THE ECONOMICS OF CROP RESPONSE TO IRRIGATION QUANTITY by

THE ECONOMICS  OF CROP RESPONSE TO IRRIGATION QUANTITY by

THE ECONOMICS OF CROP RESPONSE TO IRRIGATION QUANTITY

AND SCHEDULING: AN ARIZONA CASE STUDY by

Peter Brooks Stearns

A Thesis Submitted to the Faculty of the

DEPARTMENT OF AGRICULTURAL ECONOMICS

In Partial Fulfillment of the Requirements

For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

1 9 8 0

STATEMENT BY AUTHOR

This thesis 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 borrow­ ers under rules of the Library.

Brief quotations from this thesis 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 judg­ ment the proposed use of the material is in the interests of scholar­ ship.

In all other instances, however, permission must be obtained

from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

.

l

J.

I

HARRY W. AXhR

Adjunct Associate Professor

Agricultural Economics

f

//

Date

^

ACKNOWLEDGMENTS

Appreciation is extended to my advisor Dr. Harry Ayer for his

direction throughout this research.

Constructive evaluation of this

thesis by Roger Fox and Dr. Jimmye Hillman, members of my graduate

committee was beneficial.

Paul Hoyt deserves credit for his effort in our cooperative

derivation of the crop-water production functions.

Mr. and Mrs. William B. Stearns, Jr. are thanked for their

inexhaustive supply of encouragement and motivation.

iii

TABLE OF CONTENTS

Page

LIST OF TABLES ............................................. vi

LIST OF ILLUSTRATIONS......................................... viii

A B S T R A C T .................................................... ix

1. INTRODUCTION ................................................ 1

Problem and Setting ......................................

Objectives of the Research ..............................

Organization ............................................

2. LITERATURE REVIEW ............................................

1

4

7

8

8

Physical Response to Water Scheduling .................... 10

General Models........................................ 10

Water Scheduling and Wheat 12

Water Scheduling and Cotton Growth..................... 13

Economic Models of Crop Response to Irrigation.............. 19

3. THEORY, METHODS, AND D A T A .................................... 22

Economic Theory .......................................... 22

Statistical Technique .................................... 28

Data...................................................... 28

Crop-Water Data for Arizona Wheat and Cotton.......... 28

Prices......................

Scheduling....................................

31

33

S u m m a r y .................................................. 34

4. EMPIRICAL ANALYSIS— CROP RESPONSE MODELS...................... 35

Evapotranspiration Models Applied 35

S t e w a r t .................... 35

Minhas. .............................................. 37

B l a n k ................................................ 38

Other Models Applied to W h e a t ............................ 39

Square-root M o d e l ..................

Cobb Douglas Model........................

39

40

Quadratic Models ....................................... 41

The Best Crop-Water Production Functions For Wheat........ 45

Fine-textured Soils . . . . ......................... 46 iv

V

TABLE OF CONTENTS— Continued

Page

Medium-textured Soils. . . . ......................... 47

Coarse-textured Soils............. 48

Evapotranspiration Models Applied to Cotton.................. 49

Other Models Applied to C o t t o n .............................. 49

Cobb Douglas M o d e l ...................................... 49

Quadratic Models ...................................... 49

The Best Crop-Water Production Functions for Cotton........ 50

Fine-textured Soils...................................... 50

Medium-textured Soils................................... 51

Coarse-textured Soils.................................... 51

5. EMPIRICAL RESULTS— ECONOMIC ANALYSIS .......................... 53

Wheat........................................................ 54

Profit Maximizing Quantity and Number of

Irrigations............................................ 54

Comparison of Soil Texture Models with Other Models. . . 58

Demand and Elasticity of Demand for Water. ............... 62

Water Quantity Restrictions.............................. 66

C o t t o n ...................................................... 66

Profit Maximizing Quantity and Number of

Irrigation-Cotton...................................... 66

Comparison of Soil Texture Models with Other Models. . . 71

Demand and Elasticity of Demand for Water............. 73

Water Quantity Restrictions................. 74

6. IMPLICATIONS.................. 78

Farm Management............................................ 78

Water Conservation Policy............ 79

R e s e a r c h .....................................................80

REFERENCES 82

LIST OF TABLES

Table

1.

Estimated Withdrawals of Fresh Water for 1975 and

1985 for Domestic and Commercial, Manufacturing,

Irrigation, and Minerals in Five Western Regions............

2. Crop Value arid Consumptive Water Use of Principal

Irigated Crops in Selected Western States ..................

Page

2

5

3. Water Requirement, Harvested Acreage, Total Revenue,

and Percentage of Total Revenue of Principal Crops in

Arizona in 1972, 1976, and 1977 ............................ 6

A. Selected Soil and Climatic Data for Five Experimental

Sites in Arizona............................................ 30

5. Profit-maximizing Quantity of Water and Number of

Irrigations at Different Wheat and Water Prices for

Wheat Raised on Fine-textured soil.......................... 55

6. Profit-maximizing Quantity of Water and Number of

Irrigations at Different Wheat and Water Prices for

.

56

7

Profit-maximizing Quantity of Water and Number of

Irrigations at Different Wheat and Water Prices for

Wheat Raised on Coarse-textured Soil........................ 57

8 Water Applications Implied by the Six Wheat "Models" for Soils of Different Texture, Medium Wheat Price ........ 59

9. Arc and Point Elasticity of Demand for Water in the Production of Wheat ..................................... 65

10. Water Restrictions and Change in Returns over Total

Costs for Wheat, Water Cut to 90 and 80 Percent of

Profit Maximum Level, Medium Price of W h e a t ................ 67

11. Profit-maximizing Quantity of Water and Number of

Irrigations at Different Cotton and Water Prices for

Cotton Raised on Medium-textured S o i l .................. 68 vi

vii

LIST OF TABLES— Continued

Table Page

12. Profit-maximizing Quantity of Water and Number of

Irrigations at Different Cotton and Water Prices for Cotton Raised on Medium-textured Soil. ................... 69

13. Profit-maximizing Quantity of Water and Number of

Irrigations at Different Cotton and Water Prices for Cotton Raised on Coarse-textured Soil................... 70

14. Water Applications Implied by Six Cotton "Models" for Soils of Different Texture, Medium Cotton Prices ........ 72

15. Arc and Point Elasticities of Demand for Water in

the Production of Cotton, by Water Source, Water

Price, Output Price, and Soil Textures . ..................... 76

16. Water Restrictions and Change in Returns over Total

Variable Costs for Cotton, Water Cut to 90 and 80

Percent of Profit Maximum Level, Medium Price of

C o t t o n .......... 77

LIST OF ILLUSTRATIONS

Figure Page

1. Five Western Water Resource Regions................ .. 3

2. Daily and Semi-monthly Consumptive Water Use, Four

High-yielding Wheats, Mesa, Arizona........................ 14

3. Cumulative Consumptive Water Use, Four Highyielding Wheats, Mesa, Arizona,............................ 15

4. Daily and Seasonal Consumptive Use, Cotton,

Mesa and Tempe, Arizona, 1954-1962 ........................ 17

5. Cumulative Consumptive Use, Cotton, Mesa and

Tempe, Arizona, 1954-1962. . . . .......................... 18

6. Hypothetical Production and Marginal Physical

Product Functions............................................. 23

7. Marginal Value and Average Value Products.................... 24

8.

Short-run Normative Demand Curves for Water in

the Production of Wheat by Soil Type, 600-foot

Lift; Price of Output, $.0525/lb .......................... 63

9.

Short Run Normative Demand Curves for Water in the

Production of Cotton by Soil Type, 600-foot Lift,

Price of Output, $.62/lb of Lint........................... 75 viii

ABSTRACT

This research provides crop-water response functions and asso­

ciated economic analysis for cotton and wheat on fine-, medium-, and

coarse-textured soils in Arizona.

Crop-water response data is analyzed

using regression analysis.

The economic analysis estimates the impact

of changing surface water prices, water lift depths, energy prices, and

product prices on profit maximizing levels of water use, profits, and

the demand of irrigation water.

The profit maximizing quantities of

water predicted from this research are compared to common practice,

yield maximizing models, and other models.

Highlights of the empirical results for wheat production

include: (1) the estimated crop-water production functions explain a large part of the variation in yield; (2)

the soil texture models

generally call for 6 inches or less water than yield maximizing models;

and (3)

the demand for-water is very inelastic except at the 600-foot

pump level.

Highlights of the empirical results for cotton production include: (1) estimated crop-water production functions exhibit high

2

R s; (2) water applications suggested by the profit maximizing models

correspond closely with all other models and (3)

the demand for water

in the production of cotton is very inelastic.

Implications on farm management, government water policy, and

research are given.

ix

CHAPTER 1

INTRODUCTION

Problem and Setting

There is little useful empirical knowledge of crop response to

water quantity and scheduling in the arid Southwest or Arizona, although

a number of current circumstances suggest that knowledge of these rela­ tionships is important.

First, the quantity of water used in irrigated

agriculture is far greater than water used in any other sector.

As

shown in Table 1, water used for irrigation has typically been, and is

projected to be in 1985, nearly 90 percent of total water use in all

Southwestern states (Figure 1).

Second, although surface water is still very inexpensive com­

pared to ground water, there are increasing pressures from urban users,

Native Americans, Mexico, and California to divert water from commercial

agriculture in Arizona.

Third, the rising price of energy has increased the cost of

pumping ground water.

For example, in Pinal County, Arizona, the

price of electricity is estimated to increase from 7 mils per kilowatt

hour in 1963 to 40 mils per kilowatt hour in 1980, The variable

cost of pumping ground water in Pinal County for cotton and wheat is

approximately 18 to 25 percent of the total variable cost of their

production.

1

Table 1. Estimated Withdrawals of Fresh Water for 1975 and 1985 for

Domestic and Commercial, Manufacturing, Irrigation, and

Minerals in Five Western Regions.

Withdrawal, 1975

Acre-feet per Day

Percent of Total

Withdrawal, 1985

Acre-feet per Day

Percent of Total

California

Domestic and

Commercial

Manufacturing

Irrigation

Minerals

3,388

796

34,611

297

8.7

2

88.5

.7

3,809

830

34,863

359

Lower Colorado

(Arizona)

Domestic and

Commercial

Manufacturing

Irrigation

Minerals

498

89

7,989

184

5.7

1

91.2

2.1

612

92

7,299

252

Rio Grande

(New Mexico)

Domestic and

Commercial

Manufacturing

Irrigation

Minerals

Upper Colorado

(Colorado)

Domestic and

Commercial

Manufacturing

Irrigation

Minerals

327

19

5,684

190

5.2

.3

89.1

.3

352

42

5,498

221

80

4

6,400

.32

1.2

0.0

96.7

2

86

2

7,223

195

Texas-Gulf

(Texas)

Domestic and

Commercial

Manufacturing

Irrigation

Minerals

1,490

1,932

11,538

1,044

9.3

12.1

72.1

6.5

1,697

2,559

9,333

1,133

Source: United States Water Resources Council, 1978.

9.6

2.0

87.5

.9

7.4

1.1

88.4

3.1

5.8

.7

89.8

3.6

1.1

0.0

96.2

2.6

11.5

17.4

63.4

7.3

2

Key to Regions:

1 = California

2 = Lower Colorado

3 = Upper Colorado

5 = Texas Gulf

Figure 1. Five Western Water Resource Regions.

Source: U. S. Resources Council,>1978.

LO

4

Many alternative irrigation practices may be employed to

decrease the cost of irrigation and conserve water. But the profitabil­

ity of these practices, and hence the likelihood that they will be

adopted by farmers, depends directly upon the underlying crop-water

response function. The yield response to water quantity and scheduling

will affect farm profits, crop production, and water use.

These impacts

are of importance to both individual farmers and to those who formulate

water and energy policy.

In spite of the importance of the underlying crop-water produc­ tion relationships, little empirical knowledge of them exists.

This is

true for the response of cotton and wheat to water quantity and

scheduling in Arizona, the crops upon which this research focuses.

The importance of cotton and wheat in Arizona agriculture (and

in the agriculture of the arid Southwest) may be seen in Tables 2 and 3.

In terms of total crop value and total quantity of water used, cotton

and wheat are very important and have been so over time.

Objectives of the Research

The specific objectives of this research are:

1.

To determine the physical response of cotton and wheat produced

on specific soil textures in Arizona to various irrigation

quantity and scheduling practices.

2.

To estimate the profit maximizing quantity and scheduling of

water and determine the sensitivity of the solution to alterna­ tive water and electricity prices, lift depths, and soil textures.

Table 2.

Crop Value and Consumptive Water Use of Principal Irrigated Crops in Selected Western

States

State

Cotton Vegetables

Value3 c . u . b

Value

C.U.

Value

Hay

C.U.

Wheat

Value C.U.

Sorghum

Value c .u i

Arizona

California

Colorado

Texas

Total

318

733

1,302

2,353

1.9

3.6

6.0

11.5

104

1,515

29

245

1,893

.1

2.2

.0

.31

2.6

94

456

157

231

938

1.6

7.0

2.5

5.5

16.5

26

119

120

264

529

.3

.6

.1

3.5

4.5

15

23

14

438

490

.2

.3

.1

2.8

3.4

a. Value in millions of dollars. b. Consumptive Water use in millions of acre-feet.

Source: United States Department of Agriculture (1978).

