmers are covering their variable costs with money left over to apply towards fixed costs and profits.

Values in Table

25 represent net returns above both fixed and variable costs for the same classes of farms in each district before construction of the CAP. These values are computed by subtracting the appropriate fixed cost value for the representative farm class from the net return above variable cost values shown in Table

24.

7

Although all

7. The fixed cost values are developed from Tables

7 and 17 by multiplying the appropriate fixed cost for one farm from Table

7 by the corresponding number of farms in the class as given in Table

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119 farm classes show a positive return above variable costs (Table

24), most farm classes are only partially covering all fixed costs (Table

25).

8

Table 26 also shows net returns above both fixed and variable costs, but it is computed assuming that CAP water is available and freely chosen. Values shown in Table 26 still do not consider the fixed cost of a CAP water distribution system. Thus, Table 27 is developed to illustrate farmers' willingness to pay for a distribution system. Values in

Table

27 are computed by subtracting each value in Table

25 from the corresponding value in Table

26. A value of zero in Table

27 represents no change in net returns when CAP water is introduced. A negative value in Table

27 indicates a decline in net returns when CAP water is introduced.

9

The aggregate total willingness to pay by

Pinal County farmers for a CAP distribution system is

$4,696,096. However, slightly more than

3.9 million dollars of the total, or

83 percent, is from the two Indian

Reservations in the county. The reason for the Indian farmers' high willingness to pay value is because they receive Federally subsidized CAP water. Further, Indian farmers will probably not have to incur the fixed costs of the distribution system.

8.

The farms not covering all fixed costs are not necessarily in financial trouble. Fixed capital is evaluated based on current replacement costs. To the extent that capital has a long life and was purchased at lower than current prices, the farmers are not in real trouble until the capital must actually be replaced. Still, not covering all fixed costs does indicate potential trouble.

9.

In some cases, net returns above variable costs decrease when

CAP water is introduced because of the pumped-CAP trade-off rule. In these cases the farmer actually has less water available to him because he must trade pumped water for CAP water against a historical average, rather than pump water freely.

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121

122

The aggregate total willingness to pay by non-Indian farmers in the county is $776,128. The highest value for a non-Indian irrigation district is for Maricopa-Stanfield. The projected willingness to pay for distribution system fixed costs is $445,118 for Maricopa-Stanfield.

Beck and Associates' lowest annual cost estimate of a distribution system for this irrigation district is $255,000, however, this estimate assumes that the distribution system is constructed to service only part of the district. Thus, the comparison of the willingness to pay value and the lowest estimate by Beck is not valid. A more reasonable comparison can be made to Beck's higher value which assumes that the distribution system services the entire district -- the same assumption made by this study.

The willingness to pay projection for Maricopa-Stanfield is less than half the value of Beck's higher projection.

The aggregate willingness to pay for both the New Magma and San

Carlos District are negative, reflecting the decrease in net returns when

CAP water is introduced. As mentioned earlier, the decrease in net returns in these areas is from farmers having less water available with the

CAP because of the pumped-CAP trade-off rule.

One might argue that negative willingness to pay values should be set to zero and then the representative farms in an irrigation district aggregated. If the negative values for New Magma are set to zero, the aggregate willingness to pay rises to $528. Regardless of the method used, the willingness to pay projections for both

New Magma and Central Arizona are much less than even Beck's lowest projections.

Although net returns above variable costs increase when Central

Arizona

Project water is introduced into Pinal County, very little of the

123 increase occurs on non-Indian lands. Because non-Indian farmers must incur the construction cost of a distribution system, the increase in net returns above variable costs on non-Indian lands should be greater than the annual fixed costs associated with CAP if the project is economically efficient. It does not appear likely that the net returns above variable costs will in fact exceed the associated fixed costs.

Summary

The objective of this dissertation is to make an economic evaluation of the impact of introducing Central Arizona Project water into

Pinal County, Arizona for use in irrigated agriculture. Of particular interest are the adjustments by farmers to the new CAP water which will differ in both price and quality (salinity) from local water supplies currently available. The farmer's water mix decision, i.e., how much water to use from each source, is complicated by the different salinity levels of each water supply. Because yield decreases as irrigation water salinity increases, the least cost water (either CAP or local) may have a high enough salinity to depress crop yield, and thus net farm returns, to the same or lower level obtained when more expensive lower salinity water is used.

An additional complicating factor to the farmer's decision-making process is the availability of irrigation water during each irrigation cycle of the growing season. If crop water demands are not satisfied during the growing season, yield decreases. Nearly all of the irrigation water currently used in Pinal County is pumped from the underlying groundwater aquifers. The quantity of water available for crop watering during

124 any irrigation cycle is controlled by both the size and depth of the farm's irrigation wells and the physical characteristics of the aquifers.

The farm's crop mix must be planned in order to assure that an adequate quantity of water is available during each irrigation cycle to meet total crop water demands. The introduction of CAP water into Pinal County relaxes the water availability constraint. A farmer can use CAP water to augment his local water supplies throughout the year or he can save his annual allotment for the critical high water use months. Thus, the farmer's decision-making process must consider trade-offs between water quantity, water quality (salinity) and water cost.

Several assumptions are necessary for the analyses.

Some of the major assumptions include: (1) Yield reduction due to irrigation water salinity is related to the calculated mean salinity against which water is absorbed, which is influenced more by the salinity of the irrigation water than by the salinity of the drainage water; (2) yield reductions from water shortage and from salinity are additive; (3) water is optimally allocated during the crop season; (4) the crops selected for this study will continue to be the most important ones grown in the area; (5) the ratio of product prices to input costs is constant over time; and (6) the relative prices of crops are constant over time.

A detailed description of the organizations, costs, and returns of representative farms in Pinal

County are used to develop linear programming models. The representative farm-linear programming models are the tool used for the economic analyses. The models include alternative crop production activities using various quantities of CAP and local water under alternative conditions of use.

Each water source, and thus

125 the resulting water mixes, is available in various quantities over time, at different prices and salinities. The linear programming models are designed to maximize net farm returns above variable production costs subject to the resource constraints faced by the farmers.

A total of

69 representative farm-linear programming models are needed to describe the agricultural activities in

Pinal

County. Each model is solved independently. The results are aggregated for irrigation districts and for the county as a whole. Each model is modified and solved several times in order to investigate various management schemes.

Specific results are:

(1) Delivery of CAP water will not assure groundwater conservation at anywhere near a one for one trade-off.

(2) Nearly all of the monetary benefits from the Project to agriculture in

Pinal

County will be captured by Indian farmers.

(3) Introducing CAP water will not affect cotton acreage, but will significantly increase the acreage of small grains and alfalfa.

(4) The possibility of increased salinity from CAP water should not be of concern to farmers in the county.

(5) Requiring non-Indian farmers to use a minimum quantity of

CAP water in their crop water mix considerably reduces the monetary gains realized when CAP water is made available but where the quantity used is freely chosen by the farmers.

(6) Indian farmers can use any excess CAP water from non-Indian farmers if there is no direct cost to the Indians for the water and they can use the CAP water to expand acreage.

