• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Table of Contents
 Acknowledgement
 List of Tables
 Risk and uncertainty concepts in...
 Objectives and procedure of the...
 Development and concepts of Game...
 Development of decision theory
 Survey procedure and questionn...
 Reasons and analysis of farmers'...
 Farmers' choice differences by...
 Reasons and analysis of choice...
 Summary and conclusions
 Physical and financial characteristics...
 Bibliography






Title: Farm management decisons within the framework of game and decision theory models
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Permanent Link: http://ufdc.ufl.edu/UF00055276/00001
 Material Information
Title: Farm management decisons within the framework of game and decision theory models
Physical Description: viii, 127 leaves : ; 28 cm.
Language: English
Creator: Sobering, Frederic David.
Publication Date: 1963
 Subjects
Subject: Farm management -- Mathematical models   ( lcsh )
Farm management -- Decision making   ( lcsh )
Genre: bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--North Dakota State University, 1963.
Bibliography: Includes bibliographical references (leaves 126-127).
Statement of Responsibility: by Frederic David Sobering.
General Note: Typescript.
General Note: Produced in this form by the Department of Agricultural Economics, North Dakota State University, Fargo, North Dakota.
Funding: Electronic resources created as part of a prototype UF Institutional Repository and Faculty Papers project by the University of Florida.
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Bibliographic ID: UF00055276
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 10013922

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Table of Contents
        Table of Contents 1
        Table of Contents 2
    Acknowledgement
        Acknowledgement
    List of Tables
        List of Tables 1
        List of Tables 2
        List of Tables 3
    Risk and uncertainty concepts in farm resource use decisions
        Page 1
        Risk and uncertainty defined
            Page 1
            Page 2
        Uncertainty considerations facing Noth Dakota farmers
            Page 3
            Page 4
            Page 5
            Page 6
            Page 7
        Ability of individual farmers to withstand uncertainty losses
            Page 8
            Page 9
            Page 10
        Uncertainty and the human factor
            Page 11
            Page 12
            Page 13
    Objectives and procedure of the study
        Page 14
        General hypothesis
            Page 14
        Objectives
            Page 14
        Procedure
            Page 15
            Page 16
    Development and concepts of Game Theory
        Page 17
        Commonly used Game Theory terminology
            Page 18
        Game classification according to number of persons involved
            Page 19
        Games classified according to strategies
            Page 19
        Games classified according to payoff
            Page 20
        Game theory applied to agriculture
            Page 21
        Zero-sum, two-person game
            Page 21
            Page 22
        The Maximin Strategy
            Page 23
        The Minimax Strategy
            Page 24
        The saddlepoint
            Page 24
        Properties of Maximin-Minimax Strategies
            Page 25
        Payoff matrix without a saddlepoint
            Page 25
        Mixed strategy with non saddlepoint matrix
            Page 26
            Page 27
        Determination of probability in a large non-saddlepoint matrix
            Page 28
            Page 29
            Page 30
            Page 31
            Page 32
            Page 33
    Development of decision theory
        Page 34
        Page 35
        Wald's Maximax Criterion
            Page 36
            Page 37
        The Maximax Strategy
            Page 38
        Savage's minimax regret criterion
            Page 38
            Page 39
        Hurwicz Pessimism-Optimism Criterion
            Page 40
        Laplace's Criterion of Insufficient Reason
            Page 41
            Page 42
            Page 43
    Survey procedure and questionnaire
        Page 44
        Selection of areas
            Page 44
        Selection of farmers
            Page 44
        Survey questionnaire
            Page 45
            Survey questionnaire
                Page 45
            Questionnaire 2
                Page 46
                Page 47
                Page 48
            Questionnaire 3
                Page 49
                Page 50
                Page 51
                Page 52
    Reasons and analysis of farmers' choice patterns of hypothetical enterprises...
        Page 53
        Decision theories applicable to act choices
            Page 53
            Page 54
        Alternatives by area
            Page 55
        Rationality of choices
            Page 56
        Consistency of choices by time periods
            Page 57
            Page 58
        Consistency of choices by income setting
            Page 59
            Page 60
    Farmers' choice differences by physical and financial factors
        Page 61
        Capital managed
            Page 61
        Educational level
            Page 62
            Page 63
        Age level
            Page 64
        Liabilities
            Page 65
        Farm business equity
            Page 65
        Tenure
            Page 66
        Consistency of act choices
            Page 67
            Page 68
            Page 69
    Reasons and analysis of choice patterns of the hypothetical specific resource use matrix
        Page 70
        Page 71
        Page 72
    Summary and conclusions
        Page 73
        Implications of findings
            Page 74
            Age
                Page 75
            Education
                Page 75
            Dependents
                Page 76
            Capital managed
                Page 76
        Other inferences
            Page 77
        Application to agricultural policy
            Page 78
    Physical and financial characteristics of farmers surveyed
        Page 79
        Page 80
        Page 81
    Bibliography
        Page 82
        Page 83
        Page 84
Full Text
Peter E. HIdebrand
A'rcuiturai Economics






FARM MANAGEMENT DECISIONS
WITHIN THE FRAMEWORK


OF GAME AND
THEORY A


DECIS ION


MODELS


Frederic David Sobering







Produced in this form by the
Department of Agricultural Economics
North Dakota State University
Fargo, North Dakota











FARM MANAGEMENT DECISIONS WITHIN THE FRAMEWORK

OF GAME AND DECISION THEORY MODELS











BY

FREDERIC DAVID SOBERING


A thesis submitted to the faculty of the North Dakota
State University of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree; Master of Science

North Dakota State University


March 1963









TABLE OF CONTENTS

Chapter Page

I. RISK AND UNCERTAINTY CONCEPTS IN FAIM RESOURCE USE
DECISIONS . .... . . 1

Risk and Uncertainty Defined .. .... 1
Uncertainty Considerations Facing North Dakota Farmers 3
Ability of Individual Farmers to Withstand Uncertainty
Losses . . . . 8
Uncertainty and the Human Factor . . 11

II. OBJECTIVES AND PROCEDURE OF THE STUDY . 14

General Hypothesis ..... ..... . .... 14
Objectives . . . .. .. 14
Procedure. . . . . 15

III. DEVELOPMENT AND CONCEPTS OF GAME THEORY ... .. .. 17

Commonly Used Game Theory Terminology . . 18
Game Classification According to Number of Persons
Involved . . . . . 19
Games Classified According to Strategies . . 19
Games Classified According to Payoff . . 20
Game Theory Applied to Agriculture . . 21
Zero-Sum, Two-Person Game. . . . 21
The Maximin Strategy . .... . 23
The Minimax Strategy . . . 24
The Saddlepoint. . ... . . . 24
Properties of Maximin-Minimax Strategies . . 25
Payoff Matrix Without a Saddlepoint. . . 25
Mixed Strategy with Non Saddlepoint Matrix . 26
Determination of Probability in a Large Non Saddlepoint
Matrix . . . . .. .. 28

IV. DEVELOPMENT OF DECISION THEORY ... 34

Wald's Maximin Criterion ......... ... 36
The Maximax Strategy .. ................ 38
Savage's Minimax Regret Criterion . . 38
Hurwicz Pessimism-Optimism Criterion . . 40
Laplace's Criterion of Insufficient Reason . .. 41

V. SURVEY PROCEDURE AND QUESTIONNAIRE. . . 44










Chapter


Selection of Areas ... . .
Selection of Farmers .. ... .. ,
Survey Questionnaire .. .... .

Questionnaire Section 1 .. .. .
Questionnaire Section 2 ...... .
Questionnaire Section 3 ..

VI. REASONS AND ANALYSIS OF FARMERS' CHOICE PATTERNS OF HYPO-
THETICAL ENTERPRISES UNDER FOUR SETTINGS OF TIME AND
SUPPLEMENTARY INCOME. . . . .

Decision Theories Applicable to Act Choices . .
Alternatives by Area. . . .
Rationality of Choices . . . .
Consistency of Choices by Time Periods.. . .
Consistency of Choices by Income Setting . .

VII. FARMERS' CHOICE DIFFERENCES BY PHYSICAL AND FINANCIAL


FACTORS .. . . .


Capital Managed . . .
Educational Level . . .
Age Level . ........
Liabilities . . . .
Farm Business Equity .. .
Tenure. . . .
Consistency of Act Choices . .

VIII. REASONS AND ANALYSIS OF CHOICE PATTERNS O
THETICAL SPECIFIC RESOURCE USE MATRIX .


IX. SUMMARY AND CONCLUSIONS


Implications of Findings .. .

Age . . . . .
Education . .. .
Dependents. . . .
Capital Managed . .
Equity in the Farm Business .
Tenure ..... . .

Other Inferences. ., .
Applications to Agricultural Policy ..


APPENDIX. . .. . a

BIBLIOGRAPHY, ..... . .


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Page








NORTH DAKOTA STATE UNIVERSITY
OF AGRICULTURE AND APPLIED SCIENCE
FARGO, NORTH DAKOTA

AGRICULTURAL ECONOMICS










July


TO: Members and Associat of GP-2
FRi Laurel D. Loftsgard

At our annual meeti g held in Fargo last spring, it
was decided that Fred Sobering's M.S. Thesis should be re-
produced and made available to GP-2 personnel.


We found time to get the job done here and a copy
is enclosed. Also, we have some extra copies so if you
want an additional copy or two, let me know.


"Buy Dkota Mad Flour"









LIST OF TABLES


Table Page

1. Selected Descriptive Data on 1960 Record Route Farms .. 9

2. Income After Cash Expenses Under Variable Wheat Yields on
a Hypothetical North Dakota Wheat Farm with a 200-Acre
Wheat Base and a 20-Bushel Per Acre Normal Yield ... 10

3. Solution of Modified Simplex Programming Method Matrix 5 31

4. Code Numbers and Size Ranges Used in Classifying Sample
Farms.. . a ... 44

5. Decision Theories Applicable to Each Alternative and the
Number of Farmers Selecting Each Act Under the Four
Settings of the Hypothetical Decision Problem. . 55

6. Number of Farmers Selecting Each Alternative Under the
Four Settings of the Hypothetical Profit Decision
Matrix, by Area. . . . . 56

7. Occurrence of Pairs of Choices by Farmers in the Short
and Long Run Under the Setting of No Added Income. 59

8. Occurrence of Pairs of Choices by Farmers in the Short
and Long Run Under the Setting of Added Income . 59

9. Occurrence of Pairs of Choices Made by Farmers in the No
Added Income and the Added Income Setting in the Short
Run . . . . 60

10. Occurrence of Pairs of Choices Made by Farmers in the
No Added Income and the Added Income Setting in the
Long Run . . . . .. . 60

11. Alternative Choices by Farmers Under Low and High
Levels of Capital Managed. ... . . 62

12. Alternative Choices by Farmers Under Low and High Levels
of Education . . . 63

13. Alternative Choices by Farmers Under Low and High Level
Age Groups . . . . . 64

14. Alternative Choices by Farmers According to Liability
Level. . . . . . 65











15. Alternative Choices by Farmers According to Equity in
the Farm Business . . ... 66

16. Physical and Financial Characteristics of Farmers by the
Consistency of Act Choices and/or Combinations Under
Four Settings of Time and Income .... .. 67

17. Physical and Financial Characteristics of Farmers by
Consistency of Act Choices and/or Combinations Under
the Long and Short Run No Added Income Settings . 69

18. Decision Theories Applicable to Each Alternative; Number
of Farmers Selecting Each Act .. . .. 70

19. Physical and Financial Characteristic of Farmora by Act
Choices . ...... .. .. 72

20. Relative Uncertainty Comparisons of Selected Decision
Criteria and Their Applicability to the Hypothetical
Matrix Choices . . ...... 74


Appendix Tables

1. Farm Size Distribution by Area ...... ... 80

2. Livestock Enterprises and Size of Operations .. .. 80

3. Personal and Financial Characteristics by Area 81


Table


Page










LIST OF CHARTS


Page


1. Decision Flow Pattern Under Four Different Settings with
the Hypothetical Profit Decision Matrix . .


Chart













CHAPTER I


RISK AND UNCERTAINTY CONCEPTS IN FARM
RESOURCE USE DECISIONS

Pure economic theory makes extensive use of the concepts of
perfect knowledge in analyzing an economic system as it affects (a) pro-
ducers in their efforts to maximize returns, and (b) consumers in maxi-
mizing utility from goods consumed. In real life, perfect knowledge is
more an exception than a rule. However, perfect knowledge analysis
provides the basic framework for understanding economic relationships
from which one can adapt phenomena associated with risk and uncertainty.

This study concerns how farmers arrive at their management
decisions under conditions of imperfect knowledge. Since the terms "risk"
and "uncertainty" will be used throughout this dissertation, and because
these concepts are fundamentally different, the following section is
devoted to definitions and differences between the two terms.

Risk and Uncertainty Defined

Webster defines risk as "a hazard; danger; peril; exposure to lose;
injury; disadvantage or destruction."1 He also defines uncertainty as
"not certain to occur; not assured or reliable; not beyond doubt; not
constant; changeable; variable or fitful." In these definitions, risk
refers primarily to the occurrence of a loss, and uncertainty to the
indeterminateness of the occurrence.

Knight was one of the earliest writers to distinguish between
risk and uncertainty as they are commonly used in economic writings to
date.2 He distinguished three types of probability situations:

1. A Priori probability. The assumption is made here that under
identical circumstances, identical consequences will result. Before a
perfectly balanced coin is tossed, the probability of it falling on one
side or the other is exactly 50-50. There would be nothing gained in
tossing such a coin a thousand times to determine whether this proba-
bility would hold exactly true. If in a thousand throws the coin does
not fall exactly 500 times on one side and a like number on the other
side, the probability of such an occurrence would not change.

2. Statistical probability. This type differs from a priori
probability in that it is based on the empirical evaluation of a large
number of occurrences. The calculations of the probability of future


1Nutson, W. A., Knott, T. A., and Carhart, P. W., Webster's New
International Dictionary of the English Language. Second Edition,
Unabridged, G. and C. Merrian Company, Springfield, Massachusetts, 1949.

2Knight, F. H., Risk Uncertainty and Profit, Houghton-Mifflin
Company, Boston and New York, 1921, p. 198.













CHAPTER I


RISK AND UNCERTAINTY CONCEPTS IN FARM
RESOURCE USE DECISIONS

Pure economic theory makes extensive use of the concepts of
perfect knowledge in analyzing an economic system as it affects (a) pro-
ducers in their efforts to maximize returns, and (b) consumers in maxi-
mizing utility from goods consumed. In real life, perfect knowledge is
more an exception than a rule. However, perfect knowledge analysis
provides the basic framework for understanding economic relationships
from which one can adapt phenomena associated with risk and uncertainty.

This study concerns how farmers arrive at their management
decisions under conditions of imperfect knowledge. Since the terms "risk"
and "uncertainty" will be used throughout this dissertation, and because
these concepts are fundamentally different, the following section is
devoted to definitions and differences between the two terms.

Risk and Uncertainty Defined

Webster defines risk as "a hazard; danger; peril; exposure to lose;
injury; disadvantage or destruction."1 He also defines uncertainty as
"not certain to occur; not assured or reliable; not beyond doubt; not
constant; changeable; variable or fitful." In these definitions, risk
refers primarily to the occurrence of a loss, and uncertainty to the
indeterminateness of the occurrence.

Knight was one of the earliest writers to distinguish between
risk and uncertainty as they are commonly used in economic writings to
date.2 He distinguished three types of probability situations:

1. A Priori probability. The assumption is made here that under
identical circumstances, identical consequences will result. Before a
perfectly balanced coin is tossed, the probability of it falling on one
side or the other is exactly 50-50. There would be nothing gained in
tossing such a coin a thousand times to determine whether this proba-
bility would hold exactly true. If in a thousand throws the coin does
not fall exactly 500 times on one side and a like number on the other
side, the probability of such an occurrence would not change.

2. Statistical probability. This type differs from a priori
probability in that it is based on the empirical evaluation of a large
number of occurrences. The calculations of the probability of future


1Nutson, W. A., Knott, T. A., and Carhart, P. W., Webster's New
International Dictionary of the English Language. Second Edition,
Unabridged, G. and C. Merrian Company, Springfield, Massachusetts, 1949.

2Knight, F. H., Risk Uncertainty and Profit, Houghton-Mifflin
Company, Boston and New York, 1921, p. 198.










occurrences from past occurrences must of necessity rest on the
assumption that future probabilities will occur with the same frequency;
that is, follow the same identical pattern.

Under this probability situation, an insurance company dealing in
hail insurance would calculate the probability of hail losses for an
area in a particular year from data on past observations and occurrences.
Based on this information, it would determine a risk premium that would
be used for that area. The calculation based on a large number of past
occurrences over a sufficiently large area would result in a risk
premium level adequate to cover the company's annual loss claim payments,
administrative costs and allow for a reasonable risk return or profit.
For the individual farmer, such a calculation would be impossible.
Though the individual farmer may know from past experiences that hail
has occurred on a particular field in damaging amounts on the average of
every five years, there is no particular assurance that any one specific
year will be free of hail or vice versa.

3. Estimates. With estimates, there is no valid basis for
classifying the probability of occurrence. In this situation, each case
is a separate entity and rests on its own subjective prediction of
future occurrence in the mind of the decision maker.

Knight then goes on to combine the first two classifications which
can be reduced to an objective, quantitatively determinant probability
under the term "risk." This is measurable uncertainty. His third
classification is not measurable and to this he applies the term
"uncertainty."

Knight further states that the terms "objective" and "subjective"
probability could be employed to designate risk and uncertainty,
respectively. Under risk, the distribution of the outcome, with enough
observations, can be calculated. This would be impossible under
uncertainty where each occurrence was unique and grouping impossible

Heady closely follows Knight's distinction between risk and
uncertainty.3 He states that if the outcomes are measurable in an
empirical manner, then this constitutes a risk. The parameters of the
probability distribution can be established and risk is insurable in the
actuarial sense. Because it is insurable, risk can be incorporated into
the cost structure of the firm and does not enter into the firm's
decision-making process. He points out, however, that the probability
of an occurrence can be established only if the number of cases is large
and randomly distributed. For example, risk to a hail insurance company
may be uncertainty to the individual farmer.

According to Heady, the probability of outcome cannot be
established under uncertainty. Uncertainty is subjective in that it
refers to the anticipation of future happenings and is peculiar to the


3Heady, Earl 0., Economics of Agricultural Production and
Resource Use, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1957,
pp. 439-464.











mind of the individual. Uncertainty cannot be insured in the actuarial
sense and cannot be incorporated in the cost structure of the firm. It
must therefore enter into the decision-making process.

Under both Knight's and Heady's distinction between risk and
uncertainty, the differences are not absolute. What is risk in one case
may be uncertainty in another and vice versa. Though the probability of
a damaging hail storm occurring on a particular field in a given year is
risk to an insurance company, it is uncertainty to the farmer. The
farmer, however, may transfer the uncertainty of hail occurrence to the
insurance company.

In this study, the distinctions between risk and uncertainty as
defined by Knight and Heady will be followed.

Uncertainty Considerations Facing
North Dakota Farmers

The ever recurring problem facing the individual farmer in his
decision-making process concerns the determination of optimum resource
use. Under a static economy with perfect knowledge of future occurrences,
this problem would be of minimum importance. Perfect knowledge implies
that the producer is aware of the exact costs, product prices, and
production functions pertaining to his operations and, with a few simple
calculations, can equate marginal costs with marginal benefits under an
unlimited resource situation, or employ the opportunity cost principle
under a limited resource situation. In so doing, he can attain maximum
available benefits and/or highest profits to the farm business.

However, most real farm situations concern imperfect rather than
perfect knowledge. The individual farm producer operates within a frame-
work of uncertainty. Most decisions relating to the amounts and combi-
nations of resources must be made through individual subjective predic-
tions of the future, often based on meager evidence.

There are five main types of uncertainty that face agricultural
producers and particularly those in the Great Plains region which
includes North Dakota. These types of uncertainty are discussed in the
succeeding sections.

Yield variability: Specific yields, whether measured in bushels
of grain per acre or pounds of milk per cow, often are largely beyond
the control of the individual producer within a certain specified time
period. Yields of grain are a function of moisture, temperature, insect
and disease conditions. Yields of livestock and livestock products
depend on the inherent capacity to produce that is bred into the animal.
Recommended management practices definitely influence the yields of
crops/livestock in the attempt to maximize gains or minimize losses.
This influence is confined, however, to the boundaries delineated by
such exogenous forces as weather phenomena, inherent yield capacity,
and so on.












Timely spraying of weeds and insects, tillage practices to
conserve and fully utilize available moisture, and applications of
recommended levels of plant nutrients will influence crop yields within
a range only. Use of above average management practices does not
guarantee above average yields. In a year of widespread drought and
complete crop failure, "good" and "poor" managers alike will suffer.
A virulent strain of rust, against which no grain variety is resistant,
will damage the crops of the farmer who carefully weighed each production
decision on his unit as completely as his counterpart who farms in a
much more haphazard manner. In fact, in a year of complete crop failure,
the "poor" manager may be better off financially because of lower pro-
duction cost outlays by not using fertilizer, spraying for insects and
weeds, treating his seed, or purchasing and seeding the most recently
released and more highly recommended seed variety at a higher unit cost.

The major source of yield variability in North Dakota results
largely from the vagaries of weather. Past records from 1931 through
1958 indicate that average precipitation in the state ranged from a low
of 2.53 inches in the three-month period, April through June4 1936, to
a high of 12.09 inches for the corresponding period in 1953. Annual
precipitation during the same period of years varied from a low of
8.83 inches in 1936 to a high of 23.22 inches in 1941.

Yields of crops are specifically a function of the amount of
moisture received in the forms of rain and snow. State average wheat
yields, for example, have fluctuated during the 1931-1960 period from
a low of 5.2 bushels per acre in 1936 to a high of 23.1 bushels per
acre in 1958. The geographic location and rainfall pattern in the state
are such that state averages do not reflect the fluctuations occurring
in smaller areas of the state. For the period 1926-1948, the coefficient
of variation for county average wheat yields varied inversely with the
amount of rainfall.