Table 3. Water Requirement, Harvested Acreage, Total Revenue, and

Percentage of Total Revenue of Principal Crops in Arizona

in 1972, 1976, and 1977

6

Water Require­

ment (acre-

feet)3

Harvested

Acreage

Total

Revenue

(in $1000)

Percentage

of Total

Revenue

(All Crops) Crop

Cotton^

Vegetables0

Hay (Alfalfa)

Citrus

Wheat

-

Year

1977

1976

1972

1977

1976

1972

1977

1976

1972

1977

1976

1972

1977

1976

1972

Grain Sorghum

1977

1976

1972

3,184,416

1,945,555

1,780,755

176,755

171,366

215,555

2,167,083

2,167,083

2,218,680

374,618

389,254

418,480

495,833

1,526,458

602,083

275,000

278,055

326,944

556,500 355,321

340,000 318,067

311,200 111,574

65,600

124,421

63,600 118,781

80,000 84,467

210,000 94,965

210,000 105,764

215,000 48,020

56,310

58,510

62,903

35,841

30,986

31,160

140,000

26,514

431,000 126,497

170,000

18,680

90,000

91,000

107,000

16,344

15,943

18,246

54

44

35

19

16

27

14

14

15

4

18

6

5

4

9

2

2

6

Source: Arizona Crop and Livestock Reporting Service, 1978.

a. A crop's water requirement is based upon its estimated consumptive

use per acre and an irrigation delivery efficiency of 60 percent.

b.

Total revenue from cotton includes the value of both cotton fiber

and seed, and assumes 1.65 pounds of seed for each pound of fiber.

c.

The water requirement for vegetables is based upon the average

consumptive use of 19.4 inches per acre for eight vegetables and an irrigation delivery efficiency of 60 percent.

7

3.

To estimate the elasticity of demand for water on a per acre

basis in the production of wheat and cotton on specific soil

textures.

A. To evaluate alternative water quantity and scheduling recommen­ dations and practices of public agencies and individual pro­ ducers relative to the results obtained in Objective 2.

5.

To estimate the change in returns over total variable costs for

wheat and cotton production should water use be cut to 90 and 80

percent of the profit maximizing level.

6. To draw policy implications for farm management, water conserva­ tion policy, and research.

Organization

The thesis is divided into six chapters.

Chapter 2 reviews the

literature related to key physical and economic models of crop response

to irrigation.

Chapter 3 discusses economic theory, statistical

methods, and data.

Empirical results derived from the crop response

models are presented in Chapter A.

Chapter 5 gives the empirical

results of the economic models, the elasticity of demand for water in

the production of wheat and cotton, and compares the empirical results

to current recommendations and practices. Policy implications are

provided in Chapter 6.

CHAPTER 2

LITERATURE REVIEW

The literature cited described (1) the physical response of

crops to total water applied, (2) the physical response of crops to

water scheduling, and (3) economic models of crop response to irriga­ tion.

Physical Response to Total Water Applied

Slayter (1967) discussed the importance of water to plant

growth processes. Water contributes to the structural composition of

biological molecules which constitute plant cells and tissues. Trans­

location of foodstuffs and minerals throughout the plant organism is

conducted in a water-based medium. Water combined with carbon dioxide

forms the initial substances for photosynthesis.

Glucose, the product

of plant respiration, is composed of water, starch, and related com­

Evapotranspiration is the process of water transfer into the

atmosphere from soil-water evaporation and plant transpiration (Arkin,

1978). Brix’s (1962) research indicated that transpiration and photo­

synthesis are closely related. Photosynthesis is the plant process that

converts the sun's energy to carbohydrates for plant dry weight gain.

Evaporation around a plant, stimulated by low humidity, high tempera­

tures, and high winds, increase water loss through transpiration.

Evapotranspiration in excess of root absorption causes a negative

8

9 moisture balance. If water is not replenished through rainfall or irri­ gation, plants lose turgidity, wilt, and die.

Research to estimate evapotranspiration from climatic and

meteorological data has been done by Blaney-Morin (1942), Thomwaite

and Holzman (1942), Jensen and Raise (1963), Beringer (1961), Fleming

(1964), Moore (1961), and Stewart, Hagan, and Pruitt (1974, 1977). Plant

growth is a function of the parameters associated with plant moisture

stress.

The rate of moisture intake by the plant roots from the soil,

and the rate of moisture loss from the plant leaves to the atmosphere

are the most relevant parameters. Beringer (1961) developed the Inte­

grated Moisture Index which aggregated the moisture deficiency over

the growing season. Plant growth and yield may be estimated by deter­

mining the relationship between the potential evapotranspiration and

actual evapotranspiration according to Stewart et al. (1977). Moore

(1961) felt plant growth and yield could be reduced before the avail­ able soil moisture fell below the permanent wilting point.

Hexem and Heady (1978) derived crop-water production functions

for cotton, sugar beets, wheat, c o m , and corn silage in several Western

States.

The research sought to measure the productivity of water in

terms of crop yields for different soils and climatic conditions.

Irrigation treatments were based upon a predetermined available soil

moisture depletion level.

Timing or scheduling of irrigations and

methods of application were not considered in their analysis.

Graphic

analysis of the estimated functions shows a declining total physical

product to high water applications (a third stage of production), but

graphs are projected beyond the range of the data. Climatic variables

are not induced in their site models. And, finally, little economic

analysis or comparison of experimental results with field situations

is given.

10

Physical Response to Water Scheduling

Crop response to water scheduling is discussed in terms of

(1) general models, (2) water scheduling and wheat growth, and (3)

water scheduling and cotton growth.

General Models

Numerous research efforts have emphasized the importance of

water applications in particular stages of plant growth. Focusing

solely on the total quantity applied throughout the season can be

misleading. Moore (1961) indicates that irrigation decisions should be

primarily based upon plant needs in specific growth stages.

Black and Hay (1978) described the general relationship between

water and plant growth at specific growth stages. Moisture stress dur­

ing the plant's reproductive stage prevents or reduces pollination and

retards kernel formation. Water stress prior to the reproductive stage

decreases plant size. Late stress reduces filling out of the seed.

Dudley, Howell, and Musgrave (1971) determined the optimal

timing of irrigations over a season in an uncertain environment. A

plant growth-soil moisture simulation model is incorporated into a two-

state variable stochastic dynamic programming model to determine an

intraseasonal allocation pattern for irrigation water in a variable environment.

11

Anderson, Yaron, and Young (1977) developed mathematical models

to predict yield response to soil moisture stress at different growth

stages.

The models depict outcomes when limited water is applied

throughout the growing season.

Yaron and Strateener (1973) detailed the reduction in crop yield

resulting from water stress at particular growth stages based upon

critical days. A "critical day" occurs when the available soil moisture

falls below a predetermined level. A critical day during the tassle

stage will reduce corn yield an estimated 2 to 2.5 percent.

Critical

days before or after tassling will reduce yield by only .75 to 1.0

percent.

Hanks (cited in Stewart et al., 1977) examined variations in

plant growth and yield resulting from water deficiencies in specific

growth stages of corn in four Western states. Hanks estimated plant

water loss in each growth stage on transpiration data.

Stewart et al. (1977), in the identical four-state project,

focused upon the importance of conditioning.

They determined that

plants stressed in an early growth stage would be less sensitive to

stress at later growth stages.

Jensen (1969), with data from southern Idaho from 1966-1970,

developed irrigation scheduling models designed to prevent plant growth

stress.

Daily evapotranspiration was derived from climatic data to

estimate the rate of soil-water depletion. Jensen's model sought to

predict the optimum time for the next irrigation.

Kincaid and Heerman

(1974) modified the model to fit small desk calculators. Heerman,

Haise, and Nickelson (1976) adapted the model to fit center pivot

12 irrigation systems.

The Salt River Project in Arizona used Jensen's

irrigation scheduling program for three years.

The United States Bureau of Reclamation, collaborating with the

Idaho State Extension Service, provided Idaho farmers with the Irriga­

tion Management Service. Weekly estimates of evapotranspiration for

numerous crops were provided (Buchheim and Floss, 1977). Agricultural

producers were able to estimate the available soil moisture in their

fields with this service. The objective was to improve their irriga­ tion allocations.

Water Scheduling and Wheat Growth

Dennis et al. (1978) discussed irrigation application categories

for wheat production in Arizona during preplant, first irrigation, and

midseason irrigations.

A preplant or emergence irrigation in November is necessary to

wet the soil profile to a depth of 5 to 6 feet.

One application of 12

inches of water per acre will satisfy the preplant irrigation require­ ments in dry or heavy soils.

Sandy soils receive 12 inches of water

divided into two applications.

The first irrigation should be applied by early March.

Cool

temperatures and minimal plant growth in the early season generate

minimal evapotranspiration and water loss. An average rainfall in

Arizona of 3 inches in this period supplements the preplant irrigation.

Variances in rainfall, temperature, and planting dates affect the tim­

ing of the first irrigation. A 6-inch application for the first

irrigation refills most soil profiles.

/

The second through the final irrigations are spaced closer

13

together to accommodate increased crop needs stimulated by additional

plant foliage and higher temperatures.

The quantity and timing of the

water application depends upon the available water holding capacity of

the soil, the depth of the plant root system, and the adequacy of the

irrigation system. Moisture stress should be avoided to ensure normal

seed development through the dough stage.

Erie, Bucks, and French (1973) and Halderman (1975) provided

graphs of daily, semi-monthly, and cumulative water consumption of

high-yielding wheat varieties in Arizona (Figures 2 and 3).

Their

graphs are based upon experiments in which enough water was applied to

prevent plant stress and thereby maximize yield. Midseason irrigations

can be planned by accounting for the date of the first and last irriga­

tion and knowledge of the crop's consumptive use. For example, if the

first irrigation occurs on March 1, and the final irrigation on April

25, 54 days transpired.

Subtracting a preplant irrigation of 6 inches

from 22 Erie et al.'s (1973) consumptive use figure between March 1 and

April 25 equals 16 inches. Figure 3 shows that four applications will

provide adequate water to maximize crop yield.

Dennis et al. (1976) indicated which irrigations should be

foregone if water is restricted. The ordering of foregone irrigations

is (1) the last, (2) the second, and (3) the second to last.

Water Scheduling and Cotton Growth

Grimes and Dickens (1977) discussed water applied to cotton in

terms of the preplant irrigation, the first irrigation, the scheduled

Z 0 .3

SEASONAL SOIL

MOISTURE DEPLETION

^ O l ki

Y " 1 140'%.) w ‘-2 1129%)

2 2‘3

Z±ll

,,w%1

~ > 4 □2.3'(9%l

£ 4-5 ]D.8e(3X)

q

5-6 10 3“ (IX)

HEADING

BLOSSOM

SOFT DOUGH

HARD

DOUGH

3 0.1

PLANTING

DATE \

24- TALL

10" TALL

J A N U A R Y

SEASONAL USE 2 5 .8 -

SEMIMONTHLY USE IN INCHES

3.C8 I 4 83

A P R I L

Figure 2. Daily and Semi-monthly Consumptive Water Use,

Four High-yielding Wheats, Mesa, Arizona,

Source: Erie et al., 1973

iN| I eb

|

31|

DAY OF YEAR

59|

M ar

) A pr

I M ay

|

Figure 3.

Cumulative Consumptive Water Use, Four High-yielding

Wheats, Mesa, Arizona

Source: Halderman, 1975.

16 irrigations, and the final irrigation. Preplant irrigations are essen­

tial to ensure proper germination. The soil profile is saturated to

field capacity. Residual soil salts are leached below the plant's

root zone by the preplant irrigation.

Erie, French, and Harris (1965)

estimated the consumptive use of water for cotton prior to the first

irrigation in mid-June to be 4.4 inches. Water demands early in the

season are low because of cool temperatures and minimal plant foliage.

Farmers can be flexible in selecting the date of the first

irrigation.

Light, sandy soil may require an irrigation the last week

in May. Heavy, clay soils may not require an irrigation until mid-

June.

By delaying the first irrigation, causing stress, the irrigator

can "condition" the plant to withstand future water shortages.

Insect

damage is reduced when plants undergo water stress. Other researchers

disagree with "conditioning" a plant and recommend providing sufficient

water throughout the season (Grimes and Dickens, 1977).

The second through the final irrigations often involve follow­

ing a set schedule designed to prevent water stress and maximize crop

yield.

Set schedules assist the planning efforts of farm irrigators

and regional allocators of water.

Erie et al. (1965) and Halderman (1973) gave daily, semi­

monthly, and cumulative water use for cotton (Figures 4 and 5), again

under no stress conditions. Figure 4 shows that from mid-June until

the final irrigation on Agusut 31, the consumptive use is 25.09 inches

(Erie et al., 1965). As the season progresses, additional plant

growth combined with rising temperatures cause increased evapotranspira-

tion and water loss.

3 0.2

SEASONAL

SOIL MOISTURE DEPLETION

1 (2 0 % )

1 (3 9 % )

£ 3 - 4 o 4 - 5

2 ] 2.9" (7 % )

F irs t blossom peok

F irs t blossom

Last blossoms that

rusually mature

SEASONAL USE 41.2

SEMIMONTHLY USE IN INCHES

August September

O ctober

Figure 4. Daily and Seasonal Consumptive Use, Cotton, Mesa and Tempe, Arizona,

1954-1962.

Source: Erie et al., 1965,

H

Last blossom that

usually matures

8/15 8/31

Figure 5.

