ECONOMIC IMPACTS OF ALTERNATIVE IRRIGATION SYSTEMS UNDER INCREASING IRRIGATION WATER COSTS

ECONOMIC IMPACTS OF ALTERNATIVE IRRIGATION SYSTEMS UNDER INCREASING IRRIGATION WATER COSTS
ECONOMIC IMPACTS OF ALTERNATIVE IRRIGATION SYSTEMS
UNDER INCREASING IRRIGATION WATER COSTS
IN SOUTHEASTERN ARIZONA
by
ismail Hakki i5zsabuncuo4lu
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF ECONOMICS
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1977
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by
entitled
Ismail Hakki Ozsabuncuoglu
Economic Impacts of Alternative Irrigation Systems under
Increasing Irrigation Water Costs in Southeastern Arizona
be accepted as fulfilling the dissertation requirement for the
degree of
Doctor of Philosophy
vfk
Dissertation Director
r
Date
As members of the Final Examination Committee, we certify
that we have read this dissertation and agree that it may be
presented for final defense.
Final approval and acceptance of this dissertation is contingent
on the candidate's adequate performance and defense thereof at the
final oral examination.
STATEMENT BY AUTHOR
This
requirements
is deposited
rowers under
dissertation has been submitted in partial fulfillment of
for an advanced degree at The University of Arizona and
in the University Library to be made available to borrules of the Library.
Brief quotations from this dissertation are allowable without
special permission, provided that accurate acknowledgment of source
is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by
the head of the major department or the Dean of the Graduate College
when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission
must be obtained from the author.
SIGNEDC-
ACKNOWLEDGMENTS
There were a great number of people who helped me in this research. Although their contributions were made at different times and
in varying degrees, their significance cannot be undervalued. However,
in this limited space I will be able to mention only a few of those
names.
I wish to express my sincere thanks to Dr. Roger Fox who invaluably instructed me during this research not only as a dissertation
director but also as a scientist who realizes the limitations of research and the researcher.
Dr. William Martin was very instructive in his directives to
clear up a number of problems and misrepresentations. His great experience in research methods and his appropriate suggestions were instrumental in completing this study.
The programming models were efficiently utilized by Dr. James
Wade whose past experiences and knowledge both in computer science and
economics made it possible to adopt a computer programming algorithm
(which was developed for physical sciences) to an economic problem.
appreciate the time he so generously devoted to endless discussions on
this study without any sign of boredom.
I wish to express my respect to Dr. John Wenders who taught me
the importance of getting down to basics upon which all the economic
iv
theories are built. The time and effort he gave for this research in
spite of his tight schedule are greatly appreciated.
My special thanks go to Dr. John C. Day who was the director of
this dissertation in its earlier stage. His comments and suggestions
that helped to found this study were invaluable. Also at that stage of
the study the efforts of Dr. Scott Hathorn, Jr., who developed the
Arizona farm crop budgets, are appreciated.
During the data collection period the then retired Cochise County
Agricultural Extension agent, Mr. Carmy Page, and graduate student, Mr.
Na0.t Yakan, generously helped me to interview the farmers. Their willingness to give up their comfort and time is greatly acknowledged here.
I would also like to thank the Cochise County Agricultural Extension
Office personnel, and the farmers and dealers who were very cooperative
and informative during the interviews.
Mrs. Isabel Farrington Richards actualized my entire doctoral
education by her financial and humanistic support. I am deeply grateful
for her generosity and modesty in this matter.
My oldest friend in the U. S., Mrs. Eileen M. Fitzpatrick, has
been extremely supportive by her influential comments on my progress
throughout my education. Her patience in maintaining her support helped
me a great deal in my accomplishments.
My very special and sincere thanks go to my beloved wife, Ozden,
whose unending support both materially and through her love and encouragement, made my entire education possible.
I also wish to thank the Department of Agricultural Economics,
U. of A., for granting me a research assistantship and the Government
of the Turkish Republic that permitted me to complete my doctoral
degree.
Finally, I sincerely thank the secretaries of the Department of
Agricultural Economics, U. of A., especially Miss Carol Schwager and
Mrs. Adele Goodberry who typed numerous drafts of this dissertation. I
also thank Mrs. Gillespie who typed the final copy.
TABLE OF CONTENTS
Page
LIST OF TABLES ix
LIST OF ILLUSTRATIONS xiv
ABSTRACT xv
CHAPTER
I. INTRODUCTION
1
Agricultural Characteristics of Southeastern
Arizona
Agricultural Production and Economic
Conditions
Topographic and Soil Conditions
Climatic Conditions
Problem Setting Natural Conditions Increasing Cost of Irrigation Water
Impacts of Sprinkler Systems on the
Valley's Economy
Objectives of the Research
Organization of the Dissertation
2
2
6
11
13
13
13
18
20
21
23
THEORETICAL FOUNDATION AND RESEARCH PROCEDURE Theoretical Foundation
A Brief Review of the Pure Theory
of the Firm
Mixed Integer Programming and the Pure
Theory of the Firm Research Procedure Overall Research Plan Review of Related Studies Source and Collection of Data
23
24
31
40
40
42
50
54
III. THE REPRESENTATIVE FARM BUDGETS Characteristics of the Sample
Farm Size
Cropping Patterns
Machinery and Equipment Inventory Irrigation Facilities
vi
54
54
56
60
60
vii
TABLE OF CONTENTS--Continued
Page
62
Complete Unit Budgets Costs of Irrigation Water by Sprinkler
System and Energy Source Calendars of Operation for Selected Crops
Fixed Cost of Farms Variable Cost of Milo Returns Over Variable and Total Costs 66
88
91
98
105
110
IV. THE MIXED INTEGER PROGRAMMING MODEL Formulation of the Mixed Integer Programming
Model Objective Function Activities Constraints Sensitivity Analyses Crop Price Variations Energy Cost Variations Aggregating the Model Determination of Regional Cropland Base Determination of Aggregate Resource
Availability Aggregating the Farm Fixed Costs Aggregating the Representative Farm,
Mixed Integer Programming Results
V.
RESULTS OF THE MIXED INTEGER PROGRAMMING MODELS
110
111
115
118
126
126
127
128
130
132
132
134
Farm Level Conditions
Initial Analysis Sensitivity Analyses Macro Level Conditions Initial Regional Conditions and Variations
. .
Under Changing Cotton Lint Prices
Variations in the Initial Regional Conditions Under Increasing Natural Gas Prices
Summary of Results VI.
SUMMARY AND CONCLUSIONS Summary Conclusions Final Comments and Recommendations for
Further Research 137
137
138
148
181
. .
181
• • • •
192
197
199
199
200
205
viii
TABLE OF CONTENTS--Continued
Page
APPENDIX A: LONG TERM AVERAGES OF SOME OF THE CLIMATIC
FACTORS OF DOUGLAS AND WILLCOX 209
APPENDIX B: WITHDRAWALS AND RECHARGES OF UNDERGROUND
WATER OF SULPHUR SPRINGS VALLEY , 211
APPENDIX C: ESTIMATED ANNUAL GROUNDWATER PUMPAGE IN
WILLCOX AND DOUGLAS BASINS (1915-1973) 213
APPENDIX D: A SAMPLE QUESTIONNAIRE 215
APPENDIX E: THE MACHINERY AND EQUIPMENT INVENTORY
OF THE SAMPLED FARMS 224
APPENDIX F: CALCULATIONS OF CONSUMPTIVE USE OF WATER 232
APPENDIX G: DETERMINATION OF INITIAL INVESTMENT AND
VARIABLE COSTS OF 10- AND 20-ACRE SIDE
ROLL SPRINKLER UNITS
APPENDIX H: SAVINGS AND ADDED COSTS DUE TO SPRINKLER SYSTEMS
234
237
APPENDIX I. CALCULATIONS OF FIXED AND VARIABLE COSTS OF
MACHINERY AND EQUIPMENT 239
APPENDIX J; WATER IRRIGATION SCHEDULES OF CROPS 243
APPENDIX K: COEFFICIENTS OF THE REPRESENTATIVE FARMMIXED INTEGER PROGRAMMING MATRIX 245
APPENDIX L: VARIATIONS IN THE OPTIMUM REGIONAL CROP
PRODUCTIONS UNDER CHANGING COTTON LINT PRICES, 1976
REFERENCES 253
254
LIST OF TABLES
Page
Table
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Land Ownership and Allocation in Cochise and
Graham Counties
3
Harvested Acreages of Principal Crops Grown in
Cochise and Graham Counties, 1966-1975
5_
Cash Receipts of Cochise and Graham Counties by Source, 1970-75
7
The Water Balance Sheet of Willcox and Douglas Basins for 1970 Normalized Conditions
17
Comparison of Linear Programming and the Pure Theory
of the Firm in Terms of Their Assumptions 32
Projections of Crop Acreage, Water Use, and Gross and
Net Farm Income in Cochise County, 1966-2015 46
Economies of Size in Total Variable Cost and Yield of
Corn Production Under Center Pivot Irrigation System
48
Distribution of Sample Farms by Size, Sulphur
Springs Valley, 1976 55
Characteristics of Sample Farms, by Size,Sulphur
Springs Valley, 1976
57
Crop Acreages of the Sample Farms Under Gravity, Side
Roll, and Center Pivot Irrigation Systems,
Sulphur Springs Valley, 1976
58
Typical Cropping Patterns of the Sample Farms, by Size,
Sulphur Springs Valley, 1976
59
Irrigation Wells and Equipment on the Sample Farms,
by Size, Sulphur Springs Valley, 1976
61
Sprinkler Systems on the Sample Farms, by Size,
Sulphur Springs Valley, 1976
63
Water Application Rates and Irrigation Efficiencies
. . .
.....
by Crop, Sulphur Springs Valley, 1976 65
ix
LIST OF TABLES--Continued
Table
15.
16.
17.
Page
Initial Investment Costs of Well Development for
Gravity Irrigation, Sulphur Springs Valley, 1976 67
Total Initial Investment for Well Development by Farm
Size and Energy Source, Sulphur Springs Valley, 1976
70
Annual Fixed Costs of Gravity Irrigation Systems for
Four Farm Sizes and Three Energy Sources,
Sulphur Springs Valley, 1976
18.
Depreciation Schedule for Well Equipment
19.
Variable Costs of Gravity Irrigation System by Farm
Size and Energy Source, Sulphur Springs Valley, 1976 .
20.
Initial Investment Costs of Three Side Roll Sprinkler
Systems, 1976
21. Annual Added Fixed Costs Due to Three Side Roll
Sprinkler Systems, 1976
71
72
74
76
78
22. Annual Added Variable Costs Due to Three Side Roll
Sprinkler Systems, 1976
23.
Initial Investment Costs of a Center Pivot Sprinkler
System, 1976
80
82
24. Annual Added Fixed and Variable Costs Due to Center
Pivot Sprinkler Irrigation System, 1976
25.
Irrigation Labor Cost of Three Irrigation Systems,
Sulphur Springs Valley, 1976
26. Variable Water Cost by Farm Size, Energy Source, and
Irrigation Systems, Sulphur Springs Valley, 1976
27.
28.
Calendars of Operation for Selected Crops, Sulphur
Springs Valley, 1976 Specifications of Machinery and Equipment by Farm
Size, Sulphur Springs Valley, 1976 29. Annual Total and Per Acre Fixed Costs by Farm Size
and Energy Source, Sulphur Springs Valley, 1976 30,
Estimated Value of Land and Its Improvements,
Sulphur Springs Valley, 1976 84
86
• • •
87
89
92
93
96
xi
LIST OF TABLES--Continued
Table
31.
Page
Calendar of Operations and Machinery, Equipment, and
Materials of Milo Under Gravity Irrigation
System (Natural Gas, Small Farm Size) 99
32.
Calendar of Operations and Machinery, Equipment and
Materials for Milo Under 10-Acre Unit Side Roll
Irrigation System (Natural Gas, Small Farm Size) . . . . 101
33.
Costs of Milo Production by Farm Size and Energy
Source Under Gravity and Side Roll Irrigation,
Sulphur Springs Valley, 1976
103
Product Prices, Yields, and Gross Returns for
Selected Crops, Representative of Sulphur
Springs Valley, 1976
107
Variable Production Costs Excluding Irrigation
Costs: Selected Crops by Farm Size, Sulphur
Springs Valley, 1976
109
34.
35.
36.
37.
38.
39.
Critical Period and Annual Water Constraints of
Four Representative Farm Sizes 122
Estimated Variable Water Costs for 1977 and 1978
(Natural Gas), ($/A1) 129
Aggregated Land Allocations and Number of Farms,
Sulphur Springs Valley, 1976 131
Aggregated Available Water for Four Farm Sizes,
Sulphur Springs Valley, 1976 133
40.
Aggregated Fixed Costs, Sulphur Springs Valley, 1976
41.
Optimum Cropping Patterns of Four Farm Sizes Under
Three Energy Sources, Sulphur Springs Valley, 1976
139
Optimum Resource Utilizations, Sulphur Springs Valley,
1976 143
42.
43.
44.
• •
135
The Optimum Utilization of the Sprinkler Units by
Farm Size and Energy Source, Sulphur Springs
Valley, 1976
145
Output, Costs, and Returns from Optimal Solutions,
by Farm Size, and Energy Source, Sulphur
Springs Valley, 1976
147
xii
LIST OF TABLES--Continued
Table
45.
46.
47.
48.
49.
Page
Total Cost-Gross Return Ratios of Four Farm Size
Groups, Sulphur Springs Valley, 1976 149
Optimum Cropping Patterns Under Changing Cotton
Lint Price for Four Farm Size Groups, Sulphur
Springs Valley, 1976
151
Optimum Resource Utilizations Under Changing Cotton
Lint Prices for Four Farm Size Groups, Sulphur
Springs Valley, 1976
160
Changes in Total Crop Production Under Varying Cotton
Lint Prices for Four Farm Size Groups, Sulphur
Springs Valley, 1976
166
Changes in Total Costs and Returns Under Varying
Cotton Lint Prices for Four Farm Size Groups,
Sulphur Springs Valley, 1976
171
50. Variations in Total Cost-Gross Return Ratios Under
Changing Cotton Lint Prices, Sulphur Springs
Valley, 1976
176
51. Optimum Cropping Patterns Under Increasing Natural
Gas Prices, Sulphur Springs Valley, 1976
1978
177
52.
Optimum Resource Utilizations under Increasing
Natural Gas Prices, Sulphur Springs Valley,
1976-1978 53.
Changes in Total Crop Production Under Increasing
Natural Gas Prices, Sulphur Springs Valley,
1976-1978 54.
180
Changes in Total Costs and Returns Under Increasing
Natural Gas Prices, Sulphur Springs Valley,
1976-1978 55.
179
182
Optimum Regional Cropping Patterns Under Changing
Cotton Lint Prices, Sulphur Springs Valley, 1976184
• • •
56. Optimum Regional Resource Utilization Under Changing
Cotton Lint Prices, Sulphur Springs Valley, 1976186
• • •
57. Regional Returns Over Variable and Total Costs, by
Energy Sources, Sulphur Springs Valley, 1976 191
LIST OF TABLES—Continued
Table
58.
Page
Optimum Regional Cropping Patterns Under Increasing
Natural Gas Prices, Sulphur Springs Valley,
1976-1978 59.
194
Optimum Regional Resource Utilization Under Increasing
Natural Gas Prices, Sulphur Springs Valley,
1976-1978 195
60. Regional Crop Productions and Returns Over Variable
and Total Costs Under Increasing Natural Gas
Prices, Sulphur Springs Valley, 1976-1978 196
LIST OF ILLUSTRATIONS
Page
Figure
1.
The General Map of Sulphur Springs Valley
8
2.
The General Soil Conditions of Cochise and Part of
Graham Counties (Scale: 1/1,000,000)
10
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
(A) Long Term Mean Monthly Temperatures ( 0 F), Monthly
Total, and (B) Cumulative Precipitations (inches)
of Willcox and Douglas Functional Relationship Between Output (Y i ) and
Input (X i2 ) (Hypothetical)
12
Isoproduct Curves Between the Production Factors
X and X
(Hypothetical)
i2
25
27
Production-Possibility Frontier of Outputs Y i and Y 2
(Hypothetical)
Linear Production Functions of Outputs Y i and Y 2
with Respect to Input X 1 (Hypothetical)
Development of Isoquant Curves of Linear Programming
Technique (Hypothetical)
29
35
36
Product Transformation Process in Linear Programming
Technique (Hypothetical)
38
Cost Functions of (A) Linear and (B) Integer Programming
Techniques (Hypothetical)
39
Irrigation Schedules of Selected Crops Under
Sprinkler and Gravity Irrigation Systems,
Sulphur Springs Valley, 1976 124
Aggregate Supply Schedule of Cotton Lint, Sulphur
Springs Valley, 1976 189
xiv
ABSTRACT
Increasing irrigation water cost due to higher pump energy price
and falling groundwater tables is a critical problem of the agricultural
sector in Sulphur Springs Valley of Southeastern Arizona which is characterized as an arid region with low annual precipitation and high temperatures. Water saving irrigation techniques, side roll and center
pivot sprinkler systems, are analyzed as alternatives of gravity irrigation. Natural gas, electricity, and diesel fuel are commonly available
energy sources for pumping groundwater in the area. Four representative
farm size groups, five crops, and five irrigation techniques are adopted
for representative farm mixed integer programming models. The problem
is treated as a complete switch from one energy source to another and
twelve separate sets of computer data are developed for four farm sizes
and three energy sources.
Sensitivity analyses based on cotton lint price and natural gas
cost variations are analyzed. The results are aggregated to determine
the regional level impacts of energy source changes, cotton lint price
declines, and natural gas price increases.
The major conclusion of these analyses is that upland cotton is
a dominant crop with wheat using residual land and water. July water
and available land restrict the crop production. Increasing energy costs
reduce the total annual water consumption through adopting the water
saving sprinkler systems and/or crops. Under the initial conditions
XV
xvi
(cotton lint price is at $58.11/cwt and natural gas price is at $.1167
per therm) the farmers generate gross returns that cover their annual
total cost. Decreasing price of cotton decreases the return above total
cost and annual water consumption. Wheat production changes as a complement of upland cotton, but corn production varies as substitute because of irrigation water and land constraints and relative crop
profitability.
CHAPTER I
INTRODUCTION
In elementary textbooks, economics is defined as the study of
ways to satisfy man's unlimited wants subject to nature's limited resources. However, men continually search for ways to overcome the
limits for satisfying their wants, for example, living in the desert
with the air conditioner's comfort, with green grass in the front yard.
When they live in this type of environment, naturally they use more natural resources than in other, more suitable areas, i.e., they use more
energy for cooling systems and more water for irrigating lawns than they
would have in the more suitable areas.
This problem can be readily seen in Arizona where irrigated agriculture is about the only way of growing crops and where groundwater is
a primary source of irrigation water. All of the above factors are present in the Sulphur Springs Valley of Cochise and Graham Counties of
Southeastern Arizona, viz., unlimited wants, limited resources (especially water), underground water as the only source of irrigation water,
and water depletion under current conditions. In a situation such as this
where the limited resources are being depleted in order to satisfy human
needs, it is important to analyze the consequences of alternative actions
in a comparative statics framework, viz., estimation of the impacts of a
change in one variable upon other technical and economic variables.
In this study, the impacts of the introduction of side roll and
center pivot sprinkler irrigation systems in the Sulphur Springs Valley
1
2
will be estimated. These impacts are expected to be on energy requirements, water consumption and groundwater depletion rates, general cropping patterns, land distribution among the farmers, and on the other
sectors of the economy which are closely related to the region's agricultural sector. Although there are previous studies of the agricultural economy of Sulphur Springs Valley, there is no empirical study
that deals with the impacts of new irrigation techniques.
The general order of presentation of this study is as follows:
a brief discussion of the region's agricultural, physical, and economic
conditions will be followed by a detailed presentation of the research
problem and objectives. In the second chapter, certain aspects of economic theory are reviewed and related studies are discussed. The next
two chapters deal with data collection and the construction of the mixed
integer programming models used in the analysis.
In the fifth chapter the results of the representative mixed integer programming models are presented and analyzed. The study concludes
with a summary chapter and recommendations for future research.
Agricultural Characteristics of Southeastern Arizona
Agricultural Production and Economic Conditions
There are not many private agricultural lands in Cochise and
Graham Counties. Inspection of Table 1 shows that only 9.6% of the total
area is privately owned in Graham County, while in Cochise County, the
figure is 40.9%. More than 50% of the total land area of both counties
belong to Federal, State, and County agencies including the Forest Service, Bureau of Land Management, State of Arizona, National Park Service,
3
Table 1.
Land Ownership and Allocation in Cochise and Graham Counties
Cochise Co.
Acres
Percent
(1,000)
Graham Co.
Percent
Acres
(1,000)
Public Landa
2,365.0
59.1
1,668.0
56.5
Indian Land
-
-
1,000.0
33.9
Private Land
1,639.0
40.9
282.0
9.6
TOTAL LAND
4,004.0
100.0
2,950.0
100.0
171.0
4.3
64.0
2.2
125.5
(73.4)
23.5
(36.7)
45.5
(26.6)
40.5
(63.3)
Total Cropland Acres
In Sulphur Springs Valley b
Out of Sulphur Springs Valley b
Other Land Acres
TOTAL LAND
3,833.0
95.7
2,886.0
97.8
4,004.0
100.0
2,950.0
100.0
a Includes Forest Service, Bureau of Land Management, State of Arizona,
National Park Service, Department of Defense, Bureau of Sport Fisheries
and Wildlife, Bureau of Reclamation and other miscellaneous County,
State, and Federal land.
bFigures in parenthesis are percentages of total cropland acres.
Sources: Arizona Crop and Livestock Reporting Service, 1976, p. 63,
and 1974, pp. 7, 10, 12, 22, 23.
4
Department of Defense, Bureau of Sport Fisheries and Wildlife, and
Bureau of Reclamation.
Cochise and Graham Counties are among the first five counties
in the state in terms of their total cropland acres. Even though only
4.3% and 2.2% of total land in Cochise and Graham Counties is cultivated,
they are above or at the state average, which is 2.2% (Arizona Crop and
Livestock Reporting Service, 1976, p. 63, and 1974, p. 1).
In Sulphur Springs Valley there are 149,000 acres of cropland of
which 15.8% are in Graham County and the balance in Cochise County. As
is seen in Table 1, about 74% of the total agricultural lands of Cochise
County lies in the Sulphur Springs Valley; for Graham County the proportion is much smaller, 36.7%. Thus, Sulphur Springs Valley's contribution to Cochise County's crop production is somewhere around 70-75%
while it is 35-40% of Graham County's crop production.
In Table 2 the harvested acreages of the principal crops grown
in Cochise and Graham counties are given for the 1966-1975 period. In
both counties grain sorghum (milo) has been the most commonly raised
crop. However, comparisons of three year averages, 1966-68 and 1973-75,
of these crops indicated that grain sorghum acreage dropped about 8% in
Cochise County while it increased about 27% in Graham County. The most
severe reduction happened in corn acreage, 86.6% in Cochise County and
its complete elimination in Graham County. On the other hand, wheat
acreage more than tripled in Cochise County, while acreage increased by
4,433 acres between these two periods in Graham County. Cotton acreage
almost doubled in Cochise County while it declined 23.5% in Graham
County. Barley and sugar beets declined in Graham County while they
5
Table 2. Harvested Acreages of Principal Crops Grown in Cochise and
Graham Counties, 1966-1975. a
Years
Cotton
Cochise
1966
1967
1968
1969
1970
1971
1972,
1973
1974
1975
Barley
Sorghum
Wheat
Corn
(Acres)
Alfalfa
Hay
Other
Hay
Sugar
Beet
5,600
3,500
1,700
1,700
1,800
1,800
2,100
2,000
2,100
2,100
1,530
3,670
7,280
1,660
930
2,280
2,210
2,830
4,330
20.1
County
8,800
8,550
13,100
13,900
14,828
20,116
20,950
19,030
22,550
13,550
2,500
4,300
5,100
5,000
5,600
7,000
6,500
6,000
6,000
6,200
59,500
64,500
61,400
53,000
52,400
61,700
50,500
54,500
55,500
61,000
1,300
14,700
12,000
11,200
21,000
27,000
26,500
35,000
40,000
51,300
2,900
5,500
2,800
4,000
1,000
800
200
500
7,200
8,300
8,300
8,000
8,700
9,500
9,500
9,500
9,500
9,600
Percent c 81.1
52.9
-7.8
351.1
-86.6
20.2
-42.6
15,500
13,100
16,300
17,300
15,150
16,610
14,310
11,160
13,950
9,250
6,600
11,000
8,600
9,000
9,500
6,800
3,000
7,000
7,500
13,600
21,000
26,500
23,800
19,000
18,100
23,500
23,000
28,500
29,000
33,300
900
1,500
500
2,500
3,400
7,400
400
300
100
100
400
600
100
5,200
5,300
5,500
6,000
6,900
7,000
6,000
8,000
8,200
8,100
900
600
200
200
200
200
300
1,500
500
500
Percent c -23.5
-7.3
27.4
4333.3
51.9
47.0
Graham County
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
b
100
100
b
b
b
b
b
880
880
760
b
b
b
b
b
360
-59.1
a Source: Arizona Agricultural Statistics, by Arizona Crop
and Livestock
Reporting Service, 1972 and 1976.
bAcres planted and/or harvested are too small to
warrant quantitative
estimate.
c Percentage changes between the periods of 1966-68 and
1973-75.
6
increased in Cochise County. Alfalfa hay acreage increased in both
Cochise and Graham Counties.
Cash receipts from the sale of agricultural products can be
used to characterize the economic conditions of both counties. As is
indicated in Table 3, cash receipts from field crops have made considerable contributions to the region's agricultural income. In Cochise
County the cash receipts from field crops were greater than from livestock and livestock products in the 1970-75 period. During the six year
period, the contribution of field crops to the county's cash receipt has
never been less than 54%. However, livestock has had, with the exception of 1974, a more important place in Graham County's economy by providing larger cash receipts for the county than the field crops.
Government payments, which have not been used since 1974, were
low when compared with total cash receipts. For example, in 1973 they
were only 5.1% and 3.3% of total cash receipts of Cochise and Graham
counties, respectively.
Topographic and Soil Conditions
Sulphur Springs Valley extends in a north-south direction covering the Douglas Basin to the south and the Willcox Playa to the north.
The Valley itself is surrounded by the Mule, Dragoon, Little Dragoon,
Winchester, and Galiuro Mountains to the west, and the Persilla, Swishelm,
Chiricahua, Dos Cabezas, and Pinaleno Mountains to the east (see Fig. 1).
The elevation of the Valley varies between 4,100 and 4,300 feet above
sea level. The mountains on the west and east rise abruptly above the
nearly level togently sloping valley floor (USDA, Soil Conservation
Service, 1976, p. 69). There are three drainage areas in the Valley:
7
Table 3. Cash Receipts of Cochise and Graham Counties by Source,
1970-75.a
Years
Crops
($1000)
% of
Total
Receipts
Livestock
and
Livestock
Products
($1000)
Government
Payments
($1000)
Total
($1000)
Cochise County
1970
1971
1972
1973
1974
1975 b
13,957
20,069
19,837
27,590
41,127
44,250
54,4
59.5
53.9
57.1
78.7
66.0
8,482
10,552
13,476
18,229
11,125
22,809
3,238
3,098
3,056
2,477
c
c
25,677
33,719
36,819
48,296
52,252
67,059
30.7
37.9
31.8
33.0
57.0
39.5
12,279
12,868
15,176
21,565
15,803
28,060
1,303
1,195
1,217
1,106
c
c
19,584
22,645
24,036
33,832
36,664
46,382
Graham County
1970
1971
1972
1973
1974
1975 b
6,002
8,582
7,643
11,161
20,861
18,322
aSource: Arizona Crop and Livestock Reporting Service, 1972, 1975, 1976.
b
c
Preliminary data.
Program terminated.
8
11\
1
/V\
Little 11 1
Dragoon '1
Mts A
1 /IA
/1
4
t
1/1
C
I
,BENSON
1;
o
‘
I
1
4,4
0
I
I
McNEAL
SIERRA
. VISTA
/IA
4/0A
Mule Mts
0
5
10 15 20 25
IZ
DOUGLAS
Perilla
Mts
MEXICO
MI LES
Figure 1. The General Map of Sulphur Springs Valley. -- (Adapted from
U. S. Geological Survey, 1974, p. 13.)
9
the North and Central drainage areas slope down toward the Willcox
Playa and the South drainage area drains into Mexico by means of Whitewater Draw (Lee, 1967, p. 4).
The general soil conditions of Sulphur Springs Valley are shown
in Figure 2. About 90-95% of the Valley is covered by thermic semiarid
soil association (TS) whose general characteristics are relatively high
annual soil temperatures of 59 0 to 72 0 F. and 10-16 inches of mean annual precipitation (USDA, Arizona Agricultural Experiment Station, 1975).
From an agricultural standpoint, this group of soil has very low potential for surface irrigation. However, two subgroups are moderately
suitable for gravity irrigation (TS2 and TS3 on the soil map.) These
two subgroups constitute about 80-85% of total agricultural area of
Sulphur Springs Valley. Torrifluvents association (TS2) is deep, moderately coarse to moderately fine-textured, nearly level to strongly sloping soils on floodplains and alluvial fans. On the other hand, TubacSonoita-Grabe association (TS3) has the same features of torrifluvents
association except these soils are located on uplands and in drainage
ways.
The last two types of soils belong to mesic subhumid (MH) and
frigid subhumid (FH) soil classes and their suitability to gravity irrigation is very low. The general characteristics of these classes are
gravelly and coblely, fine to moderately coarse textured, shallow to
deep soils. They are found on nearly level to very steep basaltic
plains, mesas, hills and mountains. (For more detailed discussion of
the subject, see USDA, Soil Conservation Service, 1971 and 1973).
10
SCALE
1 • 1,000,000
MM.
hAH1
AAH2
152
153
FH5
CASTO-MARTINEZ -CANELO
TH1C-HAP LUSTOLLS-L1THIC -ARGUISTOLLS-ROCK
TORR1FLUVENTS
TUBAC-SONOITA-GRABE
miRABAL- BALDY- ROCK
Figure 2. The General Soil Conditions of Cochise and Part of Graham
Counties (Scale: 1/1,000,000)
11
•
Soil conditions of an area are significant factors to be considered in irrigated agriculture. As is discussed above, the general
soil characteristics of Sulphur Springs Valley are not very suitable
for surface (gravity) irrigation. Therefore, a different kind of irrigation system which is more applicable to the prevailing soil conditions
could be important to the area.