A North Dakota study by Thair reported that in Traill County, in
the eastern Valley area, wheat yields had a coefficient of variation of
28 per cent; Foster County, in the central area, 55 per cent; Stark
County, in the western range and wheat area, 60 per cent. These per
centages mean that wheat yields in these respective counties could vary
below their mean by the quoted percentage 66 2/3 per cent of the time.


Taylor, Fred R., and Heltemes, C. J., North Dakota Crop and
Livestock Statistics, 1958 Agricultural Experiment Station, North
Dakota Agricultural College, and Agricultural Marketing Service, United
States Department of Agriculture, Fargo, North Dakota, April, 1959, p. 9.

5Thair, P. J., Stabilizing Farm Income Against Crop Yield
Fluctuations, Bulletin No. 362, North Dakota Agricultural Experiment
Station, North Dakota Agricultural College, Fargo, North Dakota,
September 1950.













Compounding the yield variability problem, and therefore the
prediction of outcomes in a particular year, is the fact that below and
above average years are not randomly distributed but tend to bunch into
periods of good and poor yield levels and averages. Thair reported that
for a 70-year period, 1879-1948, there were three separate periods when
North Dakota wheat yields were above average for a rgn of three of more
years, and two of these runs lasted nine years each. In four separate
periods, yields were below average consecutively for three or more years.
In one period there were five consecutive below average years, and in
another period there were 12 consecutive below average years.

Further evidence of bunching of poor and good years were found by
Greve, Plaxico, and Lagrone through the use of statistical tests on
rainfall and production levels of wheat and grain sorghums in the
Southern Plains area of Oklahoma.7 They found evidence of cyclical
tendencies. One test indicated that cycles of four years or more were
of major consequence in rainfall, wheat yields, and grain sorghum
production.

Vockrodt, employing Walli and Moore's XS test, concluded that
the major portion of the total *p value of dryland production of wheat,
barley, rye, and wild hay in Bottineau County in North Central North
Dakota was contributed either by runs of three years or by runs of four
years or more.

Time variability: The second major source of uncertainty facing
farmers is caused by changes that occur between the time that resource
use decisions are made and the time the product is ready for market.
Factors such as changes in demand, consumer disposable income, tastes,
habits, national prosperity, and employment will affect the magnitude
of prices received for farm products. These changes and fluctuations
are often unpredictable and usually beyond the producer's control.

Historically, farm product prices have been highly unstable.
During periods of inflation, they rise more rapidly than wages and
prices of other goods and services but fall more rapidly in times of
recessions and depressions. Not only do farm prices fluctuate in the
long run, but also they fluctuate considerably in the short run,
depending on annual and seasonal production plus storage and marketing
conditions of a particular commodity.


6'bid

7Greve, R. i., Plaxico, J. S., and Lagrone, W. F., Production and
Income Variability of Alternative Farm Enterprises in Northwest Oklahoma,
Bulletin B-563, Oklahoma State University, Stillwater, Oklahoma, August,
1960.

8Vockrodt, Duane C., Risk Measures for Production and Income of
Crops and Livestock on Irrigation and Dryland, M.S. Thesis, Unpublished,
North Dakota State University, Fargo, North Dakota, 1961.













Annual average prices received by farmers for barley, as an
example, during the period 1945-1957 ranged from a low of $.85 per
bushel in 1957 to a high of $1.90 per bushel in 1947.9 These prices
represent an average for all grades and qualities of both feed and
malting barley sold during one particular year. Considerably more
variation in a commodity price may be experienced by the individual
producer. Product quality may be above or below average on a specific
farm in a particular area because of weather, disease, moisture, and
insect conditions unique to that particular farm.

When yield uncertainty is combined with price uncertainty, it
becomes apparent that it is difficult with many farm enterprises to plan
for and attain income stability and to equate marginal costs with
marginal revenue such that profits are maximized. This does not imply
that the farmer is completely without knowledge of future expectations.
For example, spring subsoil moisture conditions may indicate to some
extent current production possibilities. Forecasts of probable prices,
based on a careful analysis of projected future supply and demand
conditions, are helpful though not infallible. Government agricultural
programs in the form of price supports, subsidy and incentive payments,
coupled with loan and storage programs, aid in establishing a guaranteed
minimum price level, although these factors do not preclude prices well
above the support level which could dictate a different resource use mix
for profit maximization.

Cost uncertainty: A considerable time span elapses between the
resource use level decision and marketing the finished product. A live-
stock feeder may purchase a group of 400-pound feeder calves during the
fall season. A full feeding regime will require 10 to 12 months to
finish these calves to the desired grade and weight. In addition to the
probability of product price variation within this time period, factor
input costs also may vary. In finishing cattle, feed costs constitute
a relatively high percentage of the total cost. Therefore, variations
in the costs of feed are a major factor in determining whether the
operator will realize a positive, zero, or negative return to his
resource inputs.

For example, if a particular feeder had budgeted his profit
potential in November of 1946 when barley prices were $1.31 per bushel
and then was forced to purchase added feed barley supplies in July of
1947 when the price of barley had increased by 36 per cent or to $1.78
per bushel, it is apparent that the original budgeting results would
have lost much of their value. A significantly lower than anticipated
return to labor and management would be realized under the conditions
of the above example, under the assumption that the product price was
close to the budget price employed.



9Taylor, Fred R., and Heltemes, C. J., Price Trends in North
Dakota, 1910-1957, Agricultural Experiment Station, North Dakota Agri-
cultural College and Agricultural Marketing Service, United States
Department of Agriculture, Fargo, North Dakota, February, 1958, p. 19.











Technological uncertainty: The fourth type of uncertainty facing
farmers centers around the rapid changes that have been and are occurring
in the production, storage, and marketing of agricultural products. The
efficient farmer is concerned with production in the most economical
manner. A new innovation or machine may reduce labor requirements and
thereby reduce production costs. However, often the farmer who purchases
the first machine of its type on the market experiences rapid changes in
this particular type of machine, and in a relatively short time the
machine may be obsolete. /An excellent example of this situation would be
the early broadleaved weed killers that required large amounts of water
per acre to be effective. A few years later the development of improved
weedicides that required relatively small amounts of water per acre made
the early weed sprayers obsolete and economically impractical.

Changes in government agricultural programs: Generally, govern-
mental policies towards agriculture have aimed to (a) ensure an abundant
supply of food and fibre and (b) maintain or increase agricultural
income at a reasonable cost to society. Support price and loan and
storage programs tend to remove some of the price uncertainties generally
associated with agricultural production. However, short run program
changes occur. Therefore, long run plans developed by farmers, based on
their best considered opinion of future occurrences, may be altered
because of unforeseen and unpredictable changes in crop acreage allot-
ments, voluntary and mandatory land retirement programs, changes in
absolute and relative price support levels, grazing permits, and/or
other measures.

The extreme variability of yields, product and factor prices,
technological changes, and government programs all add to the complexity
and uncertainty under which the farm operator operates and manages his
farm unit for profit.

One other factor that also may be important is the bunching of
"poor" and "good" years into lengthy periods. Farm survival in an
extended period of below average crop yield years and/or low price
periods may be threatened without adequate strategies to minimize such
uncertainty. If these fluctuations over time were randomly dispersed so
that poor and good years tended to alternate, the problem of income
stability would be mitigated.10 There is general agreement that this
bunching of good and poor years does occur, but the conclusion is more
or less unanimous that no definite pattern of length of occurrence of
cycles can be established.1



10Schickele, R., "Farm Business Survval Under Extreme Weather
Risks," Journal of Farm Economics, Vol. 31, No. 3, August 1949.

11Halcrow, H. G., "Problem of Farm BIsiness su ivL-al-Discussion,"
Journal of Farm Economics, Vol. 31, No. 3, August 1949.












A tree ring study designed to show annual variation in North
Dakota rainfall included a period of 534 years, from 1406 to 1940.1
This study illustrates the bunching of high and low precipitation over
this time span, but the author concluded that there was no definite
cyclical trend established. Out of the 534 years, 479 were included in
cycles ranging in length from 1 to 39 years, which could be classified
as either above or below average rainfall. Only 55 of the 534 years, or
about 10 per cent, were classified as average rainfall years.

A conclusion from this study is that year-to-year changes in the
weather must be regarded as random fluctuations over a long time period.
The possibility exists that over a sufficiently long period of time,
possibly 100 years or more, the general level of precipitation could be
predicted and long run maximization plans developed accordingly. How-
ever, this would be of no particular interest to the individual farmer
concerned with the immediate future or, at the most, with the period of
20 to 30 years during which he operates a farm. According to the Will
tree ring study, such a time span could include all above average rain-
fall, mostly below average, or a combination of above, below, and
average annual precipitation.

Ability of Individual Farmers to
Withstand Uncertainty Losses

Parallel resource situations do not exist among all farms. Much
of the phenomena concerning agricultural production is explained by
measures such as the average size of farm, farm investment, liabilities,
yields, and so on. But average data does not explain the heterogeneity
among farm resource situations, or the physical and economic framework
unique to each operator. The variations that occur for a group of farms
in a relatively homogenous type of farming area are illustrated by the
data shown in Table 1 for the 74 farn rs included in the 1960 summary of
the North Dakota Farm Records Route.

It is evident from Table 1 that wide differences exist in
physical size, capital investment, yields, and returns among farm units.
Therefore, it is logical to assume that differences must exist among
farm units in their ability to withstand uncertainty losses. These
differences are likely accentuated by the peculiar nature of the firm
household relationships which are unique to agricultural production
units. Household living requirements are relatively fixed and require
at least a fixed minimum expenditure. Also, the household unit must



12Will, G. F., Tree Ring Studies in North Dakota, Bulletin
No. 338, North Dakota Agricultural College Experiment Station, North
Dakota Agricultural College, Fargo, North Dakota, April 1946.

13Dorow, N. A., and Sobering, Fred D., 1960 Ann"ual Rearti ou the
North Dakota Farm Records Summary, AriLultuxal Experiment Station,
North Dakota State University, Fargo, North Dakota, May 1961.












have priority on funds needed for minimum living requirements. An
appetite cannot be postponed for a year, whereas replacement of an old
machine with a new one can, and often must, be postponed when realized
production and income falls below an anticipated level.


TABLE 1. SELECTED DESCRIPTIVE DATA ON 1960 RECORD ROUTE FARMS

High-Income Low-Income
Item Group Group


Land owned 1,135 acres 599 acres
Land rented 818 acres 206 acres
Total acres operated 1,953 acres 805 acres
Average capital invested $155,337 $61,537
Index of crop yields 105.3% 88.3%
Returns to capital and labor $ 16,867 $ 3,092



In addition to household fixed income requirements, many farm
production costs are fixed or incurred before production is realized.
Income expectations due to yield, price, and other uncertainties are
highly variable. Similar amounts of inputs and expenses in successive
years may produce highly variable physical production outputs and income.
This holds true particularly in the Great Plains area with its highly
variable rainfall pattern.

For example, wheat yields on a North Dakota farm may vary from as
low as 10 bushels per acre to well over 25 bushels per acre. Table 2
illustrates the corresponding variation that would occur in spendable
income with these variable wheat yields.

From Table 2 and assuming a normal yield expectation of 20 bushels
per acre, there is $5,000 left for family living, debt repayment obli-
gations, machinery replacement, savings, and other expenditures. A 25
per cent decrease in yield under weather condition B results in a
decrease of 40 per cent in income over cash expenses. Similarly, a 50
per cent decrease and a 25 per cent increase in per acre yields as in
weather conditions C and D result respectively in income over cash
expense changes of minus 80 per cent and plus 40 per cent.

Under the assumption that minimum family living costs are $3,000
annually, it is apparent that the normal yield of 20 bushels per acre
would yield sufficient income over expenses to satisfy family living
requirements plus some income remaining for debt retirement and other
expenditures. The 10-bushel per acre yield, with its resultant
$1,000 income over cash expenses, would either force the farm family
to draw on past savings, if available, or increase the debt load. If,




























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-11-


however, this family had reached the point at which additional borrowed
capital was not available, the farm firm may be forced to liquidate a
part of the farm's assets because of the firm household relationship
unique to the farm business.

Certain specific differences among farms determine the ability
of the unit to withstand uncertainty. Equity position, annual debt obli-
gations, and level of minimum family living needed or desired play a
prominent role in determining how well a farm firm can survive a year,
or series of years, of adverse yield, price, and/or income conditions.

It would be realistic to carry this example one step further.
This farm, in addition to $3,000 annual living needs, could have debt
repayment obligations of $2,000 annually. With this debt repayment
obligation, the break even yield is 20 bushels rather than 15 bushels
per acre. As the needed break even yield increases, the probability of
the actual yield dropping below this critical point also increases and
the first becomes increasingly vulnerable to bankruptcy. Accordingly,
contiguous farms that are comparable in size and other physical
attributes could be entirely dissimilar from the standpoint of ability
to withstand losses attributed to uncertainty.

Uncertainty and the Human Factor

During the course of a lifetime, human beings are faced with
financial risks and often make commitments which they may have no
assurance of being able to meet. For example, a family purchasing a
home under a 20-year repayment plan is gambling that payments over this
extended period of time will be met regularly; that deflation will not
devalue the dollar to the point where commitments made at the outset will
be impossible to meet; and that the family breadwinner will be able to
retain his health and steady employment with a regular paycheck to meet
mortgage payments over and above fixed living expenses.

People also indulge in games of chance, often by choice. Without
gamblers willing to risk small and/or large sums of money, the pari-
mutuel windows at the race track would be empty and gambling casinos
would close their doors for lack of business. Although there are
impulsive gamblers who may risk savings, home, and future security at
the expense of their families' welfare, the majority of gamblers are
indulging in a pastime or game by wagering small amounts that will not
jeopardize the rent money or insurance payments, but sums large enough
to make the game "interesting." Gambling to many individuals is a form
of entertainment that can be exercised as personal circumstances dictate.

Farming also is a gamble. The farmer finds himself in the same
category as the impulsive gambler. Unless he combines seed, fertilizer,
and other production factors with land, he will have no chance of a crop.
Moreover, these production factors invested in the hope of obtaining a
return sufficient to cover family living and other obligations may be
lost completely unless the correct combination of conditions, many of
which are beyond his control, occurs.








-12-


Traditional analyses of farm management problems have assumed
(a) that the objectives of the farm operator/manager are to maximize net
income, and (b) that farmers have quite definite expectations about the
consequences of alternative lines of action. These two assumptions
correspond closely to the purely theoretical perfect knowledge concept.
Both assumptions are open to criticism. Similar to other entrepreneurs,
farmers are motivated by prospects of profit. But farmers, because of
the firm household relationship and the uncertainty involved, also must
be concerned about security and welfare of the family. Difficulty
exists in determining the combination of security and profit that is
optimum to the individual and what factors influence the decision for
determining this combination.

The second assumption stated above cannot hold true in farmer
decision making. It is impossible to formulate definite expectations
of the future with uncertain weather, prices, and other conditions that
will prevail and change between the time production decisions are made
and the actual product becomes marketable. Decisions by the farmer must
rest on the subjective formulation of future expectations. Again, it is
difficult to determine how a farmer's expectations are influenced by his
goals, his psychological reactions to risk and uncertainty, habits,
customs, and/or other factors.

Katona, in his analysis of economic behaviour of businessmen,
indicated two different types of environment that influence decision
making on the part of businessmen. Two human beings can well be
confronted with identical situations. This would mean they had the same
"geographic environment." Their reactions to this geographic
environment might not be identical. Consequently, the "behavioral
environment" of the two individuals must be different.

This can be illustrated by hypothesizing the actions and
reactions of farmers to identical situations. All farmers in a par-
ticular community may be confronted with relatively identical weather
and price outlook information when the production decision is reached.
Many of them may have very similar resource situations. Yet, based on
a relatively homogenous situation comparable to Katona's geographic
environment, many different enterprise and factor input combinations
will likely occur. That is, the individuals react differently to the
geographic environment. Their behavioral environments are different.

An Iowa study supports the above hypothesis.15 Fifty-four
farmers were interviewed in six central Iowa counties to determine


14Katona, G., Psychological Analysis of Economic Behaviour,
McGraw-Hill, New York, 1951.

15Brownlee, 0. H., and Gainer, Walter, "Farmers Price Antici-
pations and the Role of Uncertainty in Farm Planning," Journal of Farm
Economics, Vol. 31, No. 3, February 1959, pp. 266-275.








-13-


farmers' expectations for the most probable future prices of specific
commodities, the dispersion of these price expectancies, their production
plans, and the uncertainty preferences of these farmers. The survey was
conducted in early spring of 1947 and specific price expectations were
for December of the same year. Results showed that the most probable
anticipated price per bushel of corn ranged from a high of $1.50 to a
low of $.75 per bushel. The mode of the frequency distribution was
$1.00 per bushel, which was actually below the cash price of corn at the
time of the interview. For soybeans, the probable anticipated price
range was from $3.70 to $1.80 per bushel.

Another important aspect of this study was that the majority of
the farmers' answers to a question on most probable average expected
yield for the coming five-year period indicated that they anticipated a
yield very similar to what they had received in the immediate past five
years. This reaction was not unanimous. Some indicated higher expected
averages due to anticipated technological advances and some indicated
lower expected averages due primarily to unfavorable weather expectations.

The farmers in this study also were questioned about the differ-
ences in their actual 1946 acreages and their plans for the coming 1947
season. In corn acreage, 76 per cent indicated they were planning to
either increase or decrease acreage and the remaining 24 per cent to
hold close to the 1946 acreage. The reasons for the changes planned were
as follows:
Per Cent

Last minute contingencies of the weather 7
Feed and livestock requirements 20
Price and anticipated profitability 30
Soil improvement and rotational influence 43

This data indicated considerable inflexibility in crop plan
changes as a result of anticipated price changes. Additional support
was given to this hypothesis when these farmers were questioned as to
what their reaction would be to a 20 per cent increase in anticipated
price. Only two farmers indicated that they would expand their corn
acreage. Another conclusion from this study indicates that farmers'
plans are highly inflexible and that they lack confidence in their
anticipations. Another point brought out in this study was that farmers
in this group attached considerable more confidence in anticipated
future yields than in anticipated future prices. Apparently, they
attached more uncertainty to prices than to the weather.








-14-


CHAPTER II

OBJECTIVES AND PROCEDURE OF THE STUDY


An agricultural producer, faced with imperfect knowledge of
future events and occurrences, must base his decisions on subjective
predictions of future occurrences. These predictions of expectations
will vary among individuals in that each individual may interpret
differently the uncertainties associated with yields, product prices,
factor costs, technological changes, and government programs. Such
predictions and consequent action may well be influenced by the desire
for maximum income or profits, tempered by recognition on the part of
the individual that an incorrect decision, or a series of incorrect
decisions, may work a hardship on the household or threaten the existence
of the firm under his control.

General Hypothesis

This study is based on the hypothesis that differences do exist
in the individual's subjective prediction of future occurrences and that
the basic factors causing these differences, and therefore affecting the
individual's decision-making process, include the (a) physical farm firm
characteristics such as business size, equity, debt structure, and
capital position, (b) personal characteristics of the individual such as
age and educational level, and (c) existing unique firm-household
relationship.

It is further hypothesized that the inter-relationship of these
basic factors affects the emphasis that each individual will place on
the desire for maximum profits weighed against the desire and need for
security. This profit versus income security conflict therefore allows
categorizing individual decision makers into (a) security-seeking
maximiners, (b) maximaxers aiming towards the highest attainable profit
regardless of security cost, and (c) the group between who sacrifice
varying amounts of profit returns for varying degrees of income security.

Objectives

The broad objectives of this study are to determine (1) the
influences of physical farm characteristics, inherent psychological
makeup, and firm-household relationships on the decision-making patterns
of North Dakota farmers, and (2) if the variations in behavioral
patterns lend themselves to the broad classifications of game/decision
theory models.

If classification of behavioral patterns is possible, it could be
of great assistance to both agricultural workers concerned with releasing
experimental findings in the form of recommendations to farmers and
farmers concerned with making maximum use of new technology on their own
farm unit under their own unique circumstances.








-14-


CHAPTER II

OBJECTIVES AND PROCEDURE OF THE STUDY


An agricultural producer, faced with imperfect knowledge of
future events and occurrences, must base his decisions on subjective
predictions of future occurrences. These predictions of expectations
will vary among individuals in that each individual may interpret
differently the uncertainties associated with yields, product prices,
factor costs, technological changes, and government programs. Such
predictions and consequent action may well be influenced by the desire
for maximum income or profits, tempered by recognition on the part of
the individual that an incorrect decision, or a series of incorrect
decisions, may work a hardship on the household or threaten the existence
of the firm under his control.

General Hypothesis

This study is based on the hypothesis that differences do exist
in the individual's subjective prediction of future occurrences and that
the basic factors causing these differences, and therefore affecting the
individual's decision-making process, include the (a) physical farm firm
characteristics such as business size, equity, debt structure, and
capital position, (b) personal characteristics of the individual such as
age and educational level, and (c) existing unique firm-household
relationship.

It is further hypothesized that the inter-relationship of these
basic factors affects the emphasis that each individual will place on
the desire for maximum profits weighed against the desire and need for
security. This profit versus income security conflict therefore allows
categorizing individual decision makers into (a) security-seeking
maximiners, (b) maximaxers aiming towards the highest attainable profit
regardless of security cost, and (c) the group between who sacrifice
varying amounts of profit returns for varying degrees of income security.

Objectives

The broad objectives of this study are to determine (1) the
influences of physical farm characteristics, inherent psychological
makeup, and firm-household relationships on the decision-making patterns
of North Dakota farmers, and (2) if the variations in behavioral
patterns lend themselves to the broad classifications of game/decision
theory models.

If classification of behavioral patterns is possible, it could be
of great assistance to both agricultural workers concerned with releasing
experimental findings in the form of recommendations to farmers and
farmers concerned with making maximum use of new technology on their own
farm unit under their own unique circumstances.








-14-


CHAPTER II

OBJECTIVES AND PROCEDURE OF THE STUDY


An agricultural producer, faced with imperfect knowledge of
future events and occurrences, must base his decisions on subjective
predictions of future occurrences. These predictions of expectations
will vary among individuals in that each individual may interpret
differently the uncertainties associated with yields, product prices,
factor costs, technological changes, and government programs. Such
predictions and consequent action may well be influenced by the desire
for maximum income or profits, tempered by recognition on the part of
the individual that an incorrect decision, or a series of incorrect
decisions, may work a hardship on the household or threaten the existence
of the firm under his control.