Cumulative Consumptive Use, Cotton, Mesa and Tempo, Arizona,

1954-1962.

Source: Ualderman, 1973.

19

The date of the final irrigation affects the cotton harvest.

In Arizona, if the last irrigation is made on August 15, the harvest

date will fall within the first week of October.

Delaying the last

irrigation to September 1 will push the appropriate harvest date back

to the first week in November.

Cooler temperatures late in the growing

season reduce plant growth and lessen the demand for water.

Figure 4

depicts the consumptive use from September 1 until harvest to be 11.72

inches.

Early termination of the final irrigation is considered the best

way to allocate water when the total water available is limited.

Kittock at the Cotton Research Laboratory in Phoenix, Arizona, has

attempted to quantify the effect on yield of early irrigation termina­ tion.

Economic Models of Crop Response to Irrigation

An extensive review of economic models of crop response to

irrigation was conducted by Ayer (1978). His review of basic production

function models and models that account for the timing of water applica­ tions are summarized here.

Since 1972, basic production function work has been conducted

by Delaney (1978); Dyke (1977); Hexem and Heady (1978); Holloway and

Stevens (1973); Hogg and Vieth (1977); Wu and Liang (1972), and Yaron

(n.d.).

Crop yield is postulated to be a function of water quantity,

quality, and non-water inputs.

The underlying production function is

estimated by regression analysis with the units of observation being

experimental plots, farm fields, or counties. The yield response may

20

be described by estimating the total response curve, or by taking the

average yield at particular application levels.

The marginal value

product (MVP) is equated to. water price, utilizing the regression

^production function. The optimum quantity of water to apply is esti­ mated.

Basic production functions are most useful in regional analysis.

Aggregated crop water production functions may be used to determine the

impacts of water pricing policy on yields and input use. The marginal

value product of output for the region can be calculated and compared to

the price of providing additional irrigation water.

The absence of

irrigation scheduling, multicrop situations, and risk, weaken the reli­ ability of basic production functions for farm level decisions.

Dudley et al. (1971), Flinn and Musgrave (1976), Hall and

Butcher (1968), Minhas, Parikh, and Srinivasan (1961), Moore (1961),

Moore, Snyder, and Sun (1974), and Stewart et al. (1974, 1977) estimated

economic models based upon dated crop-water production functions. Dated

production functions account for a plant's water demand in different

growth stages.

Identical quantities of total water applied will

result in different yields, if the timing of application varies among

vegetative, pollination, and maturation stages.

Stewart et al. (1977)

included "conditioning" effects in their recent work.

Derivation of dated production functions is more complex than

for basic production functions. Water applied or evapotranspiration

(ET) per growth period represent the independent variable. Other vari­ ables are held constant.

Production functions are estimated by

regression analysis from experimental data. Economic optimums are

21

computed by setting the marginal value product (MVP) of water per

growth period equal to the marginal factor cost of supplying water

during that period.

To handle the intertemporal nature of scheduling

water, dynamic programming has been employed. Water quantity restric­ tions and prices per period are key consideration.

Dated production functions possess inherent weaknesses. Most

models fail to acknowledge the interdependence of growth stages and the

riskiness of crop production.

Omission of climatic, soil, and other

factors restricts transferability among fields. On farm application of

dated production functions are limited, despite their improvements over

basic production functions.

The research reported here focuses on the estimation and

economic analysis of undated crop-water production functions for cotton

and wheat on various soil textures in Arizona, Additional years of data

from agronomic sites in Arizona will supplement data generated by Hexem

and Heady’s (1978) earlier efforts. Pan evaporation data is included

in the modeling effort.

Scheduling is not directly considered in the

production function estimates, but is considered in side calculations.

CHAPTER 3

THEORY, METHODS, AND DATA

The economic theory, statistical technique of analysis, and

data sources and descriptions are summarized here.

Economic Theory

A production function indicates the relationship between

alternative amounts of an input and the resulting output if inputs are

applied in a technically efficient way.

Curve OA of Figure 6 depicts

a hypothetical production function with crop yield shown to vary with

the level of input X.

The added output from each additional unit of input is the

marginal physical product (MPP), and in Figure 6 is shown as curve MN.

By multiplying the MPP times the price of the product, the marginal

value product (MVP) is derived, and indicates the added value of output

for each additional unit of input. Profit maximization with a single

variable input takes place where the MVP equals the price of the input

(and the value of the average physical product [AVP] is declining).

Figure 7 depicts the MVP, AVP, and input price line.

Point X is the

profit maximizing level of input use.

When more than one input is variable and some factors of

production are fixed, the production function may be expressed in

functional notation as:

22

Total Physical Product

Yield

.Marginal Physical Product

Input X

Figure 6,

Hypothetical Production and Marginal Physical

Product Functions

M w

Dollars

Price of

Marginal Value Product

Average Value

Product

Input X

Figure 7. Marginal Value and Average Value Products

25

Y = f(X1 ,X2 ,X3 where

Y = yield

X- . . . X = variable inputs n

Xn+^ . . . X fc = fixed factors of production

Profits are expressed as

7T = PyY = (P X. + P X- + P X

+

J x 1 x 2 x nt where

7f = profits

Py = price of product Y

Y = yield

P^ = price of input x^, i = 1 to n

+ P X ) - FC

PC = fixed costs of inputs X ^ ^ . . . X^.

Profits are maximized when the derivative of profits, with respect to

all variable inputs, are equal to zero ( and the value of the average

products are declining): n n

26

And since Py i is the MVP

, each set of equations indicates that at

xi profit maximization the MVP must equal the price of X . , as was true

Xi 1 the single variable input case. ,

Solution of this system of "n" equations yields the profit

maximizing level of input use.

Substitution of the input levels into

the response and objective functions, respectively, provides the level

of output and profit under profit maximization.

The form of the production function equation affects the esti­ mated profit maximizing quantity of water to apply.

Quadratic, square-

root, and three halves equations will be discussed.

The quadratic function (Y = b + b-.X. + b_X_ + b X.X„)

O JL1 d Z S 1 Z

permits the yield response surface to curve downward, displaying

negative marginal products at high levels of input use (water, fertil­ izer, etc.).

The marginal product curve is linear with the quadratic

equation.

The quadratic equation is attractive because it accounts for

declining marginal yields as water applications increase and for

declining crop yields resulting from excessive applications of water,

fertilizer, or other inputs.

The square-root function (Y = bQ + b ^ + b2X*5 + b ^ + b^X*5

+ bj-X^Xg) has properties comparable to the quadratic. The marginal

product curve for each input variable declines at a decreasing rate.

This feature is consistent with known agronomic relationships.

The three halves function (Y = bo + h

X;

+ b ^ * 5 + b3X 2

1.5

+ ^y^2* + b^X^Xg) has several properties similar to the square-root,

however, the marginal product curve of the input (X^) declines at an

increasing rate.

27

The marginal value product (MVP ) function is also the demand

Xi

function for input X^, because the MVP curve indicates, as shown above,

the amount of input which will be used at different prices of the

input.

From the demand curve, the elasticity of demand is derived.

Elasticity of demand is the percentage change in quantity demanded with

1 percent change in input price.

Elasticity of demand may be computed

either as arc or point elasticity. Arc elasticity is:

Arc E,

* b - * a

*b +

Xa

P - P

*b

X*

P + P

*b X,

Where a and b are the limits of the arc for the quantity and price.

Point elasticity is:

Point E^ =

3X Px

3P X x

Elasticity of demand may be elastic, inelastic, or unitary.

If the

elasticity of demand is greater than one, demand is elastic, and the

percentage change in quantity demanded is greater than the percentage

change in its price.

Inelastic demand, when elasticity is less than

one, means that the percentage change in quantity demanded is less than

the percentage change in price. Unitary elasticity, when the elasticity

equals one, means the percentage change in quantity demanded is equal

to the percentage change in price.

28

Statistical Technique

Regression analysis is used to estimate the production func­

tions. Regression is a descriptive tool that may be used to (1) find

the best linear prediction equation, (2) evaluate prediction accuracy,

(3) control for other confounding factors to evaluate the contribution

of a specific variable or set of variables, and (4) find structural

relationships and provide explanations for complex multivariant rela­ tionships .

Ordinary least-squares regression is a statistical technique to

estimate the intercept and slope of a line from observations of the

levels of an independent variable(s) and the associated levels of the

dependent variable.

The intercept and slope are estimated by finding

the intercept and slope that minimizes the sum of the squared differ­ ences between the actual observations and the regression line.

Several tests of the statistical reliability of the estimated

equation can be made with regression analysis. The coefficient of

2

determination, R , denotes the variation in the dependent variable

explained by the independent variables. The t test indicates the

level of significance of individual intercept and slope coefficients.

Data

Discussion of the data focuses on crop-water data for Arizona

wheat and cotton, and the prices of water, wheat, and cotton,

Crop-Water Data for Arizona Wheat and Cotton

An exhaustive search was conducted to collect all agronomic

data that related crop response to water for major crops in Arizona.

29

Because of differing agronomic objectives and associated experimental

design, much of the available data failed to provide the necessary

information for derivation of crop-water response functions.

One major crop-water research effort did exist, providing sufficient

data for this research.

In a study sponsored by the Bureau of Reclamation, Hexem and

Heady (1978) designed, administered, and analyzed crop-water experiments

for major and minor crops in the western United States.

In Arizona,

experiments were conducted on cotton, wheat, beets, and corn.

Cotton

data analyzed by Hexem and Heady (1978) are from the experiment stations

located at Yuma Mesa, Yuma Valley, Tempe, and Safford, and for experi­

ments conducted in 1971. The current study uses this same cotton data,

additional data from Phoenix for 1975 and 1976, plus additional data

on pan evaporation. Wheat data analyzed by Hexem and Heady are from

experiment stations located at Yuma Mesa, Yuma Valley, Mesa, and

Safford for experiments done in 1971 and 1972. These same data, addi­ tional data from Mesa from 1973 through 1975, and data on pan evapora­ tion are used to analyze the impact of water on wheat yield.

Variation among the soil and climatic conditions for the

Arizona field stations are depicted in Table 4. Yuma Valley, with a

"fine" soil texture, has the highest available water holding capacity

(AWHC) at 9,9 inches. Yuma Mesa, with a coarse soil texture, records

and lowest AWHC 3.1 inches. Both Yuma sites are hotter and dryer than

Mesa or Tempe.

The electrical conductivity, although high in Yuma

Valley, does not adversely affect yield because of the high salt

tolerance of wheat and cotton.

Site

Table 4. Selected Soil and Climatic Data for Five Experimental Sites in Arizona

Soil

Texture

Available

Water

Holding

Capacity

(in./ft)

Hydrologic

Conductivity

(in/h)

Electrical

Conductivity

(milllmhos

per cm

at 25°C) pH

Alkalinityacidity

Ratio

Average

Annual

Temperature

(°F)

Average

Annual

Precipitation

(in.)

Yuma Valley Fine

Yuma Mesa Coarse

Mesa

Tempe

Safford

Medium

Medium

Fine

9.9

3.1

7.3

5.6

7.5

.18

2.9

.64

.9

.47

3.55

1.5

1.22

2.41

5.65

7.81

7.97

8.03

7.84

8.01

87.8

87.1

84.6

84.8

80.3

2.37

3.38

8.06

7.66

8.95

Source: Hexem and Heady (1978, Appendix, Table 2).

31

The agronomic experiments employed the incomplete block design

involving factorial treatments.

The factorial arrangement, referring

to the specification and distribution of various treatment combinations,

was selected for two reasons. First, this design allows estimation of

coefficients for second order polynomial square root and other polyno­ mial forms of production functions.

Second, sufficient points are

provided for a balanced goodness of fit test. Treatment combinations

were randomly assigned to specific plots. Most experiments incorporated

two blocks, each containing 22 experimental plots.

Irrigation quantity and timing was based upon the level of

soil moisture tension as measured by neutron probe tubes and/or mois­

ture blocks. Water was applied when the available soil moisture

reached a predetermined level for each site in the top 4 feet of soil.

Adequate water was applied to restore the soil moisture to field

capacity with each irrigation. The quantity of water applied to each

plot was metered at the plot's entry point. Borders, constructed

after germination, prevented irrigation runoff. Rainfall in excess of

one-quarter inch was included in the total water applied amount.

Prices

The price of pump irrigation water is the cost of energy,

repairs, maintenance, and lubrication to pump an acre foot of water.

These costs may vary with lift depth, pump efficiency, the price of

electricity (or other fuel), and the field irrigation efficiency.

The

price per acre-foot of pump irrigated water applied is:

32

P

KWH to lift

one acre-

foot

overall pump

efficiency power cost per

* KWH including

+

sales tax

(R * lift

depth in

feet) irrigation delivery efficiency where:

R = Cost of plant repairs, maintenance, lubrication, and attendance per acre-foot per foot of lift.

Prices for water cost computations are from Hathorn’s 1979

Arizona Field Crop Budgets (Hathorn and Armstrong, 1979; Hathorn and

Cluff, 1979; Hathorn and Farr, 1979; Hathorn, Howell, and Hazlitt, 1979).

Surface water costs are from the same publication. Pump efficiency, as

per Hathorn, is assumed to be 60 percent, and the delivery efficiency

is assumed to be 60 percent for flood irrigation.

Three water sources at three prices are examined in the sensitivity analysis.