126

(7) While provision of CAP water to the farm headgate at a price of

$16.67 per acre-foot would increase some non-Indian farmer's net income, the aggregate increase in net income in non-Indian districts would not be enough to pay for the necessary CAP distribution system.

APPENDIX A

YIELD-WATER QUANTITY-SALINITY POINTS ON THE

PRODUCTION SURFACE FOR CROPS TYPICALLY GROWN IN

PINAL COUNTY, ARIZONA

127

128

Table A-1. Yield-Water Use-Salinity Relationships for American-Pima

Cotton by Irrigation District and Pumping Lift.

IOW

Total Amount

Amount of of Irrigation Local Water

Water Applied

Applied

(acre-feet) (acre-feet)

Amount of

CAP Water

Applied

(acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

. Yield Reduction

Due to:

-

Estimated

Relative

Yield

Salinity Water

Shortage

Yield

Per

Acre

(percent) (percent) (percent) (pounds)

Ak-Chin

Indian Reservation

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

6.0

"Middle" pumping depth

6.0

5.0

4.0

3.0

2.0

1.0

0.0

5.0

5.0

5.0

5.0

5.0

5.0

"Deep" pumping depth

4.0

4.0

4.0

4.0

4.0 .

4.0

3.0

2.0

/.0

0.0

5.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0

1.0

2.0

3.0

4.0

5.0

P.O

1.0

2.0

3.0

4.0

0.6

0.8

0.9

1.1

1.2

1.4

0.6

0.7

0.9

1.2

1.1

1.3

1.4

0.6

0.8

1.0

1.2

1.4

Central Arizona Irrigation and Drainage District

"Middle"

pumping

depth

5.0

5.0

5.0

5.0

5.0

5.0

5.0

4.0

3.0

2.0

1.0

0.0

"Deep" pumping depth

0.0

1.0

2.0

3.0

4.0

5.0

1.1

1.2

1.2

1.3

1.3

1.4

4.0

4.0

4.0

4.0

4.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

1.1

1.2

1.3

1.3

1.4

0.6

0.8

0.9

1.1

1.2

1.4

0.6

0.7

0.9

1.0

1.1

1.3

1.4

0.6

0.8

1.0

1.2

1.4

1.1

1.2

1.2

1.3

1.3

1.4

1.1

1.2

1.3

1.3

1.4

0.0

0.0

0.0

0.0

0.0

0.0

0.0

3.7

3.7

3.7

3.7

3.7

3.7

8.6

8.6

8.6

8.6

8.6

8.6

8.6

8.6

8.6

8.6

3.7

3.7

3.7

3.7

3.7

3.7

99.4

99.3

99.1

99.0

98.9

98.7

98.6

95.7

95.5

95.4

95.2

95.1

94.9

90.8

90.6

90.4

90.2

90.0

95.2

95.1

95.1

95.0

95.0

94.9

90.3

90.2

90.1

90.1

90.0

547

546

544

543

542

573

573

573

572

572

572

599

598

597

596

596

594

594

576

575

575

573

573

572

544

543

543

543

542

129

Table A-1. (continued), American-Pima Cotton.

Total Amount of Irrigation

Water Applied

Amount of

Local Water

Applied

Amount

CAP of

Water

Applied

Weighted

Average

Salinity of

Water

Applied

(mmhos/cm)

(acre-feet)

(acre-feet)

(acre-feet)

Hohokam

Irrigation and Drainage District

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

"Middle" pumping depth

5.0

5.0

5.0

5.0

5.0

"Deep" pumping depth

5.0

4.0

3.0

2.0

1.0

0.0

4.0

4.0

4.0

4.0

4.0

4.0

3.0

2.0

1.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

1.0

2.0

3.0

4.0

5.0

0.0

1.0

2.0

3.0

4.0

1.8

1.7

1.7

1.6

1.5

1.5

1.4

1.8

1.7

1.6

1.6

1.5

1.4

1.8

1.7

1.6

1.5

1.4

Maricopa-Stanfield

Irrigation and Drainage District and

New Magma Irrigation and Drainage District

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

6.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

"Middle" pumping depth

5.0

5.0

5.0

5.0

5.0

5.0

5.0

4.0

3.0

2.0

1.0

0.0

"Deep" puuing depth

4.0

4.0

4.0

4.0

4.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0

1.0

2.0

3.0

4.0

5.0

0.0

1.0

2.0

3.0

4.0

0.9

1.0

1.1

1.2

1.2

1.3

1.4

0.9

1.0

1.1

1.2

1.3

1.4

0.9

1.0

1.2

1.3

1.4

Yield Reduction

E stimated Yield

Due to:

Shortage

Relative

Water

Salinity Yield

Per

Acre

(percent) (percent) (percent)

(pounds)

1.8

1.7

1.7

1.6

1.5

1.5

1.4

1.8

1.7

1.6

1.6

1.5

1.4

1.8

1.7

1.6

1.5

1.4

0.9

1.0

1.1

1.2

1.2

1.3

1.4

0.9

1.0

1.1

1.2

1.3

1.4

0.9

1.0

1.2

1.3

1.4

0.0

0.0

0.0

0.0

0.0

0.0

0.0

3.7

3.7

3.7

3.7

3.7

3.7

8.6

8.6

8.6

8.6

8.6

0.0

0.0

0.0

0.0

0.0

0.0

0.0

3.7

3.7

3.7

3.7

3.7

3.7

8.6

8.6

8.6

8.6

8.6

98.2

98.3

98.3

.98.4

98.5

98.5

98.6

94.5

94.6

94.7

94.7

94.8

94.9

89.6

89.7

89.8

89-.9

90.0

99.1

99.0

98.9

98.8

98.8

98.7

98.6

95.4

95.3

95.2

95.1

95.0

94.9

90.5

90.4

90.2

90.1

90.0

591

592

592

593

593

593

594

569

570

570

570

571

572

540

540

541

541

542

575

574

573

573

572

572

545

544

543

543

542

597

596

596

595

595

594

594

130

Table A-1. (continued), American-Pima Cotton.

Total Amount of Irrigation

Water Applied

(acre-feet)

Amount of

Local Water

Applied

(acre-feet)

Amount of

CAP Water

Applied

Weighted

Average

Salinity of Water

Applied

(acre-feet) (mmhos/cm)

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

6.0

"Middle"

pumping depth

6.0

5.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

4.0

3.0

2.0

1.0

0.0

"Deep"

pumping depth

4.0

4.0

4.0

4.0

4.0

4.0

-3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

0.0

1.0

2.0

3.0

4.0

1.3

1.3

1.3

1.4

1.4

1.4

1.4

1.3

1.3

1.3

1.4

1.4

1.4

1.3

1.3

1.4

1.4

1.4

Yield Rcduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Relative

Yield

Per

Acre

(percent) (percent) (percent) (pounds)

1.3

1.3

1.3

1.4

1.4

1.4

1.4

1.3

1.3

1.3

1.4

1.4

1.4

1.3

1.3

1.4

1.4

1.4

0.0

0.0

0.0

0.0

0.0

0.0

0.0

3.7

3.7

3.7

3.7

3.7

3.7

8.6

8.6

8.6

8.6

8.6

98.7

98.7

98.7

98.6

98.6

98.6

98.6

95.0

95.0

95.0

94.9

94.9

94.9

90.1

90.1

90.0

90.0

90.0

594

594

594

594

594

594

594

572

572

572

572

572

572

543

543

542

542

542

131

Table A-2. Yield-Water Use-Salinity Relationships for Upland Cotton by

Irrigation District and Pumping Lift.

