COMBINING SIMULATION AND LINEAR
PROGRAMMING IN STUDYING
FARM FIRM GROWTH

Thesis for the Degree of Ph. D.
MICHIGAN STATE UNIVERSITY
ROGER PRIVETTE STRICKLAND, JR.
1970

 

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thesis entitled

COMBINING SIMULATION AND LINEAR PROGRAMMING
IN STUDYING FARM FIRM GROWTH

presented by

Roger Privette Strickland, Jr.

has been accepted towards fulfillment
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PhoDo degree in AgriCUItural Economics

 

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ABSTRACT

COMBINING SIMULATION AND LINEAR PROGRAMMING
IN STUDYING FARM FIRM GROWTH

BY

Roger Privette Strickland, Jr.

Growth of the farm firm has been, and is projected to be,
a continuous trend confronting farm firm operators. Since most
of the causal factors tend to be industry wide, a large portion
of farm operators are affected and find it necessary to expand
their operation. With this situation in mind, the objectives of
this study were to measure the effects of incorrect production
decisions, to make a comparison of four alternative growth
strategies and two levels of managerial ability, and to determine
the impact of the various stochastic elements on the achievement
of growth. A model which consisted of a simulator and a linear
programming routine was used to analyze a size category of dairy
farms common throughout southern Michigan, the 35 to 40 cow herd
size.

The major portion of this study was based on eight individual
firms, one for each of four strategies operating under each of two
levels of managerial ability. The four strategies included a vertical
strategy and three lateral strategies. The two levels of managerial
ability were both better than average farmers who were regarded as

being the group most likely to successfully achieve growth.

Roger Privette Strickland, Jr.

The effect of incorrect production decisions, as measured by
variation in net income, was found to be quite large. This was true
even though an attempt was made to simulate realistic combinations
of enterprises. The increases in net income had two sources of
causation. One was decisions that were incorrect with regard to
the assumed decision criterion, expected net cash incomes. The
other was the stochastic variables. The incorrect decisions were
the primary causal factor as they accounted for 87 percent of the
income foregone through nonoptimal decisions in one five year test
period. The occurrence of these incorrect decisions in actuality
could be due to the farmers' failure to properly utilize their in-
formation and/or to the fact that they do not have adequate infor-
mation. In either event, there exists the possibility of a rather
substantial payoff for ensuring that more nearly optimal decisions
are made where optimal is defined in terms of maximizing expected
net cash income. The linear programming solutions differed from
the simulator solutions primarily in terms of two activities to
which it allocated land. One was the persistent renting-out of
a portion of the land under the control of the farmer. The second
was the inclusion of field beans in a large proportion of the
optimum solutions.

The analysis of the four types of strategies was divided
into two parts: (1) What is the potential for growth under each
strategy? and (2) What is the relative strength of the various
strategies under adverse conditions? No single strategy was superior
under both tests. The vertical strategy was the most resilient in

the face of adversity but permitted the achievement of a small amount

Roger Privette Strickland, Jr.

of growth relative to two of the other strategies. The weakest all-
around strategy was expansion by renting land under a long term con-
tract as it was always the first firm to succumb to adverse condi-
tions and was also relatively weak in the amount of growth allowed.
Due to its leadership in achieving growth and demonstrations of
strength in withstanding adverse conditions, expanding laterally by
means Of a land contract arrangement was found to be the best all-
around strategy. Based on the findings of this study, purchasing
land under a contract offers certain advantages to farmers if such
an arrangement is available. With its small down payment, it offers
the possibility of either acquiring control of additional quantities
of land or of releasing additional funds for other uses. It does,
however, present the imprudent operator with a means to financial
ruins through too much indebtedness. On the other hand, with
reasonable use, it offers the opportunity to acquire additional
resources beyond what could be purchased with larger down payments
which can be eSpecially important in the case of those assets sub-
ject to capital gains.

With regard to the two included levels of managerial
competency, that designated as above average was able to achieve
growth only at a rather moderate rate. On the other hand, the
exceptional level of management achieved growth at a rate that can
only be described as bordering on phenomenal. The fact that this
utterly fantastic rate of growth was achieved under stochastic
market and yield conditions would seem to increase the incredulity
of the results. However, the finding that this level of managerial

ability is able to prOSper under unfavorable conditions that could

Roger Privette Strickland, Jr.

lead to bankruptcy for the majority of farmers would tend to support
the conclusions about growth rates.

This strength in the face of adversity was due primarily to
the greater profitability of the firm under more normal operating
conditions. In fact, the firms possessing exceptional management
were so Successful under the stochastic conditions that they
accumulated cash at a faster rate than they could reealistically
expect to utilize it in acquiring assets within the price range
included in the simulator. This concluSion is based on the assump-
tion that the supply curve for land facing a firm would tend to be
rather inelastic in the snort run. The result is that these firms
would uSually have proportionately lower debt commitments and more
liquid portfolios of assets that allow it to successfully endure
conditions of adversity.

Another point that came under investigation was the impact
of variations in stochastic elements on the growth possibilities
of a firm. The conclusion was that given a bundle of assets and
a set of production decisions1 variations in stochastic elements
had very little effect on the growth of a firm during a one-year
period. Of all the stochastic influences, it appeared that land
purchasing was the biggest factor in determining the increase in
size. This means that the failure to acquire land, whether due to
its unavailability at certain times or to the failure or inability
to submit an adequate bid, can be critical to the growth prospects
of a firm. This point is, of course, consistent with the finding
that a land contract offers certain advantages because it allows
more land to be controlled. Yield was found to have a cumulative

effect over time but not a very large one.

COMBINING SIMULATION AND LINEAR PROGRAMMING
IN STUDYING FARM FIRM GROWTH

By

Roger Privette Strickland, Jr.

A THESIS
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHI IDSOPHY
Department of Agricultural Economics

1970

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ACKNOWLEDGMENTS

The author gratefully acknowledges the invaluable advice
and constructive criticism of Dr. Larry J. Connor and Dr. David L.
Armstrong under whose guidance this study was carried out. Their
encouragement during the course of this study is sincerely
appreciated.

Appreciation is also extended to Dr. Marvin L. Hayenga,
Major Professor, for his counsel throughout my graduate program
and to Dr. John R. Brake for reviewing the manuscript and offering
many helpful suggestions.

Thanks are due to Drs. L.L. Boger and D.E. Hathaway and the
Department of Agricultural Economics for the financial assistance
and the facilities which made possible this portion of my education.

The author expresses his sincere gratitude to his wife,
Carole, for her patience, understanding, and encouragement through-
out his graduate program.

Finally, a special word of appreciation to the parents of
the author who have been a source of inspiration throughout his

career .

ii

TABLE OF CONTENTS

Page
Acknowledgments ii
List of Tables V
List of Figures Vii
List of Appendix Tables Viii
Chapter

I Introduction 1
Objectives 5
Organization of Thesis 9

References 11

II Review of Literature 12
Summary 28

References 30

III A Conceptual Framework for Studying Growth 32
Goals 32

Economic Theory 34

Product Substitution 37

Input Substitution 39

Simulation 42

Theoretical Connotations of Simulation 47

Linear Programming 51

Theoretical Connotations of Linear Programming 53

Combining Simulation and Linear Programming 57

Fitting the Objective into a Conceptual Framework 59

References 65

IV Methodology 66
Farm Simulation 66

Policy Variables 70

Output 73

Linear Programming Model 73

As 8 umpt ions 7 6

Procedure 77

Phase 1 77

Phase 2 79

Phase 3 79

Phase 4 80

References 81

iii

Table of Contents Continued

Chapter

V Presentation of Results
Investment Decisions
Phase 1
Realistic Expectations
Cumulative Effect of Optimal Decisions
Year-to-Year Variation
Renting-Out Land
Unrestrained Acquisition of Assets
Phase 2
Selected Years
Modifications
Phase 3
Manner of Presentation
An Adjustment
Phase 4
Stochastic Routine

VI Analysis of Results
Effect of Optimality
Organizational Changes
Case for Additional Information
Strategies
Growth Potential
Withstanding Adverse Conditions
Summary
Managerial Ability
Potential for Growth
Withstanding Adverse Conditions
Stochastic Elements
Combined Effects
Yield
Distribution of Random Deviates
Limitations of Study
Implications for Future Research
Summary of Analysis
References

VII Summary and Conclusions
Appendices

Bibliography

iv

Page

82
84
86
86
97
98
99
100
102
102
102
107
107
108
108
109

117
118
123
126
127
127
129
132
134
134
136
136
137
138
140
145
148
151
154

155

161

176

Table

10.

11.

12.

LIST OF TABLES

Initial Characteristics of Farm Used in Study
Explanation of Firms Included in Study

Five Year Average of the Profitability of Selected
Enterprise Arrangements Under Two Managerial
(technology) Levels on Class I Land

Selected Characteristics for Comparison of Simulator
and Linear Programming Results at End of Year 15
for Eight Firms

Additional Value of Assets Obtainable with Optimum
Production Decisions Over a 15 Year Period for a
Specific Set of Investment Decisions Under Stochastic
Conditions

Selected Characteristics for Comparison of Simulator
and Linear Programming Solutions in Year 6 for Eight
Firms

Proportion of Total Acres Farmed Over 15 Year Period
by Simulator that was Rented Out by Linear Program

Selected Characteristics of Eight Firms Representing
Four Growth Strategies Under a High Level of
Managerial Ability, Year 16

Number of Years Eight Firms were able to Survive
Out of Five Year Periods of Adverse Conditionsat
Various Stages of Growth

Selected Characteristics for Comparison of Firms
Surviving Five Year Period of Adverse Conditions:
Study-Year 3, Adversity Level 1

Selected Characteristics for Compariosn of Firms
Surviving Five Year Period of Adverse Conditions:
Study-Year 6, Adversity Level 1

Selected Characteristics for Comparison of Firms
Surviving Five Year Period of Adverse Conditions:
Study-Year 6, Adversity Level 2

Page

83

84

87

91

92

96

101

103

104

105

106

List of Tables Continued

Table

13.

14.

15.

Number of Stochastic Results that Fall in Each of
Four Divisions of the Complete Range Over Which Four
Independent Samples Occurred

Partitioning Annual Losses From Nonoptimal Solution
into the Two Sources: Incorrect Decisions and

Stochastic Elements

A Summary Comparison of Strategies

vi

Page

116

121

128

Figure

10.

11.

12.

13.

LIST OF FIGURES

Product-Product Diagram
Factor-Factor Diagram
Product-Product Diagram with Expansion Path

Factor-Factor Diagram with Line of Least Cost
Combination

Product-Product Diagram with Alternative Expansion
Paths

A Product-Product Diagram Under Linear Programming
Assumptions

Product-Product Diagram for Simulator and E5 Post
Linear Program

A Flow Diagram of Simfarm

Frequency Distribution of Number of Firms by Value
of Assets Demonstrating the Effects in One Year of
all Stochastic Elements Combined

Frequency Distribution of Number of Firms by Value
of Assets Demonstrating the Effects in One Year of
Stochastic Price and Yield Conditions When no
Additional Land was Purchased

Frequency Distribution of Number of Firms by Value
of Assets Demonstrating the Effects in One Year of
Stochastic Price and Yield Conditions When 80 Acres
of Additional Land were Purchased

Frequency Distribution of Number of Firms by Value
of Assets Demonstrating the Effects in One Year of
Stochastic Price and Yield Conditions When 160 Acres
of Additional Land were Purchased

Frequency Distribution of Number of Firms by Value

of Assets Demonstrating the Cumulative Effect of
Stochastic Yields Over a 10 Year Period

vii

Page
38
38

41

41

50

54

60

67

111

112

113

114

115

Appendix
Table

LIST OF APPENDIX TABLES

Simfarm Transmittal Form
Simfarm Output Form
Linear Programming Matrix
Prices Received

Crop Yields

Input Prices

Livestock Rules

Labor Requirements by Enterprise

viii

Page

161
163
167
171
172
173
174

175

GIL-137T ER. I

Introduction

There has been a continuous trend in agriculture of growth

in the'average size of individual farm operations over the last

half century. Since 1920, the growth in the size of the farm firm

has been tremendous with the average, in acreage, having increased

by approximately 140 percent and 50 percent for the United States

and Michigan, respectively. Furthermore, the rate of growth in

farm firm size is expected to accelerate in the next decade.

*
Wright [1] has made the following projections with regard

to Michigan in 1980:

(1)

(2)

(3)

About one-half as many farms as in 1964, with a
sharp reduction in the number of general farms
with less than 180 acres and those with sales of
less than $10,000 a year.

Consolidation and enlargement of farms, where
there are adequate resources and management
ability, with a faster increase in average size
than in the past.

Over twice as many farms with sales of $20,000
or more as in 1964, with their percentage of all
farms increasing from 10 percent in 1964 to
nearly 40 percent by 1980, and with them produc-
ing over 80 percent of Michigan's agricultural
production.

In more precise terms, Wright has projected that in Michigan

the average acreage per farm will increase by 67 percent between

1964 and 1980 with an 87 percent increase in the number of farms

 

* All references and footnotes appear at the end of each chapter.

1

with more than 500 acres and a 68 percent decrease in the number of
farms with less than 180 acres.

Therefore, indications are that farm firm growth, which is
defined for the purposes of this study as the acquisition of addi-
tional productive resources that result in increased output, will
continue to be a force in agriculture in the coming decade, 1970-
1980.

The continual nature of farm firm growth tends to cause prob-
lems for the individual farm firm Operator who may find himself in
what seems to be a perpetual state of adjustment. One of the
principal factors which result in a general trend of growth among
farm firms is the constant occurrence of technological innovations.
These innovations tend both to require fewer hours of labor and to
expand the least-cost size of a productive entity. Thus, the farmer
needs a larger operation in terms of increased quantities of land
and/or livestock to reduce his costs in order to remain competitive
in the face of expansion by other farmers and to more fully utilize
his own labor. In addition these innovations are often of a
capital-using nature, so the farmer may find himself in the seemingly
chronic position of needing additional capital and credit with which
to purchase additional inputs.

A second factor that may contribute to a general trend of
continuous growth among farm firms is the fact that individual
proprietorship is the most dominant form of ownership. This factor
tends to lead to the breaking up of existing operations upon the
death or retirement of the present operator which means farm

operations often have to be rebuilt each generation in order to

achieve economies of size.

A third factor, the personal goals of the owner-operator
may also provide some incentive for the expansion of an individual
farm firm. Among the goals which are likely to influence the
decision to expand an operation are:

(1) the desire of the operator to be a full-time farmer;

(2) the desire of the operator to maintain his family's
level of living;

(3) the desire of the operator to attain the same in-
crease in level of living as his associates and
neighbors.

Thus, for these three reasons, and perhaps others, farmers are
generally faced with a reoccurring problem. Namely, an unending
struggle to acquire additional productive assets.

Resources may occasionally be acquired through inheritance,
marriage, or gifts but probably the most relevant means of obtain-
ing resources is to purchase, rent, or custom hire the desired
quantity with capital acquired internally through retained earnings
or externally through credit. In either case, growth necessitates
the existence of income beyond a basic standard of living that can
be retained by the firm since credit is to a great extent dependent
upon net worth.

Brake and Wirth [2] have the following to say about financ-
ing growth:

Farming generally requires a larger capital base to pro-

duce a given income stream than many other types of

business. For that reason, the process of capital
accumulation in farming is of great importance. (After
establishment)...there is often a substantial need for
capital to expand the business. Part of this need is

met by credit, but a large part comes from earnings

which are reinvested in the business. It is often the
case that in the expansion stage of growth, the farmer

must commit a large proportion of his income to the
payment of debts.

Under individual proprietorship, which is the dominant form of
ownership in the United States, the process of retaining earnings
is complicated by the interdependence of the production operation
and the consumption of the operator's household. An increase in
the use of capital by one decreases the amount of capital avail-
able to the other.

Farm firm growth is a complex process to study and there
are several factors other than raising investment and working
capital that contribute to this complexity. One factor is that
growth generally involves a time period of a duration that exceeds
what could reasonably be defined as short run so forces that are
usually assumed constant for static economic analysis are changing.
In fact, the achievement of growth intrinsically means that the
quantity of scarce resources is changing which tends to void any
previous solution of static economics. Irwin [3] recognizes this
problem‘with the following observation:

.A fundamental issue in studying growth is the inter-

relating of the short run production theory3 which

involves at least some fixed resources and the longer

run investment theory, which varies them.

The human element is another factor contributing to the complexity
of the growth process. The human factor may vary as to managerial
ability, technical knowledge, credit rating and marginal propensity
to save.

Empirical studies involving firm growth have generally employed

one of two techniques--simulation or linear programming including

such extensions of linear programming as polyperiod and recursive

programming--and have been unable to take all three factors--capital
accumulation, length of run and the human element--into account.
This study combines the two techniques to improve the handling of
at least two of these factors--length of run and the human element.

The length of run problem is handled by using the simulator
to give the firm continuity of operation in successive production
periods-while the linear program provides the short-run optimum
solution. The human element is handled in three ways: (1) Two
different technology levels are used to represent two qualitative
levels of management. (2) Four growth strategies are utilized to
represent variations in risk preferences and variations in owner-
ship preferences. (3) Decisions as to enterprise combinations in
the simulator are made to reflect the predominant enterprise

arrangements on existing southern Michigan dairy farms.
Objectives

Several aSpects of the growth process are of particular
interest. A simulator and an 35 Egg; linear program are combined
into a single model and used as the technique of analysis in
achieving the objectives presented below:

1. To study the effects of optimum decision making versus
incorrect decisions on the growth process of farm firms.

2. To evaluate alternative growth strategies.

3. To study the effects of stochastic variables on the
growth potential of a firm.

4. To obtain a measure of the potential for growth of
firms operating under either of two levels of managerial

compentency.

The overall objective of this study was to analyze the growth
process of a selected size category of southern Michigan dairy farms.
Dairying was selected because it is the most common type of farm firm
in Michigan at the present time. Because the relationships contained
in the simulator used in this study are for southern Michigan farms,
the included operations are assumed to be southern Michigan dairy
farms. The initial characteristics of the firm used in this study

are given in Table 1.

Table 1. Initial Characteristics of Farm Used in Study1

 

 

 

Item Unit Amount
Cows Head 39
Land Acres 280
Assets Dol. 136,000
Gross Income Dol. 49,000
Net Income Dol. 19,000
Net Worth Dol. 53,000
Cash-on-hand Dol. 10,000

1

The initial situation was obtained by
manipulating the simulator until the desired
characteristics were obtained.
The life cycle of a farmroperator will usually involve three
stages in the acquisition and operation of his firms.
1. Establishment

2. Expansion

3. Consolidation

Only the second stage has relevance for this study because this is
the stage in which growth is achieved and because an established
firm is used in the initial time period.

One of the first steps in this study is to investigate the
effect of decisions that deviate from the optimum. Any divergence
from the optimum that occurs could result from either involuntary
conditions (weather, market, etc.) or voluntary conditions (pre-
ferences as to ownership, risk, etc.). The point that is of
particular interest is the effect of inefficiency of resource use.
The question involved here deals with determining just how critical
management is to the rate of growth achieved by a firm, particularly
in the area of choosing the correct combination of enterprises given
a specific resource situation and an uncertain environment. The
35.2235 linear program provides a measure of management at its
best, i.e., the optimum set of decisions based on perfect knowledge,
and thus provides a norm with which to evaluate other sets of
decisions. The primary means of guaging the effect of nonoptimal
decisions is the difference in both absolute and relative terms
between the two net income figures arrived at separately by the
simulator and linear program.

In order to study the effect of incorrect decisions partic-
ularly those resulting from voluntary conditions, it is necessary
to concentrate on both the vertical growth strategy and the lateral
growth strategy. An evaluation consisting of two principle stages
is directed at the alternative growth strategies. The first stage
is a comparison of the amount of growth that can be achieved under

the various strategies during a given time period. The second is

a test of the weakness of the various strategies under unfavorable
conditions. The principle hypothesis involved in this latter test
is that firms following strategies that involve a high level of
commitment to debt payment and/or fixed costs cannot withstand
adverse conditions to the degree that they could under alternative
strategies.