Surface water, pumping at 300 feet and at 600 feet,

serve as the water sources.

Expected costs for 1979, a 50 and 100

percent increase in tne cost of electricity are the price levels.

Surface water prices are increased 50 and 100 percent.

Three cotton prices are examined in the sensitivity analysis.

Cottonseed and cotton lint are combined to provide a composite value

per pound of cotton lint.

There are 1.65 pounds of cottonseed per

pound of lint.

Review of 10 years of historical data showed an annual

low cotton lint price of $.234 per pound in 1969. The historical

(1976) high cotton lint price is identical to the estimated high price

33

of $.66 per pound forecast for 1979. The medium range value for cotton

lint is $.54 per pound.

Three values of cotton seed, $.055, $.05, and $.045 per pound

are used. Marketing specialists from Arizona Producers forecast no

greater than a 10 percent positive or negative change in the current

$.05 per pound price of cottonseed for the next 5 years in Arizona.

The aflatoxin situation causes Arizona producers to receive a lower

value for cottonseed than cotton producers in other regions.

The composite cotton lint and cottonseed values are:

$.234 per pound + 1.65 * .045 per pound = $.31 per pound (low)

.54 per pound + 1.65 * .05 per pound = .62 per pound (medium)

.66 per pound + 1 . 6 5 * .055 per pound = .75 per pound (high)

Three output prices are examined in the sensitivity analysis

on wheat. Review of 10 years of historical data showed the lowest

price for wheat to be $.0235 per pound ($47/ton) in 1970.

The high

wheat price was $.065 per pound ($130/ton) in 1976.

The 1979 expected

price is $.0525 per pound ($105/ton).

The output values used in the

sensitivity analysis are a low or $.0235, a medium of $.0525, and a

high of $.065 per pound.

Scheduling

The agronomic experiments from which data for the production

functions are taken were not designed to evaluate the impact of water

scheduling on yield. Rather, some "optimum" scheduling was used.

Supplemental agronomic information is used here to indicate the number

of irrigations and something about the scheduling. Gravity irrigation,

34

which accounts for nearly 95 percent of all irrigation in Arizona, is

assumed.

On fine- and medium-textured soils preplant irrigations

generally total about 12 inches to bring soil moisture to field capac­ ity. A total of 10 inches is usually sufficient for preplant irriga­ tions on coarse soils.

Each remaining irrigation usually applies 6

inches of water on fine- and medium-soil textures and 5 or less inches

on coarse soils to wet the soil to root zone. Applications should be

applied at particular times based on soil moisture and vegetative

conditions.

Summary

In summary, data from agonomic experiment stations are used in

regression analysis to estimate crop-water production functions for

cotton and wheat in Arizona.

In the economic analysis, the profit

maximizing level of water is estimated.

The sensitivity of the profit

maximizing level of water to soil textures, cotton fiber and seed

prices, wheat prices, and three water sources (surface, 300-foot lift,

and 600-foot lift) and water prices is also examined.

The scheduling

of water is not considered directly in the productin function estimates

but is recognized through the use of supplemental agronomic information

The demand and elasticity of demand for water are estimated from the

underlying production functions for each soil type.

CHAPTER 4

EMPIRICAL ANALYSIS— CROP RESPONSE MODELS

Production functions for wheat are derived for (1) evaporatran-

spiration models similar to those of Stewart et al. (1977), Minhas et

al. (1974), and Blank (1975); (2) a square-root function; (3) a Cobb

Douglas function; (4) a quadratic functions; and (5) the "best" crop

water functions for fine, medium and coarse soil textures in Arizona.

Empirical results -for cotton are derived for (1) a Cobb Douglas func­

tion; (2) a quadratic function; and (3) the "best" crop-water functions

for fine, medium, and coarse soil textures in Arizona. Detailed equa­

tion results are given for the "best" functions for each soil type,

but for brevity, only the highlights of other production functions

are described.

Evapotranspiration Models Applied to Wheat

Stewart

Stewart et al. (1977) offered two evapotranspiration models for

use in crop-water analysis.

Both were applied to aggregate wheat data

from Mesa for 1973, 1974, and 1975. Their S-l model can be utilized

when the amount of vegetative growth, temperature, and solar radiation

associated with each crop growth period is not of practical signifi­ cance. The model predicts crop yield as a function of evapotranspira­ tion without reference to individual growth stages.

35

36

Stewart et al.'s (1977) evapotranspiration model without growth stages is labeled model S-l and is: y m

where:

= Actual marketable yield in pounds per acre

= Maximum yield (in pounds per acre) attainable

according to the varietal genetics as modified by

climate, soil, and management

ETp = Evapotranspiration deficit = ET - ET ; seasonal

total depth in inches per acre

ET^ = Maximum evapotranspiration = the upper limit of ET^

= ET required to maximize yield; a seasonal total

depth in inches per acre

ET a

= Actual ET = ET(ASWP) + ET(R) + ET(IRR); all as

seasonal depths in inches per acre

ET(ASWP) = ET resulting from soil water already stored when

roots reset the profile layers concerned; a seasonal

depth in inches per acre

ET(R) = ET resulting from rainfall during the crop season;

a seasonal depth in inches per acre

ET(IRR) = ET resulting from IRR: a seasonal depth in inches

per acre

IRR

= Depth of irrigation water applied in specified time

period in inches per acre q

= A dimensionless slope that relates the decline in

Y^ per unit decrease in ET^.

Stewart et al.'s (1977) S-2 model shows yield to depend on evapotranspiration per growth stage:

where:

(evETD,v +

W .

p +

BMETp tM>

'

and subscripts v, p and M refer to the vegetative, pollination, and maturation periods, respectively.

ET ; ET

; ET M , and ETn = ET deficits anticipated in each

,V ’ three growth states and their sum.

Stewart et al.'s (1977) models based upon total evapotranspira­

tion (S-D and evapotranspiration broken into growth stages (S-2) failed

to provide usable functions with aggregated Mesa wheat data. The

coefficients of determination are only near .20.

Stewart et al. based the two models on corn production. The

model did not effectively transfer to Arizona wheat production.

Minhas

A crop response model by Minhas et al. (1974) is applied to

aggregated wheat data from Yuma Valley, 1970-71 and 1971-72; Yuma

Mesa, 1970-71 and 1971-72; and Mesa, 1970-71 through 1974-75.

Minhas' multiplication model is:

Y = a[l - (1 - X;L)2] bl[l - C l - x 2)2] b2 . . .

[1 - (1 x^)2] n where:

38

Y = crop yield in pounds per acre

= relative (i.e., fraction of maximum) ET in period j

a, b^, . . . bn = coefficients.

The coefficient of determination is .735. Some of the coeffi­

cients are statistically significant at the 10 percent level but fail

to show the expected sign.

Blank

Additive and multiplicative models by Blank (1975) are applied

to aggretated wheat data from Yuma Mesa and Yuma Valley for 1970-71 and

1971-72; and Mesa for 1970-71 through 1974-75.

Crop yield is a function

of evapotranspiration in three growth stages.

Blank's additive model is: max

= A.

1 ET maxi

+ A,

2 ET max2

+ A

3 EG max3

+ A, where:

Y

= actual crop yield in pounds per acre

Ymax = max^mum crop yield in pounds per acre

ETi = measured evapotranspiration (ET) in period i (1,2,3)

ETmax = maxilnuia evapotranspiration (ET) in period i (1,2,3)

A^ = a constant.

The coefficient of determination is .31.

The coefficient for

the ratio of the actual to the maximum evapotranspiration in the first

stage of growth (A^) is statistically significant only at the

39

50 percent level and showed an unexpected sign. The two other coeffi­ cients are statistically significant at the 1 percent level.

Blank's (1975) multiplicative model is:

Y

Ymax

EI1 ^ ET2

ETlmax ET2max

X2 ET- X3 ET.

3 4

ET.

3max

ET.

4max

X4

where:

Y = actual crop yield in pounds per acre

^max = max*-mum crop yield in pounds per acre

ET.

= measured evapotranspiration (ET) in period

1 (1,2,3,4) in inches

ET = maximum evapotranspiration (ET) in period maXi (1,2,3,4) in inches

A = a constant

= coefficients

The coefficient of determination is .25.

The ET coefficients

are not statistically significant or show unexpected signs.

Other Models Applied to Wheat

Square-root Model

Hexem and Heady (1978) recommended square-root functions for

crop-water analysis. The square-root function employed is

y = bo + *>1 VT + b 2 FERT + t>3 AWHC + bA EC + b5 PH + b6 EVAP

+ b? WT*5 + b g PERT*5 where:

40

Y = yield in pounds per acre

WT = total water applied to the crop in inches per acre

FERT = nitrogen applied in pounds per acre

AWHC = available water holding capacity in inches per foot

of soil

EC = electrical conductivity in mill! inches per cm at 25°C

PH = alkalinity/acidity ratio of the soil

EVAP = total pan evaporation for the season

b through b0 = coefficients,

o o

Wheat data for Yuma Valley for 1970-71 and 1971-72, Yuma Mesa

for 1970-71 and 1971-72, and Mesa for 1970-71 through 1974-75 were

aggregated for analysis with the square-root function. With soil fac­

tors included, the square-root function provided a coefficient of

determination of .76.

Total water applied failed to show the expected

sign and was statistically significant at the 10 percent level.

Other

variables are statistically significant with expected signs.

Cobb Douglas Model

The Cobb Douglas functional form is applied to aggregated wheat

data from Yuma Valley for 1970-71 and 1971-72, Yuma Mesa for 1970-71

and 1971-72, and Mesa for 1970-71 through 1974-75.

The Cobb Douglas function is: b0Hl

EVAP AWHC PERI where:

41

Y = crop yield in pounds per acre

W1 = water applied in the first stage in inches per

W2 = water applied in the second stage acre

W3 = water applied in the third stage in inches per

AVJHC = available water holding capacity in inches per foot of soil

EVAP = total pan evaporation for the season in inches per acre

FERT = nitrogen applied in pounds per acre

bg-b^ = coefficients.

The coefficient of determination is .68 with the log of total

evaporation not significant at the 10 percent level.

Other variables

are statistically significant at the 10 percent level and exhibit

expected signs.

Quadratic Models

A quadratic production function is used to evaluate wheat data

from Yuma Valley for 1970-71 and 1971-72, Yuma Mesa for 1970-71 and

1971-72, and Mesa for 1970-71 through 1974-75. Both squared and inter­ action terms are in the equation.

The interaction terms included water

applied in each stage interacting with (1) evaporation in that stage,

(2) water applied in another growth stage, and (3) total fertilizer

applied.

The equation is:

42

Y = bQ + b^Wl + b2W2 + b3W3 + b^FERT + b^Xl + bgX2 = byX3

= bgX4 + bgX5 + b1()X6 + b^^X7 + b12X8 + b^^XS + b^^XlO

+ b15EVAPl + b16EVAP2 + b^yEVAP3 + b^gPR + b^gEC + b^AWHC where:

Y =

W1 =

W2 =

W3 =

FERT = nitrogen applied in pounds per acre

EVAP1 = pan evaporation in stage 1 in inches per acre

EVAP2 = pan evaporation in stage 2 in inches per acre

EVAP3 = pan evaporation in stage 3 in inches per acre

AWHC = available water holding capacity of the soil in inches

EC = electrical conductivity of the soil in millimhos per

cm at 25°C.

PH = acidity/alkalinity ratio of the soil

XI = W1*W1

X2 = W2*W2

X3 = W3*W3

X4 = FERT*FERT

X5 = W1*EVAP1

X6 = W2*EVAP2

X7 = W3*EVAP3

X8 = W1*FERT

X9 = W2*FERT

X10 = W3*FERT

^ 0 ^ 2 0 = coefficients.

43

For wheat, equations with the interaction terms provided a

coefficient of determination of .83, and all variables show the expected

sign. Coefficients for AWHC, X3, X4, X7, W3, are statistically signifi­ cant at the 1 percent level.

Evaporation in the third stage (EVAP3), is

statistically significant at the 5 percent level. Water applied in the

second stage, W2, is statistically significant at the 10 percent level.

All other coefficients are not statistically significant at the 10 per­ cent level.

A quadratic equation is applied to Arizona wheat data from

Mesa for 1970-71 through 1974-75 and Yuma Mesa and Yuma Valley for

1970-71 and 1971-72.

The equation is:

Y = bn + b,W + b 0N + b-EVAP + b.AWHC + b cNIRR + b,W2 + b-,N2

U 1 Z j 4

j o 7

where:

Y = crop yield in pounds per acre

N = nitrogen applied in pounds per acre

W = total water applied to the crop in inches per acre

EVAP = total pan evaporation over the season in inches per acre

AWHC = available water holding capacity in inches

NIRR = number of irrigations applied to the crop

bg-by = coefficients

The coefficient of determination is .48. The number of irri­

gations is correlated with water (r = .46) and available water holding

capacity (r = .63). Coefficients not statistically significant at the

10 percent level include water, the number of irrigations, and water

44 squared. The number of irrigations failed to show the expected sign.