Total Amount

Amount of of Irrigation

Local Water

Water Applied

Applied

(acre-feet)

(acre-feet)

Ak-Chin

Indian Reservation

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

6.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

"Middle" pumping depth

5.0

5.0

5.0

5.0

5.0

5.0

"Deep"

pumping depth

5.0

4.0

3.0

2.0

1.0

0.0

4.0

4.0

4.0

4.0

4.0 .

4.0

3.0

2.0

1.0

0.0

Amount of

CAP Water

Applied

(acre-feet)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0

1.0

2.0

3.0

4.0

5.0

0.0

1.0

2.0

3.0

4.0

Weighted

Average

Salin ity of Water

Applied

(mmhos/cm)

0.6

0.8

0.9

1.1

1.2

1.4

0.6

0.7

0.9

1.0

1.1

1.3

1.4

0.6 .

0.8

1.0

1.2

1.4

Central Arizona Irrigation and Drainage District

"Mid dle" pumping depth

5.0

5.0

5.0

5.0

5.0

5.0

5.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

1.1

1.2

1.2

1.3

1.3

1.4

"Deep" pumping depth

4.0

4.0

4.0

4.0

4.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

1.1

1.2

1.3

1.3

1.4

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated

Relative

Yield

Yield

Per

Acre

(percent)

(percent)

(percent)

(pounds)

0.6

0.7

0.9

1.0

1.1

1.3

1.4

0.6

0.8

0.9

1.1

1.2

1.4

0.6

0.8

1.0

1.2

1.4

1.1

1.2

1.2

1.3

1.3

1.4

1.1

1.2

1.3

1.3

1.4

2.1

2.1

2.1

2.1

2.1

2.1

0.0

0.0

0.0

0.0

0.0

0.0

0.0

5.5

5.5

5.5

5.5

5.5

2.1

2.1

2.1

2.1

2.1

2.1

5.5

5.5

5.5

5.5

5.5

99.4

99.3

99.1

99.0

98.9

98.7

98.6

97.3

97.1

97.0

96.8

96.7

96.5

93.9

93.7

93.5

93.3

93.1

96.8

96.7

96.7

96.6

96.6

96.5

93.4

93.3

93.2

93.2

93.1

1,089

1,088

1,087

1,085

1,084

1,069

1,067

1,066

1,064

1,063

1,061

1,032

1,030

1,028

1,025

1,023

1,064

1,063

1,063

1,062

1,062

1,061

1,027

1,025

1,024

132

Table A-2.

(continued), Upland Cotton.

Total Amount of Irrigation

Water Applied

(acre-feet)

Amount of

Local Water

Applied

(acre-feet)

Amount of

CAP Water

Applied

(acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

Hohokam Irrigation and Drainage District

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

6.0

"Middle"

pumping depth

5.0

5.0

5.0

5.0

5.0

5.0

5.0

4.0

3.0

2.0

1.0

0.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0

1.0

2.0

3.0

4.0

5.0

.

1

2.

1

2aL....E1-11

1

21

1

2.L.E.

1

_e_ELL

4.0

4.0

4.0

4.0

4.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

1.8

1.7

1.7

1.6

1.5

1.5

1.4

1.8

1.7

1.6

1.6

1.5

1.4

1.8

1.7

1.6

1.5

1.4

Maricopa-Stanfield

Irrigation and Drainage District and

New

Magma Irrigation and Drainage District

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

6.0

"Middle" pumping depth

6.0

5.0

4.0

3.0

2.0

1.0

0.0

5.0

5.0

5.0

5.0

5.0

5.0

"Deep" pumping depth

4.0

4.0

4.0

4.0

4.0

4.0

3.0

2.0

1.0

0.0

5.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0

1.0

2.0

3.0

4.0

5.0

0.0

1.0

2.0

3.0

4.0

0.9

1.0

1.1

1.2

1.2

1.3

1.4

0.9

1.0

1.1

1.2

1.3

1.4

0.9

1.0

1.2

1.3

1.4

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Relative

Yield

Per

Acre

(percent) (percent) (percent) (pounds)

1.8

1.7

1.7

1.6

1.5

1.5

1.4

1.8

1.7

1.6

1.6

1.5

1.4

1.8

1.7

1.6

1.5

1.4

0.9

1.0

1.1

1.2

1.2

1.3

1.4

0.9

1.0

1.1

1.2

1.3

1.4

0.9

1.0

1.2

1.3

1.4

0.0

0.0

0.0

0.0

0.0

0.0

0.0

2.1

2.1

2.1

2.1

2.1

2.1

5.5

5.5

5.5

5.5

5.5

0.0

0.0

0.0

0.0

0.0

0.0

0.0

2.1

2.1

2.1

2.1

2.1

2.1

5.5

5.5

5.5

5.5

5.5

98.2

98.3

.

98.3

98.4

98.5

98.5

98.6

96.1

96.2

96.3

96.3

96.4

96.5

92.7

92.8

92.9

93.0

93.1

99.1

99.0

98.9

98.8

98.8

98.7

98.6

97.0

96.9

96.8

96.7

96.6

96.5

93.6

93.5

93.3

93.2

93.1

1,079

1,080

1,080

1,081

1,083

1,083

1,084

1,056

1,057

1,058

1,058

1,060

1,061

1,019

1,020

1,021

1,022

1,023

1,089

1,088

1,087

1,086

1,086

1,085

1,084

1,066

1,065

1,064

1,063

1,062

1,061

1,029

1,028

1,025

1,024

1,023

133

Table A-2. (continued), Upland Cotton.

Total Amount

Amount of of Irrigation Local Water

Water Applied Applied

Amount of

CAP Water

Applied

(acre-feet)

(acre-feet)

(acre-feet)

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District

"Shallow" pumping depth

6.0

6.0

6.0

6.0

6.0

6.0

6.0

6.0

5.0

4.0

3.0

2.0

1.0

0.0

"Middle"

pumping depth

5.0

5.0

5.0

5.0

5.0

5.0

5.0

4.0

3.0

2.0

1.0

0.0

"Deep"

pumping depth

4.0

4.0

4.0

4.0

4.0

4.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

4.0

0.0

1.0

2.0

3.0

4.0

5.0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

1.3

1.3

1.3

1.4

1.4

1.4

1.4

1.3

1.3

1.3

1.4

1.4

1.4

1.3

1.3

1.4

1.4

1.4

Yield Reduction

Due to:

Salinity

Water

Shortage

Estimated Yield

Relative

Yield

Per

Acre

(percent) (percent) (percent) (pounds)

1.3

1.3

1.3

1.4

1.4

1.4

1.4

1.3

1.3

1.3

1.4

1.4

1.4

1.3

1.3

1.4

1.4

1.4

5.5

5.5

5.5

5.5

5.5

2.1

2.1

2.1

2.1

2.1

2.1

0.0

0.0

0.0

0.0

0.0

0.0

0.0

98.7

98.7

98.7

98.6

98.6

98.6

98.6

96.6

96.6

96.6

96.5

96.5

96.5

93.2

93.2

93.1

93.1

93.1

1,085

1,085

1,085

1,084

1,084

1,084

1,084

1,062

1,062

1,062

1,061

1,061

1,061

1,024

1,024

1,023

1,023

1,023

134

Table A-3. Yield-Water Use-Salinity Relationships for Barley by Irrigation District and Pumping Lift.

