by

by

RISK AND DIVERSIFICATION IN ARIZONA

CROP FARM PRODUCTION by

Richard Clifford Shane

A Thesis Submitted to the Faculty of the

In Partial Fulfillment of the Requirements

For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

1 9 7 1

STATEMENT BY AUTHOR

This thesis has been submitted in partial fulfill­ ment of requirements for an advanced degree at The

University of Arizona and is deposited in the University

Library to be made available to borrowers under rules of the Library.

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowl­ edgment 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 inter­ ests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED

4/

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

23

7

/

JOHN R. WILDERMUTH

AAssistant Professor of Agricultural

ACKNOWLEDGMENTS

Many individuals have influenced and directed my

graduate work at The University of Arizona.

Recognition of

all these individuals by name is impractical. Therefore,

the author expresses a general thank you to everyone who

made my graduate work possible.

The author wishes to express a special word of

thanks to Dr. John Wildermuth for his constructive criticisms

and recommendations throughout the various stages of pre­ paring this thesis.

Thanks to Dr. Russell Gum for his contributions

during the initial stages of development and to other

members of the Agricultural Economics Department who offered

guidance and constructive criticism.

Acknowledgment is also extended to Mrs. Paula Tripp

and the other secretaries of the Agricultural Economics

Department for their assistance and understanding throughout

the various steps of this thesis.

acknowledgment for their sacrifices, encouragement, and

understanding throughout all phases of my graduate work.

iii

TABLE OF CONTENTS

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

Page

Vi

A B S T R A C T ......................................... .. . x

CHAPTER

I. INTRODUCTION ........ . .......... ..

. i t

Farm Size and Capital Requirements

Increase . ....................

Credit Squeeze ..................

Government Payment Changes . . . .

The Principle of Increasing Risk .

Objectives .................... .

Procedure .................... .

II. METHODS OF A N A L Y S I S ................

1

11

Variability in Crop P r o d u c t i o n ............ 11

Sources of Data and P r o c e d u r e ............ 13

Crops Selected and Sources of

D a t a ........................

The Variate Difference Method ........

13

17

21 Diversification and Variability ..........

Diversification by Adding

R e s o u r c e s ..........................

Diversification With Redistribution

21 of Fixed R e s o u r c e s .................. 23

Break-Even Returns .................... 25

III. YIELD, PRICE, AND INCOME VARIABILITY OF

SELECTED ARIZONA CROPS ...................... 29

Yield Variability of Arizona Crops ........

Price Variability of Arizona Crops ........

Gross Income Variability of Arizona

C r o p s ...................................

Return Above Variable Cost Variability of Arizona C r o p s ........................

29

32

32

37 iv

V

TABLE OF CONTENTS— Continued

CHAPTER

IV. DIVERSIFICATION AND SHORT-RUN BREAK-EVEN

R E T U R N S ..... ................................

Effects of Diversification on Returns

Above Variable C o s t ............

Sugar Beets, M i l o ..............

Potatoes, Watermelons ................

C a n t a l o u p e s ...........................

, ........

Sugar Beets-Cotton vs. Fall

Lettuce-Cotton ......................

Short-Run Break-Even Returns ..............

Page

45

APPENDIX. SUPPLEMENTARY TABLES

REFERENCES CITED

....................

69

73

92

45

48

51

54

56

60

61

LIST OF TABLES

Table Page

1. Amount of Sales per Farm, by Sales Classes,

1960-1969

2. Prices of Selected Farm Inputs, 1960-1970 . . .

3. Cash Receipts from Marketings of Farm

Products in Arizona, 1966, 1967, and 1968 . .

.

4. Acreage Harvested in 1969 and Mean Price and Yield for 1965-1969 of Selected

Arizona C r o p s ................

5. Selected Crops: Ranking by Yield

Variability Coefficients ............ . . . .

6. Selected Crops: Ranking by Price

Variability Coefficients ........

7. Selected_Crops: Ranking by Gross Income

Variability Coefficients ........ . ........

6

14

30

33

11. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

.2 Acre of Barley, and Variable

Proportions of .6 Acre Allocated to

Cotton and Milo ............................. vi

35

8. Per Acre Variable Costs of Producing

Arizona Crops Based on 1970 Input

Prices and 1960-1969 Yield Levels .......... 38

9. Selected Crops: Variability of Returns

Above Variable Cost for 320 and 800

Acre Arizona Crop F a r m s .................... 40

10. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

.2 Acre of Barley, and Variable

Proportions of .6 Acre Allocated to

Cotton and Sugar Beets ...................... 49

50

3

4

Proportions of .6 Acre Allocated to

Cotton and C a n t a l o u p e ................ ..

15. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

.2 Acre of Barley, and Variable

Proportions of .6 Acre Allocated to

Cotton and Fall L e t t u c e ....................

16. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

.2 Acre of Barley, and Variable

Proportions of .6 Acre Allocated to

Cotton and O n i o n s ...........................

17. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

.2 Acre of Barley, and Variable

Proportions of .6 Acre Allocated to

Cotton and C a r r o t s ........................... vii

LIST OF TABLES— Continued

Table

12. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

.2 Acre of Barley, and Variable

Proportions of .6 Acre Allocated to

Cotton and P o t a t o e s ................ ..

13. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

.2 Acre of Barley, and Variable

Proportions of .6 Acre Allocated to

Cotton and Watermelons ......................

14. Return Above Variable Cost Levels and

Variabilities on 320 and 800 Acre Farms

in Arizona with .2 Acre of Alfalfa,

Page

52

53

55

57

58

59

18. Cash Fixed Costs Per Acre on Arizona Farms . . .

19. Variable Production Costs on 320 Acre

Arizona Crop Farms

63

74

viii

LIST OF TABLES— Continued

Table

20. Variable Production Costs on 800 Acre

Arizona Crop F a r m s ..........................

21. Return Above Variable Cost Levels and

Variabilities on 320 Acre Farms in

Arizona With One Acre Allocated

Equally Between Two Crops ..................

22. Return Above Variable Cost Levels and

Variabilities on 800 Acre Farms in

Arizona With One Acre Allocated

Equally Between Two Crops ..................

Page

75

76

80

23. Return Above Variable Cost Levels and

Variabilities on 320 Acre Arizona

Farms with One Acre Allocated Equally

Among Three Crops for Selected

Diversification Systems ....................

24. Return Above Variable Cost Levels and

Variabilities on 800 Acre Arizona

Farms with One Acre Allocated Equally

Among Three Crops for Selected

Diversification Systems ....................

25. Return Above Variable Cost Levels and

Variabilities on 320 Acre Arizona

Farms with One Acre Allocated Equally

Among Four Crops for Selected

Diversification Systems ....................

26. Return Above Variable Cost Levels and

Variabilities on 800 Acre Arizona

Farms with One Acre Allocated Equally

Among Four Crops for Selected

Diversification Systems ....................

27. Return Above Variable Cost Levels and

Variabilities on 320 Acre Arizona

Farms with One Acre Allocated Equally

Among Five Crops for Selected

Diversification Systems

84

85

86

87

88

ix

LIST OF TABLES— Continued

Table

28. Return Above Variable Cost Levels and

Variabilities on 800 Acre Arizona

Farms with One Acre Allocated Equally

Among Five Crops for Selected

Diversification Systems . . . . ............

Page

89

29. Annual Fixed Cost for a Representative

320 Acre General Crop Farm in Arizona . . . .

30. Annual Fixed Costs for a Representative

800 Acre General Crop Farm in Arizona . . . .

90

91

ABSTRACT

This study estimates the degree of variability in

prices, yields, and incomes associated with various crops

and crop diversification systems in Arizona.

Relationships

among variabilities, returns above variable cost levels,

equity levels, and farm sizes associated with various

cropping systems are investigated.

The variate difference method of calculating varia­

bility is used to derive estimates of income variability for

various crops and crop diversification systems based on

state price, yield, and cost data over a series of years.

The results show that vegetable crops have high

expected returns and high variability in returns in contrast

to field crops with low expected returns and low variability

in returns.

However, in some specific diversification

systems vegetable crops result in higher variability and

lower returns than field crops.

Further, the results indicate that a farmer should

consider his scale and equity level when deciding what to

produce.

Varying degrees of risk are inherent in different

equity and scale levels.

A farmer at either of the two

scales of operation considered in this study, 320 or 800

acres, and with a low equity level can easily go bankrupt in

one bad year.

x

CHAPTER I

INTRODUCTION

of the factors increasing the complexity of the decision

making process for Arizona farmers and agribusinessmen.

Now,

men need reliable and accurate statistics and an adequate

procedure for analyzing alternative courses of action in

order to make effective decisions.

This study is designed to augment the information

base currently available for decision making in Arizona crop

farm production by estimating the degree of variability in

prices, yields, and income associated with various crops and

crop diversification systems.

Also investigated is the

degree of risk inherent in alternative income levels, equity

positions, and scales of operations.

A formal statement of

the objectives appears later in this chapter.

However, first

the magnitudes and interrelationships among the forces of

change referred to above will be discussed in order to

establish why knowledge of the relationships investigated in

this study is essential for effective decision making.

1

2

Farm Size and Capital Requirements Increase

The scale of farms in Arizona has been increasing

through the past decade.

Table 1 shows that the number of

farms with sales greater than $40,000 increased 87 per cent

from 1960 to 1969.

During the same period farms with sales

under $10,000 decreased over 39 per cent.

As farm size increases, the amount of mechanical

equipment and other inputs needed increases. "Mechanical

O '

power and machinery as farm inputs have increased by one-

third and fertilizer and liming material inputs have tripled

in the past two decades" (Menzie, 1970, p. 12). Over the same period the price of farm machinery increased 40 per

cent, farm wage rates 71 per cent, and the value of farm

real estate increased 115 per cent (Table 2).

i

Credit Squeeze

From personal interviews, it was found that many

equipment loans.

The average interest rates on farm

mortgages from all lenders in the southern plains states

and Montana) has increased from 4.7 per cent in 1961 to 5.7

per cent by January 1, 1968 (U.S. Department of Agriculture,

"Agricultural Statistics," 1969, p. 494).

Increasing interest rates have affected the amount

of capital borrowed for farm investment. The exact extent

Table 1.

Amount of

Sales per Farm, by Sales Classes,

1960-

1969

3

Year

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

$40,000 &

Over

1,000

113

123

135

144

146

160

184

182

193

211

254

267

268

287

320

317

Farms with sales—

$20,000-

$39,999

1,000

$10,000-

$19,999

1,000

497 227

239 494

493

491

482

487

502

331

357

491

494

505

Under

$10,000

1,000

3,125

2,965

2,803

2,659

2,546

2,406

2,233

2,156

2,036

1,898

Source: U. S..Department of Agriculture, "1970

Handbook of Agricultural Charts" (1970, p. 4).

4

Table 2. Prices of Selected Farm Inputs, 1960- 1970

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970a

Year

Farm Wage

Rates

163

171

185

199

148

151

155

159

216

238

253

Farm

Machinery

(1950 = 100)

138 106

141

107

106

144

146 106

149

154

160

167

175

184

193

Fertilizer

105

106

106

106

103

99

101

Farm Real

Estate

^Preliminary.

Source: U. S. Department of Agriculture, "1970

Handbook of Agricultural Charts" (1970, p. 10).

171

172

182

189

202

214

231

246

262

275

286

r

5

of its dampening effects are unknown but it is known that

despite the increase in interest rates Arizona farmers

continue to borrow more money.

The farm mortgage debt in

Arizona from all sources was $118.6 million at the beginning

of 1960 and increased to $269.7 million by January 1, 1968

(U.S. Department of Agriculture, "Agricultural Statistics,"

1969, p. 498).

Government Payment Changes

Cotton has long been the single most important crop

in Arizona.

In the last decade, the average acreage of

cotton harvested per year was 333.5 thousand acres.

The

closest crop to cotton in the same time period was milo with

an average of 164 thousand acres harvested per year (Arizona

Cash receipts from marketings of crops in Arizona

are presented in Table 3.

Cotton accounted for 38.4 per cent

of.total cash receipts in 1966, 27.2 per cent in 1967, and

32.4 per cent in 1968.

Note the importance of cotton in

that cash receipts from cotton exceed all vegetable crop

cash, receipts in two of the three years.

However, government payments on cotton have been

limited to $55,000 per farm.

Furthermore, there are

indications that cotton payments will be limited even

further in the future.

The exact impact this will have on

cotton production is only speculation. The limitations will

Table 3. Cash Receipts from Marketings of Farm Products in

Arizona, 1966 , 1967, and 1968

6

Commodity Group

Cotton Lint

Cottonseed

Feed Grains

Hay

Wheat

Sugar Beets

Vegetables

Citrus

Grapes

Other Miscellaneous

Crops

1966

89,802

14,224

26,117

22,119

1,415

73,717

19,697

3,268

20,307

1967

1,000 dollars

67,981

9,935

31,843

24,799

3,493

2,143

89,443

23,352

5,369

27,723

1968

82,150

15,650

31,379

19,830

3,405

4,179

83,638

38,511

5,306

17,488

Total, All Crops 270,666 286,081

Source: Arizona Crop and Livestock Reporting

Service (1970, p. 7).

301,536

7

not affect all farmers but those who are affected may be

seeking crops to replace part of the cotton in their

diversification system.

The farmer who does shift from

cotton to another crop may be forced to increase his capital

investment even further.

As new types of machines are

more capital investment in the farm enterprise.

Farmers face a number of problems when deciding how

to adjust their operations in light of these developments.

For example, if land is diverted from cotton production,

lack of experience in producing alternative crops may limit

the range of alternatives the farmer has open to him and/or

make it very difficult for him to rationally evaluate the

potential consequences of a given crop rotation or farm plan.

have at their disposal a number of publications to provide

a more comprehensive, reliable decision making base

(Wildermuth, Martin, and Rieck, 1969; Young et al., 1968;

annual issues 1960-1970; Arizona Crop and Livestock

Reporting Service,

These publications incorporate

data from a large number of farms.

However, the data are in

the form of averages and in discrete terms such as tons per

acre, cost per unit, expected returns above growing and

8 harvest costs, etc.

"These references are of limited

application when the mean is provided without some notion of

the error or degree of risk which applies to a single year"

(Heady,

An example vis a vis the "Principle

of Increasing Risk" will serve to illustrate just how

serious such a limited planning base can be.

The principle of increasing risk states that as a

business is expanded through the use of borrowed capital, out of business) increases.

Consider the case of a farmer

who with $100,000 of equity capital borrows $100,000 in

order to increase the size of his business and/or invest in

new equipment which will enable him to grow a high-value

vegetable crop and thereby decrease his dependence on cotton

production.

Further assume that the farmer's decision to do

this was based on the knowledge that on the average such a

plan would allow him to realize a return of 50 per cent on

invested capital.