Climatic Conditions
Appendix Table A contains mean monthly temperatures of two locations in Sulphur Springs Valley, Willcox and Douglas. These data are
presented graphically in Figures 3A and B. It can be seen that the
Valley has a dry climate with the maximum temperature in July reaching
81 0 F
in Douglas and 79
°
F
in Willcox. Similarly, the monthly precipi-
tations in both locations follow a similar pattern of temperature variations (Figure 3A). During October-June period the monthly precipitation
never exceeds 1 inch (Figure 3B). For example, only 33.9% of the total
annual precipitation of Douglas (4.01 inches) falls during the ninemonth, October-June, period. The comparable figure for Willcox is 42.5%,
which represents 4.75 inches of precipitation. Consequently, more than
55% of the total annual precipitation falls in a three-month period,
July-September. The summer precipitations accompanied by thunderstorm
activities originate from the Gulf of Mexico and enter the area from the
southeasterly direction. The scattered winter precipitations originate
from the Pacific Ocean and move to the Valley via southern California
(Green and Sellers, 1964, pp. 8, 153, 465).
12
/
75
/
/
..
/ ---,
N.
.
.
TEMP
/
/
o
t
/
N
/
t
/
t
/
a_
%
/
F
5
0 45
t
/
..
n
z
/
/
/
4
%
%
/
/
1
t
/
LL.f
ce
D 65
‘n
/
/
/
/
/
/
/ PREC
I
%
---%
%
%
%
%
%
k
.
.
2
IP
LU
35
A
-----
WI
LLCOX
DOUGLAS
5
°
Figure 3. (A) Long Term Mean Monthly Temperatures ( F), Monthly
Total, and (B) Cumulative Precipitations (inches) of
Willcox and Douglas.
13
The low amount of rainfall and high temperatures make production
without irrigation almost impossible. Because of this situation about
97% of total farmed acreage is irrigated.
Problem Setting
Natural Conditions
The Willcox Playa and the Douglas Basin are characterized as
arid regions with approximately 11-12 inches of annual precipitation
and a long term, annual mean temperature of 59.1-63.1 0 F. Because of
the lack of total precipitation and of its general pattern of occurence,
farming without irrigation is not feasible. For years, this lack of
precipitation has been compensated for by conventional irrigation systems relying completely upon groundwater aquifers. The conventional or
gravity systems traditionally in use are those such as row irrigation,
furrow irrigation, and wild-flooding.
a
In order to control the applica-
tion of water to the crop and provide an even distribution of it throughout the field, borders, furrows, or corrugations are used.
Increasing Cost of Irrigation Water
Irrigation water cost has two components, fixed and variable
costs. The fixed cost of using groundwater is derived from the depreciation, taxes, interest, and insurance payments computed on the initial
investments in the well and pump assembly. The variable cost of pumping
irrigation water, our main concern in this chapter, depends upon the
price of energy, pump lift, overall pumping efficiency and two
a
Conventional, flood, and gravity irrigation systems are used as
synonyms in this study.
14
additional energy multipliers as indicated in Equation 1 (Hathorn, 1976).
Variable cost of pumping irrigation water has also two components:
energy cost, the first part of Equation 1, and the cost of plant maintenance, repair, lubrication, and attendance (m).
VC = [(ke . p • g)/E + m] h
(1)
where,
VC = the variable cost of pumping water ($/acre feet).
ke = the energy multiplier (thousands of cubic feet of
natural gas to lift 1 AF of water 1 foot at 100%
overall pumping efficiency) . a
P = price of energy (in dollars per thousand cubic
feet (MCF) for natural gas; dollars per gallon
for diesel and LP gas).
g = MCF of natural gas equivalent derived from the
energy source.b
= overall pump efficiency in decimal fraction.
in
= cost of plant maintenance, repair, lubrication,
and attendance per foot of lift.
h = water lift in feet.
It is clear from the above formula that energy cost (ke - p g/E)
and pumping lift (h) are two major sources of the variations in the variable cost of pumping irrigation water for a given energy source, effiof
ciency (E), and maintenance cost (m). Energy cost is the dollar cost
an energy source for pumping one acre-foot of water from a given depth.
a k = 0.00318 for natural gas, diesel, and LP gas; and 1.024 for
electricity.
g = 1 per KWH of electricity,
10.68 per therm of natural gas,
7.63 per gallon of diesel, and
11.3 per gallon of LP gas
15
As indicated by Willett et al. (1975), the uninterrupted natural gas
supply from Texas has been open to curtailment since the Federal Power
Commission's (FPC) Directive 697-A issued on December 19, 1974, changed
the priority status of natural gas used to power irrigation pumps from
priority two (commercial use) to priority three (industrial use). Although, later on the decreased priority status of agricultural use of
natural gas was reversed by FPC, because expected shortages in natural
gas supply and more profitable offers coming from industrial users, it
, is reasonable to anticipate that natural gas used for irrigation pumps
will be subject to some curtailment.
At the same time, domestic and foreign oil suppliers have increased crude oil prices thereby increasing both the prices of diesel
gas and electicity which is generated by using crude oil products.
Percentage price increases of natural gas, electricity, and
diesel fuel between 1975 and 1976, and estimations for 1977 and 1978 are:
Expected Increases
Increase in 1976Percent
Price in 1975Percent
1977
1978
Natural gas
$.09644/therm
Electricity
$.37020/KWH
Diesel gas
$.02765/gallon
21.0
12.7
12.5
6.0
4.0
4.0
10.0
3.5
3.5
1975 and 1976 prices were obtained from Arizona Pump Water Budgets
Cochise County (Hathorn and Willett, 1975,' and Hathorn, 1976). Estima-
tions are based on the personal communications with Dr. H. Frank (1976).
Pumping lift is the other major source of increasing irrigation
water cost. The effect of lift on the variable cost of water is twofold:
16
one, a greater lift requires more energy to pump the same amount of
water; two, a larger lift requires more maintenance and attendance costs.
According to unpublished data collected by USGS office from a
sample of 75 wells in Sulphur Springs Valley, the water table has been
declining about two feet per year in the 1971-1976 period. The past
five year averages of both basins show that the water level declined
about 14.18 ft/5 years in Willcox and 11.41 ft/5 years in Douglas Basin
(USGS, 1976). This is simply because annual groundwater pumpage exceeds
the total recharged amount of water. (See Appendix B on recharge sources
of the area). As is seen in Table 4, the overdrafts in 1975 from Willcox
and Douglas Basins were 182,000 AF and 64,000 AF, respectively. The
6,000 AF of imported water was pumped from Upper San Pedro Basin to
Douglas Basin for a copper mine. However, after the copper mine closed
down the water importation was stopped. It is clear from this table that
the agricultural sector is primarily responsible for the groundwater
overdraft, i.e., in the Willcox Basin 99% of the total depleted water in
1970 was used by the agricultural sector, and in Douglas Basin the fig-
ure was 86%. The falling groundwater table is clearly a more serious
problem for the agricultural sector than for the industrial sector.
(See Appendix C for historical trends of annual groundwater pumpages in
both basins).
In summary, the increasing prices of energy and the greater
pumping lifts are two major sources of higher irrigation water cost.
Higher irrigation water costs could result in changes in irrigation
practices, crop growing technique, and general cropping patterns. It is
17
Table 4. The Water Balance Sheet of Willcox and Douglas Basins for
1970 Normalized Conditions. a
Items
Willcox Basin
Douglas Basin
1000 AF Supply of Water
(1) Surface Water Diverted
(2) Return Flows
(3) Surface Water Available
for Use [(1) - (2)]
(4) Natural Groundwater Recharge
(5) Basin Import
(6) Total Water Supply
[,(3) + (4) + (5)]
0
0
0
15
0
11
6c
15
17
Demand for Water
0
(7) Basin Export
Agricultural
288
(8) Withdrawal
0
(9) Return Flow
93
(10) Recharge
(11) Depletion
195
[(7) -I- (8) - (9) - (10)]
Municipal and Industrial
2
(12) Withdrawal
0
(13) Recharge
2
(14) Depletion [(12) - (13)]
290
(12)]
(15) Total Withdrawal [(8)
197
(14)]
(16) Total Depletion [(11)
-182
(17) Overdraft [(6) - (16)]
a
Source: Arizona Water Commission, 1975, p. 111.
b
c
Probable but unknown values.
See text.
0
0
103
0
33
70
13
2
11
116
81
-64
18
important to determine what kind of changes might occur in order to suggest ways to minimize losses to those who are affected by the higher irrigation water costs.
Impacts_of Sprinkler Systems on the Valley's Economy
A number of studies in other areas of Arizona have shown that
by using sprinkler irrigation systems a 30 to 35% water saving can be
achieved in addition to increasing crop output (Gordon, 1970, pp. 13,
63). However, there are only a limited number of studies related to the
agricultural and hydrologic conditions of Sulphur Springs Valley. Moreover, there are no empirical studies dealing with the economics of adopting sprinkler systems, even though there are significant numbers of such
systems currently operating in Valley with expectation that more systems
will be introduced in the near future (Lucas, 1976a, p. 5). Therefore,
growers are making their decisions based upon the information provided
by either manufacturers, other growers, or other non-analytical sources.
For the individual farmer, to save irrigation cost through the
savings in total water, energy, and labor usages, sprinkler systems may
be a desirable alternative to the conventional flooding systems now in
use. However, impacts of this shift to sprinkler systems may occur
at the regional level as well. A number of impacts may be identified,
as discussed in the following sections.
Impacts on Groundwater Table. Assuming that the present crop
acreage and cropping patterns are given, shifting from gravity irrigation to sprinkler systems will reduce the amount of water required for
irrigation because of the higher efficiency of the sprinkler systems.
19
This will in turn, reduce the pumpage of the groundwater and, eventually, slow or stop the decline in the groundwater table.
Impacts on Energy Requirements. The potential savings in irrigation water have two important implications for energy use: one is the
direct impact, i.e., a reduction in the total water consumption results
in reduction in the energy requirement at a fraction of the amount of
water saved. Moreover, the indirect or longer run impact of decline in
annual water consumption on total energy use will be through the reduction in the rate at which the groundwater table is falling. That is,
for a given cropland acres in a region, groundwater level may go down at
a slower rate and eventually may not change at all by means of water saving measures. Accordingly, the rate of increase in energy cost may decline or become zero as the depth from which the water is pumped decreases
or stays at a constant level.
Impacts on Irrigation Practices. Gravity irrigation requires a
number of specialized operations in order to achieve even distribution of
water in the field. These operations includé bordering, row bucking, and
disking ends. Since evenness in water distribution is provided directly
by the sprinkler system, those operations necessary for gravity irrigation are not required. Moreover, in order to eliminate dry spots or
overruns, land leveling is unavoidable for gravity irrigation. However,
this operation is not necessary for sprinkler irrigation unless the land
is extremely steep and rough. The aggregate effects of eliminating certain practices, with the possible addition of others, will be on labor
use and machinery purchases. That is, a sprinkler system itself requires
less irrigation labor than gravity, but more capital investment (capital/
20
labor ratio increases). On the other hand, reductions in the number of
irrigations and related operations reduce both labor and machinery.
The new capital/labor ratio in this case depends on the amount of reductions in capital and labor.
Land Reorganization Practices. Replacing gravity irrigation
with sprinklers requires adjustment and modifications in general farm
management practices. For example, the common center pivot sprinkler
system operates on a minimum 160 acres of land. The capacity of side roll
sprinkler systems varies from 2 to 50 acres, although the common sizes
in the study area operate on 20-50 acres. The minimum land requirements of the sprinkler systems may necessitate some reorganization
and/or the acquisition of additional land per farm. One can expect that
there will be a reallocation of land and other resources from the less
to the more efficient farmers in the area.
Objectives of the Research
The overall objective of this research is to analyze the economic and water conservation impacts of converting gravity irrigation
systems to sprinkler irrigation in the Sulphur Springs Valley.
Specifically, the following objectives, grouped under three categories, will be studied:
1. Farm level objectives
a.
The additional capital investments required for adoption
of sprinkler systems will be identified.
b.
The calendars of operations and annual fixed and variable costs of growing major field crops in the county
21
will be determined for both sprinkler and gravity irrigation systems.
c.
The existence of economies of size for sprinklers, if
any, in production of agricultural crops will be examined.
d.
The optimum crop mix will be determined for each representative farm size, in each representative groundwater
pumping area, for both gravity and sprinkler irrigation
systems.
2. Regional objectives
a.
The aggregate regional added fixed and variable costs,
as well as the savings arising from the adoption of
sprinkler systems, will be estimated.
b.
The effects of sprinkler system usage on the groundwater
table and on regional energy requirements for irrigation
will be determined.
3. Policy recommendations will be made either for promotion or limitation of sprinkler adoptions, depending on these research findings.
Organization of the Dissertation
In the next chapter the theoretical concepts that are related to
the specific problems of the Sulphur Springs Valley's agriculture are
reviewed. Then, in the same chapter, the research procedure is discussed.
Moreover, the studies that are focused on these problems, economic and
technical, are reviewed. The third chapter deals with the summary results of the sample, and the development of representative farm unit
22
crop budgets by farm size, energy source, and irrigation systems. In
Chapter IV the construction of representative farm mixed integer programming problems are presented. The detailed description of determination of the coefficients of the program is given. Chapter V deals
with the results of the representative farm mixed integer programming
problems in terms of optimum cropping pattern, resource utilizations,
and return over total costs at farm and regional levels. A summary and
conclusions are given in the final chapter.
CHAPTER II
THEORETICAL FOUNDATION AND RESEARCH PROCEDURE
Theoretical Foundation a
The main task of a farm manager is to make the following decisions in such a way that he maximizes his net returns or profit. He
must decide - How to produce? How much to produce? and What to produce?
with the given resources, markets, and production periods. All three
questions involve both technical relationships between production inputs
and outputs and economic questions involving resource limitations and
market pricing systems. These three concepts are often called factorfactor, factor-product and product-product relationships. In other
words, the most profitable way of producing a given output is determined
by comparing alternative inputs, production technologies, and products
in terms of availability and marketing conditions reflected in input and
output prices. In the study area, the situation involves all of the
above relationships. In other words, increasing water cost can imply a
new set of both inputs and outputs, and/or the same inputs and outputs
used and produced at different levels. More water saving irrigation
methods might be utilized; those crops that need less water could be
preferred, or other relevant factor-factor, factor-product, and productproduct combinations might be adjusted accordingly. Therefore, these
relationships will be reviewed briefly.
a There is a long list of excellent references available for this
section. Three of them are Baumol, 1961; Ferguson, 1969; and Henderson
and Quandt, 1958.
23
24
A Brief Review of the Pure Theory of the Firm
Production theory concepts were first introduced into economics
by Wicksell, Clark, Wickstead in 1885, 1890, and 1910, respectively, and
other classical economists (Blaug, 1962, Chapters 11 and 12). This
theory centers around marginal analysis and depends upon the comparison
of the last unit (or marginal) of benefit and cost for decision-making.
Factor-product or input-output relationships are mathematical
relationships between inputs and outputs, i.e.,
Yi = f (X ii ) i = 1, 2,
j = 1, 2,
n
(2)
Where Y. is the i th output and X. is the
1
1D
.th
.th
D input used for the i output.
If there is more than one input used in the production of Y.,
1
then Equation 2 is written as follows:
Y. = g (X. , X.
X. 1
12 , 13 ,
1 1
X.in)
(3)
Analysis of problems in economics are carried on, generally by
keeping all other factors constant except one, and then inspecting
changes in output with respect to only one varying factor.
Yi = g (X i2
IX il , X i3 ,
Xi n )
(4)
For example, in Equation 4 only the factor X i2 is allowed to change,
ceteris paribus.
Figure 4 shows a hypothetical production function between an
output and one production factor. The specific shape of this function
is determined by analysis based on the data collected from the technical experiments.
25
UNITS
Yi
Yi
g(X; 2 1 X11,X 1 3.• •,Xin)
UNITS X1 2
)
Figure 4. Functional Relationship Between Output (Y1 ) and Input (X.
12
(Hypothetical).
26
In economics the one factor production function concept is
treated unrealistically, for educational purposes. In agriculture this
situation cannot be found at all. Therefore, more than one factor
should be included in the analysis. When two factors of production are
used the vertical reflection of isoproduct contour lines from a productionsurfacetoahorizontal - x12
X il . plane can be determined and the
isoproduct curves converted to a managable form (see Figure 5). The
equation for the isoproduct or isoquant line is
Yi * = n (Xil , X i2 I Xi3 , Xi4 ,
Xi)(5)
for a given level of putput, Y i * and inputs X II ,
Xin. The different
combinations of two inputs give constant units of output as shown in
Figure 5. This factor-factor relationship is used theoretically by the
manager to compare all production factors so as to select the least cost
combination of inputs to produce Yi *.
The general equation for Yi * isoproduct curve is converted to
Xil = k (X i2 I Yi*),
(6)
which states that output is held constant at a particular level and the
functional relationship, k, is between Xil and Xi2 . The particular
shape of an isoproduct curve depends upon the technical production relationships.
A third step is to determine the comparative profitability of
products under the given production and marketing conditions. A tool
for comparing these product-product relationships is the production-
possibilities frontier, "a locus showing the maximum attainable output
27
UNITS
Xi i
UNITS X12
Figure 5. Isoproduct Curves Between the Production FactorsX il and
Xi2(Hypothetical).
28
of one commodity for every possible volume of output of the other commodity, given the fixed resource base (Ferguson, 1969, p. 440)." The
general formula for this relationship is
h (Y1 , Y 2X 1 j, X 2j ) = 0
(7)
where X ij and X 2j are the endowed input levels and Y1 and Y2 are products
which may be produced using X lj and X 2j . Y1 and Y 2 vary while X lj and
X 2j are kept constant. Under the prevailing market conditions the maneger has to decide on the level of production of Y 1 and Y 2 (see Figure 6).
In the previous paragraphs, the physical relationships among inputs, input-output and outputs have been discussed. To make an economic
decision, the prices of inputs and outputs are required.
In the general situation a manager faces m production inputs and
n outputs from which to choose to maximize profit. Equation 8 expresses
this choice as a general profit function. In short, the first part of
the right hand side of Equation 8 is the total gross return from n outputs produced, and the second part is the total cost of m production
factors.
=E
i=1
P•Y•
-E
j=1
(9)
r •X •j
where P and r are the prices of outputs and inputs respectively. Maximizing Equation 8 subject to the equation of the production possibility
frontier gives
H(Y1 ,Y2 ,
Ynli X , X 2 ,
Xm ) = 0
(9)
29
UNITS
Y1
UNITS Y2
Figure 6. Production-Possibility Frontier of Outputs Y 1 and Y 2
(Hypothetical).
30
Treating Equation 9 as restraint and forming the Lagrangian equation
gives
Z =
y:
2::
P.Y.
i=1
j=1
r.X. - )[H(Y ,Y
1 2
Y ,X ,X
n 1 2
X )]
m
(10a)
From Z the first order conditions for each i and j are
3z
a Yi
(10b)
z = r .
ao X.
3
6X
= 0
(10c)
Finally, the first order conditions can be reduced to the marginal condi. tions
P
P
1
P 2
3
P 2
en-1 .
Pn
6 H/ay
H/6Y 2
= ii/Y3 = • • •
6 H/6Y4
r
r
r
H/6X
n-1 = 1 = 3 =...= m-1 =
1
6H/ byn.r
r
r
a
H/ax
2
4
m
2
6H/ bY
H/6 X
3
b H/6X4
1-1/
m-1
3 H/ 6 Xm
Equation 11 says that at the equilibrium level of production and input
use, the contribution to profit of the last unit of the output or input
should be equal to the contribution to profit of each of the other competing outputs or inputs. And in turn, the ratio of these contributions
31
of inputs and outputs should be equal to their respective price ratios.
Condition (10b) defines the optimum point of production on the production possibility frontier. Condition (10c) is optimum at the intersection of the isoquant and budget constraint (isocost curve). These two
conditions on the input side and the output side are met simultaneously
and leads the manager to the Pareto optimal contract (conflict) curve on
both the production side and the consumption of input side.
Mixed Integer Programming and the Pure Theory of the Firm
Marginal analysis has some shortcomings in terms of the treatment of real life economic problems. Dorfman discusses these under two
factors:
(a) In linear programming to a greater extent than in the marginal analysis there is a conscious attempt to state the economic problem in an operationally meaningful way, that is, to
work with concepts which correspond to measureable phenomena
and to state the problems in terms of the variables with which
businessmen and other economic policy-makers actually operate.
The process [or activity], with its constant unit direct costs,
is a familiar concept to the businessman and his accounting
methods are based on this concept.
(b) Secondly, the range of choices in the real life involve the
selections among discrete alternatives rather than continuous scales
with continuous first and second order partial derivatives (Dorfman,
1951, pp. 80, 83). Because of the latter condition linear programming
techniques are often utilized when the problem has discontinuity. Linear
programming is "a mathematical technique for determining the best allocation for a firm's limited resources (Thierauf and Grosse, 1970, p.
224)." Table 5 compares the assumptions of linear programming and marginal analysis.
32
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34
The major differences between marginal analysis and linear programming are in the homogeneity and degree of the production function
(assumption B-2), its linearity (assumption B-3), treatment of production factors (assumption C-1), and divisibility of inputs and outputs.
However, the perfect divisibility assumption of linear programming might
still be a shortcoming in real life situations since many resources,
such as machinery, trucks, and the assignment of men to jobs, are indivisible. Therefore, "the class of nonlinear programming problems
(that) is obtained from the general linear programming model by imposing
the additional requirement that the variables can take on only integral
values" is called integer programming (Thierauf and Grosse, 1970, pp.
331, 332).
Particular problems may consist of both perfectly divisible
and integral variables. In such cases, mixed integer programming techniques are utilized.
The linearity assumption of linear programming is shown in
Figure 7 for two activities, production of Y1 and Y 2 by employing a
single input X l . Here it is seen that for every unit increase in X 1 results in 1 unit increase in Y
1
and 2 units increase in Y
2
regardless of
the production level of each output. This constant rate of substitution
is required by the linearity assumption.
It is known that most products can be produced by more than one
technique utilizing inputs at different rates. The derivation of isoquant curves in linear programming are shown in Figure 8 A-C utilizing
several production technologies and two inputs X 1 and X 2 .
The optimal solution of a linear program depends on the slopes
of the price line (budget constraint line) and of the particular segment
35
OUTPUT
UNITS
/
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/
/
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°...
Y2
.0"
....
..0"
/
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/
.0'
....*
.0.
.....
.....
/ ,„,.. '''... .....
.... .....
/
..0
/-
.••••
UNITS X
Figure 7. Linear Production Functions of Outputs Y1 and Y2 with
Respect to Input X 1(Hypothetical).
1
36
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37
of the isoquant curve. If the price line PP (see Figure 8) is tangent
to Y = 50 isoquant curve along the rt line segment, then any combination
of processes described by the line segment between A and B will be optimal. If the price line P'P' is tangent to the isoquant curve at point k,
then process A will be the optimum since isoquants do not have definite
slopes at the corners In a linear programming problem.
Referring back to Figure 6, in pure theory the two products
(Y 1 and Y 2 ) can be substituted at a diminishing rate. However, in linear programming there is a production region in which for each output
certain factors are limiting while others are in ample supply. Figure
9 shows the product transformation polygon for a linear programming
problem. Here ABCDE is product-transformation frontier, and RR and NN
are the maximum attainable net revenue lines. If one assumes the NN
line, then point C will be the optimal solution point where the net
revenue is maximum, Note that the net revenue line which touches the
product transformation curve indicates the quantities of the products
that will be produced and is similar to the tangency concept of marginal
analysis.
The major difference between linear and mixed integer programming is the latter has variables that possess some integer nondivisible
values. The difference between these two techniques can be pictured
best by comparing their cost functions (Figures 10A and 10B). Since in
mixed integer programming some of the resources require integral quantities, the cost function is shown by the step cost function in Figure
10E. This indicates that production of each additional unit of Y
1
re-
quires a sum of fixed and variable resources that cannot be divided into
38
UNITS
UNITS Y2
Figure 9. Product Transformation Process in Linear Programming
(Hypothetical).
Technique
39
DOLLARS
IC
"e• TVC
/e
,e
.n
- TFC
AVC . MC
A
UNITS Y 1
IC
I TVC
DOLLARS
TFC
r- 1•••
.41.41111 111•71. 111/.116
71•41m.
AVC . MC
UN ITS Y1
Figure 10. Cost Functions of (A) Linear and (B) Integer Programming
Techniques (Hypothetical).
40
smaller units. An example for this situation from irrigated farming is
center pivot sprinkler systems that require annual fixed cost computed
on the total capital investment in the sprinkler system. The additional
variable factors (land, labor, machinery, and other inputs of production)
are determined on the basis of the optimal land requirements for the
sprinkler system.
In conclusion one can state that linear programming is a technique for calculating the best means of allocating limited resources.
The choice in linear or integer programming techniques is not a choice
between alternative input utilizations or output production levels but
rather is a choice of "different ways of doing (the same) things" which
requires necessary changes in the composition of ingredients (inputs) or
outputs or both (Dorfman, Samuelson, and Solow, 1958, p. 132). Applicability of marginal and programming techniques depends upon the nature of
the problem. If the question is about the technique that should be
applied for using a particular resource for the adopted purpose, then
marginal analysis will be more appropriate. If the alternative ways of
utilization of a particular resource are to be investigated, then a programming technique should be applied.
Research Procedure
Overall Research Plan
The main objective of this research is to determine the economic
and water conservation impacts of alternative irrigation systems in the
Sulphur Springs Valley agricultural sector. In order to realize this
41
objective, representative-farm mixed integer programming models are
formulated for farms using both sprinkler and gravity irrigation systems.
The solutions of these programming models provide the optimum
crop mix, resource allocation, and net returns above total cost under
the given input and output conditions. Moreover, they indicate the next
best cropping technique when one or some of the conditions are changed,
i.e., by means of sensitivity analyses the effects of changing condition on optimum cropping pattern, resource utilization, and net return
above total cost can be measured. Also, by these models the rates of
resource utilizations (land, water, manpower, machinery, equipment,
etc.) for farm as well as regional level can be forecasted.
To provide information on net returns of various cropping alternatives representative farm budgets for both sprinkler and gravity irrigation systems are constructed. The budget data were collected through
field interviews and from studies by Willett, Hathorn, Robertson, and
Page (1975), and Willett (1976), and by Hathorn and Wright (1976).
The solutions to the representative-farm mixed integer programming models are analyzed in terms of their optimal cropping pattern,
water consumption, and returns to management (or profit). Finally, the
results are aggregated on the basis of available total agricultural
acreage in Sulphur Springs Valley and annual groundwater pumpage in
order to determine the impacts of increasing numbers of sprinkler irrigation systems upon the agricultural sector of Sulphur Springs Valley.
The following procedure, which is utilized by Kelso, Martin, and Mack
(1973, p. 75), is adopted for this purpose:
If one were to define a representative farm model for each different situation facing farmers over a large area such as the
42
state (or Sulphur Springs Valley) and then were to sum the results of all the models in proportion to the frequency with
which each model situation actually exists, one could obtain
estimates, for the entire state (Valley), of aggregate quantities of crops, gross and net income, water use, and any other
quantities of interest.
Review of the Related Studies .
Although there are numerous studies available dealing with the
supply and use of water in Arizona, none have studied the economics of
alternative irrigation systems in Sulphur Springs Valley in detail.
Studies that relate to this proposed project will be reviewed under
three categories: (a) those that relate specifically to the study area;
(b) those that analyze impacts of increased irrigation costs on farm
organization and the regional economy; (c) and those that deal specifically with sprinkler irrigation systems.
a. Two studies of the area have collected primary data from a
sample of farmers in order to construct representative farm budgets for
in
each farm size. Almond was the first to study representative farms
Cochise County. The general objective of this study was "to provide
typical data on Cochise County farms" in order to have information
available to assist farmers to reorganize their farms into "more profitable and workable units (Almond, 1962, pp. 2, 3)." Almond constructed
calendars of operations for cotton, grain sorghum, alfalfa, barley,
and 1000
safflower, and lettuce for 5 farm sizes (160, 320, 480, 640
acre farms) on the basis of information collected from 62 farms sampled
by personal interviews. In these calendars, the physical relationships
between inputs and outputs were given. Then, using appropriate prices
for those inputs and outputs, costs and returns were computed. These
43
calendars were combined with fixed cost data to provide complete descriptions of representative farm operations. The results are summarized as follows:
(a) all farm sizes were overmechanized;
(b) crop rotations were not typically used;
(c) ceteris paribus, natural gas pumps were cheaper to operate
than electric pumps;
(d)
the owner-operated, 320-acre size farms had the highest
percentage of net returns to capital investment accruing
to management (3.0%);
• (e) in all of the tenant-operated farms, leasees had larger
returns to management than the owner-operators;
(f) landlord of 160, 320, and 480-acre tenant-operated farms
have negative net returns to management.
The second economic study of Cochise County agriculture was done
by V. W. Lee (1967). The main objective of this study was to provide
technical and economic information about the crops grown, viz., cotton,
alfalfa, and grain sorghum, in the area, and to forecast the long term
situation for the period 1966-2006. Similar to Almond's study, the
calendars of operations of these crops were constructed on the basis of
personal interviews with operators of 72 old and recently established
farms. Then, costs and returns were computed and, with the aid of secondary data, the forecasts Were made. Three farm sizes were recognized,
15-160, 160-480, and 480-acre and larger farms. The results show that
the small size farms (tenant-operated alfalfa and grain sorghum growers)
were inefficient in operation and their gross returns do not cover their
total costs or even total variable costs. On the other hand, the medium
and large farms had lower cost per acre so that gross returns cover the
44
total costs with 1.3% and 3.4% returns on average
investment for medium
and large farms, respectively.
Although these two studies discuss some of the implications of
a falling water table in the area, they do not analyze
alternatives to
stop or slow down this trend.
The work by Willett and others (1975) focuses primarily
on alternative energy sources (diesel and electricity) for pumping groundwater due to expectations of scarcity in natural gas supply
in Cochise
County. They compared the fixed and variable costs of establishing and
operating a pumping plant utilizing natural gas, diesel, and electricity
as energy sources. The costs were computed on the basis of per acrefoot of water. The results showed that there was an advantage of electricity over diesel at shallow depths, and vice versa on wells deeper
than 325-350 feet, but natural gas was the cheapest energy source among
others in every case.
b. The second group of studies start from the farm level budgeting
process and then identify and analyze the regional impacts resulting
from variations in the components of irrigation water cost. Predominantly, they use linear programming as the analytical tool. Stults
(1968), Jones (1968), Mack (1969), Burdak (1970) and Hock (1973) conducted studies on areas of Arizona other than Cochise and Graham Counties and are included in this second category.
Kelso, Martin and Mack (1973) summarized the aforementioned and
other studies conducted on Arizona's water problems and its management
from economic as well as technical, social and institutional viewpoints.