A quadratic function is derived from aggregated Arizona wheat

data from Mesa for 1970-71 through 1974-75 and Yuma, Mesa, and Yuma

Valley for 1970-71 and 1971-72. The equation is:

Y = b0 + b-jW + b2W 2 + b 3N + b^N2 + b^PH + bgHC + b^EVAP where:

Y = crop yield in pounds in wheat per acre

W = acre-inches of water applied and effective rainfall from

preplant irrigation until harvest

N = nitrogen applied in pounds per acre

AWHC = available water holding capacity of soil in inches

HC = hydraulic conductivity of soil in inches per hour

EC = electrical conductivity of soil in millimhos per

centimeter at 25° C.

EVAP = total pan evaporation for the season in inches

PH = ratio of alkalinity to acidity in the soil

bg-b^ = coefficients

The coefficient of determination is a respectable .77 with no

variables displaying unexpected signs. Several variables are not sig­ nificant at usually accepted levels.

The best aggregated production function for wheat is:

45

*** ** *** *** ***

Y = -74912.94 + 116.99W - 1.17W2 + 15.2N = .03N2 + 10204.37PH

(6152.3) (52.2) (.9) (2.0) (.006) (812.8)

*** ***

-1246.12HC - 100.8EVAP

(63.7) (22.4) where:

Y = crop yield in pounds per acre

W = acre inches of water applied and effective rainfall from

preplant irrigation until harvest

N = nitrogen fertilizer applied in pounds per acre

AWHC = available water holding capacity of soil in inches

HC = hydraulic conductivity of soil in inches per hour

EC = electrical conductivity of soil in millimhos per

centimeter at 25°C.

EVAP = total pan evaporation for the season in inches

PH = ratio of alkalinity to acidity in the soil

*** = coefficient is statistically significant at the 1

percent level

** = coefficient is statistically significant at the 5

percent level

* = coefficient is statistically significant at the 10

percent level, and numbers in parentheses are standard errors of the estimates.

The coefficient of determination is .77 with no variable dis­ playing unexpected signs.

The Best Crop-Water Production Functions for Wheat

Because of the lack of fit, multicollinearity, and other

problems associated with most of the previous attempts to estimate

46

production functions from data aggregated over sites, functions were

developed for each of three soil textures (fine, medium, and coarse)

found at the experimental sites.

Overall these disaggregated production

functions are the best, and are used in the later economic analysis.

The best regression equations are presented below for each soil class.

Standard errors are below the respective coefficients.

Fine-textured Soils

Data from Yuma Valley (1971 and 1972) and Safford (1972), where

fine-textured soils are found, is aggregated.

The quadratic equation

shown below was judged the best of all investigated in terms of coeffi­

cient of determination, expected signs, statistical significance, and

provision of logical estimates.

** *** *** ** ** ***

Y = -1265.7 + 387.OW - 3.7W2 + 5.8N - .02N2 - 80.4EVAP

(558.9) (26.8) (.25) (2.0) (.01) (7.9) where:

Y = crop yield in pounds of wheat per acre

W = acre inches of water applied and effective rainfall

from preplant irrigation until harvest

N = nitrogen applied in pounds per acre

EVAP = total pan evaporation for the season in inches

*** = coefficient is statistically significant at the 1

percent level

** = coefficient is statistically significant at the 5

* = coefficient is statistically significant at the 10 percent level.

47

2

The coefficient of determination (R ) is .769.

The coefficient

for nitrogen squared is statistically significant at the 5 percent

level.

All other coefficients are statistically significant at the 1

percent level. All coefficients show the expected sign.

Medium-textured Soils

Yield-water data for wheat for 1973 through 1975, from the

medium-textured soil area of Mesa, are fitted with a quadratic equation.

The equation is:

** * *** **

Y = 1656.785 + 431.793W - 6.358W2 + 18.488N - .031N2 - 29.904EVAP

(2953.85) (186.27) (3.22) (5.08) (.01) (38.58) where:

Y = crop yield in pounds of wheat per acre

W = acre inches of water applied and effective rainfall

from preplant irrigation until harvest

N = nitrogen applied in pounds per acre

EVAP = total pan evaporation for the season in inches

*** = coefficient is statistically significant at the

1 percent level

** = coefficient is statistically significant at the

5 percent level

* = coefficient is statistically significant at the

10 percent level.

2

The coefficient of determination (R ) is .67.

The coefficient

for nitrogen is statistically significant at the 1 percent level.

The

coefficients for water and nitrogen squared are statistically signifi­ cant at the 5 percent level. The coefficient for water squared is

48

statistically significant at the 10 percent level. The coefficient

for pan evaporation is statistically significant at the 50 percent

level. All coefficients show the expected sign.

Coarse-textured Soils

Yield-water data for wheat for 1971 and 1972, from the coarse-

textured soil area of Yuma Mesa, are best fitted with a three halves or

1.5 polynomial equation. The equation is:

*** ** ** ***

***

_

Y = 12803.008 + 372.87W - 44.014W1,5 + 15.237N

- 1.368N1,5

(1826.44)

***

(143.98)

***

(19.06) (5.47) (.32)

+ .571WN - 424.168EVAP

(.11) (51.09) where:

Y = crop yield in pounds of wheat per acre

W = acre inches of water applied and effective rainfall

from preplant irrigation until harvest

N = nitrogen applied in pounds per acre

EVAP = total pan evaporation for the season in inches

WN = water applied times nitrogen applied

*** = coefficient is statistically significant at the

1 percent level

** = coefficient is statistically significant at the

5 percent level

* = coefficient is statistically significant at the

10 percent level.

2

The coefficient of determination (R ) is .77.

The coefficients

for water applied and water to the three halves are statistically

significant at the 5 percent level. All variables show the expected

sign.

49

Evapotranspiration Models Applied to Cotton

Evapotranspiration models are not used in analysis of the cotton

data.

Climatic data, necessary inputs to the models, are not available

for both Yuma Mesa and Yuma Valley, two of the three sites, despite

obvious climatic differences.

The small sample size of 3 site-years

(compared to 9 with the wheat experiments) accentuated the difficulty

of estimation.

Other Models Applied to Cotton

Cobb Douglas Model

The Cobb Douglas model uses aggregated data from Yuma Valley,

Yuma Mesa, and Tempe for 1970-71.

The coefficient of determination is

.66, but only one independent variable is statistically significant at

the 10 percent level or better.

Quadratic Models

Various quadratic models, similar to the quadratic models of

wheat production in form and independent variables, were estimated from

the aggregated wheat data. Although the coefficients of determination

tended to be high, often around .85, many key variables were not

statistically significant, or had unexpected signs.

In many cases high

multicollinearity appeared to cause statistical problems.

50

The Best Crop-Water Production Functions for Cotton

Again multicolliniarity and other problems suggested that separ-

arate equations be run for each of the three soil types— fine, medium,

and coarse. Equation results follow.

Fine-textured Soils

Yield-water data for cotton for 1971 from the fine-textured

soil areas of Yuma Valley and Safford are fitted with a three halves

equation:

Y

***

***

***

-1313.961 + 77.641W -

(380.05) (19.12)

(2.08)

***

(.8)

***

**

.203N1 *5 + 13.25EVAP

(.05) (5.5) where:

Y = crop yield in pounds of cotton lint per acre

W = acre inches of water applied and effective rainfall

from preplant irrigation until harvest

N = nitrogen applied in pounds per acre

EVAP = total pan evaporation for the season in inches

*** = coefficient is statistically significant at the

1 percent level

** = coefficient is statistically significant at the

5 percent level

*

= coefficient is statistically significant at the

10 percent level.

2

The coefficient of determination (R ) is .94. The coefficient

for evaporation is statistically significant at the 5 percent level.

The coefficients for all other variables are statistically significant at the 1 percent level. All coefficients show the expected sign.

Medium-textured Soils

Yield-water data for cotton from Phoenix (1975 and 1976) and

51

Tempe (1971), areas of medium-textured soils, are fitted with a

quadratic equation.

*** *** *** ***

Y = 2845.254 + 74.468W - .587W2 - 40.95EVAP

(467.04) (13.9) (.17) (5.40) where:

Y = crop yield in pounds of cotton lint per acre

W = acre inches of water applied and effective rainfall

from preplant irrigation until harvest

N = nitrogen applied in pounds per acre

EVAP = total pan evaporation for the season in inches

*** = coefficient is statistically significant at the

1 percent level

** = coefficient is statistically significant at the

5 percent level

* = coefficient is statistically significant at the

10 percent level.

2

The coefficient of determination (R ) is .85.

The coefficients

for all of the variables are statistically significant at the 1 percent

level. All coefficients show the expected sign.

Coarse-textured Soils

Yield-water data for cotton for 1971 from the coarse-textured

soil area of Yuma Mesa are fitted to a square root equation:

** *** *** *** ***

Y = 7209.473 - 135.807W + 2006.207W*5 - 5.341N + 106.818N*5 + .04WN

(2532.92) (40.91) (651.97) (1.72) (51.17) (.11)

where:

Y = crop yield of cotton ling in pounds per acre

W = acre inches of water applied and effective rainfall

from preplant irrigation until harvest

N = nitrogen applied in pounds per acre

EVAP = total pan evaporation for the season in inches

*** = coefficient is statistically significant at the

1 percent level

** = coefficient is statistically significant at the

5 percent level

* = coefficient is statistically significant at the

52

2

The coefficient of determination (R ) is .66.

The coefficient

for the square root of nitrogen is statistically significant at the 10

percent level. All other coefficients were statistically significant

at the 1 percent level. All coefficients show the expected sign.

CHAPTER 5

EMPIRICAL RESULTS— ECONOMIC ANALYSIS

The "best" production functions of the previous chapter are used

to estimate first the profit maximizing quantity of water and, second,

the demand and elasticity of demand for water for each crop and each

soil type.

Four comparisons of the profit maximizing level of water,

estimated from the soil specific production functions, are made.

First, they are compared with similar estimates based upon the "best"

aggregate (over time and location) production functions.

Second,

profit maximizing levels of water are compared to the most common

level of water application as indicated by Arizona extension agents.

Third, they are compared to the yield maximizing level of water appli­ cation.

Fourth, they are compared to predictions of site specific and

aggregate (over sites) models of Hexem and Heady (1978). The yield

maximizing level of water application is of particular interest because

most irrigation management services, including government agencies,

base their recommendations upon yield maximizing criteria.

Typically,

recommendations are to irrigate enough in all stages of plant growth

to avoid stress.

The sensitivity of profit maximizing water levels and elastici­

ties to the sources of water (300- and 600-feet well lift depths and

surface water), water price (current, 50 percent and 100 percent above

53

54

current), and crop prices (expected low, medium, and high) is also

estimated.

Estimates of the profits maximizing level and number of irriga­

tions is a two-step process. First, the profit maximizing level of

water is estimated by equating the MVP of water to its price. The

number of irrigations is then determined from outside agronomic infor­ mation as discussed in the previous chapter.

Wheat

Profit Maximizing Quantity and Number of Irrigations

The profit maximizing levels of water and number of irrigations,

by water source, water price, and wheat price are shown for fine-,

medium-, and coarse-textured soils in Tables 5, 6, and 7.

Estimates

are based on the soil texture models previously presented. Notable

features of the estimates may be summarized.

(1) For all soil types,

a combination of low product prices and high water prices (50-100 per­

cent increase in the price of electricity for the 600-foot lift)

results in wheat going out of production.

(2) For all soil types, the

profit maximizing level of water appears to decrease fairly substanti­

ally as the price of water increases substantially among water sources.

For example, on fine-textured soils at a 1979 price of surface water of

$.46/acre-inch, the profit maximizing level of water is 49 acre-inches,

but at 1979 electricity prices and a 600-foot pump lift, the optimum

level of water is only 20 acre-inches.

(3) For all soil types and for

surface water situations, the price of water is so low that even

doubling its price has almost no impact on the profit maximizing amount

55

Table 5. Profit-maximizing Quantity of Water and Number of Irrigations at Different Wheat and Water Prices for Wheat Raised on Finetextured Soil

Water Source and

Price Situation

Price of

Water

$/acre-in.