The farmer's position before and after

the acquisition of the borrowed capital is summarized below:

Before (100% Equity)

Assets - liabilities = Net Worth

$

100,000

-

0

= $

100,000

After (50% Equity)

Assets - liabilities = Net Worth

$200,000 - $100,000 = $100,000

Now assume, as can frequently happen where experience is limited or the farm is highly specialized, that the farmer has a bad year during the first year of his reorganized

9 operation. The effect of a 50 per cent decrease in asset value is clearly apparent below:

Before (100% equity) @ 50% decrease

Assets - liabilities = Net Worth

$50,000 - 0 = $50,000

After (50% equity) (f 50% decrease

Assets - liabilities = Net Worth

$

100,000

- $

100,000

=

0

Objectives

Therefore, it is the purpose of this study to provide

a comprehensive and reliable statistical basis for Arizona

farmers to utilize in analyzing the potential consequences

of actions that they are considering or may already be

engaged in.

More explicitly the objectives of this study

are:

1.

To derive estimates of returns above variable cost

for Arizona crops and crop combinations.

2.

To derive estimates of the variability in returns

above variable cost for Arizona crops and crop

combinations.

3.

To estimate the expected income and degree of risk

associated with alternative crops and crop combina­

tions under various equity levels and scales of

operation.

Procedure

In order to derive estimates of variability in crops

and crop combinations, data from a series of years are

10 required.

The choice of a reliable data base is not easy

and leads to an even more difficult decision in the

selection of an appropriate method of analysis.

The reasons

for selecting the methods of analysis utilized in this

thesis will be presented in Chapter II.

To reach the ultimate objective of investigating

relationships among crop combinations, a series of steps

must be taken.

Gross income variability can be calculated

utilizing the interaction of price and yield data.

This in

turn must be combined with budgets of variable cost of

production for each crop to arrive at variability estimates

of returns above variable cost for each crop.

These first

empirical steps will appear in Chapter III.

In Chapter IV, the effects of diversification will

be investigated as the data from single crops are combined

to form various crop diversification systems.

Next the

results of the diversification analysis can be combined with

equity level and scale considerations.

Simple examples will

be used to demonstrate how farmers and loan officials can

use the data generated in this study as a basis for eval-

uating the riskiness associated with a given farming situa­ tion.

Finally, in Chapter V, a brief summary will be

provided.

CHAPTER II

METHODS OF ANALYSIS

The purpose of this chapter is to present step-by-

step the methods of analysis that will be utilized to reach

the objectives as stated at the end of the first chapter.

First consideration is given to the nature of the variability

in Arizona crop farm production.

Next, the procedures for

deriving estimates of expected returns and relative and

absolute variability for each crop are presented. Third,

diversification principles showing how to combine the above

estimates for individual crops to derive similar estimates

for crop diversification systems are discussed.

Finally, the

procedure for combining the variability estimates with equity

and scale considerations and thereby to investigate the

riskiness of specific rotation schemes and farm resources

configurations is discussed.

Variability in Crop Production

"Variability in crop production stems from the fact

that yields, prices, and incomes are influenced by many

and Dean, 1960, p. 177).

Each alternative course of action

or crop combination (a crop combination is a selection of

crops composing a rotation for any farmer) has a probability

11

12

diseases, and weather cause agricultural prices, yields, and

subsequently incomes to vary on a year to year basis.

"From the standpoint of the individual farmer, what

portions of the total variation in price, yield, and income

is unpredictable or 'random' and what portion predictable?"

(Carter and Dean, 1960, p. 177).

If farmers recognize

trends from cycles, inflation, and technological advance and

utilize this knowledge in decision making, this becomes the

predictable part of variability.

Recognizing these long-run

trends, "the farmer planning crop production for the year

ahead is more likely to view the 'random' element as a

over the last five years) rather than as deviation from the

long-run mean" (Carter and Dean, 1960, p. 177).

The definition of variability inherent in the

discussion above is utilized in this study.

While empirical

variability estimates are not necessarily identical with the

traditional concepts of "risk" and "uncertainty" (Knight,

1921), they are, if appropriately derived, objective

measures of past variability in crop production.

And,

assuming that future variability of particular crops is

closely related to past variability empirical variability

estimates will provide a reasonable basis for assessing the

"degree of risk" inherent in both short-run and long-run

cropping decisions.

13

Sources of Data and Procedure

Having adopted the view of variability as outlined

above, it is now appropriate to outline the exact nature of

the data needed for the analysis.

Crops Selected and Sources of Data

The first step in this study is to select the crops

to be analyzed.

Fourteen crops were selected on the basis

of acres harvested in 1969.

All crops with 2000 or more

acres harvested in 1969, except corn, are included in this

study.

Corn was eliminated because it is not profitable to

produce and its acreage has been declining rapidly.

Table 4

presents the crops selected and their corresponding 1969

harvested acreage.

Also presented in Table 4 are the

average prices and yields over the last five years.

Having specified the crops to be included in the

price and yield series.

It would be ideal to have time

series and cross section data from a random sample of

individual farms.

However, to interview the large number of

farmers necessary for this study would have been very

expensive and time consuming.

Further, even if farmers did

have records of prices and yields for the number of years

desired, it is doubtful that costs of production would be

available from the farmers. Therefore, state time series

14 and Yield Table 4.

Acreage Harvested in 1969

for 1965

-1969 of Selected Arizona

Alfalfa

Barley

Cantaloupe

Carrots

Cotton

Fall Lettuce

Spring Lettuce

Milo

Onions

Potatoes

Safflower

Sugar Beets

Watermelons

Wheat

Crop

Acres

Harvested

000 acres

188.0

144.0

12.8

2.8

267.7

13.1

20.0

199.0

2.0

12.8

25.0

30.8

5.1

73.0

Price

Unit

26.78

$/ton

Mean

Yield

Unit

5.3

ton/acre

2.46

7.10

$/cwt

$/cwt

5.19

$/cwt

24.36

C/lb

6.12

$/cwt

6.30

$/cwt

2.17

$/cwt

3.92

$/cwt

34.1

cwt/acre

112.0

cwt/acre

182.0

cwt/acre

1085.4

Ibs/acre

169.0

cwt/acre

186.0

cwt/acre

43.7

cwt/acre

381.0

cwt/acre

3.01

$/cwt

79.40

$/ton

11.54

$/ton

2.51

$/cwt

2.51

$/cwt

1.2

20.3

162.0

29.8

ton/acre ton/acre cwt/acre cwt/acre

Source: Arizona Crop and Livestock Reporting

Service (1970).

15 data .for prices and yields (from Arizona Crop and Livestock

Reporting Service, 1970) of each crop will be used.

The use of state data may be justified because

Arizona's crop production areas are rather homogeneous.

In

with similar growing conditions.

While it can be argued

that state data does tend to average out individual varia­

bility and may understate absolute variability, state data

should still result in unbiased estimates of the relative

and absolute variabilities.

Most important is the fact that

the use of state time series data is the only basis for

analysis that is feasible.

Given a price and yield series and thereby gross in­

come estimates for each year (gross income = price x yield)

it is necessary to derive variable production cost estimates

and subtract them from the gross income estimates to yield a

time series of returns, above variable costs for each crop.

Data for compiling unit budgets for each year were

terms of 1970 input prices and adjusted for varying yields

or harvest costs and inflation or increasing input prices.

The procedure for compiling preharvest operating

costs was taken from Wildermuth et al. (1969) and Mack

(1968).

These two sources contain unit budgets which show

the various production processes (plow, plant, etc.) and

materials (seed, fertilizer, etc.) which are necessary to

16 produce each crop.

The operating costs associated with each

production process and material item were taken from

Wildermuth (1970) and totaled to arrive at the pre-harvest

operating costs for each crop.

Yields do not affect harvest costs significantly for

field crops so no annual adjustment was made in field crop

harvest costs.

Yields of vegetables do affect harvest cost

so an adjustment was necessary in the yearly harvest cost

for vegetable crops., This adjustment was made by calculating

present per unit harvest cost rate.

For example, the carrot

yield series shows yields of 165 cwt. in 1968 and 180 cwt.

in 1969.

Per cwt. harvest rates are $1.62 and at this rate

the difference.in yield between the two years results in a

harvest cost difference of $25 per acre.

A second adjustment in operating costs was necessary

due to the effects of inflation on farm input prices.

The

U.S. farm input price index (U.S. Department of Agriculture,

"Agricultural Statistics," 1970, p. 425) was used to adjust

costs arising from machine repair, fuel,

Other

input prices (fertilizer and seed) did not change signifi­

cantly over the 1960-1969 time period so they were not

adjusted.

For example, assume operating costs of $350 for

a crop, $200 of which is harvest cost and $50 for fuel,

labor, and repairs in 1970.

The yield of the crop decreases

one-fourth from 1970 to 1969 so harvest cost was adjusted

17 downward to $150.

Farm input prices in 1969 were only 95

per cent of 1970 prices so the $50 charge for fuel, labor,

and repairs was deflated by 5 per cent to $47.50 for a total

operating cost of $297.50.

This process was duplicated for

each year in the study.

Finally, additional adjustments were made for

operating a pickup, paying fees, dues, and subscriptions,

hiring additional labor, and borrowing operating capital.

These additional costs are dealth with more extensively in

Young et al. (1968, pp. 75-76).

The Variate Difference Method

Given the data base as just discussed there are

several alternative empirical procedures that can be used to

estimate the random variability inherent in this data.

One

method is to approximate the "current level" of the time

series by a fitted trend line and then to assume that

deviations from the trend represent the "random" component

(Heady, 1952).

Another method approximates the "current

level" by a moving average, and then assumes that deviations

from the moving average are the "random" element.

There are arguments for and against each of

these alternative procedures.

The authors believe

that the most reasonable of these is the trend

removal method which, is based on the assumption

that the systematic component of the time series

(i.e., general price level, technological trend,

etc.) can be characterized by linear, polynomial,

or other types of mathematical functions.

The

authors prefer a statistical method that does not

require ei

priori specification of rigid functions.

18

Because the variate difference method appears to

meet this objection, it is the technique employed

in this study (Carter and Dean, 1960, p. 177).

The first step of the variate difference method is

to calculate the variance of the original series.

This is

done by summing the squares of the deviations from the

arithmetic mean and dividing by N-l, the degrees of freedom.

Equation 1 shows the means of calculation of the

variance of the 0th difference of original series:

Vo

N

S i=l

(W^ - W )2

(N-l)

(1 ) where Vo is variance of 0th difference,

the observations,

W the mean, and (N-l) the degrees of freedom.

The next step is finite differencing.

The series

for the first finite difference is calculated by subtracting

the first item from the second item of the original series,

the result being the first item in the series of first

differences.

The second item is formed by subtracting item

two from three of the original series, the third by sub­ tracting item three from four, etc.

The series of second

difference is formed by subtracting the items of the first

difference series in the same manner as above.

The sum of squares of deviations from the arithmetic

mean is not considered the best basis for estimating

variances of finite differences.

Rather, the sum of squares

of deviations from zero are used. This is done because the

19

true mean is expected to be zero for any finite difference

series.

To form the variance for each finite difference series, sum the squares of the finite differences and divide by the degrees of freedom and then by another constant. The sum of squares of the difference is symbolized by

(1c)

, k = kth difference.

Divide this by the degrees of freedom

and the mean square results (Equation 2).

e (k)

' (N-K)

(2)

Having found the mean squares, the best estimate of

the random variance of the finite differences is yet to be

calculated.

The mean squares of each successive finite

difference series increases rapidly.

It has been found that

the original variance is multiplied by a certain binomial

coefficient (constant mentioned above) with each successive

finite differencing.

This coefficient is for the kth

difference equal to the number of combinations of 2k things

taken k at a time 2kCk (e.g., the coefficient for the second

finite difference = 2{2)C^ = 6). The mean squares are then

divided by this coefficient and the estimate of the true

variance of the random element in a series is formed.

To be sure the differencing has been taken far.

enough the kth difference and all higher differences must be

equal or nearly equal. The equality here is that

20

K q

= kq+^ = K q

+

2

, etc.

Because this is essentially dealing

in the realm of probability, a test for this equality was

devised.

It is required only that the difference between

the variances of two successive series of finite differences

be smaller than three times its standard error (Tintner,

1940).

The variate difference method explained above derives measures of absolute variability in the variance and

'

square root of the variance, the standard deviation.

The

standard deviation is in the same terms (i.e., tons, bushels)

as the observations. A measure of variability which is in­

dependent of the unit of measurement used is the variability

coefficient.

Viation x 100 (3)

The variability coefficient is a measure of relative

variation and may be used to evaluate results from different

experiments involving the same character since it is a ratio.

It is defined as the sample standard deviation expressed as

a percentage of the sample mean as shown in Equation 3

(Steel and Torrie, 1960, p. 20).

By examining Equation 3, the effect of using the

last five years' mean is readily seen.

If the last five

years' mean is smaller than for the entire period, the rela­ tive variability would increase and if the last five years'

mean is larger than the entire period mean, the relative

variability is smaller.

21

Diversification and Variability

Utilizing procedures discussed to this point, est­

imates of the absolute and relative variability can be

derived for each crop.

Now these crops can be combined as

"farmers diversify with the expectation that high risk from

one crop will be offset by low risk from another crop"

(Heady, 1952, p. 510).

Diversification can be accomplished using two

different methods. First, the resource base may be in­ creased.

If a farmer has capital totaling $10,000 to produce

A and B he may_ add $5,000 to produce C.

Second, the resource

base may be held constant and a part of it shifted to another

product.

A farmer with $10,000 capital producing A and B

may shift $3,000 to produce C and produce A and B with the

remaining $7,000.

A discussion of these two methods

follows.

This discussion is taken from Carter and Dean

(1960, pp. 189-190).

Diversification by Adding Resources

Suppose a crop farmer diversifies by adding to a fixed acreage of crop A an equal acreage of crop B. The in-

2 come variance of the crop A is represented by crA , the in-

2 come variance of crop B by aB . When enterprise B is added

2

A the total variance (crT ) becomes:

22

where rAB = correlation between the incomes of enterprises A

and Og are the standard deviations for crops A

and B ,

The assumptions made in calculating

correlation coefficients are similar to those made in

estimating variances for each crop, except that two time

series are now being considered.

Each time series consists

of the unpredictable mathematical expectation and the random

element.

Only corresponding elements of both series are

Since net income correlations between crops ordin­ resources usually increases total income variance.

However,

total net income also is usually higher, hence relative

variance (total income variance divided by mean income) may

stay the same or decrease even with positive income correla­ tions between crops.

The total variance equation for n enterpris s is

written a s : n

+ 2 E r .

a. ex.

i,j = 1,2 ij i>j n

23

Diversification With Redistribution of

Fixed Resources

The second method of diversification is to re­

distribute a fixed quantity of resources, say land, among

additional enterprises.

This method is most common for

farmers operating with relatively fixed acreage, capital,

and other resources.

In this case, the goal is to reduce

uncertainty by dividing a fixed quantity of land among a

greater number of enterprises.