They designated six irrigation regions in Arizona: Yuma County, Maricopa
45
County surface and pump water areas, Pinal-Pima Counties, Graham-Greenlee
Counties, and Cochise County. Projections for adjustment$ in crop acreages, water consumption, and gross and net farm revenues for each area
were made for the 1966-2015 period. These projections are shown in
Table 6 for Cochise County. These studies all assumed use of conventional irrigation systems.
c. The third category of studies deal with the economics of sprinkler system application in general. Gordon (1970) analyzed the costs
and savings associated with the adoption of sprinkler and trickle irrigation systems for citrus trees in two irrigation districts in Yuma
County, Arizona, viz., the Wellton-Mohawk and Yuma Mesa Irrigation and
Drainage districts. Gordon's main objective was to determine the effectiveness of alternative irrigation practices for reducing pollutants in
the Colorado River (which create "friction" between the U. S. and the
Republic of Mexico), for achieving savings in water consumption, and for
minimizing the drainage problem. These subjects are treated from economic, technical and legal perspectives. He evaluates the water resource of the county, legal questions between the states of California
and Arizona and also between Mexico and the U. S., the development of
water sources such as dams, canals, irrigation systems, and finally
economic comparisons of irrigation systems (conventional, sprinkler,
and trickle irrigation) by means of partial budgeting focusing primarily
on irrigation operations. Gordon (1970, pp. 104, 105) concluded that
either sprinkler or trickier irrigation systems could generate higher
profit for the producers than presently used conventional systems (especially in citrus).
•
46
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47
The studies by Sheffield (1971), and Retzlaff and
O'Dea (1971)
treat the operation and ownership costs of center
pivot systems, used
for irrigating corn and pasture, respectively,
in Nebraska. To avoid
repetition, only the former study will be reviewed.
The overall objective of Sheffield's study (p. 71) was "to learn
the extent of center-pivot irrigation in the Southwest Nebraska Cropping
District." Specifically, he examined the existance of economies of size
in (a) total corn production costs, (b) the marginal productivity of
capital, and (c) per acre labor requirements for operating center pivots
as the number of center pivot units increased. The author surveyed 9
Southwest Nebraska counties and identified 3 farm groups: (1) the farms
with 1 to 2 center pivots; (2) those with 3 to 5 center pivots; and (3)
those with 6 or more center pivots under operation. The data were collected from randomly selected farmers in each of the three groups. During the corn growing period in the area (May, 1970 - January, 1971),
special forms for record keeping of costs of corn growing were left with
the 19 farmers. Each month they were assisted in filling out the forms
and completing some of the questions. On the basis of those forms, a
complete farm budget for corn production under center pivot sprinkler
system was constructed. Results showed that there were no apparent
economies of size for fixed costs of the center pivot systems (Sheffield,
1971, p. 267). However, economies of size did exist relative to the
variable costs of production.
The economies of size in total variable cost (TVC) and yield of
corn are given in Table 7. The principal TVC component affecting the
economies of size for the third group were preplant and seedbed
•
48
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49
preparation, planting, land insurance, fertilizer, herbicide and
insecticide applications, and harvesting. Total costs were inconclusive
because of variations in types of power units and variations in make and
warranty coverages in the center pivot systems. Those existing economies of size in labor cost of maintenance and repairs were 68, 61,
and 564 per acre for the first, second, and third groups, respectively
(Sheffield, 1971, pp. 200, 269).
On the basis of the above results, Sheffield accepts the following three hypotheses: As the number of center pivot units under one
ownership increases, economies of size exist in (a) total costs of corn
production, (b) "marginal productivity of capital," (which is measured
by the per acre return above variable and total costs and it increases
with the number of center pivots operated), and (c) labor requirements
for operating the systems and their associated costs (Sheffield, 1971,
pp. 276, 277). The author neither compared alternative irrigation systems nor included any other crops besides corn under center pivot sprinkler irrigation systems for his analyses.
A study by Halderman and Frost (1968) deals with the technical
aspects of application of sprinkler systems under Arizona conditions.
They discuss the advantages and disadvantages of sprinkler system and
design considerations. Then they compare hand-move, mechanical-move
(side-roll, trail-line, end-tow), and center pivot systems in terms of
their technical and operational features. The managerial and economic
aspects of sprinkler system operations are presented, viz., water requirements of sprinkler systems, water application rates, soil structures, crop selection under sprinkler labor requirements and irrigation
50
efficiency of sprinkler systems. Finally, a very brief economic analysis of owning and operating the sprinkler systems is given.
Source and Collection of Data
Type.of Data. For mixed integer programming models of the type
used in this study, data pertaining to both physical relationships and
cost factors are necessary. Physical relationships are represented by
the technical coefficients for producing a crop on a unit of land, that
is, how much labor, water, irrigation equipment, etc., are necessary for
producing a certain crop on a one-acre parcel of land. Energy requirements for bringing one acre-foot of water to the head gate are based
upon the water requirement of each crop and the depth of water. For
converting the water requirement per crop to precise energy requirements,
one needs to know the operating efficiency of the pump, the lift and the
. and returns progallons of water pumped per minute. Production costs
vide information for determining net returns of selected enterprises.
that
Data are also needed on physical, soil, and climatic conditions
restrict the applicability of sprinkler systems.
procedures
Finally data are needed concerning the practices and
study period.
that are followed by the farmers in the area during the
of the activities
The calendar of operations show the detailed schedule
cycle of a
taking place in a representative farm unit during the entire
particular crop.
and
Sampling Procedure. The reports by Willett et al., 1975,
Hathorn, 1976, on the
Willett, 1976, and Hathorn and Willett, 1975, and
conversion of natural gas powered irrigation pumps to other alternative
51
power inputs, on the economics of water in Central and Southern Arizona,
and on Arizona pump water budgets provide much of the secondary data
necessary for this study. To augment these studies preliminary primary
data were collected from Cochise County farmers located mostly in the
Willcox Playa and Douglas basin in December, 1975. These data were collected in conjunction with a study designed to analyze the economics of
adaptation of sprinkler irrigation systems to Wellton-Mohawk agricultural
areas in Yuma County for controlling the Colorado River water salinity
level. During the same time period, calendars of operations of the crops
grown under gravity irrigation were collected by the Department of Agricultural Economics and Cochise County Cooperative Extension Service.
These data were updated and grouped according to the farm sizes and
irrigation systems in order to be evaluated for this study.
Additional primary data were collected from additional personal
interviews of randomly selected (but area-wide distributed) farmers in
the study area in July, 1976. Each interview took 30-90 minutes depending upon the size of the farm, number of the wells, sprinkler systems,
and the crops grown in 1976 growing season.
The random selection of farmers was achieved by utilizing maps
published in Cropland Atlas of Arizona by Arizona Crop and Livestock
Reporting Service, 1974, pp. 7, 10, 12, 22, and 23. According to this
publication the total agricultural area in Sulphur Springs Valley was
149,000 acres in 1974. On this map a borderline was drawn around each
of nine groups of cropland (see Figure 1 for the approximate location of
sampling area). Then starting from the first group these bordered areas
were numbered from 1 to 400, the total number of sections. Every 10th
52
section was selected from a random number table in order to determine
the number of the starting section. If there were more than one farmer
in a drawn section, one of them was selected randomly. If none of the
farmers in a section were available for interviewing, the next numbered
section was selected as the alternate.
Out of 40 sections, one was not available for interviewing (section #330), and four were excluded from the analysis because of the insufficient information derived from the questionnaire (sections #170,
#230, #310 and #400). Six sections were combined with others because
they were under three ownerships, i.e., sections #10 and #70, #190 and
#220, and #120, #130, #160, #180, and #360 were owned by three farmers.
Therefore, even though thirty-three farms were interviewed covering 39
sections, as a result of these exclusions, 29 farms were included in
the analysis that covered 35 sections. Since some farmers owned more
than one section, the sampled area was 17.2% of total cropland in Sulphur Springs Valley.
The information collected through these interviews consisted of
farm sizes, crop acreages, crop irrigation schedules, water application
rates, machinery (power unit) and equipment inventories, and technical
information on wells, pump, engine, gear drives, extra pressure pumps,
and sprinkler irrigation systems. The questions on wells were directed
to the depth, lift, size, and casing specifications. Additional questions about pump, engine, gear head, extra pressure pump and sprinkler
irrigation systems dealt with their make, size, pressure, water output,
type of energy'utilized, and power where applicable. Additionally, the
data were collected on type of sprinkler system, quantity of sprinklers
53
in each farm, acres irrigated by one unit, length of the system, its
pressure, rotation period, intake rate, and the soil type under each
sprinkler unit. Moreover, information about investments in wells, pump,
engine, pressure pump, gear drive, sprinkler systems, and other irrigation components were collected either from farmers or from the dealers
of those items in the Valley (see Appendix D for a sample questionnaire).
During the primary evaluations of the data the sampled farmers
and local dealers were contacted again by telephone for confirmation of
answers on certain questions that were either incomplete, inaccurate, or
missing. On some occasions the cost data for sprinkler systems as well
as other irrigation components were updated by telephone calls to
dealers who could not be reached for personal interviews in their local
offices.
CHAPTER III
THE REPRESENTATIVE FARM BUDGETS
The data collected for this study are summarized in this chapter.
The focus is on general characteristics of the sample, i.e., general farm
size, cropping pattern, machinery and equipment inventory and irrigation
facilities. Additionally, complete unit budgets including total costs of
irrigation systems are developed for alfalfa, cotton, wheat, milo and corn.
Characteristics of the Sample
In this section four groups of characteristics are analyzed,
namely, factors that determine the farm size groups, general cropping
patterns, machinery and equipment inventories, and irrigation facilities
existing in the sampled farms.
Farm Size
The size of the sampled farms ranged between 14.5 and 3470 acres.
However, after elimination of some of the farms because of insufficient
information derived from them the size of the analyzed farms in the sample varied from 120 to 3740 acres. These were grouped into four farm
sizes as shown in Table 8. The factors considered in the determination
of size limits were as follows: the number of full time laborers and
supervisors hired in a year; total tractor horsepower (HP); and the
length of dirt and concrete ditches, and pipelines. By changing the
size limits, the variance of these factors within a farm size group were
54
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minimized as much as possible. In Table 9 the per farm values of these
determinants are shown. Positive relationships between farm size and
hired labor hours, available tractor horsepower (HP), and per farm
length of dirt ditches and pipeline are observed. Although a similar
relationship is seen between farm size and hired supervisor hours, it is
disturbed by the decline in the value for the medium-large farm group
(III). The length of per farm concrete ditches increases with farm size
for small (I), small-medium (II), and medium-large (III) size groups but
falls for the large farms (IV).
Cropping Patterns
In Table 10 the crop acreages of the sample farms are shown.
The total land area occupied by the sample farms was 31,578 acres, which
was 21.2% of the total cropland area of Sulphur Springs Valley. Milo
(grain sorghum), corn for grain, and wheat were grown on 38.3% of total
sampled area, while alfalfa hay represented about 1.5% of the total area.
Cotton was grown on 8.2 percent of the land. These five crops accounted
for 47.9% of the total sampled land.
Approximately half of the total area was under gravity irrigation. Center pivot sprinkler irrigation was applied to 13.2% of the
total land, while side roll was used only on 1.5% of the available cropland., Hand move sprinkler systems were not in operation on any of the
sampled farms.
The average cropping pattern for each farm size is given in
Table 11. It is difficult to observe any kind of crop acreage-farm size
relationship. Per farm alfalfa and cotton acreages are greatest in
small-medium (II) and large farms (IV), respectively. Wheat and milo
57
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are produced mostly by medium-large farms (III). Corn growing and
fallow areas increase with farm size.
Machinery and Equipment Inventory
Results of the machinery and equipment inventories of the sampled farmers are given in Appendix Tables El and E2. The majority of
the sampled farms owned tractors with 100-124 HP. As expected, the
larger farms owned more tractors than the smaller ones. Also they
tended to own larger size tractors than the ones owned by the smaller
operations. As was seen in Table 9, per farm tractor horsepower goes up
as farm size increases.
A similar trend can be seen in Appendix Table E2. The amount of
equipment that is owned by the larger farms is more than on the smaller
size farms. However, it is not possible to observe any relationship between type and size of equipment and farm sizes.
Irrigation Facilities
In Table 12 the important items associated with wells and pumps
are shown for each size group in the sample. Here there are positive
correlations between farm sizes and the average pump size, average horsepower of natural gas engines, average acres per well, and average number
of wells. Excluding the large farm group, similar relationships exist
between the remaining farm sizes and average well depth and lift, average horsepower of electric motors, and average water output of pump (GPM).
Because of the high capital requirement center pivot systems were
installed more commonly on large farms than on the smaller ones. Another
reason for center pivots to be on large farms is that center pivot units
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operate on 160 acres of land, which means that 160 acres of a single
crop normally have to be grown under a system. Center pivots are impractical for the smaller farms that tend to diversify their farming
activities by multiple cropping in order to reduce risk. As shown in
Table 13 side roll sprinklers were utilized more frequently on the small
farms. Comparing the data for the two irrigation systems clearly indicates that the larger farms allocated a greater percentage of their farm
to center pivot systems. Small-medium and medium-large farms did not
use side roll units, while only one large farmer owned a side roll unit
that irrigated 90 acres. This situation implies that center pivot irrigation systems can be afforded and operated only on large farms. Subsequent analysis demonstrates the economic reasons for this implication.
Complete Unit Budgets
In order to determine the coefficients of the variables for the
representative-farm, mixed integer programming models, complete unit
budgets were constructed. The following assumptions were necessary:
i. The sample data do not change during the study period.
With this assumption variations in input-output combinations and changes
in capital investments and monetary returns are eliminated.
There are no significant quality differences among
sprinkler systems, machinery, tools, equipment, other inputs and outputs.
There was no interviewee collaboration during the data
collection period.
iv. There are no variations in the data due to differences
in interviewers.
63
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64
v. Sulphur Springs Valley is assumed to be homogenous;
therefore, there are no subregions in the Valley to be treated separately.
vi.
vii.
Yields are equal among different size farms.
Individual farmers are price takers, therefore input
and output prices are constant.
viii. Calendars of operations do not vary among the different
farm size groups.
ix. Irrigation efficiency does not vary among farm sizes.
The data collected from the sample farms were inconclusive in determining any irrigation efficiency farm size relationship. a Therefore, a
fixed water application rate for each crop was estimated on the basis
of the sample data. Table 14 shows the water application rates of each
crop as collected from the farmers. The efficiencies of sprinkler irrigation systems, which generate some savings in water, are definitely
higher than of gravity irrigation.
aSimple regression analyses for five crops were performed with
farm size as the independent variable and water application rate as
the dependent variable, treating the whole sample as one unit. These
results are given below:
Crop
Alfalfa Hay
Cotton
Wheat
Milo
Corn
InterceptCoefficient
-.00454
61.53
.00056
52.61
-.00059
44.21
-.01712*
56.91
-.01218
31.33
n
5
8
10
15
7
t
.272
.02998
.0225
2.248
.6659
*Significant coefficient at 5% probability level.
These results indicate that excluding milo there is no significant variation in the amount of water applied due to farm size changes.
65
Table 14. Water Application Rates and Irrigation Efficiencies by
Crop, Sulphur Springs Valley, 1976.
System and Crop
A.
63.7
36.0
21.3
22.3
16.5
76
54
44
54
36
83.82
66.67
48.41
41.30
49.71
63.7
36.0
21.3
22.3
16.5
65
39
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30
21
98.00
92.31
71.00
74.15
78.57
Sprinkler Irrigation
Alfalfa Hay
Cotton (Upland)
Wheat
Milo (Grain)
Corn (Grain)
a
Irrigation
Efficiency
eb
-6
Gravity Irrigation
Alfalfa Hay
Cotton (Upland)
Wheat
Milo (Grain)
Corn (Grain)
B.
Consumptive
Water Appli-
Use of Water
cation Rates
(AI) a(AI)
See Appendix F for calculations of consumptive use of water.
birrigation efficiencies of th crop is computed by E l
./W
ci ai
100,
where W ci and W . are the consumptive use of water and water applicaal
tion rate of i . th
crop, respectively.
66
Costs of Irrigation Water by Sprinkler System
and Energy Source
In this section partial budgets of side roll and center pivot
irrigation systems are developed. A sprinkler system can be used
either on an irrigated farm or on an area not previously irrigated. If
an irrigated farm is concerned, then the initial investments in the
sprinkler system need not include the items related to the well (such
as well digging and casing, engine, pump and gear head), since these
are already established on the farm. If, on the other hand, a sprinkler
system will be utilized on a nonirrigated farm or a newly developed
field, then the initial investment will include every item from drilling the well to the final installation of the sprinkler system. In
this study, the sample area did not contain any dry farming or newly
cleared land. Nevertheless, the budgets constructed for irrigated
farms have the associated costs of well establishment, engine, pump,
etc., in order to compute total farm fixed costs of irrigation systems.
Gravity Irrigation System. The following analysis is based on
information collected from the sampled farms. The cost estimates were
updated by figures provided by the local suppliers.
(a) Initial investment. Initial investment costs in Table
15 are given for three energy sources, natural gas, electricity and
diesel. The costs of well drilling and casing, pump assembly, and
bowls are the same for each energy source. The differences in the
power unit costs are due to the type of energy and other technical specifications related to energy. Cost figures of well drilling and casing
are based on.a 16-inch casing and 460-foot well depth.
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68
From a comparison of Tables 12 and 15, it can be seen that the
power units do not have the same horsepowers. This difference is because of the relationships among lift, water output of the pump, its
overall efficiency, and input horsepower as expressed by Equation 12a
for electric motors (Hathorn, 1976, pp. 24-28).
Input HP e = [(hxGPM) / 3960] OPE
(12a)
where,
Input HP e = Input horsepower for electric motor (HP)
h = Lift of the well (feet)
GPM = Water output (gallons per minute)
OPE = E
e
x E
where,
E
of electric motor (.90)
e = Efficiency
E =
Efficiency of pump (.80). Therefore, overall
pumping efficiency is 72% (or .72).
Input horsepower requirements for natural gas and diesel engifles are given by Equation 12b.
Input HP = Input HP /E g
e
where,
Eg =
Efficiency of the right angle gear drive (.95).
In short, Equations 12a and 12b can be expressed as
Input HPe = h • GPM/2851.20
Input HP = h • GPM/2708.64
(12b)
69
In Table 12 the average lift (h) and water
output (GPM) of each
farm size are given. By using Equations 13a and
13b, input horsepower
needs are easily determined. The calculations show
that the engines
already established are much larger than what are needed on the basis
of available well and water specifications. Some of
this excess capacity may be due to expectations of decline in the water table as
well as
the seasonal variations in quantity of water pumped.
The per well total initial investments for well development by
farm size are given in Table 16. The differences in total investment
among farm sizes are a result of differences in engine, pump, and bowl
sizes and also in the well depth.
(b) Fixed cost of irrigation water. Table 17 is designed
to show the total fixed cost items: depreciation, interest, taxes, and
insurance. Useful lives and salvage values are given in Table 18. A
straight line depreciation schedule was applied.
Interest was determined by:
Int = f x AInv
(14)
where,
f = interest rate (8.6%)
AInv = average investment which is one-half of total
initial investment.
Tax is computed by Equation 15.
Tax =txrx AInv
(15)
where,
t = the tax rate (.1056)
r = the taxed portion of the average investment (.18).
70
Table 16. Total Initial Investment for Well Development by Farm Size
and Energy Source, Sulphur Springs Valley, 1976.
Farm Size
Natural Gas
Costs per Well ($)
Electricity
Diesel
I.
(201)
$26,260.00
$24,502.00
$30,300.00
H.
(500)
29,392.00
27,634.00
33,433.00
III.
(980)
35,432.00
33,739.00
39,768.00
IV. (2137)
30,084.00
28,326.00
34,124.00
71
Table 17. Annual Fixed Costs of Gravity Irrigation Systems for Four
Farm Sizes and Three Energy Sources, Sulphur Springs
Valley, 1976.
Farm
Size
Fixed Cost
Item
Depreciation
Interest
Taxes
Insurance
I.
Total a
Total
Total
IV.
a
Total
a
a
a
Total Fixed Costs ($)
Natural Gas
Electricity
Diesel
$2,836.00
$2,495.00
$3,620.00
1,132.00
1,055.00
1,309.00
249.00
233.00
288.00
25.00
44.00
45.00
4,242.00
3,827.00
5,262.00
4,557.00
4,141.00
5,576.00
5,526.00
5,134.00
6,620.00
4,743.00
4,327.00
5,763.00
The differences in total investments among farm sizes, (resulting from
the differences in engine, pump, and bowl sizes, and also from the
well depths), are reflected in the total fixed costs above.
72
Table 18. Depreciation Schedule for Well Equipment.
Item
Useful Life
(Years)
Drilling and casing
installation
Salvage Value
(Percent)a
25
0
Casing (including perforation)
25
0
Pump assembly
15
3
Bowls
2
0
Power Unit
5
3
Other components
2
3
Installation and assembly
2
3
a Percent of new costs.
73
Fire and lightning insurance on the power unit, other well components, and installation and assembly costs are given below:
Ins = [(Inv.P + Inv_C + Inst) / 2] x m (16)
where,
Inv • P =
Investment on power units ($)
Inv.0 =
Investment on other components ($)
Inst =
Cost of installation and assembly ($)
m =
Insurance rates which are 0.0094, 0.0253, and 0.0097
for natural gas, electricity and diesel engines,
respectively.
(c)
Variable cost of irrigation water. The variable costs
of gravity irrigation water have three basic components, energy cost,
irrigation labor cost, and the cost of repairs, maintenance, lubrication, and attendance. The discussion of irrigation labor cost appears
later in this chapter where the partial costs per acre inch of water are
developed for each farm size, energy source, and irrigation system. The
equation for calculating variable costs was given in Chapter 1 (Equation 1), and is repeated below:
VC= [(k e x p x g) / E + m] h
The difference in variable costs among the farm sizes is due to the
change in average lift (h) since the other factors are constant. Variable pumping costs per acre inch of water are given in Table 19. The
annual total water pumped is computed by Equation 17.
TW = 24 x
GPM x D/448.8
(17)
74
Table 19. Variable Costs of Gravity Irrigation System by Farm Size
and Energy Source, Sulphur Springs Valley, 1976 • a
Farm
Size
Variable
Cost
Natural Gas
Energy Source
Electricity
Diesel
I.
Total per Well
Average ($/AI) b
4049.74
.7533
6791.50
1.2633
7584.46
1.4108
U.
Total per Weil l_
Average ($/AI) lj
4052.16
.8442
6795.84
1.4158
7587.84
1.5808
III.
Total per Well
Average ($/AI) b
6818.77
1.1692
11430.72
1.9600
12767.41
2.1892
IV.
Total per Weil l_
Average ($/A1)'
3881.21
.9742
6507.07
1.6333
7267.61
1.8242
aAs determined by Equation 1. Excludes irrigation labor costs.
Annual total water outputs in acre inches (AI) are given in Table 12
for each farm size.
b
c
Natural Gas = $.1167 per therm or $1.2458 per MCF.
Electricity = $.03049 per KWH.
Diesel Fuel = $.4237 per gallon.
75
where,
TW = annual total water used (AI)
D = number of days the pump is operated in a
year which is
estimated as 150 days (Hathorn, 1976, P. 2). From
an inspection of
Tables 17 and 19, it can be seen that pumping water with a diesel
power
unit is most expensive.
Side Roll Sprinkler Systems. Both the side roll and center
pivot irrigation systems require additional initial investment. The
additional cost items for these systems are combined with the total cost
of well development for the gravity irrigation system to obtain estimates of total investment costs for the sprinkler systems. However, in
order to simplify the presentation, the cost variations due to different
energy sources are given later in the chapter. In this section cost
items are developed only for natural gas energy source.
(a) Initial investment costs of side roll sprinkler systems. A summary of the cost data for side roll sprinkler systems is
given in Table 20. These data were collected from the sampled farms
and updated on the basis of cost information obtained from the local
dealers.
The common side roll systems in the area are 40-acre side roll
units. However, in order to give some flexibility to the application
of these systems, the investment costs and variable costs of 10 and 20
acre side roll units were developed by consulting local dealers and
technical personnel (see Appendix G).
The first item in Table 20,mainline,mey or may not be used depending upon the locations of the well and the field to be irrigated.
76
Table
20.
Initial Investment Costs of Three Side Roll Sprinkler
Systems, 1976. a
Item
10-Acre
20-Acre
40-Acre
$2,310.00
$2,310.00
$2,310.00
Sprinkler System Unit
2,988.00
3,657.00
5,491.00
Pressure Pump
2,250.00
2,250.00
2,250.00
Transportation, Installation,
and Assembly
1,150.00
1,250.00
1,500.00
8,698.00
9,467.00
11,551.00
869.80
473.35
288.75
Mainline
TOTAL
Per Acre Initial Investment
a Details on the estimates of these costs are given in Appendix G.
77
The costs of mainlines vary in relation to pipe size
(6" - 15"),
the
kind of pipe (plastic, aluminum, steel), and the pressure (20-60 PSI).
The example unit consists of
8"
plastic pipe with a
40-60
PSI pressure
rating. Its cost is $1.75 per foot.
The cost of the side roll unit depends upon its size, manufacturer, year, and other specifications. The 40-acre side roll unit
given in Table 20 has 5" x 1/4 mile pipe with 34 line wheels and 4 moving wheels which are 76" in diameter.
The pressure pump commonly used in the area is a natural gas,
6
cylinder engine that pressurizes the water up to 50-90 PSI, depending
upon the kind of sprinkler system. The new cost of this pump as quoted
by dealers is between $2200 and $3000, with $2250 being the most common
estimate. Because of the lower Pressure requirements, this pump costs
less than the one for center pivot systems.
As is seen in Table
20,
'the per acre initial investment cost of
the side roll sprinkler is highest for the unit that irrigates
10
acres.
There appears to be economies of size in the adoption of side roll
systems.
(b)
Added fixed costs due to side roll sprinkler systems.
In order to spread the total initial investment cost over the
useful life of a system, it is necessary to compute fixed costs as was
done for well establishment expenses. The annual fixed cost consists
of depreciation, interest, insurance, and taxes. Depreciation is computed by following the same procedure described previously in fixed
cost of irrigation water. Mainlines are depreciated over 25 years with
zero salvage value. The sprinkler system unit and the pressure pump
78
have useful lives of 10 and 15 years with salvage values of 17% and 3%,
respectively. The transportation, installation and assembly cost is
distributed among the other three items in proportion to their respective costs. Depreciation and other fixed cost items are given in Table
21.
Table 21. Annual Added Fixed Costs Due to Three Side Roll Sprinkler
Systems, 1976.
Acre Unit
Fixed Cost ($)
20 Acre Unit
Depreciation
586.55
646.94
841.79
Interest
374.01
407.08
496.69
Taxes
82.67
89.97
109.78
Insurance
28.42
31.99
41.81
1071.65
1175.98
1490.07
107.17
58.80
37.25
Item
TOTAL ($)
Per Acre Added
Fixed Cost ($/A)
10
40
Acre Unit
Insurance is not applied to mainlines since they are not subject to the atmospheric hazards (like lightning, hail, and rain) like
the sprinkler unit and pressure pumps. Generally the kind of insurance
79
policy used in the study area does not cover theft and
vandalism but
only natural hazards.
As is seen in Table 21, there are apparent economies of size
in
per acre fixed cost for side roll sprinkler units of increasing capacity.
(c) Added variable costs due to side roll sprinkler
sys-
tems. As was discussed previously any costs associated with the sprinkler systems, either side roll or center pivot, are added costs to the
cost of gravity irrigation water. For example, added variable costs
due to the side roll system are added to the variable cost of water
available for the gravity irrigation in order to calculate the variable
cost of irrigation water obtained through side roll sprinkler systems.
Variable costs of side roll sprinkler systems consists of three
components, extra pressure cost, moving cost of the system, and lubrication, maintenance and repair costs (Table 22). Extra pressure is
necessary for sprinkler systems since they require pressurized water
for irrigation, i.e., the water pumped from a well does not have enough
pressure to flow through the sprinkler pipes and nozzles. Therefore, a
pressurizer is placed between the well pump and sprinkler system in
order to supply the required pressure.
Average extra pressure costs of the side roll units ($/acre)
are assumed to be equal for each size unit. The moving cost of a system is associated with a power unit (an electric motor or conventional
engine) that moves the system during the irrigation. The costs vary
considerably among the different systems and farms. Here it is assumed
that the per acre moving costs of sprinkler units are equal for each
size unit.
80
Table 22. Annual Added Variable Costs Due to Three Side
Roll Sprinkler
Systems, 1976.
Item
10
Variable Costs ($)
Acre Unit 20
Acre Unit
40 Acre Unit
Cost Per Unit:
Extra Pressure Cost
155.63
311.27
622.53
8.30
16.60
33.20
Lubrication, Maintenance & Repair Cost
247.42
361.51
542.80
TOTAL ($/unit)
411.35
689.38
1198.53
41.14
34.47
29.96
1483.00
1865.36
2688.60
148.31
93.27
67.21
Moving Cost
Per Acre Added Variable Cost ($/A)
Total Added Cost
Per Acre Added Cost
($/A)
Lubrication, maintenance, and repair costs change significantly
depending upon the age of the system, its make, and degree of operational
skill. It was recently claimed that most of the breakdowns of the systems are due to failure of some owners to perform important maintenance
tasks (Lucas, 1976b, pp. 16-18).
Lubrication, maintenance, and repair costs are assumed to be in
proportion to the cost of the sprinkler systems. These costs were
81
derived from the experience of the sampled farms in using 40-acre units.
The per acre total added costs decline as the size of side roll units
gets larger. This decline is because of the economies of size existing
in the fixed and variable costs of side roll units.
Center Pivot Sprinkler Irrigation System. The following cost
information was collected from the sampled farms and then updated
through telephone contacts and/or personal interviews with local suppliers.
(a) Initial investment costs of center pivot irrigation
systems. As is seen in Table
23,
the items of initial investment are
the same as for the side roll systems.
Center pivot irrigation systems that irrigate
of a
160
130-140
acres out
acre square block are the commonest type in the study area.
They have
7-13
towers and some of them have the so-called "corner sys-
tem" that irrigates larger areas (up to
150
acres) by means of a corner
arm which extends from the normal retracted position as it approaches a
corner of the field. Larger systems that irrigate
360
300
acres out of a
acre block are also available, but none of these systems were util-
ized on the sampled farms. Only systems capable of irrigating
130-140
acres are treated in this study.
The costs of center pivot systems vary between
$46,840
$21,260
and
depending upon the irrigated acres, manufacturer, and drive
power (electric, water, or hydraulic driven systems are available).
The electric driven unit given in Table
23
cost about
$5,000-$6,000
electric units
more than water driven units. It was chosen because the
were the most common types in the study area.
82
Table 23. Initial Investment Costs of a Center Pivot Sprinkler System,
1976.
Item
Costs ($)
Mainlinea
Sprinkler System
$3,643.00
b
26,677.00
Pressure Pump c
2,750.00
Transportation, installation
and assbumly
2,400.00
TOTAL
Per acre initial investment
a
b
35,470.00
d
272.85
Plastic 8-inch, 1/4 miles long, 80-90 PSI, $2.76/foot.
Electric driven, irrigates 130 acres out of 160, 1299 feet long.
cNatural gas, 6-cylinder, pressurizes water 80-90 PSI.
d Total initial investment divided by 130
acres.