Total Amount

Amount of of Irrigation

Local Water

Water Applied

Applied

(acre-feet) (acre-feet)

Amount of

CAP Water

Applied

(acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

Ak-Chin

Indian Reservation

"Shallow" pumping depth

3.0

3.0

3.0

3.0

2.0

2.0

2.0

3.0

2.0

1.0

0.0

"Middle" pumping depth

2.5

2.5

2.5

2.5

2.5

1.5

0.5

0.0

"Deep"

pumping depth

2.0

1.0

0.0

0.0

1.0

2.0

3.0

0.0

1.0

2.0

2.5

0.0

1.0

2.0

0.6

0.9

1.1

1.4

0.6

0.8

1.2

1.4

0.6

1.0

1.4

Central Arizona Irrigation and Drainage District

"Middle" pumping depth

2.5

2.5

2.5

2.5

"Deep"

pumping depth

2.5

1.5

0.5

0.0

2.0

2.0

2.0

2.0

1.0

0.0

0.0

1.0

2.0

2.5

0.0

1.0

2.0

1.1

1.2

1.3

1.4

1.1

1.3

1.4

Hohokam Irrigation and Drainage District

"Shallow" pumping depth

3.0

3.0

3.0

3.0

2.5

2.5

2.5

2.5

3.0

2.0

1.0

0.0

"Middle"

pumping depth

2.5

1.5

0.5

0.0

0.0

1.0

2.0

3.0

0.0

1.0

2.0

2.5 '

"Deep" pumping death

2.0

2.0

2.0

2.0

1.0

0.0

0.0

1.0

2.0

1.8

1.7

1.5

1.4

1.8

1.6

1.5

1.4

1.8

1.6

1.4

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Relative

Yield

Per

Acre

(percent) (percent) (percent) (pounds)

0.5

0.8

0.9

1.2

0.5

0.7

1.0

1.2

0.5

0.8

1.2

0.9

1.0

1.1

1.2

0.9

1.1

1.2

1.5

1.4

1.3

1.2

1.5

1.4

1.3

1.2

1.5

1.4

1.2

0.0

0.0

0.0

0.0

6.0

6.0

6.0

6.0

15.7

15.7

15.7

6.0

6.0

6.0

6.0

15.7

15.7

15.7

0.0

0.0

0.0

0.0

6.0

6.0

6.0

6.0

15.7

15.7

15.7

99.5

99.2

99.1

98.8

93.5

93.3

93.0

92.8

83.8

83.5

83.1

93.1

93.0

92.9

92.8

83.4

83.2

83.1

98.5

98.6

98.7

98.8

92.5

92.6

92.7

92.8

82.8

82.9

83.1

3,630

3,619

3,615

3,604

3,411

3,404

3,393

3,385

3,057

3,046

3,032

3,396

3,393

3,389

3,385

3,042

3,035

3,032

3,593

3,597

3,601

3,604

3,374

3,378

3,382

3,385

3,021

3,024

3,032

135

Table A-3. (continued), Barley.

Total Amount

Amount of of Irrigation Local Water

Water Applied Applied

(acre-feet) (acre-feet)

Amount of

CAP Water

Applied

(acre-feet)

Weighted

Average

Salinity of Water

Applied

(mhos/cm)

Maricopa-Stanfield

Irrigation and Drainage District and

New Magma Irrigation and Drainage District

"Shallow" pumping depth

3.0

3.0

3.0

3.0

3.0

2.0

1.0

0.0

"Middle" pumping depth

0.0

1.0

2.0

3.0

0.9

1.1

1.2

1.4

2.5

2.5

2.5

2.5

2.0

2.0

2.0

2.5

1.5

0.5

0.0

"Deep" pumping depth

2.0

1.0

0.0

0.0

1.0

2.0

2.5

0.0

1.0

2.0

0.9

1.1

1.3

1.4

0.9

1.2

1.4

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District

"Shallow" pumping depth

3.0

3.0

3.0

3.0

3.0

2.0

1.0

0.0

"Middle" pumping depth

0.0

1.0

2.0

3.0

2.5

2.5

2.5

2.5

2.5

1.5

0.5

0.0

"Deep" pumping depth

2.0

2.0

2.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

0.0

1.0

2.0

1.3

1.3

1.4

1.4

1.3

1.3

1.4

1.4

1.3

1.4

1.4

Yield Reduction

Due to:

Salinity

Water

Shortage

Estimated Yield

Relative

Yield

Per

Acre

(percent) (Percent) (percent) (pounds)

0.8

0.9

1.0

1.2

0.8

0.9

1.1

1.2

0.8

1.0

1.2

1.1

1.1

1.2

1.2

1.1

1.1

1.2

1.2

1.1

1.2

1.2

0.0

0.0

0.0

0.0

6.0

6.0

6.0

6.0

15.7

15.7

15.7

0.0

0.0

0.0

0.0

6.0

6.0

6.0

6.0

15.7

15.7

15.7

99.2

99.1

99.0

98.8

93.2

93.1

92.9

92.8

83.5

83.3

83.1

98.9

98.9

98.8

98.8

92.9

92.9

92.8

92.8

83.2

83.1

83.1

3,619

3,615

3,612

3,604

3,400

3,396

3,389

3,385

3,046

3,039

3,032

3,608

3,608

3,604

3,604

3,389

3,389

3,385

3,385

3,035

3,032

3,032

136

Table A-4. Yield-Water Use-Salinity Relationships for Grain Sorghum by

Irrigation District and Pumping Lift.