The equation for the total

income variance where one-half of the acres used in producing

crop A and the remainder are diverted toccrop B becomes:

CT

T 2

= (

1

/

2)2 ^ 2

+

^ 2

+

2

( ^ /

2

) ( < j b/2

)

.25aA + •25cB + .50 rAB cta

aB

2

In this case, if .25cB + .5

2

> .75 T^ or, if the ratio

+ 2r

A B aA aB

3 T

A

2

>

1

,

diversion of one-half the total acres into crop B results in

an increase in total income variance; if the ratio equals

unity, no change in income variance results; if the ratio is

less than unity income variance is decreased. Thus, oppor­

tunities for reducing total income variance by this method

of diversification are much greater than by the first method

of increasing total resources. With the second method it is

24

often possible to reduce total income variance even in the

common case where incomes from crops A and B are positively

correlated and the variance of the added crop (cjg ) is

greater than the variance of the original crop ( ) .

Also,

if the variance of crop B is less than the variance of crop

A, total income variance is always reduced, regardless of

the income correlation between crops. As noted later,

however, the reduction in income variance may be achieved

only at sacrifice in income level.

When the proportion of land resources distributed

between two enterprises is unspecified, the variance

equation becomes: aT = q aA + (1-q) ctB + 2q(l-q)r^gC^Cg

where q = proportion of land resources devoted to A and 1-q =

proportion of land resources devoted to B.

land resources among n enterprises becomes:

V =i=i q 2 oi2 + 2 .

i -> j qjq-j r ij tr-L Oj

where qi (i = 1, ... n) = proportion of land resources

devoted to enterprise i and £q^ = 1.

The possible effects of diversification on absolute

variability are indicated above.

However, the farmer is

interested in relative variability also. The net results of

25 relative variability as measured by the variability co­

efficient is dependent on the degree of change in the

absolute level of the standard deviation and expected returns

for a crop or crop combination.

If the standard deviation

and expected returns vary in the same magnitude, the

variability coefficient will not change.

If they vary in

opposite directions with the mean decreasing and the standard

deviation increasing the variability coefficient will in­ crease substantially.

If they both vary in the opposite

directions the variability coefficient will decrease.

Various other degrees of change may occur depending on the

relative changes of the expected returns and standard

deviations.

Break-Even Returns

The Principle of Increasing Risk example, beginning

on page 7 of Chapter I, pointed out that the potential

impact of the variability inherent in a given crop or

operations plan is affected by the scale of operation and

the farmer's debt (equity) position.

If equity levels are

low, the farmer has a corresponding high cash fixed cost due

to large loan installments.

Insurance and taxes as well as

loan installments must be paid annually.

If these annual

payments cannot be made the farmer must either refinance his

loans, sell assets to pay cash fixed cost or file for bank­ ruptcy.

26

The amount of risk due to the variability in returns

from a crop combination that a farmer ultimately accepts

depends on his own attitude towards gambling.

"Established

farmers or those with high risk preferences might concentrate

on high risk crops.

New farmers, farmers with limited

capital or farmers who prefer not to gamble on high risk

crops could choose crop combinations which minimize risk,

thus avoiding the short-run possibility of bankruptcy"

(Carter and Dean, 1960, p. 176).

Certainly in the long run

profits will be maximized by those who are willing and able

to accept the risks.

However, if a farmer gets into a tenuous equity

position, he may not be around to realize the long run gains.

The procedure required to develop the means for making risk-

income decisions on a rational basis involves the calculation

of the Z statistic.

The Z statistic is the number of

standard deviations from the mean that are required to con­ tain a given percentage of total possible outcomes.

The Z

relationship for determining a certain outcome follows:

Z = - ---u.

a

where Z equals the value from the standard normal area table

corresponding to a given probability level, u equals the

mean of a series, a equals the standard deviation of a

series, and X equals the expected outcome for a given

probability level (Yamane, 1964, pp. 115-118). By combining

27

means and standard deviations with the Z statistic, returns

above variable costs for various probability or certainty

levels can be calculated.

For example, if returns are

estimated to have a mean of $50 and standard deviation of

$10 and a 90 per cent income certainty level is required,

the corresponding Z value is 1.65 standard deviations.

Solving for X, returns can be expected to be at least $33.50

nine times out of ten.

crop combinations can be combined with cash fixed cost to

find short-run break even returns at the desired probability

level.

For example, assume an annual cash fixed cost of $60

per acre and a resource base that can produce the two

following crop combinations in equal proportions.

Alfalfa -

Alfalfa -

Returns above variable cost

with 60 70 80 90 percent

________________________ certainty fall lettuce 130 60 -10 cotton 120 100 80 60

If a farmer in this position desires to take the

added risk associated with higher expected returns, he will

choose to produce alfalfa and fall lettuce. However,

the 80 per cent probability level, he will only be breaking

even (cash fixed cost = return above variable cost) and at

the 90 per cent probability level (one time out of ten) his

return above variable cost will be a negative $10.

He must

also meet a cash fixed obligation of $60, so in total he

would lose $70 per acre.

On the other hand if he chose to

produce alfalfa and cotton, his break even point would be

at the 90 per cent probability level.

Utilizing all of the above methods of analysis, it

is now possible to calculate the various measures which lead

to the ultimate objective of estimating the degree of risk

associated with various crops and crop combinations.

CHAPTER III

YIELD, PRICE, AND INCOME VARIABILITY

OF SELECTED ARIZONA CROPS

This chapter contains empirical estimates of the

returns above variable cost for 14 major Arizona field

crops.

As explained in Chapter II, a variate difference

analysis of state price, yield, and variable cost data is

utilized to derive these variability estimates. First,

consideration is given to the absolute and relative price

and yield variabilities.

Next, the price and yield data are

combined to arrive at estimates of gross income variability.

Finally, variability in returns above variable cost is

presented.

Yield Variability of Arizona Crops

Yield variability is the deviation or error from the

mean yield of a crop expressed in units of the crop harvested

brought about by random or unpredictable sources.

The yield

variability data are presented in Table 5 with the crops

being ranked on the basis of the yield variability co­ efficients.

These coefficients are derived using the method

described in Chapter II by combining the standard deviations

29

30

Table 5. Selected Crops: Ranking by Yield Variability

Coefficients

Crop

34.10

169.00

5.30

230.00

162.06

20.30

1 085.40

43.70

186.00

1.20

29.80

381.00

182.00

112.00

1965-1969 Standard Variability

Mean Deviation Coefficient

1.51

7.47

.25

12.48

12.69

1.62

90.15

3.93

16.87

.14

4.34

69.10

37.30

25.20

8

8

8

(%)

4 "

4

5

5

12

15

9

9

18

20

22

Unit

Barley

Fall Lettuce

Alfalfa

Potatoes

Watermelon

Sugar Beets

Cotton

Milo

Spring Lettuce

Safflower

Wheat

Onions

Carrots

Cantaloupe

Source: Data compiled and calculated utilizing

Arizona Crop and Livestock Reporting Service (1970).

cwt/acre cwt/acre ton/acre cwt/acre cwt/acre ton/acre

Ibs/acre cwt/acre cwt/acre ton/acre cwt/acre cwt/acre cwt/acre cwt/acre

31 calculated by the variate difference method with the last five years' means (VC standard deviation

).

65-69 mean

As would be expected, given the favorable weather

conditions existing in Arizona and the availability of water

is quite low. The ranking of the crops, contrary to beliefs,

does not appear to have any pattern as vegetable and field

crops are interspersed throughout the entire range of varia­ bility coefficients. Barley, efficients of 4.

Potatoes and watermelons rank among the

low relative variability group with 5 and 8 respectively.

Then three field crops appear in the rankings followed by a

vegetable and two field crops and three more vegetable crops.

The most variable crop is cantaloupe, with a variability

coefficient of 22.

Vegetable crop yields were expected to be relatively

more variable than field crops because of special skills,

For example, melons are affected by the weather as high

temperatures can cause sun spots and cooking.

The fact that

some of the vegetable crops have relatively stable yield

variabilities may be explained by the fact that frequently

vegetable crops are not harvested unless yields are high

enough to cover harvesting costs. This would tend to

32

stabilize yields as low yields are not recorded as the data

used in this study is based on acres harvested.

Price Variability of Arizona Crops

Price variability is the deviation or error from the

mean value of a crop unit as affected by variables such as

random quality changes, the number of units produced in the

state, and the number of units produced in other states.

The ranking of price variability coefficients for

Arizona crops presented in Table 6 ranges from the most

27 per cent.

In general, the most stable crops are those

which have come under much direct government control (i.e.,

wheat, cotton, and sugar beets).

As expected field crops

which usually are not characterized by widely fluctuating

prices have relatively low price variability coefficients.

Also as expected, the vegetable crops which are normally

considered specialty vegetable crops and produced to be sold

in limited markets are characterized by high variability co­ efficients relative to field crops.

Gross Income Variability of Arizona Crops

Gross income variability is the deviation or error

from the mean arising from the interaction of price and

yield. Therefore, both price and yield variability.

If high prices are

associated with high yields, the correlation of price and

33

Table 6. Selected Crops: Ranking by Price Variability

Coefficients

Crop i

Barley

Milo

Alfalfa

Sugar Beets

Safflower

Wheat

Cotton

Carrots

Cantaloupe

Watermelon

Potatoes

Onions

Spring Lettuce

Fall Lettuce

1965-1969

Mean

Source: See Table 5

24. 36

5.19

7.10

2.51

3.01

3.92

2.46

2.17

26.78

11.54

79.40

2.51

6.30

6.12

Standard

Deviation

.13

.12

2.54

1.18

9.49

.42

4.38

.95

1.32

.52

.66

.91

1.57

1.66

Variability

Coefficient Unit

(%)

5 $/cwt

$/cwt 6

10 $/ton

10

12

17

18

18

19

21

22

$/ton

$/ton

$/cwt

C/lb

$/cwt

$/cwt

$/cwt

$/cwt

23

25

27

$/cwt

$/cwt

$/cwt

34

yield is positive and gross income variability tends to be

high. However, if prices and yields are negatively corre­ lated or vary in opposite directions, gross income varia­ bility tends to be lower.

Table 7 presents gross income variability coeffici­

ents for Arizona crops ranging from the least variable

barley to the most variable onions.

The ranking by price

variability and gross income variability (Tables 6 and 7)

are similar.

The field crops are at the least variable end

of the range of variability and vegetables at the most

variable end in both rankings.

Because price and gross

income variability rankings are similar, it would appear

that price variability is more important than yield

variability in determining gross income variability.

The

greater effect of price variability is especially noticeable

in fall lettuce which ranks second in yield variability

(Table 5), fifteenth in price variability (Table 6), and

eleventh in gross income variability (Table 7).

Although it appears that price variability has a

greater impact on gross income variability than yield

variability, it can be shown that yield variability exerts

influence through its impact on price.

Arizona's yield

variability may have only slightly noticeable effects on

price and therefore price variability appears to be

dominant in determining gross income variability. However, vegetables in Arizona are produced for limited markets and

35

Table 7. Selected Crops: Ranking by Gross Income Varia­ bility Coefficients

Crop

1965-1969

Mean

Barley

Alfalfa

Milo

Sugar Beets

Wheat

Cotton

Potatoes

Safflower

83.63

142.93

94.57

234.81

74.19

263.48

686.62

93.52

Watermelon

Fall Lettuce

413.90

1,034.90

Spring Lettuce

1,189.60

Carrots

944.00

Cantaloupe

Onions

781.20

1,531.26

Source: See Table 5.

4.70

15.37

11.24

29.88

10.10

50.29

132.02

18.41

106.66

279.10

354.12

288.00

240.31

560.40

Standard

Deviation

Variability

Coefficient

(%)

7 '

11

12

20

26

27

30

31

31

37

13

14

19

19

Unit

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

$/acre

36

yields or production in other areas influence Arizona's

price.

For example, Arizona spring lettuce production de­

creased from 1967 to 1968 and the price of lettuce dropped

also.

This unexpected price drop can be explained if

California and New Mexico production for 1968 are acknow­ ledged.

New Mexico spring lettuce production icreased by

50 per cent from 1967 to 1968 and California which had nearl

nearly half the total U.S. spring lettuce production in 1967

increased spring lettuce production by two-thirds, 67 per

cent from 1967 to 1968 (U.S. Department of Agriculture,

"Agricultural Statistics," 1969, Table 263, p. 179).

This

explains the decrease in Arizona prices even though Arizona

production decreased and exemplifies the impact of yield,

total production from all states, on gross income variability

Carrot price and production provide another example

of the same point made above.

Arizona carrots are harvested

in the spring following the California and Texas harvests

of winter carrots.

Arizona carrot production decreased by

only 10 per cent from 1967 to 1968 but the Arizona carrot

prices nearly doubled.

However, the winter carrot harvest

in Texas decreased from 3.5 million cwt. to 2.6 million cwt.

during the same period and California production increased

from 2 million cwt. to 2.7 million cwt. for a net decrease

of .4 million cwt.

This seems small but the total carrot

production for that period was only 5.3 million cwt. and the

37

.4 million cwt. decrease created a substantial price rise.

(Figures stated in the example were taken from United

States Department of Agriculture, "Agricultural Statistics,"

1969, Table 245, p. 170.)

Return Above Variable Cost Variability

of Arizona Crops

Variability in returns above variable cost is the

deviation from mean returns as determined by the interaction

of price, yield, and variable cost.

A farmer ultimately

must consider cash fixed cost and total fixed cost as well

as variable costs if he is to assess the riskiness of his

farming situation.

It is inappropriate to assign fixed

costs on an individual crop basis as all crops grown on a

farm must help meet fixed costs.

As this section deals with

single crop returns, only variable costs will be considered

at this stage. The fixed cost considerations will be intro­ duced subsequent to the development of alternative diversifi­

cation systems which permits the consideration of fixed costs

on a total farm basis.

In order to calculate returns above variable cost

for each crop y e a r , budgets were prepared using the pro­ cedure discussed in Chapter II.

Table 8 presents the average variable production

costs derived for two farm sizes in Arizona.

The larger

farm size enjoys lower variable production costs for all

crops. The lower production costs arose from the use of

38

Table 8.

Per Acre Variable Costs of Producing Arizona Crops

Based on 1970 Input Prices and 1960-1969 Yield

Levels

Potatoes

Safflower

Sugar Beets

Watermelon

Wheat

Crop

Alfalfa (establishment)

Alfalfa

Barley

Cantaloupe

Carrots

Cotton

Fall Lettuce

Spring Lettuce

Milo

Onions

320 Acres

60

Farm

Size

800 Acres

58

100

66

541

446

228

645

707

71

834

557

87

203

307

62

93

64

533

440

216

639

701

69

832

553

84

198

302

60

Source:

Data compiled and calculated utilizing

budgets from Wildermuth et al. (1969), Mack (1968), and

Wildermuth (1970).