83
The pressure pump for the center pivot system is about $500-$700
more expensive than the one for a side roll system, since center pivot
sprinklers require higher pressure. As in the case of the side roll
units, a natural gas pressure pump is specified.
Transportation, installation, and assembly cost includes labor
and parts for installing a system in the field.
(b) Added fixed costs of center pivot sprinkler system.
By following the same procedure described in the section describing the
fixed cost of irrigation water (p. 69), the fixed cost items of a center
pivot were computed (Table 24). The depreciation schedule is identical
to that of the side roll sprinkler systems.
(c) Added variable costs due to center pivot sprinkler system. As is seen in Table 24, the added variable cost items of a center
pivot system are the same as for side roll systems. Comparing Tables
22
and 24 indicates that the pressure cost of a center pivot system is
much higher than for the side roll. So are the other components of
variable cost. These higher costs are mainly due to the greater size
and capacity of the center pivot system.
The costs of lubrication, maintenance, and repairs vary considerably among farmers. These costs depend upon such items as the
make, age, type, dealer's warranty, management, soil and topographic
conditions. Labor costs associated with lubrication and maintenance
are included in this category and comprise about 30-50% of it. If the
system is covered by a dealer's warranty, then in most cases this item
will be zero during the first year.
84
Table 24. Annual Added Fixed and Variable Costs Due to Center Pivot
Sprinkler Irrigation System, 1976.
Variable Cost
Fixed Cost
Item
Depreciation
Interest
Taxes
($)
$2,761.64
1,525.21
337.11
Insurance
148.34
TOTAL
4,772.30
Per acre added fixed
cost ($/A) a
36.71
Total added cost ($)
Per acre total added cost (S/A) a
a Total costs divided by 130 acres.
Item
Extra pressure cost
Moving cost
Lubrication, maintenance & repair cost
TOTAL
Per acre added vanable cost ($/A) a
($)
$2,531.10
91.00
959.40
3,581.50
27.55
8,353.80
64.26
85
From the comparison of Tables 22 and 24, it can be concluded
that center pivot sprinkler irrigation system is the most preferable one
since its per acre total cost is the lowest. This result holds for both
per acre added fixed and variable costs of these systems. The 40-acre
side roll unit is the next best alternative. As an example, in Appendix
H the savings and added costs of the alternative sprinkler systems are
computed and compared for use in milo production on Farm Size I (small).
Irrigation Labor Cost. Irrigation labor cost is determined on
the basis of the labor wage ($3.0354 per hour) and the labor requirement per acre inch of irrigation water. The sample data indicated that
labor costs per acre inch of water were constant for all farm sizes.
However, there is a reduction in labor requirements as one moves from
gravity irrigation to side roll sprinklers and to the center pivot system. It is assumed that the labor requirements per acre inch for 10acre, 20-acre, and 40-acre side roll units are equal. Labor requirements
for the three irrigation systems are given in Table 25. Labor requirements of the center pivot and side roll sprinkler systems are 46% and 87%
of gravity irrigation, respectively.
In Table 26, information from Tables 19 and 25 is aggregated in
order to compare the per acre inch variable water cost excluding added
variable costs of sprinklers), by farm size, energy source and irrigation system. From inspection of this table, it can be seen that the
cheapest water is obtained with the center pivot sprinkler unit that
utilizes natural gas as the energy source. When one compares the different farm sizes, the small farms have the cheapest water while the
medium-large farms have the most expensive. So, the ranking of farms
86
Table 25. Irrigation Labor Cost of Three Irrigation Systems, Sulphur
Springs Valley, 1976.
Irrigation System
Irrigation Labor
Requirement (H/AI)
Cost ($/AI) a
Relativeb
Gravity Irrigation
0.1730588
0.5253
100
Side Roll Sprinkler '
0.1500833
0.4556
87
Center Pivot Sprinkler
0.0796043
0.2416
46
a Labor wage is $3.0354 per work hour.
bSide roll and center pivot relative to gravity.
c
40-acre side roll system.
87
Table 26. Variable Water Cost by Farm Size, Energy Source, and Irrigation Systems, Sulphur Springs Valley, 1976 • a
Irrigation Systems
Energy
Sources
I
Water Costb (s/AI)
IV
III
II
Gravity Irrigation
Natural Gas 1.2786
Electricity 1.7886
Diesel 1.9361
1.3695
1.9411
2.1061
1.6945
2.4853
2.7145
1.4995
2.1586
2.3495
Side Roll Sprinkler c
Natural Gas 1.2089
1.7189
Electricity
1.8664
Diesel
1.2998
1.8714
2.0364
1.6248
2.4156
2.6448
1.4298
2.0889
2.2798
Center Pivot Sprinkler
Natural Gas 0.9949
1.5049
Electricity
1.6524
Diesel
1.0858
1.6574
1.9224
1.4108
2.2016
2.4308
1.2158
1.8749
2.0658
aDerived from Tables 19 and 25.
b Includes only variable cost of pumpin g water and irrigation labor cost
Does not include added variable costs of sprinkler irrigation systems.
c Irrigation labor cost ($/AI) assumed to be constant among 10, 20, and
40-acre side roll units.
88
that obtain irrigation water from the
most expensive to the least will
be in this order: Small,
Small-Medium, Large, and Medium-Large.
Natural gas is the cheapest energy source
when compared to
electricity and diesel. The most expensive energy
source is diesel
fuel.
Calendars of Operations for Selected Crops
Review of the previous studies on the area and data from the
sampled farms indicated that the calendars of operations for alfalfa
hay, cotton, wheat, milo, and corn grain were fairly standard among
the
farmers. Therefore, calendars of operations of each crop represent the
entire Sulphur Springs Valley. In Table 27 the list of operations and
the application frequency for each crop are given. Irrigation figures
indicate total application of water for each crop in acre inches and
are given for both gravity and sprinkler irrigation systems.
The operations specifically related to gravity irrigation (i.e.,
preirrigate, buck rows, making and knocking borders, and disking ends),
and other operations like mulching beds and fungicide application, do
not exist when a crop is grown with a sprinkler system.
Unit budgets of alfalfa hay, cotton, wheat, milo grain, and
corn grain were developed for the three irrigation systems (gravity,
side roll, and center pivot), three energy sources (natural gas, electricity, and diesel) and for four farm sizes. In order to illustrate
their formulation, the budgets for milo are described in this section.
89
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91
Fixed Cost of Farms
Fixed costs are defined as the costs that do not change with
the level of production, such as depreciation, taxes, interest and
insurance. Total fixed costs for a given farm size are computed on machines, equipment, tools and land. In Appendix I the calculations of
fixed cost for machines and equipment are given (see also Arizona Farm
Machinery Costs, 1976, by Hathorn and Wright, 1976). The quantity of
machinery and equipment for each farm size was determined from the
representative crop plan that requires certain machinery and tools for
growing operations. Table 28 was developed on the basis of representative crop plans for each farm size, rather than the actual inventories
of machinery and equipment of the sampled farms (Appendix E).
Crop acreages were determined on the basis of average cropping
patterns for each farm size category. A computer program was used to
calculate the annual hours of machinery and equipment use on the basis
of given crop acreages. It also calculated the appropriate fixed and
variable costs by evaluating the annual use rates and new purchase
prices. In Table 29 the total depreciation and taxes, housing, interest and insurance costs are given for tractors, trucks, and other farm
tools and equipment. One-third alfalfa stand establishment costs are
added when the optimal cropping patterns are determined.
General farm:maintenance cost was estimated to be $12.00 per
acre for the entire valley. Therefore, the product of this figure and
average farm size gives the total general farm maintenance cost for each
farm size.
92
Table 28.
Specifications of Machinery and Equipment by Farm Size,
Sulphur Springs Valley, 1976. a
Itern
Wheel Tractor
Wheel Tractor
Wheel Tractor
Wheel Tractor
1/2 Ton Truck
( 80
(100
(125
(150
HP)
HP)
HP)
HP)
Chisel Plow (7-Shank)
Cultipacker (13-foot)
Cultivator (4-Row Sweep)
Cultivator (6-Row Sweep)
Disk Offset (10.5 Foot)
Disk Offset (16.5 Foot)
Float (12 x 36 Foot)
Harrow (3-section)
Lister (5-Bottom)
Lister (7-Bottom)
Moldboard Plow (3-16 2-Way)
Moldboard Plow (4-16 2-Way)
Grain Drill (12-Foot)
Grain Drill (14-Foot)
Planter (Hill Drop, 4-Row)
Planter (Hill Drop, 6-Row)
Rood (2-Row with Basket Cleaner)
Fertilizer Injector (4-Row)
Fertilizer Spreader (Dry, 12-Foot)
Stulk Cutter (2-Row, Rotary)
Stulk Cutter (4-Row, Rotary)
I
II
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
III
IV
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
aBased on representative crop plans. Each x represents one item
•
93
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95
For alfalfa hay, a fraction of the alfalfa stand establishment
cost has to be considered as a fixed cost item. In the study area, an
alfalfa field is abandoned generally every fourth year. Therefore, the
total stand establishment cost is distributed equally among three years.
However, this item is not shown in Table 29 since it is not known at
this stage if alfalfa hay will be in the optimal solution of the mixed
integer program.
Total fixed costs of well development were determined for three
energy sources and four farm sizes in Table 17. Those values were multiplied by the average number of wells for each farm size (Table 12) and
used in Table 29 as total fixed cost of wells.
The tax rate on land is 10.68% and computed on 18% of the value
of land and improvements (see Table 30 on estimates of land values and
its improvements by farm size and energy source). The average value of
land in Sulphur Springs Valley was estimated to be $260 per acre. This
figure includes the value of land itself and improvements (canals, barns,
houses, etc.) plus irrigation wells and pumps. Since the tax on irrigation wells and pumps is given separately in Table 29, adjustments were
required to determine the tax on land. The tax on land was computed by
Equation 18.
/2)
LT.=t
axin x r x (260 x A. - q.x Inv.
in
where,
= 1, 2, 3, 4 (farm size)
n = 1, 2, 3 (energy sources)
LTax = Total tax on land
(18)
96
Table
30.
Estimated Value of Land and Its Improvements, Sulphur
Springs Valley, 1976.a
Value of Land by Farm Size
II
III
Energy Source
($)
IV
Natural Gas
Total
Per Acre b
25,999.35
129.35
75,215.00
150.43
166,217.80
169.61
405,196.57
189.61
Electricity
Total
b
Per Acre
27,758.10
138.10
74,730.00
149.46
170,451.40
173.93
413,979.64
193.72
Diesel
Total
Per Acre b
21,959.25
109.25
63,135.00
126.27
155,379.00
158.55
385,001.92
180.16
a Does not include irrigation wells and pumps.
b
Total land value divided by average farm size.
97
t =
tax rate (10.68%)
r =
taxed portion of land value (18%)
A = average farm size
q =
average number of wells of each farm
Inv = total initial investment for each well
Interest on land is computed on land value in a similar way:
Int
in
f x (260 x
A . - q. x Inv /2)
in
(19)
where f is the interest rate, 8.5%.
As is seen in Table 29, average fixed costs ($/A) decline as
farm size increases up to the large farm size. Therefore, in terms of
fixed cost considerations the 980-acre farm has the lowest dollars per
acre fixed cost.
Comparing different energy sources indicates that wells with
electric motors have the lowest fixed cost for all farm sizes. As a
conclusion, one can state that the medium-large (980-acre) farms that
utilize electricity for pumping water have the least costs in terms of
the fixed farm resources while the small (201-acre) farms that use
diesel engine for pumping water are the most expensive.
In Table 30 the total and per acre value of land and improvements on it (excluding irrigation wells) is given by farm size and
energy source. As is seen, the per acre value of land gets larger
relative to the farm size. The lowest per acre land value is observed
for the small farms utilizing diesel engines as power units. This is
because diesel engines require higher initial investment than the other
power units, electric motors and natural gas engines. Large farms,
98
therefore, utilizing electric motors on wells have the
highest land
value ($/Acre).
Variable Cost of Milo
Tables 31 and 32 present the complete lists of operations for
milo production and their respective rates and costs. Since the only
difference among crops grown under different irrigation systems is in
their water costs, Tables 31 and 32 compare milo produced with a 10-acre
side roll unit and gravity irrigation in order to show this difference.
In these tables each operation is specified in terms of its timing,
power and equipment combinations, machinery and labor operation rates,
name and quantity of materials used and variable cost.
Comparison of these two calendars of operations indicates that
with a sprinkler irrigation system such operations as bordering, knocking borders, bucking rows, preirrigating, mulching beds, disking ends,
and some cultivations are not necessary. Moreover, because of the
higher irrigation efficiency of sprinkler irrigation, the water applied with the side roll sprinkler system is 24-acre inches less than
under gravity irrigation.
Variable costs are those cost items that are determined on the
basis of the level of production. In other words, if production is
stopped, then the variable cost will be zero. Variable costs consist
mainly of wages for labor, fuel, oil, material expenses and service
charges.
In Tables 31 and 32 variable costs are presented under four
categories, variable expenses on machinery (fuel, oil, etc.), labor
(wage), custom operations (chemical applications, combining, and hauling)
99
Table 31. Calendar of Operations and Machinery, Equipment, and
Materials of Milo Under Gravity Irrigation System
(Natural Gas, Small Farm Size).
Equipment
Operation Rates (Hr/A)
Mach.
Labor
Kind
Materials
Quantity
Machinery
Variable Costs ($/A)
Labor
Service
Row
Period
Times
1
Nov.-Dec,
2
Disk
Wheel tractor (100 HP)'
Disk offset (10.5')
.450
.500
$ 2.45
$ 1.58
2
Dec,
1
Chisel or rip
Wheel tractor (100 HP)
Chisel plow (7-shank)
.180
.200
.80
.63
3
Dec.-Jan •
1
Fertilize (broadcast)
Wheel tractor ( 80 HP)
Fertilizer spreader, dry (12')
.060
.067
.21
.21
4
Jan.
1
Plow
Wheel tractor (100 HP)
Moldboard plow (2-16 2-way)
.360
.400
1.93
1.26
3.19
5
Jan.
1
Float
Wheel tractor (100 HP)
Float (12 x 36')
.180
.200
.79
.63
1.42
6
Feb.
I
Fertilize (inject)
Wheel tractor ( 80 HP)
Fertilizer injector (4-row)
.225
.250
1.10
.79
7
Feb.
1
List or bed
Wheel tractor ( 80 HP)
Lister (5-bottom)
.180
.200
.66
.63
1.29
8
Feb.
1
Make borders
Wheel tractor ( 80 HP)
Disk border (6-disk)
.150
.167
.53
• 53
1.06
9
March
1
Buck rows
Wheel tractor ( 80 HP)
Rowbuck (10')
.030
.033
.10
.11
.21
10
March
1
Preirrigate
9.04
6.30
15.34
11
April
1
Mulch
Wheel tractor ( 80 HP)
Harrow (3-section)
.164
.182
.51
.57
1.08
12
May
1
Plant
Wheel tractor ( 80 HP)
Grain drill (12')
.225
.250
1.18
.79
13
May
1
Remove cap
Wheel tractor ( 80 HP)
Harrow (3-section)
.164
.182
.51
.57
14
May
1
Herbicide app.
15
June-Sept.
5
Buck rows
Wheel tractor ( 80 HP)
Rowbuck (10')
.150
.167
.49
.53
1.02
16
June-Sept.
4
Disk ends
Wheel tractor (100 HP)
Disk offset (10.5')
.585
.650
.98
.63
1.61
17
June-Sept.
7
Irrigate
31.64
22.06
53.70
18
July-Sept.
3
Cultivate
2.26
2.10
4.36
19
July
1
Insecticide app.
20
Oct.
1
Knock borders
Wheel tractor ( 80 HP)
Scraper (10')
.082
.091
.28
.29
.57
21
Oct.
1
Prepare ends-harvest
Wheel tractor ( 80 HP)
Disk offset (10.5')
.045
.050
.20
.16
.36
Operation
Machinery
2.077
13-39-0
NH 3
Water (1X)
Seed
Treflan
7.612
Wheel tractor ( 80 HP)
Cultivator (4-row sweep)
.600
Water (6X)
100 lb.
100 lb.
12 AI
8 lb.
1.5 pt.
42 AI
.667
Methyl Parathion
$
Total Variable Costs
$ 4.03
1.43
11.64
15.37
3.66
12.06
17.26
5.63
1.08
4.50
1 qt.
Material
2.10
4.87
2.34
9.37
4.44
100
Table 31 (Continued)
Row Period
Times
Operation
Machinery
$
22
Oct.
1
Combine
23
Oct.
1
Haul
24
Dec.
1
Residue disposal
Wheel tractor (100 HP)
25
Pickup use (60 miles)
1/2
26
Production credit
at 8.5% interest
TOTAL
Machinery
Variable Costs ($/A)
Labor
Service
$
$25,60
Material
$
9.57
ton truck
.70
.57
1.27
7.77
7.77
$49.54
Operation Rates (Hr/A)
Mach. Labor
$25.60
7.72
$40.94
••n•
Equipment
9.57
7.72
$64.08
Total Variable Costs
$37.88
$192.44
Stalk cutter (2-row, rotary)
.164
2.000
.182
Materials
Kind
Quantity
101
Table 32. Calendar of Operations and Machinery, Equipment and Materials
for Milo Under 10-Acre Unit Side Roll Irrigation System
(Natural Gas, Small Farm Size).
Row
Period
Times
Operation
Machinery
Equipment
Operation Rates (Hr/A)
Mach.
Labor
Materials
Kind
Quantity
Machinery
Variable Costs ($/A)
Labor
Service
Material
Total Variable Costs
1
Nov.-Dec.
2
Disk
Wheel tractor (100 HP)
Disk offset (10.5')
.450
.500
$ 2.45
$ 1.58
$ 4.03
2
Dec.
1
Chisel or rip
Wheel tractor (100 HP)
Chisel plow (7-shank)
.180
.200
.80
.63
1.43
3
Dec.-Jan.
I
Fertilize (broadcast)
Wheel tractor ( 80 HP)
Fertilizer spreader, dry (12')
.060
.067
.21
.21
4
Jan.
I
Plow
Wheel tractor (100 HP)
Moldboard plow (3-16 2-way)
.360
.400
1.93
1.26
3.19
5
Jan.
1
Float
Wheel tractor (100 HP)
Float (12 x 36')
.180
.200
.79
.63
1.42
6
Feb.
1
Fertilize (inject)
Wheel tractor ( 80 HP)
Fertilizer injector (4-row)
.225
.250
1.10
.79
7
Feb.
1
List or bed
Wheel tractor ( 80 HP)
Lister (5-bottom)
.180
.200
.66
.63
8
May
1
Plant
Wheel tractor ( 80 HP)
Grain drill (12')
.225
.250
1.18
.79
9
May
1
Remove cap
Wheel tractor ( 80 HP)
Harrow (3-section)
.164
.182
.51
.57
10
May
1
Herbicide app.
11
June-Sept.
10
Irrigate
12
July-Sept.
1
Cultivate
13
July
1
Insecticide app.
14
Oct.
1
Prepare ends-harvest
15
Oct.
1
Combine
16
Oct.
1
Haul
17
Dec.
1
Residue disposal
Wheel tractor (100 HP)
18
Pickup use (60 miles)
1/2 ton truck
19
Production credit
at 8.5% interest
TOTAL
6.599
Wheel tractor ( 80 HP)
Cultivator (4-row sweep)
.600
13-39-0
NH 3
Seed
Disk offset (10.5')
Stalk cutter (2-row, rotary)
.045
.164
2.000
150 lb.
8 lb.
Treflan
1.5 pt.
Water (4X)
44 AI
.667
Methyl parathion
Wheel tractor ( 80 HP)
100 lb.
.050
.182
12.06
15.37
13.64
17.26
1.29
3.66
5.63
1.08
4.50
4.87
9.37
63.74
13.67
77.41
2.26
2.10
4.36
2.10
1 Qt.
.20
.70
2.34
.36
.16
25.60
25.60
9.57
9.57
1.27
.57
7.72
7.72
6.96
$84.25
4.44
$23.59
$48,73
-
-
$37.88
6.96
$194.45
102
and materials (fertilizers, insecticides, herbicides). Irrigation cost,
which includes water and labor costs, is the largest variable cost item
among others.
Production credit is charged on variable cost items at 8.5%
interest rate. The computation of interest charges was done separately
for each item, starting from the month when the expense is made until
the harvest month which is assumed to be the repayment time. This
charge represents the opportunity cost of money spent for operation
activities.
Table 33 demonstrates the nature of variations in costs among
different farm sizes, energy sources, and irrigation systems. Gravity
and the 10-acre side roll unit serve sufficiently for this purpose. As
is seen, the variable costs (VC) that exclude water are constant among
energy sources. They vary among different farm sizes and irrigation
systems because of economies of size and changes in the calendar of
operations.
There is a general order of farm size groups in terms of the
total variable cost (TVC) and total cost (TC) of producing milo under
gravity irrigation, regardless of the energy sources. This order, from
the least costly production of milo to the most is as follows: small
(I), small-medium (II), large (IV), and medium-large (III) farm size
groups. In other words, the small farms produce mil° least expensively,
while medium-large farms do it most expensively. The main factor in
this sense is the water cost, since the production cost excluding water
cost (C) presents a reverse order of farm sizes (without regarding the
case of electricity).
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Similarly, the production of milo under side roll sprinkler system exhibits economies of size in production cost (C) excluding variable
water cost (VCW), i.e., production cost (C) goes down as the farm size
becomes larger. However, when variable water cost (VCW) are included
in the cost figures (TVC), this relationship becomes almost reverse,
(almost because medium-large (III) farm's production cost is higher than
the large (IV) farm's). Energy source affects the results only when
total production cost (TC) is considered. For natural gas and diesel
the order of the farm size groups from the least expensively producing
group is large (IV), small-medium (II), small (I), and medium large
(III). This relationship changes when the electricity is utilized in
such a way that small (I) and small-medium (II) farms switch their positions.
In order to analyze the other crops in a similar way one has to
calculate the water cost of each crop and then add the cost to the variable and fixed costs of that crop and irrigation system. a By doing this
the total variable cost and total cost of a crop for a given energy
source, irrigation system, and farm size can be determined.
Returns over Variable and Total Costs
Returns over variable cost measure the short run profitability
situation. If there is no positive return above variable cost, then we
can say that the particular crop should not be grown since the gross
a The following tables are to be utilized for this purpose: Table
21 and 22 on fixed and variable costs of side roll units, Table 24 on
fixed and variable costs of center pivot unit, Table 26 on variable cost
of pumping water including irrigation labor cost, Table 29 on farm fixed
costs, and Table 35 on variable production costs of crops.
106
return on that crop does not even cover the out-of-pocket cash cost. If
this situation holds for whole farm, then it would be economical to stop
farming or search for a profitable crop plan.
On the other hand, the return over total cost may or may not be
positive. If the return over total cost is positive, there will be
some profit on that particular activity in the short run, and this
profit will be zero in the long run, assuming that market operates in a
perfectly competitive manner. But, if the gross return covers the total
variable cost (TVC) but is less than total cost (TC), the farm will have
short-run losses. In this case it is expected that these short-run
losses will be neutralized by the gains of the future years.
Total revenue (gross return) per acre is the product of crop
yield and its price. The prices of crops were obtained from Agricultural Outlook, July through August, 1976. The minimum and maximum
prices reflect the lowest and highest price levels occurring during the
January-August, 1976, period.
Yields for each crop initially were developed by averaging the
values given for 1968-1975 (Arizona Crop and Livestock Reporting Service,
1976). The yield figure of grain corn in this reference is 37.42 cwt
per acre which is about half of the value given in Table 34. From personal interviews with Cooperative Extension Service personnel of the
Department of Agricultural Economics, Cochise County Agricultural Extension Office, and H. M. Mayes who is in charge of The Arizona Crop and
Livestock Reporting Service, it was determined that that figure was not
applicable to the Sulphur Springs Valley agricultural areas. It was
determined that irrigation systems (gravity vs. sprinkler) make a
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108
difference in corn yields since sprinkler systems provide
a humid microclima troposphere above corn fields which is important in
preventing
corn tassels from burning in the hot and dry months. This condition
cannot be provided by gravity irrigation, and as a result yield reduction occurs. Since these variations were not reflected in the above
source, a weighted average of corn yields collected from the sample
farms was used in this analysis.
Table 35 provides the variable cost data excluding the total
irrigation cost by farm size and irrigation system for the selected
crops. As far as variable costs are concerned (excluding water cost)
there are no variations among the farms that utilize different energy
sources and different side roll sprinkler system units. Comparing the
farm sizes does not reveal anything about economies of size. The general trend for alfalfa hay, wheat, and milo is increasing variable cost
for the first three sizes and declining on large farms. For cotton and
corn variable cost vary inconsistently with farm size.
On the other hand, sprinkler irrigation systems (side roll and
center pivot) have a definite advantage over gravity irrigation in terms
of variable cost. This occurs because of reductions in the operations
necessary for gravity irrigation when one switches to sprinkler system.
109
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CHAPTER IV
THE MIXED INTEGER PROGRAMMING MODEL
Integer programming is a mathematical programming technique that
maximizes or minimizes a given objective function subject to a number of
constraints such that the variables take only integer values. Since
only some of the variables are integer, a mixed integer programming technique is used to treat integer and non-integer variables simultaneously.
A Branch and Bound Mixed Integer Programming (BBMIP) algorithm developed
by R. Shareshian is utilized for the purpose of this study (Shareshian,
1969). The program can solve both pure and mixed integer problems of
limited size and is designed to minimize the objective function.a
Through a sign transformation, maximization problems can be easily
handled.
Formulation of the Mixed Integer Programming Model
The mixed integer programming model is composed of an objective
function which is maximized subject to given land and irrigation water
constraints for March, July, and annually. As described fully below,
the objective function gives the total returns above variable cost for
a given farm size and energy source. It has two components: (a) sum of
gross returns of each crop growing activity, and (b) variable cost of
that activity, expressed as variable production cost including the annual
a
See McMillan, 1975, Chapter 9, for a detailed discussion of
Branch and Bound Mixed Integer Programming.
110
111
amortized fixed cost of an initial investment
in a sprinkler system and
the variable sprinkler water cost excluding
irrigation labor cost. The
detailed descriptions of these concepts are
given below.
Objective Function
It is assumed that a farmer's general objective is to maximize
the return above variable cost in the short-run and above
total cost in
long-run. The profit function can be expressed in a
general form as
Max(
Z .
j =1 "
=
b..
X..)
1]1]
j=1
(20)
i = 1, 2, 3, 4 (farm sizes)
1, 2,...,J (activities)
where Z ij is the net return above total cost (profit) generated from the j th activity (crop growing) of the i th farm size, bij
the net return above total cost of j th activity (X ij ). More explicitly,
the net returns above total cost generated from each activity are summed
to give total net return above total cost realized by a farming unit.
The objective function value shows the profit realized by a production
unit (a farm) that produces certain crops by alternative production
techniques. For example, wheat produced under gravity and center pivot
irrigation systems are two alternative production techniques (activities)
and may generate different profit for the farm.
1
In this model Equation 20 is expressed as a minimization objective as in Equation 21.
112
'II
Min. -21 Z. . = Min
C..X
13n
17 ij j=1
j=1
( J
'
5
K
E
P k Ykm
k=1
(21)
5
yl
j=1 m=1
R
imn jm
where,
in = 1, 2, •.., 5 (irrigation systems),
n = 1, 2, 3 (energy sources)
I = 1, 2, •.., 4 (farm size)
j
=
k
=
1,
1,
2,
2,
(crop growing activity)
6 (crops)
-C.. = Production cost including per unit fixed
costs of
13
sprinkler systems ($/total activity acreage)
Pk = Price of product ($/cwt)
Yk = Yield of product (cwt/total activity acreage)
IW imn = Irrigation water cost including variable pumping
cost, irrigation labor cost by farm size, irrigation system, and energy source ($/AI of water)
Rjm
• = Water requirements of crops (AI per total activity
acreage
the cost of production of a
Inthisformulation—represents
C 13
specified crop for a given farm size including the annual total cost of
a sprinkler irrigation system. Annual total costs of the sprinkler irrigation systems are included as a "variable" cost, since the model is
viewed as a planning model, to be analyzed before the investment is made.
Tables 21, 22, 24 and 35 are utilized to determine the C ii coefficients.
113
These costs do not include the total pumping cost and the irrigation
labor costs of the sprinkler systems.
Variable costs of crops are given in Table 35 by farm size and
irrigation system. The C ij values for the programming matrix are calculated as follows:
C ijm =t
Vij(F
+S )d
min m
(22)
where,
m is the number of acres available to each irrigation
t
system and tin = 1 (gravity irrigation system)
= 10 (10-acre side roll unit)
= 20 (20-acre side roll unit)
= 40 (40-acre side roll unit)
= 130 (center pivot irrigation system)
= Variable cost of production ($/acre)
th..
Fm = Annual fixed cost of the in irrigation system ($/system)
S
variable cost of the m th irrigation system
m = Annual
($/system)
gravity irrigation
m = 0 for
d
= 1 for sprinkler irrigations
Each variable cost (given in Table 35) is multiplied by appropriate acreage of a given irrigation system and added to the total annual
cost of the sprinkler system, given in Tables 21, 22, and 24. The dummy
variable (dm ) is zero if the irrigation system is gravity which does not
bear the added annual total cost of sprinkler systems.
114
P 's and Y's are the prices and yields (cwt/total activity
km
k
acreage) of each crop.
Ykm
= tmy k
(23)
where y k 's are the yields (cwt/acre). In other words, in
order to obtain the gross return for each activity the yields have to be
multiplied by the respective acreages of each irrigation system and the
selling price of each crop. P k 's and Yk 's are given in Table 34.
The third term of Equation 21 is water cost. IWi is the vanable irrigation water cost (VAT) for i th farm size, mth irrigation system, and n th energy source. This coefficient changes with irrigation
systems, energy sources, and farm sizes. The variation in the water
cost (IW) due to the energy source (natural gas, diesel, or electricity)
originates from the differences in the cost of these energy sources.
These variations are reflected in the irrigation water costs byadjusting the cost according to the different energy sources. It is assumed
that no more than one energy source is used on a farm at any one time.
This assumption is confirmed by the actions of many of the sampled
farmers. Water costs were developed and programs were run separately
for each energy source.
The irrigation water requirements (R im ) for each cropping activity and irrigation system are calculated by Equation 24:
Ri m = tm x r i(24)
where r 3. is the water requirements of 3
. th crop as shown in
Table 14. Irrigation costs, dollars per acre inch of water, are given
for gravity, 10, 20, and 40-acre side roll units, and center pivot
115
systems. Irrigation cost is expressed in a general formula as
IWimn = Gn /W + L m
(25)
where,
G
n = Variable cost of pump and well assembly ($ per well)
W i• = ,Average water output of each pump (acre inches)
Lm = Irrigation labor cost determined for each irrigation
system ($/A1)
The first item on the right hand side of Equation 25 represents
the average variable cost of pump and well assembly ($/A1 of water).