Total Amount of Irrigation

Amount of

Local Water

Amount of

CAP

Water

Weighted

Average

Salinity

Yield Reduction

Due to:

Yield

Water Applied

Applied

Applied of Water

Applied

Salinity

Shortage

Estimated Yield

Per

Acre

(acre-feet)

(acre-feet) (acre-feet)

(mmhos/cm) (percent) (percent) (percent) (pounds)

Ak-Chin Indian Reservation I

& II

"Shallow" pumping depth

3.67

3.67

3.67

3.67

3.67

3.67

2.67

1.67

0.67

0.00

"Middle" pumping depth

3.17

3.17

3.17

3.17

3.17

3.17

2.17

1.17

0.17

0.00

"Deep"

pumping depth

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

3.00

3.67

0.00

1.00

2.00

3.00

3.17

0.00

1.00

2.00

2.67

Ak-Chin

Indian Reservation III

& IV

"Shallow" pumping depth

3.67

3.67

3.67

3.67

3.67

3.17

3.17

3.17

3.17

3.17

3.67

2.67

1.67

0.67

0.00

"Middle"

pumping depth

3.17

2.17

1.17

0.17

0.00

0.00

1.00

2.00

3.00

3.67

0.00

1.00

2.00

3.00

3.17

"Deep" pumping depth

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

2.67

0.6

0.8

1.0

1.3

1.4

0.6

0.9

1.1

1.4

1.4

0.6

0.9

1.2

1.4

0.6

0.8

1.0

1.3

1.4

0.6

0.9

1.1

1.4

1.4

0.6

0.9

1.2

1.4

1.0

1.4

1.7

2.2

2.3

1.0

1.5

1.8

2.3

2.3

1.0

1.5

2.0

2.3

1.0

1.4

1.7

2.2

2.3

1.0

1.5

1.8

2.3

2.3

1.0

1.5

2.0

2.3

0.0

0.0

0.0

0.0

0.0

5.2

5.2

5.2

5.2

5.2

10.6

10.6

10.6

10.6

0.0

0.0

0.0

0.0

0.0

5.0

5.0

5.0

5.0

5.0

10.2

10.2

10.2

10.2

99.0

98.6

98.3

97.8

97.7

93.8

93.3

93.0

92.5

92.5

88.4

87.9

87.4

87.1

99.0

98.6

98.3

97.8

97.7

94.0

93.5

93.2

92.7

92.7

88.8

88.3

87.8

87.5

3,509

3,495

3,484

3,467

3,463

3,325

3,307

3,296

3,279

3,279

3,133

3,116

3,098

3,087

3,714

3,699

3,688

3,669

3,665

3,526

3,508

3,496

3,477

3,477

3,331

3,312

3,294

3,282

137

Table

A-4. (continued),

Grain

Sorghum.

Total Amount

Amount of of Irrigation Local Water

Water Applied

Applied

(acre-feet)

(acre-feet)

Amount of

CAP Water

Applied

(acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

Yield Reduction

Due to:

Water

Salinity

Shortage

Central Arizona Irrigation and Drainage District I

&

II

"Middle" pumping depth

3.17

3.17

3.17

3.17

3.17

"Deep" pumping depth

3.17

2.17

1.17

0.17

0.00

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

3.00

3.17

0.00

1.00

2.00

2.67

1.1

1.2

1.3

1.4

1.4

1.1

1.2

1.3

1.4

1.8

2.0

2.2

2.3

2.3

1.8

2.0

2.2

2.3

Central Arizona Irrigation and Drainage District III

&

IV

"Middle" pumping depth

3.17

3.17

3.17

3.17

3.17

"Deep" pumping depth

3.17

2.17

1.17

0.17

0.00

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

3.00

3.17

0.00

1.00

2.00

2.67

1.1

1.2

1.3

1.4

1.4

1.1

1.2

1.3

1.4

Hohokam Irrigation and Drainage District I

&

II

"Shallow" pumping depth

3.67

3.67

3.67

3.67

3.67

3.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

3.00

3.67

"Middle" pumping depth

3.17

3.17

3.17

3.17

3.17

3.17

2.17

1.17

0.17

0.00

"Deep" pumping depth

0.00

1.00

2.00

3.00.

3.17

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

2.67

1.8

1.7

1.6

1.5

1.4

1.8

1.7

1.6

1.4

1.4

1.8

1.7

1.5

1.4

1.8

2.0

2.2

2.3

2.3

1.8

2.0

2.2

2.3

3.0

2.9

2.7

2.5

2.3

3.0

2.9

2.7

2.3

2.3

3.0

2.9

2.5

2.3

5.2

5.2

5.2

5.2

5.2

10.6

10.6

10.6

10.6

5.0

5.0

5.0

5.0

5.0

10.2

10.2

10.2

10.2

0.0

0.0

0.0

0.0

0.0

5.2

5.2

5.2

5.2

5.2

10.6

10.6

10.6

10.6

Estimated Yield

Relative

Yield

Per

Acre

(percent) (percent) (percent) (pounds)

93.0

92.8

92.6

92.5

92.5

87.6

87.4

87.2

87.1

93.2

93.0

92.8

92.7

92.7

88.0

87.8

87.6

87.5

97.0

97.1

97.3

97.5

97.7

91.8

91.9

92.1

92.5

92.5

86.4

86.5

86.9

87.1

3,296

3,289

3,282

3,279

3,279

3,105

3,098

3,091

3,087

3,496

3,489

3,481

3,477

3,477

3,301

3,294

3,286

3,282

3,438

3,442

3,449

3,456

3,463

3,254

3,257

3,265

3,279

3,279

3,063

3,066

3,080

3,087

138

Table A-4. (continued), Grain Sorghum.

Total Amount of Irrigation

Water Applied

(acre-feet)

Amount of

Local Water

Applied

(acre-feet)

Amount of

CAP Water

Applied

(acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

Yield Reduction

Due to:

Salinity

Water

Shortage

Estimated Yield

Relative

Yield

Per

Acre

(percent) (percent) (percent) (pounds)

Hohokam Irrigation and Drainage District III

&

IV

"Shallow" pumping depth

3.67

3.67

3.67

3.67

3.67

3.67

2.67

1.67

0.67

0.00

"Middle"

pumping depth

3.17

3.17

3.17

3.17

3.17

"Deep"

pumping depth

3.17

2.17

1.17

0.17

0.00

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

3.00

3.67

0.00

1.00

2.00

3.00

3.17

0.00

1.00

2.00

2.67

1.8

1.7

1.6

1.4

1.4

1.8

1.7

1.5

1.4

1.8

1.7

1.6

1.5

1.4

Maricopa-Stanfield Irrigation and Drainage District and

New Magma Irrigation and Drainage District I

&

II

"Shallow" pumping depth

3.67

3.67

3.67

3.67

3.67

"Middle" pumping depth

3.17

3.17

3.17

3.17

3.17

3.67

2.67

1.67

0.67

0.00

3.17

2.17

1.17

0.17

0.00

0.00

1.00

2.00

3.00

3.67

0.00

1.00

2.00

3.00

3.17

0.9

1.0

1.2

1.3

1.4

0.9

1.1

1.2

1.4

1.4

LE2.2ELEITTJILE5121atJa

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

2.67

0.9

1.1

1.3

1.4

1.5

1.7

2.0

2.2

2.3

1.5

1.8

2.0

2.3

2.3

3.0

2.9

2.7

2.3

2.3

3.0

2.9

2.7

2.5

2.3

3.0

2.9

2.5

2.3

1.5

1.8

2.2

2.3

0.0

0.0

0.0

0.0

0.0

10.2

10.2

10.2

10.2

0.0

0.0

0.0

0.0

0.0

5.0

5.0

5.0

5.0

5.0

5.2

5.2

5.2

5.2

5.2

10.6

10.6

10.6

10.6

97.0

97.1

97.3

97.5

97.7

92.0

92.1

92.3

92.7

92.7

86.8

86.9

87.3

87.5

98.5

98.3

98.0

97.8

97.7

93.3

93.0

92.8

92.5

92.5

87.9

87.6

87.2

87.1

3,639

3,643

3,650

3,658

3,665

3,451

3,455

3,462

3,477

3,477

3,256

3,260

3,275

3,282

3,491

3,484

3,474

3,467

3,463

3,307

3,296

3,289

3,279

3,279

3,116

3,105

3,091

3,088

139

Table

A-4. (continued),

Grain

Sorghum.