39

larger more efficient machinery and fewer custom charges, as

the larger farm owned more machines than the smaller farm.

The apparent pattern in differences of costs between the

farm sizes arises because most of the gains of the larger

farm were in land preparation practices which are similar in

nearly all of the crops.

By subtracting variable costs from gross income, returns above variable cost are derived.

The results of the

analysis of the return above variable cost for each crop and

farm size are presented in Table 9.

Crops are ranked by

relative variability as evidenced in the variability co­ efficients , column 3.

As expected, field crops are the

least variable and vegetable crops the most variable.

The

rank of variability coefficients does change from one size

to another due to the economics of the larger farm size.

Also, the larger farm size has a smaller range of variability

coefficients brought about by its lower production costs.

The lower production costs of the 800 acre farm allow higher

mean returns than for the 320 acre farm.

The standard

deviations are nearly the same for both farm sizes, and,

therefore, the variability coefficients for the larger farm

are smaller.

Also, as expected, return above variable cost for

crops with variable costs which are fairly stable from year

to year (Appendix, Tables 19 and 20) have standard deviations

similar to those for gross income (Tables 7 and 9). Crops

Table 9.

Selected Crops: Variability of Returns Above Variable Cost for 320 and

800 Acre Arizona Crop Farms

Crop

320 Acre Farm

Cotton

Barley

Sugar Beets

Milo

Carrots

Alfalfa

Onions

Spring Lettuce

Wheat

Cantaloupe

Fall Lettuce

Watermelon

Potatoes

Safflower

800 Acre Farm

Cotton

Barley

Sugar Beets

Milo

Alfalfa

Carrots

Wheat

Mean

Net Income

($)

197

20

92

26

500

27

697

468

14

250

375

123

155

17

210

21

97

27

34

506

15

Standard

Deviation

($)

34.2

3.8

27.9

9.5

240.5

14.7

464.3

324.8

10.1

184.0

277.9

106.5

138.2

18.6

34.0

3.8

27.9

9.3

14.9

240.4

10.1

Variability

Coefficient

(%)

17

19

30

37

48

54

67

69

72

74

74

87

89

108

16

18

29

34

43

47

65

(% of Time

60% 70% 80% 90%

Return Above Variable

Cost Greater Than

($) ($) ($) ($)

189

19

180 169 154

18 17 15

85

23

78

21

69

18

56

14

375 298

192

439

24 20

581

456

15

307

9

103

387 299 195

52

11 9

204 154

6

95

1

14

305

230 142

96

121

13

67

83

9

33

39

19

-13

-22

2

-17

201

192

181

20

90

19

82

18

73

25

31

445

166

16

61

22

27

19

22

15

15

380 304

198

13 10 7 3

Table 9.— Continued

Onions

Spring Lettuce

Cantaloupe

Fall Lettuce

Watermelon

Potatoes

Safflower

700

473

258

381

128

159

19

464.3

324.1

184.0

277.9

106.5

138.2

19.2

66

68

71

73

83

87

97

584 458 310 106

392 304 200 58

212 162

103

311 236 147

22

25

102 73

124

14

87

9

39 -8

43 -18

2 -6

Source: Data calculated utilizing gross income and budget data derived in this study.

42

whose yields are highly variable and therefore have highly

variable harvest costs do not have standard deviations

similar to those for gross income.

The standard deviations

are unequal because if a constant is subtracted from gross

income every year, the standard deviation remains the same.

However, where yields are more variable, and therefore,

harvest costs, a constant amount is not subtracted from

gross income and hence, differing standard deviations result.

Therefore, as a decision making tool, variability in return

above variable cost is superior to variability in gross in­ come. Consider the example of onions.

The gross income

standard deviation for onions is $560 (Table 7, col. 2) and

the return above variable cost standard deviation for onions

is $464 (Table 9, col. 2) for a difference of $96.

As well as relative and absolute variability

estimates, a range of expected returns at various probability

levels are calculated.

This is done utilizing the normal

curve table, standard deviation, and mean as components of

the Z relationship discussed in Chapter II.

Table 9, columns 4, 5, 6, and 7 present the expected

returns at varying probability levels for each crop.

Interpretation of return above variable cost at

varying probability levels means that the estimated return

above variable cost levels or greater should be realized 60,

70, 80, or 90 per cent of the time or alternatively returns

should fall below the given levels only 40, 30, 20, or 10

43 per cent of the time. Consider cotton on a 320 acre farm.

In column 4, return above variable cost of $189 or more

should be realized 60 per cent of the time or alternatively

a return lower than $189 should occur only 40 per cent of

the time or four out of ten years.

The range of returns at the given probability levels

is quite small for crops with low absolute variability

(Table 9, column 2).

The crops with low absolute variability

are the field crops.

The vegetable crops with higher

absolute variability exhibit a wide range in expected returns

depending on the desired probability level.

For example,

cantaloupe on a 320 acre farm has an expected return level

of $204 or greater 60 per cent of the time.

Expected return

falls to $154 or greater at 70 per cent probability and way

down to $14 at 90 per cent probability.

A more stable field

crop, cotton, on a 320 acre farm has expected returns ranging

from $189 at 60 per cent probability to $154 at 90 per cent

probability resulting in a range of $35 as compared to a

$190 range in cantaloupe returns.

This exemplifies further

the greater amount of risk inherent in vegetable production.

Also, apparent in Table 9 is the advantage of larger

scale production.

For the returns of the different crops

presented, expected returns at all probability levels on an

800 acre farm are greater than expected returns on a 320 acre

farm.

For example, at 60 per cent probability, the expected

return from an acre of cotton on a 320 acre farm is $189

44

compared with an expected return of $201 on an 800 acre

farm.

At 70, 80, or 90 per cent probability, the expected

returns from an acre of cotton on a 320 acre farm are $180,

$169, and $154 respectively compared with $192, $181, and

$166 on an 800 acre farm.

CHAPTER IV

DIVERSIFICATION AND SHORT-RUN

BREAK-EVEN RETURNS

In the preceding chapter, relative and absolute

variability estimates were presented for various single

crops.

As indicated in the methods of analysis in Chapter

II, it is now time to combine the individual crop data in

order to investigate the effects of diversification on the

level and variability of returns above variable costs.

After variability estimates are derived for various

diversification systems, it will be possible to take the

final and most intersting step of this thesis.

This step is

to investigate vis a_ vis the Principle of Increasing Risk,

the risk inherent in alternative equity levels and scales of

operation.

As in the last chapter the results will be keyed

via the Z statistic to returns at alternative probability

levels.

Effects of Diversification on Returns

Above Variable Cost

Diversification is practiced by many farmers in an

attempt to decrease the variability in their incomes.

opposite effect (higher variability). In addition,

45

46 diversification can lead to a reduction in expected returns above variable cost.

The expected returns and variability in returns

associated with various crop diversification schemes are

calculated using fixed asset diversification.

As explained

in Chapter II, fixed asset diversification reallocates a

fixed resource base to adjust the proportions of crops in a

diversification scheme.

An infinite number of crop combinations are possible

using varying proportions of each of the 14 crops in this

study.

There are 3,558 combinations of 2, 3, 4, and 5 crop

diversification schemes when equal proportions of each crop

are used per acre (i.e., 2 crop combination: .5 acre cotton

and .5 acre barley).

It is apparent that all possible

combinations cannot be presented in this thesis; therefore, only selected combinations are presented.

In Chapter I, the section entitled Government Program

Changes pointed out the possible need for altering diversifi­ cation systems to include less cotton.

Farmers forced to

produce less cotton will be seeking a crop to replace cotton

in their rotation.

Since the crop production experience of

many farmers is limited to cotton, alfalfa, barley, and milo,

and only selected diversions can be discussed, this section

emphasizes diversion of cotton acreage to alternate crops.

Before getting to the diversification systems

emphasizing cotton diversion, it should be noted that

47

information on numerous other diversification schemes is

contained in the Appendix.

Only equal proportions of crops

cotton, .25 acre barley, .25 acre milo, and .25 acre alfalfa)

are considered in the 2, 3, 4, and 5 crop diversification

systems selected.

All possible two crop diversification

systems are presented and only a few 3, 4, and 5 crop

diversification systems are presented in the Appendix,

Tables 21 through 28.

The only comment about these results

is that, in general, as more crops are added to the diversi­

fication systems, the range of relative variabilities

decreases.

Now, attention focuses on the diversion of cotton

.acreage to alternative crops.

Tables 10 through 17 present

the effects of diverting cotton acreage to other crops.

All

the crop combinations include constant proportions of

alfalfa and barley at .2 acre each and .6 acre at varying

proportions of cotton and the alternate crops. The alter­ natives will be discussed in the context of decreasing pro­ portions of cotton and increasing proportions of the alter­ nate crop.

Data are presented for both the 320 and 800 acre

farms but absolute variability and expected returns for both

sizes are similar.

Therefore, discussion of results is in

terms of 320 acre farms and of the crop replacing cotton and

applied to 800 acre farms by simply replacing 320 with 800.

48

Sugar Beets, Milo

Diversion of cotton to sugar beets or milo (Tables

10 and 11), which are considered stable irrigated field

crops, resulted in decreasing expected returns as more of

either sugar beets or milo was produced. Absolute varia­

bility (standard deviation) decreases in both cases but

relative variability (variability coefficient) increases.

As relative variability depends on the interrelationsip of the changes in expected income and absolute variability changes (variability coefficient

standard deviation

x 100) , expected income it may increase even though both expected income and absolute variability decrease. In these two cases,

income decreases proportionally more than the absolute

variability.

Thus, the net result is an increase in relative

variability under diversion to both sugar beets and milo.

The range of expected returns at varying probability

levels for both sugar beets and milo is quite low (columns

4, 5, and 6).

Recall from Chapter III that returns at

various probability levels refers to that return which can

be expected a given per cent of the time.

For example, returns at 60 per cent probability

refer to those returns which can be expected 60 per cent of

the time or six times out of ten.

Alternatively, four out

of ten years' returns will be less than the given amount.

The small range of expected returns at varying levels of

probability further indicates the relative stability of

Table 10. Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with .2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Sugar Beets

320 Acre Farm

60%

(% of Time)

70%

80% 90%

Acres

Used For v c e

Return Above

Variable Cost

Greater Than Ca SBb

M C ad

. 60 0 128 21.0

16 123

117

110 101

.55

.05

123 20.3

17 117

112

105 97

.50

.10

117

19.6

17 112 107 101

.45

.15

112 19.0

17 107

102

96

92

88

.40

.20

107 18.4

17 102

.35

.25

101 18.0

18 97

97

92

91

86

83

78

.30

.25

.30

.35

96

91

17.6

17.3

18

.19

92 87

81

74

87

82 76 69

.20

.15

.10

.40

.45

.50

86

80

75

17.1

17.0

17.0

20

21

23

.05

.55

70 17.1

25

0 .60

65 17.1

27

81 81 71 64

76

72

66

59

71

66

60

66

61 55 48

56

61

50

53

42

800 Acre Farm

60%

(% of Time)

70% 80% 90%

Return Above

Variable Cost

Greater Than uc cd VC

137 21.0

15 132 126 119 110

131 30.3

16 126

121 114 105

126 19.6

16 121 115 109 100

120 19.0

16

115 110 104 96

114 18.5

16

103 17. 7 17

110

99

105

109 18.0

17 104 99

94

99

94

88

90

86

80

97 17.4

18

92

17.1

19

93

87

88

83

83

77

75

70

79 16. 6 21

80 17.1

21

75

17.2

23

69 17.4

25

75 71

76 72

71

65

66

60

65 58

66 59

60

55

53

47

f*C = Cotton

“SB — Sugar Beets

CH = Mean Returns Above Variable Cost d(j = Standard Deviation eVC = Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970).

^

^

Table 11. Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with .2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Milo

320 Acre Farm v c e

60%

(% of

T i m e )

70% 80% 90%

Acres

Used For

C a

Mb

|iC ad

Return Above

Variable Cost

Greater Than

.60

0 128 21.0

17

123 117 110

101

.55

.05

119 19.6

16

114 109

103

94

.50

.10

111

18.1

16 106 101

.45

.15

102 16.8

16 98 93

95

88

87

81

.40

.35

.20

.25

93

85

15.4

14.1

17

17

.30

.30

76 12.8

17

.25

.35

68

11.6

17

.20

.40

59

10.5

18

90 85 81 74

81 78 73 67

73 70 66 60

65

57

62

54

58

50

53

46

.15

.45

51 9.6

19

.10

.50

42

8.8

21

.05

.55

0

33 8.3

25

.60

25

8.0

32

48 46 43

49

37 34

38

31

31 29 26 23

23

21

18 15

800 Acre Farm

60%

(% of

Time)

70% 80% 90% vc' e

Return Above

Variable Cost

Greater Than nc od

137

21.0

15 132 126 119 110

128

19.6

15 123 118 111 103

119

18.2

15

114

109

103 95

110 16.8

15 105 101

100 15.4

15

95 88

97 92 87 81

91 14.1

16 88

84

79

73

82 12.9

16

73

64

55

11.7

10.6

9. 6

16

17

18

46 8.8

19

79 75 71 66

70 67

61

58

63

55

58

50

52

50 47

42

37

27

8.3

8.0

23

29

43 41

34

38 34

32

30 26

25 23

21

17

^C = Cotton

bM = Milo

CH = Mean Returns Above Variable Cost do = Standard Deviation eVC = Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970).

U1

o

51 returns from sugar beets and milo.

It also indicates that

probability levels higher than 99 per cent are required

before variable costs exceed gross income resulting in

negative returns.

Potatoes, Watermelons

Diversion of cotton to what have been traditionally

considered high risk vegetable crops shows varied results.

The crops are groups according to changes in expected

returns.

As acreage is diverted from cotton to potatoes or

watermelons which are very unstable relative to the other

single crops in this study (Table 9), the expected returns

decrease only moderately but the absolute variabilities

increase substantially (Tables 12 and 13).

The relative

changes in expected returns and absolute variability yield a

net result of a greatly increased variability coefficient in

both cases.

A farmer diverting acreage from cotton to potatoes

or watermelons is accepting greater amounts of risk and

also lower expected returns.

Observe the range of expected

returns at varying probability levels.

An acre of potatoes,

for example, at 60 per cent probability (six out of ten

years), yields an expected income of $82.