Gn values were developed in Table 19 for three energy sources and four
farmsizes.4Lvalues for each farm size were determined from the
sampled farmers and presented in Table 12. And the second item in
Equation 25 is the irrigation labor cost for each irrigation system
($/AI) (see Table 25).
As was mentioned above, the mixed integer algorithm minimizes
the objective function. Therefore, Equation 20 is multiplied by -1 so
that positive signs are assigned to cost coefficients and negative signs
are assigned to return coefficients (profit, and prices of crops) as is
presented in Equation 21.
Activities
Crop Production Activities. For the analyses of this study,
five crops are grown under each of five irrigation systems. These 25
crop production activities produce alfalfa hay, upland cotton, wheat,
milo for grain, and corn for grain under gravity irrigation, 10-acre
116
side roll, 20-acre side roll, 40-acre side roll, and center pivot sprinkler irrigation systems. These five crops represented 84.55% and 71.71%
of total 1975 harvested acres of Cochise and Graham Counties respectively (Arizona Crop and Livestock Reporting Service, 1976). Crops excluded from this analysis are American Pima cotton, barley, sugarbeets,
vegetables, and other miscellaneous fruits and nuts.
Considering only the Sulphur Springs Valley, the omitted crops
are even less significant because the portion of agricultural land of
Sulphur Springs Valley which is in Cochise County is 73.4% of total
agricultural land of the county. Therefore, only 11.34% of agricultural
land in the Valley was in the omitted crops in 1975. Only 10.38% of the
agricultural land of Sulphur Springs Valley in Graham County was in crops
that are omitted from this analysis. (See Table 1 for percentage values
of land in those counties).
Moreover, there is no significant difference between upland and
American Pima cotton in terms of their operation, water, fertilizer, and
chemical requirements. Differences do occur in price and yield. Therefore, any kind of break-even analysis obtained by manipulating the price
and/or yield might cover the variations between these two crops. Barley
and wheat also have similar cost characteristics.
On the other hand, sugar beet production is quite controlled by
contracts between farmers and sugar companies. Farmers interviewed for
this study do not grow sugar beets under sprinkler systems as part of
these agreements. Therefore, sugar beets are not considered in the cropping systems.
117
Vegetables and other fruits and nuts are outside the scope of
this research which focuses primarily on the field crops. The primary
reason for omitting vegetables is that they are high-cost, high-valued
crops which are not the main activity of farmers. Water costs are not
the main costs that effect the profitability of vegetables. Since
prices fluctuate radically within a year, it is difficult to estimate
short and/or long term net returns for these crops.
The fixed cost payments on non-irrigation machinery, equipment,
land, wells, and pumps are not included in this program directly but
subtracted from the total return above variable cost (Z) computed for
each farm size and energy source (see Table 29). These costs are sunk
in the farm and have to be borne regardless of the level of production
activities taking place. In other words, the question is not whether
or not to open up new land and start farming. But rather to determine
if installation of a new sprinkler system is profitable under a given
set of farming conditions. In this situation, the fixed costs associated with those items that already exist on the farm should not enter
the decision-making process of the manager. Such costs are computed
separately and subtracted from the total return above variable cost to
give total net profits.
Commodity Marketing Activities. The model is structured such
that crop selling activities are required to determine the gross returns
generated from each cropping system. The unit price of each crop ($/cwt),
in the objective
which is assumed constant among all farms, is utilized
function row.
118
Water Purchasing Activities. Water purchasing activities are
added to the model to give flexibility in choosing among the irrigation
systems. Fixed costs, as defined above, are those items that do not
change with the level of the activities. Since the primary objective of
this research is to analyze the economic and water impacts of the utilization of sprinkler systems, the fixed cost of new investment must be
treated in such a way as to allocate costs between the crop production
system, the irrigation system and pumping. In this case, the question
involves the profitability of sprinkler systems under the prevailing
agricultural, economic, and physical resources conditions. The farmer
has to consider both annual fixed and variable costs of a sprinkler system before making a decision either to install it or not. Therefore, for
an investor who is going to convert a gravity irrigation system to a
sprinkler system, the annualized fixed cost of the sprinkler unit has to
be treated as a variable cost. In formulation of the mixed integer programming model of this study, the total cost of sprinkler units (excluding irrigation labor cost), is added to the variable cost of crop growing
activities in order to be consistent with the above argument. The costs
are then spread over the maximum amoung of land that can be serviced by
the systems.
Constraints
Any farm is restricted by technical, physical, financial and
institutional limits. These limits or constraints are imposed upon the
alternative crop producing activities to construct a mathematical model
that represents the actual decision-making situation as accurately as
possible. The models normally deviate from real life conditions
119
depending upon the restraints imposed upon the decision-maker. For perfect representation it is necessary to study every single factor that
affects decision-making. Since it is impossible to cover all the aspects
of life, an approximation is made that gives up a statistically insignificant quantity of information. In this study constraints on land, water
and commodity production are considered to be the important factors that
bound the crop production ,activities.
Land Constraint. Land is a physical factor that limits the expansion of crop acreages. Average farm acreage for each of four farm
sizes was determined on the basis of data collected from the farmers.
As is seen in Table 8 these average farm sizes are 201, 500, 980, and
2137 acres for small (I), small-medium (II), medium-large (III), and
large (IV) farm sizes, respectively. These figures represent the total
farm land including cropped land, fallow land, and the land that is
used for farmsteads, roads, ditches, etc. It is assumed that fallow
land is suitable for agricultural use but kept idle because of limitations on water, disease control, capital, etc. Land allocated for more
permanent items is assumed not available for agricultural use. Therefore, the cropland base for each farm size is reduced by removing the
average use for permanent noncropland items. Almond (1962, p. 10)
estimated that farmers used 6% of their land for such purposes regardless of farm size. However, Lee (1967, p. 12) indicated that small and
medium farmers used 6% of their land for houses, roads, and ditches,
while large farmers used 5%. It is reasonable to argue that the size
of land allocated for the noncropland purposes does not expand proportionately with the farm size. Therefore, the average size of small and
120
small-medium farms are reduced 6%, while
medium-large and large farm
sizes are reduced 5% to obtain the cropland
base of each farm size. The
resulting land constraints are: small farm size
of 189 acres, smallmedium farm size of 470 acres, medium-large
farm size of 931 acres, and
large farm size of 2030 acres.
Various publications show that soil conditions and
topography
may be limiting factors of sprinkler system applications.
However, inspection of the information on soil conditions and distribution of
cropland in the Valley shows that the major soil type
is thermic semiarid
soil association and does not have the features that restrict
the applicability of the sprinkler systems (see Figure 2).
When the soil intake rate is less than the rate of water applied
through the sprinklers, then the soil can be a limiting factor in
utilization by sprinkler system. However, in the study area there is almost
always some kind of possibility for adjusting the sprinkler system's
water intake rate according to a specific soil intake rate. From personal conversations with Mr. A. Halderman (1976) it was concluded that
in the Sulphur Springs Valley soil intake rate is high enough (quite
light soil) to make this adjustment possible. Therefore, soil condition
is not considered as a restraining factor in this study.
Topography (or the slope of the land) may limit the sprinkler
application rate. From the inspection of Figures 1 and 2 it was concluded that cropland was predominantly located on floodplains and aluvial valleys rather than mountainous parts of the region characterized
by mesmic and frigid subhumid soil classes. Therefore, extreme slope of
121
land is also assumed not to be a major
problem limiting the application
of sprinkler systems in the Sulphur Springs Valley.
Total Water Constraint. The amount
of water annually available
for a farm is determined by the average number of
wells and the average
water pumped from each well for each farm size. Table 36 shows
that the
annual quantities of water available for the four farm sizes
are 10,752
AI, 19,200 AI, 29,160 AI and 39,840 AI, respectively. The quantities
are the product of average number of wells for each farm size
and water
pumped from each well estimated to operate 150 days per year (Hathorn,
1976, p. 3). Water output in gallons per minute (GPM) is converted to
acre inches per year by Equation 17.
March Water Constraint. The amount of water required by crops
may exceed the maximum amount available for a farm in certain critical
periods. Two water constraints are added to the mixed integer programming Model for two critical periods, March and July.
In Figure 11 the seasonal per acre water requirements of the
five crops under gravity and side roll irrigation systems are presented.
In this figure March and July are two critical periods during which
large amounts of water are required. The six-week period (42 days)
starting in the last week of February and ending in the first week of
April is when preirrigation activities take place for gravity irrigation
systems.
Fifty acre inches of water are required in March by the 5 crops
under gravity irrigation in the following fashion: 12 AI each for preirrigation of cotton, milo, and corn; 8 AI for alfalfa hay, and 6 AI
for wheat. Although all the preirrigations are shown in March in
122
Table
36.
Critical Period and Annual Water Constraints of Four
Representative Farm Sizes
Farm Sizes
March
(42
days)
Water Constraints (AI)
July (14 days)
Annual
(150
days)
Small
3,011.0
1,004.0
10,752.0
Small-Medium
5,376.0
1,792.0
19,200.0
Medium-Large
8,165.0
2,722.0
29,160.0
11,155.0
3,718.0
39,840.0
Large
123
Figure 11, the expansion of this period to six weeks gives a
flexibility
to the irrigator in terms of scheduling the watering activities.
The
total quantity of water that can be supplied in this 42-day period is
3011.0 AI, 5376.0 AI, 8165.0 AI, and 11155.0 AI for the small, small-
medium, medium-large, and large farm sizes, respectively.
March is not a critical period for sprinkler systems, since preirrigation is not required. Therefore, the March water constraint is a
non-restricting factor for activities that utilize side roll and center
pivot sprinkler irrigation systems (see Appendix J for crop irrigation
schedules).
July Water Constraint. The second critical period for irrigation water is July. A 14-day period is designated as a critical time in
supplying enough water for the crops. All crops except wheat have a
maximum water consumption in July. Alfalfa hay, cotton, and milo under
gravity irrigation require 12 AI each, while corn needs only 6 AI in
this critical period. Wheat, on the other hand, needs a first irrigation in September (4 AI) and a last irrigation in May (9 AI) before
harvesting sometime in June or July. Wheat production is not restricted
by the July water constraint.
Table 36 shows the maximum amount of water that can be pumped
for each farm size in each of the three restraining periods. As expected, the larger the farm the more water is pumped because of the
larger number of wells on the larger farms. The maximum amount of water
available in 14 days in July is 1,004 AI to the small farms, 1,792 AI to
the small-medium farms, 2,722 AI to the medium-large farms, and 3,718 AI
to the large farms.
124
Z
(-%
>-
<
2
- 3 u
0<
u
Fe
LU
11
D3CI
AON
'DO
d 3S
onv
mi
Nnr
AVW
•::* •
•
•'•
.
&IV
2JVW
83
1=11
NVf
0
o
0
O
0
D3CI
AON
'DO
d3S
11
onv
inr
Nnf
AVW
NdV
NVW
83A
NVf
0
0
in
1.1.1
Ce
V)
LU
=
L) U
< Z
—
et
0
CI
0
c‘i
0
v-
125
Balancing Constraints. There are twenty-one restrictions in the
model other than land and water restraints. Six are balance restraints
on alfalfa hay, cotton lint, cotton seed, wheat, milo and corn, which
sell all crops produced.
The fifteen additional restrictions are water balancing constraints which allocate water required to each crop growing activity
to the proper irrigation system. These restrictions are on March water,
July water, and annual water for the five irrigation systems--gravity,
10-acre, 20-acre, and 40-acre side roll sprinkler units, and center
pivot sprinkler irrigation systems.
For example, in wheat production under center pivot irrigation,
the total yield is 5025.80 cwt on 130 acres of land (which requires 160
acres of land use), sold at $6.23/cwt. This activity costs to the small
farm $23,332.40 per one center pivot irrigation unit plota (see Appendix
K for complete list of coefficients of the program).
The fifteen water balancing restrictions generate the cost of
irrigation water. Using the previous example it can be seen that 3900
AI of water is needed costing $0.9949, $1.5049 and $1.6524 per acre
inch of water for natural gas, electric and diesel energy sources,
respectively.
a
Includes total variable cost and total added sprinkler irrigation cost.
126
Sensitivity Analyses
"Sensitivity analysis is a series of recalculations of . .
impacts using alternative data. It is a methodical approach to the
testing of the stability of
. . [mixed integer programming results] to
data subject to risk and uncertainty" which may exist in input and output markets (Day, 1974, p. 33 8). If the results do not change considerably with the variations in those data, then the solutions will be said
to be quite stable with respect to the given changes. By using sensitivity analysis it is possible to determine the critical factors that
influence the decision making process. Such analyses are carried on
for two parameters in this study: crop price variations, and energy
cost variations.
Crop Price Variations
The crop Price sensitivity analyses are primarily directed to
cotton lint price variations, since cotton is a high valued crop relative to other crops. On the other hand, cotton prices are subject to
significant variations within a growing season. Table 34 shows a maximum variation in cotton lint price of 52.4% of the minimum price in
1976. The second most variable crop prices are corn grain (15.6%).
Others vary as follows: milo (11.6%), wheat (9.9%), alfalfa hay (6.3%),
and cotton seed (4.7%). In view of these data a sensitivity analysis
is performed by changing only cotton lint prices.
The maximum and minimum cotton lint prices were $76.50/cwt and
$50.20/cwt, respectively, in January-July 7-month period of 1976. The
simple average in this period was $58.11/cwt which is utilized for the
127
basic analyses. On the other hand, the 1976 government target price,
which was the lowest price that could be received by growers, was
$43.20/cwt
of cotton lint, a , i.e., if the market price of cotton falls
below the target price, the government pays the difference between the
market and the target price to the cotton growers (Rasmussen, Baker, and
Ward, 1976, p. 19). Therefore, the target price is the minimum price
considered, and the sensitivity analysis is carried on by changing the
cotton lint prices at intervals between these two extremes, namely maximum price in January-July, 1976 period ($76.50/cwt) and the government
target price ($43.20/cwt). Cotton, as a high valued crop, is expected
to dominate the mixed integer programming solutions at high prices.
Increases in cotton prices above the average price level are expected
to result in single crop solutions which are not observed in the study
area. Therefore, it is more informative to decrease the cotton lint
price in order to determine the other activities that are potentially
profitable under the changing profitability conditions of the competing
activities. Price levels used are $43.20/cwt (1976 target price),
$48.00, $53.00,
and $58.11.
Energy Cost Variations
Three energy sources are considered in this study: natural gas,
electric, and diesel fuel. As discussed in the previous chapter, natural gas is the cheapest and diesel fuel is the most expensive source of
energy in the area. Because natural gas is the cheapest energy source
a Government target price was determined according to U. S. Congress Public Law 93-86 in 1973 which was amended in 1974 and 1975.
128
in the area, natural gas engines were operated very commonly among interviewed farmers. Electric motors were installed on only 33 wells out
of 190 (17.4% ot total number of wells). The rest of the wells used
natural gas engines. The sample did not include any diesel fuel engines. Therefore, the aggregate economic impact of any change in the
price of natural gas will be much more than a price change for the
other two energy sources.
As was discussed in Chapter I, the farmers of the region may
face natural gas curtailments and/or price increases. For this reason
they are quite concerned about the adjustment processes with increasing
natural gas prices. Thus, natural gas price changes are analyzed. This
study implicitly assumes that the adjustment processes do not take place
instantaneously, rather it takes one year or more depending upon the
type of adjustment. Therefore, short-run price increases in 1977 and
1978 could be expanded further to the future, if forecasting was the
main focus of this study.
It is predicted that the natural gas price will increase 12.7%
in 1977 and 12.5% in 1978. Thus, natural gas prices are expected to be
$.1315 per therm (or $1.404/MCF) and $.1479 per therm (or $1.5795/MCF)
in 1977 and 1978, respectively. On the basis of these prices, the variable water costs for each irrigation system and farm sizes are given in
Table 37. This table is prepared the same way as Table 26 by substituting 1977 and 1978 estimated natural gas prices for 1976 prices.
Aggregating the Model
The results obtained from the mixed integer programming models
are expanded to apply to the Sulphur Springs Valley as a whole. The
129
Table 37. Estimated Variable Water Costs for 1977 and 1978 (Natural
Gas), a (VAI). b
Irrigation
Systems
Years
I
Farm Sizes
II
III
IV
($/A1) Gravity Irrigation
Side Roll Sprinkler
Center Pivot Sprinkler
1977
1.3528
1.4527
1.8077
1.5954
1978
1.4353
1.5448
1.9370
1.7017
1977
1.2831
1.3830
1.7380
1.5257
1978
1.3656
1.4751
1.8673
1.6320
1977
1.0691
1.1414
1.4964
1.3117
1978
1.1516
1.2335
1.6257
1.3904
a Natural gas prices: 1977: $.1315 per therm
1978: $.1479 per therm
b
Derived from Tables 19 and 25.
130
expansion is accomplished by considering regional resource constraints,
viz, land and total available irrigation water. The total profit generated by each representative farm size is determined by subtracting total
farm fixed costs from the return above variable cost on a regional basis.
Total available land and irrigation water, and farm fixed costs for each
farm size are discussed in the following four sections. Estimates of
these aggregate resource availabilities enable estimation of aggregate
resource utilizations upon obtaining results from the models.
Determination of Regional Cropland Base
The total croplands in Sulphur Springs Valley are allocated to
the four farm size groups according to Arizona Crop and Livestock Reporting Service (1974) data. In 1974 there were 149,000 acres of crop
land in Sulphur Springs Valley. The sampled farms are divided into four
farm size groups consisting of 3.18% of total sampled lands in the small
farms, 11.08% in small-medium farms, 24.82% in medium-large farms, and
60.92% in the large farms. Extending the sampled proportions to the
149,000 total acres, yields 4,738 acres in small farms, 16,509 acres in
small-medium farms, 36,982 acres in medium-large farms, and 90,771 acres
in large farms (Table 38).
The average farm sizes were determined in Chapter III (Table 8).
The average number of farms that falls into each farm size is calculated
by dividing the aggregated cropland of each farm size group by its respective average size.
• 0•
131
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132
Determination of Aggregate Resource Availability
Once the average number of farms in each farm size is estimated,
then the land and water that are available at the farm level can be expanded by multiplying them with respective number of farms. Similarly,
the amount of water used can be determined for March, July, and annually
from the data of Table 36. Table 39 presents a summary of the aggregated availability data.
Total annual water available to the farms of the Sulphur Springs
Valley is 306,669.6 AF. The Arizona Water Commission (1975) estimated
that the agricultural sector's water consumption was 391,000 AF which is
about 84,330 AF more than the 306,669.6 AF estimate (see Table 5).
Several factors might explain this deviation. First, the Arizona Water
Commission (1975, p. 119) indicates that the data given in Table 5 may
deviate from the actual values about 25%. Secondly, the above estimation was based on the sampled data which were collected primarily from
the field crop growers in Sulphur Springs Valley. The Arizona Water
Commission's estimate was for the entire agricultural sector of the
Valley consisting of the field crop growers, ranchers, and other groups
in this sector. Finally, the data given in Tables 5 and 39 were collected and estimated by different groups and in different time periods.
Aggregating the Farm Fixed Costs
As previously indicated, the objective function of the representative farm mixed integer programming model maximizes the return above
variable cost and annualized fixed cost of the sprinkler systems. Net
return above total cost is computed by subtracting farm total fixed
costs from the total returns above variable costs. The farm total fixed
133
Table
39.
Aggregated Available Water for Four Farm Sizes, Sulphur
Springs Valley, 1976.
Farm Sizes
March
(42 days)
Aggregate Available Water
July
(14 days)
Annual
days)
(150
AF 5,914.6
1,972.2
21,120.6
Small-Medium
14,792.1
4,930.7
52,828.8
Medium-Large
25,676.7
8,559.9
91,700.2
Large
39,484.9
13,160.5
141,020.0
85,868.3
28,623.3
306,669.6
Small
TOTAL
134
costs for the four farm sizes and three energy sources are presented in
Table 29. The estimated number of farms of each farm size group (see
Table 38) was multiplied by the farm fixed costs to determine aggregate
fixed costs for each size group and energy source (Table 40).
The values given in Table 40 do not include 1/3 of alfalfa stand
establishment costs (when the establishment costs are applicable).
Therefore, in determination of aggregated net return above total cost
this item is also added to the aggregated fixed cost.
Aggregating the Representative Farm, Mixed Integer
Programming Results
Optimum solutions of the mixed integer programming problems generate information on net farm returns, optimal resource utilizations,
cropping patterns, and production levels.
A simple multiplication of the above information by the estimated number of farms in each farm size category (see Table 38) gives
the aggregate values for resource utilization and crop production. Then,
by assuming a complete switch from one energy source to another, one can
determine the regional impacts of energy source changes on cropping
patterns, resource consumption, total crop production and aggregated net
return above total cost. Similarly, sensitivity analyses at the farm
level can be expanded to trace the impacts of ceteris paribus cotton
lint price variations on adjustment pattern of farmers in the Sulphur
Springs Valley.
The expected natural gas price increases may in the very shortrun result in some adjustments in input and output combinations. These
135
H
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136
adjustments and the resulting impacts on the aggregate returns and resource usages are estimated by a similar procedure.
Briefly in summary, the sensitivities of the aggregated cropping
pattern, resource utilization, total crop production, and net returns
above total cost with respect to energy source, cotton lint price, and
natural gas price are estimated at the macro (regional) level on the
basis of the results obtained from the micro (farm) level mixed integer
programming models. Aggregated
,values
are obtained by multiplying the
estimated numbers of farms in each size category by the optimal values
of the several variables determined from the representative farm mixed
integer programming problems at farm level.
CHAPTER V
RESULTS OF THE MIXED INTEGER PROGRAMMING MODELS
Increasing cost of irrigation water is one of the major problems
faced by the farmers in the Sulphur Springs Valley. Alternative adjustments to this problem were investigated in the previous Chapters and a
mixed integer programming model was developed for analyzing the alternatives. In this chapter the results of the model investigations will be
reviewed under two categories, (a) micro or farm level and (b) macro or
regional level. In both of these categories optimal cropping patterns,
returns to variable and total costs and optimal resource utilizations
will be analyzed. Moreover, the impacts of variations in the prices of
natural gas and cotton lint on resource utilizations and farm income
will be studied. These variables are analyzed to determine the potential technical and economic adjustments of farmers in the Sulphur Springs
Valley under various conditions that they may face in the future.
Farm Level Conditions
Farmers adjust to changes in the factors that influence their
economic welfare. For example, the prices of production inputs (energy,
machinery, etc.) and/or production outputs (cotton, wheat, etc.) might
change. Or the groundwater level may go down which would be reflected
in the increasing cost of pumping irrigation water. In this section,
the decision-making of a representative farmer under given land and
137
138
irrigation water constraints, input and output prices, and production
activities is analyzed.
Initial Analysis
The farm level results for various resource and input-output
conditions are reviewed in this section. Variables such as optimum
cropping pattern, resource utilizations, and return over variable and
total costs are the major topics discussed.
Optimum Cropping Patterns. The representative farm, mixed integer program problem was designed to treat alfalfa hay, upland cotton,
wheat, milo, and corn grain under five irrigation systems: 10-acre,
20-acre, 40-acre side roll units, center pivot sprinkler and gravity
irrigation systems. As is clearly seen in Table 41 only upland cotton
and wheat appear in the optimum solutions indicating that these crops
have relative economic and physical advantages over other crops in the
initial analysis.
In Table 41, individual crop acreages are summed for each irrigation system and farm size and for natural gas, electric, and diesel
energy sources. In the discussion of this table and similar tables
which follow, the individual crops and farm size groups will be analyzed
for significant adjustments to changing the physical and economic conditions of the Sulphur Springs Valley.
Under profit maximizing conditions only upland cotton and wheat
are selected regardless of farm size because of limited water available
especially in July. As is seen in Figure 11, of the crop irrigation
schedules only wheat does not require summer water. Therefore, even
though there are more profitable crops than wheat, the summer water
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restriction limits the acreage of
high valued crops chosen and wheat
serves a role in the production
scheme. Thus, upland cotton is grown
with 40-acre side roll, center pivot, and
gravity irrigation systems,
while wheat utilizes only gravity irrigation. This
is because of the
relative economic profitability of wheat under gravity
irrigation and
the physical constraints on land and water.
The typical small farm (size group I) utilizing natural gas does
not use sprinkler irrigation in its optimal production scheme
of approximately 80% cotton and 20% wheat. However, with electric
or diesel pump
energy sources two 40-acre side roll sprinkler units were utilized to
produce cotton. Additional cotton and wheat were produced under gravity
irrigation. This land reallocation among crops is because of the increasing cost of irrigation water pumped using more costly energy sources,
i.e., electricity and diesel. In other words, as the energy source becomes more expensive, irrigation water cost increases and water saving
irrigation systems (sprinkler irrigation units) are adopted. Consequently, the use of sprinkler systems goes up while gravity irrigated
acreage goes down. However, the cost increase from electricity to diesel
fuel is so small that the optimum cropping pattern does not change.
The small-medium farm (size group II) has a similar trend, i.e.,
as energy costs increase acreages of cotton under center pivot sprinkler
irrigation also increases while gravity irrigation decreases by more
than 87%. Moreover, the switch from natural gas to diesel reduces wheat
production by 62 acres. However, cotton under 40-acre side roll is not
highly sensitive to energy cost increases. Thus, the small cost
141
difference between electricity and diesel fuel does not influence the
optimal land allocation among the sprinkler systems.
Optimum crop mixes of medium-large (III) and large (IV) farms are
quite stable as energy and water costs increase. However, for the mediumlarge farms when the energy source is changed from electricity to diesel
fuel, wheat drops out completely with some cropland remaining idle.
The stability of medium-large and large farms as energy costs increase is because of the adoption of water saving technologies at lower
energy cost. For example, on the medium-large farms 77% of the land is
in cotton of which 80 acres are under side roll and 640 acres are under
center pivot sprinkler irrigation. The small amount of gravity irrigated cotton acreage limits the transfer of land to sprinkler technologies as energy costs increase by changing energy sources. Moreover,
limits of available summer water prevent extension of these technologies
to land previously under wheat. Thus, energy cost increases do not
greatly influence the optimal crop mix of medium-large and large farm
size groups. Wheat under gravity irrigation drops out when diesel fuel
is utilized, i.e., the water becomes so expensive that the farmer cannot
cover the variable cost of growing wheat and some land is held idle.
The general conclusions of these individual cases are given in
the total columns of Table 41. When the energy source is changed from
natural gas to electricity, i.e., the cost of pumping water goes up,
sprinkler irrigation acreages increase at the expense of gravity for
small (I) and small-medium (II) farm size groups, but stays constant for
medium-large (III), and large (IV) farms. Change of energy source from
electricity to diesel fuel generally does not affect sprinkler and
142
gravity irrigation acreages except for the medium-large farm size group
in which some gravity irrigation acreage is transferred to fallow land.
Optimum Resource Utilization. Water consumption for March,
July and annually, and total used and unused land of four farm sizes are
shown in Table 42. The percentage changes in these resources due to
change in energy sources are also given in separate columns.
All of the farm sizes, excluding the small-medium farm size,
under all energy sources use July irrigation water at the maximum attainable level. Small farms also are restricted by the available land.
The quantity of water in 42-day period around March is not a limiting
constraint.
Changing energy sources do not affect total land utilization and
water consumption in July for small farms. However, the use of electric
pump motors reduces the annual water consumption by 10% from natural gas
engines because water saving sprinkler irrigation systems are used as
the water costs increase. Since the cost differential between electricity and diesel is quite small, the annual water consumption does not
change when diesel replaces on the small farms.
Small-medium farms that use natural gas or electricity as energy
sources are restricted in crop production by annual available irrigation
water, but irrigation water in July and March are not used to the limit.
size,
Although there is 0.5 acre of slack land available in this farm
land can also be considered as a limiting physical resource.
Changing from natural gas to electricity does not affect water
from
and land utilization of small-medium farms. However, the change
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electricity to diesel fuel increases the water use in July to its limit
(600 AI), and decreases annual water (15.2%) and land use (0.1%).
For medium-large and large farm size groups land is not a restricting factor. However, available July and annual water do limit
crop production for most solutions. An exception is noted for the
medium-large farms that utilize diesel engines and have slack annual
water (5,562 AI).
Energy source variation affects medium-large farms' resource
utilization, but it has no major affect on large farms. Energy cost increases change the resource utilization of medium-large farms when electric motors are replaced with diesel engines, i.e., annual water
consumption goes down 19.1% and land utilization declines 24.4%.
The Rate of Adoption of Sprinkler Units. By inspecting Table
41, one can see that the number of 40-acre side roll units goes down
while the number of center pivot units goes up as the farm size increases. These adjustments are summarized in Table 43. As is observed
here the number of sprinkler units is not affected by the higher energy
cost in the medium-large (III) and large (IV) farm groups. However, on
small farms, two 40-acre side roll units enter the optimum solution
when the energy source was changed from natural gas to electricity. As
was stated before, this is because of the tendency to adopt water saving sprinkler irrigation systems to reduce total water costs.
Center pivot units require a high capital investment and the
commitment of a large sum of complementary resources. Small and smallmedium farms are more limited in terms of physical resources than are
145
Table 43. The Optimum Utilization of the Sprinkler Units by Farm Size
and Energy Source, Sulphur Springs Valley, 1976.
Farm
Size
Natural Gas
Side
Center
Roll
Pivot
Electricity Diesel
Side
Center
Side
Center
Roll
Pivot
Roll
Pivot
Number of Sprinkler Units I
0
0
2
0
2
0
Ii
3
1
3
2
3
2
III
2
4
2
4
2
4
IV
1
6
1
6
1
6
Source: Representative Farm, Mixed Integer Programming Results.
medium-large and large farms. Therefore, a positive correlation is observed between the number of center pivot systems applied and farm size,
which closely agrees with the sampled farms' practice.
However, because of higher per acre total cost of side roll systems, they are less profitable to operate than center pivot sprinkler
systems (see Appendix H). Therefore, for the larger farm sizes the physical and financial limitations are less binding and the center pivot
units are substituted for side roll systems.
146
Returns Over Total Cost. Return over total cost is the residual
after all the operational (variable) and annual fixed expenses are deducted from gross returns. It is defined as the return to land and
management which includes pure profit and the opportunity cost of management. Detailed information on total production, costs and returns
are given in Table 44. For all farm size groups switching to more expensive energy sources causes cotton production either to increase or
stay constant. Wheat declines drastically in small and small-medium
farm size groups, and does not change in large farms, when energy source
changes from natural gas to electricity or diesel fuel. Medium-large
farms do not produce wheat when diesel fuel is utilized.
The percentage decline in returns over variable cost due to a
change from natural gas to electric or diesel is at a maximum in mediumlarge farms (24.2% and 8.9%) and at a minimum in small farms (14.9% and
8.9%). Changing from electricity to diesel fuel makes relatively smaller
reductions in returns over variable cost.