Two general types of growth strategies are evaluated in
this study. The first is referred to as a vertical growth strategy
in which emphasis is placed on the acquisition of nonland inputs
while maintaining a constant land base and making additional
acquisitions only of nonland inputs. The second strategy is a
lateral growth strategy in which emphasis is placed on expanding
the land base that is under the firm's ownership by purchasing or
renting additional acreage. Because of the large amounts of capital
that is usually involved in purchasing land, variations in such
policy decision variables as downpayment and amortization greatly
affect the amount of cash available to the firm at any point in
time. Therefore two levels of downpayment are included as varia-
tions of the lateral strategy to permit a comparison that would,
when effected, provide additional insight into the significance
of the variable, size of downpayment. Therefore, this study in-
cludes a vertical strategy and three variations of the lateral
strategy:

1. Expanding only the cow herd with the associated equip-
ment and facilities (the vertical strategy).

2. Expanding the cow herd and land base by renting

additional land.

3. Expanding the cow herd and land base by purchasing
additional land with a land contract involving a five percent
downpayment.

4. Expanding the cow herd and land base by purchasing
additional land with a mortgage involving a 25 percent downpayment.

A third objective and another area that comes under scrutiny
is the effect of the uncontrollable variance in prices and yields
which is largely exogenous to the firm. The question to be asked
here is whether the occurrence of different sequences and/or com-
binations of values greatly affect the success of firm seeking to
achieve growth.

To meet the fourth objective an attempt was made to isolate,
and then to consider, two levels of managerial competency from
the much broader spectrum that is thought to exist. The two in-
cluded levels of competency were designated as above average and
exceptional. The reason behind the elimination of the operators
in the lower ranges of the spectrum was that their chances of
achieving a substantial amount of growth was considered to be
negligible. The evaluation of managerial ability was carried
out in conjunction with the first two objectives by effecting a
measurement in both relative and absolute terms of the realistic
and optimal growth possibilities of each level of managerial

ability under each strategy.

Organization 2£_Thesis

The procedure followed in this study is that of first
reviewing past and present concepts and theories related to the

farm firm growth process. In Chapter II a review of some of the

10

literature that is relevant to this study is presented. Chapter
III is devoted to relating production economic theory to invest-
ment theory to explain the concept of firm growth and to include
how the objectives of this study will be handled. The actual
methodology used is presented in Chapter IV showing how linear
programming is combined with simulation to achieve the objectives
of this study. Chapter V contains a presentation of the results
of the study and is followed by Chapter VI containing the analysis
along with the limitations of the study and the implications for
future research. Chapter VII contains the summary and conclusions

of the completed study.

11

References

1. Wright, Karl T., '
Now and in 1980, Agricultural Experiment Station Research
Bulletin 47, Department of Agricultural Economics, Michigan
State University, East Lansing, 1966.

2. Brake, J.R. and MNE. Wirth, Michi an a m ed ane : 1L

History of Capital Accumulation, Research Report 25, Michigan
State University Experiment Station, East Lansing, 1964,

pp. 268.

3. Irwin, G.D., "A Comparative Review of Some Firm Growth Models,“
Ag. Econ. Res., No. 3, 1968, 20:82-100, p. 82.

CHAPTER II

Review of Literature

A number of recent papers and articles have been devoted to
the concept of farm firm growth. However, as of now there seems
to be little or no agreement as to the answers to such basic
questions as to how to measure growth or as to the way to best
use the various techniques that are available for studying growth.
A rather inclusive review of literature was undertaken in an attempt
to shed some light on these two questions in order to enhance the
relevance of the findings of this study.

The purpose of Renborg's paper [1] in his own words, is to
expose--not to solve--a number of problems that the operator faces
when he attempts to expand his farm firm. Among other things, he
explores operator goals, defines terms, and investigates char-
acteristics of various classes of inputs that lend themselves to
or impede the growth process. He also discusses the effect of
taxes, the effect of different borrowing conditibns, and the
abilities required of an operator.

Renborg defines size of a firm as "some measure of the total
sum of all means of production which the firm commands" [2]. He
then defines growth of the firm as an "increase of its size" [3].
With the definition he admits that it is possible to say that the
firm has grown only when there is an increase in at least one
dimension with no decrease in the other dimensions. Thus, when a

12

13

substitution of one input for another occurs as has happened in
the case of capital and labor, not only can the change in size not
be measured but not even the direction of change can be determined.

Renborg's paper is quite useful as a source of ideas for
study dealing with farm firm growth. One objectionable aspect of
his study is that Renborg's apparent acceptance of the definition
of size of the firm as "some measure of the total sum of all the
means of production which the firm commands" could be misleading.

The measure of size is a critical aspect of any growth study and

a mensuration of the firm's resources has not won complete acceptance
as a superior gauge of firm size either on theoretical or practical
grounds.

Bailey [4] defines firm growth; gives the necessary conditions
for the occurrence of growth; briefly discusses alternative strategies;
and presents a simple, illustrative example of a Montana wheat farmer
achieving growth. Firm growth is defined by Bailey as an increase
in the volume of business accompanied by an increase in inputs.

Thus, there are two ways of measuring the rate of growth; either in
units of production or in the associated units of inputs. He
specifically excludes increases in net worth and increased output
arising solely from a more efficient use of the same stock of
resources. In addition, Bailey lists the necessary conditions which
must exist for growth to occur and provides a brief discussion for
each one. His five major conditions are excess managerial capacity,
profitability of the business, minimum starting size, some unused
resources, and procurability of additional resources.

The discussion of the necessary conditions is probably the

most useful part of this study; mainly, because it emphasizes the

14

fact that not all firms are capable of achieving growth and that
those who do possess the capability will lilely achieve growth at
different rates. The author also performs a valuable service by
emphasizing the importance of future research in the area of farm
firm growth. Bailey's exclusion of increased efficiency from a
measure of growth implies the existence of "costless" production.

A more likely explanation of "increased efficiency" in many cases
is a qualitative improvement in some factor, particularly the

human agent, which is not accounted for in a quantitative summation
of inputs.

Irwin goes beyond Bailey's definition of growth with his
observation that... "the principle of growth is to acquire control
of the services of additional productive resources by paying a
price less than they will earn...(and that)...the process of growth
is at its core, obtaining funds to purchase the resources" [5].
Irwin also notes that two crucial aspects in considering growth
are (1) the concept of the decision process used, and (2) the
handling of internal and external flows of funds.

Irwin focuses on an important point with his statement that
"A fundamental issue in studying growth is the interrelating of
the short run production theory, which involves at least some fixed
resources, and the longer run investment theory, which varies them."
This point is particularly pertinent to the model used in this study
since the simulation model permits the purchase and sale of fixed
resources and the linear programming subroutine maximizes profit

over a one-year period given a set of fixed resources in accordance

with production theory.

15

In the recent publications by agricultural economists of
research completed in the area of firm growth have been several
computer-oriented models. In his article, Irwin evaluates and
compares the growth features included in three types of models--
polyperiod programming, recursive programming, and simulation.
Recursive and polyperiod programming may be distinguished from
simulation by noting that they are optimizing techniques while
simulation is a nonoptimizing technique. Irwin indicates that
optimizing applies to single goal mathematical models and such
models are valued for their analytic convenience and deductive
fertility. The difficulty with such models is with the realism
of their assumptions. Simulation as a multiple goal, nonanalytic
approach can be made to include more realism but has less deductive
elegance.

Irwin provides a description of the techniques used in the
various studies including a presentation of a simplified version
of the model in tabular form in most cases. He delineates the
relevant strong points and shortcomings of each study and provides
a brief evaluation. One important contribution of this article
is as a review of the relevant literature and as an introduction
to the understanding of the three models mentioned above. The
article includes such a large number of studies that there is
really not enough substance in each synopsis to allow a complete
evaluation of the individual studies or the three techniques. How-
ever, the article does serve a useful purpose by condensing a
number of relevant ideas pertaining to objectives and variations
in each technique into a convenient source from.which the more

interesting ones can be followed up.

16

The belief is expressed by Lee [6] that American agriculture
is on the threshold of an era of significant change in the structure
and organization of its production. Lee defines farming as "...the
bringing together of resource services for the production of so-
called agricultural commodities" [7]. Lee emphasizes the fact that
his definition says nothing about resource ownership. He points out
that, historically, the farmer has found it expedient to specialize
in putting services together to produce agricultural products and
to transfer many of his traditional activities to specialists. Lee
firmly believes that in the future there will be a tendency for the
ownership of resources to be in the hands of a group other than
farmers. He concludes that, in an economic sense, this process is
beneficial and, perhaps, steps should be taken to facilitate it.

Lee cites a number of advantages from the separation of resource
use and ownership including (1) increased flexibility, (2) more
leverage and growth, (3) easier entry for beginners, (4) more
efficiency from the additional specialization, and (5) minimization
of the problems of disinvestment.

Lee's paper has two particularly important implications for
this study. One is his definition of a farmer and, thus, as to
what constitutes firm growth. His definition of a farmer makes it
clear that he regards a firm as the total of the assets under the
control of the farmer; and therefore, firm growth consists of the
net increase in the volume of assets controlled by the firm. The
second implication arises from his predictions and conclusions about
the roles in future agricultural production of ownership of resources

and of owner's equity. These two points are particularly relevant

17

for the problem of choosing the appropriate strategies under which
the study will allow a firm to achieve growth.

Baker [8] uses linear programming to make an original investiga-
tion of one of the more difficult components of the forces affecting
a firm--the liquidity aspect of a credit reserve. The financial
component of a firm is only one of several components, but it is one
of the most important ones since the supply of capital available to
a firm is often the most restrictive factor. The financial component
has two major aspects--cash and credit--each of which has two char-
acteristics--quantity and liquidity--of which liquidity is the most
difficult to discern and measure, eSpecially in the case of a credit
reserve. The liquidity aSpect of credit is particularly difficult
to gauge because it originates in the policies of the lending in-
stitutions and is formulated by the representative of the institution
who applies it to a specific firm. Thus, borrowing not only gen-
erates a cost due to the more obvious interest charges, but, also,
due to loss of liquidity. I

Baker's main point is that this cost due to a loss of a
liquidity varies according to the type of load or source of collateral.
In his study he works with two types of loans as determined by the
purpose of the loan-~1ivestock and machinery. He assumes that the
lender's preference is to make livestock loans rather than machinery
loans. Thus, for each dollar of credit obtained to purchase machinery,
a greater proportion of the credit reserve is depleted than would
be the case for a dollar of credit obtained to purchase livestock.
To incorporate this relationship into a linear programming model,

the credit restraint row is altered so that the amount of credit

18

reserve consumed per dollar of loan is inversely related to lender
preference. However, in the linear programming model in this study,
only short term credit is available within the program, and it is
used primarily for meeting cash expenses because a determination

of lender preference would probably require a study within itself.

The bulletin by Martin and Plaxico [9] is a study of capital
accumulation and the growth of farm firms using linear programming
in a polyperiod framework. Since growth is involved, their analysis
was conducted in a nonstatic economic environment and thus it re-
presents an attempt to shed some light on the firm growth process.
The study is restricted primarily to the effect of different farm-
operator objectives on the growth process and to the effect of such
variables as tenure situation, beginning farm size, and consumption
levels on capital accumulation. Martin uses a total of six different
objective functions including the commonly used one of maximizing
the present value of the stream of net returns. While the other
five may not be entirely original, they do represent an attempt to
investigate a difficult area of economics and are rather suggestive
for future research. Other laudable features include making the
consumption function an explicit part of the model involving a base
value and a marginal propensity to consume, and allowing borrowing
to be based on equity and type of asset to be purchased.

Martin provides a rather extensive composite of the activities
involving the acquisition and use of capital. Besides allowing
borrowing to be based on equity and type of asset to be purchased,
his attempts to reproduce the relationships between years are note-

worthy. Three aspects of his relationships between years are

19

important: (1) An investment equation computes reinvestment
capital at the end of a production period as the capital generated
during that period plus the amount of owned capital available at
the beginning of the period. (2) An equipment buying activity
purchases additional amounts as farm size increases and as machinery
depreciates out. Machinery or land capacity added in any period
is made available for future periods and creates additional loan
capacity in those periods. (3) If the firm's operation remains
unchanged from one year to the next, it is still obligated to pay
overhead costs and amortization of land and equipment loans. Con-
sidering the emphasis placed by Irwin on the handling of internal
and external flow of funds, Martin's preoccupation with activities
dealing with capital makes his study particular germane as a
reference when setting up programming and simulation models for
future studies.

Martin's study does have its limitations resulting both from
its assumptions and the use of the polyperiod programming technique.
By the author's own admission, this is a dynamic certainty or
deterministic model since the input-output coefficients and prices
are assumed to be known with certainty. Also, in their attempts
to portray the capital accumulation characteristics of a typical farm,
the authors assume that the operator has the necessary managerial
ability. These are all unrealistic assumptions, but there is really
no alternative to the managerial assumption in an optimizing model.
Also, in an effort to facilitate the analysis, the authors selected
an operation activity representing an aggregation of enterprises.
Therefore, the combination of enterprises is predetermined and not

to be solved as a Specific part of the problem. This assumption is

20

particularly objectionable because it eliminates specialization
within a structure which could lead to reduced costs and be one

of the primary reasons for growth. The necessity of limiting
enterprise activities is due to the fact that polyperiod programming
tends to get bulky rather quickly and that Martin's model already
included a number of activities dealing with capital.

In addition to the weaknesses of this particular model,
polyperiod programming has some objectionable features as a technique
for studying growth. Besides the limitation on the number of
activities, another disadvantage is that it is difficult to change
the restriction from year to year which makes the structural char-
acteristics in the first year very important. In view of this
shortcoming, it is not surprising that the authors concluded "the
environment within which farm operations occur may tend to over-
whelm specific operator objectives." Another disadvantage of poly-
period programming is that the results are a simultaneous solution
for all future periods and thus does not yield any information on
the steps involved in the process.

In regard to the objectives of this study, Martin's study
has some relevance for the section dealing with growth strategies
since he considers the effects of alternative land acquisition
methods. His study is not so pertinent for the objectives pertain-
ing to the effect of stochastic variables and to the year to year
adjustment process since it is deterministic and since each solution
in his model covers a five year period.

Duvick developed a polyperiod programming model to represent

a south central Michigan dairy farm [10]. Variations in the basic

21

model were used to compare the alternative means of financing
expansion of farm firms. The model encompasses a 10 year period
and allows investments to occur in three of the ten years. Borrow-
ing is limited by institutional restraints based on equity by type
of asset and repayment capacity.

The items examined for their effect on growth of the firm
were: length of repayment, level of beginning cash, downpayment
requirements, operator goals, appreciation of land values, invest-
ment credit, and changing prices. The effects of these different
items on production, income and financial progress of the farm
operation were examined through comparative analysis of modifica-
tions made on the basic model.

Heidhues [ll] develops a recursive programming model of
individual farm changes which explicitly includes savings invest-
ments, and growth. His model emphasizes the behavioral and
objective structure of the money capital and investment constraints.
Some of the strong points of Heidhues' study is that he takes into
account some of the human elements in considering subjective
barriers to change such as the resistance to sudden shifts in a
world of uncertainty either explicitly as behavioral restraints
such as limits on the total level of debt and the rate of borrowing
or implicitly through asset fixity and rotational practices and in
allowing for a "learning period” lag in the adoption of new tech-
nology. He takes into account the divergence between acquisition
price and salvage value and recognizes that a low salvage value is
an objective barrier to rapid change. In addition, his behavioral
constraints reflect shortages in factor supplies connected with a

rapid increase in the demand for a particular asset. Among the

22

growth parameters that can be manipulated and thus subject to some
degree of analysis are prices, depreciation or obsolescence of
durables, and rate of growth in private consumption and the gen-
eral wage rate. These last two variables--consumption and wage
rates-~reflect the effect of a rising nonfarm standard of living
on farmer income expectations which is an important consideration
in a firm growth study involving a lengthy time period.

Recursive means essentially that the prediction for a given
year is based entirely on data given from the preceeding year.
Under recursive programming, a linear programming model for a
single year is repeated a number of times with the restraints in
each year depending on the optimum solution for the previous year.
Since it can be made dynamic from year to year, it can be used to
trace out adjustments in the growth process. As in any linear
programming model, all prices are single-valued but this is
appropriate for this particular study since the author is in-
vestigating alternative government policies in which prices would
be determined externally. However, single-valued price expecta-
tions are not so appropriate for a model dealing with an individual
farm firm facing an uncertain market in either a given year or over
a period of years. Among the other shortcomings of recursive pro-
gramming are those characteristics that tend to make models in gen-
eral less realistic. These include single-valued production co-
efficients, necessity of assuming that the operator has adequate
‘managerial ability, and the limitation of objectives to pecuniary
ones by the use of Optimality in determining solutions which pre-
clude other types of motivation from influencing the behavior of

producers.

23

S.R. Johnson [12] set up a multiperiod stochastic model of
firm growth that is similar in many ways to Martin's except that
it brings the additional concept of risk into the analysis. John-
son's model determines yield as the sum of an average value plus
a random component. There are essentially two steps to his model.
First, crop yields are determined for each year of a 15 year planning
period; and then, the model is solved for the 15 year period using
the series of yields. The model maximizes undiscounted accumulated
wealth-~net worth--and is interrelated between years only on credit
reserve.

Johnson's thesis contains two points that are specifically
related to this study. The first is his inclusion of a stochastic
element for yield. This study will also determine yield stochas-
tically along with commodity prices and land prices. The second
point is that Johnson operates his model repeatedly to establish
the variance. In this study, the variance of the stochastic
simulator will be established'via two different designs through
repeated Operations. The idea is to establish the variance of the
yield component alone and to establish the variance of all the
random components taken together.

Patrick and Eisgruber [13] used a simulation model of farm
firm behavior to determine the impact of different levels of man-
agerial ability and different capital market structures. They con-
cluded that managerial ability and long-term loan limits are the
major factors among those considered, influencing farm firm
growth.

They begin their study with a discussion of human behavioral

theory in which they conclude:

24

(1) Human behavior is goal oriented.

(2) An individual does not strive solely for the
satisfaction of a single goal.

(3) Goals can change in relative importance over the
course of time.

(4) Limitations on time and computational ability

cause the farmer to consider only a subset of

the possible alternatives available to him.
This discussion of goals is particularly pertinent to this study
because of the need to evaluate the realism of simulation which
can incorporate several goals as opposed to linear programming
which, as an optimizing technique, is restricted to a single
objective function.

The control variables were managerial ability and three
elements of the capital structure: interest rate, long-term loan
limit, and intermediate-term loan limit. Three levels of each of
the four controlled variables were simulated over a 20 year period
giving 81 combinations involving three different levels of managerial
ability and 27 different capital market structures. Their results
indicated that managerial ability as measured by technical trans-
formation rates is a major factor in determining the rate of growth
of the farm firm. They found that long-term loan limits are
important in determining the rate at which the farm firm can expand.
They found the primary influence of the interest rate to be on the
ability of the firm to survive the early years of operation. The
primary importance of this aspect of the study would seem to be in
delineating the variables that might be important in future research

involving simulation and in suggesting a way of including a measure

of managerial ability.

25

In addition Patrick emphasizes a particularly important
step in the growth process by including an evaluation of last year's
outcome as a separate stage in his simulation model. "Feedback"
is an important feature of any growth model and a simulation which
incorporates an ex 2235 linear programming subroutine, as is done
in this study, allows an evaluation of the previous year's outcome
that is difficult to surpass by means of a comparison of the
"optimum" solution with the actual outcome.

Lins notes that "increasing emphasis is being given to the
analysis of the dynamics of firm growth." He concludes that "this
has resulted from a general dissatisfaction with static equilibrium
models in explaining the movement from one equilibrium position to
another" [14]. Because empirical studies involving the dynamics
of firm growth have generally employed either linear programming
or simulation, he concerns himself with a comparison of the results
of the two techniques in the matter of choosing an optimal expan-
sion strategy.

Lins applied a recursive LP and simulation models to six
alternative land investment strategies to test for differences in
the techniques. He lists three basic differences as being inherent
in the use of simulation as compared with linear programming (1) the
requirement of complete divisibility for all inputs by linear pro-
gramming, (2) the fact that linear programming generates a mathe-
matically optimal solution, and (3) the assumption of perfect know-
ledge by linear programming. He concludes that there is a differ-
ence between the solutions of the two techniques due both to the
assumptions about perfect knowledge and divisibility and that some

attempt should be made to measure it.