This figure

decreases rapidly to a -$3 at 90 per cent probability (nine

out of ten years returns from potatoes are expected to

Table 12. Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with .2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Potatoes

320 Acre Farm

60%

(% of Time)

70% 80% 90%

Acres

Used For

Return Above

Variable Cost

Greater Than

Ca Pb

n c

cd VC

e

. 60 0 128 21.0

17

122

117 110 101

.55

.05

126 22.4

18

120 114 107

.50

.10

124 25.5

21

117 110

102

97

91

.45

.15

122 29.7

24 114 106 97

.40

.20

119 34.6

30

.35

.25

117 39.9

34

111

101

90

107 97 84

94

75

66

. 30

.30

115 45.6

40 104 91 77 57

.25

.35

113 51.5

46 100

86 70 47

.20

.40

111 57.5

52

.15

.45

109 63.6

58

97

93

89

81

76

63

55

37

27

71 48 17

.10

.50

107

69.8

65

.05

.55

105 76.0

73

0 .60

103 82.3

80

86

82

65

58

41

33

7

-3

800 Acre Farm

60%

(% of

Time)

70% 80%

90%

u c

od

vc' e

Return Above

Variable Cost

Greater Than

137 21.0

15 132 126 119 110

134 22.4

17 129 123 116 106

132

25.5

19

124 119 110

129 29.6

23

122

114

104

99

91

127 34.6

27 118 109 98 83

124 39.9

32

114

103 91 73

122 45.6

38 110 98 83 63

119 51.5

43 106

92

76 53

117 57.5

49

102 87

68

43

114 63.6

56 98 81 61 33

112

69.8

63

109

76.0

70

107

82.3

77

94 75

53 22

90 70 45

12

86 64 37 1

aC = Cotton

kp = Potatoes cia = Mean Returns Above Variable Cost d

<7

= Standard Deviation eVC = Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970).

m

M

Table 13. Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with .2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Watermelons

Acres

Used For

Ca Wab ad

320 Acre Farm

60%

(% of

Time)

70% 80% 90% v c e

Return Above

Variable Cost

Greater Than

. 60 0 127 21.0

17 123 117 110 101

.55

.05

124

22.0

18 119

113 106 96

.50

.10

120 24.0

20 114 108 100

.45

.15

117 26.8

23 110 103

90

94

82

.40

.20

113

30.2

27

105 97

88

74

.35

.25

109 34.0

31 101

92

81 66

.30

.30

105 38.0

36

.25

.35

102 42.3

42

.20

.15

.40

.45

.10

.50

.05

.55

0 .60

98 46.7

.48

94

51.2

54

91

87

60.4

70

83

55.8

65.1

62

78

96

86 74 57

91 80

66

48

86 74 59 38

82

68

51 29

77

62

44 19

72 55 36 10

67 49 28 0

800 Acre Farm

60%

(% of

Time)

70% 80% 90% nc ad v c e

Return Above

Variable Cost

Greater T h a n '

137 21.0

15 132 126 119 110

133 22.0

17 127

121

114 105

129 24.0

19 123 116 109 98

125 26.8

22 118 111 102 90

121 30.2

25 113 105 95

82

117

34.0

29 108 99

112

38.0

34 103

93

108

42. 3

39

104 46.7

45

98

86

93 80

100

96

92 60.4

66

88

51.3

55.8

65.1

51

58

74

65 45

87 74

57 35

82

67 49 25

77 61

72 54

88

80

73

41

33

73

64

54

.15

5 aC = Cotton

bWa =

C,, -

Watermelon

Mean Returns Above Variable Cost

eVC =

Standard Deviation

Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970).

w u>

54 exceed -$3).

Recal that returns exceed $42 nine years out

of ten for .6 acre of sugar beets compared to -$3 for .6

acre of potatoes (milo and watermelons are similar).

This

comparison of potatoes and sugar beets shows the greater

element of risk involved in producing potatoes or water­ melons compared to sugar beets or milo.

Also, remember that

expected returns at the other end of the probability scale

(one out of every ten years) are much greater for potatoes

or watermelons than for sugar beets or milo.

It is the high

returns at the upper end of the probability scale that induce

farmers to undertake the greater risk and produce potatoes

or watermelons.

Cantaloupes

Table 14 yields results similar to potatoes and

watermelons but of a smaller magnitude.

The expected return

actually increases by a small amount but the absolute

variability increases substantially giving a net result of

increased relative variability.

The relative variability is

not as great as for potatoes and watermelons because the

small increase in expected return moderates the large

increase in absolute variability but the range of expected

returns at various probability levels follows the same

pattern as potatoes and watermelons only slightly higher.

Table 14. Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with .2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Cantaloupe

320 Acre Farm

60%

(% of

Time)

70% 80% 90%

Acres

Used For

C a

Cab uc od v c e

Return Above

Variable Cost

Greater Than

. 60 0 128 21.0

17 123 117 110 101

.55

.05

130 22.0

17 125 119

112 102

.50

.10

143 27.5

19 136 129 120 108

.45

.15

136 33.0

24 127

119 108

93

.40

.20

138 40.7

29 128 117 104 86

.35

.25

141

49.0

35 129 115 100

.30

.30

144 57.6

40 129 114

95

78

70

.25

.35

146 66.5

46

.20

.40

149 75.4

51 130 110 85

52

.15

.45

151 84.5

56 130 108 80

43

.10

.50

154 93.6

61

129 112

131 105

.05

.55

157

102.8

66 131 103

90 61

75

70

34

25

0 .60

159 112.0

70 131 101 65 16

800 Acre Farm

60%

(% of Time)

70% 80% 90%

Return Above

Variable Cost

Greater Than hC od

VC

137 21.0

15

132

126

119

110

139

22.0

16 134 128

121

111

142

26.5

19 135 128

119 108

144 33.1

23 136 127 116

102

147 40.8

28

136 125

112

94

149 49.1

33 137 123 108

86

151 57.7

38

137 121 103

154

66. 6

43

137

119

98

77

69

156 75.5

48 137 117 93 59

159 84. 6 53 137 115 87 50

161 93.7

58 138

112 82 41

163

166

102.8

112.0

63

68

138

138

110

107

77

32

72 22

j^C = Cotton

^Ca = Cantaloupe cia = Mean Returns Above Variable Cost

° ct

= Standard Deviation eVC = Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970).

in

in

56

Fall Lettuce, Onions, Carrots

Diversion of cotton acreage to fall lettuce, onions,

and carrots increased expected returns substantially.

For

example, expected returns increased from $128 with .6 acre

of cotton to $234 with .6 acre of fall lettuce (Table 15).

Even greater increases occur with diversion to carrots and

onions (Tables 16 and 17).

Absolute variabilities also make

large increases yielding relative variabilities which lie

between sugar beets or milo and potatoes or watermelons.

In the case of fall lettuce, expected returns at

various probability levels remain relatively high up through

80 per cent probability levels and decrease to as low as $20

with .6 acre fall lettuce and 90 per cent probability levels

(one out of ten times) the return from fall lettuce will be

lower than $20.

Onions and carrots both have pretty high expected

returns at the probability levels given.

For example, .6

acre of onions are expected to result in a $70 return nine

years out of ten and .6 acre carrots $127 nine years out of

ten.

However, if the rate of decrease in expected income

between probability levels is noticed, it is apparent that

at 95 per cent probability the expected return from onions

will be nearly zero and the expected return from carrots

approximately $100.

A very high probability level is needed

to make expected return from carrots decrease to the level

of expected return from sugar beets or milo which are

Table 15. Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with .2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Fall Lettuce

Acres

Used For

320 Acre Farm

60%

(% of Time)

70% 80% 90% vce

Return Above

Variable Cost

Greater Than

Ca

FLb crd

. 60 0 128 21.0

17

123 117 110 101

.55

.05

137 23.2

21

130

122

113 100

.50

.10

146

38.8

27 136 125 123 96

.45

.15

154 50.7

33

142

128

112

90

.40

.20

163 63.2

39 148 130 110

82

.35

.25

172 75.9

44

.30

.30

181 88.9

49

153

159

133

135

108

106

75

67

.25

.35

190 101.9

54 164 137 104

.20

.40

199 115.0

58 170 139

102

.15

.45

208

128.2

62

60

52

176

141

100 44

.10

.50

217 141.4

65 181 143 98 36

.05

.55

226 154.6

69 187 145

96

28

0

.60

234 167.8

72 192

147 93 20 nc od

800 Acre Farm

VC

60%

(% of

Time)

70% 80% 90%

Return Above

Greater Than

137

21.0

15 132 126

119 110

145

28.2

19 138 136

122

109

154 38.8

25 144 134

121

104

163

50.7

31 150

136 120 98

171

63.2

37 155 138 118

90

180 76.0

42 161 140 116

82

188

88.9

47 166

142

113

197 102.0

52

171 144 111

74

66

205 115.0

56 176

145

109

58

214

128.2

60

182

146 105

49

222 141.4

64 187 149 -104 41

231 154.6

67

192

150 101

239 167.9

70 197

152

98

33

25 aC = Cotton kpL = Fall Lettuce

C H

= Mean Returns Above Variable Cost

^cr = Standard Deviation eVC = Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970).

Table 16. Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with .2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Onions

Acres

Used For ad

320 Acre Farm

VCe

60%

(% of

Time)

70%

80% 90%

Return Above

Variable Cost

Greater Than

Ca 0b

M C

.60

0 127 21.0

17 123 117 110 101

.55

.05

153 33.1

22 145 136

125

110

.50

.10

178 53.0

30 165 150 133 110

.45

.15

203 74.8

37 184 164 140 107

.40

.20

228

97.2

43 204

177

146 103

.35

.25

253 119.8

47 223 191

152

100

.30

.30

278 142.5

51 242 204 158 95

.25

.35

303 165.4

55 262 217 164 91

.20

.40

328 188.2

57 281 230 170

.15

.45

353

211. 2 60 300 243 175

.10

.50

378 234.1

62

319 256 181

.05

.55

403 257.1

64 339 269 187

0 .60

428 280.1

66 358

282

193

87

83

78

74

70 cd

800 Acre Farm

60%

(% of

Time)

70% 80%

90%

VCe

Return Above

Variable Cost

Greater Than

137

161

21.0

15

132 126

119 110

33.2

21 153 144 136 119

186

53.2

29 173 158

141

118

210 74.9

36 192 171 148 115

235

97.2

41 211 184 153 110

259 119.9

45 230 197 159 106

284 142.6

50

248

210 164 101

309 165.4

54 267

222

160 97

333

188.3

57 289 235 175 93

358

211.2

59 305 248 180 87

382 234.2

61 324 260 185

82

407 257.1

63

342 273

191

431 280.1

65 361 285 196

77

73

aC = Cotton

bo = Onions cia = Mean Returns Above Variable Cost do = Standard Deviation eVC = Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970).

Table 17 .

Return Above Variable Cost Levels and Variabilities on 320 and 800 Acre

Farms in Arizona with..2 Acre of Alfalfa, .2 Acre of Barley, and

Variable Proportions of .6 Acre Allocated to Cotton and Carrots

320 Acre Farm

60%

(% of

Time)

70% 80% 90%

Acres

Used For

Return Above

Variable Cost

Greater Than C a Crb nc ad VCe

.60

0 128 21.0

17 123 117 110 101

.55

.05

143 24.2

17 137 130 123

112

.50

.10

158

31.7

20 150 142 131 117

.45

.15

173

41.2

24 163

152

139 120

.40

.20

188

.35

.25

203

51.7

27 172 161 145

122

62.6

31 188 171 151 123

.30

.25

.30

.35

218

234

.20

.40

249

73.7

34 200 180 157 124

85.0

36

212

189

162

125

96.5 .

225 199 168

125

.15

.45

264 107.9

41 237

208

173 126

.10

.50

279 119.5

43 249 217 179

126

.05

.55

294

131.0

45 261

362

184 126

0

.60

309 142.6

46

274 235

189

127

60%

(% of

Time)

70% 80% 90% nc od v c e

Return Above

Variable Cost;

Greater Than

137

152

21.0

15 132 126 119 110

24.2

16 146 139

131 121

166 31.7

19 159 150 140 126

181

41.2

23 171 160 147 129

196 51.6

26 183 159

153

130

211 62.5

30 195 178 158 131

226 73.7

33

207 187 164 131

240 85.0

35

219

196 169 132

255 96.4

38

231

205 174

132

270 107.9

40 243 214 179

132

285 119.5

42

255 223 184

132

300

131.0

44 267 231 187 132

314 142.6

45 279 240 195

132

aC = Cotton

kcr = Carrots

CH = Mean Returns Above Variable Costs dg = Standard Deviation eVC = Variability Coefficient

Source: Data compiled and calculated using state price and yield series from Arizona Crop and Livestock Reporting Service (1970). o, vo

60 considered more stable.

The expected return from carrots

has large fluctuations from year-to-year but at high enough

levels to insure a reasonable expected return at very high

probability levels.

Sugar Beets-Cotton vs. Fall Lettuce-

Cotton

As an example of how a farmer or agribusinessman may

choose between alternatives with the information presented,

consider sugar beets at .3 acre and cotton at .3 acre (Table

10).

This diversification shows a range in expected returns

of $18 from 60 to 90 per cent probability.

Under the same

acreage conditions cotton and fall lettuce (Table 15)

exhibit a range of $92.

However, with sugar beets the

expected returns range from $92 to $74 while with fall

lettuce the expected returns range from $159 to $67.

This

example shows that fall lettuce would be a more rational

crop to include in a diversification than sugar beets as

even at high probability levels (90 per cent) lettuce yields

expected returns as high as sugar beets and at a lower

probability level (60 per cent) expected returns from

lettuce exceed sugar beet returns by over $60.

However, if a farmer adds more sugar beets or more

lettuce to the diversification system (.6 acre of both), it

is shown that at higher probability levels the expected

returns from sugar beets are greater than expected returns

from lettuce by $22 but at a lower probability level (60 per

1

61 cent) lettuce exceeds sugar beets by $132.

The attitude of

the farmer on acceptance of risk will have an influence on

the combination chosen.

If one farmer wants only 60 per

cent certainty of a given return level, he will probably

plant lettuce.

However, a second farmer who requires 90 per

cent probability of a given return level will probably

produce sugar beets.

The second farmer is trading chances

of receiving higher income for a more stable income and the

first farmer is accepting more risk for a chance to receive

a high income.

Short-Run Break-Even Returns

As discussed in Chapter II, short-run break-even

return is the return level from a diversification system

required to pay cash fixed costs.

These cash fixed costs

play an important role in determining the amount of risk

inherent in a given rotation, equity level, and scale of

operation.

Not only cash fixed cost but all fixed costs

must be paid in the long-run for the farm business to remain

viable.

However, in the short run, only variable and cash

fixed cost are of major concern to the farmer.

Cash fixed

costs are fixed obligations which must be paid each year and

If returns above variable cost are not high enough to pay

these fixed costs, the farm business may be rendered in­ solvent.

62

In order to arrive at cash fixed cost estimates for

any farm, fixed costs must be compiled.

Since return data

are completed for 320 and 800 acre farms, fixed costs are

compiled for the same two sizes.

Fixed costs are compiled

assuming a typical machinery complement for each farm size

(Jones, 1967; Mack, 1968).

The fixed costs per farm are

found in Appendix Tables 29 and 30.

Using the fixed costs from Tables 29 and 30, cash

fixed costs (Table 18) can be derived.