Total Amount of Irrigation

(acre-feet)

Amount of

Local Water

Amount of

CAP Water

Applied

(acre-feet) (acre-feet)

Weighted .

Average

Salinity of Water

Applied

(mmhos/cm)

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Relative Per

Yield Acre

(percent) (percent) (percent) (pounds)

Maricopa-Stanfield

Irrigation and Drainage District and

New Magma Irrigation and Drainage District III &

IV

LHULLÈL.E2111

1

.22-1tEÈ1

3.67

3.67

3.67

3.67

3.67

3.67

2.67

1.67

0.67

0.00

"Middle" pumping depth

3.17

3.17

3.17

3.17

3.17

3.17

2.17

1.17

0.17

0.00

"Deep" pumping depth

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

3.00

3.67

0.00

1.00

2.00

3.00

3.17

0.00

1.00

2.00

2.67

0.9

1.0

1.2

1.3

1.4

0.9

1.1

1.2

1.4

1.4

0.9

1.1

1.3

1.4

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District I

&

II

"Shallow" pumping depth

3.67

3.67

3.67

3.67

3.67

3.67

2.67

1.67

0.67

0.00

"Middle" pumping depth

3.17

3.17

3.17

3.17

3.17

"Deep" pumping depth

3.17

2.17

1.17

0.17

0.00

0.00

1.00

2.00

3.00

3.67

0.00

1.00

2.00

3.00

3.17

1.3

1.3

1.4

1.4

1.4

1.3

1.3

1.4

1.4

1.4

2.67

2.67

2.67

2.67

2.67

1.67

0.67

0.00

0.00

1.00

2.00

2.67

1.3

1.3

1.4

1.4

1.5

1.7

2.0

2.2

2.3

1.5

1.8

2.0

2.3

2.3

1.5

1.8

2.2

2.3

2.2

2.2

2.3

2.3

2.3

2.2

2.2

2.3

2.3

2.3

2.2

2.2

2.3

2.3

0.0

0.0

0.0

0.0

0.0

5.0

5.0

5.0

5.0

5.0

10.2

10.2

10.2

10.2

0.0

0.0

0.0

0.0

0.0

5.2

5.2

5.2

5.2

5.2

10.6

10.6

10.6

10.6

98.5

98.3

98.0

97.8

97.7

93.5

93.2

93.0

92.7

92.7

88.3

88.0

87.6

87.5

97.8

97.8

97.7

97.7

97.7

92.6

92.6

92.5

92.5

92.5

87.2

87.2

87.1

87.1

3,695

3,688

3,676

3,669

3,665

3,508

3,496

3,489

3,477

3,477

3,312

3,301

3,286

3,282

3,467

3,467

3,463

3,463

3,463

3,282

3,282

3,279

3,279

3,279

3,091

3,091

3,087

3,087

140

Table A-4. (continued),

Grain Sorghum.

Total Amount

(acre-feet)

Amount of

Amount of

Local Water CAP Water

Applied

Applied

(acre-feet) (acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

Yield Reduction

Due to:

Salinity

Water

Shortage

Estimated Yield

Per

Acre

(percent) (percent) (percent) (pounds)

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District III

&

IV

"Shallow" pumping depth

3.67

3.67

3.67

3.67

3.67

3.67

2.67

1.67

0.67

0.00

"Middle"

pumping depth

0.00

1.00

2.00

3.00

3.67

1.3

1.3

1.4

1.4

1.4

3.17

3.17

3.17

3.17

3.17

"Deep" pumping depth

2.67

2.67

2.67

2.67

3.17

2.17

1.17

0.17

0.00

2.67

1.67

0.67

0.00

0.00

1.00

2.00

3.00

3.17

0.00

1.00

2.00

2.67

1.3

1.3

1.4

1.4

1.4

1.3

1.3

1.4

1.4

2.2

2.2

2.3

2.3

2.3

2.2

2.2

2.3

2.3

2.3

2.2

2.2

2.3

2.3

5.0

5.0

5.0

5.0

5.0

0.0

0.0

0.0 .

0.0

0.0

10.2

10.2

10.2

10.2

97.8

97.8

97.7

97.7

97.7

92.8

92.8

92.7

92.7

92.7

87.6

87.6

87.5

87.5

3,669

3,669

3,665

3,665

3,665

3,481

3,481

3,477

3,477

3,477

3,286

3,286

3,282

3,282

141

Table A-5. Yield-Water Use-Salinity Relationships for Alfalfa Grown With

Summer Water by Irrigation District and Pumping Lift.

Total Amount of Irrigation

Water Applied

(acre-feet)

Amount of

Amount of

Local Water

CAP Water

Applied Applied

(acre-feet) (acre-feet)

Weighted

Average

Salinity of Water

'

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Relative

Yield

Per

Acre

Applied

(mmhos/cm)

(percent) (percent) (percent) (tons)

Ak-Chin Indian Reservation

"Shallow," "Middle," and "Deep" pumping depths

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

5.58

, 4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

6.58

0.6

0.7

0.8

1.0

1.1

1.2

1.3

1.4

Central Arizona Irrigation and Drainage District

"Shallow," "Middle," and "Deep" pumping depths

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

5.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

6.58

1.1

1.1

1.2

1.2

1.3

1.3

1.4

1.4

Hohokam Irrigation and Drainage District

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

5.58

4.58

3.58

2.58

1.58

0.58

0.00

an d "Deep' pumping depths

0.00

1.00

2.00

3.00

4.00

5.00

6.00

6.58

1.8

1.7

1.7

1.6

1.6

1.5

1.4

1.4

Maricopa-Stanfield

Irrigation and Drainage District and

New Magma Irrigation and Drainage District

"Shallow," "Middle," and "Deep" pumping depths

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

5.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

6.58

0.9

1.0

1.1

1.1

1.2

1.3

1.4

1.4

2.0

2.3

2.6

3.3

3.7

4.0

4.3

4.7

3.7

3.7

4.0

4.0

4.3

4.3

4.7

4.7

6.0

5.7

5.7

5.4

5.4

5.0

4.7

4.7

3.0

3.3

3.7

3.7

4.0

4.3

4.7

4.7

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

98.0

97.7

. 97.4

96.7

96.3

96.0

95.7

95.3

96.3

96.3

96.0

96.0

95.7

95.7

95.3

95.3

94.0

94.3

94.3

94.6

94.6

95.0

95.3

95.3

97.0

96.7

96.3

96.3

96.0

95.7

95.3

95.3

6.08

6.06

6.04

6.00

5.98

5.96

5.94

5.91

5.98

5.98

5.96

5.96

5.94

5.94

5.91

5.91

5.83

5.85

5.85

5.87

5.87

5.89

5.91

5.91

6.02

6.00

5.98

5.98

5.96

5.94

5.91

5.91

142

Table A-5.