General Hypothesis

This study is based on the hypothesis that differences do exist
in the individual's subjective prediction of future occurrences and that
the basic factors causing these differences, and therefore affecting the
individual's decision-making process, include the (a) physical farm firm
characteristics such as business size, equity, debt structure, and
capital position, (b) personal characteristics of the individual such as
age and educational level, and (c) existing unique firm-household
relationship.

It is further hypothesized that the inter-relationship of these
basic factors affects the emphasis that each individual will place on
the desire for maximum profits weighed against the desire and need for
security. This profit versus income security conflict therefore allows
categorizing individual decision makers into (a) security-seeking
maximiners, (b) maximaxers aiming towards the highest attainable profit
regardless of security cost, and (c) the group between who sacrifice
varying amounts of profit returns for varying degrees of income security.

Objectives

The broad objectives of this study are to determine (1) the
influences of physical farm characteristics, inherent psychological
makeup, and firm-household relationships on the decision-making patterns
of North Dakota farmers, and (2) if the variations in behavioral
patterns lend themselves to the broad classifications of game/decision
theory models.

If classification of behavioral patterns is possible, it could be
of great assistance to both agricultural workers concerned with releasing
experimental findings in the form of recommendations to farmers and
farmers concerned with making maximum use of new technology on their own
farm unit under their own unique circumstances.








-15-


The major function of the Cooperative Extension Service has been
to supply agricultural producers with data that will assist them in
formulating expectations of future occurrences. In the past, the
majority of these recommendations have been based on average results
determined over a period of time and released in the form of single-
valued expectations with little, if any, emphasis on the variance or
probable range of results that have and could occur through the use of
this particular recommended practice. The assumptions underlying these
recommendations inherently assume that (1) all farmers will benefit from
the acceptance of this particular resource use method, and (2) all
farmers are one large homogenous group with identical expectations, risk
and uncertainty preference levels, capital and equity positions, discount
rates, and ends or goals to be maximized.

The homogeneity referred to above does not exist. If it did, all
North Dakota farmers would be applying fertilizer at recommended rates
for their specific area and soil type, It is a proven fact that they do
not. However, if resource use recommendations from experimental data,
released through Experiment Station and Extension Service media, were
tailored to the widely divergent economic and psychological character-
istics of the farm-firm-family complex, these recommendations should
gain faster and more complete acceptance and thereby benefit a larger
percentage of the agricultural producers.

The specific objectives of this study are:

1. To trace the development of game-decision theory models
and their application to empirical data under risk and
uncertainty situations.

2. To apply the concepts of decision theory to actual
decision making under uncertainty of North Dakota farm
operators.

3. To determine the relative uncertainty preferences of
farmers as affected by their age, educational level,
family responsibilities, equity in the farm business,
amount of capital managed, and tenure position.


Procedure

A cursory understanding of the general structure that forms the
framework for the theory of games and related decision theories is
mandatory for this study. Thus, the two succeeding chapters of this
treatise discuss (a) the development and underlying hypothesis within
the structure of game and decision theory, and (b) the mechanical
application of game and decision theory hypotheses to payoff matrices
in general and to matrices with farmer-nature resource use-return
conflicts.








-16-


A random sample of North Dakota farm operators, in selected areas,
was personally interviewed.1 Survey questions were designed to
establish (a) the physical and financial position of each individual,
and (b) the relative uncertainty preference of each farmer through the
use of hypothetical enterprise and resource use matrices. The choices
in each matrix were designed to coincide with one or more of the
presently developed decision theories.













































Refer to Chapter V for detailed discussion of sample selection,
survey questions, hypothetical payoff matrices, and relevant decision
theory applications.











-17-


CHAPTER III

DEVELOPMENT AND CONCEPTS OF GAME THEORY

The purpose of this chapter is to briefly trace the development
of game theory, its applicability to agricultural production decisions,
and review the basic framework that has been incorporated into the
decision theories designed to fit the farmer versus nature decision
problems.

The theory of games to explain economic behavior was first
published by J, Von Neumann in 1928.1 He was a mathematician interested
in developing a mathematical approach to describe and determine conflicts
of interest which could be classified as rational economic behavior.

His original papers apparently stimulated little interest in the
empirical sciences that should be most interested in conflicts of
interest. Von Neumann's paper, written by a mathematician, was of prime
interest to other mathematicians. Later, Von Neumann and Oskar
Morgenstern, an economist, collaborated to write the now generally
accepted reference to game theory, with the original edition appearing
in 1944 and the revised edition in 1947.2 This volume, though highly
technical, was written so that scientists with a more limited mathe-
matical training could absorb the motivation, reasoning, and conclusion
of the theory.

The decision making alternatives of earlier literature, before
the development of the theory of games, were based on the neoclassical
utility approach of Jevons and Menger and the indifference approach of
Pareto, Hicks, and Allen which ranked or indicated indifference between
two or more choices.

Von Neumann and Morgenstern went beyond the ordinal utility
measure which assigns a ranking to a set of items with a non-numerical
preference scale. That is, the ordinal utility measure simply indicates
alternative A may be preferred to alternative B, but this measure does
not indicate the degree of preference involved. The Neumann-Morgenstern
cardinal utility index measure is designed to convey additional infor-
mation with preference ranking. It is specific in that it is intended
for use in predicting which of several risky propositions may be
preferred. It can be used to indicate which of two risky alternatives,
such as two lottery tickets with different winning odds and prices, a
person would prefer. The index is calculated after the decision maker



1Von Neumann, John, "Zur Theorie der Gesellschaftsspiele,"
Mathematical nal, Vol. 10, 1928.
2Von Neumann, John, and Morgenstern, Oskar, Theory of Games and
Economic Behavior, Princeton University Press, Princeton, New Jersey, 1947.







-18-


has indicated his ranking of alternative prizes, given the odds on each
prize.

Commonly Used Game Theory Terminology

The theory of games employs a more or less standardized set of
terms that must be understood to keep the various concepts in their true
perspective.

Game: As commonly used in the English language, the term "game"
is ambiguous when applied to game theory. This can be illustrated with
two statements such as (a) "Should we play a game of cribbage?" and
(b) "How many games should we play?" The word "game" has two distinctly
different meanings in statements (a) and (b). In statement (a), it
refers to the complete set of rules governing cribbage. A player
familiar with cribbage would immediately recognize what was referred to
when the word game is used in this context. In statement (b), the word
"game" refers to the number of times that the set of rules governing
cribbage will be applied,

In the theory of games, the word "game" will refer to the set of
rules or conventions which specify what the players must do. This is
similar to the meaning as used in statement (a).

Play: This term refers to the set of moves that comprise a
complete game. "Play," as used in the theory of games, has the same
meaning as implied by the word game in statement (b) above. In this
context, the second phrase would then read "How many 'plays' of cribbage
should we play?"

Move: A selection of one alternative from a set of alternatives;
a "move" is part of the "play."

Choice: This term signifies the alternative actually selected.

Strategy: A set of moves open to a player.



3For a more complete discussion of the Neumann-Morgenstern
cardinal utility measure, refer to (a) Von Neumann, John, and Morgenstern,
Oskar, Theory of Games and Economic Behavior, Princeton University Press,
Princeton, New Jersey, 1947; (b) Luce, R. Duncan, and Raiffa, Howard,
Games and Decisions, Introduction and Critical Survey, Wiley, New York,
1957; or, for a simple discussion, refer to (c) Baumol, W. J., Economic
Theory and Operations Analysis, Prentice-Hall, Inc., Englewood Cliffs,
New Jersey, 1961.

4The majority of the definitions are drawn from (a) Beady, Earl 0.
and Candler, Wilfred, Linear Programming Methods, The Iowa State College
Press, Ames, Iowa, 1958; and (b) McKinzie, J. C. C., Introduction to
Theory of Games, McGraw-Hill, New York, 1952.







-19-


Solution of the game: The selection of the best strategy by each
player from the payoff matrix.

Payoff matrix: This term refers to the table which indicates the
returns or results that will accrue to the player from the alternative
strategies open to him.

Payments: In discussing economic applications of game theory,
this term normally refers to monetary payments under the assumption that
all plays or game solutions are for gain or profit. This assumption,
that all plays are for monetary gains, does not necessarily always hold
true. But, under this assumption, it is possible to measure gains and
losses by either player. For example, in a cribbage game there are three
payoff alternatives open to the players when the play is completed. The
first alternative may be that, after totaling the score, a sum of money
changes hands, the amount depending on the number of points by which the
winner outscored his opponent. The second alternative may be to announce
that player A win by X points. Player A would reap a certain amount of
satisfaction representing his gain from, first, winning and, second, a
certain amount of satisfaction from the point spread under the
assumption that this spread tends to indicate the relative skills of the
players. Alternative three may be simply to announce that player A won.

In the examples and the analysis used in this study, the latter
two alternatives will be ignored and only the first alternative, the one
measurable in dollars and cents, will be used. Thus, at the completion
of a play the size of payment will indicate the satisfaction derived by
the winner.

Game Classification According to
Number of Persons Involved

Two person game involves two opponents or factions in a common
situation such as may be found in a game of chess, a conflict between
nations, a tenant and landlord in a leasing arrangement, or two
industrial giants battling for the highest percentage of a relatively
fixed total market. Although this term may imply that only one "person"
can be involved on either side, this is not necessarily so. For example,
in a conflict between two nations, one player or opponent could consist
of several nations on one or either side as long as this group has a
specific common interest.

N person game refers to one played by more than two players or
opponents. Therefore, in an "n" person game there are more than two
opponents or interests.

Games Classified According to Strategies

In game theory, differentiation also is made between the choices
open to a player. These choices are classified either as "pure" or
"mixed" strategies as the case may be.







-19-


Solution of the game: The selection of the best strategy by each
player from the payoff matrix.

Payoff matrix: This term refers to the table which indicates the
returns or results that will accrue to the player from the alternative
strategies open to him.

Payments: In discussing economic applications of game theory,
this term normally refers to monetary payments under the assumption that
all plays or game solutions are for gain or profit. This assumption,
that all plays are for monetary gains, does not necessarily always hold
true. But, under this assumption, it is possible to measure gains and
losses by either player. For example, in a cribbage game there are three
payoff alternatives open to the players when the play is completed. The
first alternative may be that, after totaling the score, a sum of money
changes hands, the amount depending on the number of points by which the
winner outscored his opponent. The second alternative may be to announce
that player A win by X points. Player A would reap a certain amount of
satisfaction representing his gain from, first, winning and, second, a
certain amount of satisfaction from the point spread under the
assumption that this spread tends to indicate the relative skills of the
players. Alternative three may be simply to announce that player A won.

In the examples and the analysis used in this study, the latter
two alternatives will be ignored and only the first alternative, the one
measurable in dollars and cents, will be used. Thus, at the completion
of a play the size of payment will indicate the satisfaction derived by
the winner.

Game Classification According to
Number of Persons Involved

Two person game involves two opponents or factions in a common
situation such as may be found in a game of chess, a conflict between
nations, a tenant and landlord in a leasing arrangement, or two
industrial giants battling for the highest percentage of a relatively
fixed total market. Although this term may imply that only one "person"
can be involved on either side, this is not necessarily so. For example,
in a conflict between two nations, one player or opponent could consist
of several nations on one or either side as long as this group has a
specific common interest.

N person game refers to one played by more than two players or
opponents. Therefore, in an "n" person game there are more than two
opponents or interests.

Games Classified According to Strategies

In game theory, differentiation also is made between the choices
open to a player. These choices are classified either as "pure" or
"mixed" strategies as the case may be.







-20-


Pure strategy refers to a single strategy or move that a player
makes or has open to him. Use of this choice would be in a situation
where the player's best alternative is the highest security or payoff
level, or, where even though several strategies may be open to him before
the move is made, there is only one final choice. This situation is
typical of a cattle feeder with a single lot in which to feed cattle.
When the lot is empty, the feeder has alternatives of feeding steer or
heifer calves, short or long yearlings, cows, bulls, dairy or beef stock
and so on. There are many alternatives, but he has to settle for one
specific alternative. That is, the only move open to him is whether or
not to feed cattle. When this decision is made, a single class of live-
stock must be selected because of the physical limitations of the
facilities. In this example, a pure strategy choice is involved.

However, if a portable divider was available for this single
feedlot, the feeder could select two classes of livestock to feed. In
this situation, a "mixed" strategy would be involved.

Mixed strategy refers to the possibility of using a random
devices) to select the order of the strategy moves in a play that
involves more than one move. If the game is to be played only once, a
mixed strategy will indicate the probabilities of the strategies avail-
able. When a combination of choices is possible, a mixed strategy will
indicate the degree in which each strategy should be employed.

This can be illustrated and clarified by the example of a farmer
determining his annual cropping program. The alternatives open to him
may include growing oats, barley, wheat, flax or any cultivated grain
crop. His best strategy will depend on his past yield history, which
indicates the productive capacity of his soil types for the various
crops and the price outlook for each. The corresponding data would make
up his "payoff matrix," A pure strategy would mean growing only one of
the alternative crops open to him. A mixed strategy would be to place a
percentage of his tillable land in two or more of the available alterna-
tive grain crops.

Games Classified According to Payoff

Game theory also employs a classification according to the payoff
or the payment involved.

Zero-sum game is a classification in which the sum of the payments
upon completion of the game is zero. That is, the sum won by player A is
exactly equal to the sum lost by player B, Most parlor games would fall
into this classification.

Non-zero-sum game is a classification in which the total payments,
that is, the gain of one player and the loss of the other, do not cancel
out or equal zero. An example of this would be a card game in a gambling







-21-


casino when the casino withholds a certain percentage of the stakes
wagered. The gains of the winning players would then be less by the
amount withheld by the casino than the losses of the losing players.

Much literature on game theory has dealt with the zero-sum, two-
person games. However, many of the real life problems, particularly
those associated with ologopolistic types of business firms where
collusion and cooperation in one form or another may likely be profitable,
involve non-zero-sum and often n-person,games.

Game Theory Applied to Agriculture

In agricultural production where pure competition and relatively
inelastic product demand is prevalent, the individual farmer could
conceivably regard himself as one player and all other farmers combined
as the other player or opponent. This situation becomes unrealistic
when consideration is given to the minute percentage of the total that
one farm operator produces and the insignificant effect one individual's
production will have on the price received by all producers.

There may be times, however, when the individual producer could
regard all other producers as an opponent and when his actions,
different from the majority action, will increase his profits. Such
would be the case in the occurring and reoccurring price and production
cycles of livestock. That is, when the majority of producers are
decreasing herd size, an individual farmer would find it profitable to
increase herd size to take advantage of the higher cattle prices that
occur when total supply decreases over time. In so doing, the individual
farmer is making use of all information available in his future payoff
matrix. However, most producers tend to make their decisions on the
basis of the present payoff matrix and not on the matrix that would be
in effect when either the increased or decreased production reaches the
market, as the case may be.

Since the individual farmer does not have a single identifiable
opponent, the two-person game does not lend itself well to analysis of
farmer situations. However, additional theories adaptable to the farmer-
nature relationship have been developed. A review of the theory behind
the two-person, zero-sum game is necessary to obtain adequate background
information to fully understand the "complete ignorance of future
occurrences" which more accurately fits the farmer versus nature concept.

Zero-Sum, Two-Person Game

A two-person, zero-sum game involves a competitive struggle
between two players opposing each other. Every gain by one player
represents a loss to the other. An example of this situation is a war
between nations or with two firms competing for their respective share
of a predetermined market for a similar or identical product. Each
player or opponent has a finite number of courses of action called a







-21-


casino when the casino withholds a certain percentage of the stakes
wagered. The gains of the winning players would then be less by the
amount withheld by the casino than the losses of the losing players.

Much literature on game theory has dealt with the zero-sum, two-
person games. However, many of the real life problems, particularly
those associated with ologopolistic types of business firms where
collusion and cooperation in one form or another may likely be profitable,
involve non-zero-sum and often n-person,games.

Game Theory Applied to Agriculture

In agricultural production where pure competition and relatively
inelastic product demand is prevalent, the individual farmer could
conceivably regard himself as one player and all other farmers combined
as the other player or opponent. This situation becomes unrealistic
when consideration is given to the minute percentage of the total that
one farm operator produces and the insignificant effect one individual's
production will have on the price received by all producers.

There may be times, however, when the individual producer could
regard all other producers as an opponent and when his actions,
different from the majority action, will increase his profits. Such
would be the case in the occurring and reoccurring price and production
cycles of livestock. That is, when the majority of producers are
decreasing herd size, an individual farmer would find it profitable to
increase herd size to take advantage of the higher cattle prices that
occur when total supply decreases over time. In so doing, the individual
farmer is making use of all information available in his future payoff
matrix. However, most producers tend to make their decisions on the
basis of the present payoff matrix and not on the matrix that would be
in effect when either the increased or decreased production reaches the
market, as the case may be.

Since the individual farmer does not have a single identifiable
opponent, the two-person game does not lend itself well to analysis of
farmer situations. However, additional theories adaptable to the farmer-
nature relationship have been developed. A review of the theory behind
the two-person, zero-sum game is necessary to obtain adequate background
information to fully understand the "complete ignorance of future
occurrences" which more accurately fits the farmer versus nature concept.

Zero-Sum, Two-Person Game

A two-person, zero-sum game involves a competitive struggle
between two players opposing each other. Every gain by one player
represents a loss to the other. An example of this situation is a war
between nations or with two firms competing for their respective share
of a predetermined market for a similar or identical product. Each
player or opponent has a finite number of courses of action called a








-22-


"strategy set" that are open to them. These courses of action may be
expressed as:

S, = al,a2,a3 .. am

S2 = b1,b2,b3 .* bn

where S1 and 82 indicate the strategy choices for players 1 and 2,
respectively. The decision of the players must be made simultaneously or
without knowledge of each other's decisions. These choices of action
will then determine the payoff that each player will receive. These are
usually presented in tabular form called a "payoff matrix." The payoff
matrix indicates the payoff for one player and implies the payoff for the
other. Each player has a payoff matrix and the selection of which
player's payoff matrix is used is entirely arbitrary. Either one will
give the same results.

A numerical example of a zero-sum, two-person game can be
illustrated by assuming that there are only two firms producing a product
for a predetermined market and that each firm is interested in obtaining
the largest possible share of the total market. Under the assumption
that each player has three alternative strategies, such as three methods
of advertising their respective products, the payoff matrix for player A
could appear as follows:


Matrix 1 PLAYER A's PAYOFF MATRIX

B's strategy choices

1 2 3

A's 1 28 20 26

Strategy 2 13 18 60

Choices 3 40 16 17


If A chose strategy I, his percentage share of the market would
be 28, 20, or 26 per cent, depending on whether player B chooses
strategy 1, 2, or 3, respectively. Under the assumption of only two
firms producing the product, their combined market share would be 100
per cent. Therefore, player B's payoff in this example would be 100
per cent minus player A's payoff or market share. This would give
player B the following payoff matrix:








-23-


Matrix 2 PLAYER B's PAYOFF MATRIX

B's strategy choices

1 2 3

B's 1 72 80 74

Strategy 2 87 82 40

Choices 3 60 84 83


From Matrix 1, with player A selecting strategy 2 and player B
choosing strategy 3 (referred to as an A2B3combination), player A would
obtain 60 per cent of the total market. From matrix 2, which represents
B's payoffs, the same A2B3 combination would result in player B
attaining a 40 per cent market share. Therefore, player A's and player
B's shares total up to 100 per cent. In tabulating the payoff matrix
in game theory, it is necessary to indicate only one player's matrix
because his opponent's payoff is implied. For illustrative purposes in
the remainder of this section, A's payoff matrix will be arbitrarily
used. Player A is also then considered as the maximizing player in that
he will try to obtain the highest return from his payoff matrix.
Conversely, player B will be considered as the minimizing player.

The Maximin Stratevg

With A2B3 strategy combination in the foregoing example,
player A would receive 60 per cent of the total market ahare. It is
apparent that player A would be well satisfied with this combination of
strategies and the resulting payoff because it is the highest share
attainable for him. However, in the two-person, zero-sum game, an
implicit assumption is that the information contained in the payoff
matrix is known to both participating players. It would then be apparent
to player B that his strategy 3 would be a poor choice because it could
give player A the maximum share and player B the minimum share of the
available market.

The cautious method of approaching this problem is for both
players to assume that their opponents would use the strategy that limits
the other player to the lowest payoff. Under this criteria, each player
would then act accordingly.

Player A, in considering the use of strategy 1, would assume that
player B would employ strategy 2 and leave player A with only 20 per cent
of the total market (combination A1B2 from matrix 1). It follows that
with player A's strategy 2 the best tactic for player B would be to
employ his strategy 1 and limit player A to 13 per cent of the total
market share (combination A2B1 from matrix 1). With player A's strategy







-24-


3, player B would employ strategy 2 and player A would receive 16 per
cent of the total market share (combination A3B2 from matrix 1).

The optimum strategy for both players, under the assumption that
both adopt the fatalistic viewpoint that the other will employ the most
beneficial strategy for himself, would be to employ the strategy that
will guarantee them the "best of the worst," or the maximum of the
minimum payoffs. By considering again matrix 1, the minimum payoffs in
each of A's strategies (the rows) are Al--20 per cent, A2--13 per cent,
and A3--16 per cent. The largest or maximum of these minimums would be
Al. Player A, by selecting strategy 1, would guarantee himself that
whatever act player B selects it is impossible for player A to obtain
less than20 per cent of the total market share. This course of action,
or selecting the maximum of the minimums, is called following the
"maximin" strategy by the maximizing player.

The Minimax Strategy

Player B's aim is to keep player A's share of the market as low
as possible; that is, trying to minimize player A's share. In so doing,
player B retains the highest possible share for himself. If player B
selected strategy 1, player A might select strategy 3 (A3B1 combination
from matrix 1). This would give player A a 40 per cent market share.
With player B's strategy 2, player A could select strategy 1 and get a
20 per cent market share. With player B's strategy 3, player A would
most likely select strategy 2 and obtain a 60 per cent market share.
The maximum payoffs that player A could obtain with each of player B's
strategies would be 40 per cent, 20 per cent, and 60 per cent,
respectively. Under the assumption that player A is rational and would
like to guarantee himself the highest attainable share, player B,
acting rationally and trying to limit player A to the lowest share
possible, would select the minimum of the maximums that player A could
get with each of player B's strategies. This is called following the
"minimax" strategy by the minimizing player.