It should be noted

that every farmer will have a unique cash fixed cost

position, therefore, these particular figures in Table 18

cannot be used in general, but only by farmers in a similar

fixed cost situation.

Taxes and insurance in Table 18 were

taken from Appendix Tables 29 and 30 and assumed constant at

all equity levels. Equipment loan installments were cal­

culated assuming a four-year term and an 8 per cent interest

rate in the average value of investment.

Real estate loan

payments were amortized at 8 per cent for 25 years at $800

per acre.

Each of these costs for varying equity levels

assumes equal percentage of equity in all assets.

For

Example, 50 per cent equity means 50 per cent equity in

equipment and 50 per cent equity in real estate. Deprecia­

tion is taken from Appendix Tables 29 and 30, and opportunity

cost is figured at 8 per cent of the value of owner's equity.

Farmers should be interested in the short-run break­ even return as defined by the equality between returns above

Table 18. Cash Fixed Costs Per Acre on Arizona Farms

Taxes, In­

surance , and

Equity Miscellaneous

Real Estate

and Equip­ ment

Cash Fixed

Cost = Col.

1 & 2 Total

Depreciation

100%

Interest

(Opportunity

Cost)

Total

Fixed

Cost

(320) (800) (320) (800) (320) (800) (320) (800) (320) (800)

15 13 0 0 15 13 49 31 76 69 140 113

90%

80%

70%

15

15

15

15

13

13

13

13

14

28

43

57

11

23

34

45

29

43

58

72

24

36

47

58

49

49

49

31

31

31

31

68

61

54

46

62

146 117

55 153

122

48

161

126

41 167 130

60%

50% 15 13 71 57 86 70

49

49

40% 15 13 85 68 49

31

31

38

31

34 173 135

28 180 140

30%

20%

15

15

13

13

100

114

79

91

100 81

92

115

129 104

49

49

31

31

25

15

21

14

189

193

144

149

10% 15 13

128 102 143 115 49 31 8 7 200 153

Source: Calculated and compiled from Jones (1967, pp. 8-17) and

Wildermuth (1970).

64 variable cost and cash fixed costs.

An agribusinessman

extending credit to.a farmer should also be concerned with

the break-even point of various alternatives to estimate the

potential repayment ability of the loan applicant.

To

demonstrate the use of these empirical data in the above

context, various examples follow.

farmer or businessman can take the following steps to

evaluate various crops and crop combinations as to their

potential to yield short-run break-even returns.

1. Pick farm size.

2. Pick equity level.

3.

Locate cash fixed cost on Table 18 which corresponds

to the chosen farm size and equity level.

4.

Choose crop combination and locate table for the

chosen combination in Chapter IV for the appropriate

farm size.

5.

Compare returns above variable cost data with cash

fixed cost to find short-run break-even return above

variable cost.

For example, assume a farm size of 320 acres and a

100 per cent equity level.

From Table 18, cash fixed cost

is $15 per acre.

Compare this figure with various returns

above variable cost in Table 10 (crop combination alfalfa-

barley-cotton-sugar beets). It is apparent that a farmer in

65

this equity position is in little danger of decreasing his

equity by realizing .return above variable.cost that is less

than cash fixed cost even at high probability levels.

A

farmer in this equity situation, no matter which crop

combination chosen (Tables 10 through 17), would expect

cash fixed cost to exceed returns only at very high

probability levels.

A farmer working 800 acres in the same

equity position is in an even better position as cash fixed

costs are $2 lower per acre and expected returns at all

probability levels are larger than for the 320 acre farm.

Secondly, assume a farmer is operating 320 acres

and owns 70 per cent of his assets.

From Table 18, cash

fixed cost per acre is $58.

Again referring to Table 10,

break-even returns are exceeded except with .6 acre sugar

beets at 70 per cent probability, .55 and .6 acre sugar

beets at 80 per cent probability, and .45 acre sugar beets

and .15 acre cotton and increasing amounts of sugar beets at

90 per cent probability.

If the farmer working 320 acres and having 70 per

cent equity considers other crop combinations, break-even

returns occur with various amounts of cotton production.

For example, with cotton-fall lettuce, break-even returns

occur only at 90 per cent probability levels w th .2 acre

cotton and .4 acre fall lettuce; with carrots on the other

hand returns are above cash fixed cost even at high

probability levels. Again, a farmer operating 800 acres is

66

in a better position as his cash fixed costs are $11 per acr

acre less and returns are higher than on the 320 acre farm.

A final example assumes a farmers operating 320 and

800 acres with 30 per cent equity.

Cash fixed costs are

$115 and $92 per acre respectively.

On Table 10, returns

above variable cost exceed cash fixed cost for the 320 acre

farm only at .6 acre cotton with 70 per cent probability and

.55 acre cotton and .05 acre sugar beets at 60 per cent

probability.

The 800 acre farmer can produce more sugar

beets than the 320 acre farmer in this equity situation,

again showing the advantage of the larger farm.

There are a large number of examples that could be

given here.

However, these examples suffice to show the

relative positions of 320 acre and 800 acre farmers at

varying equity levels.

Farmers with low amounts of equity

must be considerably more careful in choosing crops with

high enough returns and stable enough returns to cover cash

fixed cost. As shown by these examples,

cent probability) will have little if any effect on a farmer

with 100 per cent equity, but a farmer with only 30 per cent

equity can wipe out a considerable amount of his equity in

one bad year.

To show that a farmer can decrease his equity, consider the following example.

A farmer with 320 acres

decides to expand his operation to 800 acres using borrowed

capital. The farmer has 100 per cent equity before

67

expanding or $306,000 in net worth (Appendix, Table 29).

After expanding, his assets are $688,000 (Appendix, Table

30).

The amount of borrowed capital must therefore be

$688,000 less $306,000, or $382,000.

This results in an

equity level of about 45 per cent.

Assuming the real estate

loan was amortized at 8 per cent for 25 years and the equip­

ment loan was figured at 8 per cent for four years, Table 30

can be used to estimate cash fixed cost per acre.

Cash

fixed cost for 45 per cent equity on an 800 acre farm is

approximately $15 per acre.

Assume further that this

farmer was a lettuce producer before the expansion and has

decided to remain in lettuce production.

At his former 100

per cent equity level cash fixed costs were low and profits

for the short run high assuming the farmer had above average

and average returns for the last five years (a possibly

biased sample of years on which to base a decision to

produce more lettuce).

However, this year's crop is not

very good and returns above variable cost are only $10 per

acre.

The farmer must pay cash fixed costs of $75 per acre

and, therefore, must use up part of his equity to pay these

obligations.

At a loss of $65 per acre, the total loss in

equity is $52,000.

The farmer's position now is $688,000

assets minus $434,000 liabilities equals $254,000 equity or

net worth.

If depreciation is also subtracted, the farmer's

equity position decreases another $24,800 for a net result

of $229,200 equity.

68

If this same farmer had chosen to remain at 320

acres and 100 per cent equity, the loss in equity could have

been only $5 per acre or $1,600 compared to a loss of

$52,000 after expansion.

Position Before Expansion:

Assets - liabilities = net worth (equity)

$306,000 - 0 = $306,000

$306,000 - $1,600 = #304,400

$306,000 - ($1,600 + $15,680 Depr.) = $288,720

Position After Expansion:

Assets - liabilities = net worth (equity)

$688,000 - $382,000 = $306,000

$688,000 - $434,000 = $245,000

$688,000 - ($343,000 + $24,800 Depr.) = $229,200

Thus, exemplifying the Principle of Increasing Risk:

as a farm or business is expanded through the use of borrowed

capital, the probability of decreasing one's equity increases.

CHAPTER V

SUMMARY

The purpose of this the fifth and final chapter of

this thesis is, as implied by the title, to summarize the

major stages of the analysis.

As will be apparent in the

summary, the objectives of this thesis were directed at

providing farmers and agribusinessmen with information to

aid them in making their own decisions regarding risk income

tradeoffs in Arizona crop farm production.

Thus, the results

are not conclusive in nature.

The best crop combinations

were not computed as such and, therefore, no specific

recommendations as to which crop combinations to produce can

be made.

The introductory chapter pointed out that as a

result of farm size increases, technological advances,

inflation, and government program changes Arizona farmers

have been and are being forced to make adjustments involving

increased capital requirements and uncertain outcomes.

A

simple example via the Principle of Increasing Risk was then

introduced to show the potential consequences of not intro­

ducing variability concepts into a farm planning process

involving such complexities as those introduced above.

Thus, the general objective of the study was stated to be

69

70

that of deriving objective measures of the variability and

risk inherent in alternative Arizona crops and diversifica­ tion schemes.

With this goal in mind, Chapter II was

utilized to present and explain the reasons for the data and

methods of analysis employed in this study.

As discussed,

the lack of a better data base necessitated the use of state

time series data on crop prices, yields, and production

costs. Given the data base, the variate difference method

• """" t

was then selected as the best available means of deriving

the appropriate variability estimates.

The estimates of the random variability in prices,

yields, and income were derived for 14 individual crops and

presented in Chapter III.

These results indicated that in

general both field and vegetable crops have low yield

variability in Arizona.

This was not found to be true for

price variability. The government supported crops (e.g.,

wheat, cotton, and sugar beets) were shown to have low

variability in prices while the majority of the vegetable

crops were found to have very high price variabilities.

The

pattern of low price variability in field crops and high

price variability in vegetable crops appeared again in the

gross income variability estimates.

The similar patterns

observed for price and gross income variabilities indicate

the dominance of price variability over yield variability in

determining gross income variability.

71

The next step was the combination of gross income

and variable production cost data to derive estimates of the

variability in returns above variable cost.

These results

clearly established the superiority of variability in return

above variable cost over variability in gross income for

decision making purposes.

This being founded on the fact

that gross income variability and return above variable cost

variability were similar for field crops but dissimilar for

'• ' t

crops affected by varying harvest cost.

In Chapter IV, the variability data derived for

individual crops were combined to estimate return levels and

variabilities associated with various crop diversification

systems.

The diversification systems emphasized the

reallocation of .6 acres of cotton to alternate crops with

alfalfa and barley held constant at .2 acres each.

As

cotton acreage was diverted to sugar beets or milo, the

relative variability was found to change very little but the

expected returns were found to decrease substantially.

In

comparison, reallocation of cotton acreage to onions,

carrots, cantaloupe, or fall lettuce resulted in higher

expected returns but also much higher variability levels

(risk).

Therefore, it was concluded that farmers forced to

divert cotton acreage to alternate crops must make a choice

involving tradeoffs between increasing returns and an

acceptable risk level.

To emphasize the importance of

making this tradeoff the expected returns at varying

72 probability levels for the diversification systems presented were combined with equity and scale considerations.

All of the above diversification systems were

analyzed for both a 320 and 800 acre farm.

The larger farm

scale was shown to have higher expected returns per acre and

the same relative risk levels as the smaller farm scale.

Further, the farmer who operates an 800 acre farm and has

100 per cent equity was shown to be in a better position

than a farmer who operates 320 acres and has 100 per cent

equity.

However, the results also indicated that farmers

with low equity levels could have a hard time paying cash

fixed cost and breaking even in the short-run.

Thus while

the larger farm size is clearly superior from an earnings

standpoint, the 320 acre farmer who attempts to realize the

gain by borrowing expansion capital may end up in worse

shape than he was before, namely bankruptcy.

APPENDIX

SUPPLEMENTARY TABLES

Table 19. Variable Production Costs on 320 Acre Arizona Crop Farms3,

Crop

Alfalfa*3

Barley

Cantaloupe

Carrots

Corn

Cotton

Fall Lettuce

Spring Lettuce

Milo

Potatoes

Onions

Safflower

Sugar Beets

Watermelon

Wheat

69

68

120 117

66 64

547

578

443 418

88

87

227 231

666 664

709 695

71 69

533

532

825

87

725

85

201 208

293 306

62 61

67

756

68

551

814

84

192

308

60

115

64

427

441

86

217

650

66 65

114

112

63 ' 62

561

476

85

221

661

543

478

84

223

668

68

660

779

66

530 509

804

1001

83

82

197

308

59

198

275

59

Year

64

110

62

594

334

84

218

622

666

66

539

865

82

198

289

58

63

110

62

692

406

220

622

779

66

554

955

82

200

306

58

62

109

61

457

544

83

221

646

753

65

538

631

81

197

292

58

61

714

65

538

648

80

191

292

57

108

61

642

479

83

215

683 aCosts are deflated using the U.

S. farm input price index and rounded to nearest whole dollar.

^Includes establishment cost.

Source: Data compiled and calculated utilizing Wildermuth et al. (1969),

Jones (1967), Mack (1968), and Wildermuth (1970).

60

108

61

557

357

83

212

645

714

65

538

684

80

195

292

57

Table 20. Variable Production Costs on 800 Acre Arizona Crop Farmsa

Crop

Alfalfa13

Barley

Cantaloupe

Carrots

Corn

Cotton

Fall Lettuce

Spring Lettuce

Milo

Potatoes

Onions

Safflower

Sugar Beets

Watermelon

Wheat

69 68

113 110

64 63

539 571

437

412

87 85

215 219

660 658

702

69

689

68

529

528

823 722

84 83

196

288

61

203

300

59

67

108

62

419

435

85

205

644

750

67

548

811

82

187

303

59

65

Year

64 66

661

66

527

802

81

192

302

107 105

62 '

61

553

467

535

442

84

208

656

83

210

654

58

773

65

506

998

80

193

179

57

104

61

586

328

82

206

617

659

64

535

863

80

194

179

57

63

104

61

684

401

206

617

772

64

550

953

80

195

301

57

62

103

60

449

538

82

208

640

747

64

535

628

79

191

287

56

61

102

60

473

82

202

677

708

64

534

646

79

186

287

56 aCosts are deflated using the U. S.

farm input price index and rounded to nearest whole dollar.

^Includes establishment cost.

Source: See Table 19

60

708

63

534

682

78

191

287

56

101

60

549

351

82

199

639

Table 21. Return Above Variable Cost Levels and Variabilities on 320 Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Barley-Cotton

Alfalfa-Cotton

Cotton-Wheat

Cotton-Milo

Cotton-Sugar Beets

Sugar Beets-Wheat

Sugar Beets-Barley

Sugar Beets-Milo

Sugar Beets-Alfalfa

Barley-Milo

Sugar Beets-Safflower

Barley-Wheat

Milo-Wheat

Cotton-Carrots

Carrots-Spring Lettuce

Carrots-Fall Lettuce

Carrots-Potatoes

Alfalfa-Barley

Cotton-Watermelon

Alfalfa-Milo

Milo-Safflower

Sugar Beets-Carrots

Cotton-Cantaloupe

23

55

17

20

348

484

437

327

24

160

109

112

106

111

145

107

53

56

59

60

26

21

296

224

Mean

Net Income

Standard

Deviation

.