On the other hand, large farms are the most sensitive to the
change in energy source, as switching to electricity results in 44% reductions in net profit. Changing energy source from electricity to
diesel results in even more drastic declines in profit which drops from
$29,543.38 to $20,613.56 (64%). Small farms, in this respect, show the
least adjustment, since the percentage reduction in their profit is the
smallest.
As observed previously, the percentage reductions in net profit
(return over total cost) is larger than the reductions in return over
147
Table 44.
Farm
Size
Output, Costs, and Returns from Optimal Solutions, by Farm
Size, and Energy Source, Sulphur Springs Valley, 1976.
Energy
Source
Total Production
Cotton
Cotton
Lint
Seed
Wheat
Costs
Fixed
Variable
Total
Gross
Return
Dollars Return
Over
Var. Cost
Return
Over
Total Cost
Change in Return Over
Variable
Total
Costa
Costa
%
(cwt)
(cwt)
D.d
1092.7
1223.3
1223.3
1880.8
2105.6
2105.6
837.6
64.4
64.4
11,193.76
10,547.06
12,812.69
45,102.13
53,955.73
55,281.73
56,295.89
64,502.79
68,094.42
78,307.13
82,225.73
82,225.73
33,205.00
28,270.00
26,944.00
22,011.24
17,722.94
14,131.31
-14.9
- 4.7
-19.5
-20.3
II
N.G.
E.
D.
2358.1
2570.6
2570.6
4059.5
4424.8
4424.8
3028.7
631.5
631.5
24,390.32
23,096.66
27,628.19
113,281.44
122,453.29
126,126.29
137,671.76
145,549.95
153,754.48
176,601.44
175,878.29
175,878.29
63,310.00
53,425.00
49,725.00
38,929.68
30,328.34
22,123.81
-15.6
- 6.9
-22.1
-27.1
III
N.G.
E.
D.
3941.9
3941.9
3941.9
6785.2
6785.2
6785.2
4887.0
4887.0
0
38,533.88
36,900.13
42,504.23
198,870.33
221,930.33
197,902.32
237,404.21
258,830.46
240,406.55
294,114.33
294,114.33
263,668.32
95,244.00
72,184.00
65,766.00
56,710.12
35,283.87
23,261.77
-24.2
- 8.9
-37.8
-34.1
IV
N.G.
E.
D.
5385.1
5385.1
5385.1
9269.3
9269.3
9269.3
6684.7
6684.7
6684.7
84,651.21
81,416.62
92,746.44
264,627.27
290,887.27
298,487.27
349,278.48
372,303.89
391,233.71
401,847.27
401,847.27
401,847.27
137,220.00
110,960.00
103,360.00
52,568.79
29,543.38
10,613.56
-19.1
- 6.9
-43.8
-64.1
I
N.G. b
E.0
(cwt)
a Percent
change in returns based on previous energy source.
b,c,d7ee
footnotes e, f, g of Table 41.
Source: Representative Farm, Mixed Integer Programming Results.
148
variable cost. This is because of the effect of different energy
sources on both farm fixed and variable costs. In other words, when the
energy source is changed from natural gas to electricity, although total
fixed cost declines, it does not exceed the increase in variable energy
cost. On the other hand, the similar shift from natural gas to diesel
increases not only farm fixed cost, but also the variable cost of water.
Therefore, the percentage declines in the return above total cost are
much greater than the reductions in returns over total variable cost.
Table 45 compares the relative profitability of different farm
size groups in terms of their total cost-gross return ratio. The farm
size group that generates the maximum return ratio is the small farm
size, i.e., only about 72% of the gross return is used for total expenses and the rest is the net profit to the farm. The total costgross return ratio increases consistently as one moves to the larger
farm size groups and to the other energy sources, electricity and diesel
fuel. The most extreme case is for large farms that utilize diesel fuel.
Moreover, for the medium-large farms that utilize diesel fuel, and for
the large farms that utilize energy sources other than natural gas, the
gross returns barely cover the total cost with some net profit, i.e.,
their total costs are more than 90% of their gross returns.
Sensitivity Analyses
The adjustment processes of the representative farms have been
analyzed under the prevailing conditions and the impacts of energy source
variations have been indicated. The sensitivity of these solutions with
respect to changes in crop prices and energy costs will be analyzed in
this section.
149
Table 45. Total Cost-Gross Return Ratios of Four Farm Size Groups,
Sulphur Springs Valley, 1976.
Farm
Size
Energy Source
Electricity Percent Diesel Fuel
71.9
78.5
82.8
78.0
82.8
87.4
III
80.7
88.0
91.2
IV
87.0
92.7
97.4
Natural Gas
Crop Price Variation. Since the optimum solutions for 1976
conditions contain only upland cotton and wheat, only the cotton lint
prices are varied from $58.11/cwt to $43.20/cwt. Thus, other potentially profitable activities not selected because of high valued cotton
will be identified and the reallocation of resources and changes in net
returns above variable and total costs will be analyzed.
a) Adjustments in the optimum cropping pattern under changing
cotton lint prices. The overall adjustment processes of optimum cropping mix by farm sizes and energy sources for changes in cotton lint
150
price are given in Table 46. The expected results are
seen in all cases
except for the small-medium farm size group utilizing diesel fuel.
That
is, total cotton acreage normally declines with the cotton lint price.
However, in the exceptional case, when cotton lint price goes down from
$53.00/cwt
to $48.00/cwt, the total cotton land increases from 138.7
acres to 150 acres. The reasons behind this result are analyzed below:
At $53.00/cwt price level it is profitable to grow some wheat
under gravity irrigation (11.3 acres), even though it generates less
net return than cotton because wheat is the only crop that does not compete for summer water with cotton and corn. However, when the cotton
price falls to $48.00/cwt, two things happen: first, corn land is divided between side roll and center pivot systems, and secondly, the
wheat land is allocated for cotton; therefore, cotton acreage goes up.
This situation which seems inconsistent with the classical supply-price
relationship is derived from the resource-cost-return relationships
among cotton, wheat and corn. The consistency of this result is illustrated below by testing several alternatives that might be considered as
optimum. For example, applying the $53.00/cwt price to $48.00/cwt solution, transferring all the land to cotton which is allocated for corn,
etc.
Any activity under center pivot irrigation requires 160 acres of
land, but net cropped acres are only 130; consequently, costs and returns
are computed on the basis of 130 acres.
•
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155
Cotton (under gravity irrigation)
Production cost
$
Water cost
Total Cost
113.73
$ 294.49
Gross Return ($53.00/cwt)
Return Above Variable cost/acre
403.41
$ 108.92
Gross Return ($48.00/cwt)
Return Above Variable cost/acre
180,76/acre
370.76
$
76.27
Wheat (under gravity irrigation)
Production cost
$
Water cost
Total Cost
92.67
$ 215.35
Gross Return ($6.23/cwt)
Return Above Variable cost/acre
122.68/acre
240.85
$
25.50
Corn (under side roll)
Production cost
$
42.76
Water cost
Total cost
$ 278.01
345.75
Gross Return ($4.61/cwt)
Return Above Variable cost/acre
235.25/acre
$
67.74
Corn (under center pivot)
Production cost
$
32.87
Water cost
Total Cost
Gross Return ($4.61/cwt)
Return Above Variable cost/acre
188.58/acre
$ 221.45
280.75
$
59.30
156
As is seen above the per acre net returns above variable costs
of cotton are the largest ($108.92 or $76.27) and wheat is the smallest
($25.50)
and takes the residual land and water after other crops are
expended as much as possible. As an alternative solution when the
$53.00/cwt
cotton price is applied to the $48.00/cwt solution, then the
reduction in the net return above variable cost due to the shift to
corn under center pivot and eliminating wheat will be,
($67.74 - $59.30) x 160
acres + $25.50 x 11.3 acres = $1,638.55
On the other hand, the increase in the net return above variable cost
due to expansion of cotton land will be,
$108.92 x 11.3
acres = $1,230.80 which is less than $1,638.55.
Therefore, reallocation of resources other than given in Table 46 are
not economical.
Secondly, since cotton generates more return above variable cost
than any other crop even when its price is $48.00, one might propose to
transfer more land from corn to cotton at the $53.00 price. This is
restricted by the July Water constraint, because the minimum land that
can be transferred from corn is 40 acres from which only 120 AI of water
can be released during 14-day period in July. But 40 acres of cotton
needs 6 x 40 = 240 AI of water in the same period.
The reason cotton acreage increases while its price goes down is
that when cotton lint price declines from $53.00/cwt to $48.00/cwt the
net return above variable cost also goes down by $1,638.55 as was explained above. However, there will be some additional water available
in July, i.e., although corn under center pivot requires 160 acres of
land, its water need is only for 130 acres. So when corn is split
157
between side roll and center pivot the amount of
water released in July
will be
(390
AI/160 acres) .30 acres = 73,035 AI.
Although this water is enough for 12.2 acres of cotton, because
of the
land restriction, only 11.3 acres of wheat land is transferred to cotton
production. With this new expansion of cotton, the increase in total
return above variable cost from cotton is
$76.27 x 11.3
acres = $861.85.
Then the overall reduction in net return above variable cost will be
$1,638.55 - $861.85 = $776.70
instead of $1,350.40. a Therefore, the
given solution is optimum, and cotton acreage does increase as its price
declines under the prevailing conditions.
For the small farm class using natural gas for pumping, cotton
under gravity irrigation is the dominant crop. Only when the cotton
lint price goes down to $43.20 cwt does corn come into the solution and
wheat goes out. Corn production under sprinkler irrigation has a relative economic advantage over gravity. Therefore, gravity irrigated corn
comes in the optimum solution when it is economically feasible. Wheat
goes out when the cotton price is $43.20 cwt because corn under sprinkler
and gravity irrigation generates more net return than wheat.
When the energy sources are utilized, the introduction of
corn to the optimum solution occurs at a higher cotton lint price
($53.00/cwt).
Because cotton needs more water than corn, and when its
a
Total reduction in return above variable cost due to corn production under center pivot instead of under side roll is (67.74 - 59.30)
x 160 = $1350.40.
158
price goes down and
water cost increases to grow cotton becomes unprofitable, as a result corn comes in the optimal solution.
Looking at the total cropland figures, a
falling cotton lint
price does not reduce the total cropped acres except when
diesel fuel is
used. This occurs because it is more profitable to keep land
idle when
water cost is high and output prices are unfavorably low.
The remaining farm size groups are more sensitive
to cotton lint
price declines. For example, corn under side roll irrigation comes into
the solution at a cotton lint price of $53.00/cwt. As cotton prices decline, not only does the total cotton acreage go down but cotton land
previously under sprinkler systems switches to gravity which generates
more net return since gravity irrigation does not bear the added cost
of sprinklers. Similarly, corn is introduced into the solution since,
under side roll irrigation, corn shifts to a position of economic advantage. As is observed in Table 46, the total land under cultivation is
not affected by decline in the cotton price.
In the medium-large farm size group, cotton under side roll irrigation is the most sensitive activity to cotton price declines and
leaves the solution as the cotton lint price decreases to $53.00/cwt.
Moreover, producing cotton under any sprinkler system is not profitable
when its price declines to $48.00/cwt, regardless of the energy source.
A more drastic decline in cotton acreage results from increasing energy
cost.
Fallow land under the $58.11/cwt cotton lint price condition is
allocated to crops when the cotton lint price is $53.00/cwt or lower.
159
This occurs because under the lower cotton prices, corn comes into the
solution and all the resources are used to their full extent.
Large farms are at the margin in terms of the cotton price variation. That is, a decline in cotton lint price of about $5/cwt makes
cotton production a residual activity. This result does not change with
energy source variation. Corn acreage increases as the price declines
from $53.00 to $48.00/cwt, but stays the same when cotton price is
further reduced to $43.20/cwt since all cotton has previously left the
solution.
Wheat takes some land from cotton when its price goes to $53.00/
cwt, but then gives way to corn as further declines in the cotton price
release July water for corn production. This occurs because wheat does
not compete for summer water with other crops at high cotton prices.
However, the large land requirements of corn under sprinkler systems,
and the economic disadvantages of wheat, reduce wheat production as the
cotton lint price declines below $53.00/cwt.
Falling cotton lint prices cause the large farms to expand total
cropped acreage at the expense of fallow lands. This occurs because all
of the land cannot be fully utilized under high cotton prices due to the
July and annual water restrictions.
b) Optimum resource utilizaticin under changing cotton lint prices.
When cotton prices decline a new combination of activities is
adopted in order to generate the maximum return under the new conditions.
Consequently, a corresponding set of changes occur in resource utilization. These results are given in Table 47 for the four farm size groups
and three energy sources.
160
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164
The first observation in this case, is that falling cotton lint
prices do not affect annual water consumption for the large farm category and only slightly affects water use in the small farm size group.
Annual water consumption on the small farms goes down 11.6% if the
cotton price falls to $43.20/cwt. The optimum solutions become more
sensitive as more expensive electricity or diesel fuel is used instead
of natural gas. In those cases water is more costly and as cotton price
goes down, water saving crops and sprinkler irrigation techniques are
utilized. All July water is used at each cotton price level under
natural gas. However, when electricity or diesel fuel is utilized with
a $43.20/cwt cotton price, only about half of the July water is consumed
as the crop mix changes. Under these conditions only corn, which uses
half as much July water as cotton, is grown.
Land utilization by the small-medium farm size group also is
relatively stable as cotton lint prices decline. However, annual water
consumption declines between 23.5% and 29.6%, as cotton price falls to
$43.20/cwt,
depending on the energy source. Cumulative reductions in
water use due to cotton lint price declines from $58,11 to $43.20/cwt
are 29.7%, 46.3%, and 36.6% for natural gas, electricity, and diesel
fuel, respectively.
July _water use for the small-medium farm size group is not restricting when cotton lint price is $43.20, but it is restricting when
price is $53.00/cwt, regardless of the energy source. There is no
general pattern of movement in July water use as cotton lint price falls.
Under natural gas July water is used to the maximum when cotton lint
prices are between $53.00 and $48.00/cwt, but July water consumption
165
decreases when the cotton price is $43.20/cwt. Under electricity, July
water consumption is reduced when cotton price is $48.00/cwt. For
diesel fuel, July water is used to the maximum at $58.11 and $53.00/cwt
but at lower cotton price levels water use is reduced.
Crop production on medium-large farms is restricted primarily
by July water and land. July water restricts production at every cotton
price level with natural gas, but only at the first three price levels
with electricity and diesel. On the other hand, land is the more restricting factor as cotton lint price decreases since lesser valued
crops are produced more extensively and land becomes restricted.
As mentioned earlier, large farms are not affected by cotton
lint price declines in terms of optimum resource utilizations. Under
the three energy sources and all specified price levels, the optimum
crop mix and relatedly resource utilizations remain constant.
c) Net returns over total cost under changing cotton lint prices.
The total return of a production activity is determined by its
selling price and production level as derived from the optimal cropping
pattern. In Table 48, variations in total production of cotton, wheat
and corn under changing cotton lint price levels are given. The percentage changes in cotton output based on the previous price level are
computed. As is observed in Table 48, the percentage decline in the
cotton lint production increases as the cotton lint price goes down.
That is percentage reduction in cotton production is higher at lower
cotton lint price levels. Generally, the larger farm size groups are
more sensitive to cotton lint price decline, i.e., decline in cotton
166
Table 48. Changes in Total Crop Production Under Varying Cotton Lint
Prices for Four Farm Size Groups, Sulphur Springs Valley,
1976.
Cotton
Lint
Price
($/cwt)
Total
Crop Production
Cotton
Cotton
Lint
Seed
Wheat
Corn
cwt
% Change
in Cotton
Productiona
Small Farm Size Group
A. Natural Gas
58.11
53.00
48.00
43.20
1092.7
1092.7
1092.7
951.2
1880.8
1880.8
1880.8
1637.3
837.6
837.6
837.6
0
0
0
0
3223.3
0
0
-13.0
2105.6
1880.8
1637.3
0
64.4
837.6
0
0
0
0
3223.3
13943.0
-10.7
-13.0
-100.0
2105.6
1880.8
1637.3
0
64.4
837.6
0
0
0
0
3223.3
13943.0
-10.7
-13.0
-100.0
B. Electricity
58.11
53.00
48.00
43.20
1223.3
1092.7
951.2
0
C. Diesel Fuel
58.11
53.00
48.00
43.20
1223.3
1092.7
951.2
0
167
Table 48 (Continued), Crop Production under Changing Cotton Lint
Prices, 1976.
Cotton
Lint
Price
($/ cwt)
Cotton
Lint
Total Crop Production
Cotton
Seed
Wheat
cwt
Corn
% Change
in Cotton
Production a
Small-Medium Farm Size Group
A. Natural Gas
58.11
53.00
48.00
43.20
2358.1
2097.2
1427.5
718.3
4059.5
3609.9
2457.2
1236.4
3028.7
3047.7
3527.7
0
0
3000.0
12009.0
27000.0
-11.1
-31.9
-49.7
4424.8
4087.6
1236.1
0
631.5
1791.2
0
0
0
0
27001.0
35010.0
-7.6
-69.8
-100.0
4424.8
1558.6
1686.5
0
631.5
438.2
0
0
0
24000.0
21747.0
35010.0
-64.8
8.2
-100.0
B. Electricity
58.11
53.00
48.00
43.20
B.
2570.6
2374.7
718.1
0
Diesel Fuel
58.11
53.00
48 • 00
43.20
2570.6
905.5
979.8
0
168
Table 48 (Continued), Crop Production under Changing Cotton Lint
Prices, 1976.
Cotton
Lint
Price
($/cwt)
Total
Crop Production
Cotton
Cotton
Lint
Seed
Wheat
cwt
Corn
% Change
in Cotton
Production a
Medium-Large Farm Size Group
A. Natural Gas
58.11
53.00
48.00
43.20
3941.9
2978.8
89.2
0
6785.2
5127.3
153.6
0
4887.0
5599.3
1443.3
915.0
0
15750.0
66000.0
67831.0
-24.4
-97.0
-100.0
6785.2
2963.6
71.2
0
4887.0
283.5
0
0
0
38250.0
67063.0
67487.0
-56.3
-97.6
-100.0
B. Electricity
58.11
53.00
48.00
43.20
C.
3941.9
1721.7
41.4
0
Diesel Fuel
58.11
53.00
48.00
43.20
3941.9
1721.7
41.4
0
6785.2
2963.6
71.2
0
0
0
0
0
0
38250.0
67063.0
67487.0
_
-56.3
-97.6
-100.0
169
Table 48 (Continued), Crop Production under Changing Cotton Lint
Prices, 1976.
Cotton
Lint
Price
($/cwt)
Total
Crop Production
Cotton
Cotton
Lint
Seed
Wheat
cwt
Corn
% Change
in Cotton
Productiona
Large Farm Size Group
A. Natural Gas
58.11
53.00
48.00
43.20
B.
5385.1
95.8
0
0
9269.3
164.9
0
0
6684.7
11983.0
11751.0
11751.0
0
90750.0
92715.0
92715.0
-98.2
-100.0
-
9269.3
164.9
0
0
6684.7
11983.0
11751.0
11751.0
0
90750.0
92715.0
92715.0
_
-98.2
-100.0
-
9269.3
164.9
0
0
6684.7
11983.0
11751.0
11751.0
0
90750.0
92715.0
92715.0
-98.2
-100.0
Electricity
58.11
53.00
48.00
43.20
5385.1
95.8
0
0
C. Diesel Fuel
58.11
53.00
48.00
43.20
5385.1
95.8
0
0
a Percent change in production based on the previous high price.
Source: Representative Farm, Mixed Integer Programming Results.
170
price results in greater percentage reductions in the
cotton production
of larger farms.
In Table 49 the changes in production costs and returns over
variable and total costs are shown for the cotton lint price changes
between $58.11 and $43.20/cwt. The percentage change in net return
above total cost is larger than net return above variable cost, because
the former reflects the changes in fixed and variable costs while the
latter is influenced only by the variable cost.
The percentage change of net return above total cost of small
farms decreases at an increasing rate as the cotton lint price goes
down. In other words, as the cotton price declines, the net return
above total cost of small farms declines at greater magnitudes. This
situation is reversed for medium-large and large farm size groups. The
conclusion is that cotton is a major crop for small farms, and even if
its price goes down significantly it will still be grown by small farms.
However, a slight decline of cotton lint price results in a considerable
reduction in its production under larger farm size groups (consequently
a large percentage decline in income occurs).
In all of the cases the representative farms generate enough return to cover variable expenses. However, they do not realize the positive net return over total cost in all cases. For example, large farms
using diesel fuel lose $1,357.44 annually when cotton price falls to
$53.00/cwt,
and more when cotton lint price declines more. Farms that
utilize natural gas as the energy source generate gross return that exceeds total cost regardless of the cotton lint price level.
171
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175
Table 50 shows relative variations in profitability under de-
clining cotton lint prices. This is measured by the total cost-gross
return ratio. It is clearly seen that the cost-return ratio goes up as
the price of cotton declines. Since the large farms are the least
profitable in terms of cost-return ratio their profitability situation
is even worse as the cotton price goes down, i.e., at $53.00 cwt and
lower cotton lint prices the total cost exceeds the gross return by 0.3%
implying a loss in return to land and management.
Energy Cost Variations. As was discussed earlier, the price of
natural gas was estimated to increase 12.7% in 1977 and 12.5% in 1978.
The adjustment processes, ceteris paribus, to natural gas price in-
creases are analyzed in this section. Adjustments in optimum cropping
pattern and related changes in crop production and farm income are dis-
cussed.
a) Adjustments in the optimum cropping pattern under increasing
natural gas prices. The optimum cropping patterns and relevant crop
productions of small, medium-large, and large farms do not change with
natural gas price increases. However, small-medium farms change their
cropping pattern as a result of the 1977 price increase, but the 1978
price increase has no additional affect. Since the optimum cropping
patterns of farms other than the small-medium size group are not differ-
ent from those given in Table 41, only the small-medium farm size will
be discussed.
In Table 51 the optimum cropping patterns of the four farm sizes
are given. Although only the small-medium farm size cropping patterns
change when the natural gas price increases, the other size groups are
176
Table
50.
Variations in Total Cost-Gross Return Ratios Under Changing
Cotton Lint Prices, Sulphur Springs Valley, 1976
Energy
Source
Natural Gas
Electricity
Diesel Fuel
Cotton
Lint
Price
($/ cwt)
Farm Size Groups
II
III
IV
Percent 58.11
71.9
78.0
80.7
86.9
53.00
77.4
83.4
86.9
91.9
48.00
83.7
87.6
89.8
91.9
43.20
88.8
90.8
89.9
91.9
58.11
78.5
82.8
88.0
92.7
53.00
83.5
88.8
93.1
96.5
48.00
88.8
92.8
94.1
96.5
43.20
94.4
93.8
94.1
96.5
58.11
82.8
87.4
91.1
97.4
53.00
88.2
94.4
96.8
100.3
48.00
95.3
97.3
97.2
100.3
43.20
98.6
97.7
97.3
100.3
Source: Derived from Table
49.
177
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178
presented for comparison. The optimality condition of the small-medium
farm size is quite sensitive to higher irrigation cost, and when
the
price of natural gas goes up to the expected 1977 level, flood irrigated cotton and wheat acreages decline to save water. At the same
time, cotton under 40-acre side roll system is abandoned and cotton
land under center pivot is doubled thereby saving additional water.
b)
Optimum resource utilization under increasing natural gas prices.
As mentioned in the previous section, when the natural gas price increases the farms in the Sulphur Springs Valley are expected to adopt
water saving irrigation techniques. This expectation is confirmed only
by the small-medium farm size group that reduces the annual water consumption (Table 52). This expected reduction in 1977 is 7.41% relative
to the water consumption level at 1976 natural gas prices. However, the
expected increase in the energy price from 1977 to 1978 is not large
enough to create an incentive for further reduction in water consumption through alternative cropping patterns and technologies. Land use
changes very little as energy cost increases.
c)
Net returns over total cost under increasing natural gas prices.
As a result of the optimum crop mix, the increasing natural gas prices
in 1977 and 1978 affect only the small-medium farm's crop production
levels. However, all of the farms' net returns above variable and total
costs decrease because of the higher irrigation cost. In Table 53 the
crop production levels for these cases are given. Cotton production
is slightly affected (0.7% increase) by the increase in natural gas
price. But, wheat production declines 40.9%, since it is a low valued
crop and any cost increase significantly influences its profitability.
179
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180
Table 53. Changes in Total Crop Production
Under Increasing Natural
Gas Prices, Sulphur Springs Valley, 1976-1978.
,Total Crop Production
Cotton Lint
Percent
(cwt)
Changea
Year
Cotton Seed
(cwt)
Wh eat
(cwt)
Percent
Changea
I. Small Farm Size Group
1976-1978
b
1092.7
0
1880.8
837.6
0
H. Small-Medium Farm Size Group
b
1976
2358.1
b
1977
2374.4
b
1978
2374.4
-
4059.5
3028.7
-
0.7
4087.6
1791.2
-40.9
0
4087.6
1791.2
0
III. Medium-Large Farm Size Group
b
1976-1978
3941.9
0
6785.2
4887.0
0
6684.7
0
IV. Large Farm Size Group
b
1976-1978
5385.1
0
9269.3
aPercent change in crop
production based on previous year's natural gas
price.
Based on natural gas prices of $.1167, $.1315, and $.1479 per therm
for 1976, 1977, and 1978, respectively.
Source: The Representative Farm, Mixed Integer Programming Results.
181
Table 54 shows the variations of
farm income due to expected
price increase of natural gas in 1977 and 1978.
Farm income declines
relatively more for the larger farm size groups.
For example, from 1976
to 1978 the small farm's profit declines 8.9%
total, while the respective
figure for the large farm group is 23.6%. These decreases
do not affect
the general farm cropping patterns and resource utilizations
of those
farm groups. As was mentioned earlier, percentagewise the magnitude of
decline in return over total cost is about double the decline in the
return above total variable cost.
Macro Level Conditions
The above results only give the situation for representative
units of the Sulphur Springs Valley agricultural economy. These results
can be expanded to the regional level by aggregating the previous results. In Chapter IV the estimated number of farms in each farm size
group was given (Table 48). The simple multiplication of those numbers
by the results of the farm level optimization models gives regional
estimates. The aggregated results of the initial analyses and the sensitivity analyses are presented and discussed in the following two sections. However, in order to reduce the repetition, the initial analyses
and sensitivity analysis based on cotton lint price variations are reviewed together.
Initial Regional Conditions and Variations under
Changing Cotton Lint Prices
Initial conditions are specified with cotton lint price at
$58.11/cwt and natural gas at the 1976 price of $.1167 per therm. By
182
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using an order similar to the previous section, the initial conditions
and deviations from them are analyzed in terms of the optimum cropping
patterns, resource utilizations, crop production, and net returns over
total costs.
Adjustments in the optimum regional cropping pattern. In Table
46 optimal cropping patterns are given by farm size and energy source.
Table 55 is obtained by multiplying the values of Table 46 by the expected number of farms in each farm size category and then summed to
give aggregate acreages of each crop grown under the different irrigation systems. This procedure is applied to the natural gas, electricity,
and diesel fuel cases.
From these aggregate results it can be seen that only cotton and
corn are grown under sprinkler systems (40-acre side roll, and center
energy
pivot) while wheat utilizes gravity irrigation. Regardless of the
other
source corn is not grown when cotton lint price is $58.11. On the
hand, when cotton price declines to $53.00/cwt cotton acreage declines
irrigation is
about 50%, and at $43.20/cwt only cotton under gravity
grown when natural gas is utilized.
In contrast, wheat is grown as a residual crop with corn and
cotton. At a $58.11/cwt cotton price wheat acreage is relatively low,
wheat is planted on
but when the cotton price declines to $53.00/cwt
total
some of the land formerly planted to cotton, thereby increasing
wheat acreage. Under natural gas, wheat acreage goes down at lower
corn has a competitive
cotton prices ($48.00 and $43.20/cwt) because
economic advantage and is grown on larger areas.
184
Table
55.
Optimum Regional Cropping Patterns Under Changing Cotton
Lint Prices, Sulphur Springs Valley, 1976.
Cotton Lint Price Levels ($/cwt)
C ro p
Irrigation System
58.11
53.00
48.00
43.20
Acres A.
Natural Gas
Upland Cotton
40-acre side roll
Center pivot
Gravity irrigation
TOTAL
Wheat
Gravity irrigation
Corn
40-acre side roll
Center pivot
Gravity irrigation
8,680
70,212
7,956
10,787
23,397
10,549
0
0
11,679
0
0
7,067
86,848
44,733
11,679
7,067
15,211
21,746
17,848
13,807
0
0
0
6,039
67,203
0
40,190
61,165
1,245
47,737
61,165
2,353
0
73,242
102,600
111,255
10,566
75,495
3,321
0
22,642
8,132
0
0
:1,305
0
0
0
89,382
30,774
7,305
0
TOTAL
Electricity
B.
'Upland Cotton
40-acre side roll
Center pivot
Gravity irrigation
TOTAL
Wheat
Gravity irrigation
14,739
15,485
12,913
12,913
Corn
40-acre side roll
Center pivot
Gravity irrigation
0
0
0
6,227
79,279
0
43,209
67,203
1,500
48,679
67,203
1,500
0
85,506
111,912
117,382
TOTAL
C. Diesel Fuel
40-acre side roll
Center pivot
Gravity irrigation
10,566
75,495
3,321
89,382
0
12,076
14,241
26,317
0
0
3,673
3,673
Wheat
Gravity irrigation
7,922
14,053
12,913
12,913
Corn
40-acre side roll
Center pivot
Gravity irrigation
0
0
0
0
16,793
79,279
0
96,072
36,605
72,486
1,500
110,591
48,679
67,203
3,240
119,122
Upland Cotton
TOTAL
TOTAL
0
0
0
0
185
Changing from natural gas to electricity or diesel fuel induces
farmers to concentrate on water and energy saving production techniques.
Therefore, the side roll and center pivot acreages go up when electricity
or diesel fuel is utilized, and gravity irrigated lands go down.
When the cotton lint price is $58.11/cwt, regional cotton acreage increases 2,534 acres as the energy source is shifted from natural
gas to electric or diesel. However, gravity irrigated wheat acreage
goes down because of increased use of water saving sprinkler irrigation
as water gets more expensive. Similar trends are observed for cotton
and wheat at lower price levels of cotton lint, i.e., total acreage decline as shifts occur from less expensive to more expensive energy
sources. However, corn has a reverse pattern; shifting to the higher
energy sources increases the land allocation for corn. The reason behind this is that corn under sprinkler irrigation has a higher yield
than for gravity. Because of this advantage, corn production is more
profitable under sprinkler than under gravity irrigation. Since there
is an incentive to save more water as the cost of water increases, the
corn acreage under sprinkler irrigation (which saves water and energy)
increases as energy gets more expensive. Based on Table 55, maximum
corn acreage under gravity irrigation is only 2.7% of the total regional
corn acreage (diesel fuel, $43.20/cwt cotton lint price).