(continued), Alfalfa Grown With Summer

Water.

Total Amount

(acre-feet)

Amount of

Amount of

Local Water CAP Water

Applied

Applied

(acre-feet) (acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District

"Shallow," "Middle," and "Deep" pumping depths

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

6.58

5.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

6.58

1.3

1.3

1.3

1.3

1.4

1.4

1.4

1.4

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Per

Acre

(percent) (percent) (percent) (tons)

4.3

4.3

4.3

4.3

4.7

4.7

4.7

4.7

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

95.7

95.7

95.7

95.7

95.3

95.3

95.3

95.3

5.94

5.94

5.94

5.94

5.91

5.91

5.91

5.91

143

Table A-6.

Yield-Water Use-Salinity Relationships for Alfalfa Grown

Without Summer Water by Irrigation District and Pumping Lift.

Total Amount of Irrigation

Water Applied

(acre-feet)

Amount of

Amount of

Local Water CAP Water

Applied

Applied

(acre-feet) (acre-feet)

Weighted

Average

Salinity of Water

Applied

.

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Relative

Per

Yield

Acre

(mmhos/cm)

(percent) (percent) (percent) (tons)

Ak-Chin Indian Reservation

"Shallow," "Middle," and "Deep" pumping depths

4.58

4.58

4.58

4.58

4.58

4.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

4.58

0.6

0.8

0.9

1.1

1.3

1.4

Central Arizona Irrigation and Drainage District

"Shallow," "Middle," and "Deep" pumping depths

4.58

4.58

4.58

4.58

4.58

4.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

4.58

1.1

1.2

1.2

1.3

1.4

1.4

Hohokam Irrigation and Drainage District

"Shallow," "Middle," and "Deep" pumping depths

4.58

4.58

4.58

4.58

4.58

4.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

4.58

1.8

1.7

1.6

1.5

1.5

1.4

Maricopa-Stanfield

Irrigation and Drainage District and

New Magma Irrigation and Drainage District

"Shallow," "Middle," and "Deep" pumping depths

4.58

4.58

4.58

4.58

4.58

4.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

4.58

0.9

1.0

1.1

1.2

1.3

1.4

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District fa all ""

"indeths

4.58

4.58

4.58

4.58

4.58

4.58

4.58

3.58

2.58

1.58

0.58

0.00

0.00

1.00

2.00

3.00

4.00

4.58

1.3

1.3

1.3

1.4

1.4

1.4

2.0

2.7

3.0

3.7

4.3

4.7

3.7

4.0

4.0

4.3

4.7

4.7

6.0

5.7

5.4

5.0

5.0

4.7

3.0

3.3

3.7

4.0

4.3

4.7

4.3

4.3

4.3

4.7

4.7

4.7

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

98.0

97.3

97.0

96.3

95.7

95.3

96.3

96.0

96.0

95.7

95.3

95.3

94.0

94.3

94.6

95.0

95.0

95.3

97.0

96.7

96.3

96.0

95.7

95.3

95.7

95.7

95.7

95.3

95.3

95.3

4.05

4.02

4.01

3.98

3.96

3.94

3.98

3.97

3.97

3.96

3.94

3.94

3.89

3.90

3.91

3.93

3.93

3.94

4.01

4.00

3.98

3.97

3.96

3.94

3.96

3.96

3.96

3.94

3.94

3.94

144

Table A-7. Yield-Water Use-Salinity Relationships for Wheat by Irrigation District and Pumping Lift.

Total Amount of Irrigation

Water Applied

(acre-feet)

Amount of

Amount of

Local Water CAP Water

Applied Applied

(acre-feet) (acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

Ak-Chin Indian Reservation

"Shallow" pumping depth

3.5

3.5

3.5

3.5

3.5

"Middle" pumping depth

3.5

2.5

1.5

0.5

0.0

3.0

3.0

3.0

3.0

3.0

2.0

1.0

0.0

"Deep" pumping depth

2.5

2.5

2.5

2.5

2.5

1.5

0.5

0.0

0.0

1.0

2.0

3.0

3.5

0.0

1.0

2.0

3.0

0.6

0.8

1.1

1.3

1.4

0.6

0.9

1.1

1.4

0.0

1.0

2.G

2.5

Hohokam Irrigation and Drainage District

"Shallow" pumping depth

3.5

3.5

3.5

3.5

3.5

3.5

2.5

1.5

0.5

0.0

"Middle"

pumping depth

0.0

1.0

2.0

3.0

3.5

3.0

3.0

3.0

3.0

3.0

2.0

1.0

0.0

0.0

1.0

2.0

3.0

"Deep" pumping depth

2.5

2.5

2.5

2.5

2.5

1.5

0.5

0.0

0.0

1.0

2.0

2.5

0.6

0.9

1.2

1.4

Central Arizona Irrigation and Drainage District

"Middle"

pumping depth

3.0

3.0

3.0

3.0

3.0

2.0

1.0

0.0

"Deep"

pumping depth

2.5

2.5

2.5

2.5

2.5

1.5

0.5

0.0

0.0

1.0

2.0

3.0

0.0

1.0

2.0

2.5

1.1

1.2

1.3

1.4

1.1

1.2

1.3

1.4

1.8

1.7

1.6

1.5

1.4

1.8

1.7

1.5

1.4

1.8

1.6

1.5

1.4

.

Yield Reduction

Shorta

Estimated Yield

Due to:

Relative

W ater

Salinity

Yield ge

Per

Acre

(percent) (percent) (percent) (pounds)

0.8

1.1

1.6

1.8

2.0

0.8

1.3

1.6

2.0

0.8

1.3

1.7

2.0

1.6

1.7

1.8

2.0

1.6

1.7

1.8

2.0

2.6

2.4

2.3

2.1

2.0

2.6

2.4

2.1

2.0

2.6

2.3

2.1

20

0.0

0.0

0.0

0.0

0.0

-

6.8

6.8

6.8

6.8

15.8

15.8

15.8

15.8

6.8

6.8

6.8

6.8

15.8

15.8

15.8

15.8

0.0

0.0

0.0

0.0

0.0

6.8

6.8

6.8

6.8

15.8

15.8

15.8

15.8

99.2

98.9

98.4

• 98.2

98.0

92.4

91.9

91.6

91.2

83.4

82.9

82.5

82.2

91.6

91.5

91.4

91.2

82.6

82.5

82.4

82.2

97.4

97.6

97.7

97.9

98.0

90.6

90.8

91.1

91.2

81.6

81.9

82.1

82.2

4,322

4,309

4,287

4,279

4,270

4,026

4,004

3,991

3,974

3,634

3,612

3,595

3,581

3,991

3,987

3,982

3,974

3,599

3,595

3,590

3,581

4,244

4,252

4,257

4,266

4,270

3,947

3,956

3,969

3,974

3,555

3,569

3,577

3,581

145

Table A-7. (continued),

Wheat.