Surface

Expected 1979 price $0.46

50% increase

100% increase

.69

.92

300-foot Lift

Expected 1979 price 2.77

50% increase in price

of electricity 4.06

100% increase in price

of electricity 5.35

600-foot Lift

Expected 1979 price 5.52

50% increase in price

of electricity 8.08

100% increase in price

of electricity 10.65

Wheat Prices

-----------------------------------

Low Medium High

($.0235/lb) ($.0525/lb) (.065/lb)

— acre-in. (number of irrigations)—

49

48

46

36

29

21

20

6

0

(7)

(7)

(7)

(5)

(4)

(3)

(2)

(0)

(0)

50

49

49

45

41

38

38

31

24

(7)

(7)

(7)

(6)

(6)

(5)

(5)

(4)

(3)

51

50

50

46

43

41

40

35

30

(7)

(7)

(7)

(7)

(6)

(6)

(6)

(5)

(4)

56

Table 6. Profit-maximizing Quantity of Water and Number of Irrigations at Different Wheat and Water Prices for Wheat Raised on

______ Medium-textured soil____________________

Price of

Price of Wheat ($/lb)

-----------------------------------

Water Source and Water Low Medium

Water Price situatin $/acre-inch ($.0235/lb) ($.0525/lb)

High

($.065/lb)

--acre-in (number of irrigations)—

Surface

Expected 1979 price

50% increase

100%

.46

.69

.92

300-foot Lift

Expected 1979 price 2.77

50% increase in price

of elictricty 4.06

100% increase in price

of electricity 5.35

32

32

31

25

20

16

(4)

(4)

(4)

(3)

(2)

(2)

33

33

33

30

28

26

(5)

(4)

(4)

(4)

(4)

(3)

33

31

29

28

(5)

33 (5)

33

(4)

(4)

(4)

(4)

600-foot Lift

Expected 1979 price

5.52

50% increase in price

of electricity 8.08

100% increase in price

of electricity 10.65

'

16

7

(2)

(0)

(0)

26

22

18

(4)

(3)

(2)

27

24

21

(4)

(3)

(3)

57

Table 7. Profit-maximizing Quantity of Water and Number of Irrigations at Different Wheat and Water Prices for Wheat Raised on

Coarse-textured Soil

Water Source and

Price Situation

Wheat Prices

Price of

----------------------------------

Low Medium High

Water ($.0235/lb) ($.0525/lb) ($.065/lb)

$/acre-in

— acre-in(number of irrigations)—

Surface

Expected 1979 price

50% increase

100% increase

.46

.69

.92

300-foot Lift

Expected 1979 price 2.77

50% increase in price

of electricity 4.06"

100% increase in price

of electricity 5.35

600-foot Lift

Expected 1979 price 5.52

50% increase in price

of electricity 8.08

100% increase in price

of electricity 10.65

45

43

41

27

19

12

12

3

0

(8)

(7)

(7)

(4)

(3)

(1)

(1)

(0)

(0)

47

46

45

38

34

29

29

22

14

(8)

(8)

(8)

(7)

(6)

(5)

(5)

(3)

(2)

47

46

46

40

36

33

32

26

20

(8)

(8)

(8)

(7)

(6)

(6)

(5)

(4)

(3)

58 used— no matter the price of wheat.

(4) For all soil types and for

both pump lift depths, profit maximizing water use decreases by at

least one-third as the price of electricity doubles, and (5) there is a

very sizable difference in the optimum amount of water to apply depend­ ing on soil type.

Comparison of Soil Texture Models with Other Models

The profit maximizing level of water use under conditions of

medium wheat prices and expected 1979 water prices shown in Tables 5,

6, and 7, are compared with water use projected by various other models.

Comparisons are made with the profit maximizing level of water predicted

by the aggregate (over soil types and time) wheat model, with the common

practice amount of water applied, with a yield maximizing model, and

with the profit maximizing level of water estimated from site specific

and aggregate (over sites) models of Hexem and Heady.

Comparisons are

shown in Table 8.

Comparison with Aggregate Models.

If the results for models

of particular soils are nearly equal to those of the aggregate model,

then the applicability of the generalized aggregate functions is veri­ fied: otherwise analysis for particular soil types should rely on production functions for those particular textures.

The profit maximizing level of water for each soil type, the

medium wheat price, and for .the expected 1979 price of surface, 300-

foot lift and 600-foot lift water is shown in Table 8.

2

2

The aggregate model has approximately the same R (R = .77) as

the soil texture models, but it fails to distinguish among soil types in

59

Table 8. Water Applications Implied by the Six Wheat "Models" for

Soils of Different Texture, Medium Wheat Price

Water Source and Model

Surface

Soil Texture

Aggregate

Common Practice

Yield-maximizing ^

Hexem and Heady Site

Hexem and Heady Aggregate

^

300-foot Lift

Soil Texture

Aggregate

Common Practice

Yield-maximizing ^

Hexem and Heady Aggregate

^

600-foot Lift

Soil Texture

Aggregate

Common Practice

Yield-maximizing ^

Hexem and Heady Site

Hexem and Heady Aggregate

^

Expected

1979

Price of Water

$/acre-in.

$0.46

2.77

5.52

50

47

52

32

148

45

28

52

30

84

38

5

52

28

46

Fine

39-50

39-50

39-50

Soil Texture

Medium

33

47

36-40

34

26

198

30

28

36-40

34

25

94

26

5

36-40

34

23

46

Coarse

-- — — acre-in.-- — — ————

47

47 a

72-84*

49

44

148

38

28 a

72-84

49

36

94

28

5 a

72-84

49

26

46

a. Yuma Mesa is the only site in Arizona with coarse-textured soil,

and almost no wheat has been grown on Yuma Mesa for the past 5 years.

Hazlitt (1979) estimates 72-84 acre-inches of water are required to

produce wheat.

b. Models used in computations are from Hexem and Heady (1978,

pp. 106, 115, 116, 181, and 182).

60 profit maximizing computations. As shown in Table 8, there is fre­

quently a very considerable difference between the profit maximizing

levels of water projected from the soil texture model versus the aggre­ gate model.

Since agronomic information suggests that soil texture does

affect wheat yield, the better of the models are the soil texture • models.

Comparison with Common Practice. The most common level of

water application in the county represented by each soil texture is

given in Table 8.

The common practice levels are based upon estimates

of county extension specialists who survey farmers (Hathorn and

Armstrong, 1979; Hathorn and Cluff, 1979; Hathorn and Farr, 1979;

Hathorn et al., 1979; and Hathorn, Liddle, and Stedman, 1979)

For the fine-textured soils, such as those found in the Yuma

Valley and Safford areas, common practice may not be greatly different,

at low and medium water prices, than the profit maximizing level

projected from the soil texture model.

At higher water prices, however,

the spread widens. For the other two soil textures, there is often a

considerable difference between common practice and the level of water

suggested by the soil texture model.

The difference is often more than

6 inches, an amount which would account for at least one irrigation.

Comparison with Yield Maximizing Models.

Several agencies of

the U. S. Government, including the Bureau of Reclamation, the Salt

River Project, and the Extension Service, plus various private firms,

offer irrigation management services. In general, their recommendations

61 are designed to avoid plant stress and thereby maximize yield. Consid­

erable literature exists that details the consumptive use of particular

crops under particular soil and climatic conditions when water is

readily available. Most irrigation management services then try to

match the actual water consumption to potential water consumption of

the plants.

Estimates of the yield maximizing amount of water which irriga­

tion management services, using usual criteria, would recommend may be

made from the soil specific production functions.

These estimates are

given in Table 8.

The estimates show that the profit maximizing and

yield maximizing levels of water are nearly the same at the very low

water price, but at expected 1979 water prices for both the 300- and

600- foot lifts, there is generally a 6-inch or greater difference.

For the medium and expensive water then, the results suggest that at

least one irrigation could often be avoided if attention is paid to

the profit maximizing versus yield maximizing level.

Comparison with Hexem-Heady Models. Much of the data used in

the current analysis is taken from the agronomic experiments originally

organized and analyzed by Hexem and Heady (1978) and reported in their

book and other publications.

The current study differs from theirs

in that additional years of data are obtained from some of the experi­

mental sites, separate models are estimated based upon soil texture,

which provides a better representation of the data than Hexem and

Heady's aggregate models, and alternative functional forms and variable

specifications are investigated.

62

For the fine textured soil, the profit maximizing level of

water predicted with the Hexem and Heady site specific model is consid­

erably lower than the soil texture model. For the medium and coarse

texture soils, results from the two models are not greatly different.

The aggregate model (over sites) of Hexem and Heady does not provide

realistic estimates for any. soil type.

Demand and Elasticity of Demand for Water

Normative demand curves for water and associated elasticities

help illustrate the effect of rising water prices on irrigation water

use. Although the demand relationship is implicit in the profit tables

given earlier, actual demand schedules and computed elasticities of

demand provide a sharper portrayal of the effect of price changes on

water use.

Of course, projections of actual changes in water use must

be hedged, because the demand equations are normative in the sense that

they predict what the water use will be if farmers maximize profits and

if only a single crop is considered.

The demand schedules, derived from the production functions by

soil type, are shown in Figure 8. For illustration, the schedules have

been constructed for the 600-foot lift and a medium price of wheat.

Given the assumptions, the demand schedule indicates the amount of water

used per acre of wheat as the price of water changes. Figure 8 shows,

for example, that if the price of water is $5.52 per acre inch, approxi­

mately 38 acre inches of water will be applied per acre on fine-textured

soil planted to wheat.

Coarse

Texture

Medium

Texture

Soil

Fine

Texture

•H <3

28 32

Acre Inches of Water

Figure 8.

Short-run Normative Demand Curves for Water

in the Production of Wheat by Soil Type,

600-foot lift; Price of Output, $,0525/lb,

64

The responsiveness of the quantity of water demanded to changes

in water price is perhaps best shown through elasticities.

Elasticities

show the percentage change in quantity demanded with a 1 percent change

in price. Demand is said to be elastic if the elasticity is greater

than one, of unitary elasticity if equal to one, and inelastic if less

than one. Table 9 shows the arc and point elasticity of demand for

water in the production of wheat by water source, water price, output

price, and soil texture.

For each water source, the arc elasticities are computed over

the demand schedule from the 1979 expected price to a price which

reflects a 100 percent increase in the price of electricity or, in the

case of surface water, a 100 percent increase in its price. As an

example, the arc elasticity of demand for surface water on fine soils

is computed over the price range of $.46 per acre inch to $.92 per

acre-inch on fine soils.

The elasticity of .09 for surface water and

low wheat prices indicates that on average, a 1 percent change in the

price of water will result in only a .09 percent change in quantity demanded. That is, demand under these conditions is very inelastic.

The estimates indicate that for all soil types, for all product

price levels, and for both-surface and water pumped from 300 feet, the

demand for water is very inelastic.

Only at the deep lift depths is the

demand for water substantially affected by price rises— and even in this

case the effect may be exaggerated because a large price increase (100

percent) is assumed from an already high base level ($5.52 per acre-

inch).

The point elasticity of demand at $5.52 per acre-inch of water

for the three soil types and for each output price level is greater than

one at the low output price on all 3 soil textures.

65

Table 9. Arc and Point Elasticity of Demand for Water in the Produc­ tion of Wheat

Soil Texture and

Water Source

Price Range

($/acre-in.)

Low

($.0235/lb)

Price of Wheat

Medium

($.0525/lb)

High

($.065/lb)

Arc Elasticity

Fine

Surface

300-foot Lift

600-foot Lift

Medium

Surface

300-foot Lift

600-foot Lift

Coarse

Surface

300-foot Lift

600-foot Lift

$0.46-$0.92

$2.77- 5.35

$5.52-$10.65

$0.46-$.92

$2.77-$5.35

$5.52-$10.65

$0.46-$0.92

$2.77-$5.35

$5.52-$10.65

0.09

.82

3.22

.05

.69

4.03

.14

1.20

3.20

0.03

.26

.73

.03

.22

.59

.06

.42

1.12

0.03

.18

.46

.00

.16

.40

.03

.30

.74

Point Elasticity

Fine

600-foot Lift

Medium

600-foot Lift

Coarse

600-foot Lift

$5.25

$5.25

$5.25

1.60

1.19

2.09

.38

.32

.61

.28

.24

.45

66

Water Quantity Restrictions

Water policy may call for restricted water use. The soil tex­

ture models are here used to estimate the change in returns over total

variable cost for wheat production should water use be cut to 90 and

80 percent of the profit maximizing level.

For brevity, a medium price

of wheat is assumed. The estimates are shown in Table 10.

The most notable findings are:

(1) Variable costs are greater

than returns for all soil types and for all water applications at a

600-foot lift.

(2) If fixed costs are assumed to be $90 per acre, a

reasonable figure, then in the long run only wheat irrigated with sur­ face water is economically viable. And (3), for surface water situa­

tions, assuming fixed costs of $90 per acre, profits (returns to

management and risk) are cut from 20 to 100 percent as water is

decreased to 80 percent of the profit maximizing level.

Cotton

Profit Maximizing Quantity and

Number of Irrigation-Cotton

Tables 11, 12, and 13 show the profit maximizing level of water

to apply by fine, medium, and coarse soil texture, respectively. Again,

estimates are based on the soil texture models presented earlier.

Levels are also shown to depend on the source and price of water, and

upon the price of cotton.

The most notable results are as follows:

1. For all soil types, as the price of water increases greatly

between surface and 600-foot lift situation, and when product

67

Table 10. Water Restrictions and Change in Returns over Total Variable

Costs for Wheat, Water Cut to 90 and 80 Percent of Profit

Maximum Level, Medium Price of Wheat3

Water Source and

Restrictions

Price of

Water

($/acre-in.) Fine

Soil Texture

Medium Coarse

Surface

Returns over TVC at profit

maximum

Change in returns over TVC

at water cut to 90% of

profit maximum level

Change in returns over TVC

at water cut to 80% of

profit maximum level

300-foot Lift

Returns over TVC at profit

maximum

Change in returns over TVC

at water cut to 90% of

profit maximum level

Change in returns oyer TVC

at water cut to 80% of

profit maximum level

$0.46

$2.27

600-foot Lift

Returns over TVC at profit

maximum

Change in returns over TVC

at water cut to 90% of

profit maximum level

Changes in returns over TVC

at water cut to 80% of

profit maximum level

$5.52

$197

- 6

- 22

$108

- 5

- 19

- 27

- 2

$102

- 5

— 16

43

- 4

- 14

- 49

- 2

$147

- 3

- 10

67

- 4

- 12

- 44

- 2

- 10

- 8

- 13

a. A rough estimate of fixed costs (including those for machinery,

well depreciation, general farm maintenance, taxes on land, and interest

on land) for a wheat farm in Graham County, Arizona, 1979, are $90 per

acre (Hathorn and Cluff, 1979).