26

Lins' research has particular relevance for this study be-
cause of his finding that the difference in the assumption about
perfect knowledge is of consequence and his conclusion that it
should be measured. This is the precise reason for the inclusion
in this study of the objective dealing with the determination of
the effect of the stochastic element. His investigation of the
effect of the lumpiness of land purchases will not be repeated
but his findings as to the effects of various growth strategies
are useful both as a guide in constructing a set of strategies
for this study, even though an exact duplication will not be made,
and as a comparison for the results of the strategy section of
this study.

It is important to recognize that Lins did not combine the
two techniques-~simulation and recursive linear programming--into
one model. He used the same initial situation and followed the
same strategy in his comparison of models but he did not relate
the two models to each other at any intermediate stage in the
growth process.

Harl [15] conducted a bi-disciplinary inquiry into the legal
and economic effects of the corporate form upon small, closely-
held business. Harl applies a model comprised of linear programming
and simulation segments to test the effects of the legal form of
doing business upon the firm. He uses a linear programming model
as a subroutine in the simulator to handle annual optimizing. The
linear programming portion of the model generates gx_gngg production
plans based upon decision-making expectations which are converted
to gx_pgg£ plans using the actual price and yield data. The use

of an g§_post linear programming subroutine to generate production

27

plans based on actual prices and yields is identical to the concept
involved in this thesis; and thus indicates that while it is not
an entirely novel idea, it is a feasible one.

Day [16] has a pertinent discussion dealing with the rela-
tionships which an economic model should include. His list of
forces associated with production changes which an adequate model
should include is rather exhaustive and should represent a challenge
to any prospective model builder. His list of forces includes:

(1) the interdependence of outputs using common inputs; (2) adjust-
ments over time; (3) technological change; (4) the change in both
the acreage and yield components of field crops; (5) uncertainty;
(6) demand, supply and price interaction.

Day discusses the dynamic phenomena which underly producer
and consumer behavior and which he indicates can only be described
within a model by lags in response to price changes. He lists two
groups of factors as being responsible for this behavior: (1) the
first is associated with capital, i.e., the growth and reallocation
of stocks of inputs that are in the short run fixed or extremely
inflexible; and (2) the second is associated with uncertainty of
prices, i.e., the inability of producers to distinguish a given
price change as "permanent" or as "transitory" which leads to their
responding cautiously to price changes once they have occurred.

Of particular interest is his explanation of how to place functional
limitations on changes to occur within the model which gives it
stability and increases its realism. Day's pertinent comments on
model building are particularly relevant for this study since it

utilizes two models.

28

Day also has some interesting observations on predictions
that reflect on the tendency to judge models according to their
predictive abilities. He concludes that it is not just the in-
adequacy of economic understanding that prevents accurate pre-
dictions. He further concludes that, in fact, an adequate
understanding of economic phenomena demonstrates the virtual
impossibility of exact predictions. In addition, he presents
some informative comments on comparative statics versus dynamic

economics.

Summary

This review of literature was helpful in clarifying the two
questions proposed at the beginning of the chapter. First, three
alternative ways of measuring growth include inputs, assets, and
output. Any attempt to account for changes in inputs will gen-
erally have problems with the qualitative variations that occur
both at a point in time and over time. This is especially true
when dealing with the human agent and with inputs that did not
enter the market during that production period. Inputs that are
not acquired via the market during each production period also
present a problem when valuing assets. Land is particularly a
problem since it is usually the largest component of the assets'
value and since it so seldom enters the market. The value of out-
put would seem to be the best measure of firm size, and thus growth,
particularly for reasons of accuracy and of computational ease since

it is usually determined by the market during each production period.

29

Regarding the second question as to the appropriateness of
the alternative techniques for studying growth, it seems clear that
each technique has its strengths and its weaknesses. One glaring
weakness common to most of the techniques is their inability to
adequately reflect the shorter-run, tactical type decisions that
operators face each production period. It is in this area of
tactical decision making that it is hoped this study will have its

greatest impact.

2.
3.

4.

10.

ll.

12.

13.

14.

30

References

Renborg, Ulf., Growth of the Firm in Relation to Problemfi_gf
Factor Acquisition: The Swedish Experience. Paper presented
to WAERC Farm Management Research Committee, Las Vegas,
Nevada, November 7-8, 1967.

Ibid., p. 2.
Ibid., p. 3.

Bailey, W.R., "Necessary Conditions for Growth of the Farm
Business Firm." g. Econ. Res., 1967, 19:1-6.

Irwin, G.D., "A Comparative Review of Some Firm Growth Models,"
Ag. Econ. Res., No. 3, 1968, 20:82-100, p. 82.

Pugh, C.R., The Structure of Southern Farms of the Future,
Proceedings of the two day conference by the Agricultural
Policy Institute held August 1968, North Carolina State
University, Raleigh.

Ibid., p. 86.

Baker, C.B., "Credit in the Production Organization of the
Firm." Journal of Farm Economics, 1968, 50:507-520.

Martin, J.R. and J.S. Plaxico, Polyperiod Analysis of Growth
and Capital Accumulation of Farms in the Rolling Elains 9;
Oklahoma and Texas, Agricultural Experiment Station Technical
Bulletin No. 1381, Department of Agricultural Economics,
Oklahoma State University, Stillwater.

Duvick, R.D., Alternative Methods of Financing Growth of
Michigan Dairy Farms, Unpublished Ph.D. thesis, Michigan
State University, East Lansing, 1970.

Heidhues, T., "A Recursive Programming Model of Farm Growth in
Northern Germany," Journal Farm Economics, 1966, 48:668-684.

Johnson, S.R., An Analysis of Some Factors Determining Farm
Firm Growth, Unpublished Ph.D. thesis, Texas A & M University,
College Station, 1966.

Patrick, G.F. and L.M. Eisgruber, "The Impact of Managerial
Ability and Capital Structure on Growth of the Farm Firm."
Journal of Farm Economics, 1968, 50:491-506.

 

Lins, D.A., "An Empirical Comparison of Simulation and Re-
cursive Linear Programming Firm Growth Models," Ag. Econ.
Res., 1969, 21:7-12.

15.

16.

31

Harl, N.E., Identification and Management of Selected Legal-
Economic Effects of the Corporate Form of Business Organiza-
tion Upon a Small, Closely Held Firmb Unpublished Ph.D.
thesis, Iowa State University, Ames, 1965.

Day, R.H., Recursive Programming and Production Eggpgnggg,
Amsterdam: North Holland Publishing Company, 1963.

CHAPTER III

A Conceptual Framework for Studying Growth

A theoretical presentation is developed in this chapter to
elucidate the methodology by which the major objectives of studying
the growth process on a year-to-year basis and of comparing growth
strategies over time are accomplished. The model is developed
starting with the fundamentals of the theory of the firm, relating
these concepts to the two techniques to be used in the study--linear
programming and simulation--and then combining these two techniques
within the framework of the theory to illustrate how the pertinent
characteristics of maladjustment--degree, cost, and time required
for correction--will be determined and interpreted in light of the

objectives.

Goals

In order to have a body of theory about economic activities
that will explain real world situations, one must incorporate
elements of human behavior. For a theoretical concept in economics
to be of value, it must be predictable which means human behavior
in economic activity must have some degree of predictability. If
all events of economic consequences were one-time occurrences,
completely independent of all other events, an analysis of an event
would be of no theoretical value. We would simply have an infinite
number of explanations with very little or no future value.

32

33

This chaotic situation is avoided in economic theory by
assuming that people are rational and that their behavior follows
consistent patterns due to the fact that behavior is goal oriented.
Thus, human wants become the mainspring of economic activity. These
wants are the economy's motivation as all economic activities are
directed towards achieving these ends [1].

Since the owner-operator type of organization predominates
in agriculture, the operator is likely to have at least four dominant,
and often conflicting, goals--increasing net revenue, increasing net
worth, increasing leisure time, and decreasing risk--which he will
seek to attain simultaneously. It goes without saying that the two
goals of increasing both earnings and leisure are likely to lead to
conflict. Also, the two goals of increasing earnings and decreasing
risk may involve conflicts that result in a compromise. Thus, the
existence of multiple, conflicting goals increases the complexity
of the problems associated with growth.

An assumption that the operator is likely to have several
goals which he will seek to achieve simultaneously has implications
for the realism associated with simulation and linear programming.
0f the two techniques only simulation permits the "operator" to
attempt to achieve a number of goals at once. Linear programming,
of course, being an optimizing technique, has only a single objective
function. In general terms, linear programming can be said to give
the "best" solution (in terms of its objective function) while

simulation permits the achievement of a more realistic solution.

34

Economic Theory

 

In economic theory, maximization of profits is generally con-
sidered to be the only goal. The use of a single goal is necessary
for the sake of simplicity because the first differential of a
mathematical function can be used to find a point of optimization.
Profit maximization is easy to express in marginal terms and per-
haps is the most appropriate single goal for a theoretical firm.
Net worth is generally increased by appreciation in the value of
assets, primarily land, and by savings from earnings; thus, the
attainment of a high level of profit is not inconsistent with in-
creased net worth. Leisure can be handled by controlling the amount
of operator labor made available for use. Risk is more difficult
to handle but one way of controlling risk is by the selection of
enterprises considered.

The basic equation with which the theory of the firm begins
and around which it revolves is simply a definitive one indicating
how profit is computed:

(l) n - TR - TC
The equation can then be differentiated with respect to the inputs
or outputs--which are limited to one of each for simplicity--and
the first differential set equal to zero to define a point of
maximization.

' MR - MC ' 0
MR ' MC

dfflz . dSTRz _ dSTCZ B 0
dx dx dx

(2)

35

MVP -MI-'C = o
(3) MVP-MFG

In a more sophisticated economic theory acknowledging the
existence of imperfect knowledge, of no fixed factors, and of the
opportunity cost of time intervals; the total revenue and total

cost symbolized in equation (1) would be computed as follows:

ECUt
(4) X'£-—-? XBTR or TC
(1+1)

where: E(X)t ' 2 P(XJ t) ' Xj t

This theory requires that estimates of both the range of values

in each year (xj,t) and a probability of occurrence of each value
P(xj,t) be made if they are not known. An expected value E(X)t
is then derived and discounted to a common year with a discount
rate that reflects the opportunity cost of the resources and the
confidence placed in the expected values.

In short run production theory, four highly simplifying
assumptions are made (1) that perfect knowledge exists, (2) that
no technological changes occur, (3) that some resources are fixed,
and (4) that the time interval is of such short duration, its
opportunity cost is insignificant and can be ignored. Under these
assumptions, still Speaking in terms of one input and one output,
both total revenue and total cost become the product of quantity
and the appropriate price. The terms in equations (2) and (3) are

then defined as follows:

 

 

d(P)
MR-ifl. P+ Y
dy y dy
d(P )
nae-MTG -d—"(p)+ x x
dy dy x dy
d(P )
mp.—(—l"m -91(P)+—J—Y
dx d dx
d(P )
dx x dx

If the additional simplifying assumption of constant prices

is made, equations (2) and (3) take the following forms, respectively:

5 I
( ) P; MC

(6) VMP . Rx

Equations (5) and (6) are simply two ways of expressing the
same condition; namely, that profit maximization is achieved at the
level of production where the change in receipts is equivalent to

the change in costs:

P ' MC VMP ' P
Y x
y dy x dx y x
dy ' P - dx ' P dy ° P = dx ° P
y x y x

Two dimensional graphs can be used to express relationships
that are more complex than those represented by equations (5) and
(6) but yet illustrating the same principles. Equation (5) can be
expressed in a product-product diagram involving two products and
one input. Equation (6) can be expressed in a factor-factor diagram

involving two inputs and one product.

37

The reason for attempting to express more complex relation-
ships in terms of theory is to develop a model that will give a better
representation of reality without expecting to ever completely
duplicate it. The impossibility of the duplication of reality is
expressed in the following statement by Viner [2]: "Theory is
always simpler than reality. Even when it seems terribly complex,
it is still simpliste, as compared to the range of factors, operat-
ing as conditions, as means, or as ends, in any actual concrete
situation." This point of view, however, does not reduce the need
for theories or their significance.

Given that it is essential for an economic model to be
realistic, there is another equally important characteristic that
must be taken into consideration--a model must be comprehensible
by finite human minds. The possibility usually exists for a trade-
off between realism and understandableness, and the final form of
an effective model may involve a delicate balance between the two.
The implications of these two characteristics for simulation and
linear programming will become more obvious after theoretical models
of increased complexity have been discussed and related to the two

techniques.

Product Substitution

Equation (5) can be expressed in a product-product diagram
(Figure 1) relating two products and one input. A series of points
which make up the expansion path can be determined from such a dia-
gram with each point representing the optimum combination of the two
products given a specific level of the input and given the input and

1
product prices. The curve SS in Figure l is the production

38

 

 

'1
N
S
0
s1 N1 Y2
Figure 1. Product-Product Diagram
x1
T

 

 

T1 x2

Figure 2. Factor-Factor Diagram

39

possibilities curve which represents the maximum amount of the two
products that can be obtained with a specific level of technology.
The slope at any point on the curve is given by

dy2 Mnyl '
This slope is called marginal rate of transformation and represents

the rate of substitution between the two products in production.

1
The line NN is an isorevenue line with a slope equal to the

P
- - dyl yz
inverse of the product price ratio, a;— I P_— , and represents the
7- y
1

rate of substitution between the two products in the market.
1 1
At point 0, the point where NN is tangent to SS , the

MRS is identical to the price ratio:

(7) MC

 

A combination of products meeting this condition can be determined,

one such point for each level of the input.

Input Substitution

Equation (6) can be expressed in a factor-factor diagram
involving two inputs and one product. A series of points can be
determined from such a diagram representing the line of least-cost
combination (LLCC) with each point representing the least-cost
combination of the two inputs for producing a given level of out-
put. In Figure 2, the curve I is an isoproduct line with a
slope that is referred to as the marginal rate of technical

substitution (MRTS) which represents the rate of substitution

40

between the two inputs in a technical sense and is given by:

 

dx up VMP
__l . y"2 . 2
dx MP VMP

2 y"1 yx1

1
The line TT is an isocost line with a slope equal to the inverse

AX1 Bx
of the input price ratio, AX . P_— , represents the rate of sub-
2 x
l

stitution between the two inputs in the market. At point R, the
1
point where TT is tangent to I, the MRTS is identical to the

price ratio:

(8) VMP P
i . .112.

VMP P
yx1 "1

A combination of inputs meeting this condition can be determined
for each level of output; one combination for each level of output.
The product-product and factor-factor diagrams can be used
to illustrate how a firm would achieve growth in accordance with
production theory. To achieve growth, a firm must acquire addi-
tional productive resources which it might do, for example, with
money saved out of labor income or from excess profits resulting
from a disequilibrium situation. In the product-product diagram,
the firm would be able to reach a higher production possibilities
curve with each acquisition of an additional amount of the input.
According to theory, the firm would adjust to the new situation
by choosing a point--combination of products--on the appropriate
production possibilities curve such that the condition illustrated
by equation (7) is satisfied. Thus, as the firm achieves growth
it will follow the expansion path (Figure 3) on which every point

satisfies the condition expressed in equation (7).

 

41

Expansion Path

 

 

Figure 3.

Y2

Product-Product Diagram with Expansion Path.

LLCC

 

Figure 4.

x2

Factor-Factor Diagram with Line of Least Cost

42

The achievement of growth can likewise be illustrated on a
factor-factor diagram where as a firm acquires additional capital
with which to purchase inputs, it is able to obtain a higher
isoproduct line, and thus a higher level of output. The exact
amount of each input that should be purchased, and thus how they
should be combined, will be dictated by the condition expressed
in equation (8). After the firm has taken several steps into the
growth process, a line of least-cost combination (LLCC) can be
traced out (Figure 4) and every point along this line will meet
the condition expressed in equation (8).

The product-product diagram is more relevant to this study
since the primary objective is to scrutinize the maladjustment of
the firm after the acquisition of additional inputs. The decision
as to which class of inputs to expand will be dictated by the
growth strategy that the firm is assumed to be following such as
lateral or vertical strategies. Basically a firm*will be located
on a production possibilities curve, and the problem will be to
determine how far it is from the optimum combination of enterprises,
how long it will take to correct the maladjustment, and the cost
of the maladjustment in terms of profit foregone. As additional
capital resources become available, the firm will move to a new
production possibilities curve and the study of maladjustment will

be repeated.

SIMULATION

The term simulation has recently begun to appear with in-
creased frequency in the professional media of a number of scientific

disciplines. Webster's definition of the verb "simulate" is "to

43

create the effect or appearance without the reality." It is obvious
from this definition that simulation is not a new concept. The use

of war games by the military to simulate actual battlefield con-
ditions has been in practice for centuries. Other familiar uses

are the use of simulation in training drivers, pilots, and astronauts.
The economist has long been attempting to simulate reality with his
graphical models and mathematical functions, with which he attempted
to trace out the effects of various decisions and of changes that
might occur in variables. It is appropriated to refer to two
dimensional graphical models and mathematical expressions as simulation
because it is unimportant whether models superficially look like the
thing modeled. What is important is that the response of the model

to changes in variables be similar to those of the real system.

The reason that simulation has come to be used so extensively
in the last decade, particularly in economics, was the development
of the high speed computer in the early 1950's. With the advent
of the computer, simulation took on added meaning for the economist
because it became possible to experiment with more complex mathe-
matical models that describe some system of interest. As Naylor
[3] put it:

For the first time the social scientists found that,

like the physicists, they too could perform controlled

laboratory like experiments; they, however, used

electronic computers rather than physical devices such

as a nuclear reactor.

A rather complete definition of a simulation as it applies
to economics is given by Shubik [4].

A simulation of a system...is the operation of a model

or simulation which is a representation of the system...

The model is amenable to manipulations which would be
impossible, too expensive, or impractical to perform on

44

the entities it portrays. The operation of the model can

be studied and, from it, properties concerning the behavior

of the actual system or its subsystems can be inferred.

Thus it is obvious that the technique of simulation has several uses
within economics--providing information, teaching, and research.

For instance a simulation of a firm could be used by the manager

to gain insight into the outcome of alternative decisions. It could
be used to teach young executives by giving them a feel for the
business that could otherwise only be gained from experience which
may be costly and involve lengthy periods of time. It could be

used for research in experiments where manipulations are carried

out and studied to ascertain the preperties and characteristics

of the systems and its subsystems.

Of course the value of any information provided by or in-
ferences drawn from a simulation model depends upon how well the
actual responses to the variables are duplicated in the model.

Given the complexity of most economic relationships, this duplication
may be quite difficult; which raises the question of whether the
duplication of such complexity should even be attempted. The

answer to such a question would seem to be an emphatic affirmative.
The following quote by Rosenblueth [5] lends support to this answer:

No substantial part of the universe is so simple that

it can be grasped and controlled without abstraction.

Abstraction consists in replacing the part of the

universe under consideration by a model of similar

structure. Models...are thus a central necessity of

scientific procedure.

Thus given that model building is a useful undertaking,
it might be beneficial to delineate the preperties of a functional

model. According to Orcutt [6]: "a model of something is a

representation of it designed to incorporate those features deemed

45

to be significant for one or more Specific purposes." As stated
earlier it is usually unimportant whether models look like the
thing that they represent. A model may be a physical representa-
tion, or described by pictorial geometry, or set forth in the
language of formal mathematics, or presented as a computer program.
The appropriate form for a given situation will be primarily a
matter of feasibility and convenience.

A scientific model is an abstraction of some real system
that can be used for purposes of prediction and control. A
scientific model should be designed so as to allow the analyst to
determine how one or more changes in aspects of a modeled system
may affect other aspects of the system. In order to be functional
a scientific model must necessarily incorporate elements of two
conflicting attributes--realism and simplicity. A model should
serve as a reasonably close approximation to the real system and
embody most of the important aspects of the system; however, it
must not be so complex that it is impossible to understand and
manipulate.

The elements that make up models of economic systems are
components, variables, and relations [7]. Components of a firm
consist of the activities which in case of a farm firm would be
the crop and livestock enterprises. Thus, components can be
characterized by the conversion or transformation of inputs into
outputs. The variables that appear in economic models may be
conveniently classified as exogenous variables, status variables,
and endogenous variables.

Exogenous variables are the input variables of the model

and are assumed to have been predetermined and given independently

46

of the system being modeled. These variables may be viewed as in-
fluencing the system but not being influenced by the system. The
direction of causation is assumed to be irreversible as it flows
from the exogenous variable to the system. Examples of variables
that are exogenous to farm firms are weather and prices. Status
variables are simply descriptive variables that describe the state
of the system or one of its components either at the beginning,
or at the end, or during a time period. These variables are affected
by the level of the exogenous variables and by the relationship
between exogenous and endogenous variables. Pertinent examples
in the case of a firm are profit, net worth, and debt-asset ratios.
Endogenous variables are the output variables of the system and
would consist of anything which is generated by a component.