Optimum Regional Resource Utilizations. The aggregated effect
of changes in energy type and cotton lint price can be observed in Table
56. Here annual water consumption and land use are given for the entire
region. Results similar to those obtained at the farm level are seen at
the regional level. As the energy becomes more expensive, less water is
r-
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187
used. For example, at a $58.11/cwt
cotton price, shifting from natural
gas to electricity or to diesel reduces the
annual water consumption by
0.6% and 8.3%, respectively. The total savings in
energy used for pumping the water can be calculated by Equation 24.
M = (W x k e x g x h)/E
(24)
where,
M = Total energy in thermal units for natural gas, KWH
for electricity, and gallon for diesel fuel.
W = Amount of water pumped in acre feet (AF).
E = Overall pumping efficiency which is .131 for natural
gas, .54 for electricity, and .16 for diesel fuel. a
(Hathorn, 1976).
The weighted average lift (h) of Sulphur Springs Valley was determined as 295 feet. By using the above formula, the total energy savings will be (45,213 x .00318 x 10.68 x 295)/.131 = 3,304,940 therms of
natural gas, when the cotton lint price declines from $58.11 to $43.20/
cwt. The regional amounts of water conserved as the cotton lint price
declines from $58.11 to $43.20/cwt are 45,213 AF (15%), 65,120 AF (22%),
and 39,586 AF (14%) for natural gas, electricity, and diesel fuel, respectively. b The corresponding energy use reductions are 3,304,940
therms of natural gas, 36,428,610 KWH of electricity, and 1,770,905
gallons of diesel fuel.
aSee Equation 1, Chapter I, for the definitions of the other
Symbols of Equation 24.
b
See note (a), P. 192.
188
At a $58.11/cwt cotton price, total cropland acreage does not
change with the adoption of electricity, but declines 4,753 acres, or
12%, when diesel fuel is used (Table 56).
Declining prices of cotton affect the water and land utilizations in opposite directions. As cotton becomes less profitable, other
crops and technologies that use less water are adopted.
Total regional cropland acreage increases as the low valued,
extensively grown crops replace cotton as its price declines. Total
cropland use is about 5% smaller than the 149,000 acres on which these
analyses are based. This difference is attributed to the land used for
houses, barns, ditches, roads, etc.
Regional Returns Over Total Costs. Returns over total costs
(or profits) are affected by the variations in total crop production
which in turn are influenced by the adjustments in optimal cropping
patterns under changing cotton lint prices. The optimal cropping patterns at the farm level, given in Table 48, are aggregated in Appendix
L. On the basis of these data a regional industry supply schedule of
cotton is derived. The level of cotton lint productions for the given
cotton lint prices are plotted in Figure 12. Although, the production
schedule of cotton obtained from the mixed integer programming results
should be expressed as a step function, the plotted points are connected
by straight lines in this figure. Because in this study range analyses
among those four price levels ($43.20, $48.00, $53.00 and $58.11/cwt)
were not available from the computer algorithm. Thus, the behavior of
the supply function between these prices could not be exactly determined.
189
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in
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In
to
v.
(1MD/$) 3DIZid i i Nip
O
Tr
190
The connecting lines are the average change in cotton production between
two prespecified price levels.
As is seen in Figure 12, the industry supply function of cotton
is fairly steep in the price range between $43.20 and $53.00. However,
the elasticity increases between $53.00 and $58.11/cwt price interval.
In other words, cotton production is substantially reduced if price
goes down from $58.11 to $53.00/cwt, but further reductions in price do
not significantly reduce production.
In the remainder of this section the returns above variable and
total costs will be determined for the entire Sulphur Springs Valley.
Also, variations in returns as cotton lint price changes, are shown.
In Table 49, the detailed components of farm production costs
and returns were given by farm size and energy source. In Table 57,
total cost and returns above total and variable costs for the entire
Valley are determined using data from Table 49.
As is seen in Table 57, aggregated total cost, which is the sum
of aggregated fixed and variable costs, increases for two reasons:
First, shifting to the more expensive energy sources, and secondly, replacing cotton with other more costly crops. At the $58.11 cotton lint
price level, by shifting from natural gas to electricity, the aggregate
total cost increases 7.6%; shifting to diesel fuel increases total cost
about 9%, ceteris paribus. On the other hand, for natural gas, the increase in production costs as cotton price falls from $58.11 to $43.20/
cwt is 22.5%. For electricity and diesel, the figures are about 19% and
22%, respectively. These costs are incurred because, as cotton price
declines, other crops (corn or wheat) are substituted causing additional
191
Table 57. Regional Returns Over Variable and Total Costs, by Energy
Sources, Sulphur Springs Valley, 1976
Cotton Lint
Prices
($/cwt)
Aggregated
Total Cost
(TC)
Return Over
Variable Cost
(ROVC)
Return Over
Total Cost
(ROTC)
Dollars A.
Natural Gas
58.11
29,667,427
12,295,819
6,177,191
53.00
34,825,983
10,562,038
4,443,080
48.00
36,249,224
9,963,337
3,844,379
43.20
36,340,553
9,689,290
3,573.330
B. Electricity
58.11
31,907,584
9,867,482
4,005,527
53.00
36,496,577
8,219,210
2,357,256
48.00
37,644,496
7,855,030
2,023,114
43.20
37,993,956
7,717,051
1,855,117
C.
Diesel Fuel
58.11
32,371,947
9,149,048
2,392,227
53.00
38,363,205
7,554,530
796,849
48.00
39,306,678
7,241,273
483,665
43.20
39,449,365
7,157,417
399,710
192
expenses. Moreover, as the cotton price declines from
$58.11 to $43.20/
cwt the returns over total costs decrease
42%, 54% and 83% for natural
gas, electricity, and diesel respectively . a
Returns over total cost decline drastically when electricity
or
diesel fuel are utilized instead of natural gas, even at 1976
gas prices.
For example, at an initial cotton price of $58.11/cwt,
return over total
cost declines 35% and 61%, respectively, when natural gas is replaced by
electricity or diesel fuel. Reductions in the returns over variable
cost are smaller than the reductions in the returns over total costs
which are 42.2%, 53.7% and 83.3% for natural gas, electricity and diesel
fuel, respectively.
Variations in the Initial Regional Conditions
under Increasing Natural Gas Prices
Initially, the cotton lint price was set at $58.11/cwt and the
1976 natural gas price was given at $.1167/therm. A set of solutions
based on estimated natural gas prices for 1977 and 1978 were obtained
at the farm level with the cotton price at $58.11/cwt. Those results
are aggregated and the regional level conditions are analyzed in this
section.
aAccording to the recent publication of Arizona Agricultural
Stabilization and Conservation Service the upland cotton target price
is $47.80/cwt for 1977 (USDA, Arizona Agricultural Stabilization and
Conservation Service, 1977, p. 3). Therefore, the above results were
recalculated for the cotton price changes from $58.11 to $48.00. As
a result of this reduction the annual water consumption goes down 9%,
17%, and 7% for natural gas, electricity, and diesel fuel respectively.
On the other hand, the respective reductions in the returns above total
costs are 38%, 50% and 80% for natural gas, electricity and diesel fuel.
193
Adjustments in the Optimal Regional Cropping Pattern. Table 58
is an aggregation of the micro level adjustments in the optimum cropping
patterns under increasing natural gas prices (Table 51). Increasing
energy cost results in the previously observed adjustment patterns,
i.e., crops under gravity irrigation decline and more water conserving
sprinkler systems are adopted. Moreover, the crops under side roll
sprinklers decline about 50% when the price of natural gas increases
12.7%
in 1977. However, the expected increase in the natural gas price
from 1977 to 1978 is not large enough to induce any further adjustments
in the optimum cropping pattern.
Total cotton acreage increases about 1,000 acres at the expense
of wheat, but total regional cropland is affected very little with
natural gas price increases expected for 1977 and 1978.
Optimum Regional Resource Utilizations Under Increasing Natural
Gas Prices. Table 59 is derived by utilizing Table 52 which gives micro
-
level resource utilizations. Here neither land nor annual water usages
change between 1977 and 1978 when natural gas prices increase. However, total water consumption goes down 3,916 AF (about 2% of 1976 consumption) when the natural gas price increases 12.7% in 1977. This
results in a saving of 299,497 therms of natural gas. As was mentioned
previously, total land use declines slightly.
Regional Returns Over Total Costs Under Increasing Natural Gas
Prices. As a result of the expected increase in the natural gas price
in 1977, the total production of cotton is increased slightly and wheat
production goes down 7% (Table 60). This situation indicates that
cotton is less sensitive to energy cost increases than wheat, because
194
Table 58.
Optimum Regional Cropping Patterns Under Increasing Natural
Gas Prices, Sulphur Springs Valley, 1976-1978.
Crop
Irrigation System
1976a
1977a
1978a
Acres
Upland Cotton
40-acre side roll
Center pivot
Gravity
Total
Wheat
REGIONAL TOTAL
Gravity
8680
4718
4718
70212
75495
75495
7956
7708
7708
86848
87921
87921
15211
14155
14155
102059
102076
102076
aBased on natural gas prices of $.1167, $.1315, and $.1479 per therm
for 1976, 1977 and 1978, respectively.
195
Table 59. Optimum Regional Resource Utilization Under Increasing
Natural Gas Prices, Sulphur Springs Valley, 1976-1978.
Resource
Annual Water (Used) (AF)
Annual Water (Unused) (AF)
TOTAL
Land (Used)
(Acres)
Land (Unused)
TOTAL
(Acres)
1976a
1977
a
1978a
305,171
301,255
301,255
1,499
5,415
5,415
306,670
306,670
306,670
102,059
102,076
102,076
39,275
39,258
39,258
141,334
141,334
141,334
a Based on
natural gas prices of $.1167, $.1315, and $.1479 per therm for
1976, 1977 and 1978, respectively.
196
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197
wheat is a marginal crop and it becomes uneconomical in
response to a
slight change in its cost.
In the second part of Table 60, variations in aggregated total
cost and returns over total and variable costs are given for the 19761978 period.
The increase in the cost of natural gas increases the
total cost only slightly, 0.4% by 1977 and 1% by 1978. However, reductions in returns over variable and total costs are larger. From 1976
to 1977 and 1978 return over variable cost declines 3% in each period.
The reductions in return above total cost is 5% in 1977 and 6% in 1978.
Summary of Results
In summary, the optimum cropping mix under present conditions
includes cotton and wheat in varying proportions among different farm
sizes. Center pivot sprinkler systems are applied more by the larger
'farm size groups than the smaller ones. July water and land are restricting factors for small farms, while annual available water is a
more restricting resource for the large farm size group.
Switching from natural gas to electricity or diesel fuel decreases total farm income and annual total water consumption. Land
utilization stays about the same.
Decreases in cotton lint prices from the present level, $58.11/
cwt, result
in reductions in farm income and savings of some irrigation
water as corn production increases.
The effects on crop patterns of increasing natural gas prices
to expected 1977 and 1978 levels are nil for small, medium-large, and
large farm size groups. But small-medium farms change the relative
198
acreages of sprinkler and gravity irrigation (in favor of sprinkler systems) at the 1977 natural gas price level. From 1977 to 1978 there is
no change in the crop mix of this farm size group. The major effect of
increasing the cost of natural gas is on farm income, which goes down
as energy cost increases.
The aggregated analysis resembles the farm level results.
Switching to energy sources other than natural gas and decreasing cotton
lint prices, result in reductions in annual water consumption. However,
cropland usage varies between 97,304 and 132,129 acres when cotton lint
prices and/or natural gas prices are changed.
The major effect of natural gas price increases is on total
regional farm income. Optimum regional cropping patterns and resource
utilizations are affected only slightly.
CHAPTER VI
SUMMARY AND CONCLUSIONS
Summary
The economy of Sulphur Springs Valley is influenced mainly by
the agricultural sector. The Valley is characterized as an arid region
with low annual precipitation and high temperature. Therefore, water is
an important factor that is critical to the existence of a profitable
agriculture in the area. Water is obtained from underground water stocks
which are subject to increasing pump lifts over time. Moreover, energy
used for pumping water is expected to be more expensive in the future.
Under these conditions farmers continually search for alternative production techniques that save irrigation water as well as energy
for pumping water. In recent years, attention has focused on sprinkler
irrigation technologies as alternatives to the conventional gravity systems. This study investigates the farm level and regional impacts of
these technologies.
A random area sample of 29 farms in the Sulphur Springs Valley
were interviewed, and the data collected from them were utilized to
develop representative farm unit budgets and mixed integer programming
models for four farm sizes. The analyses included alfalfa hay, upland
cotton, wheat, milo, and corn which were produced by small, small-medium,
medium-large, and large farm size groups. Side roll (10-acre, 20-acre,
and 40-acre units), center pivot, and gravity irrigation systems were
199
200
considered as alternative production techniques for the five crops.
Moreover, natural gas, electricity, and diesel fuel were separately
specified as potential energy sources for comparison purposes. Farm
level cropping systems that maximized net returns above variable costs
were obtained for each farm size and energy source.
Sensitivity analyses were conducted by reducing cotton lint
price levels and increasing natural gas prices. As a final stage, the
results of the initial models and the sensitivity analyses were aggregated and the regional impacts of energy source changes, cotton lint
price declines, and natural gas price increases were investigated in
order to determine the technical and economic adjustments of farmers
under those variations.
Conclu s ions
The major conclusions of the farm level optimum solutions with
cotton lint price at $58.11/cwt and natural gas price at the 1976 ($.1167
per therm) are summarized below.
Upland cotton is the basic crop grown by all farm sizes under
initial conditions with wheat grown as a supplemental crop. Wheat
utilizes off-season (winter) water on land not planted to cotton as
summer water becomes limited. Gravity irrigation is frequently utilized
by the smaller farm size groups. On the other hand, sprinkler systems,
especially center pivot units, are more commonly used by the larger farms
because of capital and resource requirements.
July water is the main factor that limits the expansion of production. For the smaller farm size groups, crop land availability is
201
also a restricting factor in addition to July water. On the other hand,
water that is available during the six week preplanting and planting
period around March is not a restricting factor regardless of the farm
size. For the medium-large and large farm size groups July and annual
available water are the primary constraints.
Natural gas is the cheapest energy source measured in terms of
cost of pumping an acre inch of water. Diesel fuel is the most expensive and electricity is in between. Generally, when the energy source
is shifted from a less expensive one (natural gas) to a more expensive
one (electricity or diesel), water conserving production techniques are
utilized, as gravity irrigation is replaced by sprinkler systems. Consequently, total water consumption goes down as energy becomes more expensive, while land use stays the same. As expected, increasing the
cost of energy results in reductions in returns above total and variable
costs.
Profitability, measured in terms of total cost-gross return
ratio: is the highest for the small farm size group and the lowest for
the large farm class. Profitability goes down (or total cost-gross return ratio goes up) when electricity or diesel fuel is utilized instead
of natural gas. Therefore, small farms using natural gas engines generate proportionately more profit than the large farms using diesel
engines.
Sensitivity analyses were carried out by reducing the cotton
lint price levels from $58.11 to $43.20/cwt and by increasing natural
gas prices 12.7% in 1977 and 12.5% in 1978.
202
As the cotton lint price goes down, the dominance of cotton in
the optimum crop mixes also declines, and corn adds revenue to the net
returns. Small farms are less sensitive to cotton price reductions than
larger farms, since they do not readily shift to other crop growing activities. This occurs because under the limited capital, physical resources, and profitability conditions, gravity irrigated cotton is the
best crop growing activity for these farms. On the other hand, the
larger farm size groups adopt corn a s the cotton price goes down by $5
'
to $10/cwt of lint. Wheat production changes generally parallel the
changes in cotton production, but corn production moves in the opposite
direction. That is, as cotton production goes down, corn production
goes up. When the price of cotton declines, corn under sprinkler systems uses land formerly producing cotton under gravity irrigation. This
results in a reduction in annual water consumption while total land
utilization declines insignificantly.
At the $58.11 cotton price level returns over variable and total
costs are positive regardless of the farm size and energy source, i.e.,
the total cost-gross return ratio varies between 71.9 and 97.4% for all
farm sizes and energy sources. Returns over variable and total costs
decline in reaction to price reductions for cotton lint. Because the
reduction of cotton price reduces the relative profitability of cotton,
for the previous conditions lower valued corn comes into most of the
optimum solutions.
There are no reactions to expected 1977 and 1978 natural gas
price increases of crop production patterns and resource utilizations
by small, medium-large, and large farm size groups. However, total
203
farm income declines as the natdral gas price increases. When the natural gas price is specified at the expected 1977 level, the small-medium
farms increase the amount of land under sprinkler system by reallocating
lands among the basic crops in order to conserve water. A natural gas
price increase to the expected 1978 level has no further effect for this
farm size.
The important conclusions of the regional level aggregation of
the above results are presented below.
With the cotton price at $58.11/cwt and the natural gas price
at $.1167/therm (1976 price level), cotton and wheat are the only crops
that are grown in the area. Decreasing the price of cotton reduces
total cotton and wheat acreages but increases the total corn acreage.
Relatedly, cotton production declines with the reduction in cotton lint
price and corn production increases. However, wheat production first
goes up (substituting cotton) then goes down (not being able to compete
with corn) as price of cotton declines. Decreasing cotton lint prices
and increasing energy costs result in reductions in annual water and
energy consumption with only small changes in land use.
Shifting to more expensive energy sources, electric or diesel
or increasing the cost of natural gas, results in reductions in total
wheat acreage, increases in cotton and corn acreages. Consequently,
regional returns over variable and total costs decline with cotton lint
price reductions and energy cost increases (shifting from natural gas to
electric or diesel).
Generally, the 12.5% increase in natural gas price from 1977 to
1978 does not affect regional cropping patterns at a cotton price of
204
$58.11/cwt. However, from 1976 to 1977, cotton acreage increases while
wheat land declines with the expected 12.7% increase in the natural gas
price. Increasing cost of natural gas reduces annual regional irrigation water consumption by 1.3% or 3,916 acre feet and annual natural gas
used for pumping water by 299,497 therms. But, total regional cropland
use is almost constant under these conditions. Increases in the natural
gas price to 1977 levels result in greater cotton production and decreases in wheat production. Additionally, regional returns over total
cost declines 5% and 6% for 1977 and 1978, respectively, due to increases
in natural gas prices.
The overall regional impacts of energy cost increases on annual
water consumption are not very significant under the present conditions
($58.11/cwt cotton lint price level). For example, shifting from natural
gas to electricity reduces annual water use by only 0.6% and a similar
shift to diesel fuel decreases water use by 8.3% as the crop mix changes.
The regional impacts of possible energy shifts from natural gas to electricity or diesel fuel on return over total cost are significant because
of higher overhead and energy costs (35% and 61% reductions, respectively). At $58.11/cwt cotton price, increases in natural gas prices result
in insignificant reductions (or no reduction) in annual water use. However, returns over total cost decline 5% and 6% in 1977 and 1978, respectively.
Declines in cotton lint price have larger impacts on annual
water consumption and regional return over total cost than do expected
changes in energy costs. For example, when cotton lint price declines
from $58.11 to $43.20/cwt total annual water consumption goes down 15%,
205
22%, and 14% for natural gas, electricity, and diesel fuel, respectively.
The respective reductions in the returns above total costs are 42.2%,
53.7%, and 83.3% for natural gas, electricity, and diesel fuel.
Final Comments and Recommendations for Further Research
Every economic activity is restricted by certain physical,
social, institutional, and financial factors. All of these limitations
surrounding the farming activities in this study influence the results
directly or indirectly by reactions through the other factors. Similarly, no research is free to continue forever without limitation.
Financial and time constraints have influenced this research also;
therefore, it can not claim to be free of omissions and error. Risk
consideration is a major factor ignored in this research. Risk and uncertainty are important factors that a rational decision-maker considers.
For example, according to the available cropland statistics milo (grain
sorghum) is a commonly grown crop in the Sulphur Springs Valley. The
sample data also indicate that in more than 16% of total sampled area
milo is grown. However, the optimal cropping patterns of the representative farm, mixed integer programming models did not contain milo since
it was not as profitable as upland cotton, wheat, or corn. Risk in the
production of cotton and corn is an important factor accounting for the
difference between the model results and the observations in the field.
Although upland cotton appeared to be the most profitable crop,
its expansion in Sulphur Springs Valley might be limited by unsuitable
climatic conditions, especially unseasonal spring frosts.
as
On the other hand, corn seemed to be the next best choice
cotton becomes less profitable. Nevertheless, the following factors
206
have to be considered before uncritically accepting this result. Although corn needs less water than milo, it is more sensitive to the lack
of water in hot summer months than milo. Therefore, those farmers who
have limited amounts of water, especially in critical growing periods,
tend to grow milo rather than corn.
Furthermore, risk is minimized by many farmers growing the best
known crop, milo, which has been quite common for several decades. Corn
is a new crop in the area and farmers need to gain experience in growing
it and test its relative profitability before it will be widely accepted.
The above discussion illustrates the necessity of further studies
searching for the importance of risk and uncertainty in the decisionmaking process of farmers in the region.
In this study the average well depth of each farm size group is
assumed to be constant and its effect on farm income is reflected in the
water cost. Well depth could be treated as an exogenous variable, and
sensitivity analyses could be done by changing water table levels at
certain intervals. However, this is essentially equivalent in terms of
effects on returns and crop mix to changing the cost of the irrigation
water pumped by the three energy sources and the three levels of natural
gas prices as was done in this study. To analyze the reactions to declining groundwater levels over a period of time, another technique
would be an economic model that evaluates the results of an electronic
(digital) analog model (Burdak, 1970).
A regional model that includes different farm size groups growing various crops under alternative irrigation systems and utilizing
alternative energy sources could be developed for the macro level
207
analyses. For a problem like this, the number of crop growing activities would be approximately 4 x 5 x 5 x 3 = 300, where 4 farm size
groups, 5 crops, 5 irrigation systems, and 3 energy sources are specified. A problem of this dimension exceeds the limited capacity of the
presently available mixed integer programming algorithm. Therefore,
separate runs for each farm size and energy source were utilized in this
study. Further research is needed at the macro level to treat the entire Sulphur Springs Valley as one problem unit and to study the impacts
of relaxing some of the homogeneity and ceteris paribus assumptions used
in this study.
As was concluded before, the expected natural gas price increases
in 1977 and 1978 were not large enough to induce any significant adjustment in the cropping pattern of the majority of the farmers. Further
research needs to be conducted to investigate the impacts of greater
magnitudes of natural gas price increases on optimum cropping pattern,
resource utilizations, and return over total cost at farm and regional
level.
Finally, future research is recommended to investigate the exis-
tence of economies of size in the operation of sprinkler irrigation
units and the yield difference between crops grown under gravity and
sprinkler irrigation systems. In this study, the variable costs of
operating sprinkler units are assumed to be constant over the study
area. In a previous study, Sheffield (1971) found that there are economies of size, measured in terms of per acre variable cost of center
pivot units, among the farmers who own more than two center pivot units.
208
Existence of yield differences originating from gravity and
sprinkler systems has not been studied in the Sulphur Springs Valley
area. The yield experiences of the sampled corn growers were reflected
in this study. However, comprehensive technical information is needed
to complete the sample data in terms of the
occutence
of yield differ-
ences between the crops grown under gravity and sprinkler irrigation
systems.
APPENDIX A
LONG TERM AVERAGES OF SOME OF THE CLIMATIC
FACTORS OF DOUGLAS AND WILLCOX
209
•
210
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APPENDIX B
WITHDRAWALS AND RECHARGES OF UNDERGROUND
WATER OF SULPHUR SPRINGS VALLEY
211
212
LEGEND
•
CITIES
Grant Creek
I>: GAGING STATION Numbers Represent
Average Annual Flow In Thousands Of
Acre Feet Per Year, 1959-73.
RESERVOIRS
Infrequently Contains Storage
Frequently Contains Storage
Rar
-
X Wash
SCALE: 1 Inch = 5 Million Acre
Feet Per Year. Not To Scale For Flows
Less Than 2 Hundred Thousand Acre Feet
Per Year
• WILLCOX
V;
Walnut
Creek
Wil c o x
PI aya
0
0
Big Draw
o
•
Turkey
Creek
Rucker
Canyon
o
6
• DOUGLAS
MEXICO
Source: Arizona Water Commission,
1975, p. 182.
—
APPENDIX C
ESTIMATED ANNUAL GROUNDWATER PUMPAGE IN WILLCOX
AND DOUGLAS BASINS 1915-1973 (1,000 AF)
Years
Willcox Basin
Douglas Basin
Total
1915
2
1
3
1920
a
a
b
1925
a
a
b
1930
1
1
2
1935
1
2
3
1940
2
5
7
1945
9
8
17
1950
35
35
70
1955
110
50
160
1960
195
60
255
1965
250
90
340
1970
289
103
392
1973
305
110
415
4,679
1,862
6,541
(71.53%)
(28.47%)
TOTAL c
a
500 AF or less.
b 1000 AF or less.
cNot column total, but it is sum of the yearly pumpages.
Source: Arizona Water Commission, 1975, P. 85.
213
214
300
THOUSAND
AF
250
200
150
100
50
1910
1920
1930
1940
1950
1960
1970
YEAR
Figure Cl. Estimated Annual Groundwater Pumpage in Willcox and
Douglas Basins 1915-1973 (1,000 AF).
1980
APPENDIX D
A SAMPLE QUESTIONNAIRE
Economic Evaluation of Sprinkler Irrigation Systems
1.
Your name:
2.
Your address and telephone:
3. Size of the land under:
(a) Your ownership
A,
(h) Leased out
A,
(c) Rented in
A.
4.
Please show a chart-of your farm showing the approximate locations
of wells, crops, and sprinkler system. (Please indicate the assignment of wells to each crop parcel).
5.
Cropping pattern:
Crops
Gravity Irr.
Acreages
Side Roll Center Pivot
Hand Move
Cotton
Wheat
Barley
Alfalfa
Milo
Sugar Beet
Pinto Beans
215
216
Acreages
Gravity Irr. Hand Move Side Roll Center Pivot
Crops
Lettuce
Others
Fallow
Total
6. How many full-time laborers do you hire?
in 1975-76.
7. How many full-time supervisors do you hire?
in 1975-76.
8. Please check the following machinery and equipment:
Machinery and
Equipment
Size
a) Wheel tractors
(HP)
b)
Crawler tractors
(HP)
c)
Trucks
(Ton)
d) Tillage
Quantity
equipment
Bed shaper
Rows
217
d) Tillage equipment
Chisel plow
Shanks
Cultivator (Rolling)
Rows
Cultivator (Sweep)
Rows
Cul tipacker
Feet
Disk Border
Disks
Disk offset
Feet
Disk tandem
Feet
Disk tandem offset
Float
X
Feet
X
Feet
218
d) Tillage equipment
Lan dplane
X
Feet
Harrow
Sections
Lister
Bottom
Moleboard plow 3 - 16 2-way
4 - 16 2-way
5 - 16 2-way
Mulcher
Rows
Rotary hoe
e)
Rows
Subsoiler (heavy duty)
Shanks
Vibra shank
Feet
Planting equipment
Broadcast seeder
Grain Drill
Feet
Planter (Drill type)
Planter (Hill drop)
Rows
Rows
f) Trailed harvesting equipment
Baler
Bale wagon (pull type)
Wire
219
f) Trailed harvesting equipment
Cotton trailer X X
Feet
XX
XX
Forage harvester (PTO)
Forage wagon
PTO unloader
Mower
Feet
Rake
Feet
Rood with basket cleaner
Rows
Hesston stackhand
Hesston stack mover
g) Self-propelled harvesting equipment
Bale wagon (Roadsider)
Combine
Cotton picker
Cuber with wagon
220,
g) Self-propelled harvesting equipment
Forage harvester
Swather
h) Miscellaneous Equipment
Ditcher
Feet
Fertilizer injector
Rows
Fertilizer spreader
Feet
Fertilizer sidedresser
Feet
Rowbuck
Feet
Scraper
Feet
Sprayer (trailed)
Rows
Sprayer 2 saddle tank
Stalk cutter (rotary)
Stalk cutter (flail)
Rows
221
1.4
1=4
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o
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4-)
4-)
0
4-)
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APPENDIKE
THE MACHINERY AND EQUIPMENT INVENTORY OF THE SAMPLED FARMS
El. The Machinery Combinations of the Sampled Farms
Wheel Tractors
HP
I
II
40 HP and smaller
5
3
6
4
18
50-59 HP
1
1
0
1
3
60-69 HP
0
3
1
3
7
70-79 HP
0
0
0
5
5
80-99 HP
2
3
0
9
14
100-124 HP
1
5
6
24
36
125-149 HP
1
2
1
6
10
150-174 HP
0
1
7
9
17
175-275 HP
0
0
1
4
5
10
18
22
65
115
TOTAL
224
Quantities
III
IV
Total
225
E2. The Implements and Equipment Combinations of the Sampled Farmers.
1.
2.
3.
4.
5.
Quantities
III
IV
Items
I
II
Shaper
Row
Row
Row
Row
1
0
0
0
2
0
1
0
1
1
0
0
8
3
0
1
12
4
1
1
TOTAL
1
3
2
12
18
Chisel Plow
4 Shank
5 Shank
7 Shank
9 Shank
0
0
1
0
1
0
3
0
0
1
3
2
0
3
3
3
1
4
10
5
TOTAL
1
4
6
9
20
0
0
0
0
0
0
2
1
0
9
7
2
11
8
2
TOTAL
0
0
3
18
21
Cultivator (Sweep)
2 Row
4 Row
5 Row
6 Row
7 Row
8 Row
J.
2
0
1
0
0
0
4
1
1
2
0
0
7
0
2
1
8
0
16
0
9
0
2
1
29
1
13
3
10
TOTAL
4
8
18
27
57
Cul tipacker
6 Foot
12 Foot
12.5 Foot
16 Foot
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
4
1
4
1
4
TOTAL
2
0
2
6
10
Bed
4
6
7
8
Cultivator (Rolling)
4 Row
6 Row
8 Row
Total
226
E2 (Continued)
Items
6.
7.
Disk border
2 Disk
3 Disk
4 Disk
6 Disk
1
0
0
0
0
2
1
0
2
0
0
0
2
0
2
2
5
2
3
2
TOTAL
1
3
2
6
12
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
5
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
4
0
3
1
1
8
1
3
0
2
1
1
2
11
1
4
3
2
8
3
3
1
2
3
8
8
23
42
10.5 Foot
12-12.5 Foot
13 Foot
14 Foot
17.5 Foot
18 Foot
20 Foot
21 Foot
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
4
1
3
1
1
1
1
1
5
TOTAL
1
4
5
4
14-
15-15.5 Foot
18 Foot
0
1
0
0
3
0
0
0
3
1
TOTAL
1
0
3
0
4
4
6
8
10
28
Disk offset
TOTAL
9.
10.
Total
II
5 Foot
6 Foot
9-9.5 Foot
10-10.5 Foot
11 Foot
12-12.5 Foot
13-13.5 Foot
14-14.5 Foot
15-15.5 Foot
16 Foot
18 Foot
20 Foot
21 Foot
8.