Table 11. Profit-maximizing Quantity of Water and Number of Irrigations

at Different Cotton and Water Prices for Cotton Raised on

Medium-textured Soil.

Water Source and

Price Situation

Price of

Water

----------------------------------

Low

($.31/lb)

Cotton Prices

Medium

($.62/lb)

High

($.75/lb)

$/acre-in — acre-in. (number of irrigations)

Surface

Expected 1979 price

50% increase

100% increase

.46

.69

.92

62

51

60

(9)

(9)

(9)

63

63

62

(10)

(10)

(9)

63

63

62

68

(10)

(10)

(9)

300-foot Lift

Expected 1979 price

50% increase in price

of electricity

2.77

4.06

100% increase in price

of electricity 5.35

600-foot Lift

Expected 1979 price

50% increas in price

of electricity

5.52-

8.08

100% increase in price of electricity 10.65

51

45

39

38

29

20

(7)

(6)

(6)

(5)

(4)

(2)

57

54

51

51

45

39

(9)

(8)

(8)

(7)

(6)

(6)

59

55

53

53

48

43

(9)

(8)

(8)

(8)

(7)

(6)

69

Table 12. Profit-maximizing Quantity of Water and Number of Irrigations

at Different Cotton and Water Prices for Cotton Raised on

Medium-textured Soil.

Water Source and

Price Situation

Cotton Prices

Price of

Water

Low

($.31/lb)

Medium

($.62/lb)

High

($.75/lb)

$/acre-in — Acre in.(Number of irrigations)

Surface

Expected 1979 price

50% increase

100% increase

.46

.69

.92

300-foot Lift

Expected 1979 price 2.77

50% increase in price

of electricity 4.06

100% increase in price

of electricity 5.35

600-foot Lift

Expected 1979 price 5.52

50% increase in price

of electricity 8.08

100% increase in price

of electricity 10.65

62

62

61

56

52

49

48

41

34

(9)

(9)

(9)

(8)

(8)

(7)

(7)

96)

(5)

63

63

62

60

58

56

56

52

49

(9)

(9)

(9)

(9)

(9)

(8)

(8)

(8)

(7)

62

62

62

60

59

57

57

54

51

(9)

(9)

(9)

(9)

(9)

(9)

(9)

(8)

(8)

70

Table 13. Profit-maximizing Quantity of Water and Number of Irrigations at Different Cotton and Water Prices for Cotton Raised on

Coarse-textured Soil.

Water Source and

Price Situation

Cotton Prices

P r i c e -----------------------------— — — --of

Water

Low

($.31/lb)

Medium

($.62/lb)

High

($.75/lb)

$/acre in.

— acre-in. (number of irrigations)

Surface

Expected 1979 price .46

.69

50% increase

100% increase .92

300-foot Lift

Expected 1979 price 2.77

50% increase in price

of electricity 4.06

100% increase in price

of electricity 5.35

600-foot Lift

Expected 1979 price 5.52

50% increase in price

of electricity 8.08

100% increase in the price of electricity 10.65

64

64

63

57

54

51

50

45

40

(12)

(12)

(12)

(10)

(10)

(9)

(9)

(8)

(7)

65 (12)

65

64

61

60

58

57

54

40

(12)

(12)

( I D

( I D

( I D

(10)

(10)

( 9)

65

65

65

62

60

59

39

56

53

(12)

(12)

(12)

( I D

( I D

(11)

( I D

(10)

(10)

71

prices are low to medium, there is a large difference in the

optimum aount of water to apply.

In general, there is a

decrease of two or more irrigations. At high product prices,

the profit maximizing levels of water tend to show much smaller

differences between low and high priced water.

2. For all soil types and using surface water, there is virtually

no difference in the profit maximizing level of water to apply,

no matter the price of cotton, the percentage increase in the

price of water, or soil type.

The amount of water to apply is

simply 62-65 acre inches, although the number of irrigation is

dependent upon soil type.

3.

Increases in the price of electricity from 50 to 100 percent,

and hence in the price of pumped water, results in varying

degrees of water use adjustment.

In these pumping cases, both

soil type and product price have a significant effect on the

amount of adjustment.

Comparison of Soil Texture Models with Other Models

The profit maximizing level of water, as predicted from the soil

texture models and given in Tables 11, 12, and 13. are compared with

water application suggested by the aggregate model, common practice,

the yield maximizing model, and two Hexem and Heady (1978) models.

Predictions assume a medium price for cotton ($.62 total value if lint

and seed per pound of lint), and the 1979 expected price of water for

each source.

Comparisons of water application by model, soil type, and

water source are shown in Table 14.

72

Tablet 14. Water Applications Implied by Six Cotton "Models" for

Soils of Different Texture, Medium Cotton Price

Expected

1979

Price of Water

Soil Texture

Water Source and Model Fine Medium

--- acre-in.--

Coarse

Surface

Soil Texture

Aggregate

Common Practice

Yield-maximizing ^

Hexem and Heady Site

Hexem and Heady Aggregate

^

$/acre-in.

$0.46

63

66

48—60

65

60

74

63

66

42—60

64

37

74

65

66 a

72-84

66

58

74

300-foot Lift

Soil Texture

Aggregate

Common Practice

Yield-maximizing ^

Hexem and Heady Site

Hexem and Heady Aggregate

^

2.27

57

61

48—60

65

57

65

60

61

42-60

64

37

65

62

61 *

72-84a

66

56

65

600-foot Lift

Soil Texture

Aggregate

Common Practice

Yield-maximizing ^

Hexem and Heady Site

Hexem and Heady Aggregate

^

5.52

51

55

48-60

65

52

55

56

55

42-60

64

37

37

59

55 a

72-84

66

51

55

a. Yuma Mesa is the only site in Arizona with coarse-textured soil,

and almost no cotton has been grown on Yuma Mesa for the past 5 years.

Hazlitt (1979) estimates 72-84 acre-inches of water are required to

produce cotton.

b. Models used in the computations are from Hexem and Heady (1978,

pp. 134, 135, and 182).

73

Comparison with the Aggregate Model. The "best" aggregate equa-

2

tion, given earlier, had an R of .85. For each soil type and each

water source-price situation, the profit maximizing levels of water, as

estimated from the two models, are within 4 acre inches of each other.

For cotton then, the aggregate model appears to work well across soil

types.

Comparison with Common Practice.

In general, the commonly

applied amounts are not greatly different than the profit.maximizing

levels.

Comparison with Yield Maximizing Models.

Only at the highest

water price, i.e., that for the 600-foot lift, is there a notable

difference between the profit maximizing and yield maximizing quantity

of water to apply.

Comparison with Hexem-Heady Models. For fine soils, the soil

texture model and the Hexem-Heady model gave very similar results.

For the medium-textured soil, the Hexem-Heady model is greatly different

and projections from their models are unreasonable.

For coarse soils,

the results are similar although the Hexem-Heady model estimates about

a 6-inch lower amount of water to maximize profits. Their aggregate

model predicts nearly a foot more surface water, but similar amounts of

pump water for profit maximization.

Demand and Elasticity of Demand for Water

Normative demand schedules for cotton produced on fine, medium,

and coarse soils, with all the assumptions attendant to the demand

equation for wheat, are shown in Figure 9.

The curves indicate that

74

there is not a great deal of difference among soil types in the demand

for water as the price of water increases.

Arc elasticities of demand by water source, water price, output

price, and soil texture are given in Table 15. Arc elasticities for

each water source are again computed for the range between the 1979

expected price and the price when energy costs increase 100 percent.

The estimates indicate that for all soil types, all output

prices, and all water sources, except one, demand for water is inelastic.

Only for a situation of low cotton price and deep water lifts is the

elasticity of demand at one.

Similar to wheat, this arc elasticity

is taken over a range of very high water prices. The point elasticity

at the 1979 expected price of water for the 600-foot lift is between

.02 and .83, depending on soil type.

Water Quantity Restrictions

The effect on profits of cutting water applications to 90 and

80 percent of the profit maximizing level is shown in Table 16.

The

estimates indicate that with a posited fixed cost of $230 per acre,

profits (returns to management and risk) are very high for fine and

medium soils for all water source situations.

However, for all soils

and all water sources, a reduction in water availability to 80 percent

of the profit maximizing level reduces profits by $20 to $55 per acre—

a rather substantial amount.

Fine

Texture

Soil

Medium

Texture

Soil

40 42 44 46 48 50 52 54 56 58

Acre Inches of Water

Figure 9.

Short-run Normative Demand Curves for Water

in the Production of Cotton by Soil Type,

600-foot lift, Price of Output, $.62/lb. of

Lint

Table 15. Arc and Point Elasticities of Demand for Water in the

Production of Cotton, by Water Source, Water Price, Output

Price, and Soil Textures.

76

Price of Cotton

Low

($.30/lb)

Medium

($.62/lb)

High

($.75/lb)

Soil

Texture Water Source

Fine:

Arc Elasticity

Surface

300-foot Lift

600-foot Lift

Point Elasticity

for 600-foot Lift

at

Medium:

Arc Elasticity

Surface

300-foot Lift

600-foot Lift

Point Elasticity

for 660-foot Lift

at

Coarse:

Arc Elasticity

Surface

Price Range

$/acre-inch

0.46-0.92

2.77- 5.3:

5.52-10.65

5.52

0.46- 0.92

2.77- 5.35

5.52-10.65

5.52

300-foot Lift

600-foot Lift

Point Elasticity

for 600-foot Lift

at

0.46- 0.92

2.77- 5.35

5.52-10.65

5.52

.05

.42

1.00

.59

.02

.21

.55

.31

.02

.17

.36

.24

.02

.17

.43

.26

.02

.11

.21

.14

.02

.08

.18

.13

.02

.17

.34

.22

.00

.08

.18

.11

.00

.08

.17

.11

j

77

Table 16 Water Restrictions and Change in Returns over Total Variable

Costs for Cotton, Water Cut to 90 and 80 Percent of Profit

Maximum Level, Medium Price of Cotton3

Water Source and

Restrictions

Price of

Water

($/acre-in.) Fine

Soil Texture

Medium Coarse

Surface

Returns over TVC at profit

maximum

Change in returns over TVC

at water cut to 90% of

profit maximum level

Change in returns over TVC

at water cut to 80% of

profit maximum level

300-foot Lift

Returns over TVC at profit

maximum

Change in returns over TVC

at water cut to 90% of

profit maximum level

Change in returns over TVC

at water cut to 80% of

profit maximum level

600-foot Lift

Returns over TVC at profit

maximum

Change in returns over TVC

at water cut to 90% of

profit maximum level

Change in returns over TVC

at water cut to 80% of

profit maximum level

$0.46

$2.27

$5.52

$603

— 8

- 34

489

- 11

- 32

312

- 5

$610

- 16

- 58

495

- 15

- 55

306

- 11

$284

- 14

- 55

170

- 13

- 55

- 25

- 5

- 20 — 44

- 33

a. A rough estimate of fixed costs (including those for machinery,

well depreciation, general farm maintenance, taxes on land, and interest

on land) for a cotton farm in Graham County, Arizona, 1979, are $230 per

acre (Hathom and Cluff, 1979).

j

CHAPTER 6

IMPLICATIONS

The results of the previous chapter are used here to draw

implications for farm level irrigation management, government policy

with respect to water conservation, and needed irrigation research.

Farm Management

Several farm level implications may be summarized. For wheat

production, (1) there is a significant difference in the profit maxi­

mizing level of water to apply as the price of water goes from the

lowest (surface water) to the highest (600-foot lift) price.

(2) It is

not profitable to produce wheat in deep lift areas.

This conclusion

corresponds to an observed sharp decrease in wheat production in deep

lift areas of the state.

(3) In surface water areas, even doubling

the price of water will not change the profits maximizing level of water

use by any significant (6 inches or more) amount. And (4) there is a

great difference in the profit maximizing level of water to apply

depending upon soil type.

For cotton production, the principle management implications

are that (1) there is a significantly large difference (6 inches or

more) in the profit maximizing level of water to apply between the

lowest and highest priced water (except in the case of very high product

prices). However, (2) only at the highest water prices is there a

notable difference between the profit and yield maximizing levels of

78

79 water case.

(3) Even doubling the price of surface water does not

significantly alter the optimal amount of water to apply.

And, (4) a

50-100 percent increase in the price of electricity results in varying

degrees of water use adjustment, depending on both soil type and product

prices.

Water Conservation Policy

Water conservation is an important policy goal by several

levels of government.

Results from the economic analysis may be used

to draw implications for water conservation policy. For wheat produc­ tion, (1) the demand for water tends to be very inelastic, and there­

fore marginal changes in the institutional price of water will not

significantly decrease water use.

(2) The price of water on several

irrigation projects administered by government agencies is so low that

even doubling the price of water will not lead to meaningful (6 inches

or more) decreases in water use. Water prices would need to increase

several-fold to significantly reduce water applications on wheat.

(3) There is a significant difference between the profit maximizing and

yield maximizing level of water to apply for medium and high priced

water.

Government agencies which provide irrigation management services

to farmers should recognize this difference, and base water recommenda­ tions on economic rather than traditional yield maximizing criteria.

And (4) should government policy restrict the quantity of water used to

90-80 percent of the profit maximizing level, profits per acre of wheat

will be cut 20 to 100 percent, depending on the magnitude of the

restriction and soil type.

w ..

80

For cotton production, (1) the demand for water is very inelas­

tic, and therefore meaningful water savings will be difficult to obtain

via the price mechanism.