The Saddlepoint

An equilibrium or "saddlepoint" exists in a payoff matrix when
one player's maximin strategy coincides with the opposing player's
minimax strategy. This can be illustrated by repeating the data in
matrix 1 as follows:

Matrix 3 PLAYER A's PAYOFF MATRIX

B's strategy choices

1 2 3
A's 1 28 20* 26

Strategy 2 13 18 604
Choices 3 40# 16* 17

*The minimums of the rows -- A's strategies.
#The maximums of the columns -- B's strategies.







-24-


3, player B would employ strategy 2 and player A would receive 16 per
cent of the total market share (combination A3B2 from matrix 1).

The optimum strategy for both players, under the assumption that
both adopt the fatalistic viewpoint that the other will employ the most
beneficial strategy for himself, would be to employ the strategy that
will guarantee them the "best of the worst," or the maximum of the
minimum payoffs. By considering again matrix 1, the minimum payoffs in
each of A's strategies (the rows) are Al--20 per cent, A2--13 per cent,
and A3--16 per cent. The largest or maximum of these minimums would be
Al. Player A, by selecting strategy 1, would guarantee himself that
whatever act player B selects it is impossible for player A to obtain
less than20 per cent of the total market share. This course of action,
or selecting the maximum of the minimums, is called following the
"maximin" strategy by the maximizing player.

The Minimax Strategy

Player B's aim is to keep player A's share of the market as low
as possible; that is, trying to minimize player A's share. In so doing,
player B retains the highest possible share for himself. If player B
selected strategy 1, player A might select strategy 3 (A3B1 combination
from matrix 1). This would give player A a 40 per cent market share.
With player B's strategy 2, player A could select strategy 1 and get a
20 per cent market share. With player B's strategy 3, player A would
most likely select strategy 2 and obtain a 60 per cent market share.
The maximum payoffs that player A could obtain with each of player B's
strategies would be 40 per cent, 20 per cent, and 60 per cent,
respectively. Under the assumption that player A is rational and would
like to guarantee himself the highest attainable share, player B,
acting rationally and trying to limit player A to the lowest share
possible, would select the minimum of the maximums that player A could
get with each of player B's strategies. This is called following the
"minimax" strategy by the minimizing player.

The Saddlepoint

An equilibrium or "saddlepoint" exists in a payoff matrix when
one player's maximin strategy coincides with the opposing player's
minimax strategy. This can be illustrated by repeating the data in
matrix 1 as follows:

Matrix 3 PLAYER A's PAYOFF MATRIX

B's strategy choices

1 2 3
A's 1 28 20* 26

Strategy 2 13 18 604
Choices 3 40# 16* 17

*The minimums of the rows -- A's strategies.
#The maximums of the columns -- B's strategies.








-25-


In matrix 3, the minimums of the rows are 20, 13, and 16 for rows
Ai, A2, and A3, respectively. Player A, following the maximin rule,
would select strategy Al, the maximum of the minimums, which guarantees
him that player B cannot make a strategy choice that will give player A
less than 20 per cent of the market share.

The maximums of the columns are 40, 20, and 60 for columns Bl, B2,
and B3, respectively. Player B, following the minimax strategy, would
select strategy B2, which will guarantee him that whatever move player A
makes he cannot possibly get more than 20 per cent of the total market
share. Thus, player A's maximin strategy is identical to player B's
minimax strategy and the saddlepoint for this matrix is at A1B2. Such
an equilibrium point does not necessarily exist on every payoff matrix.
This situation will be discussed later.

Properties of Maximin-Minimax Strategies

Several deductions relative to the properties of the maximin-
minimax strategies can be made from matrix 3.

1. This strategy affords both parties the maximum protection
against each player's attempts to reduce the opponent's share below a
certain level. If player A selects strategy Al in the preceding example,
it is impossible for player B to select a strategy that will reduce
player A's share below 20 per cent. Conversely, if player B selects
strategy B2, there is no strategy available to player A that will
increase his market share over 20 per cent and therefore reduce player
B's share below 80 per cent.

2. A maximin-minimax strategy would be a poor move against a non
minimax-maximin strategy. The assumption has been made throughout that
both players A and B are equally well informed on the makeup of the
payoff matrix and that each is economically rational. If player B, for
various reasons such as ignorance or a gambling tendency, does not pursue
the minimax strategy, player A's maximin strategy would not be the most
profitable even though by following it he would still guarantee himself
a minimum of the market share. However, if player B employed strategy
B1 instead of his minimax B2, player A's best move would be A3 with a
resultant market share of 40 per cent. Obviously, the non maximin-
minimax strategies introduce instability and uncertainty into the frame-
work.

3. The maximin-minimax strategy combinations tend to create
internal stability in that each player recognizes that he will receive
the largest security share of the payoff.

Payoff Matrix Without a Saddlepoint

As indicated earlier, a payoff matrix does not necessarily have
the extremely handy saddlepoint that was found in matrix 3. Consider
the following payoff matrix:








-25-


In matrix 3, the minimums of the rows are 20, 13, and 16 for rows
Ai, A2, and A3, respectively. Player A, following the maximin rule,
would select strategy Al, the maximum of the minimums, which guarantees
him that player B cannot make a strategy choice that will give player A
less than 20 per cent of the market share.

The maximums of the columns are 40, 20, and 60 for columns Bl, B2,
and B3, respectively. Player B, following the minimax strategy, would
select strategy B2, which will guarantee him that whatever move player A
makes he cannot possibly get more than 20 per cent of the total market
share. Thus, player A's maximin strategy is identical to player B's
minimax strategy and the saddlepoint for this matrix is at A1B2. Such
an equilibrium point does not necessarily exist on every payoff matrix.
This situation will be discussed later.

Properties of Maximin-Minimax Strategies

Several deductions relative to the properties of the maximin-
minimax strategies can be made from matrix 3.

1. This strategy affords both parties the maximum protection
against each player's attempts to reduce the opponent's share below a
certain level. If player A selects strategy Al in the preceding example,
it is impossible for player B to select a strategy that will reduce
player A's share below 20 per cent. Conversely, if player B selects
strategy B2, there is no strategy available to player A that will
increase his market share over 20 per cent and therefore reduce player
B's share below 80 per cent.

2. A maximin-minimax strategy would be a poor move against a non
minimax-maximin strategy. The assumption has been made throughout that
both players A and B are equally well informed on the makeup of the
payoff matrix and that each is economically rational. If player B, for
various reasons such as ignorance or a gambling tendency, does not pursue
the minimax strategy, player A's maximin strategy would not be the most
profitable even though by following it he would still guarantee himself
a minimum of the market share. However, if player B employed strategy
B1 instead of his minimax B2, player A's best move would be A3 with a
resultant market share of 40 per cent. Obviously, the non maximin-
minimax strategies introduce instability and uncertainty into the frame-
work.

3. The maximin-minimax strategy combinations tend to create
internal stability in that each player recognizes that he will receive
the largest security share of the payoff.

Payoff Matrix Without a Saddlepoint

As indicated earlier, a payoff matrix does not necessarily have
the extremely handy saddlepoint that was found in matrix 3. Consider
the following payoff matrix:







-26-


Matrix 4 PLAYER A's PAYOFF MATRIX

B's strategy choices

1 2

A's 1 30# 10*

Strategy 2 20 40#

Choices

*Minimums of the rows--player A's strategies.
#Maximums of the columns--player B's strategies.


Player A's maximin strategy would be A2 because 20 is the largest
of the two minimum payoffs in each row. The minimum payoffs in the two
rows are starred. Player B's minimax strategy would be Bl; that is, the
smallest of the largest payoffs in the columns. Accordingly, an equi-
librium or saddlepoint does not exist in matrix 4. The maximin strategy
A2B1 does not coincide with the minimal: strategy BlA1. If both players
A and B pursue the maximin-minimax approach, player A's payoff would be
the 20 that he anticipated receiving which is less than the 30 that
player B expected him to get when he selected strategy B1. Player B
would be pleasantly surprised.

Even without the saddlepoint, the maximin-minimax strategy for
both players affords the highest degree of protection. It is apparent
that, if player A suspects that player B will follow the minimax
strategy and choose strategy B1, player A should use strategy Al and get
a 30 per cent share of the market. Conversely, if player B suspects that
player A will not follow his maximin strategy because player A is willing
to gamble that player B will not follow his minimax strategy, then player
B should use his non minimax B2 and restrict player A's share to 10. It
is apparent that the stability of player's choices is lost in the matrix
without a saddlepoint.

Mixed Strategy With Non Saddlepoint Matrix

A game without a saddlepoint calls for special strategy treatment.
With a saddlepoint, a pure strategy will afford maximum protection to
both players. As indicated earlier, without the saddlepoint, player A
could profitably employ a non maximin strategy if player B employs the
minimax strategy and, conversely, player B could profitably employ the
non minimax strategy if he suspects that player A will follow the non
maximin strategy. Without the saddlepoint, the wise business policy to
follow would be to keep the opponent guessing as to which strategy will
be employed. One method of executing such a policy is to use a random
device to select the strategy choice, thus avoiding establishment of a








-27-


pattern which the opponent may recognize and advantageously utilize.
This procedure is called using a "mixed strategy."

With the non saddlepoint payoff matrix, it is possible to
increase the security levels of both competitors through the use of a
mixed random strategy.

To illustrate this concept, one can arbitrarily assign a
probability of 1/3 to player A's strategy Al and 2/3 to strategy A2. If
player B then employs strategy Bl, the value of player A's probable
share from matrix 4 would be:

(1/3 X 30) + (2/3 X 20) = 22 2/3

If player B employs strategy B2, player A's probable share would be:

(1/3 X 10) + (2/3 X 40) = 30

Both of these probable shares are larger than the 20 guaranteed
to player A with the use of the maximin strategy. Player A has thus
increased his payoff security level through the use of the mixed strategy.
If the game was played often enough, the mixed strategy would be more
profitable than the maximin strategy for player A. It is possible, of
course, that the payoffs which player A can anticipate would range from
a high of 40 with strategy combination A2B2 to a low of 10 with strategy
combination AlB1.

The probability with which player A should play either choice
strategy in the game where the moves are repeated can be calculated
mathematically. Using as an illustration the simple 2 X 2 example in
payoff matrix 4, one can assign a probability of "p" to player A's
strategy 1 and a probability of "1 p" to player A's strategy 2. The
total probability must add to 1. The next step is to calculate the
payoffs for player A with these assigned probabilities under player B's
strategies as follows:

Formula 1 30 p + 20 (1 p)

Formula 2 10 p 40 (1 p)

One can now set formula 1 equal to formula 2 and solve for p as follows:

30 p -- 20 (1 p) = 10 p + 40 (1 p)
30 p -- 20 20 p = 30 p :- 40
10 p + 20 = 30 p +- 40
40 p = 20
p = 1/2










From the above solution, if player A is to maximize his security
level through the use of a mixed strategy under payoff matrix 4, he
should employ a random device that would give him a mixed strategy use
of Al and A2 on a 50-50 basis. Substituting p = 1/2 into either formula
1 or 2 shows that player A should obtain a security payoff level of 25
with the random mixed strategy method using a probability of 1/2.

Determination of Probability in a
Large Non Saddlepoint Matrix

Simple mathematics can be used to determine the strategy play
probability in a simple 2 X 2 payoff matrix. 'ith a larger than 2 X 2
matrix, the strategy play probability and the optimum security level can
be solved with a modified simplex method of linear programming.

A very basic and fundamental difference exists between the
solution of the conventional linear programming problem and the solution
of a game theory payoff matrix. The conventional program is not
competitive in the sense that two or more players are involved. However,
the alternative processes in the problem are competitive with each other
for use of total available resources or restraints. If part or all
resource supplies are used in one process, it is impossible to reuse
these resources in another process.

The following 3 X 3 payoff matrix is used to illustrate how
strategy probabilities for both players A and B can be calculated
through the use of the modified simplex: method. Both their respective
gain and loss security levels can be maximized or minimized, depending
on the situation.

Matrix 5 PLAYER A's PAYOFF MATRIX

B's strategy choices

1 2 3

A's 1 0.2* 2.01 4.0

Strategy 2 1.0# 0.6* 2.0

Choices 3 0.8 0.5 0.2*

Minimums of the rows--A's strategies
#Maimums of the columns--B's strategies.


No saddlepoint exists in matrix 5. Consequently, it is likely that
a mixed strategy would give players A and B their highest security levels.
If player A, the maximizing player, considered a pure maximin strategy,
his choice would be strategy A2. Player B, the minimizing player,







-29-


considering a pure minimax strategy, would select strategy B1. Player A
in determining his maximin decision, would expect a gain of 0.6 (combi-
nation A2B2) but actually would receive a payoff of 1 (combination A2B1).
Accordingly, a mixed strategy for player B would be more advisable than
the minimax strategy.

The mixed strategy determined by player B would be designed to
minimize his losses regardless of the strategy choice made by player A.
In the simplex method, this probability of strategy use is designated
as an unknown "v." Player A wants to select a mixed strategy which will
guarantee that his gains will be as large or larger than the unknown "v"
regardless of what strategy combination player B chooses. Both players
are looking for strategy combination probabilities which will give
maximum gains or minimum losses as the case may be. Both are trying to
create an artificial saddlepoint with its inherent built in stability and
security.

Player B's probabilities of employing strategy B1, B2, or B3 arc
designated respectively as ql, q2, and q3. When each row of payoff
matrix 5 is multiplied by these q's the result is:

<
0.2 ql + 2.0 q2 + 4.0 q3= v

1.0 q1 + 0.6 q2 + 2.0 q3 v

0.8 q + 0.5 q2 + 0.2 q3 v

where

q + q2 q3 = 1

and

0 qi Z. I

The first three relationships in (1) represent the outcomes for player B
according to whichever strategy player A chooses. The outcome (loss)
would be equal to or less than the unknown "v". The fourth relationship
in (1) guarantees that the total strategy probability play will equal 1.

The first three relationships of (1) are comparable to the
production possibility equaticns in the conventional linear programming
problem which indicate that total resources used must not exceed
available resource supplies. In the game theory simplex probability
determination, these first three relationships sum up to the payoff for
player B if player A would play a pure strategy only.

There is a fundamental difference in the final results of the
conventional versus game programming problems. In conventional linear
programming, the purpose is to determine the kind and amount of resource
use that will result in maximum profits without exceeding available
resource supplies. In the game problem, the purpose is to determine the
size of the qi's or, in this case, the frequency with which a strategy
will be played to keep player B's losses to a minimum.







-30-


In conventional programming, the amount of resource supplies or
restraints are a known quantity and the program as set up in (1) could
be solved because the v's on the right hand side would be quantitative
figures.

In game programming, the "v" is an unknown quantity and must be
eliminated to make the program solution possible. Each relationship in
(1) must be divided through by "v" such that qi has been redefined as
4i where %i = qi/v:
0.2 -i1 2.0 -2 + 4.0 3 = 1

1.0 q1 + 0.6 q2 + 2.0 3 1

0.8 1 0.5 2 + 0.2 43 = 1

This manipulation eliminates the unknown "v" from the first three
relationships and makes a solution possible by the use of the standard
simplex procedure in that the problem now becomes one of maximization.
The fourth relationship of (1) becomes

i1 "'! 2 + 4 3 = 1/v
after dividing through by "v". Then, if 1/v is maximized, v auto-
matically will be minimized for player B.

As in conventional programming, the inequalities in (2) must be
changed to qualities through the addition of dummy strategies or slack
variables. These are signified as q4, q5, and q6 and added to each
relationship in (2) as follows:

0.2 q1 + 2.0 q2 + 4.0 q3 + q + 0 -- 0 = 1

1.0 q -1 0.6 q2 + 2.0 q3 +: 0 + q5 + 0 =

0.8 q1 0.5 q2 + 0.2 q3 +: 0 +- 0 -:- q6

The above can now be set up in the conventional linear programming form
of Table 3 because of the following relationships:

1. Activity columns PI P6 are equivalent to the payoff
columns indicated in matrix 3.

2. The l's on the right side of the qualities in the Po column
correspond to resource supplies.

3. Weights of the qi's from the fourth relationship of (1) are
equivalent to the prices used in conventional programming.

In the final matrix of Table 3, the figures in the Z C row under
the real activities Pi, P and P are all positive, which indicates that
the optimum strategy as een established.







-31-


TABLE 3. SOLUTION OF MODIFIED SIMPLEX PROGRAMMING METHOD MATRIX 5

C 0 0 0 1 1 1

Po P4 P5 P6 PI P2 P3 R

0<- P4 1 1 0 0 .2 2_ 4 .5
0 P5 1 0 1 0 1 .6 2 1.667

0 P6 1 0 0 1 .8 .5 .2 2

Z 0 0 0 0 0 0 0
*
Z C 0 0 0 0 -1 -1 -1


1 P .5 .5 0 0 .1 1 2 5

0 < P5 .7 -.3 1 0 .94 0 .8 .7447

0 P6 .75 -.25 0 1 .75 0 -.8 1

Z .5 .5 0 0 .1 1 2

Z-C 0 0 0 0 -.9 0 1


1 P2 .4255 .5319 -.1063 0 0 1 1.9149

1 >P .7447 -.319 1.063 0 1 0 .851

P .1915 -.0107 -.7973 1 0 0 -1.4382
6
Z 1.1702 .2129 .9567 0 1 1 2.7659

Z C 1.1702 .2129 .9567 0 0 0 1.7659








-32-


The quantities for rows P1 and P2 in the P column are '2 = .4255
and -1 = .7447, the sum of which is 1.1702 and appears in the Z C row
of the same column. This sum is equivalent to 1/v. Since qi i v,
the values for ql, q2, and q3 are:
.7447
7 = 63.64%
l = 1.170----
.4255
q = 1. = 36.36%
0
3 1.1702 = 0%

Accordingly, for player B to minimize his losses, he should
employ his B1 strategy 63.64 per cent of the time and his B2 strategy
36.36 per cent of the time. The unknown "v" would then be equal to the
reciprocal of
1
4,1 -'2 + -3 or 1.170 .85

Player B, using his strategies 1 and 2 in the above ratios, would
maintain his losses at a maximum of .85. Player B would not employ his
strategy B3 at all.

The strategy probabilities for the maximizing player A also may
be computed from the simplex programming (Table 3). For player B,
activities P4, P and P were dummy strategies. For player A, they
represent real strategies. The quantities in the Z-. C rows of the
disposal activities P4 and P which are equivalent to strategies 1 and
2 for player A, sum up to l. 696. The computations for strategy
probabilities use by player A, representing his row strategies as P1, P2,
and P3 are:
.2129
1= 1.1696 = 1.20
.9567
P2 = 1.1696 81.80%

P = 0 = 0%
S 1.1696

For player A to maximize his gains, he should employ his strategy A1
18.20 per cent of the time and his A2 strategy 81.80 per cent of the
time. Through this strategy use, player A would maintain his gains at
a minimum of .85.

This calculation of probabilities for both the maximizing player
and the minimizing player has created an artificial saddlepoint in a
game with a large number of moves with the same alternatives being
offered for each play.

5-3 = 0 because it does not appear in the final matrix.











The theory of games, therefore, does not necessarily point out
exactly what the participating players must do. It does point out the
strategy, or combination of strategies, if this is allowed, that should
result in the highest security level. Normally, this would be a pure
strategy where a saddlepoint exists, or it may involve a mixed strategy
in a game without a saddlepoint. The theory of games in the mixed
strategy setting determines the probabilities with which one or more
strategies should be played when the games are reported. Also, it may
indicate the percentage of each strategy that may be employed in a once
only game if a combination of strategies is feasible.








-34-


CHAPTER IV

DEVELOPMENT OF DECISION THEORY

The payoff matrix examples used in the preceding section illus-
trated the basic concepts of game theory in the two-person, zero-sum
game. There are further ramifications in non-constant sum games,
cooperative and non-cooperative games and n-person games, which may or
may not include coalitions where players combine against one another or
another combination of players.

In the examples thus far, the implicit assumption is that both
players or opponents have available to them all the information
contained in the payoff matrix, and that gains that occur to one player
with a certain strategy combination mean a loss to the opposing player.

These assumptions become irrelevant in the light of usual farmer
production decision making. In many cases, the farmer's opponent is
nature with its idiosyncracies of drought, average or abundant rainfall,
insects, diseases, hail and so on. But nature cannot be classified as a
conscious opponent as assumed in game theory, because nature neither
lies in wait to make the worst countermove against the strategy or
combination of strategies used by the farmer, nor does it count a gain
when the farmer incurs a loss. Game theory does not suffice for such
decision conditions.

The classic concepts of game theory fit well into the classi-
fication of risk as defined earlier, where, though the outcome is not
certain, the parameters for probabilities of outcomes can be calculated.
Uncertainty does not lend itself to the calculation of the parameters
of probability and the prediction of future outcomes. Thus uncertainty,
as exemplified in the farmer versus nature decision making problem,
falls under the classification of a refinement of game theory referred
to as decision theory.

Many of the concepts and definitions used in game theory are
used also in decision theory. The player has many strategies or
alternatives at his disposal. Nature has counter strategies though not
as a conscious opponent. The payoff matrix showing various farmer
strategies versus nature combinations also are used in decision theory.
Also, pure and mixed strategies, as defined earlier, are used.

The fundamental difference between game and decision theory is
that the player is completely ignorant of what act or state his so-called
opponent will choose to follow. Although the term "complete ignorance,"
as used in the farmer-nature decision theory, does not infer that the
player is an idiot, it does infer that the player is completely
uncertain (ignorant) of what his opponent's act will be in the future.

The farmer player knows or can ascertain past conditions and
results that have occurred from different farmer-nature strategy








-35-


combinations. This knowledge may come from his own experiences, his
neighbor's experiences, or from experimental and research data. For
example, the farmer is cognizant of the results obtained from a
combination of production factors and fertilizer levels, such as 0, 15,
25, 35, and 45 pounds of phosphate fertilizer, and the states of nature
that existed when the trials, farm or experimental, were carried out.
He knows, or can calculate, the added yield increments from each level
of fertilizer and relate these results to added returns in terms of
dollars and cents. This type of information makes up the payoff matrix
in decision theory.