17.7

18.6

18. 3

19.5

28. 3

21.4

13.2

14.3

15.3

16.1

6.1

17.2

5.6

7.1

125.4

176.5

170.7

123.0

8.9

61.4

10.2

8.5

122.3

- 93.2

(% of Time)

60% 70% 80% 90%

Return Above

Variability Variable Cost

Coefficient Greater Than

16 -

17

17

18

20

20

25

26

26

27

27

31 -

33

36

38

38

39

40

41

42

36

37

37

38

104 99

108 103

101

94

97

86

88

96 90

82

107 101 95 87

138 130

121

108

102 96 89 80

50 46

42

36

53 48 44 38

55 51 46 39

56 51 46 39

21 20 18 15

50 46 40 33

15

14 12 10

.

16 14 11

317

283 243

188

440 392 336 258

397 353 301 230

297 263 224 170

21

19

16 12

145 128 108 81

24 21 18 13

19

17 14

11

265

232

193 139

200

175 145 104

<r>

Table 21.— Continued Return Above Variable Cbst Levels and Variabilities on 320

Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Carrots-Cantaloupe

Carrots-Watermelon

Cotton-Potatoes

Carrots-Alfalfa

Alfalfa-Wheat

Carrots-Onions

Carrots-Milo

Carrots-Barley

Carrots-Wheat

Potatoes-Cantaloupe

Fall Lettuce-Onions

Carrots-Safflower

Cantaloupe-Spring Lettuce

Cotton-Spring Lettuce

Cotton-Fall Lettuce

Alfalfa-Safflower

Barley-Safflower

Cantaloupe-Fall Lettuce

Cotton-Onions

Potatoes-Watermelon

Sugar Beets-Watermelon

Sugar Beets-Cantaloupe

Onions-Watermelon

Fall Lettuce-Watermelon

Fall Lettuce-Spring Lettuce

Mean

Net Income

258

359

333

286

22

18

312

447

139

107

171

410

249

422

375

311

176

263

21

599

263

260

257

203

536

Standard

Deviation

124.6

174.7

169.0

146.3

11.4

9.5

161.0

235.0

76.5

59.2

156.5

134.1

76.8

117.0

9.4

273.4

120.0

119.4

120.9

96.8

256.9

95.1

229.5

. 140.0

238.8

(% of Time)

60% 70% 80% 90%

Return Above

Variability Variable Cost

Coefficient Greater Than

56

56

56

57

51

51

52

53

55

55

42 .

43

44

44

46

46

46

46

47

48

48

48 -

49

50

51

336 293 243 174

278 241 199

140

157 136

112

78

234 203 165 114

18

16 13

9

530 456 369 249

233 200

162

109

230 198 159 107

229

194 155 102

178

152 121

79

491 403 320 207

227

194 154 99

315 268

112

35

290 245 191 116

250 210

162

99

19 16

13

16 14 10

272

229

177 107

389 325 250 147

120

93

353

99

77

147 121

291

75

8

6

41

58

32

91

217

214

176

131

49

116

70

362

297 220 116

-j

Table 21.— Continued Return Above Variable Cost Levels and Variabilities on 320

Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Spring Lettuce-Onions

Sugar Beets-Spring Lettuce

Spring Lettuce-Watermelon

Sugar Beets-Onions

Sugar Beets-Potatoes

Potatoes-Onions

Spring Lettuce-Potatoes

Sugar Beets-Fall Lettuce

Fall Lettuce-Potatoes

Cantaloupe-Onions

Milo-Onions

Alfalfa-Onions

Cantaloupe-Watermelon

Barley-Onions

Onions-Wheat

Onions-Safflower

Spring Lettuce-Milo

Spring Lettuce-Barley

Spring Lettuce-Alfalfa

Spring Lettuce-Wheat

Cantaloupe-Milo

Cantaloupe-Barley

Safflower-Wheat

Fall Lettuce-Safflower

Spring Lettuce-Safflower

Mean

Net Income

Standard

Deviation

356

357

247

244

248

241

138

135

16

196

243

233

265

474

362

362

186

359

583

280

295

395

124

426

312

340.5

164.0

173. 5

232.8

73.0

253.3

185. 5

141.7

162.3

291. 3

233.8

235.1

121.2

233.0

232.0

234.5

163.7

163.9

166.9

162.5

94.0

92. 3

10.7

135.2

167.2

Variability

Coefficient

68

69

69

69

69

65 -

65

65

65

66

66

67

67

67

58 ,

59

59

59

59

59

60

61

61

62

65

(% of Time)

60% 70% 80% 90%

Return Above

Variable Cost

Greater Than

498 406 297 147

329 195 142 70

252

205 150 73

336 274 199 97

105 86

62

30

363 295 214

102

265 215

156 74

198

160 114

52

225 181 129 57

401

322

229 101

303 240 165

62

304 240

165 61

156 123 85 31

300 237 163 60

298

299

206

235

235

162

161

160

109

203 159 106

206 161 108

200 157 105

59

57

37

34

35

33

114 89

112 87

13 10

59

57

7

17

17

2

162 126 83 23

201

156 102

29

-j

03

-

Table 21.— Continued Return Above Variable Cost Levels and Variabilities on 320

Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Cantaloupe-Wheat

Cantaloupe-Alfalfa

Cantaloupe-Safflower

Fall Lettuce-Alfalfa

Fall Lettuce-Barley

Fall Lettuce-Milo

Fall Lettuce-Wheat

Milo-Watermelon

Alfalfa-Potatoes

Alfalfa-Watermelon

Barley-Watermelon

Watermelon-Wheat

Milo-Potatoes

Safflower-Watermelon

Safflower-Potatoes

Barley-Potatoes

Potatoes-Wheat

Mean

Net Income

132

139

134

201

197

200

194

90

70

86

88

85

74

91

75

71

68

Standard

Deviation

91.1

95.8

89.4

140.9

139.8

141.9

141.0

54.6

67.3

56.1

53. 6

51.9

70.9

55.2

68.3

69.5

68.5

(% of Time)

60% 70% 80% 90%

Return Above

Variability Variable Cost

Coefficient Greater Than

69 -

69

70

70

71

71

73

74

74

75

75

76 -

78

79

79

79

81

109 85 55 15

115 89

111 87 58 19

166 128 83

21

162

125 80 18

81 19 165 127

121

61 46

74

61

56

46

73 54

58

76

28

35

28

58 43 26

55 41 25

31

16

14

4

5

3

3

2

0

-

56 41 24 -1

51 29 -1

70 51 29 -1

68 49

27 -3

Source: Calculated using gross income and variable production cost data derived in this study.

Table 22. Return Above Variable Cost Levels and Variabilities on 800 Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Cotton-Barley

Cotton-Alfalfa

Cotton-Wheat

Cotton-Milo

Cotton-Sugar Beets

Cotton-Safflower

Sugar Beets-Wheat

Sugar Beets-Barley

Sugar Beets-Milo

Sugar Beets-Alfalfa

Barley-Milo

Sugar Beets-Safflower

Barley-Wheat

Alfalfa-Barley

Alfalfa-Milo

Milo-Wheat

Cotton-Carrots

Carrots-Spring Lettuce

Cotton-Watermelon

Carrots-Fall Lettuce

Carrots-Potatoes

Milo-Safflower

Alfalfa-Wheat

Cotton-Cantaloupe

(% of Time)

60% 70% 80% 90%

115

122

113

118

153

115

56

59

62

66

24

58

18

28

31

21

358

489

169

443

332

23

25

234

Mean standard Variability

Net Income Deviation Coefficient

17.6

18.8

18.3

19.4

28. 3

21.4

13.2

14.3

15.3

16.2

6.1

17.2

5.6

9.1

10.3

7.2

125.3

176.3

61.5

162.0

123.0

8.6

9.5

93.4 -

15 -

15

16

16

18

19

24

24

25

25

25

30 -

31

33

33

34

35

36

36

37

37

37

38

40

Return Above

Variable Cost

Greater Than

111 106 101 93

117 112 106

98

108 103 97 89

114 108 102 93

146

139

129 117

110 104 97 88

53 45

28

55

5

52

48 41

58 54 49

42

62 57

52

45

23

21

19 16

54

49

44 36

17 15 14 11

80 77 74 70

, 25

22 18

20 18 15

12

326 293

252 197

445 397 341 264

154 137

117 90

403 359 307

236

302 268 229 175

21 19 16

12

23 20

17 13

210 185 155 114 oo o

Table 22.— Continued Return Above Variable Cost Levels and Variabilities on 800

Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Carrots-Sugar Beets

Carrots-Cantaloupe

Cotton-Potatoes

Carrots-Watermelon

Alfalfa-Safflower

Alfalfa-Carrots

Carrots-Milo

Carrots-Onion

Carrots-Barley

Carrots-Wheat

Cantaloupe-Potatoes

Barley-Safflower

Carrots-Safflower

Fall Lettuce-Onion

Cantaloupe-Spring Lettuce

Cotton-Spring Lettuce

Cotton-Fall Lettuce

Cantaloupe-Fall Lettuce

Cotton-Onion

Sugar Beets-Watermelon

Potatoes-Watermelon

Sugar Beets-Cantaloupe

Fall Lettuce-Watermelon

Onion-Watermelon

Mean

Net Income

540

365 .

341

295

319

455

113

144

177

254

414

301

382

184

317

27

270

266

603

263

260

208

20

262

Standard

Deviation

122.3

156.5

76.7

134.2

11.5

117.0

120.1

273.4

119.4

120.9

96.8

9.5

124.6

257.0

174.6

168.6

146.2

161.0

235.1

59.2

76.5

95.1

140.0

- 229.5

(% of Time)

60% 70% 80% 90%

Return Above

Variability Variable Cost

Coefficient Greater Than

53

53

54

55

55

41 -

41

42

42

43

43

45

45

45

46

47

47 -

48

48

48

49

50

50

52

270 238 198 145

342

300 250 181

165 144 120 86

283 247 204 145

24

21

17

12

241 209 172 120

236

204 165 113

534 461 373 253

233 201 163 110

230 198 159 106

184

158

127 84

18 15

12

8

231 198 158 103

476 407 324

211

322 274 219

142

299 253

200 124

259 219

172

108

279 236

184 113

396 333 257 154

98

82 63

124 104

37

79

46

153 128 97 56

219

182 137 75

357 295

221 120 co

H

Table 22.— Continued Return Above Variable Cost Levels and Variabilities on 800

Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Mean

Net Income

Fall Lettuce-Spring Lettuce 427

Sugar Beets-Potatoes 128

Sugar Beets-Spring Lettuce 285

Spring Lettuce-Watermelon

Spring Lettuce-Onion

Sugar Beets-Onion

300

586

398

Spring Lettuce-Potatoes

Potatoes-Onions

Sugar Beets-Fall Lettuce

Fall Lettuce-Potatoes

Cantaloupe-Onion

Safflower-Wheat

Cantaloupe-Watermelon

Milo-Onion

Alfalfa-Onion

Cantaloupe-Safflower

Barley-Onion

Wheat-Onion

316

430

239

270

479

17

193

364

Safflower-Onion

Spring Lettuce-Milo

Alfalfa-Spring Lettuce

Alfalfa-Cantaloupe

Cantaloupe-Milo

Cantaloupe-Barley

Spring Lettuce-Wheat

367

138

361

358

360

250

254

146

142

139

244

Standard

Deviation

73.0

163.7

173.3

232.3

185.2

253.3

141.8

162.3

291.3

10.7

121.2

233.8

235.2

89.4

233.0

232.0

234.5

163.4

166.2

95.9

93.8

_ 92.3

162.2

(% of Time)

60% 70% 80% 90%

65

65

65

65

62

63

64

64

65

66

66.

66

66

66

56 -

57

58

58

58

58

59

59

59

60

61

Return Above

Variability Variable Cost

Coefficient Greater Than

367 303 227

122

110 90 67 34

244 200 147 75

257 210 155

79

501 409

300

150

340 277 203 100

270

220

160

79

366 298 217 105

203 165 120

229 185 134

57

62

406 367 233 106

15 12 8 4

163 130 91 38

305

242 167

64

308 245 170

116

92 63

302

239 165

66

24

62

300 237 163

301 238

163

61

59

209 165 113 41

212

164

114 41

122

96 66 23

119 94 64

22

116 91

62 21

204 160 108 36 oo

to

Table 22.— Continued Return Above Variable Cost Levels and Variabilities on 800

Acre Farms in Arizona With One Acre Allocated Equally Between Two Crops

Crop Combination

Spring Lettuce-Barley

Cantaloupe-Wheat

Fall Lettuce-Safflower

Spring Lettuce-Safflower

Alfalfa-Fall Lettuce

Alfalfa-Watermelon

Alfalfa— Potatoes

Barley-Fall Lettuce

Fall Lettuce-Milo

Milo-Watermelon

Fall Lettuce-Wheat

Barley-Watermelon

Wheat-Watermelon

Safflower-Watermelon

Milo-Potatoes

Potatoes-Safflower

Potatoes-Barley

Potatoes-Wheat

Source: See Table 21.

(% of Time)

60% 70% 80% 90%

Mean Standard Variability

Return Above

Variable Cost

Net Income Deviation Coefficient Greater Than

204

78

198

75

72

74

93

89

90

87

247

137

200

246

208

81

97

201

163.5

91.1

135.2

166.9

141.0

56.2

67.3

139.8

141.8

54.5

141.1

53.6

51.9

55.2

70.9

68. 3

69.5

68.5

66 -

67

68

68

68

69

70

70

70

70

71

72 -

72

75

76

77

77

79

206

162

110 38

114

89

60

20

166

130 86 27

204 159 106 32

172

134 89

67

52

34

27

9

80

62

40

10

166 128 83

22

168 130 85

22

64 49

32

8

163 125

61 47

79

30

17

6

58 45 28

60 45

27

5

3

.

56 33

72

54

32

73 54

70

52

31

2

1

1

30 -1

84

Table 23. Return Above Variable Cost Levels and Varia­ bilities on 320 Acre Arizona Farms with One Acre

Allocated Equally Among Three Crops for Selected

Diversification Systems

'

Varia­

Crop

Mean Standard bility

Net

Combination Income

Devia­ tion

Coeffi­ cient

A-C—Ba

C-B-M

A-C-SB

C-SB-Wh

B—M—Sa

A-B-M

A—Ca—Cr

A-C-Ca

C-B-P

SL-Cr-0

A-Cr-Wh

Ca-SL-SB

C-SL-M

A-P-SB

FL-SB-P

A-Ca-SB

SL-O-P

A-FL-SL

SL-M-SB

A-SB-SL

A—Wa—Ca

A-Wa-B

81

80

104

100

21

24

256

157

123

549

178

267

- 228

91

205

122

436

287

193

194

132

56

13.0

13.4

19.4

18.7

6.2

7.9

103.1

64.1

51.0

235.3

77.7

117.0

112.5

47.1

109.4

65.3

237.4

160.1

109.1

110.8

82. 6

37.4

44

44

49

52

53

54

55

56

56

57

63

67

16

17

40

41

42

43

19 :

19

30

33

(% of Time)

60% 70% 80% 90%

Return Above

Variable Cost

75 74 70 64

77 73

69 63

100

94

88

80

95 90 84 76

19 17 16 13

22

20

17 14

231 203 170 124

141 123

103

110 96

80

75

58

491 427

352

248

159 138 113 79

238 206

169 118

200 170 134

79

84

66 51 .30

178

148 113

105 88

67

65

38

376 312 236

132

247 204 153

166

111

137

89

102

166 136 101

63

82

54

52

26

47 37 25 8 aFor Tables 23-28 , symbols- -crop A, Alfalfa; B,

Barley; C , Cotton; Ca, Cantaloupes; C r , Carrots; FL, Fall

Lettuce; S L , Spring Lettuce; Wa, Watermelons; Wh, Wheat.