In addition to components and the variables relating to
the components, a model of a firm must also contain relationships
if it is to generate behavior. Relationships specify how the
different variables in the model are related to each other and
how the endogenous and status variables are generated. Rela-
tionships are of two broad types: identities and operating char-
acteristics. Identities are generallly accounting statements
which may be introduced for convenience, for example, net worth
equals assets less liabilities. An Operating characteristic is
a relationship specific to a given component which Specifies how
output variables of the component are related to its input vari-
ables. An example would be a production function. Operating
characteristics embody much of whatever knowledge is made use of
in a model by Specifying how components in a model are to reSpond

to input variables.

47

Simulation models are nonanalytic, i.e., that is, they do
not guarantee an optimum. Hutton [8] concludes that if analytic-
optimizing models can handle the situation they are to be pre-
ferred. If this view is accepted, the appropriate use for Simula-
tion models is when the decision process to be described is extremely
complex, and analytic approaches either have not been or cannot be
developed. Irwin (1968) includes the following situations as being
appropriate for simulation: (1) multiple goals, (2) indivisibilities,
(3) sequential decisions within the planning period, using different
criteria, (4) nonlinear functions, and (5) concepts of organizational,

managerial, and behavioral theories.

Theoretical Connotations of Simulation

Simulation does not fit readily into the models of production
economic theory because it is a nonOptimizing procedure which may
have more than one objective. However, in relating simulation to
theory, one can say with certainty that the solution cannot be out-
side of the area bounded by the appropriate production possibilities
curve because such points are not technically feasible. Also, one
can reason that if a high level of net income is one of the goals,
the actual solution will likely be near the theoretical solution.
Thus, all that can be said in an g§_gg£g sense is that the solution
to the Simulation model must be within the area bounded by the pro-
duction possibilities curve and that for a successful farmer, it
might be expected to lie near the optimum solution in terms of pro-

fit maximization.

48

Y , 5 Y imax where j I l...m, the individual products
where i I l...n, the proportions in which the
products may be combined

n z n max

The identical problems are present when an attempt is made
to relate simulation to a growth model such as the concept of the
expansion path on the product-product diagram. Again, the state-
ment can be made with certainty that the Simulation solution must
lie within the production possibilities curve applicable to that
production period and determined by the available resources and the
state of the arts. The simulation solution can reasonably be
expected to move outward from the origin as the production possi-
bilities curve shifts outward, in other words, the firm will expand
production as the Supply of available inputs is increased. A series
of solutions to the simulation model in which input acquisitions
are made over time will trace out a line of expansion different
from the expansion path except in the case where profit maximiza-
tion is one of the primary goals and the manager is successful in
his efforts to achieve this goal. In this case, the line of expan-
sion would in all likelihood, be near the expansion path. If the
manager has alternative goals or is not successful, than the line
of expansion could go in any direction or assume any Shape.

The effect of nonoptimal solutions on the growth achieved
by a firm can perhaps be explained more fully with a conceptual
presentation. Given the production possibilities curve, the pro-
duct combinations that lie above or to the right of this curve are

not feasible solutions in that it is technically impossible to

49

attain these. There is one combination of products lying on the
production possibilities curve at which net income is maximized.

Any movement away from this solution, staying in the range of feas-
ible solutions of course, will decrease the level of net income
obtained from production. There are two possible sets of conditions

under which the maximization is not achieved:

1 dyl yz
'57 " T
2 y1
P
a——-I -—— but the point is below the highest attainable
3'2 Py
1

production possibilities curve.

In relating the solutions of the nonoptimizing procedure to
a growth model in graphical form, these same conditions are applic-
able. The combination of‘products representing a solution at any
point in time must lie on or within the appropriate production
possibilities curve and it can be expected to shift outward as the
quantity of the inputs increases resulting in an outward movement
of the production possibilities curve. Assuming that the retention
of a portion of earnings above and beyond production expenses and
some basic standard of living is the primary source of growth, the
occurrence of a series of nonoptimal solutions would likely have
a cumulative effect as the theoretical production possibilities
curve would, in all probability, exceed the firm's actual level

of production by successively greater increments over time (Figure 5).

50

 

 

Less than Optimal,

Theoretically Optimal ......

 

 

v

Figure 5. Product-Product Diagram with Alternative
Expansion Paths.

51

Linear Programming

Linear programming is primarily a conditionally normative pro-
cedure for providing answers to problems which are so formulated. By
conditionally normative it is meant the course of action which Should
be taken by an individual or business unit given:

(a) the goal or objective

(b) the restraints Surrounding the action.

Using linear programming, a plan indicating the product to be pro-
duced and techniques to be used can be Specified when the objectives
of profit maximization and restraints in kind and amounts of resources
are given.

There are three quantitative components to a linear programming
problem: an objective, alternative processes for attaining the
objective, and restraints. Typically, the objective will be either
the maximization of income or the minimization of cost but the
objective does not have to be so restricted. Given the objective,
there is no problem to be analyzed unless it can be attained by
more than one process--different enterprises or different techniques
of producing the enterprises. Given several alternative processes
for attaining the objective, the program chooses the process or com-
bination of processes that is most efficient in converting resources
into the objective. Given an objective and several processes, a
linear programming problem does not exist unless one or more resources
is restricted.

Linear programming assumes the existence of several conditions
[9] and for the solution obtained to be realistic, the assumptions

must apply to the problem under consideration. The assumptions are

52

listed below:

Linearity-~All relationships and coefficients are constant. Thus to
double the production of an enterprise requires twice as
many units of each resource.

Additivity--All processes are independent. To get the resource
requirements for a bundle of enterprises, one simply
takes the summation of the individual enterprise re-
quirements.

Divisibility--Resources can be used and enterprises can be pro-
duced at any nonnegative level. Thus, fractional
units are possible.

Finiteness--There is a limit to the number of activities and

resource restrictions that need to be considered.

Single-value expectations--All resource restrictions, input-output
coefficients, and prices are known with certainty.

In linear programming, most of the technical and economic
phases of a problem can be expressed explicitly and treated
directly in the analysis. On the other hand, many qualitative and
intangible human factors cannot be handled in the analysis. Also,
the implications of the two basic assumptions common to all linear
programming methods--1inearity and certainty--must be recognized
explicitly in framing the problem, in solving it, and in interpret-
ing the results. The following statement by Stockton [10] rein-
forces the point:

The primary contribution by any quantitative method is in

narrowing the judgment portion of decision making not in

eliminating it. It is important, therefore, to recognize
that the optimal solution from a linear programming model

is not necessarily an optimal overall solution to the
problem. Managerial judgment rather than mathematics must

53

be used in large part for the selection of the best alter-
native course of action and, of course, for the implementa-
tion of the decision.
Thus the effectiveness of linear programming, which is really quite
simple in its mathematical structure, depends to a great extent on

human judgment to make it adaptable to a wide range of practical

applications.

Theoretical Connotations of Linear Programming

Linear programming can be related to the models of economic
theory discussed earlier in this chapter. Simple linear programming
problems can be discussed in terms of the two-dimensional product-
product or factor-factor diagrams, reSpectively, depending on whether
the objective is income maximization or cost minimization. Only
the relationship between the product-product diagram and linear
programming will be discussed here. This relationship is more
relevant for this particular study Since profit maximization is one
of the major goals involved and maladjustments in enterprise com-
binations is one of the major issues of concern.

Because of the linearity assumption, the marginal rate of
transformation between two enterprises is constant, thus the pro-
duction possibilities curve in the product-product diagram becomes
a straight line. Thus, if the problem is limited to two enter-
prises but includes several resources of limited quantity and all
of the individual production possibilities curves are Superimposed
on one graph, a diagram such aS Figure 6 is obtained. Since all
points outside of a given production possibilities curve are
unattainable, the feasible or attainable part of the diagram is

the area bounded by abcd. AS in any other product-product diagram,

54

Wheat

land

labor

a b wheat allotment

 

 

 

 

Corn

Figure 6. A Product-Product Diagram Under Linear Programming
Assumptions.

55

the optimal solution is at the point where the isorevenue line is
tangent to the production possibilities curve which equates the
marginal rate of transformation and the product price ratio and,

in a linear programming problem, exhausts at least one of the
resources. The solution will be at a corner on the production
possibilities curve except on infrequent occurrances where the
slope of the isorevenue line is the same as that of a segment of

the production possibilities curve. In the latter case, the
optimum is a range of points each of which meets the conditions
expressed in equation (7). In the more likely case where the
solution is at a corner point, which means that two or more inputs
are restricting production, the condition of equality expressed

in equation (7), does not apply and an inequality becomes necessary.
The price ratio must be greater than the Smallest marginal rate of
transformation (MRT) associated with one of the two restricting
inputs and less than the largest MRT associated with the two inputs.

P
y2
MRT < —--< MRT
X. P x
1 3'1 j

The principles of asset fixity theory can be incorporated
into a linear program; however, the asset fixity theory is not
applicable to the linear programming model used in this particular
study. Linear programming determines the optimum solution Subject
to resource restrictions which in this case are predetermined out-
side of the model. Asset-fixity theory would be involved in the
determination of what amount of resources will be made available to
the firm for the production period. This would be accomplished by

adjusting the supply of the restricting resources prior to the

 

56

beginning of the production period, if prices and technical con-
ditions (MP) indicate such action is warranted. However, since the
linear program in this study iS presented with a predetermined
resource situation; asset-fixity theory would be applicable only

to decision processes in the simulator but not within the linear
programming model. However, in this Study asset-fixity theory is
excluded altogether due to the fact that acquisitions of re-
sources is governed by set strategies.

The concept of growth via an expansion path can be in-

hwsflhmo

corporated into a product-product diagram drawn under the assump-
tion of linear programming such as Figure 6 but there is one
major difference. Due to the greater complexity of this "effective"
production possibilities curve (abcd), it may not shift in its
entirety each time additional inputs are purchased. Only that
section of the production possibilities curve associated with the
input that is expanded will Shift. If the firm purchases an
additional amount of only one input, only one section of the pro-
duction possibilities curve will shift. On the other hand, if
additional amounts of all inputs are purchased, the entire curve
will Shift outward. This fact has an important implication in
that the optimum combination of enterprises will change only if
the available supply of one of the restricting inputs is increased.
Increasing the supply of one of the nonrestrictive inputs will have
no effect on the optimum combination of products and thus could be
viewed as an irrational move which the alert manager would not
attempt.

When changes do occur in the optimum combination of enter-

prises under linear programming, a series of changes will trace

57

out an expansion path similar in concept to that of the one-input
product-product diagram. The changes in the Supply of input avail-
able to the firm will be governed in this study to a greater extent
by the particular strategy than by the asset fixity theory; but as
indicated above, changes in inputs do not necessarily lead to a
movement along the expansion path under linear programming if the

restricting inputs are left unchanged.

' MN”:- c-T—-—'
Iv

Combining Simulation and Linear Programming

‘:

“T.,-T

A number of potential Strengths can be listed for using
simulation in studying farm firm growth. It can be (a) environ-
mental rich, (b) capable of handling multiple goals, (c) able to
solve cases of indivisibility, (d) capable of altering decision-
making processes relative to changing criteria, (e) adaptable to
real world nonlinear relationships, (f) capable of learning and
response, or feedback process, and (g) able to incorporate
Stochastic variables. Such a model is appealing because of its
inherent realism, but is staggering because of its size and
complexity.

It appears that simulation can be a more useful tool for
conducting growth research if its realism can be more effectively
harnessed. Combining linear programming and Simulation provides
a means whereby not only "realistic" but also "good" or optimizing
results may be obtained. Such an approach combines the inherent
realism of Simulation with the optimizing capabilities of pro-
gramming [11].

AS a tool of economic analysis, linear programming has

several uses; one of which is for predictive purposes. It can be

58

used to approximate the optimum combination of activities in an 35.
3235 sense and, thus, to serve as a guide to decision making for
existing operations. Of course, with an g§_gggg linear program,
the ideal Situation is to have perfect knowledge of all future
conditions. In which case, the firm, i.e., the simulator, would
merely have to duplicate the linear programming solution to achieve
the highest level of profit that is possible in every production
period. Obviously an ex ante linear program is highly unlikely to
possess perfect knowledge, and the value Of the solution as a guide
for firm's decisions decreases as the accuracy Of the information
about future conditions decreases.

For diagnostic purposes, linear programming also has its
greatest value when perfect knowledge exists so that the Optimum
solution is made available with absolute certainty and thus a
normative situation is provided with which to evaluate sets of
decisions after they are made or in an g§.pgg£ sense. Such a
linear program possessing perfect knowledge in an g§_pggg sense is
easily set up in conjunction with a stochastic simulator since all
the data are available after each run of the simulator.

The value Of an gfi Egg; linear program is that it provides
a measure of the degree Of maladjustment and Of the resulting cost
due to lost profits. In conjunction with this, it serves as an
indicator of the value of an g§.§2£g linear program that possesses
perfect knowledge since the two would yield identical solutions
given the same set Of activities and restraints. Thus, knowing
the value of an fig 333; linear program at its best, decisions can
be made as to whether an g§_g§£g linear program is worthwhile, and

if so, as to how much accuracy is desirable for the included

‘. “,“~

59

relationships. Because of the fact that it yields the same solution
as an identical g§_ante linear program possessing perfect knowledge
and because of the objective concerned with Studying maladjustment,

only an 25 post linear program is used in this study.

Fitting the Objectives into a Conceptual Framework

The objective Of Studying the effects of optimum decision
making versus incorrect decisions can be expressed explicitly in
a neat conceptual framework. As stated earlier, the line of
expansion under simulation does not have a neat, theoretical basis
and thus is not predictable, i.e., it can go in any direction and
assume any shape.

The linear program will yield the Optimum solution--a point
on the production possibilities curve--which will, in all prob-
ability be a different solution. The g§_pg§£ linear program will
not, however, trace out an expansion path since it only indicates
what could have happened in the short run. Its solution is based
on the previous year's simulation solution and the subsequent
decisions concerning the input levels and mix as reflected by the
production possibilities curve applicable to the simulator for any
given year (Figure 7). This is a basic difference between the
SE 225; linear program and other models such as polyperiod and
recursive programming which do trace out an expansion path since
they permit decisions to be made about the fixed plant.

Because these other growth models do permit changes in the
fixed plant, they are useful primarily for evaluating a given set
of decisions over a large period of time. None of these models

are very good as tactical devices to indicate what a farmer Should

 

 

60

Expansion Path

 

Figure 7.

Product-Product Diagram for Simulator and
Ex Post Linear Program

 

u.

61

do once he has deviated from the Optimal solution. Assuming that

a farmer is frequently in a state of maladjustment, then a pro-
cedure that provides greater sensitivity in an analysis Of tactical
decision making should be of value and should complement these
other longer run models.

With regard to Figure 7, if the assumption is made that pro-
fit maximization is the dominant, or at the least, a primary goal
Of the Operator; it might be reasoned that the expansion line under
simulation Should lie near the imaginary line traced out by the
25.2225 linear programming solution. This line of reasoning holds
if the Operator is Successful in achieving this goal. Under this
aSSumption the expansion line becomes a norm with which to guage
the position Of the firm at a point in time and its performance
over time.

At a given point in time, a comparison of the position of
the firm--location on the expansion path--with the position it
should have attained--linear programming solution--would indicate
the degree Of maladjustment. In addition, a comparison of the
profitability of the two enterprise combinations at a point in
time would serve as a measure of the cost Of the maladjustment.
This is in line with the Objective Of determining the maladjust-
ment due to incorrect decisions. Thus, differences between the
composition of the activities in the simulator and linear program
solution serve as an indicator of maladjustment and differences
between the profitability of the two solutions serve as a measure
of the cost involved resulting from lost revenue.

The Objective dealing with the determination of the variance

can also be related to a product-product diagram. First, consider

 

62

the case where only yield varies among otherwise identical firms
and all firms face the same prices. Thus, the Slope Of the price
line facing each firm would be the same in every case; but each
firm would have a different production possibilities curve. The
production possibilities curve for the individual firms would
likely be at different levels and have different configurations
even though they would still be concave to the origin. The set
of factors--weather conditions, etc.--that affect yield would
determine the level and Shape Of the production possibilities curve
which could be intersecting if Superimposed on one graph even
though this is not really appropriate Since each one represents a
different set of production coefficients.

The result would be that the Optimum combination Of enter-
prises would vary depending On the yield conditions. Also, the
combinations of outputs that accrue to identical firms from a
given set of decisions, which may not be optimum, would vary
according to the yield conditions. Given a set of prices,
variation in combinations Of output will cause variations in net
income which will cause variations in other Status variables Such
as net worth or value of assets. Thus, a variance--as indicated
by frequency of occurrence--can be established for the effect of
yield on any of the status variables. Therefore, if a large number
of firms are Operated over a period of years with all conditions
among firms identical except for yield, the range and frequency
distribution at the end of the period of the Status variables that
serve as a measure of growth would indicate the effect of variance

in yield on growth.

 

63

Secondly, consider the case where several stochastic variables--
yield, comodity prices, land prices-oare allowed to vary in order
to present alternative Situations for a given firm. With the pur-
chase of additional land involving a stochastic element that in-
fluences the size of the acquisition, a large number Of situations
are possible. In the case where land is the input or one of a
package of inputs represented by the production possibilities curve,
any one Of a number of potential production possibilities curves
could result, even with constant production coefficients, depending
on the amount of land that is actually under the control of the
firm. With the inclusion of variable production coefficients as
reflected by differing yield levels, the number of alternative pro-
duction possibilities curves is greatly increased. Combining this
with a number of alternative price lines due to variable prices,
the total Of different situations may become quite large.

Each Situation yields a net income and a subsequent set of
Status variables, some of which may serve as a measure Of firm Size.
If the stochastic elements are applied a number of times to an
identical set of firm characteristics using the same set of decisions,
the result would be to establish the potential effects in any one
year Of all random elements combined on one firm as indicated by
the range and frequency distribution of the status variables.

The remaining Objectives Of evaluating growth strategies
and levels Of management are accomplished in essentially two parts,
neither Of which requires a rigorous theoretical explanation. The
first part is a test of the ability Of a firm Operating under a

particular Strategy or level Of management to withstand a series

 

64

Of adverse conditions at different stages in the growth process.
The second part is an evaluation of the growth potential of a
firm operating under a given strategy or level of management
relative to that Of the available alternatives. In relation to
theory, this would consist in part of determining which strategy

or level Of management allow the attainment Of the highest pro-

duction possibilities curve at the end of the lS-year time period.

—.' iv F9249.- “winner-—

65

References

See R. H. Leftwich's comments in The Price System and Resource
Allocation, New York: Holt, Rinehart and Winston, 1966, pp. 1-4.

 

Viner, J. International Trade and Economic Development,
Oxford: Clarendon Press, 1953, p. l.

Naylor, T. H., Balintfy, J. L., Burdick, D. S. and K. Chu.
Computer Simulation Technigyes, New York: John Wiley & Sons,
Inc., 1966, p. l.

Shubik, M. "Simulation of the Industry and the Firm", Am,
Econ. R. 1960, 50:908-919, p. 909.

Rosenblueth, A., and N. Wiener, "The Role of Models in Science,"

Ehllgg‘_figi., No. 4, 1945, 12:316-321, p. 317.

Orcutt, G. H., "Simulation of Economic Systems," Am. Econ. R.,
1960, 50:893-907, p. 897.

Ibid., p. 898.

Hutton, R. F. A Simulation Technique for Making Management
Decicions in Dairy Farming, Agricultural Economic Report 87,
U.S. Department of Agriculture, Washington, 1966.

Heady, E. O. and W. Candler. Linear Programming Methods,
Ames: The Iowa State University Press, 1958.

Stockton, R. S. Introduction to Linear Programming, Boston:
Allyn and Bacon, Inc., 1963, p. 34.

Vincent, W. H. and L. J. Connor. An Orientation for Future
Farm Planning and Information Systenga Department Of Agri-
cultural Economics, Michigan State University, Ag. Econ. Misc.
1968-5.