Other information that the decision-making player has available
pertains to his own unique circumstances of firm-household relationship
which probably enters into and influences the decision ultimately made.
Whether the decision.centers around a farmer or other businessman, he
alone knows best.

1. Whether his ultimate aim is profit maximization or a
level of profit just large enough to give the house-
hold the level of living standard and the rate of
business growth desired.

2. What his own enterprise preferences are. It is con-
ceivable that a farmer may choose one enterprise over
another because of personal preference, even though
resource use efficiency and returns may be higher in
a different enterprise.

3. What his psychological makeup is as it pertains to
risk taking in the face of uncertainty conditions
which may be affected by his equity position, his
family living obligations, tenure, age, etc.

There is obviously no one set of rules that will suffice to cover
the many and varied decision-making situations that may arise. Several
decision-theory models have been developed and proposed to cope with the
majority of such situations.

These theories are as follows:
1. Maximin criterion of Wald

2. Maximax criterion

3. Savage's minimax regret criterion

4. Hurwicz criterion

5. Laplace's criterion of insufficient reason

In the explanation and criticisms of each theory, the commonly
used nomenclature for the alternative acts open to the farmer will be
indicated by A, A2 ., Am and the states of nature as Sl, S2 .., Sn.
M2 n







-37-


The Wald maximin criterion then selects the ingle strategy act
that will assure the decision maker a certain given return with a
minimum of uncertainty against nature's worst act.

Matrix 6 points out the highly conservative aspect of the maximin
criterion. It also points out one of the objections to this criterion.
In selecting the act that will give the highest security level, all data
in the payoff matrix are ignored except the minimum returns for each act.

In comparing the two alternative acts under each state of nature,
it is apparent that payoff AlSl is only slightly higher than A2S1; that
is, 30 versus 28. Similarly, AlS3 is slightly higher than A2S3; that
is, 3 versus 2. But, in comparing AIS2, a large difference in payoffs
exists; namely, 4 versus 25. This relatively large difference under
nature's S2, which favors act A2, is completely ignored in the selection
of the maximum criterion. Instead, the relatively small advantage that
combination A1S3 has over A2S3 determines the selection of act Al over
A2.

This objection can be pointed out more dramatically with the
following matrix:

Matrix 7 HYPOTHETICAL FARMER-NATURE PAYOFF MATRIX

States of Nature

S1 S2


Strategy A, 1 1

Acts A2 0 50

*Minimum payoff of the rows or strategy acts.

In matrix 7, the Wald criterion would select strategy Al over A2 because
the payoffs under strategy act A1, though equal under both states of
nature, are both larger than the minimum payoff under act A2. This
criterion considers only the maximum of the minimums of the rows and,
therefore, completely ignores the wide payoff value difference that
exists between A1S1 of A1S2 and A2S2.

Would a mixed strategy overcome this objection to the criterion
and take into consideration all the values in the matrix? Using a
mixed strategy probability calculation, as explained earlier, would give
the following result:

I p + 0 (1 p) = 1 p + 50 (1 p)

Collecting terms and solving for p results in


p= 1







-36-


Wald's Maximin Criterion

This theory is based on the selection of the maximum of the
various minimum returns associated with each combination of farmers'
acts and states of nature; that is, each A S Pure or mixed strategies
may be used. The pure strategy would be one that allows the farmer a
single course of action only, such as using one grain variety, seeding
either oats or barley, feeding only one class of cattle in one time
period and so on.

The maximin strategy, as in game theory, will guarantee the
decision maker the highest possible return if nature used the worst
possible counter strategy or its worst state. This is conceivable in a
game with an active opponent such as found in a game of chess or
checkers. However, it is slightly farfetched to imagine that nature
always consciously lies in wait to come up with the worst possible
countermove against the farmer's decision.

The maximin criterion then is an extremely conservative approach.
As described by Baumol, "The maximin approach is rather clearly a
manifestation of pure cowardice. This does not imply that cowardice
is necessarily irrational." Recognition must be given to the fact that
a farmer's situation conceivably could be such that a maximin approach
would be entirely rational. For example, a farmer who had committed
himself to a large fixed annual payment on a mortgage and left himself
liable to foreclosure if the payment is not met on the deadline date
might consider this conservative approach.

To illustrate the manner in which the maximin criterion works,
one can consider the following payoff matrix:

Matrix 6 HYPOTHETICAL FARMER-NATURE PAYOFF MATRIX

States of Nature

s1 S2 s3


Strategy A1 30 4 3

Acts A2 28 25 2

Minimum payoff of the rows or strategy acts.


The minimum payoff of Al is 3 and for A_ is 2. The maximin
criterion would therefore select strategy act A,; that is, the maximum
of the two minimums. The farmer player guarantees himself that even if
nature employs her worst state, S3, his payoff cannot drop below 3.


1Baumol, 1. J., Economic Theory and Operations Analis.a, Prontiec-
Hall, Inc., Englewood Cliffs, New Jersey, 1961, p. 370.








-30-


Since p was assigned as the probability for Al and I p as the
probability of A2, the above calculation indicates a pure strategy use
of A Considering the game theory approach of active opponents with
complete knowledge of the payoff matrix, a good case can be argued for
the maximin approach. But, in a farmer-nature decision problem where
nature is not a conscious opponent, it is difficult to justify the
selection of Al as the best alternative in matrix 7. This then is the
major weakness and objection to the maximin strategy in the farmer-
nature decision situation.

The Maximax Strategy

This strategy considers only the highest return that is available
to the player in his payoff matrix. It is the exact opposite of the
former maximin criterion.

Consider the following example matrix:

Matrix 8 HYPOTHETICAL FARMER-NATURE PAYOFF MATRIX

States of Nature

S1 S2 S3


Strategy Al 30* 4 3

Acts A2 28 25 2

*Maximum payoff of the rows or strategy acts.


The maximax criterion would select act Al in matrix 8 because the
highest payoff, A1S1 or 30, is larger than the highest payoff of act A2
which is A2S1 or 28. Again, as in the maximin criterion, all data in
the payoff matrix except the maximum of the maximums of each act are
ignored. It would appear that the maximax criterion would be suited
only to the psychological temperament of either a determined plunger, a
gambler, or a desperate man.

As in the maximin criterion, the major objection to this criterion
is that the decision is based only on one value or payoff in each
strategy act.

Savage's Minimax Regret Criterion

The reasoning behind this criterion is to protect the player
against the costs--measured in units of dollars, utility, or satis-
faction--of mistakes made in selecting alternatives; that is, to
minimize the regret ex post.








-30-


Since p was assigned as the probability for Al and I p as the
probability of A2, the above calculation indicates a pure strategy use
of A Considering the game theory approach of active opponents with
complete knowledge of the payoff matrix, a good case can be argued for
the maximin approach. But, in a farmer-nature decision problem where
nature is not a conscious opponent, it is difficult to justify the
selection of Al as the best alternative in matrix 7. This then is the
major weakness and objection to the maximin strategy in the farmer-
nature decision situation.

The Maximax Strategy

This strategy considers only the highest return that is available
to the player in his payoff matrix. It is the exact opposite of the
former maximin criterion.

Consider the following example matrix:

Matrix 8 HYPOTHETICAL FARMER-NATURE PAYOFF MATRIX

States of Nature

S1 S2 S3


Strategy Al 30* 4 3

Acts A2 28 25 2

*Maximum payoff of the rows or strategy acts.


The maximax criterion would select act Al in matrix 8 because the
highest payoff, A1S1 or 30, is larger than the highest payoff of act A2
which is A2S1 or 28. Again, as in the maximin criterion, all data in
the payoff matrix except the maximum of the maximums of each act are
ignored. It would appear that the maximax criterion would be suited
only to the psychological temperament of either a determined plunger, a
gambler, or a desperate man.

As in the maximin criterion, the major objection to this criterion
is that the decision is based only on one value or payoff in each
strategy act.

Savage's Minimax Regret Criterion

The reasoning behind this criterion is to protect the player
against the costs--measured in units of dollars, utility, or satis-
faction--of mistakes made in selecting alternatives; that is, to
minimize the regret ex post.










Consider the following payoff matrix:


Matrix 9 HYPOTHETICAL FARMER-NATURE PAYOFF MATRIX

States of Nature

S1 S2 S3


Strategy A 30 4 3

Acts A2 28 25 2


Matrix 9 is identical to matrix 8 used previously and is the standard
payoff matrix format used in decision theory applications. The regret
matrix is calculated from the payoff matrix by subtracting the payoffs
in each column from the largest payoff in the column. The resulting
matrix, ignoring the signs, is supposed to indicate numerically, in the
payoff units used in the original matrix, the regret for each AmSn
combination ex post.

The calculated regret matrix for matrix 9 would be as follows:

Regret Matrix 9.1 CALCULATED REGRET MATRIX

States of Nature

S1 2 S3


Stragegy A 0 21 0

Acts A2 2 0 1

Maximum regret of the rows or strategy acts.


With combinations AlSi, A2S2, and AS3, there would be zero regret
because each combination respectively indicates the lowest regret or
highest payoff under the respective states of nature. However, if the
player selected Al in anticipation of nature's S1 or S3 and S, resulted,
then an ex post regret would accrue to him. To avoid this, the
minimax rule is applied to the regret matrix. This rule would select
act A2 and the player would be protected against excessive loss what-
ever state of nature actually occurs.

The Savage regret criterion, as compared with the Wald and
maximax criterion, assumes that the worst possible state of nature
will occur and therefore attempts to protect the player against this
state.








-40-


Hurwicz Pessimism-Optimism Criterion

The Wald maximin and the Savage regret criterion are both
extremely conservative in assuming that the worst possible state of
nature will occur. As with the maximax criterion, they all ignore much
of the data in the payoff matrix for determining the alternative
decision choices.

The Hurwicz pessimism-optimism criterion partially overcomes this
objection. In arriving at the strategy choice, this criterion considers
both worst and best states of nature that can occur with each player
strategy act. In this criterion, a weighted combination of best and
worst are used to make a decision.

The decision-making player must supply the weights to be used.
In applying the Hurwicz criterion, the decision maker must choose an
index reflecting his subjective evaluation of the importance to him of
the worst state occurring. This is the pessimism index. The same
process for an evaluation, based on his own cricumstances of the
importance of the best state occurring, is the optimism index.

These indices are not supposed to in any way serve as an indi-
cator of the probability of occurrence of any of nature's states.
Numerically, the pessimism index would be a number between zero and 1
assigned to the importance of the worst state occurring by the decision
maker. The optimism index would follow from this in that it can then
be determined by subtracting the pessimism index from 1. The two
indices must add2up to 1. They may then be designated respectively as
"X" and "1 X".

Assigning the numerical X value or pessimism index to the
importance of the worst state occurring would of necessity be influenced
by the decision maker's need or desire for security, or the importance
to him of not having returns fall below a certain dollar level.
Conversely, assigning the 1 X or optimism index could be influenced by
or reflect the desire for maximization of returns. Accordingly, as the
individual decision maker's situation varies, so will the numerical
assigned values of X and 1 X vary amongst individuals and with an
individual over time.

To illustrate the selection of the decision maker's act under the
Hurwicz pessimism-optimism criterion, one can consider the following
matrix:




The commonly used symbols for the pessimism and optimism index
are alpha and 1 minus alpha. To facilitate typing, X and 1 X will be
used here.










-41-


Matrix 10 HYPOTHETICAL FARMER-NATURE PAYOFF MATRIX

States of Nature

s1 S2 S3

Strategy Al 30* 4 3

Acts A2 28 25 2

#Maximum payoffs of rows or strategy acts.
#Minimum payoffs of rows or strategy acts.


Assume, under matrix 10, that the decision-making player assigns a
pessimism index of 2/3; the optimism index would then be 1/3. The
minimum and maximum values of the two alternatives, A1 and A2 in
matrix 10, would then become

A1 = (3 X 2/3) +- (30 X 1/3) = 12

A2 = (2 X 2/3) + (28 X 1/3) = 10 2/3

The calculated value of act A is larger than that of act A2. It
follows that the Hurwiez pessimism-optimism index with selected values
of x = 2/3 and 1 x = 1/3 would select act Al in matrix 10.

Like the Hald and maximax criterion, this criterion also ignores
some data in the payoff matrix. In the above matrix, this criterion
ignored the A1S2 and A2S2 combinations completely. It does, however,
give weights to both maximum and minimum payoffs based on the importance
assigned to each by the decision maker.

It is apparent that with an assigned pessimism index of 1, indi-
cating complete pessimism ou the decision maker's part, the Hurwicz
criterion would be identical to the Wald maximin criterion. With a
pessimism index of zero, indicating complete optimism, it would be
identical to the maximax approach. The value and usefulness of the
Hurwicz criterion rests on the individual decision maker attaching his
own pessimism-optimism evaluations, bazed on his own circumstances, to
the payoff matrix.

Laplace's Criterion of Insufficient Reason

"The criterion of insufficient reason asserts that if one is
completely ignorant as to which state among the S1, S2 .., Sm will








-42-


occur, then one should behave as if they are equally likely to occur."3
Consider again the following payoff matrix:

Matrix 11 HYPOTHETICAL FARMER-NATURE PAYOFF MATRIX

States of Nature

S1 S2 S3


Strategy Al 30 4 3

Acts A2 28 25 2


With the Laplace criterion, equal probabilities of occurrence would be
assigned to each of nature's states in matrix 11 and the values of acts
Al and A2 computed as follows:

Al = (30 X 1/3) + (4 X 1/3) *-: (3 X 1/3) = 12 1/3

A2 = (28 X 1/3) + (25 X 1/3) -:- (2 X 1/3) = 18 1/3

Strategy A2 has the highest value and would be selected. In assigning
equiprobabilities of occurrence to each state of nature, the value
computed is the average value for each act available to the decision
maker.

Most recommendations released by research and extension agri-
cultural workers are based on this criterion. There are several
objections and criticisms of this criterion.

First, it is sometimes difficult to determine which results or
states of nature should be included in the Laplace criterion. This is
particularly true if, in one year, an odd occurrence happens which in
all likelihood may not happen again in many years. In such a case, one
can question whether or not it is correct to allow a weight for this one
year, or state of nature, which is equal to each of the other states
included in the payoff matrix. If the payoff matrix is based on results
from many years, the one odd year may have little effect on the calcu-
lated value of each act. However, if results from a short period of
time only are included in the matrix, a weight far outweighing the
probability of reoccurrence is attributed to the odd result.

A second objection is that the Laplace criterion, in giving equal
weights to all states of nature and the subsequent results, assures
maximum long-run profits to the player who selects the highest Laplace
value; but this criterion ignores the short-run effects and results that
could seriously impair the financial structure of the farm firm if its
capital position is such that it cannot withstand a short-term loss.







-43-


Consider the following payoff matrix:

Matrix 12

HYPOTHETICAL STATES OF NATURE OVER A FOUR-YEAR PERIOD
INDICATING PHYSICAL GRAIN YIELDS FROM TWO VARIETIES

States of Nature

S S2 S3 S4 Laplace
Value

Strategy A1 15 42 18 45 30

Acts A2 24 26 23 27 25


Using the Laplace criterion, the decision maker would select act
Al. This should assure him of the highest yield and return over the
long run. Under the assumption that 20 bushels per acre represents the
break-even yield for this farm and the financial structure is such that
a hardship would be worked on the firm-household with below break-even
yields, the individual faced with this situation and this payoff matrix
would possibly select act A2. The long-run yield would be lower but he
would be assured that in no year would he receive a yield less than his
break-even of 20 bushels per acre. Consequently, the long-run consider-
ations inherent in this criterion may be rational only for the farmer
with the ability to absorb short-run losses.






-44-


CHAPTER V

SURVEY PROCEDURE AND QUESTIONNAIRE

Selection of Areas

The state of North Dakota is divided into three fairly distinct
agricultural areas--the Red River Valley, particularly well adapted to
small grains and speciality crop production; the Central transitional
small grains and livestock production area; and the Western ranch-wheat
area.

Grand Forks and Traill counties were selected for study in the
East, Foster and Wells counties in the Central area, and Stark and Dunn
counties in the West.

Selection of Farmers

This study is based on data collected by personal interview from
a randomly selected sample of 90 farm operators. A randomly selected
list of names was obtained by Agricultural Economists from the Agri-
cultural Stabilization and Conservation Service mailing lists in
representative North Dakota counties in 1960. This list was used to
obtain the farmers' names in the above six counties.

The original list of names from each of the three areas of the
state were classified according to farm size in the frequency distri-
bution shown in Table 4.

Partnerships and father-son agreements were eliminated before
any names were selected in any of the three areas. This was done under
the assumption that with arrangements of this type decision making may
be a joint effort and sufficiently complex to not lend itself to the
analysis considered in this study.

TABLE 4. CODE NUMBERS AND SIZE RANGES
USED IN CLASSIFYING SAMPLE FARMS

Code Size Range
Number in Acres

1 100-179
2 180-259
3 260-499
4 500-599
5 1,000-1,999
6 2,000 and over



In the two eastern counties of Traill and Grand Forks, 168
farmers were classified into code size ranges 1, 2, and 3 and 123
farmers into 4, 5 and 6. Thus, only two major size stratification
groups were used for this area. After size classification, a total of
36 names--l1 in each of the two grouped size ranges--were randomly






-44-


CHAPTER V

SURVEY PROCEDURE AND QUESTIONNAIRE

Selection of Areas

The state of North Dakota is divided into three fairly distinct
agricultural areas--the Red River Valley, particularly well adapted to
small grains and speciality crop production; the Central transitional
small grains and livestock production area; and the Western ranch-wheat
area.

Grand Forks and Traill counties were selected for study in the
East, Foster and Wells counties in the Central area, and Stark and Dunn
counties in the West.

Selection of Farmers

This study is based on data collected by personal interview from
a randomly selected sample of 90 farm operators. A randomly selected
list of names was obtained by Agricultural Economists from the Agri-
cultural Stabilization and Conservation Service mailing lists in
representative North Dakota counties in 1960. This list was used to
obtain the farmers' names in the above six counties.

The original list of names from each of the three areas of the
state were classified according to farm size in the frequency distri-
bution shown in Table 4.

Partnerships and father-son agreements were eliminated before
any names were selected in any of the three areas. This was done under
the assumption that with arrangements of this type decision making may
be a joint effort and sufficiently complex to not lend itself to the
analysis considered in this study.

TABLE 4. CODE NUMBERS AND SIZE RANGES
USED IN CLASSIFYING SAMPLE FARMS

Code Size Range
Number in Acres

1 100-179
2 180-259
3 260-499
4 500-599
5 1,000-1,999
6 2,000 and over



In the two eastern counties of Traill and Grand Forks, 168
farmers were classified into code size ranges 1, 2, and 3 and 123
farmers into 4, 5 and 6. Thus, only two major size stratification
groups were used for this area. After size classification, a total of
36 names--l1 in each of the two grouped size ranges--were randomly






-44-


CHAPTER V

SURVEY PROCEDURE AND QUESTIONNAIRE

Selection of Areas

The state of North Dakota is divided into three fairly distinct
agricultural areas--the Red River Valley, particularly well adapted to
small grains and speciality crop production; the Central transitional
small grains and livestock production area; and the Western ranch-wheat
area.

Grand Forks and Traill counties were selected for study in the
East, Foster and Wells counties in the Central area, and Stark and Dunn
counties in the West.

Selection of Farmers

This study is based on data collected by personal interview from
a randomly selected sample of 90 farm operators. A randomly selected
list of names was obtained by Agricultural Economists from the Agri-
cultural Stabilization and Conservation Service mailing lists in
representative North Dakota counties in 1960. This list was used to
obtain the farmers' names in the above six counties.

The original list of names from each of the three areas of the
state were classified according to farm size in the frequency distri-
bution shown in Table 4.

Partnerships and father-son agreements were eliminated before
any names were selected in any of the three areas. This was done under
the assumption that with arrangements of this type decision making may
be a joint effort and sufficiently complex to not lend itself to the
analysis considered in this study.

TABLE 4. CODE NUMBERS AND SIZE RANGES
USED IN CLASSIFYING SAMPLE FARMS

Code Size Range
Number in Acres

1 100-179
2 180-259
3 260-499
4 500-599
5 1,000-1,999
6 2,000 and over



In the two eastern counties of Traill and Grand Forks, 168
farmers were classified into code size ranges 1, 2, and 3 and 123
farmers into 4, 5 and 6. Thus, only two major size stratification
groups were used for this area. After size classification, a total of
36 names--l1 in each of the two grouped size ranges--were randomly







-45-


selected and 30 of these--15 in each group--were interviewed. The
additional names were selected to avoid callbacks in case the farmer
was not at home when the interviewer called.

In the central counties of Foster and Wells, 55 farmers were
classified into code sizes 1, 2, and 3; 75 into code 4; and 36 into code
size ranges 5 and 6. This stratification resulted in three major size
groups for analysis purposes. Again, 36 names in total were selected,
12 from each of the above groups, and a total of 30 farmers were
interviewed in the central area.

In the western counties of Stark and Dunn, 48 farmers were
classified into code size ranges 1, 2, and 3 group 1; 73 into code size
4 group 2; and 58 farmers into code sizes 5 and 6 group 3. As in the
other areas, a total of 36 names, 12 from each of the three size groups,
were selected and a total of 30 farmers were interviewed.

A combined total of 90 interviews were taken, 30 in each of the
three areas of the state.

Survey Questionnaire

The survey questionnaire used in the personal interviews
consisted of three separate sections. Each section was designed to meet
a particular study need.

Questionnaire Section j

Section 1 of the questionnaire, reproduced below, was designed
to establish the background information on (1) physical farm character-
istics, (2) personal and family relationships, (3) financial structure
and equity of the firm, and (4) interdependence of firm income and
household requirements.

Most of the survey questions in section 1 are self-explanatory
and do not need any further explanation, except for the following:

Question 4: The years of experience included only the total
years in which the farmer had actually managed and made the decisions on
a farm unit. Work as a hired man or working with a relative did not
count towards operations experience. The answer requested was to reflect
the decision-making years of experience.