Large price increases would be required to

conserve water used in cotton production.

(2) Water prices set by

government agencies for surface water is so low that even doubling its

price will not cut water applications on cotton by a meaningful amount.

Only a several-fold price increase would conserve water.

(3) If the

quantity of water used on cotton is cut to 80 percent of the profit

maximizing level, cotton profits are cut a substantial $20-$55 per acre.

Research

Related research is needed in several areas.

(1) Crop-water

response functions are needed for other crops and other regions of the

arid southwest. (2) The economic analysis of crop response to alterna­

tive irrigation quantities needs to be expanded to a multi-crop analysis

where optimization among crop mix and input levels is simultaneously

determined. (3) Risk should be incorporated into the analysis.

The

current analysis was based upon profit maximizing criteria, but many

people argue that farmers respond not only to expected profits, but also

the riskiness of obtaining particular profit levels. (A) Alternative

irrigation technologies should be included to analyze their impact on

water conservation, farm profit, crop output and other factors. Part

of this analysis may be simply incorporated into the profit computations

of the current research by altering the effective price of water. Fur­

ther analysis may require programming models of various sorts to account

for lumpy investments and the time dimension of investments.

81

(5) Finally, more basic agronomic research on crop response to low

levels of water and alternative levels at difference plant growth stages

needs to be conducted. For years agronomic research has focused on

measuring the amount of water lost through evapotranspiration when

water is applied to avoid plant stress. This extensive research has

resulted in recommendations for irrigation which avoid plant stress and

thereby maximize plant yield. As demonstrated in the current research,

profits can often be maximized and water conserved by applying a lessor

amount of water.

REFERENCES

Anderson, Raymond L . , Dan Yaron, and Robert Young,

"models Designed to

Efficiently Allocate Irrigation Water Use Based on Crop

to Soil Moisture Stress." Economic Research Service, USDA,

Tech. Rep. No. 8, May 1977.

Arizona Crop and Livestock Reporting Service. Arizona Agricultural

Statistics, Bulletin S-13, Economics, Statistics, and Cooper­ atives Service, USDA, April 1978.

Arkin, G. F. "Crop Response to Available Soil Water. Symposia on

Crop Response to Irrigation: A State of the Arts Assessment of

What is Known and Practices." An unpublished report for the

American Agricultural Economics Association (AAEA) and Canadian

Agricultural Economics Society (CAES), 1978.

Ayer, Harry W.

"Economic Models of Crop Response to Irrigation: A

State-of-the-Arts Assessment." Unpublished paper for the

American Agricultural Economics Association (AAEA) and Canadian

Agricultural Economics Society (CAES), 1978.

Ayer, Harry W. and David J. Cormier. "Impacts of increasying Energy

Scarcity in Irrigated Agriculture: An Empirical Study from the

Arid Southwest." Proceedings of the International Conference,

Energy Use Management, Vol. I, New York, Pergamon Press, 1977,

pp. 709-718.

Beringer, C.

"An Economic Model for Determining the Production Function

for Water in Agriculture." California Agricultural Experiment

Station, Giannini Foundation Res. Rept. No. 240, Berkely, 1961.

Black, Richard D. and DeLynn R. Hay.

"Soil-Water-Plant Relationships,"

Irrigation Water Management Series, Cooperative Extension

Service, MF-466, Manhattan, Kansas, Kansas State University

September 1978.

Blaney, H. F. and K. V. Morin.

"Evaporation and Consumptive Use of

Water Empirical Formulas." Transactions of the American

Geophisics Union, Vol. 23, 1942, pp. 76-83

Blank, Herbert G.

"Optimal Irrigation Decisions with Limited Water."

Doctoral dissertation, Colorado State University, 1975.

82

83

Brix, H. "The Effect of Water Stress on the Rates of Photosynthesis and

Respiration in Tomatoe Plant and Loblolly Pine Seedlings."

Physiol. Plant. 15 (1962:10-20)

Buchheim, J. T. and L. F. Ploss.

"Computerized Irrigation Scheduling

Using Neutron Probes." American.Society of Agricultural

Engineers. Paper No. 77-2004, 1977, 14 p.

Clyde, H. S., W. Gardner and 0. Israelson.

"The Economical Use of

Irrigation Water Based on Tests." Engineering, News Record,

91, 1923, pp. 549-52.

Delaney, Ronald H . , James J. Jacobs, John Borralli, Richard P. Clark

and Warren E. Hedstrom.

"Economic and Agronomic Effects of

High Irrigation Levels on Alfalfa and Barley." Water Resources

Research Institute, Research Journal No. 121, Laramie, Wyoming,

January 1978.

Dennis, Robert E., Rex Thompson, Arden D. Day and Ernest Jackson.

"Growing Wheat in Arizona." Bulletin A32, Cooperative

Extension Service, The University of Arizona, Tucson,

October, 1976.

Dudley, Norman J., David T. Howell, and Warren F. Musgrave.

"Optimal

Intraseasonal Irrigation Water Allocation." Water Resources

Research, Vol. 7, No. 4, August 1971, pp. 770-788.

Dyke, Paul T. "Yield Response Handbook." Prepared for Western Governor

Drought Conference, Denver, Colorado, December 1-3, 1977.

Erie, Leonard J . , Dale Bucks and Orring F. French. "Consumptive Use and

Irrigation Management for High Yielding Wheats in Central >

Arizona." Progressive Agriculture in Arizona, Vol. 25,

March-April 1973.

Erie, Leonard J . , Orrin F. French and Karl Harris.

"The Comsumptive

Water Use by Crops in Arizona." Agricultural Experiment

Station, The University of Arizona, Tucson, May 1965.

Fleming, P. M.

"A Water Budget Method to Predict Plant Response and

Irrigation Requirements for Widely Varying Evaporative Condi­

tions ." Sixth International Congress of Agricultural Engineers,

Switzerland, 1964, pp. 1-12.

Flinn, J. C. and W. F. Musgrave. "Development and Analysis of Input-

Output Relations for Irrigation Water." The Australian Journal

of Agricultural Economics, Vol. 11, No. 1, June 1976, pp 1-19.

84

Grimes, Donald W. and W. L. Dickens. "Cotton Responses to Irrigation."

California, Division of Agricultural Sciences, California

Agriculture, University of California, Vol. 31, Number 5,

May 1977.

Haldeman, Alan D. "Wheat Water Use, irrigate According to Crop Needs."

Cooperative Extension Service, University of Arizona, Q211,

1973.

Hathorn, Scott, Jr. and James Armstrong, 1979 Arizona Field Crop Bud­

gets, Pima County, Cooperative Extension Service, The University

of Arizona, 1979.

_ _ _ _ _ _ and Ron du l l . 1979 Arizona Field Crop Budgets, Graham County,

Cooperative Extension Service, The University of Arizona, 1979.

Hathorn, Scott, James Little and Sam Stedman.

1979 Arizona Field Crop

Budgets, Pinal County, Cooperative Extension Service, The

University of Arizona, 1979.

Hazlitt, James R,, Agronomist at The University of Arizona Field Station,

Yuma, Arizona. Telephone interview June, 1979.

Hexem, Roger W. and Earl.O. Heady. Water Production Functions for

Irrigated Agriculture. Ames, Iowa: The Iowa State University

Press, 1978.

Heerman, D. F., H. R. Haise and- R. H. Nickelson.

"Scheduling Center

Pivot Sprinkler Irrigation Systems for Corn Production in

Eastern Colorado." Transactions of the American Society of

Agricultural Engineers, Vol. 19, No. 2, 1976, pp. 284-293.

Hogg, Howard C. and Gary R. Vieth.

"Method for Evaluating Irrigation

Projects." Journal of the Irrigation and Drainage Division.

March 1977, pp. 43-52.

Holloway, Milton L. and Joe B. Stevens. An Analysis of Water Resource

Productivity and Efficiency of Use in Pacific Northwest

Agriculture. Agricultural Experiment Station, Special Report

383. Economic Research Service, Natural Resources Economic

Division, U.S. Department of Agriculture, Oregon State

University, Corvallis, Oregon, May 1973.

Jensen, M. E.

"Scheduling Irrigations with Computers." Journal of Soil

Water Conservation, Vol. 24, 1969, pp. 193-195

Jensen, M. E. and H. R. Haise.

"Estimating Evapotranspiration from

Solar Radiation." Journal of Irrigation Drainage Division,

American Society of Civil Engineers, Vol. 89, 1963.

85

Kincaid, D. C. and D. F. Heerman. "Scheduling Irrigations Using a

Programmable Calculator." USDA. Agricultural Resource Service

Publication, ARS—NC—12, 1974.

Kittock, D. L. and C. R. Farr, "Effect of Date of Irrigation Termination

of Yield on Upland and Pima Cotton." USDA-SEA-RF, proposed

Western Bulletin.

Minhas, B. S., K. S. Parikh, and T. N. Srinivasan. "Toward the

Structure of a Production Function for Wheat Yields with Dated

Inputs of Irrigation Water." Water Resources Research, Vol. 10,

No. 3, June 1974, pp. 383-393.

Moore, C. V. "A General Analytical Framework for Estimating the

Production Function for Crops Using Irrigation Water." Journal

of Farm Economics, 43, pp. 876-888.

Moore, C. V., J. H. Snyder and Peter Sun.

"Effects of Colorado River

Water Quality and Supply on Irrigated Agriculture." Water

Resources Research. Vol. 10, No. 2, April 1974, pp. 137-144.

Slayter, R. 0. Plant-Water Relationships. Academic Press, Inc.,

London and New York, 1967.

Steward, J. I., Robert M. Hagan and William 0. Pruitt.

"Optimizing Crop

Production Through Control of Water and Salinity Levels in the

Soil." Utah Water Research Laboratory Utah State University,

Logan, Utah, September, 1977.

Steward, J. I., Robert M. Hagan and William 0. Pruitt. "Functions to

Predict Optimal Irrigation Programs." Journal of the Irrigation

and Drainage Division, June 1974, pp. 179-199.

Thornwaite, C. W. and B. Holzman. Measurement of Evaporation from

Land and Water Surfaces. U.S. Department of Agriculture,

Technical Bulletin No. 817, 1942, 75 p.

U.S. Department of Agriculture. Agricultural Statistics, 1978. United

States Government Printing Office, Washington, D.C., 1978.

U.S. Water Resources Council.

"The Nation’s Water Resources, 1975-2000."

Volume 1: Summary, Second National Water Assessment, December

1978.

Wu, I-pai, M. Asce and Tung Liang. "Optimal Irrigation Quantity and

Frequency." Journal of the Irrigation and Drainage Division,

March 1972, pp. 117-144.

Yaron, Dan. "Economics of Irrigation and the Institutional and Pricing

Systems of Water in Israel." Unpublished paper.

85

Kincaid, D. C. and D. F. Heerman. "Scheduling Irrigations Using a

Programmable Calculator." USDA. Agricultural Resource Service

Publication, ARS-NC-12, 1974.

Kittock, D. L. and C. R. Farr, "Effect of Date of Irrigation Termination

of Yield on Upland and Pima Cotton." USDA-SEA-RF, proposed

Western Bulletin.

Minhas, B. S., K. S. Parikh, and T. N. Srinivasan. "Toward the

Structure of a Production Function for Wheat Yields with Dated

Inputs of Irrigation Water." Water Resources Research, Vol. 10,

No. 3, June 1974, pp. 383-393.

Moore, C. V. "A General Analytical Framework for Estimating the

Production Function for Crops Using Irrigation Water." Journal

of Farm Economics, 43, pp. 876-888.

Moore, C. V . , J . H. Snyder and Peter Sun.

"Effects of Colorado River

Water Quality and Supply on Irrigated Agriculture." Water

Resources Research, Vol. 10, No. 2, April 1974, pp. 137-144.

Slayter, R. 0. Plant-Water Relationships, Academic Press, Inc.,

London and New York, 1967.

Steward, J. I., Robert M. Hagan and William 0. Pruitt.

"Optimizing Crop

Production Through Control of Water and Salinity Levels in the

Soil." Utah Water Research Laboratory Utah State University,

Logan, Utah, September, 1977.

Steward, J. I., Robert M. Hagan and William 0. Pruitt. "Functions to

Predict Optimal Irrigation Programs." Journal of the Irrigation

and Drainage Division, June 1974, pp. 179-199.

Thomwaite, C. W. and B. Holzman. Measurement of Evaporation from

Land and Water Surfaces. U.S. Department of Agriculture,

Technical Bulletin No. 817, 1942, 75 p.

U.S. Department of Agriculture. Agricultural Statistics, 1978. United

States Government Printing Office, Washington, D.C., 1978.

U.S. Water Resources Council.

"The Nation’s Water Resources, 1975-2000."

Volume 1: Summary, Second National Water Assessment, December

1978.

Wu, I-pai, M. Asce and Tung Liang. "Optimal Irrigation Quantity and

Frequency." Journal of the Irrigation and Drainage Division,

March 1972, pp. 117-144.

Yaron, Dan. "Economics of Irrigation and the Institutional and Pricing

Systems of Water in Israel." Unpublished paper.

Yaron, Dan and G. Strateener.

"Wheat Response to Soil Moisture and the

Optimal Irrigation Policy under Conditions of Unstable Rainfall.

Water Resources Research, Vol. 9, October 1973, pp. 1145-1154.

I

%

417

Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project