 

CHAPTER IV

METHODOLOGY

To achieve the Objectives of this study a simulation model
is combined with an 31 post linear programming model to take ad-
vantage of the Strong points of each model in a fashion that will

Offset the weaknesses of the other. Linear programming yields an

 

optimum Solution that may not always be very realistic. On the
other hand, simulation tends to incorporate more realism but the
solution may not be the best possible one in terms of achieving
the goals of the particular firm. It is hoped that by combining
the two techniques, additional insight can be gained as to what
is, and how to achieve, a realistic solution in view of the goals
assumed for the firm. This involves a Study of some of the
maladjustment situations that a firm can get into, including a
determination of the cost of maladjustment and a Specification
of means of correcting or avoiding particular maladjustment
situations. It also involves an evaluation of growth Strategies
as to any tendencies towards leading to maladjustment Situations

and as to the growth possibilities under each strategy.

Farm Simulator

The simulation model used in this Study is one that is in
operation at Michigan State University except for a few modifica-
tions for compatability with this study. This particular model

66

 

67

called Simfarm was developed by Warren Vincent and John Brake [1],
and the components and relationships are assumed to be represen-
tative of those that exist for southern Michigan farms.

Simfarm is a complex, computerized farm firm Simulator which
contains alternative land, livestock and machinery financing arrange-
ments, alternative means of acquiring land, alternative crop and
livestock enterprises, technology levels, and so forth. Perhaps
the best way to begin a description of it is with the following
diagram and depiction of its Subroutines which were prepared by

its designers.

F1Sure 8. A Flow Diagram of Simfarm.l/
SIMFARM I

MARKET ’%__
00518 F

 

 

 

 

 

LAND

 

 

 

 

DRECTCST "]

 

 

BUILDNGS

 

'4 =2 tn (3 =2 DH .<

MACHINESJ

 

IABORHRS J

 

 

ONFMI

. NET WORTHH__DEBIS_J

v

 

 

 

OUTPUT ]

 

lv'v i 1

1/ Source: Taken from unpublished notes used by Warren Vincent for

a presentation to the CAP seminar group, January 13, 1969.

Agricultural Economics Department, Michigan State
University.

“1 “M‘—
3.

68

This represents 13 subroutines plus the main control program
"Vincent." The master program "Vincent" monitors the model, per-
forms counting and bookkeeping functions and directs the sequences
of Operations. A brief description of each of the subroutines is
presented below:

1. MARKET determines the prices to be paid the farmer
for all feasible products in the program.

2. COSTS determines the direct costs to be charged to
individual enterprises and the amount that will be
paid for farm investments (exclusive of buildings
and machinery).

3. LAND tabulates the inventory of land owned and the
tillable land available for crop production (con-
sidering both rented and owned land).

4. CROPTBL establishes land use, computed yields, pro-
duction, and value of crOps produced (sold).

5. LIVESTCR updates the livestock inventory, computes
mortality, production rates, total production and
value of livestock production sold.

6. DRECTCST computes costs of production for all pro-
ductive enterprices excluding labor, taxes, de-
preciation and other overhead.

7. BUILDNGS computes building needs, buys buildings
where needed, figures depreciation and, in general,
provides that needed for the farm building and
residence inventory.

8. MACHINES computed machinery and equipment require-
ments for crop and livestock enterprises, buys where
needed, figures depreciation and, in general, pro-
vides that needed for the machinery and equipment
inventory.

9. LABORHRS computes the labor requirements for all
enterprises on a quarterly basis, compares the
requirement with family labor available, and
computes the hired labor hours required.

10. NETWORTH tabulates the assets and liabilities as
of the end of the year. The liabilities may be
reduced by principal payments or increased by
voluntary long term or intermediate debt or by
involuntary Short term debt or involuntary debts
resulting from unanticipated needs.

 

69

11. The Status of the liabilities is determined by routine
DEBTS which updates debts outstanding from previous
years and sets up the payments on debts incurred this
year. It also sets up the beginning and ending in-
ventories of all liabilities. Livestock and machinery
purchases are intermediate term debt, as opposed to
real estate which is a long term debt.

12. Four subroutines may involve a random disturbance. If
called for, routine RSNDF will generate a random
standard normal deviate which is used in subroutines
MARKET, COSTS, CROPTBL and LIVESTK. Values drawn
by RSNDF will range between 1 3, and be drawn randomly
with mean 0 or preset at the values of 0, -3 or + 3.

13. NONFMING consists of three types of nonfarm investments:

Type I: On the average will yield seven
percent per year but will vary from
-12.9Z to 25.9%
Type II: On the average will yield Six
percent per year but will vary
from 0 to + 12%
Type III: A four percent return is a sure thing
A brokerage fee of three percent of the amount involved will
be assessed in all Types I and II investments bought and sold. The
brokerage fee is assessed only once for each transaction.

The model may be either Stochastic or deterministic. If

it is deterministic, the operator has perfect knowledge, i.e., the

value of each parameter is known with certainty in advance of the

production period. Thus the model becomes essentially a budgeting

procedure in which there are no shocks or disturbances in the System.

This procedure may be desirable for use as a norm for purposes of
comparison with Stochastic results to determine the effects of
certain types of Stochastic variables.

Under the Stochastic form of the model, the results should
be more realistic but less predictable. The range of values and

the probabilities associated with the stochastic elements were

1... ._i. _ __. .__§|

 

70

derived from historical evidence. The particular value of a Sto-
chastic variable that is drawn is the result of a random selection
from the probability distribution describing the several events.
It must be emphasized that the stochastic model is a teaching and
research device and cannot be used to make predictions. For
example, it can be used to indicate the results if low corn prices
occur in a given year, but it cannot yield any information as to the
chances of low corn price occurring beyond the probability dis-
tribution describing the range of included corn prices.

Simfarm is a complex farm business simulator. Within limits,
a large number of alternative uses can be made Of the program.
Among the possibilities are a comparison of the following:

1. Alternative cropping programs on a given farm

2. Differing crop-livestock program relationships

3. Alternative livestock programs on a given farm

4. Like programs on different farms

5. The debt paying capacity of like programs on farms
of the same size but different productive capacity

6. Farm earnings with nonfarm investment earnings

7. Returns from alternative technology levels

In addition, Simfarm can be used to trace the growth char-
acteristics of particular farm firms over time; which is the

primary purpose for which it will be utilized in this study.

Policy Variables

Simfarm contains a number of policy decision variables that
permit alternative courses of action or that allow a certain amount

of choice as to the level at which Specific factors come into play.

 

71

The alternatives available to the operator or experimenter are
perhaps best exemplified by an enumeration of the choices avail-
able on the transmittal form (Appendix A). The first set of
decisions on the transmittal form have to do with real estate.
Land can be bought, sold, and rented in or out. Purchases of

land can be made in 40 acre units or in the form of three types

of farms that vary as to the proportion in which they combine
three classes of land. When purchasing land, there are Six al-
ternatives available as to the level of down payment--three each
under a mortgage or contract arrangement--and four different
lengths of time over which the loan is amortized. Buildings are
not handled as a policy decision variable. A predetermined amount
of building Space is acquired with control of a farm and additional
Space is purchased automatically to meet livestock requirements.
The terms on which additional Space is acquired are governed, how-
ever, by the selected down payment level and length of amortiza-
tion.

The second set of decisions deals with the selection of field
crops to be included in the operation for that production period.
There are Six different crops (1) corn, (2) soybeans, (3) field
beans, (4) wheat, (5) oats, and (6) hay. The actual activities
are 11 rotations consisting of one or more crOps where an individual
crop makes up either 20, 40, 60, or 100 percent of the land allocated
to that rotation. The proportions in which crops may be combined in
the Operation are restricted to some degree by the use of rotations
but this is not a major problem Since each crop is included in at

least three rotations. In addition there are three variations in

“’77-'33 M 4.1-). ”yr——

72

the level of technology available to the firm. The choice of
technology level affects the profitability of the enterprise.

Each technology level has different yields and different production
costs which may to some extent be a reflection on the managerial
ability of the Operator.

The third major set of decisions pertains to the acquisition
and sale of livestock enterprises. The livestock activities include
dairy cows, beef cows, bred giltS, feeder pigs, and feeder steers;
however, only dairy cattle will be discussed Since they are the
only livestock enterprise considered in the Study. Dairy cows may
be purchased in any quantity desired within the limits of capital
and debt resources. Also, any cows owned may be sold with the re-
striction that not less than 16 percent is sold in any year to
ensure the disposal of cull cows. This minimum culling rate also
leads to an expectation of upgrading the herd which is reflected
in a higher yield of both pounds of milk and calves. Both
categories of yield are subject to stochastic influences, as is
the sexual composition of the group of calves. All male calves
are automatically sold. The livestock activities also offer three
levels of technology. When cowS are purchased, the transaction
may be on a cash basis or through the use of intermediate credit--
five year repayment--with a choice of 40 percent or 60 percent down
payment. Machinery and labor are both provided as needed. However,
machinery purchasing arrangements is a policy decision variable.

The Operator must decide whether to purchase the necessary machinery
on a cash basis or through the use of intermediate term credit. If
he chooses intermediate term credit, he may control repayment terms

through his selection from among five levels of down payment.

73

The remaining two items on the transmittal form have to do
with nonfarm investments and control of the exogenous forces affect-
ing the firm. The Operator can invest in, or disinvest from, three
distinct classes of nonfarm investment. Each class of investment
has a different average yield but the range associated with the rate
of return increases with the level of the average yield. In controlling
exogenous factors, the experimenter has three deterministic Situations

and a stochastic Situation under which to operate the program.

Output

An illustration of the output form is presented in Appendix
B. It is rather self-explanatory with the exception of the computa-
tion of the NET CASH, END OF YEAR and SHORT TERM DEBT. Net cash,
at end of year is computed by summing the cash on hand at the be-
ginning Of the year and gross income and then deducting direct
costs, taxes, hired labor, interest, debt and investment, family
living, and income taxes. If this figure is negative, it is
entered as a zero and enough short-term credit is taken out to
cover the deficit. Short-term debt is limited to $25,000 and if
the deficit is larger than this amount, the Simulator does not

give a solution, which could be considered bankruptcy.

Linear Programming Model

The linear programming model used in this study was designed
to determine the combination of enterprises that would have been
optimum given the restraints, the conditions of production, and the
market facing the simulated firm. The enterprises, their resource

requirements, and their associated costs are duplications Of those

74

included in Simfarm. The resource restraints for a given period are
taken directly from Simfarm so that the firm is facing the same con-
ditions at the beginning of the period under both models (Appendix C).

The profitability in absolute terms of each enterprise in the
linear programming model is identical to that of Simfarm. As
mentioned previously, product prices and yields are determined
Stochastically within Simfarm to Simulate the uncertainty facing
a firm. These selected values are incorporated into the linear pro-
gram as if perfect knowledge existed, i.e., they were known with
certainty in advance of the production period. The process is
automatic starting with (a) simulator input, (b) simulator output,
(c) linear programming input and matrix development, and (d) linear
programming output. To summarize, the linear program matrix is
automatically tailored to the previous situation evaluated by the
simulator, and uses actual yields and prices obtained by the
simulator.

Thus, because of the duplication, the two models represent
the same firm; however, the two solutions have entirely different
meanings. The Simfarm solution is intended to represent a realistic
outcome to a set of decisions similar to those which existing farmers
make [2]. The linear programming solution represents the optimum
level of each enterprise, given the resource restraints and assuming
perfect foresight in the case of future production and marketing
conditions. Thus, Simfarm provides the results to a set of decisions
under stochastic production and market conditions and the linear
program indicates both what that set of decisions should have been
and what the results of this "correct" set of decisions would have

been. Thus, the linear program is utilized in a manner to take

75

advantage of its diagnostic capabilities rather than in a predictive
sense.

The linear programming model contains the same set of
activities as does Simfarm. The actual activities are 11 rotations
consisting of one or more crOpS where an individual crop makes up
20, 40, 60, or 100 percent of the land allocated to that rotation.
There is also a 12th rotation that permits land to be rented out.
In addition there are several livestock activities (1) dairy,

(2) beef cow-calf, (3) fat cattle, (4) market hogs, and (5) feeder
pigs.

The restrictions in the linear programming model include
family labor, land operating capital, hired labor, credit, and
livestock facilities. The availability of family labor is expressed
in quarterly amounts giving four categories. Land is divided into
three classes with specifications as to what can be grown on each
type. Operating capital makes up a single category with a given
amount for all enterprises over the production period. Five
categories of hired labor, each carrying a different wage rate,
are also made available in quarterly amounts making a total of 20
categories of hired labor serving as restraints. In addition, four
credit categories are included with each carrying a different
interest rate charge. Finally, an upper restraint is placed on
the quantity of each type of livestock that the firm may have in
each of its operations according to the capacity of the facilities
that the firm owns.

There is one aspect Of the program dealing with hired labor
and credit that deserves Special mention. Each category associated

with these two inputs is included as an activity as well as a

76

restraint. As a restraint it has a quantitative limitation as to
the amount available for use by the firm. As an activity, it has
its cost included in the objective function which serves two pur-
poses. It results in the order in which categories of both hired
labor and credit enter into the program being an inverse function

of the associated cost, and it causes the cost of the total quantity
used to be deducted from the Objective function--the firm's net

income.

Assumptions

 

Given the described Simulator and linear programming model,
all farms represented in this study are obviously synthetic firms.
It is equally obvious that any pronouncements extolling the virtues
of the findings of Such a study in terms of their application
necessarily imply an assumption that the characteristics and
relationships represented by the synthetic firms, at the very
least, bear a high degree Ofsimilarity to those of existing firms.

The prices and production coefficients incorporated into
the simulator (Appendix D) are considered to be presently realistic
but no pretense is made that these data would remain unchanged in
an absolute sense over a 15 year period. However, the assumption
is made that the data would remain unchanged in a relative sense.
For instance, if one enterprise is more profitable than another
at the present, it is assumed that it will remain so throughout
the period. This does not prevent shifts in the aggregate supply
and demand curves for agriculture, but it does preclude independent
shifts in the curves Of individual enterprises. The simulator does

not permit inflationary effects to be incorporated, but this is

77

not critical since a change in the general price level, ceteris
paribus, does not affect real relationships.

In all appearances, Simfarm does seem to involve an accept-
able degree Of realism so as to warrant its inclusion in this
study of the growth process of southern Michigan dairy farms. Any
loss of realism is assumed to be more than offset by the added
advantage provided by Simfarm in studying the various aspects of
the firm. Simfarm, as a Simulator, provides a laboratory-like
setting in which the individual components of the firm may be con-
trolled and manipulated in a manner to facilitate the analysis of
their relationships.

The results Of the study are deemed as being applicable to
two groups of southern Michigan dairy farms characterized by dif-
ferences in managerial ability. The higher level of technology
(a) is considered to represent the upper five to ten percent Of
farmers in terms of managerial ability. The second level of
technology (b) is considered to be representative of those Operators
ranking between the 50th to 90th percentiles. These groupings
are, of course, approximations but they are assumed to be accurate

enough to make the conclusions valid.

Procedure

The analysis section of this Study is based on four computer
programming phases, each of which is designed to facilitate the

attainment of one or more of the Objectives.

Phase 1
The simulator and linear program were both run on a stochastic

basis for a 16 year period. There were eight firmS--one for each of

78

two technology levels within each of the four StrategieS--all of
which began, in the initial year of the study, from a common
starting point (Table 1). According to the experimental design;
years 1, 6, 11, and 16 were to be acquistion years in which pur-
chases Of additional real estate and cows were to be made. The
acquisition decisions were resolved by purchasing as large a
quantity of inputs as permitted by cash-on-hand and down payment
requirements. The four-year periods separating these acquisition
years were run on the basis of one set of decisions SO that the
operation and size were stationary during this interval. The
composition of included enterprises was governed by a preference
for maintaining a high degree of similarity to existing operations.

Acquisitions of assets were made at Specified intervals so
that large quantities could be purchased to give the semblance of
buying existing operations. This was considered to be especially
important in the case of land where the alternative of buying a
few acres each year was not realistic in terms of the supply
situation.

Throughout Phase 1, no attention was given to the linear
programming solutions concerning enterprise combinations until the
end of the period under Study. At the end of the period, one
particular variable--net income--which was considered to be especially
important, was handled by taking the difference between the net
incomes of the linear programming solution and Simfarm and then
compounding the difference forward at an assumed internal rate of
return of six percent [3]. The difference in any given year was
computed to get a measure of the annual loss in income due to

incorrect production decisions, i.e., the cost of inefficiency of

79

resource use. The sum of these compounded differences was used as
an indication of the total loss from incorrect decisions over a
period of years in terms of the amount of potential growth of

which the firm was deprived.

Phase 2

In order to obtain additional information on the eight
firms--two for each strategy--at different stages in the growth
process, the Situations at the end of the first, second, and fourth
acquisition years in Phase 1 were singled out for additional study.
After the completion of the acquisitions in these years, a common
transmittal form that purchased no additional cows or land was
submitted and iterated deterministically for five years and adverse
elements consisting of one of two levels of severity were induced.
This was done to permit an evaluation of the ability of a firm
Operating under a given Strategy to withstand adverse conditions,
i.e., to evaluate the riskiness of each strategy.

In the case where a firm survived its five years of adverse
conditions, the principle criterion used in these evaluations was
the financial position of the firm at the end of the period. If
the firm was unable to meet its debt commitments at any point
during the five years, it was considered to be bankrupt. In the

case of bankruptcy, the year in which it occurred was noted.

Phase 3

In Phase 3 using a given initial set of characteristics
(Table l), a single year was repeated 50 times to establish the

range of the effects of all stochastic elements combined. This

80

Operation was carried out by submitting one set of decisions to the
simulator for all 50 runs and returning to the same previous Situa-
tion for each run. The range and probability distribution of the
resulting values of certain variables--value of assets, gross in-
come, net income, and net worth--were used as measures of the total
effect of all stochastic elements.

Simfarm's stochastic elements have three basic components--
commodity prices, enterprise yields, and land prices. Commodity
prices and yields directly affect both gross income and net income.
Indirectly they also affect the other status variables such as value
of assets and net worth through cash-on-hand. The land price com-

ponent governs the acquisition of land if a bid is submitted.

Phase 4

In this, the last of the four phases, one set of decisions,
permitting no additional land or cows to be purchased, was iterated
over a ten year period for 50 firms. Each firm had the same initial
characteristics and all differences in subsequent years were due to
variations in the stochastic elements. Simfarm is designed so that
if a number of sets of decisions for an equal number of firms are
programmed at one time, every firm faces identical land and commodity
prices. However, each firm is Subjected to different yield con-
ditions. Thus, given the same initial Situation and the same set of
decisions in each year, any differences that occurred between firms
is attributable to yield variation. Therefore, divergences in the
status variables (gross income, net income, value of assets, net
worth, etc.) of the 50 firms at the end of the ten year period serve

as a measure of the effect Of yield variations.

81

References
Warren Vincent and John Brake are both professors of agricultural
economics at Michigan State University.
Hepp, R. E. and L. H. Brown. Telfarm Business Analysis Summary
for Southern Dairy General, 1967. Agricultural Economics Report
No. 104, Michigan State University, 1968.

The compounding formula is as follows:

FV - D(l+r)t
where
FV I future value at end of period compounded
D I income difference
r I interest rate
t I number of years compounded and is determined
as the portion of the 15 year period not yet

completed.

CHAPTER V

Presentation of Results

Chapter V is a presentation of the results of the four computer
phases. This is done with the aid of tables and graphs according to
the numerical arrangement of the four phases of the research. Such
ordering is partly a matter of necessity and partly a matter of
preference. In the case of phase 1 and phase 2, the occurrence and
presentation of the results are dictated by the sequential nature
of the research process. The results of the final two phases follow
those of the first two phases.

In recognition of the earlier definition of firm growth
(Chapter 1), the value of assets will be the principle means of
measuring the size and growth of firms in all four phases. How-
ever, other variables may be brought into the analysis from time
to time in situations where they might direct attention to a
particular aspect of the growth process.

A total of eight firms was used in phase 1 and phase 2 (Table
2). These consisted of four firms for each of two technology levels;
one for each of four strategies. The four Strategies were a vertical
Strategy under which only the cow herd and associated equipment were
expanded and three variations of the lateral Strategy under which
both the cow herd and the land base were expanded. The lateral
strategies differed as to the terms under which control over addi-
tional land was gained. The two levels of technology were viewed

as representing two distinctive levels of management, above average
82

83

and exceptional.