Source: See Table 21

85

Table 24. Return Above Variable Cost Levels and Varia­ bilities on 800 Acre Arizona Farms with One Acre

Allocated Equally Among Three Crops for Selected

Diversification Systems

Crop

Combination

A-C-B

C - B - M .

A-C-SB

A-SB-Wh

B-M-Sa

A-B-M

A-C-Ca

A-Ca-Cr

C-B-P /

A-Cr-Wh

SL-Cr-0

SL-Ca-SB

C-SL-M

A-SB-P

A-SB-Ca

FL-SB-P

SL-O-P

A-FL-SL

SL-M-SB

A-SL-SB

A-Ca-Wa

A-B-Wa

Mean

Net

Income

88

85

113 •

48

22

128

210

439

293

197

199

139

61

Standard

Devia­ tion

13.2

13.4

19.5

10.5

27

166

263

6.3

7.9

64.2

129

183

554

273

103.2

50.9

77.7

235.3

116.9

- 234 112.3

96 • 47.2

65.4

109.4

237.5

159.6

108.9

110.7

82.7

37.5

Source: See Table 21

.15

.16

.17

.22

.28

.29

.39

.39

.40

.42

.43

.43

.48

.49

.51

.52

.54

.55

.55

.56

. 60

.62

Varia­ bility

Coeffi­ cient

(% of Time)

60% 70% 80% 90%

Return Above

Variable Cost

Greater Than

84 81 76

82 78 74

71

68

108

102

96 88

46 43 40

21

19 17

35

14

25 23 21 17

150 132 , 112 83

237

210

177 131

116

102

86 63

164 143 118 84

495 431 356 263

244 212 175 123

206 176

140 90

84 71 56 35

112 94 56 45

183

153

118 70

380 316 240 135

253 210 159

170 140 105

89

57

172 142

106 58

118 96 69 33

51 41 29 13

86

Table 25. Return Above Variable Cost Levels and Varia­ bilities on 320 Acre Arizona Farms with One Acre

Allocated Equally Among Four Crops for Selected

Diversification Systems

Crop

Combination

B-C-M-Wh

A-C-M-Wh

B-C-M-Sa

A-B-C-SB

C-Wh-Sa-SB

B-M-Sa-SB

A-C-P-Cr

A-B-M-Wh

A-Cr-FL-SB

A-C-P-Ca

Ca-SL-P-SB

A-SB-P-Ca

Cr-SL-O-Wa

FL-SL-P-Ca

A-Cr-P-0

M-Cr-P-0

Ca-Cr-O-Wa

C-Ca-M-Wa

Ca-B-P-Wa

B-C-P-SL

A—Ca—B—SL

A-C-O-SL

A-Ca-SB-Wa

A-P-O-SB

Mean

Net

Income

248

157

241

113

447

312

345

344

392

149

137

210

191

348

123

243

64

66

65

65

84

80

39

220

22

Standard

Devia­ tion

94.8

51.9

178.5

128.2

142.4

143.0

165.9

63.5

59.1

97.4

90.9

174.5

64.7

128.4

10.7

11.4

11.7

11.7

15.1

15.7

8.9

63.6

6.7

82.3

52.1

Source: See Table 21

Varia­ bility

Coeffi­ cient

29

31

33

33

39

40

17

17

18

18

18

20

23

40

41

41

42

42

43

43

46

48

50

53

53

(% of Time)

60% 70% 80% 90%

Return Above

Variable Cost

Greater Than

62

59 55

63 60

62

59

57 52

56

50

50

62 59 55 50

80 76 71 65

76

72

67 60

36 34 31 27

204 187 166 138

20 18 16 13

228 206 179 143

144 130 114 91

218

192 162

120

100

86 70 47

402

354

297

219

280

245 204 148

309 271 225 163

309 270 224 161

351 306

253 180

133 116

122 106

96 68

87 61

186 159 128

169 144 115

85

75

304

257

201

124

107 89 69 40

211

176 135 79

87

Table 26. Return Above Variable Cost Levels and Varia­ bilities on 800 Acre Arizona Farms with One Acre

Allocated Equally Among Four Crops for Selected

Diversification Systems

Crop

Combination

C-B-M-Wh

A-C-M-Wh

A—C—B—Sa

A-C-B-SB

C-B-M-Sa

SB—B—M—Sa

A-B-M-Wh

A-C-P-Cr

A—C—P—Ca

A-SB-Cr-FL

SB-Ca-P-SL

SL-FL-Ca-P

C P

A-Cr-O-P

C-M-Ca-Wa

M-O-P-Cr

0—Cr—Ca—Wa

B-P-Ca-Wa

B-P-C-SL

A—B—Ca—SL

A-C-O-SL

A-SB-Wa-Ca

A-SB-P-0

Mean

Net

Income

318

118

350

156

348

398

142

216

196

354

129

248

88

68

72

71

91

69

85

41

25

227

165

254

249

452

Standard

Devia­ tion

10.8

11.5

11.8

15.2

11.7

15.7

9.0

7.8

63.6

52.2

82.4

94.8

178.6

127.8

47.8

142.5

63.4

143.0

59.1

97.2

90.9

174.6

64.7

128.4

49.5

Source: See Table 21

Varia­ bility

Coeffi­ cient

40

40

41

41

41

41

42

42

28

28

32

32

38

15

16

17

17

17

18

22

45

46

49

50

52

56

(% of

Time)

60% 70% 80% 90%

Return Above

Variable Cost

Greater Than

66

69

63 59

55

66

62 57

68

65 61 56

87 83 78 71

66 63 59 54

81 77 72 65

39 36 34 30

23

21

19 16

211

194 174 146

152 138 121 98

234

212

185 149

223 197 167 126

407 359

302

223

286 251 210 154

106 93 77 56

314 276 230

167

140 123 102 75

312

274 228

165

356 312 259 185

127

111

92

66

191 165 134 91

174 149 120 80

311 263 208 131

113 96 75 46

215 181 140

76

83

62

46

25

88

Table 27. Return Above Variable Cost Levels and Varia­ bilities on 320 Acre Arizona Farms with One Acre

Allocated Equally Among Five Crops for Selected

Diversification Systems

Crop

Combination

Mean

Net

Income

A-C-M-Wh-SB

A-B-C-M-SB

71

72

A—B—M —Sa—SB

36

A-C-Ca-P-SB

B-C-M-Ca-SB

144

A-B-C-P-SB

98

A-Cr-FL-SL-M

279

117

A-C-Ca-SL-SB

A-C-P-O-Cr

218

207

315

C-Ca-FL-SL-Wa 283

A-B-Ca-Cr-Wh 162

345 Ca-Cr-P-O-Wa

B-M-P-Ca-SB

A-P-O-Cr-SB

A-C-P-SB-Wa

M-P-O-Cr-SB

109

294

129

294

A-M-P-O-Cr

A-P-Ca-FL-SL

281

255

B-M-P-Ca-Wa 115

O-Ca-SL-FL-Wa 383

P-O-SL-SB-Ca

A-P-SB-FL-SL

A-B-M-P-0

A-B-Sa-Wa-Ca

333

224

185

87

Standard

Devia­ tion

12.7

13.0

8.2

44.0

32. 6

95.0

49.3

78.2

75.8

116.1

104.7

62. 3

133.1

42.1

114.6

50.5

115.1

114.6

48.5

162. 3

156.8

106.0

103.3

49.7

Source: See Table 21

Varia­ bility

Coeffi­ cient

41

41

42

42

47

47

56

57

38

39

39

39

39

39

18

18

23

31

33

34

34

36

37

37

37

(% of

Time)

60% 70% 80%

90%

Return Above

Variable Cost

Greater Than

68 65 61 55

69

34

66

32

61

29

56

26

133 121 107 88

90 81 71 57

255 230 199 157

107 96 83 65

198 177

152

118

188 168 143 110

286 255 218 167

256 228 195 148

147 130 110

82

312

276 233 175

98

87 73 55

266 235 198 148

117 103 87 65

265 234 197 147

252 221

185 134

229

201 168 122

103 89 74 53

342 298 246 175

293 251 201 131

197 168

134

88

159

121

98 53

75

62 46 24

89

Table 28. Return Above Variable Cost Levels and Varia­ bilities on 800 Acre Arizona Farms with One Acre

Allocated Equally Among Five Crops for Selected

Diversification Systems

Crop .

Combination

Mean

Net

Income

A-C-M-Wh-SB

77

A-C-M-B-SB'

A-M-B-SB-Sa

A-C-SB-P-Ca

A-C-SB-P-B

78

40

152

104

A-M-Cr-SL-FL 284

C-M-B-SB-Ca

C-B-P-SL-Ca

122

224

A-C-SB-SL-Ca 214

C-SL-FL-Ca-Wa

290

A-C-P-O-Cr 322

B-M-P-SB-Ca 112

A-B-Wh-Ca-Cr - 167 a—C

135 .

P-O-Cr-Wa-Ca 350

A-SB-O-Cr-P

M-SB-P-O-Cr

299

298

A-P-SL-FL-Ca 261

A-M-P-O-Cr

B-M-P-Ca-Wa

285

119

SL-FL-Ca-Wa-0

388

A-SB-FL-SL-P

229

SB-SL-Ca-P-0

337

A-B-SB-O-SL

265

A-M-B-P-0

188

Standard

Devia­ tion

12.8

13.1

8.4

44.2

32.6

94.8

40.2

78.2

75.8

104.4

116.2

42.0

62.3

50.6

133.1

114.7

115.1

104.0

114.6

48.4

162.2

105.8

156.8

138.7

103.3

Source: See Table 21

Varia­ bility

Coeffi­ cient

38

39

40

40

41

42

46

47

52

17

17

21

29

31

33

33

35

35

36

36

37

37

37

38

55

60%

(% of

Time)

70% 80% 90%

Return Above

Variable Cost

Greater Than

74 70 66 60

75

71 67 61

38 35 33 29

140 129

114 95

96 87 77 62

260 235 204

163

112 102 .

89

71

205 183 158 124

195 175 151 117

264 236

202 156

293

261 224 173

102

91

77 41

151 134 114

87

123 109 93 70

317 281 238 180

270 240 203

152

269 238

201 150

235

207

174

128

257 226 119 138

107 93 78 57

347 303

252

180

202 174 140 93

298 256

206 137

230 193 149 88

162

135

102

56

Table 29.

Annual Fixed Cost for a Representative 320 Acre General Crop Farm in

Arizona

Resource

Automotive

Power Equipment

Land Preparation

Equipment

Planting and

Cultivating

Equipment

Harvesting Equipment

Land and Buildings

Irrigation Equipment

Miscellaneous

Equipment

Other Miscellaneous

Fixed Costs

Totals

Total Annual Fixed

Cost

Costs Per Year

Average Value of Investment Depreciation Interest Miscellaneous

($)

6,300

28,451

11,186

($)

840

3,862

1,332

($)

504

2,276

895

($)

345

210

85

7,728

24,585

224,000

3,631

305,881

1,163

4,023

4,074

479

15,773

618

1,967

17,920

290

24,470

56

192

3,636

27

300

4,851

45,094

(1969).

Source: Data calculated utilizing Jones (1967) and Wildermuth et al.

Table 30.

Annual Fixed Costs for a Representative 800 Acre General Crop Farm in

Arizona

Resource

Costs Per Year

Average Value of Investment

Depreciation Interest Miscellaneous

Automotive

Power Equipment

Land Preparation

Equipment

Planting and

Cultivating

Equipment

Harvesting Equipment

Land, Buildings, and

Irrigation Equipment

Miscellaneous Equipment

Other Miscellaneous •

Fixed Costs

($)

8,100

38,751

17,904

8,806

48,895

560,000

5,115

Totals

Total Annual Fixed

Costs

687,571

($)

1,080

5,884

1,571

1,053

8,001

6,569

710

24,868

($)

648

3,100

1,432

704

3,912

44,800

409

55,005

($)

420

285

135

63

362

8,471

37

550

10,323

90,196

Source: See Table 29

REFERENCES CITED

Arizona Crop and Livestock Reporting Service, "Arizona

Agriculture,1 6445 Federal Office Building,

Phoenix, Arizona, 1970.

Carter, H. 0., and G. W. Dean, "Income, Price, and Yield

Variability for Principal California Crops and

tural Experiment Station, Vol. 30, No. 6, October,

1960.

Heady, Earl 0., Economics of Agricultural Production and

New Jersey, Seventh edition, 1952.

Jones, Douglas M . , "Selected Data Relating to Resources,

Costs, and Returns on Irrigated Crop Farms in Yuma

County, Arizona," File Report 67-4, Department of

Agricultural Economics, The University of Arizona,

Tucson, Arizona, September 1967.

Mack, Lawrence E . , "Supplementary Material in Support of

Ph.D. Dissertation Entitled: Economic Implications

of a Dynamic Land and Water Base for Agriculture in

Central Arizona," File Report 68-2, Department of

Agricultural Economics, The University of Arizona,

October 4, 1968.

No. 5, September-October, 1970.

Steel, Robert G. D . , and James H. Torrie, Principles and

Inc., New York, 1960.

Commission for Research in Economics, Monograph

Number 5, Principle Press, Inc., Bloomington,

Indiana, 1940.

92

93

U. S. Department of Agriculture, "Agricultural Statistics,"

United States Government Printing Office,

Washington, D. C . , annual issues 1960-1970.

U. S. Department of Agriculture, "1970 Handbook of Agricul­

tural Charts," Economic Research Service, U. S.

Wildermuth, John (Ed.), "Updated Data for Arizona Crop Farm

Planning," File Report 69-12, Department of Agri­

cultural Economics, The University of Arizona,

December, 1970.

Wildermuth, John R . , William E. Martin, and Victor H.

Rieck, "Costs and Returns Data for Representative

General Crop Farms in Arizona," Report 253, Agricul­

Tucson, September, 1969.

and Row, Publishers, New York, 1964.

Young, Robert A . , William E. Martin, Dale L. Shaw, Douglas

Arizona Crop Farm Planning," Department of Agricul­ tural .Economics, The University of Arizona, Tucson,

June, 1968.

63 42

1

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