Question 5: The value requested was to reflect the operator's
best estimate of current sale value of land, buildings, machinery, and
livestock. In feeder cattle operations, the value requested was to
reflect the average annual investment in feeder cattle under the unit's
normal feeding program.

Question 11: The minimum-dollar family-living requirements were
to cover purchased food, fuel, farm share of auto expense, educational
costs, vacations and recreation, clothing, and other personal expenses







-45-


selected and 30 of these--15 in each group--were interviewed. The
additional names were selected to avoid callbacks in case the farmer
was not at home when the interviewer called.

In the central counties of Foster and Wells, 55 farmers were
classified into code sizes 1, 2, and 3; 75 into code 4; and 36 into code
size ranges 5 and 6. This stratification resulted in three major size
groups for analysis purposes. Again, 36 names in total were selected,
12 from each of the above groups, and a total of 30 farmers were
interviewed in the central area.

In the western counties of Stark and Dunn, 48 farmers were
classified into code size ranges 1, 2, and 3 group 1; 73 into code size
4 group 2; and 58 farmers into code sizes 5 and 6 group 3. As in the
other areas, a total of 36 names, 12 from each of the three size groups,
were selected and a total of 30 farmers were interviewed.

A combined total of 90 interviews were taken, 30 in each of the
three areas of the state.

Survey Questionnaire

The survey questionnaire used in the personal interviews
consisted of three separate sections. Each section was designed to meet
a particular study need.

Questionnaire Section j

Section 1 of the questionnaire, reproduced below, was designed
to establish the background information on (1) physical farm character-
istics, (2) personal and family relationships, (3) financial structure
and equity of the firm, and (4) interdependence of firm income and
household requirements.

Most of the survey questions in section 1 are self-explanatory
and do not need any further explanation, except for the following:

Question 4: The years of experience included only the total
years in which the farmer had actually managed and made the decisions on
a farm unit. Work as a hired man or working with a relative did not
count towards operations experience. The answer requested was to reflect
the decision-making years of experience.

Question 5: The value requested was to reflect the operator's
best estimate of current sale value of land, buildings, machinery, and
livestock. In feeder cattle operations, the value requested was to
reflect the average annual investment in feeder cattle under the unit's
normal feeding program.

Question 11: The minimum-dollar family-living requirements were
to cover purchased food, fuel, farm share of auto expense, educational
costs, vacations and recreation, clothing, and other personal expenses







-46-


that would make up the present family's standard of living. The answer
to this question is used again in he second section of the question-
naire.

QUESTIONNAIRE SECTION 1:

NAME ADDRESS COUNTY

1. Age of farm operator 2. Years of formal education:
Grade school
High school __
College
Other __

3. Number of dependents relying on farm operator for sole support?
Wife Number of children
Ages of children

4. Number of years experience as farm operator?

5. Present value of farm unit operated?
(a) Land and buildings $ Own $ Rent
(b) Machinery $_
(c) Livestock $___

6. Farm mortgage and other liabilities against:
(a) Land and buildings $ Owed to relative Non relative__
(b) Livestock $ Owed to relative Non relative
(c) Machinery $. Owed to relativeNon relative_
(d) Unsecured loans $ Owed to relative Non relative_

7. Total investments outside the farm unit operated? $___

8. Expected annual income from outside investments? $

9. Land operated? Owned acres Rented acres

10. Livestock Enterprises? Major Size
Major Size


11. What is the minimum annual income you would need to cover family
living expenses? $____,..


Questionnaire Section 2:

Assume that you, as a farmer, have choices A, B, C, or D which
represent equal annual investment enterprises, with profit returns
(profit over farm cash operating expenses) dependent on what choice
of conditions nature has in store for that particular year. Nature's








-47-


choice is not only unpredictable, but it will not necessarily follow
the identical past pattern established. It is possible that year 5
could be a repeat of any one of years 1, 2, 3, or 4 and year 6 (and
so on) again a repeat of any one of the four.

NATURE'S CHOICE

Farmer's Choice Year 1 Year 2 Year 3 Year 4

A $2,500 0 $5,500 $3,500

B 1,700 $ 800 3,000 2,500

C 0 0 10,000 0

D 0 0 8,000 2,000


12. WHICH OF THE ABOVE ENTERPRISES WOULD YOU CHOOSE TO INVEST IN IF:
A. You had no outside income and
1) Were making the choice for one year only
Why?
2) The choice you made would be for a 10-year period? .
Why?

B. You were assured of an outside income of $ annually and
1) Were making the choice for one year only?
Why?
2) The choice you made would be for a 10-year period?
Why?


The purpose of the questions in this section was to determine the
farm operator's risk and uncertainty aversion under (a) the long and
short run, and (b) varying conditions of firm-household relationships.

Extreme care was taken by the interviewing personnel to explain
in some detail to each farm operator (a) the purpose of the questions
asked, (b) the meaning of a payoff matrix, (c) the choices open to the
farmer, (d) the several situations involved in the short and long run,
and (e) the meaning of nature's states.

The payoff matrix of section 2 was designed to indicate profit
returns; that is, income over cash operating expenses that had occurred
ex post in the past four-year period from four different agricultural
enterprises.

Each one of the four years would indicate a state of nature. It
also was pointed out that each one of the enterprises signified equal
annual investment requirements. In other words, by investing an equal







-48-


amount of money in any one of the four enterprises, the farmer would
have realized in the past four years the profits as indicated in each
row. Extreme care was taken by the interviewers not to identify by
example any of the hypothetical acts with a real-life enterprise. The
purpose of this caution was to avoid personal preference or dislike of
a particular enterprise to influence the operator's decision choice.

It also was explained to the farmer that the payoff matrix returns
were ex post information and that, as in their real life decisions,
nature's idiosyncracies were unpredictable; that is, future returns from
identical enterprises might not follow the same or even a similar pattern.

After carefully explaining the various ramifications of the payoff
matrix, the farmer was requested to (a) keep in mind his own particular
and unique circumstances, and (b) make the enterprise investment choice
under four different circumstances.

The choice settings or circumstances delineated for analysis
purposes were classed as (a) short run with no added income, (b) long
run with no added income, (c) short run with added income, and (d) long
run with added income.

Each one of the choices in the payoff matrix of section 2 in the
hypothetical enterprise profit matrix was purposely designed to fit into
one or more of the categories of decision theories discussed earlier.

Considering the payoff matrix in section 2 of the questionnaire,
the acts selected by the decision-theory criterion would be as follows:

Walds maximin criterion: The minimum payoffs in the rows are AS2,
BS2, CSi 2 and DS The maximum of these minimum payoffs is
BS2 wit' apayoff of 800. The farmer employing this criterion would
then select strategy "B" in this matrix.

Maximax criterion: The highest payoff in the entire matrix is
found in act "C". Therefore, a farmer following this criterion would
select this act in the hope that the CS3 combination would occur with
a 10,000-unit return.

Minimax regret criterion: The regret matrix calculated from the
payoff matrix of section 2 by subtracting all payoffs from the largest
in the column would be as follows:

Regret Matrix 13
States of Nature

S1 S2 S3 S4

A 0 800 4,500* 0
Farmer's
B 800 0 7,000 1,000
Acts
C 2,500 800 0 3,500
Choices *
D 2,500 800 2,000 1,500
Maximum regret by acts or rows








-49-


Applying the rinnimax rule to the regret matrix above would result
in the selection of strategy "D". The farmer employing the regret
criterion would therefore select this act.

Hurwicz pessimism-optimism criterion: This criterion takes into
account the best and worst payoffs in each act open to the decision
maker. The final choice depends on the pessimism-optimism index assigned
by the player himself. In the matrix of section 2 of the questionnaire,
the only payoffs considered by this index would be the maximums and
minimums of each row as follows:

Act Maximum Minimum
A 5,500 0
B 3,000 800
C 10,000 0
D 8,000 0

It is apparent that act C dominates both acts A and D in that the
minimums are identical, but act C has the highest maximum. Therefore,
the choice actually involves only acts B and C. Since the individual
player's pessimism-optimism indices are not known, the values of n"x
and "1 x" can be calculated so that the player would be indifferent
between the choices of acts B and C. This is done by equating act B
to C and solving for "x" as follows:

800 x + 3,000 (1 x) = 0 x -- 10,000 (1 x)

x = 35/39

and 1 x = 4/39

With an "x" value of 35/39, the decision-making player would be
indifferent between acts B and C. Should the individual player assign
a value of less than 35/39 to his pessimism index, the Hurwicz criterion
would select act C and, conversely, select act B with a pessimism index
higher than 35/39.

Laplace criterion of insufficient reason: As indicated earlier,
this criterion assigns equal probability of occurrence to each state of
nature, and the value computed for each act is the average value. In
the payoff matrix of section 2, the highest average payoff is found in
act A, and the farmer employing this criterion would select this act and
realize the highest attainable returns over time.

Questionnaire Section 3

The third section of the questionnaire presented an additional
payoff matrix decision to the farmer. This payoff matrix, though it
contained hypothetical data, referred to a specific production factor
or resource-use decision in that it was identified with different
fertilizer-use levels and results in added returns over costs. The
third section is reproduced below.








-50-


QUESTIONNAIRE SECTION 3:

Assuming that your nearest Experiment Station showed the following
net returns in dollars over the check plot from four different rates of
phosphate fertilizer application over a period of the past four years.


Rates

E 15 #/ac.
F 25 #/ac.
G 35 #/ac.
H 45 #/ac.


S1

:-3.20
+-3.90
+4.70
+6.10


S2

$+3.80
+4.10
+2.10
0


S3

$+1.10
-1.10
-2.20
-3.50


S4

$ -:8.00
+12.20
+13.80
+15.10


13. Taking into
application
invested as


consideration
you will have
follows:


15#
25#
35#
45#


that with various rates of fertilizer
varying amounts of money per acre


$1.35/ac.
2.25/ac.
3.15/ac.
4.05/ac.


In your particular financial situation, which rate of fertilizer
would you apply on your farm if the above results pertained to
your unit though you could not predict weather conditions that
will occur? h__y?

14. Do you use fertilizer on your farm or have you used it in the past
five years?

15. Is fertilizer used every year on all summer fallow wheat acres?

16. What rate of fertilizer do you use on S.F. wheat acres?

17. Do you vary th rates from year-to-year according to soils tests?


According to o
Moisture
Available
Other (s


In explaining
to assume that the
on or near his farm
some farmers that e
different soil and
data for farmers wh
therefore, are unfa


other factors such as:
outlook at seeding time .
3 cash or credit
specify) ______


the payoff matrix data to farmers, each was asked
results in the matrix were from trials actually run
* This was done to overcome the objection voiced by
Kperimental results and trials pertain to farms under
climatic conditions, and also to supply ready made
o may never have used fertilizer on their farms and,
miliar with results that could occur.







-51-


Each farmer being interviewed was asked to place himself in the
position where it was necessary to decide what fertilization rate he
would employ on his farm. As pointed out earlier, he was also to
imagine that this payoff matrix represented returns from trial results
over the past four years pertinent to his farm. It also was stressed
again that it is impossible to predict what state of nature would exist
during the coming season, and that the pattern that existed in the
fertilizer matrix would not necessarily be repeated in the same manner
or any predictable order of occurrence.

A difference between the matrices in sections 2 and 3 was pointed
out to each farmer. In section 2, the matrix assumed that each act
represented equal annual investments. In section 3, each act or rate of
fertilizer use per acre represented an increase in investment per acre.
Each farmer was then asked to choose the act from the payoff matrix data
that he would use on his own farm under his own unique physical,
financial, and psychological circumstances.

Considering the payoff matrix in section 3 of the questionnaire,
the acts selected by the decision theory criterion would be as follows:

Wald's maximin criterion: The minimum payoffs in the rows of
the section 3 matrix are ES FS3, GS3, and HS3 with returns
respectively of +$1.10, $1.10, $2.20, and '$3.50. The maximum of
these minimums is $1.10. This criterion would therefore select act E
or a fertilization rate of 15 pounds per acre.

Maximax criterion: The highest payoff in this matrix is found in
combination HS,. Therefore, a farmer following this criterion would
apply 45 pounds of fertilizer per acre.

Minimax regret criterion: The regret matrix calculated from the
payoff matrix of section 3, by subtracting all payoffs in each column
from the largest in the column, would be as follows:

Regret Matrix 14
States of Nature

s1 S2 S3 S4

E -2.90 -.30 0 -7.10
Farmer's
F -2.20 0 -+2.20 -2.90*
Acts
G -1.40 -2.00 -+3.30 -1.30
Choices
H 0 -4.10* +:-4.60 0

*Maximum regret of the rows or acts.






-52-


Applying the minimax rule to the regret matrix would result in selection
of act G and the farmer employing this criterion would apply 35 pounds
of fertilizer per acre.

Hurwicz pessimism-optimism index: In the section 3 matrix of the
questionnaire, the only payoffs considered by this criterion would be
the maximums and minimums of each row as follows:
Act Minimum Maximum
E $-1.10 $ +8.00
F -1.10 12.20
G -2.20 13.80
H -3.50 15.10
From visual observation of the above data, one can notethat as ferti-
lization rates are increased the minimums of the rows become smaller
(that is, the negative returns become larger) and the maximums of the
rows become larger. To determine which acts would be chosen under
varying pessimism-optimism indices, one can attach the pessimism index
(x) to each minimum and the optimism index (1 x) to each maximum and
then, by setting each act equal to the one that follows, solve for x.
The results would be as follows:
Indifference
Act Pairs Value of x
E = F .65
F = G .59
G = H .50
Under this criterion, a relatively high pessimism index will select
the safest act available in the matrix. Conversely, a relatively
low pessimism index will select an act with a higher uncertainty level.
The above calculations indicate that, in the matrix in section 3, a
pessimism index of .66 or over would select act E or a fertilizer appli-
cation level of 15 pounds per acre. Acts E and F would be indifferent
to each other at a pessimism index of .65. Act F would be selected with
a pessimism index of not less than .60 and not more than .64 with acts
F and G being indifferent to each other at pessimism index level of .59.
Similarly, act G would be selected with a pessimism index of over .51
and less than .58 with acts G and H being indifferent to each other at
a pessimism value of .50. A pessimism index of less than .50 we"la
select act H.
Laplace criterion of insufficient reasons: This criteion
requires assigning equiprobability of occurrence to each rf the states
of nature. In essence, this results in determining the highest average
return for each act or row. The solution under this criterion is the
selection of act F.

The final questions in section 3 deal with past fertilizer usage
on the farm unit. The answers to these questions were designed to serve
as a check to determine whether the selection from the payoff matrix
was influenced by his own use level and whether or not fertilizer was
used on the farm.







-53-


CHAPTER VI


REASONS AND ANALYSIS OF FARMERS' CHOICE PATTERNS
OF HYPOTHETICAL ENTERPRISES UNDER FOUR SETTINGS
OF TIME AND SUPPLEMENTARY INCOME

Each farmer interviewed selected one of the alternative acts open
to him under each one of the time and supplementary income settings;
that is, under the short and long run, with and without supplementary
farm income. Each selection was accompanied by a reason for the par-
ticular choice. The reasons given by these farmers were many and varied
but did tend to form a definite pattern which, in many instances at
least, can be related to the decision theories discussed earlier.

Decision Theories Applicable to Act Choices

Act A: This alternative corresponds to the Laplace criterion of
insufficient reason with an equiprobability of occurrence based on ex
post knowledge. In the reasons given for this alternative choice under
any and all of the four problem settings, nearly all farmers indicated
that this act would assure them of the highest average return over time.
This rationale coupled with act A closely follows the perfect knowledge
maximization motive inherent in formulating and presenting most of the
farmer-directed resource-use recommendations made by agricultural
workers.

Act B: This alternative corresponds to Hald's maximin approach
and to the Hurwicz pessimism-optimism index if the pessimism index is
35/39 or larger. Both criterion always select the same act when the x
index is equal to 1. The payoffs in this matrix are such that, with a
pessimism index of over 35/39, the value of the minimum payoffs out-
weigh in value the maximum payoffs with a corresponding 1 x index.

Nearly all the farmers selecting this alternative under any of
the four problem settings indicated that their reasons were based
primarily on the relative stability of returns in that under act B a
return is realized in each one of the states of nature. Some farmers
indicated that their need for income stability was based on family
living requirements and annual fixed payments that had to be met. These
reasons strongly indicate that the Wald criterion is pertinent in the
farmer's decision-making process.

Others, of the farmers interviewed, indicated they would prefer
selecting one of the other acts with higher income potentials and oppor-
tunities, but because of the reasons given above were forced to select
act B due to its income stability. One could assume, therefore, that
their pessimism index was sufficiently high to cause selection of this
act. A corresponding conclusion is that Lhe respondents, in some cases,
were weighing the minimums of one act against the maximums of other other.
However, none of them indicated in any manner that they were thinking in
terms of a pessimism-optimism index.







-53-


CHAPTER VI


REASONS AND ANALYSIS OF FARMERS' CHOICE PATTERNS
OF HYPOTHETICAL ENTERPRISES UNDER FOUR SETTINGS
OF TIME AND SUPPLEMENTARY INCOME

Each farmer interviewed selected one of the alternative acts open
to him under each one of the time and supplementary income settings;
that is, under the short and long run, with and without supplementary
farm income. Each selection was accompanied by a reason for the par-
ticular choice. The reasons given by these farmers were many and varied
but did tend to form a definite pattern which, in many instances at
least, can be related to the decision theories discussed earlier.

Decision Theories Applicable to Act Choices

Act A: This alternative corresponds to the Laplace criterion of
insufficient reason with an equiprobability of occurrence based on ex
post knowledge. In the reasons given for this alternative choice under
any and all of the four problem settings, nearly all farmers indicated
that this act would assure them of the highest average return over time.
This rationale coupled with act A closely follows the perfect knowledge
maximization motive inherent in formulating and presenting most of the
farmer-directed resource-use recommendations made by agricultural
workers.

Act B: This alternative corresponds to Hald's maximin approach
and to the Hurwicz pessimism-optimism index if the pessimism index is
35/39 or larger. Both criterion always select the same act when the x
index is equal to 1. The payoffs in this matrix are such that, with a
pessimism index of over 35/39, the value of the minimum payoffs out-
weigh in value the maximum payoffs with a corresponding 1 x index.

Nearly all the farmers selecting this alternative under any of
the four problem settings indicated that their reasons were based
primarily on the relative stability of returns in that under act B a
return is realized in each one of the states of nature. Some farmers
indicated that their need for income stability was based on family
living requirements and annual fixed payments that had to be met. These
reasons strongly indicate that the Wald criterion is pertinent in the
farmer's decision-making process.

Others, of the farmers interviewed, indicated they would prefer
selecting one of the other acts with higher income potentials and oppor-
tunities, but because of the reasons given above were forced to select
act B due to its income stability. One could assume, therefore, that
their pessimism index was sufficiently high to cause selection of this
act. A corresponding conclusion is that Lhe respondents, in some cases,
were weighing the minimums of one act against the maximums of other other.
However, none of them indicated in any manner that they were thinking in
terms of a pessimism-optimism index.







-54-


Act C: This alternative corresponds to the maximax approach and/
or the Hurwicz index with an x index of less than 35/39. These two
criteria are identifical with an x equal to zero.

Farmers selecting this criterion expressed a strong desire to
gamble on expected outcomes. Some sample comments were (a) the chance
of hitting the big return would be very tempting, (b) one can afford to
take a chance with family living taken care of, and (c) you have to
gamble in farming. There was no indication that a thought approach
resembling the Hurwicz pessimism-optimism index was being considered by
the respondents selecting this act. The reasons given for their choice
strongly suggest that the maximax approach of striving for the "golden
goal" enters into farmers' decision making.

Act D: This alternative corresponds to the Savage regret
criterion. The reasons respondents gave for selecting this act indi-
cated that a gambling desire dictated this choice. This alternative
represented the "happy medium" between the extreme gamble of act C and
the relatively more conservative acts A and B. It is possible that,
though not aware of the formal regret criterion, the farmers selecting
this act were trying to minimize regret. Some sample comments from the
farmers' reasons for selecting this act were (a) one can gamble a little
more with outside income assured, and (b) one is willing to take more
risk for the chance of a higher annual income for a year.

Table 5 indicates the frequencies with which farmers chose the
various alternative acts open to them under the four problem settings.
From these data, one can observe that a definite difference exists in
the choice pattern. If random selections had been made, the AmSn
combinations would have formed a pattern with approximately 22
respondents in each block. The measurement that can be used to determine
whether there is a significant difference in choice patterns is the chi-
square test of independence. The calculated chi-square, with Table 5
as a contingency table, resulted in a value of 61.427. The table chi-
square with 9 degrees of freedom at the 95 per cent confidence limit is
16.919. One therefore rejects the null hypothesis and assumes that a
significant difference exists in choice patterns.

From Table 5, there is a definite pattern of change as the
problem settings move from the short run with no added income to the
long run with added income. This pattern is probably due to the inter-
related factors of (1) the ability of the farmer to bear more uncertainty
increases as the settings change from no added income to added income,
and (2) the relative uncertainty levels of the four alternative acts,
particularly as viewed from the short and long run. The four acts can
be classified in terms of increasing uncertainty in the short run in the
order of B, A, D, and C with act B the least uncertain under the
assumption that some income is better than none in any given year.

ICroxton, F. E., and Crowdon, J. D., Practical Business Statistics
Prentice-Hall, Inc., New York, 194C, p. 67.








-55-


TABLE 5. DECISION THEORIES APPLICABLE TO EACH ALTERNATIVE AND THE
NUMBER OF FARMERS SELECTING EACH ACT UNDER THE FOUR SETTINGS OF THE
HYPOTHETICAL DECISION PROBLEM


Problem Settings
Alternative Applicable No Added Income Added Income
Selected Decision Theories Short Long Short Long
Run Run Run Run
(Numbers)

A Laplace 21 35 42 55
B Hald; Hurwicza 60 52 21 23
C Maximax; Hurwicz 6 0 20 8
D Savage Regret 3 3 7 4

Totals 90 90 90 90

aWith x index larger than 35/39.
bWith x index smaller than 35/39.



Alternatives by Area

Table 6 compares the pattern of choice selections by areas of the
state. Responses from farmers in the central and western part of the
state are very similar under both the short and long run no added income
settings. About three-fourths of them selected act B in both the short
and long run no added income settings.