Of the two levels of managerial ability, the exceptional one
represented by technology A was more profitable on the average (Table
3) when either the stochastic or deterministic elements in Simfarm
were in operation. This fact was demonstrated by the values computed
for the linear programming objective function as the per unit net
income values were consistently higher for the players operating
under the higher level of management. The total cost per unit was
usually higher under superior technology but the change was generally
more than offset by a relatively greater increase in gross income

per unit.

Table 2. Explanation of Firms Included in Study

 

 

Item Characteristics
Firm 1 Technology A, Strategy 1
Firm 2 Technology A, strategy 2
Firm 3 Technology A, strategy 3
Firm 4 Technology A, Strategy 4
Firm 5 Technology B, Strategy 1
Firm 6 Technology B, strategy 2
Firm 7 Technology B, strategy 3
Firm 8 Technology B, strategy 4

 

1Definition of terms:

Technology A The upper five percent of the
operators in agriculture in terms
of managerial ability using
higher priced inputs.

Technology B The operators possessing above
average managerial ability with
exception of upper five percent.

Strategy 1 Vertical Strategy expanding only
the cow herd.

Strategy 2 Expanding cow herd and land base
by renting land.

Strategy 3 Expanding cow herd and land base
with land contract.

Strategy 4 Expanding cow herd and land base

with mortgage.

84

Table 3. Five Year Average of the Profitability of Selected Enter-
prise Arrangements under Two Managerial (Technology) Levels
on Class I Land

 

 

Enterprises2 Technology A Technology B
(dol./acre) (dol./acre)
Corn 55.15 44.19
C-C-C-FB-FB 53.31 44.30
C-C-O-H-H 43.82 33.28
C-FB-C-O-W 44.07 37.48
C-C-C-O-W 45.49 35.93
Hay 40.38 29.81

 

1Derived using results Obtained under firm 1 and firm 5 during
first five years of study. Labor costs have not been deducted

2
Each symbol represents a part equal to .20 of an acre

C I Corn 0 I Oats H I Hay
FB I Field beans W I Wheat

Investment Decisions

 

The first step in the analysis was to apply principles of
long run investment theory to the data in the simulator to determine
if growth is feasible. The particular manner in which this was
accomplished was by discounting future earnings expected to accrue
to land and dairy cows back to the present and then comparing this
present value of future earnings with the price of the asset.
Computing expected values from Simfarm data would be a simple pro-
cess because the probability distributions associated with the
-variables are known. Also, since they are identical for each and
every year, the expected value would be the same for every year.
With the assumption of infinitely long earning streams for land,
the appropriate discounting formula becomes PV I Eéxl .

To know that it is, indeed, economically feasible to pur-

chase land for growth purposes, it is only necessary to have one

85

use for the land that is profitable. Accordingly, the expected cash
rent incomes were discounted and found to have a present value in
excess of the price of land for class I and II land. All of this
indicates that a farmer could profitably invest in these two types
of land for purposes of renting them out. It did not appear pro-
fitable to rent class III land out but it did appear to be a good
investment for purposes of growing hay.

The expected annual return to dairy cattle was also cap-
italized over the expected life of a dairy cow and found to be
greater than the initial cost of the cow. The principles of long-
run investment theory can be applied in this manner to every type
of asset to be purchased. It was not applied to the purchase of
buildings and machinery. These two types of assets are purchased
automatically by the simulator as needed, and it would be difficult
to derive the marginal earnings of these two types of assets. This
omission was not considered to be of major concern since livestock
and land are the main avenues of expansion.

In making purchase of land and livestock under the lateral
Strategies, an attempt was made to roughly maintain a ratio of one
cow to five acres of land. This appeared to be a realistic figure;
and in addition, its use over all three Strategies made possible
more meaningful comparisons of the results. Since the vertical
strategy only permitted the purchase of cows, it was not possible
to maintain such a relationship between the firms' livestock and
cropping systems.

Only one application of long-run investment theory was re-
quired in the case of each type of asset due to the fact that the

expected values for each variable were the same for each production

86

period. Principles of Short-run production theory were applied in
each production period through the use of the linear programming
model to obtain an Optimum solution with regard to the maximization

of net income.

Phase 1

Phase 1 deals with three of the four objectives. It provides
all of the data used in accomplishing the first objective of com-
paring the effects of realistic and optimum decisions. It also
contributes to that part of the analysis dealing with a comparison
of growth strategies and with measuring the effects of two levels of
managerial ability. Data obtained from this phase indicate the
amount of growth to be expected over a 15 year period and represent
different sapects of the total effect of optimal decisions. These
data are presented in Tables 4, 5, 6, and 7. Among the aspects
delineated below are year-to-year variations between optimal and
realistic solutions, the cumulative effect of a series of variations
and two Specific causes of the differences-~yield and renting-out

land.
Realistic Expectations

The characteristics of the eight firms for both the Simulated
solution and the optimum solution (LP) in the 15th year of the study
are presented in Table 4. The properties listed under the Simulator
solution are the cumulation of 15 successive years of operation. A
comparison of the appropriate characteristics under the Simulator
solution in Table 4 with the identical characteristics in Table 1,
provides a measure of the amount of growth a particular firm might

realistically expect to attain over a 15 year period.

87

 

 

 

 

Table 4. Selected Characteristics for Comparison of Simulator and

Lineai Programming results at end of year 15 for Eight

Firms

. Firm 1 Firm 2 i

Item Unit Simfarm LP Simfarm .LP
cows 177 190 206 230
land ac. 280 280 1240 1240
corn ac. 120 0 696 800
sm. grain2 ac. 80 0 464 240
hay ac. 80 80 80 80
beans3 ac. 0 0 , O 120
rented-out ac. 0 200 0 0
net income dol. 95,877 104,396 117,411 126,319
gross income dol. 181,182 287,046
assets dol. 488,489 506,514
equity ratio 2 83.97 81.40

 

1See Table 2 (p. 83) for characteristics of each firm.
2
oats and wheat

3Simfarm solution: soybeans
LP solution: field beans

Table 4. --continued

88

 

 

 

 

Firm 3 Firm 4
Item Unit Simfarm LP Simfarm LP
cows 171 190 173 190
land ac. 1240 1240 1040 1040
corn ac. 696 696 576 576
am. grain ac. 464 288 384 224
hay ac. 80 80 80 80
beans ac. 0 176 0 160
rented-out ac. O 0 O 0
net income dol. 133,809 143,050 114,665 128,559
gross income dol. 260,376 236,477
assets dol. 774,711 649,656
equity ratio 1 58.32 65.16

89

Table 4. --continued

 

 

 

 

Firm 5 Firm 6

I tem Unit S imfarm LP. Simfarm LP-

cows 114 130 119 130
land ac. 280 280 1240 1240
corn ac. 120 48 696 131
am. grain ac. 80 0 464 0
hay ac. 80 O 80 80
beans ac. 0 32 0 87
rented-out ac. 0 200 O 942
net income dol. 41,704 49,398 43,129 52,738
gross income dol. 95,845 171,459

assets dol. 225,291 192,727

equity ratio % 70.75 64.04

90

Table 4. --continued

 

 

 

 

Firm 7 Firm 8
Item Unit Simfarm LP Simfarm LP
cows 108 120 111 130
land ac. 760 760 640 640
corn ac. 408 132 336 120
am. grain ac. 272 0 224 0
hay ac. 80 75 80 80
beans ac. O 0 0 80
rented-out ac. 0 553 O 360
net income dol. 53,619 64,504 62,083 73,744
gross income dol. 126,861 131,420
assets dol. 366,506 345,414
equity ratio 1 51.49 63.24

91

 

 

Table 5. Additional Value of Assets Obtainable with Optimum Pro-
duction Decisions over a 15 year Period for a Specific
Set of Investment Decisions under Stochastic Conditions.
Item1 Additional2 Maximum3
(dol.) (dol.)
Firm 1 113,872 602,361
Firm 2 170,944 677,458
Firm 3 193,430 968,141
Firm 4 184,560 834,216
Firm 5 131,820 357,111
Firm 6 184,319 377,046
Firm 7 172,977 539,483
Firm 8 175,796 521,210

 

1See Table 2 (p. 83) for characteristics of each firm.

2Derived by compounding the differences in net income over
the 15 year period forward to the final year using a 6

percent internal rate of return.

3Computed by adding the compounded net income differences

to the value of assets in Table 2.

92

Table 6. Selected Characteristics for Comparison of Simulator and
Linear Programming Solutions in Year 6 for Eight Firms1

 

 

 

 

Firm 1 Firm 2 4-
Item Unit Simfarm LP Simfarm LP
cows 90 90 90 90
land ac. 280 280 760 760
corn ac. 128 80 464 192
sm. grain ac. 48 0 144 0
hay ac. 80 80 80 80
beans ac. 24 O 72 128
rented-out ac. 0 120 0 360
net income dol. 41,399 44,752 40,049 44,273
gross income dol. 90,415 128,117
assets dol. 194,974 202,826
equity ratio 1 63.40 62.23

 

1

See Table 2 (p.

2oats and wheat

3Simfarm solution: soybeans
LP solution:

field beans

83) for characteristics of each firm

93

Table 6. --continued

 

 

 

 

Firm 3 Firm 4
Item Unit Simfarm LP Simfarm LP
cows 93 100 71 80
land ac. 760 760 640 640
corn ac. 392 200 344 344
am. grain ac. 192 0 144 144
hay . ac. 80 480 80 80
beans ac. 96 O 72 72
rented-out ac. O 80 0 0
net income dol. 55,511 64,751 46,674 50,274
gross income dol. 128,667 106,297
assets dol. 356,646 285,938
equity ratio Z 38.51 47.26

Table 6. --continued

 

 

 

 

Firm 5 Firm 6
Item Unit 3 imTarm LP 5 imfarm LP
cows 89 90 81 90
land ac. 280 280 760 760
corn ac. 128 72 464 0
sm. grain ac. 48 48 144 0
hay ac . 80 80 80 80
beans ac. 24 0 72 0
rented-out ac. 0 8O 0 680
net income dol. 29,893 33,930 19,466 28,552
gross income dol. 74,809 97,769
assets dol. 148,296 185,154
equity ratio Z 51.88 35.95

95

Table 6. --continued

 

 

 

 

Firm 7 Firm 8

Item Unit Simfarm LP- 3 imfarm LP
cows 90 90 74 80
land ac. 760 760 640 640
corn ac. 392 120 344 200
am. grain ac. 192 O 144 0
hay ac. 80 80 80 80
beans ac. 96 80 72 0
rented-out ac. 0 480 0 360
net income dol. 39,885 46,833 34,363 40,806
gross income dol. 106,157 89,830

assets dol. 304,718 244,059

equity ratio Z 29.59 38.21

96

Table 7. Proportion of Total Acres Farmed over 15 Year Period by
Simulator that was Rented Out by Linear Program.

 

 

Item1 Farmed Rented-Out
(acres) (acres) (percent)

Firm 1 4,200 1,200 28.6
Firm 2 12,600 4,145 32.9
Firm 3 12,120 600 5.0
Firm 4 10,520 2,822 26.8
Firm 5 4,200 1,920 45.7
Firm 6 12,600 6,519 51.7
Firm 7 11,320 2,953 26.1
Firm 8 9,200 3,049 33.1

 

1See Table 2 (p. 83) for characteristics of each firm.

97

Cumulative Effect of Optimal Decisions

Table 5 provides an estimate of the maximum amount of growth
that similar firms could possibly achieve with a series of optimum
production decisions over a 15 year period following Specific sets
of investment decisions. These figures were derived by adding the
sum of the compounded net income differences that occurred between
the Simfarm and optimum solutions to the appropriate value of assets
in Table 4.

Two important assumptions are implied in the manner in which
these increments of income are handled. One assumption is that these
increments of net cash income in their entirety are immediately
invested in earning assets. This assumption necessitates compounding
the increments forward to obtain an estimate of the total effect
for the 15 year period. The second assumption permits the invest-
ment of the entire increment. This assumption is that the net change
in investment that would be required to alter production plans in
accordance with the optimum solution is negligible. Variations on
the level of investment would cause a change in the amount of
depreciation. Changes in the level Of depreciation would affect the
net income gains.

This last assumption is a crucial but, in this case, valid one.
There are at least three reasons for this conclusion. First, the
model was restricted to one livestock enterprise. The purpose of
this restriction was to Specifically prevent the optimum solutions
from vacillating among livestock enterprises. A shift among live-
stock enterprises usually results in losses on fixed assets and
Often necessitates large additional investments. It was not the

intent of the Study to consider changes of this nature. Secondly,

98

the largest Single change in the use of cropland required by the
optimum solution was to shift land out of production by renting it
out. Shifting land out of production, of course, does not require
that any additional assets be purchased. It could result in the
sale of equipment but such sales were assumed to be inconsequential
for two reasons--low salvage values and the Short run nature of
production decisions. Thirdly, agricultural equipment tends to be
rather versatile. Tractors, combines, planters, etc. can be used
for a variety of crOpS so a partial shift from corn to wheat, for

example, would not require a wholesale change in equipment.
Year-to-Year Variations

Under the goal of profit maximization there can be a great
deal of variation between the actual solution and the optimal
solution. In the 120 solutions of each type arrived at for the
eight firms in 15 years, the differences, expressed in terms of
the net income arrived at by the Simulator, ranged from a low of
6.0 percent to 51.6 percent. The median difference was 15.15 with

27 percent of the differences exceeding 20 percent.
Yield Variations

That there can be a great deal of variation between the two
approaches, even within a time period as Short as a single pro-
duction period, is exemplified by the results that occurred in year
6 and are presented in Table 6. Within this year, all eight firms
received identical prices in the market and the four firms operated
under each technology faced the same costs. Also, eachifirm Operated
under an identical set of production decisions, i.e., applied the

same rotation to each type of land. Therefore, the only component

99

of production that varied among the eight firms was yield.

The range of the possible effects resulting from the stochastic
variable yield is indicated by the complete agreement in the use of
land between the simulator solution and the optimum solution under
firm 4 and the almost complete dissimilarity between the two solu-
tions under firm 6. This common set of decisions was obviously
the correct one in view of the market and yield conditions facing
firm 4 even though he could have increased his profits by $3,600
(7.7 percent) if he had had his cow operation at full capacity. In
view of the conditions facing firm 6, the set of decisions relating
to land use was almost totally wrong. Renting-in 760 acres of land
when he should not have rented a single acre plus not having his
dairy operation at full capacity cost this farmer over $9,000 and
the opportunity to have 46 percent more income. The gains from
better decision making for the other six firms fell in-between these
two extreme cases as none of these firms could have increased pro-

fits by more than 20 percent.
Cow Herd Size

A noteworthy point is the fact that firms 1 and 2 had the
optimal number of cows and could have increased their net income
by only 8.1 and 10.5 percent, respectively, with a different selec-
tion of crop enterprises. This would seem to indicate that cows are
relatively profitable and that it is essential to keep the dairy

Operation near capacity.

Renting-Out Land

Another result of the optimal decisions made by the linear

program that is worthy of reporting was the consistency in renting

100

out a large proportion of the land under the control of the firms.
As shown in Table 7, as much as 50 percent of the land was rented
out by the linear program. With the exception of one case, the
linear program rented out more than 25 percent of the land for
every firm over a 15 year period. There are reasons, peculiar to
particular strategies, for the relative standing of the proportions
but the only explanation for the consistently high proportions is
that the earnings from farming the land are often less than the

opportunity cost of renting-out.
Unrestrained Agguisition of Assets

The final step in phase 1 was to remove all restraints from
firms 1-4 and to allow them to purchase as many resources as their
reserves would permit. During the first 15 years of Study some
restraint was exercised on the rate at which the four firms operat-
ing under technology A, acquired assets. This was done to maintain
an aura of realism under the likelihood that to have acquired assets
at the maximum rate permitted by the available reserves would not
have been consistent with the prices in Simfarm and existing supply
conditions. The outcome of this unrestrained purchasing is presented

in Table 8.

Phase 2

Under this phase each firm was Subjected to a series of adverse
conditions at various stages in the study. There were two levels of
adverse conditions neither of which was generally severe enough to
make farming completely unprofitable. The two sets of adverse con-
ditions, hereafter referred to as adversity level 1 and adversity

level 2, reduced the level of profitability of the firm by about

101

 

 

Table 8. Selected Characteristics of Eight Firms Representing

Four Growth Strategies under a High Level of Managerial

Ability, Year 161
Item Unit Firm 1 Firm 2 Firm 3 Firm'4
cows 977 986 588 404
land ac. 280 2200 2840 1800
corn ac. 120 1272 1656 1032
sm. grain2 ac. 80 848 1104 688
hay ac. 80 80 80 80
net income dol. 431,639 393,759 335,669 222,182
gross income dol. 847,556 959,021 721,938 478,720
assets dol. 1,187,895 1,197,931 1,765,559 1,097,311
equity ratio Z 51.67 49.74 34.38 48.41

 

18cc Table 2 (p. 83) for characteristics of each firm.

2oats and wheat

102

30 to 40 percent and 70 to 75 percent of that of normal conditions
reSpectively.

The results of this phase make up one part of a two part
analysis dealing with the second and fourth objective--eva1uating
four alternative growth strategies and two distinct levels of
management. The two parts of the analysis consisted first of a
measurement of the growth that could be achieved under each
strategy and each level of management under both realistic condi-
tions and more nearly optimum conditions; and second, of getting
an indication of the resilienceof each strategy and level of
management under conditions of adversity. Phase 2 Studied the

latter of the two parts. The selected years are enumerated below.
Selected Years

The periods immediately following four years in which pur-
chases of assets were made--years one, three, six, and Sixteen--
were selected for experimentation with one or both of the adversity
levels. The period is hereafter identified by the number of the
purchase year which is referred to as a study year. The outcomes
of the subjection of each study year to one or both of the adversity
levels are indicated in Tables 9, 10, 11, and 12. Table 9 contains
the number of years out of each five year period that a firm was
able to Survive. Tables 10, 11, and 12 contain selected char-
acteristics of the surviving firms to permit a comparison of their

financial position at the end of each period.

Modifications

Two of the study years deserve Special mention. Study year

1 was not a purchase year in the main section of the study because

103

Table 9. Number of Years Eight Firms were Able to Survive out of
Five Year Periods of Adverse Conditionsat Various Stages

 

 

 

of Growth.
1
Strategy 1. 1‘7 2 3 4
Technology level A B A B A B A
Study Adversity2
Year level
1 2 5 l 3 l 3 1 3
3 l 5 5 5 1 5 5 5
6 1 5 5 5 O 5 2 5
6 2 5 2 5 0 5 O 5
16 2 5 3 3 0 5 2 5

 

1See Table 2 (p. 83) for explanation of Strategies and technology
levels.

2Adversity level 1: reduction of profitability by approximately
35 percent of the average

Adversity level 2: reduction of profitability by approximately
75 percent of the average

104

 

 

 

Table 10. Selected Characteristics for Comparison of Firms Surviving
Five Year Period of Adverse Conditions: Study-Year 3,
Adversity Level 1
Strategy1 1 2 3 z. 1 3
Technology level A A A A B B
Cows 63 78 73 76 61 78
Net Income dol. 33,183 34,583 39,871 41,248 23,619 29,687
Gross income dol. 67,485 92,518 89,937 92,506 54,556 79,389
Assets dol. 194,079 200,037 273,692 265,405 139,883 212,593
Equity Ratio Z 68.99 68.21 52.08 56.85 56.89 38.43
Reserves dol. 86,673 74,376 79,997 69,635 33,325 15,573

 

1See Table 2 (p. 83) for explanation of strategies and

technology levels

2Composed of cash-on-hand plus remainder of $25,000 short-

term credit

105

Table 11. Selected Characteristics for Comparison of Firms Surviving
Five-Year Period of Adverse Conditions: Study-Year 6,
Adversity Level 1

 

 

 

 

Strategy1 1 2 3 4 1
Technology level A A A A B
Cows 108 101 115 84 111
Net income dol. 54,723 40,816 61,124 46,088 42,664
Gross income dol. 106,631 125,585 136,942 105,013 91,238
Assets dol. 322,826 278,725 445,935 354,996 222,023
Equity ratio Z 80.39 77.13 58.06 64.66 69.71
Reserves2 dol. 151,862 109,153 129,573 100,939 42,394
1

See Table 2 (p. 83) for explanation of strategies and
technology levels.

2Composed of cash-on-hand plus remainder of $25,000 Short-
term credit.