Total Amount of Irrigation

Amount of

Local Water

Applied

Amount of

CAP Water

Applied

(acre-feet) (acre-feet)

Weighted

Average

Salinity of Water

Applied

(mmhos/cm)

Yield Reduction

Due to:

Water

Salinity

Shortage

Estimated Yield

Relative

Per

Acre

(percent) (percent) (percent) (pounds)

(acre-feet)

Maricopa-Stanfield Irrigation and Drainage District and

New Magma Irrigation and Drainage District

"Shallow" pumping depth

3.5

3.5

3.5

3.5

3.5

3.5

2.5

1.5

0.5

0.0

"Middle"

pumping depth

3.0

3.0

3.0

3.0

"Deep"

pumping depth

3.0

2.0

1.0

0.0

2.5

2.5

2.5

2.5

2.5

1.5

0.5

0.0

0.0

1.0

2.0

3.0

3.5

0.0

1.0

2.0

3.0

0.0

1.0

2.0

2.5

0.9

1.0

1.2

1.3

1.4

0.9

1.1

1.2

1.4

0.9

1.1

1.3

1.4

San Carlos Project Indian Lands and

San Carlos Irrigation and Drainage District

"Shallow" pumping depth

3.5

3.5

3.5

3.5

3.5

3.5

2.5

1.5

0.5

0.0

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3.0

3.0

3.0

3.0

3.0

2.0

1.0

0.0

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2.5

2.5

2.5

2.5

1.5

0.5

0.0

0.0

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2.0

3.0

3.5

0.0

1.0

2.0

3.0

0.0

1.0

2.0

2.5

1.3

1.3

1.4

1.4

1.4

1.3

1.3

1.4

1.4

1.3

1.3

1.4

1.4

1.3

1.4

1.7

1.8

2.0

1.3

1.6

1.7

2.0

1.3

1.6

1.8

2.0

1.8

1.8

2.0

2.0

2.0

1.8

1.8

2.0

2.0

1.8

1.8

1.4

2.0

0.0

0.0

0.0

0.0

0.0

6.8

6.8

6.8

6.8

15.8

15.8

15.8

15.8

0.0

0.0

0.0

0.0

0.0

6.8

6.8

6.8

6.8

15.8

15.8

15.8

15.8

98.7

98.6

98.3

98.2

98.0

91.9

91.6

91.5

91.2

82.9

82.6

82.4

82.2

98.2

98.2

98.0

98.0

98.0

91.4

91.4

91.2

91.2

82.4

82.4

82.2

82.2

4,300

4,296

4,283

4,279

4,270

4,004

3,991

3,987

3,974

3,612

3,599

3,590

3,581

4,279

4,279

4,270

4,270

4,270

3,982

3,982

3,974

3,974

3,590

3,590

3,581

3,581

APPENDIX B

BUDGETS AND CALENDARS OF OPERATIONS

The following per acre budgets and calendars of operations were developed for large farms (Size IV) operating in "Middle" pumping lift areas. Spring, 1974 costs were used. The budgets include the labor cost of irrigating with the specified amount of water but do not include the actual water cost. Water costs are calculated in the linear programming models as these values vary between districts.

These detailed 1974 budgets are used to update the 1965 budgets for smaller farms developed by Stults (1968). The increase in the variable cost of production on Farm Size IV from the 1965 budgets to the

1974 budgets is the value used to update the estimates of totavariable costs for Farm Sizes I, II, and III. The dollar increase in variable costs per acre computed for Farm Size IV is added to the smaller farm size costs per acre developed by Stults for each crop.

A comparison of the variable costs of production, other than the variable cost of water overlying "Middle" pumping depths, as developed by Stults and as adjusted for this study are given in Table 6.

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0)

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2

8

152

APPENDIX

C

NET RETURNS ABOVE VARIABLE COSTS WITHOUT

CENTRAL ARIZONA PROJECT WATER MIXING

Footnotes for Tables

C-1 through

C-7 appear on page

168.

153

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167

168

Footnotes for Tables

C-1 to C-7 a.

Irrigation water quality is the average salinity found in each irrigation district. Central Arizona Project mixing is not reflected in this table.

b.

Total revenue per acre is the product of yield per acre and the product price. Product prices are the seasonal average prices reported in the 1973

Arizona Agricultural Statistics (Arizona Crop and

Livestock Reporting Service,

1974) except for American-Pima cotton.

Because the

1973 seasonal average price for American-Pima cotton was unusually high due to short supplies, the estimated

1974 seasonal average price was selected. Prices used are as follows: Upland Cotton

$0.40 lb.,

American-Pima Cotton

$0.69 lb., Barley $79.20 ton, Grain Sorghum $102.10

ton, Alfalfa $41.50 ton, and Wheat $86.70 ton.

c.

Calendar costs include machine, material, labor, and custom costs from the farm budgets (see Appendix

B).

d.

Other variable costs are costs which farmers incur in producing the various crops, but which are not allocated to particular calendar operations. These costs are allocated among different crops on the basis of the proportion that each crop contributes to total variable costs for typical farms for each size group. For example, the variable percost of operating a farm pickup truck (or car) is estimated at five cent of the total variable cost of producing each crop. Cash overhead variable costs include cash expense for such items as electricity, telephone, and other utilities for the farm shop and office, fees, subscriptions, farm dues, accounting, bookkeeping, secretarial, and other cash farm expenses and are three percent of total variable cost. Nonfrom calendar labor accounts for the time the worker uses to get to and other reasons.

the field or times when he may be idle due to breakdown or

It is estimated at

10 percent of the calendar labor requirements. The values for other variable costs also includes interest on variable costs, and is based on a

10 percent interest rate. A common rule of thumb is to figure interest on one-half the total variable costs for the number of months required to produce the crop.

e.

Because the pumping cost varies in each irrigation district the net revenue and by pumping lift, net revenue plus pumping cost is over variable cost before the cost of water is subtracted, and is the value used in the objective function of the linear programming models.

subtract out the pumping cost

The linear programming models compute and for each representative farm.

f.

Pumping costs are calculated as described in the text. Irrigation labor costs are included in the calendar costs for labor rather than in the pumping costs.

g. Net Revenue is net revenue over variable cost.

169 h.

A net revenue value for San Carlos Project lands is not given in this table. Because of the nature of the project (see text) the linear programming model calculates the net revenue over variable cost after being given the constraints on surface, pumped, and non-project pumped water.

i.

The other variable cost figures for cotton include those costs described in footnote d plus the cost of hail insurance. The hail insurance premium is $1.30 per $100 of coverage (10 percent deductible policy). The average coverage in the area is $500, thus, the average premium is $6.50.

APPENDIX D

DETAILED RESULTS FOR EACH OF THE FIVE ANALYSES

CLASSIFIED BY IRRIGATION DISTRICT

170

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