There appears to be more of a difference in the choice patterns
between the eastern and the other two areas under both the short and
long run no added income settings. In the eastern area, a higher
percentage of farmers selected the maximization act A in both the short
and long run.

The choice patterns under the added income settings are entirely
different by areas of the state. In the East, a relatively high'
percentage of farmers chose acts A and C in the short run. In the
central area, in the short run, they were split evenly in their choices
of acts A and B. In the West, a higher percentage again chose act A,
with the remainder split nearly evenly between acts B and C. As the
setting changes from the short to the long run under the added income
assumption, nearly three-fourths of the farmers in the eastern part of
the state chose act A, the long run profit maximization choice. In the
central area, the numbers were split nearly evenly between acts A and B;
whereas, in the western portion, a larger percentage of the total
selected act A.








-56-


TABLE 6. NUMBERS OF FARMERS SELECTING EACH ALTERNATIVE UNDER THE FOUR
SETTINGS OF THE HYPOTHETICAL PROFIT DECISION MATRIX, BY AREA

Problem Settings
Alterna- No Added Income Added Income
tive .Short Run Long Run Short Run Lonr Run
Selected No. % No. 7 No. 7 No. %

EASTERN AREA

A 10 33.3 19 63.3 13 43.3 22 73.3
B 17 56.6 11 36.6 5 16.6 5 16.6
C 2 6.6 0 10 33.3 3 10.0
D 1 3.3 0 2 6.6 0

CENTRAL AREA

A 5 16.6 9 30.0 11 36.6 14 46.6
B 22. 73.3 20 66.6 11 36.6 12 40.0
C 2 6.6 0 4 13.3 2 6.6
D 1 3.3 1 3.3 4 13.3 2 6.6

WESTERN AREA

A 6 20.0 7 23.3 18 60.0 19 63.3
B 21 70.0 21 70.0 5 16.6 6 20.0
C 2 6.6 0 6 20.0 3 10.0
D 1 3.3 2 6.6 1 3.3 2 6.6



The general pattern in all areas tends to change from the
relatively conservative choice to the more uncertain choices as the
settings change from short to long run and from no added to added income.
This seems logical and rational on the part of the decision maker to
gravitate towards more uncertainty as the time period length increases
and as the dependence between the firm and household becomes divorced
under the added income assumption.

Rationality of Choices

The question arises as to how rational are the act choices made
by the farmers in the light of long run profit maximization, uncertainty
minimization, and the gambling desire, all of which affect the decision
maker.

An evaluation of the flow pattern in Flow Chart 1 under the four
different settings serves as a check on the credence of the answers
given by the respondents. It appears logical and rational that, in
moving from the short to the long run no added income setting, the








-57-


decision maker would normally make one of two moves, (a) repeat the same
choice; that is, his uncertainty aversion would remain the same in the
short and long run, or (b) move to an act with a higher uncertainty and
higher long run profit potential. It also is possible that he would
consider one other move which is a choice with a lower uncertainty but a
more assured income over the long run.

In moving from the long run no added income setting to the short
run added income setting, nearly any choice move would be rational.
However, the most rational moves would likely be to (a) stay with the
same act, particularly if this act has already been one with high
uncertainty and profit potential, or (b) move to a higher uncertainty
level. The level of uncertainty aversion would be influenced by the
decision maker's own emphasis on the amount of hardship due the house-
hold in poor income years since, under the added income setting, the
firm and household become divorced in arriving at the decision, at least
to the extent that the household is not dependent for its livelihood on
the outcomes of the firm decisions. The only irrational move in this
setting change is for the decision maker to be more conservative under
the short run added income setting than under the comparable short run
no added income setting. This choice change did occur twice in Flow
Chart 1. These irrationalities are denoted on the chart with dotted
arrows "W" and "X". In dotted arrow T, the farmer selected the Wald
maximin act B in the short run with added income, but selected the
Laplace criterion act A in the short run without added income. Similarly,
in dotten arrow X, act C with a higher uncertainty level was selected in
the short run with no added income; whereas, act D with a lower
uncertainty level was selected in the short run with added income.

In changing the problem setting from the short to the long run
under the added income assumption, every alternative move would be
rational except to select an act lower in uncertainty in the long run.
This choice was made once as shown by the dotten arrow "Y" in Flow
Chart 1.

Consistency of Choices by Time Periods

This section deals with the consistency that the respondents
showed in choice selection by time periods. Table 7 shows the pairs of
choices that farmers made as the setting changed from the short to the
long run under the no added income assumption. The junction of a
particular row and column indicates the number of farmers that selected
that particular act pair.

Nineteen farmers consistently chose act pair AA in both the short
and long run, 49 selected act pair BB, none selected act pair CC, and
two selected act pair DD consistently. Out of the 90 farmers, a total
of 70 representing 77.7 per cent of the total were consistent in their
choices as the setting varied in time period. Out of this 77.7 per cent,
only 19 farmers representing 21 per cent of the total sample consistently
selected act pair AA which would maximize income over the long run. The
act pair BB was consistently selected by 49 farmers or 54.4 per cent of








-50-


FLOW CHART 1. DECISION FLOW PATTERN UNDER FOUR DIFFERENT SETTINGS WITH
THE HYPOTHETICAL PROFIT DECISION HATRIX


No Added Income


Short Run


Long Run


Short Run


Added Income


A- 13 -- A- 13
A- 19 --( B- 1 ------- 1
A- 21 ---- A- 1
-C- 4

B- 2 A- 1 B- 1




B- 1
(Y) B- I



C- 2 A- 1
.-C- 1
D- 1 A- 1
B- 60

A- 21 A- 20
B- 1


B- 19 A- 1
.. _- B- 1C

B- 49 A- 2




A- 2

D- 3-D- 3
SD- 1

.A- 4 ; C- 4 ) A- 4
C-) 6


C- 6 B- 1---(X)- D 1--------- D- 1
D- ---C- 1 ----- D- 1


D- 3 A- 1 -- C- I------> A-
D- 2 ---- D- 2 ------ D- 2


Long Run








-59-


the total sample. This consistency in choice selection indicates that
the majority of farmers under the realistic no added income setting,
whether the choice is in the short or long run, are more concerned with
income security than with income maximization.


TABLE 7. OCCURRENCE OF PAIRS OF CHOICES BY FARMERS IN THE
SHORT AND LONG RUN UNDER THE SETTING OF NO ADDED INCOME

Choice in the Choices in the Long Run
Short Run A B C D

A 19 2 0 0
B 11 49 0 0
C 4 1 0 1
D 1 0 0 2



Table 8 shows the consistency of choice pairs under the added
income assumption as the setting changed from the short to the long run.
Out of the 90 farmers, 69 or 76.6 percent of the total were consistent
in selecting choice pairs. Thirty-nine farmers, 43.3 per cent of the
total, consistently selected act pair AA, the long run maximization
choice. Nineteen farmers, 21.1 per cent of the total, selected
consistently the act pair BB which represents the ultra conservative
choice. Eight farmers consistently selected act pair CC and three
farmers consistently selected act pair DD.


TABLE 8. OCCURRENCE OF PAIRS OF CHOICES MADE BY FARMERS
IN THE SHORT AND LONG RUN UNDER THE SETTING OF ADDED
INCOME

Choice in the Choice in the Lone Run
Short Run A B C D

A 39 3 0 0
B 2 19 0 0
C 10 1 8 1
D 4 0 0 3


Consistency of Choices by Income Settin~

A similar comparison of consistency of choice pair selections by
the 90 farmers is made in this section by income setting.

Again, the junction of a row and a column indicates the number of
farmers selecting the respooelve act pairs as the setting changed in the
short run under the added, no added income combination. It can be noted
that in table 9 forty-one farmers or 45.5 per cent of the total selected
consistent act pairs. This compares with 77.7 per cent from Table 7 and









-60-


76.6 per cent from Table 8. It is apparent from Table 9 that changes in
pairings that occurred were primarily from act B in the no added income
setting to act A in the added income setting.


TABLE 9. OCCURRENCE OF PAIRS OF CHOICES MADE BY FARMERS IN
THE NO ADDED INCOME AND THE ADDED INCOME SETTING IN THE
SHORT RUN

With Added With No Added Income
Income A B C D

A 14 28 0 0
B 1 20 0 0
C 6 8 5 1
D 0 4 1 2



A parallel trend is shown in Table 10 which compares the no added
with the added income setting, both in the long run. Consistency of
alternative act pairs in the long run was 52 out of the 90 farmers or
57.7 per cent of the total. Out of this total, over half chose the act
pair AA in the long run as compared with 15.5 per cent in the short run.
This comparison indicates that a higher percentage of farmers try for
income maximization, in both income settings, in the long run than in
the short run.


TABLE 10. OCCURRENCE OF PAIRS OF CHOICES MADE BY FARMERS IN
THE NO ADDED INCOME AND THE ADDED INCOME SETTING IN THE
LONG RUNI

With Added With No Added Income
Income A B C D

A 28 27 0 0
B 2 21 0 0
C 5 3 0 0
D 0 1 0 3




In Table 10, similarly to Table 9, the next highest act choice
to consistent pair AA was the change from act B, the maximin approach,
to act A, the long run maximization approach, as the setting changed
from the no added to added income assumption.









-61-


CHAPTER VII

FARMERS' CHOICE DIFFERENCES BY PHYSICAL
AND FINANCIAL FACTORS

This section concerns the differences in physical and financial
factors that occurred in choice acts under the four settings in the
hypothetical enterprise profit matrix described previously. The specific
factors analyzed were (a) total capital managed, (b) operator's age,
(c) equity in the farm business, (d) educational level, (e) liabilities
against the farm business, and (f) tenure.

Capital Managed

Substantial differences existed in amount of capital managed
between farmers and between areas of the state.1 The median amount of
capital managed was determined in each area such that half of the
farmers interviewed from each area would be included in the low capital
group and half in the high capital group. Table 11 summarizes the acts
chosen by farmers classified according to capital managed.

By inspection of Table 11, one finds similar results in choice
act patterns between the farmers managing a high level of capital versus
those with a low capital level. A chi-square test of independence,
using each one of the four settings as a contingency table, did not
indicate any significant difference at the 95 per cent confidence level
in any one of the four settings.

Visual observation indicates that a pattern exists in act choice
differences in the high and low capital level as settings change. In the
short run with no added income, the high capital level group tended
to choose act A more frequently, act B less frequently, and with no
meaningful differences in the choices of act D. These results suggest
that the high capital group tends towards less uncertainty aversion under
the realistic no added income setting in the long run.

As the setting changes to the long run no added income, there is
essentially no difference between act choices selected in the high and
low capital managed levels. As compared with the first setting, however,
a larger percentage of the low level group chose the more conservative
act B than the long run income maximization act A.

Under the short run added income setting, the act B choices were
nearly equal; act A choices were higher in the low capital group; and
acts C and D choices were higher in the high capital level group. This
suggests that, under the added income setting, some farmers in both
capital groups changed to the high gambling acts C and D, and a larger


1Appendix Table 3, page 124.









-61-


CHAPTER VII

FARMERS' CHOICE DIFFERENCES BY PHYSICAL
AND FINANCIAL FACTORS

This section concerns the differences in physical and financial
factors that occurred in choice acts under the four settings in the
hypothetical enterprise profit matrix described previously. The specific
factors analyzed were (a) total capital managed, (b) operator's age,
(c) equity in the farm business, (d) educational level, (e) liabilities
against the farm business, and (f) tenure.

Capital Managed

Substantial differences existed in amount of capital managed
between farmers and between areas of the state.1 The median amount of
capital managed was determined in each area such that half of the
farmers interviewed from each area would be included in the low capital
group and half in the high capital group. Table 11 summarizes the acts
chosen by farmers classified according to capital managed.

By inspection of Table 11, one finds similar results in choice
act patterns between the farmers managing a high level of capital versus
those with a low capital level. A chi-square test of independence,
using each one of the four settings as a contingency table, did not
indicate any significant difference at the 95 per cent confidence level
in any one of the four settings.

Visual observation indicates that a pattern exists in act choice
differences in the high and low capital level as settings change. In the
short run with no added income, the high capital level group tended
to choose act A more frequently, act B less frequently, and with no
meaningful differences in the choices of act D. These results suggest
that the high capital group tends towards less uncertainty aversion under
the realistic no added income setting in the long run.

As the setting changes to the long run no added income, there is
essentially no difference between act choices selected in the high and
low capital managed levels. As compared with the first setting, however,
a larger percentage of the low level group chose the more conservative
act B than the long run income maximization act A.

Under the short run added income setting, the act B choices were
nearly equal; act A choices were higher in the low capital group; and
acts C and D choices were higher in the high capital level group. This
suggests that, under the added income setting, some farmers in both
capital groups changed to the high gambling acts C and D, and a larger


1Appendix Table 3, page 124.










-62-


percentage of the low capital level group switched to act A. Even then,
the low capital groups uncertainty aversion still remains higher than for
the high capital group.


TABLE 11. ALTERNATIVE CHOICES BY FARMERS UNDER LOW AND HIGH
LEVELS OF CAPITAL MANAGEDa

Levels of Alternative Choices
Capital A B C D
Managed
(Numbers)

Short Run No Added Income

High 12 27 5 1
Low 9 33 1 2

Long Run No Added Income

High 18 26 0 1
Low 17 26 0 2

Short Run Added Income

High 18 11 12 4
Low 24 10 8 3

Long Run Added Income

High 28 10 5 2
Low 27 13 3 2


aMedian capital managed was: eastern area, $89,000;
central area, $49,000; and western area, $53,000.


Under the long run, no added income setting, the acts chosen by each
group were extremely similar.


Educational Level

The educational level of the farmers interviewed ranged from the
third grade through 16 years.2 The median level of education was between
the eighth and ninth grades. Accordingly, all farmers were classified


2Appendix Table 3, page 124.







-63-


into two levels of education such that a comparative analysis between
education groups could be made.

A chi-square test of independence was made on all four settings
in Table 12. This test indicated a significant difference at the 95
per cent confidence level for (a) the short run no added income setting,
and (b) the long run no added income setting. A significant difference
at the same confidence level was not indicated under either of the
added income settings. Because of the unreliability of the chi-square
test of independence in this case, visual observation of differences is
used.4


TABLE 12. ALTERNATIVE CHOICES BY FARMERS UNDER LOW AND HIGH LEVELS OF
EDUCATION

Level Alternative Choices
of A B C D
Education No. % No. % No. % No. %

Short Run No Added Income

High 15 36.6 22 53.7 2 4.9 2 4.9
Low 6 12.0 38 77.6 4 8.2 1 2.0

Long Run No Added Income

High 24 58.8 17 41.4 0 1 2.4
Low 12 24.5 35 71.4 0 2 4.1

Short Run Added Income

High 21 51.2 6 14.6 11 26.8 3 4.9
Low 21 42.9 15 30.7 9 18.4 4 8.2

Long Run Added Income

High 26 63.4 7 17.0 6 14.6 2 4.9
Low 29 49.2 16 32.7 2 4.1 2 4.1


3Low
education
education


level of education includes all farmers with eighth grade
and lower. High level of education includes all farmers with
over the eighth grade.


4The chi-square test is not reliable when there are few obser-
vations in some of the cells. To increase the chance of reliability, acts
C and D were combined into one cell in the short run no added income set-
ting; acts C and D were omitted in the computation of chi-square in the
long run added income setting.







-64-


Visual observation indicates that a higher percentage of farmers
in the high education level selected act A under all four settings.
Vice versa, a higher percentage of farmers in the lower educational
level group selected act B under all four settings. This difference is
more evident in the two settings under the no added income assumption as
was indicated from the results of the chi-square tests explained earlier.

Age Level

The age level of the farmers interviewed ranged from 26 to 80
years of age. The median age was 47 years. The low level age group
contains all farmers age 47 and younger and the older age group all
farmers over 47 years of age.

Table 13 indicates that, under each alternative setting, the
lower or younger age group tended to select act A more often than the
older age group. This difference becomes less pronounced as the setting
changes from no added to added income. Conversely, in each setting, the
older age group tended to select act B, the ultra-conservative maximin
approach, more often than the younger group. This apparent tendency for
the younger age group to try for income maximization and/or higher
uncertainty preference holds true in the comparative numbers of each
group selecting act C. However, more of the farmers in the older age
group selected act D, the act with an uncertainty level between those of
acts C and A.


TABLE 13. ALTERNATIVE CHOICES BY FARMERS UNDER LOW AND
HIGH LEVEL AGE GROUPS

Age Alternative Choices
Levels A B C D
(Humbers)
Short Run No Added Income
High 6 35 2 2
Low 15 25 4 1
Long Run No Added Income

High 11 32 0 2
Low 24 20 0 1
Short Run Added Income
High 21 12 5 7
Low 21 9 15 0

Long Run Added Income
High 27 14 1 3
Low 28 9 7 1


5Appendix Table 3, page 124.







-65-


Liabilities


As shown in Table 14, the average amount of liabilities
of the survey farmers was slightly over $5,600. Half of the
liabilities under $3,000 with the other half over $3,000.


for all
group had


Visual observations indicate little if any difference in choice
patterns between the low and high liability groups. A chi-square test
of independence indicated no significant difference at the 95 per cent
confidence limit. That is, no significant difference exists in choice
patterns between the two groups. As in previous analyses, the pattern
in moving from the short to the long run and from no added to added
income settings is that a larger number of farmers selected acts A, C,
and D which represent the higher uncertainty levels.


TABLE 14.


ALTERNATIVE CHOICES BY FARMERS ACCORDING TO


LIABILITY LEVEL

Liability Alternative Choices
Level A B C D
(Numbers)
Short Run Io Added Income
Under $3,000 9 29 5 2
Over $3,000 12 31 1 1
Long Run No Added Income
Under $3,000 17 27 0 1
Over $3,000 18 25 0 2
Short Run Added Income
Under $3,000 18 12 10 5
Over $3,000 24 9 10 2
Lon. Run Added Income
Under $3,000 29 12 3 1
Over $3,000 26 11 5 3




Farm Business Equity

The per cent of equity in the farm business ranged from a low of
20 per cent to a high of 100 per cent. An equity of 93 per cent and
over included half of the group with the other half having less than 93
per cent equity. A chi-square test did not indicate any significant
difference in choice settings between the groups with the high and low
levels of equity in the farm business.

Visual observation of Table 15 indicates that, in most cases, a
larger number of farmers with an equity under 93 per cent chose act A







-65-


Liabilities


As shown in Table 14, the average amount of liabilities
of the survey farmers was slightly over $5,600. Half of the
liabilities under $3,000 with the other half over $3,000.


for all
group had


Visual observations indicate little if any difference in choice
patterns between the low and high liability groups. A chi-square test
of independence indicated no significant difference at the 95 per cent
confidence limit. That is, no significant difference exists in choice
patterns between the two groups. As in previous analyses, the pattern
in moving from the short to the long run and from no added to added
income settings is that a larger number of farmers selected acts A, C,
and D which represent the higher uncertainty levels.


TABLE 14.


ALTERNATIVE CHOICES BY FARMERS ACCORDING TO


LIABILITY LEVEL

Liability Alternative Choices
Level A B C D
(Numbers)
Short Run Io Added Income
Under $3,000 9 29 5 2
Over $3,000 12 31 1 1
Long Run No Added Income
Under $3,000 17 27 0 1
Over $3,000 18 25 0 2
Short Run Added Income
Under $3,000 18 12 10 5
Over $3,000 24 9 10 2
Lon. Run Added Income
Under $3,000 29 12 3 1
Over $3,000 26 11 5 3




Farm Business Equity

The per cent of equity in the farm business ranged from a low of
20 per cent to a high of 100 per cent. An equity of 93 per cent and
over included half of the group with the other half having less than 93
per cent equity. A chi-square test did not indicate any significant
difference in choice settings between the groups with the high and low
levels of equity in the farm business.

Visual observation of Table 15 indicates that, in most cases, a
larger number of farmers with an equity under 93 per cent chose act A







-66-


as compared with act B. However, under the first three settings, more
farmers in the high equity group chose acts C or D. It seems that the
high level equity group was divided into two extremes. Either they were
extremely conservative choosing act B, or they were extreme gamblers
choosing act C or D.

TABLE 15. ALTERNATIVE CHOICES BY FARMERS ACCORDING TO
EQUITY IN THE FARM BUSINESS

Equity Alternative Choices
Percentage A B C D
(Numbers)
Short Run No Added Income
93 and over 9 30 4 3
Under 93 12 30 2 0
Long Run No Added Income
93 and over 15 29 0 2
Under 93 20 23 0 1
Short Run Added Income
93 and over 18 11 11 6
Under 93 24 10 9 1
Long Run Added Income
93 and over 28 12 4 2
Under 93 27 11 4 2



Alternative act choices under liability level and farm business
equity were nearly identical. The low liability group corresponded to
the pattern established in the high equity group. Both are measures
of financial characteristics and, therefore, similar choice patterns
should occur.

Tenure

Out of the sample of 90 farmers, 41 were full owner-operators,
12 rented all their land, and 37 were a combination of both.

Because there were only 12 renters out of the total sample, it was
impossible to make a comparative analysis. However, from the data
available under all four settings, a higher percentage of the owners
selected act B than did either the renters or owner-renters.

Under all settings, a higher percentage of the renters tended
to select the acts with a higher uncertainty level as compared to the
act choices made by either the owners or owner-renters.










-67-


Consistency of Act Choices

Some definite patterns emerge in the analysis of act choices by
physical and financial characteristics under the four settings of time
and income (Table 16). Some farmers also were quite consistent in
choosing a particular act in all four settings. That is, their uncertain-
ty aversion and/or preference did not change as the setting changed.

There appear to be some definite differences in physical and
financial characteristics of the farmers by the acts they chose and
retained as the settings were changed.

The group of farmers that consistently selected act A, the Laplace
criterion which represents highest income over time, had (a) the lowest
age, (b) the highest level of education, (c) the highest level of capital
managed, (d) the highest amount of liabilities, (e) the lowest percentage
of equity in the farm business, and (f) a nearly average number of
dependents relying on them for full support.