106

Table 12. Selected Characteristics for Comparison of Firms Surviving
Five-Year Period of Adverse Conditions: Study-Year 6,
Adversity Level 2

 

1
Strategy 1 2

 

 

 

3 4
Technology level A A A A
Cows 108 101 115 84
Net income dol. 29,657 13,852 31,886 22,389
Gross income dol. 75,707 90,128 98,155 75,598
Assets dol. 236,558 182,032 330,191 265,189
Equity ratio Z 73.24 64.98 43.34 52.69
Reserves2 dol. 65,595 10,749 13,827 11,132

1

See Table 2 (p. 83) for explanation of Strategies and
technology levels.

2Composed of cash—on-hand plus remainder of $25,000 Short-
term credit.

107

of the influence of the stochastic element which resulted in above
average bids for land not being accepted the first two years. How-
ever, because of the ease with which year one could be recreated,
it was included in order to gain additional information on the
vulnerability of the firms in the early years. The data for study
year 6W8re inadvertently lost so the data from year 7were used with
one adjustment. The sum of $20,000 was removed from cash-on-hand
and put into nonfarm investment to eliminate the net income from
the extra year of operation from the firms' available reserves.

This was the only difference between years six and seven.

Phase 3

Under phase 3 all of the Stochastically determined variables
were repeatedly allowed to engender values for the firm characterized
in Table 1 to establish the range and distribution of their com-
bined efforts. This is one of two phases undertaken to accomplish
the third objective of determining the effect of Stochastic elements
on the growth of firms. The manner in which the results are pre-

sented is explained below.
Manner of Presentation

Figure 9 contains the result of phase 3 expressed as the
number of times the firm's value of assets falls into each of a
continuous sequence of specified ranges. There was no overriding
reason for choosing the value of assets to indicate the effects of
the Stochastic elements on the amount of growth achieved within a
given time period. Four measures of Size--net income, gross in-

come, net worth, and assetS--were considered as possible indicators

108

of these effects, but they all tended to exhibit similar distribu-
tions, no doubt due to the same underlying forces, so the value of
assets was rather arbitrarily chosen from among the four.

The three distinct groupings of the data in Figure 9 are due
to the performance of the land buying procedure. The occurrence
of different values within one of these groupings is due to the
workings of the market and yield variables. These same three group-
ings are presented individually in Figures 10, 11, and 12 with an
inflated Scale on the horizontal axis to allow more detail in the
selection of categories. This was done to move a step nearer to

having a continuous function.
An Adjustment

A brief explanation is in order for the data in Figure 10
since they are a modification of the data in Figure 9. The numbers
concerned with the situation where one of two types of land was
purchased is actually two samples, one for the purchase of addi-
tional type I land and one for the purchase of additional type 11
land. The mean is slightly higher in the first case but the lower
end of the sample overlaps with the upper end of the second sample.
To get the data in Figure 10, the value of assets in the type I land
sample was adjusted downward to remove the difference between pur-
chasing type I and type II land. This resulted in a larger size
sample that still reflected the distribution of the stochastic

element.

Phase 4

In this phase, 50 identical firms were operated for 10 years

under identical sets of decision and identical conditions with the

109

exception of enterprise yields which were allowed to vary between
firms on a stochastic basis. This was the second of two phases
devoted to accomplishing the third objective dealing with the
effects of stochastic elements.

The results of this, the last of four phases, are pre-
sented in Figure 13. They indicate the range of the extreme sizes
as measured by value of assets and the frequency with which firms
fell into each of the subdivisions of the finite range over which
the results were distributed. The total range of the asset values
and the manner with which they were distributed within this range
are due entirely to the effect of yield variation. The value of
assets was utilized to demonstrate the impact of yield on growth

for the same reasons it was used under Phase 3.

Stochastic Routine

As a result of Phases 3 and 4, four samples are available
for use in determining if there is a tendency of the random
standard deviates to be symmetrically distributed about zero.
This would be indicated by symmetry in the manner in which these
samples are distributed about their mean. It was not a primary
objective of this Study to test the distribution of the random
standard deviates generated by Simfarm, but a tendency to produce
a distribution greatly different from the hypothesized normal
one could influence the conclusion regarding the Study's four
major objectives.

The frequency with which these four samples occur in two
categories on each side of the mean can be found in Table 13 and

designation of the four samples is as follows:

110

Sample A: phase 4
Sample B: phase 3, purchased both types of land
Sample C: phase 3, purchased one type of land
Sample D: phase 3, purchased neither type of land
An interpretation of the four samples is made in the following

Analysis chapter.

111

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112

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113

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114

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115

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116

Table 13. Number of Stochastic Results that Fell in Each of the Four
Devisions of the Complete Range Over Which Four Independent
Samples Occurred.

 

 

 

Categories2
:1 T
1 less (x-S) X Greater
Sample Observations than to ‘Eo than
(x -S) if (x-Ps) (Jr-*6)
A 50 7 20 15 8
B 12 l 4 6 l
C 22 4 6 9 3
D 16 l 10 3 2
Combined 100 13 4O 33 14

 

1Sample A: phase 4
Sample B: phase 3, purchased both types of land
Sample C: phase 3, purchased one type of land

Sample D: phase 3, purchased neither type of land

2§'_ sample mean

S I standard deviation of sample

CHAPTER VI

Analysis of Results

In this chapter, an interpretation of the results from the
four research phases was made. Most of the effort was directed
towards delineating the implications of these results regarding
the objectives of the study. Conclusions were drawn from the
results presented as to the gains from Optimum decision making as
opposed to decisions that a farmer might realistically be expected
to make and regarding the relative advantages of the four strategies
that were under consideration. Each of these was evaluated under
the context of two distinctive levels of management which had been
specified as being exceptional and above average.

Inferences were also drawn regarding the effects of Sto-
chastically determined variables on growth. This was done for the
effect of all stochastic elements combined and for the effect of
yield alone, the only one of the Stochastic elements that it was
possible to isolate. Also, a partial test was conducted as to the
distribution of the random standard deviates in order to determine
if they are indeed normally distributed. This was considered to be
a relevant test because, in the design of the simulator, the various
Stochastic elements were set up on the hypothesis that a normal dis-

tribution would give realistic results.

117

118

Effect of Optimality

The first Objective of the Study was to determine the effects
of optimum decision making on the growth of farm firms as opposed to
the nonoptimal decisions that operators have a tendency to make [1].
There are three aspects of the divergence between simulated and
optimal solutions that are of interest. One is a measure of the
economic cost in terms of growth foregone by the nonoptimal decisions.
The second is an indication of exactly what their incorrect decisions
were. Were they related only to combining the included enterprises
into the optimal mix or did they involve organizational changes with
the inclusion of new enterprises or exclusion of present ones. The
third aspect would be a determination of the factors leading to the
incorrect decisions.

The loss of growth from incorrect decisions can be quite
large over the Span of a single production period. This conclusion
is supported by the fact that 27 percent of the annual losses in
income exceeded a figure equal to 20 percent of the income realized
by the firm and that their losses ranged as high as 51.6 percent
of realized income. Similarly, the cumulative effect of optimality
can also be large over a 15 year period. In the case of all eight
firms, the value of assets could have been increased in excess of
$100,000 which is a relatively large increase considering the firm's
initial assets only amounted to $136,000. The actual range was
from $113,800 to $193,400 with six of the eight firms having had
the productive capability to have increased their assets by an
estimated value exceeding $170,000.

This economic loss was due to two sources. One was making

incorrect decisions in view of the available information. The

1183

second was the occurrence of unpredictable Stochastic conditions
that had one of two possible effects. It could possibly increase
the economic loss because the difference in the profitability of
the optimal mix and the operational one turned out to be greater
than expected. Alternatively, the stochastic elements could be
relatively more favorable to the chosen mix which would serve to
partially or fully offset the expected loss due toincorrect decisions.

One criterion on which an operator can base his decision
about the enterprise mix is the expected earnings Of the various
crops. Expected earnings can be derived by assigning a prob-
ability to each value from the range over which earnings may vary
and then summing the products of the respective earnings and
associated probabilities. The sum of the probabilities must, of
course, equal one. Due to the fact that the range and the prob-
abilities of enterprise earnings do not change, the expected earn-
ings are identical for every year of this study's model. Assuming
that expected earnings is the appropriate criterion on which to
base the decision, the choice of the "best" crop mix is the same
for every year of the Study. The optimal mixes differ by type of
land and are as follows:

1. Type I land: 60 percent corn, 40 percent field beans

2. Type II land: 40 percent corn, 20 percent each for oats,

wheat and field beans

3. Type 111 land: 100 percent hay

4. Dairy cows: 100 percent of capacity

'Given the assumption about the decision making criteria, any
decision pertaining to enterprise mix that differs from the combina-

tions Specified above is technically incorrect and will, on the

119

average, cost the firm the difference between the expected earnings
of the "best" enterprise mix and the one put into operation. How-
ever in any given year, the actual loss could be more or less than
the difference on expected earnings due to the effect of Stochastic
elements. Accordingly, the difference between the net cash incomes
under the Simfarm solution and the linear programming solution can
be partitioned into the loss, if any, from incorrect decisions in
view Of available knowledge and the loss or gain due to stochastic
elements, i.e., imperfect knowledge.

The operation of firm 4 in year 6 provides a good illustra-
tion of the two sets of effects. The firm planted all 200 acres of
Type I land in corn. This represented an incorrect decision accord-
ing to the assumed criterion and the firm had an expected loss in
earnings of $472. Fortunately for the firm, this year was an
exceptionally favorable one for corn in relation to the "best" enter-
prise mix. The firm earned $778 more with its all-corn selection
than it could have earned with the "best" mix. This meant that the
effect of the stochastic elements, measured in dollar terms, was
$1250 which more than offset the loss from making a decision that
was technically incorrect.

The outcome of the firm's decision relating to its 360 acres
of type II land shows a different outcome. The firm planted the
correct mix with the exception of substituting soybeans for field
beans. This decision lowered the firm's expected earnings by $1267
and because this was a rather unfavorable year for soybeans relative
to field beans, the firm lost an additional $346 due to stochastic

conditions. This gave the firm a total loss on type II land of $1613.

120

The firm planted the correct amount of hay on its type III
land which meant that no part of the difference between the net
cash incomes under the two solutions resulted from this phase of
the operation. However, the firm milked only 71 cows, nine less
than capacity, a decision which cost the firm $2765.

The $3600 by which the firm missed the maximum level of in-
come is accounted for by the gain of $778 on its production on Type
I land and losses of $1613 and $2765, on the Type II land and dairy
Operation, respectively. This $3600 loss can be partitioned another
way into a combined loss due to incorrect decision ($4504) and in
this case, a net gain due to stochastic elements ($904).

These identical steps were carried out for this firm over a
five year period, years 6-10, with its Operations consisting of
200, 360, and 80 acres, reSpectively, of class I, class II, and
class III land and of facilities for 80 cows (Table 14). The
firm's realized income during the five year period was $26,694
below the optimum earnings for the period. Of this figure, $23,101
was attributable to making wrong decisions. The net effect of the
Stochastic elements during the period was an additional loSS of
$3593 over what would have been earned with the optimum decisions
given the stochastic elements.

The primary determinant of the effect of stochastic elements
during the period was corn yields. Since there is a dairy operation,
corn was the predominant crop in the simulator solutions. Corn
yields were much higher than average in year Six and more importantly
were high relative to the yields of other crops. These favorable
stochastic conditions more than offset the losses from the incorrect

decisions. However, during the remaining four years, corn did not

121

Table 14. Partitioning Annual Losses from Nonoptimal Solutions into
the Twi Sources: Incorrect Decisiom and Stochastic Elements,

 

 

 

Firm 4 .
Source
Year Annual Incorrect Stochastic
loss decisions elements
6 -3600 -4504 -+ 904
7 -5856 -4497 -1359
8 -5268 -4148 -1120
9 -6611 -5605 -1006
10 -5359 -4347 -1012
Total -26,694 -23,101 ~3593

 

1During this five year interval, the firm's operation
consisted of 640 acres of crop land and facilities
for 80 cows.

122

fate very well, Stochastically, relative to the other crops. These
relatively unfavorable stochastic conditions served only to increase
the loss over what could initially be expected when making the
decision.

The occurrence of a net loss due to stochastic conditions
over a sustained period points out the disadvantage of specializing
in one crop. When such specialization occurs, this one crop must
do better than all other crops in every production period if the
firm is to maximize its earnings. Of course, the cost of flexibility
must be taken into consideration when evaluating the disadvantages
of Specialization.

The results from partitioning the annual economic losses among
the two sources has important implications regarding the value of
expectations of profitability and the use farmers Should make of
this information. During the included five year period (Table 14),
87 percent of the total loss was due to decisions that were in-
correct in view of the criterion, net cash incomes, assumed for
this study. Only 13 percent was due to variability in the sto-
chastic elements. This is a definite indication that there is
relatively more to be gained from increasing the use of knowledge
about expected profitability than from engaging in Speculative be-
havior.

The apparent failure of farmers to make production decisions
that are Optimum with regard to the expected profitability could
possibly mean one of two things. Either they are not properly
utilizing their information or they do not have adequate informa-

tion that would lead them to make the same production decisions.

123

Alternatively, it could be some combination of the two. It is
doubtful if many farmers have estimates of the ranges of yields
and prices and of the associated probabilities to the extent that
was assumed in this Study. No doubt there are times when farmers
try to out guess the stochastic elements and bank on the happening
of an event with a small probability of occurrence.

There are two conclusions that are particularly evident.
One is that if information on expectation regarding prices and
yields are made sufficiently available at the farm level and are
adequately used by operators, incomes can be raised to a large
extent. The second is that farmers are better off in the long
run if they base their decisions on expected value rather than
attempting to gamble on the stochastic elements.

Indications are that there is a payoff to obtaining
additional information regarding expected profitability of enter-
prises and regarding stochastic elements with the expectation having
the larger payoff. However, information is not a free good; and
additional information is economical only as long as its value
exceeds its cost. This is how a determination of what is a suf-

ficient amount of information is made.
Organizational Changes

Changes in the structure of the firm may involve purchases
of new assets or of accepting capital losses on the firm's present
assets due to low salvage values. Changes that alter the amount
controlled by the firm or that require the purchase of large, highly
specialized equipment can have a particularly large impact because

they may involve large sums of money and/or a high degree of risk.

124

Two Such changes--renting-out land and producing field beans are

discussed below.

Renting-out land

The most surprising result of the optimal decisions made by
the linear program‘was the consistency in renting out a large pro-
portion of the land under the control of the firm. In the most
extreme case, 50 percent of the land was rented-out by the linear
program. There are reasons, peculiar to particular strategies, for
the relative Standings of the prOportions but the only explanation
for the consistently high proportions is that the earnings from
farming the land are often less than the opportunity cost of rent-
ing out.

Mggggerial Ability--As would be expected, the proportion of
land rented-out is higher in every case for the lower level of
managerial ability. The potential return from renting-out land is
the same for all land of a given quality, but the earnings of land
in production is positively correlated with the quality of manage-
ment. Therefore, the expected earnings of land in production under
the lower level of management is smaller and a greater proportion
would be rented-out for this reason.

Strategies--There are also economic reasons for the pro-
portion of land rented-out being higher for the first two strategies
than for the last two strategies. Due to the lower yields for crops
grown on rented land, production on rented land is less profitable.
Combine this fact with an identical expectation across all Strategies
regarding the returns from renting-out land and an increase in the
prOportion of land rented-out is the logical result. Since the cost

of renting-in and the return from renting-out land is the same, the

125

findings indicate that renting-in this land which the linear program
in turn rented-out was a losing proposition for the farmer.

With regard to strategy 1, the reasons behind the high pro-
portion of land rented-outare also easily discernable. Due to its
profitableness, dairying is the first enterprise to enter the optimum
solution and it enters to the fullest extent allowed by the limitation
of the facilities. Due to the fact that the less expensive quantities
of labor have been hired for dairying, the profitability of the crOps
has been reduced by the necessity of hiring more expensive labor to
a level that, in many cases, is below the opportunity cost of renting-
Out. Thus, in years when the stochastic elements are not extremely
favorable, the firm could increase its profits by renting the land
out rather than keeping it in production.

There is no reason of an economic nature to expect any dif-
ference in the proportion of land rented-out under strategies 3 and
4. Any differences that occur can be attributed directly to the
stochastic elements in the Simulator. The only explanation for the
comparatively low prOportion of land rented-out from firm 3 is that
this farm received a series of more favorable crop yields than the

other farms.

Field Beans

Field beans are a crop that is not commonly produced by southern
Michigan dairy farmers. Field beans appeared quite often in the optimum
solution but generally did not occupy more than 10 to 15 percent of
total crop land. The implications of their appearance in the optimum
solutions are not clearcut. Field beans require a Specific type of

soil which is not the predominant type in southern Michigan. Obviously

126

a farm must have some of this type of land before field beans can
even enter into consideration. Secondly, field beans require some
specialized equipment that tends to be expensive. A fact which means
that an operation would need some minimum quantity of field beans

to have a profitable operation. Thus, even though an operator does
own a few acres of the appropriate type of soil; he would not

necessarily produce field beans.

Case for Additional Information

The larger profits received under the optimum solution were
due to three reasons: (1) producing the same enterprises at dif-
ferent levels, (2) renting-out land, and (3) producing field beans.
Due to the peculiarity of the field bean question which waS~ pre-
sented earlier, a discussion of the additional information is not
likely to be worthwhile and will be omitted here. The conditions
that lead to renting-out land would obviously have to be that the
level of rent payments is higher on the average than what an Operator
could earn from keeping the land in production. Given that this
condition exists, making this information available would benefit
the potential renter and have an equal, offsetting effect on the
landowner. There would be no net gain to the agricultural sector.

There are indications that a case could be made for the pro-
vision of additional information relating to the Stochastic com-
ponents, prices and yields, of the included enterprises. Dis-
regarding the cost of the information, the net income of the
operators would have been greater in every instance considered if
they had had access to and had used better information. But, of

course, the derivation and presentation of information also involves

127

economics to determine the relationship of benefits to costs. All
Of which means that there exists the possibility that additional
information could be of value, but perhaps additional study is re-

quired to determine if such information would be economical.

Strategies

A second objective of the Study was to effect a comparison
of four alternative strategies--one vertical and three lateral--
to preferably identify the best Single Strategy to be followed by
similar firms for purposes of achieving growth. When it became
apparent that no Single strategy was superior in all aSpects, both
the strengths and weaknesses of each strategy were delineated and
their relative position as to each characteristic determined (Table
15). In the case where no single strategy was superior in all
aspects, the reasoning was that the choice of Strategies would de-
pend upon the situation so the appropriate move would be to make
the facts available to management to make their own decisions.

The comparison consisted of two parts: (1) the amount of growth
achieved under each strategy over a 15 year period, and (2) the

ability to withstand adverse conditions.
Growth Potential

In attempting to compare the growth potential of the four
strategies, the choice of the size indicator to be used becomes
critical. The value of assets, net worth, and gross income are all
indicators of size; but they tend, to some extent, to measure dif-
ferent aSpects of Size. These somewhat divergent aSpects are owner-
ship, equity, and productive capacity, reSpectively. The value of

assets and net worth completely ignore rented land which does

128

1
Table 15. A Summary Comparison of Strategies

 

 

 

 

 

 

 

2 15 Year Growth Five Year Annual

Item 3 4

Ownership Equity Productive Resistence NCI
Capacity

Strategy 1 - + - ++ 0

Strategy 2 - + ++ -- 0

Strategy 3 ++ ++ + + ++

Strategy 4 4+ ++ + +~ +

1

This table represents a set of qualitative judgments on the
part of the author regarding the relative positions of the
strategies under certain Specified measures. A mark of (++)
is given to the top-ranked Strategy and the other three are
assigned one of the following marks: (+), (0), (-), or (--)
according to their position in relation to the one with the
highest rank.

2See Table 2 (p. 83) for explanation of strategies

3Resistence to bankruptcy under conditions of adversity

4

Net Cash Income

129

increase the productive capacity of the firm. Gross income reflects
the total economic production of the firm and thus the quantity of
assets under the control of the firm.

No Single strategy was found to permit the achievement of the
greatest amount of growth with regard to all three SSpects of size.
Applying a bit of qualitative judgment to the quantitative data
generated by the model leads to one rather obvious conclusion (Table
15). Purchasing land, perferably with a land contract, would appear
to permit the achievement of the greatest amount of expansion. The
verticle strategy is not conducive to increasing ownership or the
productive capacity of the firm but does lead to a moderate build-
up in equity. Renting land permits the control of a large amount
of productive capacity but with only a moderate gain in equity and

a relatively small increase in ownership.