Quantities
III
IV
I
Disk tandem
Disk tandem offset
Float
8x15-20x42 Foot
227
E2 (Continued)
Items
11.
12.
13.
3
3
8
14
Harrow
2 Section
3 Section
4 Section
6 Section
2
1
0
0
5
2
1
0
0
3
3
1
5
3
1
0
12
9
5
1
TOTAL
3
8
7
9
27
1
2
1
0
0
0
1
2
0
1
0
1
0
0
1
2
1
3
0
4
2
5
2
1
2
8
4
8
3
5
4
5
7
14
30
3
1
0
5
0
0
4
5
1
4
6
3
16
12
4
4
5
10
13
32
0
1
1
0
0
1
0
1
1
0
0
0
2
1
1
0
0
7
1
0
1
1
11
3
1
2
3
4
8
17
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
2
1
1
2
1
1
5
Lister
4 Bottom
5 Bottom
6 Bottom
7 Bottom
8 Bottom
9 Bottom
Moleboard plow
3-16 2 way
4-16 2 way
5-16 2 way
Mulcher
2 Row
3 Row
4 Row
6 Row
8 Row
TOTAL
16.
Total
0
TOTAL
15.
Quantities
III
IV
Landplane
8x30-15x60 Foot
TOTAL
14.
II
Rotary hoe
2 Row
4 Row
6 Row
8 Row
TOTAL
228
E2 (Continued)
Items
17.
18.
19.
II
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
3
2
3
1
4
3
TOTAL
3
0
3
7
13
Grain drill
6 Foot
10 Foot
11 Foot
12 Foot
14 Foot
15 Foot
18 Foot
20 Foot
21 Foot
26 Foot
28 Foot
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
1
0
0
0
1
1
0
3
3
3
1
0
1
1
1
3
4
3
3
3
4
1
1
TOTAL
2
4
7
12
25
2
1
0
0
1
1
0
0
2
7
3
0
9
5
3
3
2
2
10
17
0
0
0
6
0
0
0
2
2
1
7
2
7
9
4
0
6
4
10
20
0
0
1
0
0
0
2
2
3
2
0
1
0
4
5
Subsoiler
1 Shank
3 Shank
5 Shank
7 Shank
9 Shank
Planter (drill type)
4 Row
6 Row
8 Row
TOTAL
20.
Planter (Hill drop)
4 Row
6 Row
8 Row
TOTAL
21.
Quantities
III
IV
I
Baler
2 Wire
3 Wire
TOTAL
Total
229
E2 (Continued)
Items
22.
Cotton trailer
23.
Mower
6 Foot
7 Foot
12 Foot
TOTAL
24.
I
II
Quantities
III
IV
1
15
20
16
52
0
0
0
0
1
1
1
1
0
0
3
0
1
5
1
0
2
2
3
7
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
1
1
3
1
3
1
1
1
1
3
2
6
12
Total
Rake
4
7
8
9
10
12
13
15
Foot
Foot
Foot
Foot
Foot
Foot
Foot
Foot
TOTAL
25.
Roadsider
0
1
0
2
3
26.
Combine
1
4
7
9
21
27.
Cotton picker
1 Row
2 Row
1
0
1
3
0
4
1
2
3
9
1
4
4
3
12
o
o
o
1
o
o
o
o
1
1
1
o
o
o
o
o
1
1
1
1
1
0
1
2
4
0
0
0
0
0
0
3
0
0
0
3
0
0
1
1
2
4
1
1
0
0
1
3
1
4
1
1
3
10
TOTAL
28.
Swather
6 Foot
14 Foot
15 Foot
16 Foot
TOTAL
29.
Ditcher
3
4
6
7
8
Foot
Foot
Foot
Foot
Foot
TOTAL
0
230
E2 (Continued)
Items
30.
II
0
0
0
2
2
0
1
3
2
2
2
1
3
0
4
6
5
15
Fertilizer Spreader
8 Foot
10 Foot
12 Foot
14 Foot
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
1
1
4
1
TOTAL
0
3
2
2
7
1
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
1
0
1
0
0
2
0
Fertilizer Injector
4 Row
6 Row
8 Row
TOTAL
31.
32.
Fertilizer Sidedresser
2 Row
4 Row
6 Row
8 Row
TOTAL
33.
Quantities
III
IV
I
Total
5
7
0
1
6
10
3
1
3
1
10
15
0
3
3
0
2
0
1
1
1
5
5
2
2
1
1
7
9
18
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
3
0
3
0
1
4
1
4
1
1
1
3
2
8
14
Rowbuck
6
7
8
10
12
13
14
15
Foot
Foot
Foot
Foot
Foot
Foot
Foot
Foot
TOTAL
34. Scraper
3 Foot
5 Foot
6 Foot
7 Foot
8 Foot
9 Foot
15 Foot
TOTAL
0
0
2
1
231
E2
(Continued)
Items
35.
Sprayer
Trailed
2 Saddle Tank
TOTAL
36.
Stalk Cutter (Shredder)
Rotary 2 Row
4 Row
6 Row
7 Row
Flail 2 Row
4 Row
7 Row
TOTAL
Quantities
III
IV
I
II
4
0
4
1
6
3
5
11
19
15
4
5
9
16
34
1
0
0
0
2
0
0
1
3
1
0
0
0
0
1
4
0
1
0
0
1
2
4
2
0
0
1
0
5
11
3
1
2
1
1
3
5
7
9
24
Total
APPENDIX F
CALCULATIONS OF CONSUMPTIVE USE OF WATER
Willcox (32.15°) a
Months
January
February
March
April
May
June
July
August
September
October
November
December
TOTAL
41.6
44.8
49.5
57.1
64.8
73.7
79.1
76.3
71.4
60.5
48.8
42.1
txp = Z f = F)
p(%)C
f( %)d
7.20
6.97
8.37
8.72
9.63
9.60
9.77
9.28
8.34
7.93
7.11
7.05
3.00
3.12
4.14
4.98
6.24
7.08
7.73
7.08
5.96
4.80
3.47
2.97
60.57
a Figure in parenthesis is the latitude of Willcox.
bSource: Sellers and Hill, 1974.
c Source: USDA, Agricultural Research Service, 1962, p. 43. The values
given for 32 0 latitude are employed.
dMonthly consumptive use factor, i.e., fi = ti x pi .
232
233
Calculations of consumptive use of water by using Bladey-Criddle formula
(Erie, French, and Harris, 1968).
W c =KxF
(FI)
where W c is consumptive use of water and K is empirically
found seasonal or monthly constants (K and k respectively), and
F=
L
i=k
ti x pi
fi =
(F2)
i=k
where i is the number of the beginning month of growing
period. Since every crop is not grown year around, i may take any value
from 1 to 12, so may J.
Example: Calculations of consumptive use of water on
corn grain.
F= 1/2 f 3 + f 4 + f 5 + 1/2 f 6
= 2.07 + 4.98 + 6.24 + 3.54
= 16.83
W C =KxF
= 0.98 x 16.83
= 16.49 AI.
APPENDIX G
DETERMINATION OF INITIAL INVESTMENT AND VARIABLE COSTS
OF 10- AND 20-ACRE SIDE ROLL SPRINKLER UNITS
1.
Estimation of Initial Investments
The following cost figures are developed for three side roll
unit sizes, 10-acre, 20-acre, and 40-acre sprinkler units. When a side
roll unit smaller than 40-acre is adopted, then the size of pipe should
be 4 inch rather than 5 inch. The cost difference between these two
sizes is about $12.00 per one 40-foot joint. This ends up to $400.00
for a 1/4 mile (1320 feet) system. It is assumed, here, that the adjustments in the acreage for 10- and 20-acre units are done on the
length of the sprinkler system rather than its traveling distance.
Therefore, the systems are designed as follows:
40-acre unit covers 1320' x 1320' square feet
20-acre unit covers 660' x 1320' square feet
10-acre unit covers 330' x 1320' square feet
where the first multiplier is the length of the system, the second one
is the traveling distance. If it is more applicable, a manager can make
this adjustment in the traveling distance or both.
A 1/4 mile side roll sprinkler system has 33 joints 40 feet each,
34
line wheels, and 4 wheels of moving unit. Each joint has one sprin-
kler nozzle and one wheel on it. Therefore, the cost reductions on
234
235
smaller size units will be on the size and the length of sprinkler pipe,
line wheels, and sprinkler nozzles.
40-acre unit:
Total Cost
20-acre unit:
Savings in
Pipe size difference
$5,490.67
$200.00
Pipe length difference
887.74
Wheels
614.38
Sprinkler nozzles
131.75
TOTAL SAVINGS
1,833.87
TOTAL COST
- (1,833.87)
$3,656.80
10-acre unit: Savings in
Pipe size difference
Pipe length difference
$100.00
1,305.50
Wheels
903.50
Sprinkler nozzles
193.75
TOTAL SAVINGS
2,502.75
TOTAL COST
The costs of each joint, wheel and nozzle are
- (2,502.75)
$2,987.92
$52.22, $36.14,
respectively. Reductions in their numbers are 17 and 25 for
and
$7.75
20-
and 10-acre units, respectively.
2.
Estimation of Variable Costs
Here it is assumed that the per acre extra pressure cost of the
systems are equal to each other. Then, the total extra pressure cost
236
of a unit (Ci) is calculated by multiplying the per acre extra pressure
cost of another unit (C. /A ) by the area that is irrigated by the first
j
unit (A.).
1
Extra pressure costs for 10- and 20-acre units are computed by
Equation Gl.
C I• =
C.
3
A. • Ai.
(G1)
where C. and C. are the extra pressure cost of ith and jth
1
units respectively and A i and A i are their respective acreages.
Moving cost is computed by the similar procedure, i.e.
M.1 =
M.
7
A.
A.1
(G2)
where M's and A's are the respective moving costs and
acreages of ith and jth units.
Lubrication and maintenance costs for 10- and 20-acre units are
computed by reducing the cost of 40-acre units in proportion to the reductions in the cost of the sprinkler units.
Example:
Average cost difference between a 40-acre and a 20-acre unit:
$5490.67 - $3656.80 = $1833.87
Difference as a proportion of the cost of the 40-acre unit:
$1833.87/$5490.67 = 0.334.
Expected reduction in lubrication and maintenance cost to represent
a 20-acre unit: $542.80 x 0.334 = $181.29. Thus the maintenance
and repair cost of a 20-acre side roll unit is estimated as:
$542.80 - $181.29 = $361.51.
APPENDIX H
SAVINGS AND ADDED COSTS DUE TO SPRINKLER SYSTEMS
Table H1 is for milo produced on the small farm class utilizing
natural gas as the energy source. Savings in operations costs originate
from those irrigation operations that are not performed under sprinkler
systems, i.e., make borders, buck rows, mulch, disk ends, and knock
borders.
The savings in variable water costs are calculated in the followway way: (54 - 30) • .7533 = 18.08 for sprinkler irrigation system.
Table 14 provides water application rates (values in parenthesis above)
and Table 19 gives variable cost of pumping water (multiplier of above
equation).
The savings in irrigation labor costs are due to the savings in
water and labor requirements under sprinkler systems. Calculation of
this for side roll sprinkler units follows: (54 x .5253)
(30 x .4556)
= 14.70 which requires utilization of Table 25 which gives the cost of
irrigation labor for gravity and sprinkler systems. As is seen in Table
H1, net savings above added variable cost is the lowest for the 10-acre
side roll unit while it is the highest for the center pivot system.
Moreover, the center pivot sprinkler system is the preferable one considering the net savings above total added cost. It is clearly seen in
this table that none of the systems generate enough savings to cover
their total added costs. In this sense, 10-acre side roll unit is the
most expensive irrigation system to own and operate.
237
•
238
111
r-i
Ln
N
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cn
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c3
APPENDIX I
CALCULATIONS OF FIXED AND VARIABLE COSTS
OF MACHINERY AND EQUIPMENT
1. Depreciation (D):
D = (P - RFV)/t
where,
P = Original cost of the item.
RFV = Remaining farm value.
t = Years to trade.
t = T/a
(I2)
where,
T = Total wear out period given as a specification
of the item.
a = Annual use rate (hour) of it estimated for Arizona.
RFV. = k. x q. x P j(I3)
where,
k. and q i. are the constants of ith machinery group.
These constants are given below:
239
240
Group 3 cGroup 4d
Group 5e
Group l a
Group 2b
k
.640
.600
.560
.680
.100
q
.885
.885
.885
.920
1.000
a Bale wagon, combine, cotton picker, cotton stripper, cuber and swather.
Bed shaper, chisel plow, cultipacker, cultivator, disk border, disk
offset, disk tandem, disk tandem offset, float, harrow, landplane,
lister, moldboard plow, mulcher, rotary hoe, subsoiler, vibra shank,
broadcast seeder, grain drill, planter, bale wagon, cotton trailer,
forage wagon, mower, rake, rood, stackmover, ditcher, fertilizer injector, fertilizer spreader, fertilizer sidedresser, rowbuck, scraper,
sprayer and stalk cutter.
c Forage harvester, baler and stack hand.
dWheel tractors.
eTrucks.
2. Taxes, housing, interest and insurance (THII):
THII = (Thii) (P RFV) / (2 x 100) (I4)
where,
Thii = Percentage of average investment charged for
THII annually. The Thii values are given below:
Thii is 14.1% for Group 2 and baler (3-wire with motor) and
PTO SB8.0); 14.4% for Group
forage harvesters (PTO RC2 PTO WP 6.2, and
harvesters (SP RC 2, SP WP 6.2, and SP
4, 15.6% for Group 1 and forage
1-ton trucks; and 22.0% for
SB 12.0 JD 5400); 18.7% for 1/2-ton and
tandem truck and truck with feed bed and scales.
3. Average annual repair cost:
r = (100 x a x t) / T (15)
241
where,
r = Percentage use rate.
TAR = m x rn
(16)
where,
TAR = Total annual use rate.
in and n = constants which are given for 5 groups below:
In
Group 1
Croup 2
Group 3
Group 4
Group 5
0.0010
0.0012
0.00096
0.00127
0.00159
1.5000
1.5000
1.4000
1.40000
1.40000
R = TAR x P / t
(17)
where,
R = Repair cost.
4. Fuel and Oil Cost (FOC)
a. Tractors:
FOC = (HP x K x P f x a x 1.15) / F
(18)
where,
HP = Tractor horsepower
K = Load factor: .65 for 40-80 HP tractors and .75 for
100-175 HP tractors
P f = Price of fuel
F = 8.4 for gasoline
= 11.2 for diesel
= 6.66 for LP gas engines
-
242
b. Self-propelled equipment (trucks, cotton pickers, swathers,
balers, etc.):
FOC = GPH x P
f x a x 1.15
where,
GPH = Gallons of fuel consumed per hour of use.
(19)
APPENDIX J
WATER IRRIGATION SCHEDULE OF CROPS
,
243
244
e
-H 0
-H
(C1
> 4-1
ccs
$4 >4
1/40
1/40
1/40
1/4.0
I
I
I
.0
1/4.0
1/40
1/49
c
I
I
I
r-I
C'.)
( .0
N
r-I
N
N
I
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1
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H
o
(51
OU)
HE
$4 g a)
0
-P
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uà
cn
-H
4-)
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d 0
(t{
N
I
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>4
(.7 tn
If)
$.4
HE
g 0
-H
-1-)
cn
$4 >1
cn
0
ko
I
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-H a)
> 4-)
cn
ri
ri
1/40
al
al
C',
ri
ri
1/40
ri
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1
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N
1/49
1/40
01
N
1/40
1/40
1/40
1/40
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CO
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5
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cn
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n.0
1/40
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144
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cr
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4
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0
El
APPENDIX K
COEFFICIENTS OF THE REPRESENTATIVE FARM-MIXED
INTEGER PROGRAMMING MATRIX
Row Number 1
2
3
4
5
6 7 8
9 10
11
12
13
14
15
16
Description
Objective Function
Land Constraint
Alfalfa Hay Constraint
Cotton Lint Constraint
Cotton Seed Constraint
Wheat Constraint
Grain Sorghum (Milo) Constraint
Corn Grain Constraint
Gravity Irrigation Water Annual
10-Acre Side Roll Unit Water Annual
20-Acre Side Roll Unit Water Annual
40-Acre Side Roll Unit Water Annual
Center Pivot Sprinkler System Water Annual
Water Bound (July)
Water Bound (March)
Water Bound (Annual)
245
246
Column
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
Description
Alfalfa Hay Production Under 10-Acre Side Roll System
Alfalfa Hay Production Under 20-Acre Side Roll System
Alfalfa Hay Production Under 40-Acre Side Roll System
Alfalfa Hay Production Under Center Pivot Sprinkler System
Upland Cotton Production Under 10-Acre Side Roll System
Upland Cotton Production Under 20-Acre Side Roll System
Upland Cotton Production Under 40-Acre Side Roll System
Upland Cotton Production Under Center Pivot Sprinkler Sys.
Wheat Production Under 10-Acre Side Roll System
Wheat Production Under 20-Acre Side Roll System
Wheat Production Under 40-Acre Side Roll System
Wheat Production Under Center Pivot Sprinkler System
Milo Production Under 10-Acre Side Roll System
Milo Production Under 20-Acre Side Roll System
Milo Production Under 40-Acre Side Roll System
Milo Production Under Center Pivot Sprinkler System
Corn Production Under 10-Acre Side Roll System
Corn Production Under 20-Acre Side Roll System
Corn Production Under 40-Acre Side Roll System
Corn Production Under Center Pivot Sprinkler System
Alfalfa Hay Production Under Gravity Irrigation System
Upland Cotton Production Under Gravity Irrigation System
Wheat Production Under Gravity Irrigation System
Milo Production Under Gravity Irrigation System
Corn Production Under Gravity Irrigation System
Alfalfa Hay Selling
Upland Cotton (lint) Selling
Upland Cotton (seed) Selling
Wheat Selling
Milo Selling
Corn Selling
Water Purchasing with Gravity Irrigation System
Water Purchasing with 10-Acre Side Roll System
Water Purchasing with 20-Acre Side Roll System
Water Purchasing with 40-Acre Side Roll System
Water Purchasing with Center Pivot Sprinkler System
Constraint Values
247
Row
Number
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
(NG)
(E)
(D)
(NG)
(E)
(D)
(NG)
(E)
(D)
(NG)
(E)
(D)
(NG)
(E)
(D)
Coefficients
Column
Number a
I
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
32
32
33
33
33
34
34
34
2,740.70
4,830.76
7,719.40
24,690.90
3,147.00
5,229.36
9,416.60
30,178.20
2,637.80
4,174.96
7,307.80
23,332.40
2,653.40
4,206.16
7,370.20
23,537.80
3,136.90
5,173.16
9,304.20
29,828.50
125.97
177.58
120.68
123.40
175.11
- 2.92
- 58.11
- 5.10
- 6.23
- 4.20
- 4.61
1.2786
1.7886
1.9361
1.2089
1.7189
1.8664
1.2089
1.7189
1.8664
1.2089
1.7189
1.8664
.9949
1.5049
1.6524
35
35
35
36
36
36
II
2,741.60
4,382.56
7,723.00
24,696.10
3,190.90
5,281.16
9,520.00
30,514.90
2,653.40
4,206.16
7,370.20
23,536.50
2,676.40
4,252.16
7,462.20
23,836.80
3,163.30
5,225.96
9,409.80
30,171.70
126.03
180.76
122.68
126.67
179.01
- 2.92
- 58.11
- 5.10
- 6.23
- 4.20
- 4.61
1.3695
1.9411
2.1061
1.2998
1.8714
2.0364
1.2998
1.8714
2.0364
1.2998
1.8714
2.0364
1.0858
1.6574
1.9224
III
2,743.70
4,386.76
7,731.40
24,726.00
3,158.60
5,216.56
9,391.00
30,096.30
2,657.50
4,214.36
7,386.60
23,588.50
2,678.00
4,255.36
7,468.60
23,858.90
3,155.70
5,210.76
9,379.40
30,072.90
126.30
177.81
123.51
127.03
178.67
- 2.92
- 58.11
- 5.10
- 6.23
- 4.20
- 4.61
1.6945
2.4853
2.7145
1.6248
2.4156
2.6448
1.6248
2.4156
2.6448
1.6248
2.4156
2.6448
1.4108
2.2016
2.4308
IV
2,742.20
4,383.76
7,725.40
24,706.50
3,178.20
5,255.76
9,469.40
30,351.10
2,648.40
4,196.16
7,350.20
23,470.20
2,672.00
4,243.36
7,444.60
23,780.90
3,158.00
5,215.36
9,388.60
30,102.80
126.13
179.78
122.64
126.64
178.75
- 2.92
- 58.11
- 5.10
- 6.23
- 4.20
- 4.61
1.4995
2.1586
2.3495
1.4298
2.0889
2.2798
1.4298
2.0889
2.2798
1.4298
2.0889
2.2798
1.2158
1.8749
2.0658
248'
Row
Number
Column
ii
i
Number a
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
1.0
1.0
1.0
1.0
1.0
<, 189.0
Coefficients
III
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
1.0
1.0
1.0
1.0
1.0
<-470.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
1.0
1.0
1.0
1.0
1.0
L.931.0
IV
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
10.0
20.0
40.0
160.0
1.0
1.0
1.0
1.0
1.0
<2,030.0
_.
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
37
3
3
3
3
3
3
3
1
2
3
4
_21
26
37
- 1,067.1
- 2,134.2
- 4,268.4
- 13,872.3
- 106.71
1.0
< 0.0
- 1,067.1
- 2,134.2
- 4,268.4
- 13,872.3
- 106.71
1.0
L. 0.0
- 1,067.1
- 2,134.2
- 4,268.4
- 13,872.3
- 106.71
1.0
L. 0.0
- 1,067.1
- 2,134.2
- 4,268.4
- 13,872.3
- 106.71
1.0
4-0.0
4
4
4
4
4
4
4
5
6
7
8
22
27
37
- 65.3
- 130.6
- 261.2
- 848.9
- 6.53
1.0
4 0.0
- 65.3
- 130.6
- 261.2
- 848.9
- 6.53
1.0
4.0.0
- 65.3
- 130.6
- 261.2
- 848.9
- 6.53
1.0
40.0
- 65.3
- 130.6
- 261.2
- 848.9
- 6.53
1.0
<0.0
5
5
5
5
5
5
6
7
8
22
- 112.4
- 224.8
- 449.6
- 1461.2
- 11.24
- 112.4
- 224.8
- 449.6
- 1461.2
- 11.24
- 112.4
- 224.8
- 449.6
- 1461.2
- 11.24
- 112.4
- 224.8
- 449.6
- 1461.2
- 11.24
_
_
_
_
_
249
Row
Number
Coefficients
Column
Number
II
III
IV
5
5
28
37
6
6
6
6
6
6
6
9
10
11
12
23
29
37
- 386.6
- 773.2
- 1546.4
- 5025.8
- 38.66
1.0
4_0.0
_
- 386.6
- 773.2
- 1546.4
- 5025.8
- 38.66
1.0
4.0.0
- 386.6
- 773.2
- 1546.4
- 5025.8
- 38.66
1.0
40.0
- 386.6
- 773.2
- 1546.4
- 5025.8
- 38.66
1.0
40.0
7
7
7
7
7
7
7
13
14
15
16
24
30
37
- 495.5
- 991.0
- 1982.0
- 6441.5
- 49.55
1.0
4
0.0
_
- 495.5
- 991.0
- 1982.0
- 6441.5
- 49.55
1.0
4,0.0
_
- 495.5
- 991.0
- 1982.0
- 6441.5
- 49.55
1.0
4. 0.0
- 495.5
- 991.0
- 1982.0
- 6441.5
- 49.55
1.0
8
8
8
8
8
8
8
17
18
19
20
25
31
37
- 750.0
- 1500.0
- 3000.0
- 9750.0
- 67.0
1.0
4,0.0
_
- 750.0
- 1500.0
- 3000.0
- 9750.0
- 67.0
1.0
4,0.0
_
- 750.0
- 1500.0
- 3000.0
- 9750.0
- 67.0
1.0
4_
_ 0.0
- 750.0
- 1500.0
- 3000.0
- 9750.0
- 67.0
1.0
4,0.0
9
9
9
9
9
9
9
21
22
23
24
25
32
37
76.0
54.0
44.0
54.0
36.0
- 1.0
= 0.0
76.0
54.0
44.0
54.0
36.0
- 1.0
= 0.0
76.0
54.0
44.0
54.0
36.0
- 1.0
= 0.0
76.0
54.0
44.0
54.0
36.0
- 1.0
= 0.0
10
10
10
10
10
10
10
1
5
9
13
17
33
37
650.0
390.0
300.0
300.0
210.0
- 1.0
= 0.0
650.0
390.0
300.0
300.0
210.0
- 1.0
= 0.0
650.0
390.0
300.0
300.0
210.0
- 1.0
= 0.0
650.0
390.0
300.0
300.0
210.0
- 1.0
= 0.0
11
11
11
11
2
6
10
14
1300.0
780.0
600.0
600.0
1300.0
780.0
600.0
600.0
1300.0
780.0
600.0
600.0
1300.0
780.0
600.0
600.0
1.0
< 0.0
1.0
< 0.0
1.0
< 0.0
1.0
40.0
_
25-0
Row
Number
Column
Number
I
II
Coefficients
III
IV
11
11
11
18
34
37
420.0
- 1.0
= 0.0
420.0
- 1.0
= 0.0
420.0
- 1.0
= 0.0
420.0
- 1.0
= 0.0
12
12
12
12
12
12
12
3
7
11
15
19
35
37
2600.0
1560.0
1200.0
1200.0
840.0
- 1.0
= 0.0
2600.0
1560.0
1200.0
1200.0
840.0
- 1.0
= 0.0
2600.0
1560.0
1200.0
1200.0
840.0
- 1.0
= 0.0
2600.0
1560.0
1200.0
1200.0
840.0
- 1.0
= 0.0
13
13
13
13
13
13
13
4
8
12
16
20
36
37
8450.0
5070.0
3900.0
3900.0
2730.0
- 1.0
= 0.0
8450.0
5070.0
3900.0
3900.0
2730.0
- 1.0
= 0.0
8450.0
5070.0
3900.0
3900.0
2730.0
- 1.0
= 0.0
8450.0
5070.0
3900.0
3900.0
2730.0
- 1.0
= 0.0
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
14
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
60.0
120.0
240.0
780.0
45.0
90.0
180.0
585.0
0.0
0.0
0.0
0.0
45.0
90.0
180.0
585.0
30.0
60.0
120.0
240.0
780.0
45.0
90.0
180.0
585.0
0.0
0.0
0.0
0.0
45.0
90.0
180.0
585.0
30.0
60.0
120.0
240.0
780.0
45.0
90.0
180.0
585.0
0.0
0.0
0.0
0.0
45.0
90.0
180.0
585.0
30.0
60.0
120.0
240.0
780.0
45.0
90.0
180.0
585.0
0.0
0.0
0.0
0.0
45.0
90.0
180.0
585.0
30.0
14
14
14
14
14
14
14
19
20
21
22
23
24
60.0
120.0
390.0
6.0
6.0
0.0
60.0
120.0
390.0
6.0
6.0
0.0
6.0
3.0
<1004.0
_.
6.0
3.0
<1792.0
....
60.0
120.0
390.0
6.0
6.0
0.0
6.0
60.0
120.0
390.0
6.0
6.0
0.0
6.0
3.0
< 2722.0
3.0
< 3718.0
14
25
37
_
251
Coefficients
Row
Number
Column
Number
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
37
47.5
95.0
190.0
617.5
75.0
150.0
300.0
975.0
52.5
105.0
210.0
682.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
10.0
13.5
9.0
12.0
12.0
4,3011.0
47.5
95.0
190.0
617.5
75.0
150.0
300.0
975.0
52.5
105.0
210.0
682.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
10.0
13.5
9.0
12.0
12.0
4.5376.0
47.5
95.0
190.0
617.5
75.0
150.0
300.0
975.0
52.5
105.0
210.0
682.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
10.0
13.5
9.0
12.0
12.0
4,8165.0
47.5
95.0
190.0
617.5
75.0
150.0
300.0
975.0
52.5
105.0
210.0
682.5
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
10.0
13.5
9.0
12.0
12.0
Z. 11155.0
16
16
16
16
16
16
32
33
34
35
36
37
1.0
1.0
1.0
1.0
1.0
4.10,752.0
_
1.0
1.0
1.0
1.0
1.0
<19,200.0
1.0
1.0
1.0
1.0
1.0
<29,160.0
_
1.0
1.0
1.0
1.0
1.0
<39,840.0
III
IV
252
Coefficients changed for sensitivity analyses:
1.
Cotton lint price variations
Row No.
Coefficients
I - IV
Column No.
1
27
- 58.11
1
27
- 53.00
1
27
- 48.00
1
27
- 43.20
2. Natural gas price increases
Row No.
a
Column No. a
I
Coefficients
II
III
IV
1
32(N.G.)
(1977)
1.3528
1.4527
1.8077
1.5954
1
32(N.G.)
(1978)
1.4353
1.5448
1.9370
1.7017
1
33(N.G.)
(1977)
1.2831
1.3830
1.7380
1.5257
1
33(N.G.)
(1978)
1.3656
1.4751
1.8673
1.6320
1
34(N.G.)
(1977)
1.2831
1.3830
1.7380
1.5257
1
34(N.G.)
(1978)
1.3656
1.4751
1.8673
1.6320
1
35(N.G.)
(1977)
1.2831
1.3830
1.7380
1.5257
1
35(N.G.)
(1978)
1.3656
1.4751
1.8673
1.6320
1
36(N.G.)
(1977)
1.0691
1.1414
1.4964
1.3117
1
36(N.G.)
(1978)
1.1516
1.2335
1.6257
1.3904
Abbreviations in paranthesis are used for:
N.G. = Natural Gas
= Electricity
E.
= Diesel
D.
1977 = Coefficients with 1977 natural gas price level
1978 = Coefficients with 1978 natural gas price level
APPENDIX L
VARIATIONS IN THE OPTIMUM REGIONAL CROP PRODUCTIONS
UNDER CHANGING COTTON LINT PRICES, 1976
Cotton Lint Price Levels ($/cwt)
Energy
Source
Natural Gas
58.11
43.20
481,108
211,481
76,256
46,139
Cotton seed
828,144
364,017
131,262
79,419
Wheat
588,104
840,661
689,821
533,663
4,548,095
6,825,288
7,465,337
0
Cotton lint
491,203
173,205
47,694
0
Cotton seed
845,504
298,139
82,096
0
Wheat
490,727
598,573
499,134
499,134
5,298,117
7,436,388
7,969,516
Corn
Diesel
48.00
cwt
Cotton lint
Corn
Electric
53.00
Crop
0
Cotton lint
491,203
124,695
56,335
0
Cotton seed
845,504
214,637
96,967
0
Wheat
306,308
587,875
499,134
499,134
6,090,549
7,262,911
7,969,516
Corn
0
253
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