TABLE 16. PHYSICAL AND FINANCIAL CHARACTERISTICS OF FARMERS BY THE
CONSISTENCY OF ACT CHOICES AND/OR COiMBINATIONS UNDER FOUR SETTINGS OF
TIME AND INCOME

Avere Acts Chosen Under the Four Settings
Average Always Always Always Sometimes
Characteristics Act A Act B Act A or B Act C or D
Characteristics 90 (27
Farmers (13 (18 (32 (27
Farmers Farmers) Farmers) Farmers) Farmers)
Age in Years 47.9 43.1 55.6 46.0 46.1
Education in
Years 9.5 11.2 9.1 9.5 10.1
Number of
Dependents 3.2 3.1 2.7 2.9 4.2
Capital Managed
(Thous. Dol) 70.3 87.4 5G.3 56.0 87.2
Liabilities
(Thous. Dol) 5.6 6.9 3.7 6.8 4.7
Equity Percentage 86.6 83.7 93.0 83.4 90.0
Tenure:
(No. of Farmers)
Owners 41 4 11 20 6
Owner-Renters 37 7 7 8 15
Renters 12 2 0 4 6










-68-


In contrast, the group of farmers consistently selecting act B,
which represents the most conservative or the maximin approach, had
(a) the highest age level, (b) the lowest level of education, (c) the
lowest number of dependents relying on them for full support, (d) the
lowest level of capital managed, (e) the lowest amount of liability
against the farm business, and (f) the highest equity ration.

Combining the above two groups that consistently selected either
act A or B and adding to this total the farmers that consistently stayed
with an AB combination under all four settings, produces a group whose
physical and financial characteristics are very similar to the average
of all 90 farmers.

The group of farmers that selected either act C or D in at least
one of the settings of time and added income had physical and financial
characteristics such that the group had (a) an age level close to
average, (b) a higher than average education, (c) more than the average
number cf dependents, (d) a higher than average amount of capital
managed, (e) lower than average liabilities, and (f) a higher than
average equity ratio.

The tenure breakdown indicated that within the group consistently
selecting act A over 50 per cent were owner-renters. Those selecting
act B only were over 60 per cent full owners. The group selecting act
C or D on one or more of the settings were over 50 per cent owner-
renters. Out of the total group surveyed, only 40 per cent were owner-
renters.

The first two settings--that is, the short and long run with no-
added income--are most comparable to the actual decision-making situ-
ation facing the majority of farmers, Table 17 outlines the average
characteristics of the farmers who (a) consistently selected one act, or
(b) other specified act combinations under the long and short run no
added income settings.

A definite pattern appears in Table 17. The group that
consistently selected act A under both the long and short run no added
income settings had (a) the lowest age level, (b) the most education,
(c) next to the highest number of dependents, (d) the largest amount of
capital managed, and (e) the highest level of liabilities against the
farm business. Also, there was a substantially higher percentage of
owner-renters that consistently selected act A in comparison with the
other tenure classes.

The group of farmers that consistently selected act B represented
farmers that had (a) the highest age level, (b) the least education,
(c) the least number of dependents, (d) the lowest level of capital
managed, (e) nearly average level of liabilities, and (f) nearly average
percentage of equity in the farm business. In this group, the percent-
age of owners is substantially higher in comparison with the other tenure
classes.










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TABLE 17. PHYSICAL AID FINANCIAL CHARACTERISTICS OF FARMERS BY
CONSISTENCY OF ACT CHOICES AND/OR COMBINATIONS UNDER THE LONG AND SHORT
RUN NO ADDED INCOME SETTINGS


Average Acts Chosen Under the Two Settings
of Always Always Either Act Sometimes
Characteristics 90 Act A Act 3 A or B Act C or D
Farmers (19 (49 (13 (9
Farmers) Farmers) Farmers) Farmers)

Age in Years 47.9 42.0 52.8 42.5 45.0
Education in
Years 9.5 11.0 8.6 10,6 9.0
Number of
Dependents 3.2 3.4 3.0 3.0 4.2
Capital Managed
(Thous. Dol.) 70.3 90.0 63.5 63.5 77.9
Liabilities
(Thous. Dol.) 5.6 7.4 5.9 4.8 1.u
Equity Percentage CC.6 84.0 89.0 84.0 93.3
Tenure:
(No. of Farmers)
Owners 41 6 20 5 2
Owner-Renters 37 11 16 6 4
Renters 12 2 5 2 3



The group that selected a combination of acts A and B possesses
average characteristics which are intermediate between the groups
consistently selecting acts A and B. This group had (a) the lowest age
level, (b) higher than average education, (c) slightly lower than the
average number of dependents, (d) lower than average capital managed,
(e) lower than average liabilities, and (f) lower than average equity in
the farm business. The tenure ratio in this group follows closely the
overall distribution of the entire sample.

The group that selected act C or D as at least one of the choices
under the two settings is characterized primarily by its much lower than
average liabilities and resultant higher than average equity in the farm
business. This group had (a) slightly lower than average age level,
(b) lower than average educational level, (c) substantially higher than
average number of dependents, and (d) higher than average capital managed.
The tenure ratio in this group is 2:1 in favor of owner-renters as
compared to about 7:6 ratio of owner-renters in the total sample.










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CHAPTER VIII

REASONS AND ANALYSIS OF CHOICE PATTERNS OF
THE HYPOTHETICAL SPECIFIC
RESOURCE USE MATRIX

This chapter analyzes the choice patterns and reasons given by
farmers in their selection of acts from the specific resource use matrix.
The specific resource employed to develop the payoff matrix was hypo-
thetical cost and return data from different levels of fertilizer use.

Each of the farmers interviewed selected on of the alternative
acts in the hypothetical fertilizer return matrix. This matrix would
be most comparable to the short run no added income setting of the
hypothetical enterprise profit matrix because in both situations the
choice represents a one-year period only with the opportunity to make a
different choice in the following production period. In the fertilizer
matrix, the different acts do not represent equal annual investments;
instead the investment increases as the rate of fertilization increases.
The number of farmers selecting each act is shown in Table 18.

The choice reasons given by the respondents were many and varied.
Most consistently, the farmers selecting act E indicated their choice was
influenced by the stability of returns every year coupled with the lo:i
investment required. Two out of the 37 selecting act E indicated that
this represented the highest return per dollar invested. The physical
and financial characteristics of these two farms indicated (a) full
ownership, (b) below average size, (c) a high equity ratio, coupled with
(d) many years of farm operation. This combination of characteristics
would indicate that these two farmers were, and possibly have been
extremely conservative in their managerial decisions in the past.


TABLE 18. DECISION THEORIES APPLICABLE TO EACH ALTERNATIVE: NUMBER OF
FARMERS SELECTIITG EACH ACT

Applicable Number of Per Cent
Alternative Decision Theories Farmers of Farmers


E !Hald Maximin
(Hurwicz with = .61 37 40.1
F Laplace
(Hurwicz with .55 G Savage Regret
(Hur-,icz with .50 X 5 .55) 2 2.2
H Maximax
(Hurwicz with X-:C .50) 15 16.6










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The farmers selecting act F in nearly all cases indicated that
this alternative represented the highest average return over time. Many
farmers indicated that in this state, with the variability of rainfall
and resultant yields, a loss year must be expected. This is in direct
reference to act-state combination FS3. The implication was that even
with an anticipated negative return to a production input in some years
the wise course to follow was to attempt to maximize returns over time.

Only two out of the 90 farmers selected act G. One of these
indicated, as a choice reason, that in two out of the four past years
returns were higher--an apparent reference to act F with its higher
average over time--and that the loss year would not be too serious to
absorb. As indicated in Table 18, act G would be selected by a farmer
under the Savage regret criterion or one with a pessimism-optimism index
of about 0.50. Conceivably, this farmer was attempting to minimize
regret in following his rationalization of act G over F. In his own
mind, without actually expressing these words, he may have been
thinking, "I would be sorry if I missed the higher returns represented
in Sl and S3 in combination with act G even though there is the chance
of S2 and S" to decrease my returns." This reason would likely be an
approximation of the Savage regret index. The second farmer selecting
act G indicated that his reason was that this act most nearly followed
his past experience with fertilizer. It seems likely that this farmer
either did not understand the model he was faced with or was lacking in
logical managerial decision-making ability. This conclusion is sub-
stantiated by the responses this particular farmer gave in section 2 of
the questionnaire. Under the no added income settings, this farmer
selected act A, the Laplace criterion, and under the added income
settings he became more conservative and selected act B.1

Fifteen out of 90 farmers selected act H in the hypothetical
fertilizer return matrix. In nearly every case, the reason given by the
farmer suggested that they were following the maximax criterion. They
were, in most cases, willing to gamble for the larger return. Some of
them indicated they were willing to gamble that the higher returns would
occur more often than past results had indicated.

A comparison of the physical and financial characteristics of the
farmers against the fertilizer matrix act choices indicates some differ-
ences in average group characteristics (Table 19).

The group that selected act E, the most conservative or least
uncertain act in the fertilizer matrix, were similar in characteristics
to the group that selected the conservative act B under the enterprise
matrix. Both groups had (a) the highest age level, (b) the least
education, (c) the lowest level of capital, (d) the lowest level of
liability, and (e) the highest percentage of equity. Similarly, both
groups had a higher percentage of owners in comparison to the tenure
ratio of the total sample.


Refer to arrow "W" on Flow Chart 1, page 88.










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TABLE 19. PHYSICAL AND FINANCIAL CHARACTERISTICS OF FARMERS BY ACT
CHOICES

Matrix Act Selected
Average E F G H
Number of Farmers 90 37 36 2 15
Characteristic

Age in Years 47.9 50.6 47.1 37.0 45.0
Education in Years 9.5 9.0 9.6 13.0 9.0
Number of
Dependents 3.2 3.3 2.8 2.5 3.3
Capital Managed
(Thous. Dol.) 70.3 55.0 82.0 68.2 80.6
Liabilities
(Thous. Dol.) 5.6 4.5 7.1 13.0 3.8
Equity Percentage 88.6 92.0 85.3 72.0 90.0

Tenure:
(No. of Farmers)
Owners 41 23 10 1 7
Owner-Renters 37 11 20 1 5
Renters 12 3 6 0 3



The group of farmers selecting act F had (a) slightly lower than
average age level, (b) nearly average education level, (c) considerably
higher than average in amount of capital managed and liabilities against
the farm business, and (d) a lower than average equity percentage. Also,
a much higher ratio of owner-renters selected this act in comparison to
the tenure ratio of the total sample.

The characteristics of the farmers selecting act H indicate
(a) lower than average age and education levels, (b) higher than average
level of capital managed, but (c) lower than average liabilities, with a
resultant (d) higher than average equity percentage. The ratio of
tenants to owners and owner-renters is very similar to the overall sample
tenure ratio.







CHAPTER IX


SUMMARY AND CONCLUSIONS

Farmers are faced daily with decisions that will affect the short
and long run production and/or product price and, therefore, returns from
a particular acre, head of livestock, an enterprise, or the total farm
unit. Usually these decisions must be made under conditions of imperfect
knowledge of future occurrences concerning yield, price, costs, weather,
and technology. This decision-making uncertainty is compounded in North
Dakota as compared with many other states because of the highly variable
and unpredictable weather conditions.

The purpose of this study was to determine the pattern or corre-
lation between the physical and financial characteristics of a sample of
farmers and their apparent differences in arriving at resource use and
enterprise decisions in the face of varying degrees of uncertainty. The
results of this study are intended for use by agricultural research and
Extension Service personnel as an aid in formulating recommendations for
farmer use that will be adaptable to individual farmers with their
varying degrees of risk and uncertainty aversion, and their ability and
willingness to withstand varying degrees of risk.

The sample of farmers was drawn from six counties--Traill, Grand
Forks, Foster, Eddy, Stark, and Dunn--to represent the three different
rainfall and type of farming areas of the state. A total of 90 farmers
in these six counties were personally interviewed.

Each farmer's decision-making pattern was tested through the use
of two hypothetical profit matrices. In the first matrix, the farmer
was asked to select, under each of four settings of time and income, one
act or choice out of a total of four. Each one of the four acts was
designed to represent the payoffs or returns realized over a period of
years from a specific enterprise. In the second matrix, each farmer was
again asked to select one of four acts or choices which were described as
varying levels of fertilizer use and their respective returns over costs
over the past years. The assumption was inherent in each matrix that the
payoffs or returns were applicable to his own particular unit.

The hypothetical enterprise profit matrix had four separate
setting combinations of time and income. The most realistic, as they
pertain to actual production decision making on the part of a farmer,
would be the settings in the short and long run under the concept of no
added income. Also, the hypothetical fertilizer matrix would be
realistic in that this is the type of real life decision that farmers are
faced with in the operation and management of a farm unit.

In both matrices, the four act choices were designed to coincide
with specific choice patterns as delineated under the different game and
decision theory criteria. These criteria are based primarily on the
relative amount of uncertainty involved in the particular act in relation
to the uncertainty in the remaining act choices in the matrix. The act
choice selected by the farmer, under either matrix and in each of the
settings of time and income, is supposed to indicate the particular
individual's relative uncertainty aversion compared with the other farmers
in the sample.








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Choice reasons given by the respondents indicated thought patterns
which approximated the decision theory criteria of (a) the Wald maximum
approach, (b) the Laplace criterion of insufficient reason, "(c) the maximax
approach, and (d) the Savage regret criterion. Table 20 indicates the
relative uncertainty levels of these four decision criteria. This table
also summarizes the choices under both payoff matrices that correspond to
these criteria.


TABLE 20. RELATIVE UNCERTAINTY COMPARISONS OF SELECTED DECISION CRITERIA
AND THEIR APPLICABILITY TO THE HYPOTHETICAL MATRIX CHOICES


Relative Applicable Choices Under the
Criterion Uncertainty Hypothetical Specific
Levela Enterprise Resource Use
Profit Matrix
Matrix (Fertilizer)

Wald Maximin 1 B E
Laplace 2 A F
Savage Regret 3 D G
Maximax 4 C H


aUncertainty level increases from ratings 1 through 4.



The Wald criterion is the most conservative criteria because it
selects the maximum of the minimum payoffs of each choice act under the
assumption that nature will employ its worst state.

The Savage regret criterion attempts to minimize regret on the
part of the individual through application of the minimax rule to the
calculated regret matrix derived from the payoff matrix.

The maximax criterion ignores all the other payoff data in the
matrix except the AmSn combination that has the highest payoff.


Implication of Findings

Possibly the most unexpected and revealing result of this study
was the large percentage of the sample farmers that selected act B
(Wald) under four settings of the hypothetical enterprise matrix, and
act E (Wald) under fertilizer matrix.

In the short run no added income setting, 66 2/3 per cent of the
sample farmers selected act B (Wald). In the long run no added income







-75-


setting, this percentage dropped to 57.7 per cent. In the same income
setting, 54.4 per cent of the farmers selected this act B under both the
short and long run time setting. Under the fertilizer matrix, 41.1 per
cent of the farmers selected the Wald maximin act E.

Certainly these results indicate very strongly that the
assumption most agricultural workers tend to follow in releasing recom-
mendations for farmer use are only applicable to a portion of the farmer
clientele. Often, such recommendations are single-valued expectations
based on the highest average outcome over time. Also, in complete farm
budgeting, the income maximization approach, within realistic limits of
family labor use, is commonly employed. This study, though based on a
small sample, certainly does not bear out the assumption that the first
concern of the majority of North Dakota farmers is income maximization.

In fact, under the short and long run no added income settings,
only 23.3 per cent and 38.8 per cent of the sample, respectively,
selected act A which represents the Laplace criterion based on the
highest average return over time. Under the same income setting, 21.1
per cent of the farmers consistently selected act A under both the long
and short run time setting. In the fertilizer matrix, only 40 per cent
of the farmers selected act F which is also equivalent to the Laplace
criterion.

There is some indication from the data collected that differences
exist in physical and financial characteristics between acts selected by
classification groups under the various settings of the two matrices.
The following comparisons are based on (a) all four settings of the hypo-
thetical enterprise profit matrix, (b) the two time settings under the
no added income setting of the same matrix, and (c) the hypothetical
fertilizer matrix. Most conclusions are drawn from the groups selecting
the Wald and Laplace criteria. These two criteria contain the majority
of the sample. Also, they represent the difference between income
security and income maximization.

Age

In all settings, the group that consistently selected the Wald
criterion had the highest average age. Conversely, the group con-
sistently selecting the Laplace criterion were either the youngest group,
as in the hypothetical enterprise matrix, or at least younger than average
as in the fertilizer matrix.

This study showed that a majority of the farmers are more
concerned with security maximization than income maximization also. It
showed that the older age group was the most conservative or has the
highest uncertainty aversion.

Education

In all settings, the group consistently selecting the Laplace
criterion had the highest average educational level. In part, this is
probably due to the fact that this was also the youngest age group which







-75-


setting, this percentage dropped to 57.7 per cent. In the same income
setting, 54.4 per cent of the farmers selected this act B under both the
short and long run time setting. Under the fertilizer matrix, 41.1 per
cent of the farmers selected the Wald maximin act E.

Certainly these results indicate very strongly that the
assumption most agricultural workers tend to follow in releasing recom-
mendations for farmer use are only applicable to a portion of the farmer
clientele. Often, such recommendations are single-valued expectations
based on the highest average outcome over time. Also, in complete farm
budgeting, the income maximization approach, within realistic limits of
family labor use, is commonly employed. This study, though based on a
small sample, certainly does not bear out the assumption that the first
concern of the majority of North Dakota farmers is income maximization.

In fact, under the short and long run no added income settings,
only 23.3 per cent and 38.8 per cent of the sample, respectively,
selected act A which represents the Laplace criterion based on the
highest average return over time. Under the same income setting, 21.1
per cent of the farmers consistently selected act A under both the long
and short run time setting. In the fertilizer matrix, only 40 per cent
of the farmers selected act F which is also equivalent to the Laplace
criterion.

There is some indication from the data collected that differences
exist in physical and financial characteristics between acts selected by
classification groups under the various settings of the two matrices.
The following comparisons are based on (a) all four settings of the hypo-
thetical enterprise profit matrix, (b) the two time settings under the
no added income setting of the same matrix, and (c) the hypothetical
fertilizer matrix. Most conclusions are drawn from the groups selecting
the Wald and Laplace criteria. These two criteria contain the majority
of the sample. Also, they represent the difference between income
security and income maximization.

Age

In all settings, the group that consistently selected the Wald
criterion had the highest average age. Conversely, the group con-
sistently selecting the Laplace criterion were either the youngest group,
as in the hypothetical enterprise matrix, or at least younger than average
as in the fertilizer matrix.

This study showed that a majority of the farmers are more
concerned with security maximization than income maximization also. It
showed that the older age group was the most conservative or has the
highest uncertainty aversion.

Education

In all settings, the group consistently selecting the Laplace
criterion had the highest average educational level. In part, this is
probably due to the fact that this was also the youngest age group which







-76-


had more educational opportunities than their elders. In all settings,
the group consistently selecting the Wald criterion had the lowest level
of education.

Dependents

The group selecting the Wald criterion consistently had the
smallest number of dependents under the enterprise profit matrix. It
would appear logical that the more conservative choice could be associ-
ated with a larger number of dependents; however, there is likely
considerable correlation between age and number of dependents. In all
settings, the group that selected act C (maximax) or D (Savage regret)
at least once in the enterprise matrix had the highest number of
dependents relying on them for full support.

Capital Managed

Under all settings in both matrices, the group that consistently
selected the Laplace criterion had the highest average level of capital
managed. The next highest level of capital managed was in the group that
selected the highly uncertain act choices offered by acts C (maximax), D
(Savage regret), and/or H (Savage regret). These selections seem logical.
Under present day conditions of barely stable product prices, increasing
operational costs, and the emphasis on efficiency, the larger, more
successful farmer must have income maximization over time in mind. The
farmers in this group likely have taken risks and faced up to uncertainty
in the past to acquire control of the amount of capital presently under
their management.

Equity in the Farm Business

Under all settings, the group selecting the Laplace criterion has
the lowest percentage equity in the farm business. Conversely, the
highest percentage equity is found in the group consistently selecting
the Wald criterion. The one exception to this occurs in the long and
short run no added income settings in which the group that selected act
C (maximax) or D (Savage regret), alone or in combination with other
acts, had a very high percentage of equity in the farm business.

Tenure

In proportion to the number of owner-renters in the total sample,
more selected the Laplace criterion than did either the full owners or
full renters. This holds true under all settings in both matrices. Also,
in relation to the proportion of owners in the total sample, a pro-
portionally larger number of owners selected the Wald maximin criterion
under all four settings.







-76-


had more educational opportunities than their elders. In all settings,
the group consistently selecting the Wald criterion had the lowest level
of education.

Dependents

The group selecting the Wald criterion consistently had the
smallest number of dependents under the enterprise profit matrix. It
would appear logical that the more conservative choice could be associ-
ated with a larger number of dependents; however, there is likely
considerable correlation between age and number of dependents. In all
settings, the group that selected act C (maximax) or D (Savage regret)
at least once in the enterprise matrix had the highest number of
dependents relying on them for full support.

Capital Managed

Under all settings in both matrices, the group that consistently
selected the Laplace criterion had the highest average level of capital
managed. The next highest level of capital managed was in the group that
selected the highly uncertain act choices offered by acts C (maximax), D
(Savage regret), and/or H (Savage regret). These selections seem logical.
Under present day conditions of barely stable product prices, increasing
operational costs, and the emphasis on efficiency, the larger, more
successful farmer must have income maximization over time in mind. The
farmers in this group likely have taken risks and faced up to uncertainty
in the past to acquire control of the amount of capital presently under
their management.

Equity in the Farm Business

Under all settings, the group selecting the Laplace criterion has
the lowest percentage equity in the farm business. Conversely, the
highest percentage equity is found in the group consistently selecting
the Wald criterion. The one exception to this occurs in the long and
short run no added income settings in which the group that selected act
C (maximax) or D (Savage regret), alone or in combination with other
acts, had a very high percentage of equity in the farm business.

Tenure

In proportion to the number of owner-renters in the total sample,
more selected the Laplace criterion than did either the full owners or
full renters. This holds true under all settings in both matrices. Also,
in relation to the proportion of owners in the total sample, a pro-
portionally larger number of owners selected the Wald maximin criterion
under all four settings.




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