WithstandingyAdverse Conditions

The second part of the evaluation of Strategies subjected
the strategies to two levels of adverse conditions and resulted in
several distinct findings. As stated previously neither of the two
adversity levels were severe enough to make farming unprofitable
in the sense that firms suffered financial losses from the
operation. The point that was of primary interest was the impact
of inflexibility in the use of capital on the ability of a firm to
survive sustained periods of unfavorable, but not necessarily dis-
astrous, circumstances. Possible sources of such inflexibility would
be the commitments of financial resources to the repayment of long
term real estate loans and intermediate term livestock credit and to

the discharge of cash-rent contracts of several years duration.

130

One or more of these sources of inflexibility are found in each of

the four strategies used in the Study.
Renting Land

One Striking determination was the apparent weakness in the
face of adversity of the strategy of renting-in land. There are
two reasons for this vulnerability. One is that the rent on a given
amount of land is somewhat higher than the annual debt payment when
the loan is amortized over 25 years. Thus, in this respect, a
multi-year agreement to rent land results in a greater degree of
inflexibility in the use of capital for the length of the contract
than purchasing land when it is amortized over a twenty-five year
period. The second reason is the lower yields on rented land.
Accordingly, the Operator has a smaller Supply of capital and a
higher level of fixed commitments over the life of the rent con-
tract. This combination lessens the ability of the firm to with-

stand elements of adversity.
Vertical Growth

Another conclusion that is clearly manifested is the relative
strength of the vertical Strategy (strategy 1) in the face of ad-
versity. This is particularly evident for the firm that Operated
under the vertical strategy with the lower level of managerial
ability. This particular finding did not turn out exactly as
expected. Cows were purchased on intermediate term credit which
was amortized over a five-year period. The logical expectation
would seem to be that a firm whose major vehicle of expansion re-
quired such a rapid payoff would find itself hamstrung from lack

of capital and extremely vulnerable to adverse conditions. The

131

resilienceof these dairy farms operating under this Strategy arises
from two sources. One is that the five-year payoff of debt coupled
with the policy of only making purchases every five years prevents
debt from accumulating as it does when land is repeatedly purchased
and amortized over a much longer period.

The second source of strength lies both in the profitable-
ness of dairying and in its lack of Susceptability to declines in
both price and yield. Both the profitableness and the price
stability is, in all likelihood, due primarily to the federal milk
marketing orders. These federal orders set the minimum price for
milk which, if it is above the equilibrium price, becomes the
effective market price; and given the demand curve, indirectly
controls the supply of milk.without direct controls on production.
Price is both Stable and higher than equilibrium which, in con-
junction with the inelastic demand for milk, increases the pro-
fitability of dairying.

Dairying is, in general, also less susceptible to declines
in yield than field crops. This is due to several factors. Medical
advances have enabled the industry to exert a great deal of control
over diseases. With modern facilities, weather variations have very
little impact on the per unit production of dairy cows. The degree
of control that can be exerted over the quantity and quality of

inputs consumed by a cow is greater.

Land Purchasing
With regard to strategies 3 and 4, the implications of the
results are less clear. Under top level management, both Strategies

exhibited a great deal of strength but no differentiation between

132

the two is possible. Under the lower level of management, strategy
3 would seem to be slightly less vulnerable than strategy 4; but both
strategies would rank in between the other two; more extreme strategies;

in tendency to hold up under adverse conditions.

Summary

An overall evaluation of the four Strategies to determine which
one to follow in achieving expansion does not lead to a clearcut choice
of one strategy that is Superior in all aspects. The best that can be
done here is to present a Summary of the findings and to leave the
decision of which one to use up to the farmer since the appropriate-
ness of the strategies may depend on the characteristics of the
situation and of the operator.

The most distinct conclusion would seem to be the obvious
weaknesses of strategy 2. The subjection of a firm operating under
this strategy to adverse conditions generally leads to disastrous
consequences as it was always the first firm unable to meet its debt
and fixed contractual commitments. In terms of potential for growth
it showed strength in only one aspect, productive capacity. Under
measures of wealth and ownership, it tended to lag far behind the
land acquisition Strategies.

These findings about the generally lackluster performance of
the growth Strategy of renting land are particularly important be-
cause they run completely counter to the conclusions reached in two
other studies. Martin concluded that the maximum Size of operation
is achieved through renting land the first half of a 30 year planning
period and buying at the end of this period [2]. Lins concluded

that if indivisibility exists in the land input, then renting is the

133

preferred way to expand [3]. Again, these two studies did not consider

.0", ‘-

O» u... .-

the risk aSpect of strategies nor did they reduce the yields On rented
land.

In terms of overall performance, purchasing land is definitely
the best way for a firm to achieve growth. Strategies 3 and 4 con-
sistently demonstrated signs of Strength, and even Superiority, across
all measures relating to both rate of expansion and resistence to
adversity. Also, a comparison of the two land purchasing strategies
leads to the conclusion that when purchasing land, the rate of
expansion is inversely related to the Size of downpayment.

The case of the vertical Strategy is not so clearcut. It
compared rather unfavorably with the other Strategies in terms of
achieving growth but was superior to all other Strategies in with-
standing adverse conditions. In view of this, it would appear to
be an appropriate strategy only when risk aversion is the over-
riding criterion for choosing a strategy.

The comparison of Strategies was an evaluation of long run
investment theory and the causal factors behind the findings can
be identified with the use of short run production theory. Annual
net cash income (Table 15) is the end-product of the short run pro-
duction situation and the consistently higher earnings of the land
purchasing strategies were the primary reason for the Superior over-
all performance of these two Strategies. It also accounted for the
difference between the performance of the two. A relatively low
net cash income coupled with very high gross income for firms renting
land indicates that they had a high level of annual costs and explains

their weakness under adverse conditions. As pointed out earlier,

134

the strength of the verticle strategy under adverse conditions was
due to institutional factors. In terms of production theory it
suggests the existence of excess profits under present conditions

(P > ATC) .

Managerial Ability

A third objective of this study was to evaluate two categories
of managerial ability--above average and exceptional. This was also
to be accomplished in two measures: (1) the potential for achieving
growth under normal, stochastic conditions, and (2) the ability to
survive under conditions of adversity. As elaborated below, the
most interesting aspect of the findings related to this objective,
concerned the better of the two levels of managerial ability
particularly in relation to its potential for growth in an uncertain

environment.

Potential for Growth

The superiority of the exceptional manager over the above
average one, in achieving growth, is evidenced by the fact that after
15 years of operation, in three out of four cases, the firm of the
superior manager was more than twice as large as that of the above
average manager operating under the same strategy. With increases
in size over a lS-year period ranging from a minimum of 259 percent
for firm 1 to a maximum of 470 percent for firm 3, it is obvious
that under exceptional managerial ability the potential for growth

is tremendous.

Unrestrained Purchasing
As stated earlier, in an attempt to maintain an aura of

realism, some restraint was exercised during the initial 15 years

135

on the rate at which the four firms operating under technology A
acquired assets as these firms were not allowed to purchase as many
resources as their reserves would permit. The reasoning behind this
move was that there are 1imitations--due to supply conditions and,
perhaps, to managerial ability-~as to the quantity of land and top
quality dairy cows that can be acquired and profitably incorporated
into a feasible farming operation at any one time.

In order to obtain a better representation of the potential
for growth under this level of managerial ability, all restraints
were removed from these four firms in the sixteenth year. The firms
were allowed to purchase all the assets that their reserves would
permit and the results in terms of growth potential are even more
phenomenal. Every firm had control of over a million dollars worth
of assets with the one utilizing a land contract controlling 1.77
million dollars worth of assets, 47 percent more than the second
largest firm. In terms of growth achieved finrthe entire period,
the firm utilizing a land contract increased its size 1300 percent.
The increases in size achieved by the other three firms were in
the 800-900 percent range.

At first glance, the appropriate conclusion would seem to be
that such growth would be impossible to achieve; but given the level
of managerial ability assumed, it might be a mistake to draw any
hasty conclusions. In fact, because there is evidence [4] to support
this rate of growth, it would appear that additional research is

warranted in this area before any concrete conclusions are drawn.

Above Average Operator
The amount of growth achieved by the last four firms would

seem to represent a reasonable rate of expansion for a successful

136

farmer of more average managerial capacity. With increases in size
ranging from a modest 66 percent to a high of 169 percent over a
lS-year period, the results would seem to indicate that the more
typical farmer can achieve growth but at a rate that is less than
phenomenal. Another implication is that the choice of strategies
under which he chooses to expand may be quite important since the
growth achieved under strategy 3 is almost triple that under
strategy 1. Also, given that the rate at which these last four
firms grew would appear to be well within the expectations of the
less than exceptional farmer; this fact would tend to lend
credibility to the phenomenal rate of growth achieved by the level
of technology that has been asserted to represent a small group

of superior managers.

Withstanding Adverse Conditions

An equally obvious conclusion is the conSpicuous superiority
of the exceptional manager (technology A) in surviving unfavorable
conditions. Of course, superior management would be expected to
have higher earnings over time which would likely place the opera-
tion in a stronger financial position at any point in time. In
this study, this higher earning capacity resulted in higher equity
ratios and in access to a larger pool of liquid reserves. Which
means they had a relatively lighter debt load and a larger amount

of ready cash available to draw upon in emergency situations.

Stochastic Elements

The analysis of the stochastic components of the simulator
consisted of two major divisions. The first was to determine the

importance of the stochastic elements on the growth achieved by

137

the included frims. This consisted of deriving the effect of all
stochastic elements combined and of commodity yields alone. The
second was to test the procedure under which the random standard
deviates are generated by Simfarm to see if the numbers produced
are, indeed, normally distributed. This was considered to be a
relevant undertaking because the failure of the stochastic elements
to be distributed as previous research has apparently indicated

they should tend to bias the findings of this study as to the growth

possibilities of the included firms.

Combined Effects

'The impact of all stochastic elements combined on a firm's
growth within one year was simulated. In this one year with beginning
assets valued at $136,000, the increase in value of assets ranged
from $9,000 (6.6 percent) in the case where no additional land was
purchased and a combination of generally unfavorable market and
yield conditions occurred to $59,000 (43.4 percent) in the case where
the maximum amount of land was purchased and a combination of gen-

erally favorable market and yield conditions occurred.

Land Purchase

It is obvious that the value of assets, along with other
measures of firm size, is closely related to the amount of land
owned. However, the effect of purchasing versus not purchasing is
of interest since land cannot always be obtained when the prospective
buyer wants it at the price he would like to pay. Obviously with a
difference in excess of 30 percent in the average expected growth
Without the purchase of additional land (9 percent) and the average

exPeCted growth with the purchase of additional land (40 percent),

138

the failure to acquire land, whether due to market uncertainties or

lack of capital, has a great effect on the amount of growth achieved.

Market and Yield

Any difference between the amount of growth achieved with a
given amount of land is due to the effect of the stochastic components
of market and yield on net income. The resource situation is identical
in each case and the only component of total assets subject to change
is the level of cash-on-hand. Cash-on-hand varies directly with net
income since the debt commitment and level of direct costs are also
identical in each case.

The percentage difference in the amount of growth achieved
with a given amount of land, measured from the extremes, ranged only
from 4.0 to 4.5 percent. Considering the smallness of these dif-
ferences and the fact that they were computed from extreme values
with low probabilities of occurrance, it would appear that the
stochastic element associated with prices and yield is not of any
great importance to the rate of growth achieved by a firm in any one
year. Assuming that each of these three sets of results is normally
distributed, differences of one to two percent would occur with
greater frequency and, due to the symmetry of the outcome, even this

small effect would tend to cancel out over time.

In another phase, yield was the only Stochastically determined
variable in Simfarm that was allowed to vary among 50 firms over a
ten year Period. The stochastic component of the land purchasing
routine did not come into play since no attempt was made to pur-

chase additional land. The market routine was permitted to operate

139

stochastically in each of the ten years but all firms faced identical
market conditions each year. Therefore, all variations in the char-
acteristics of the 50 firms at the end of the ten-year period were
attributable directly to the stochastic element associated with yield.
This set of results could be interpreted as being a sample of farmers
from a region small enough for all to face identical market con-
ditions and homogenous enough to find farms of similar productive
capacity in terms of management and soil types, yet large enough to

have consequential variations in weather conditions.

Range of Effects

Obviously the range over which the results fall is quite
large--$69,000 or 39 percent of the smallest value, but it is apparent
that the extreme values are due to exceptional conditions with a low
probability of occurrence. However, this sample of results has a
standard deviation of $14,973 and according to probability theory
there is only approximately a two-thirds probability that a random
value will fall within one standard deviation of the mean. This
indicates that about one-third of the results can be expected to
fall outside a range that is $30,000 wide or 14.4 percent of the
mean. Thus, it would appear that the yields that a firm receives
under an uncertain environment can have a fairly large effect on

its growth over time.

Effect of Near Perfect Conditions

It is of interest to note that four of the 50 outcomes
averaged about $30,000 or 15 percent above the mean for the entire
sample. This would seem to indicate that the continual occurrence

of near perfect yield conditions have a noticeable effect on growth

140

over time. This would seem to indicate that an economic analysis
of various means of artificially providing such environmental con-

ditions might be in order.

Distribution of Random Deviates

The data used in the above analysis present an opportunity
to investigate the actual distribution of the random standard deviates
generated by the equation in Simfarm. Apparently the hypothesis of
a normal distribution centered on zero has not been verified statis-
tically even though a large number of values (4000) was plotted and
observed to approximate a normal curve.

Land prices are generated under the subroutine COSTS. The
price of land per acre for each class is the base price plus nine
times a random number which is generated by an equation which is
assumed to approximate a normal curve. This same equation also
generates random numbers for the subroutines MARKET, CROPTABL, and
LIVESTOK so it plays an important role in the simulator. A
significant degree of skewness in either direction in the numbers
generated could tend to affect the outcome of Simfarm. It could
cause the results to be, on the average, more or less profitable
than would be expected if the assumption that the generated values
should be normally distributed around the base price is accepted as
being realistic. Any such shift in the profitability of the firm
would likewise be found in any inferences drawn about the firm's

growth possibilities.

Land Purchasing Routine
The purchases of land that were made in phase 3 provide an

Opportunity to make a partial test of the equation to see if the

141

random numbers generated by it are, indeed, normally distributed about
zero which would result in the generated prices of land being normally
distributed about the base price. If the generated pricesof land are
normally distributed about the base value, then the function is
symmetrical about the base value. In the case where the base price

is bid for land, the symmetry of the function would lead to an
expectation of purchasing each type of land 50 percent of the time.
This means that the land purchasing subroutine can be viewed as a
sequence of binomial trials with the probability of successful pur-
chases being p O .5.

Null Hypothesis--A rejection of the null hypothesis of a
binomial distribution of p - .5 would indicate that the land prices
were not symmetrical about the base value and, thus, could not be
normally distributed about the base value. This, in turn, would
indicate that the randomly generated deviates are not normally
distributed about zero.

This test was referred to previously as a partial test be-
cause it could indicate with a high degree of probability that the
:functions are not normally distributed about the appropriate value
‘if’the null hypothesis is rejected. However, if the null hypothesis
is not rejected; the test does not conclusively prove that it is
[normally distributed. It only indicates that the function is
symmetrical about the appropriate value and there are distributions
other than the normal that could be symmetrical about the value.

The experiment consisted of attempting to purchase two types
0f leand with the decision being determined by two random numbers
both of which were generated by the equation that is the subject

0f tile test.

142

Ho: A binomial distribution with p I .5
H.: A binomial distribution with p I .5

p I .5 I probability of successfully buying land
q I .5 I l-p I probability of failing to buy land
n I 50 I number of observations

r I 2 I number of trials per observation

k I 3 I number of possible outcomes

v I 2 I k-l I degrees of freedom

The three possible outcomes of the two trials are:

1. Buy both types of land (BB)

2. Buy one type and fail to buy the other (BF I B1172 and
32171)

3. Fail to buy either type of land (PP)

The hypothesized probabilities of the three outcomes are:

P(BB) I .25
P(BF) I .50
P(FF) I .25

Chi Square--An appropriate statistic to use in testing the

above hypothesis is the chi-square (x2) test. The test that was

< 2
x .99,v

(sz) that is greater than the table value (x2 99 v) indicates
' :

conducted is P(x2v ) I .99 in which a computed value

a difference that is significant at the one percent level and that
a rejection of the null hypothesis is warranted.
2
2 (N1 ’ nPi)
X v .2 n
pi
where:

N I the number of times the three outcomes were observed

16 I #(FF)

2
I

Z
I

22 I #(BF)

2
I

12 I #(BB)

1.3625

X
8:5)
I

x.75,2 ' 2°77

143

All of which means that the null hypothesis cannot be rejected and
that it cannot be said on the basis of these data that the distribu-
tion is not normal even when one is willing to accept a 25 percent
chance of being wrong.

Alternative Hypothesis--It is also of interest to note that
while hypotheses of p I .3 and p I .6 can be rejected at the
.990 probability level, a null hypothesis of p I .4 cannot be
rejected. This means that the possibility that the sum of the
probabilities associated with the negative random deviates is slightly
greater than .50 cannot be ruled out, i.e., that the equation which
generates the random deviates might be biased towards negative values.
In terms of being normally distributed, this only says that there
exists a possibility that the various stochastically determined
variables are not normally about the base value. In such a case,
these functions could still be normally distributed about some

lower value.

Market and Yield Routines

The random standard deviate equation is also incorporated
:into the market and yield routines. The data from phases 3 and 4
composing four samples were summarized in such a manner that it
refflected only the effect of the stochastic elements on the market
and yield routines. Every firm in sample A began operating in the
initial period with an identical number of cows and acres of land.
No firm purchased any additional land or cows during the ten years
of operation. All firms within each of the other three samples
Possesssed an identical number of cows and acres of land. Thus, any

difference that occurred between the value of assets within each

144

sample was due to the effect of the stochastic elements on the market
and yield routines. For this reason, the four samples were combined
in order to increase the degrees of freedom and to have a more
sensitive test.

Because it can be divided into four categories, the data
lends itself quite readily to another chi-square test with implica-
tions about the normality of the distribution. It is again a partial
test for the same reasons stated previously. It should be emphasized
however that the use of four categories rather than two makes this
a stronger test than the previous one.

A normal distribution can be divided into four sections with
known probabilities of occurrence. This is based on the fact that
under a normal distribution there exists a probability of 0.34 that
a value will occur within a range consisting of one standard
deviation's length and bounded on one end by the mean. The four

categories and their associated probabilities are:

(1) less than (i’- S) p - 0.16
(2) between (i‘- S) and 2’ p - 0.34
(3) between i' and (i'+ S) p - 0.34
(4) greater than (i +'S) , p I 0.16

The null hypothesis to be tested is Ho: the observed data
fits the above probability distribution and it is rejected if there
is a significant difference. Otherwise, it is accepted. The com-

PUting formula is
2
2 (01 ' Bi)
X.v ' 8 E where: i I number of categories
i

 

O I observed

E I expected

 

was

Thi

P01

ma:

th:

110‘.

11'

in:

of

the

Ex;

Hat

and

M

the

145

2
A table value (xp v) such that X: >’x2 indicates a significant

P.V
difference leading to a rejection of the null hypothesis. However,
in this case, the computed value x: I 1.901 is less than the table
2
value x 50 3 I 2.37 meaning that the null hypothesis cannot be

rejected even when one is willing to accept a 50 percent chance of

being wrong.

Summary

with regard to the distribution of the random standard de-
viates used in the stochastic elements of the simulator, no evidence
was found to indicate that these deviates are not normally distributed.
This conclusion is based on tests of the stochastic elements incor-
porated independently in both the land purchasing routine and the
market and yield routines. Both tests were in complete accord in
their failure to reject probability distributions consistent with

normal distributions.

Limitations of Study

This study utilized a model which has been used relatively
little up to now, that of combining the two techniques-~simulation
and linear programming. This study involves two very important areas
of research dealing with farm firm growth. One is the selection of
the appropriate strategy to follow in acquiring assets with which to
expand. The second is the analysis of decisions of a more tactical
nature; those dealing with the handling of the productive elements
and which occur either between or during the production periods.

This model is a dynamic model in that it does incorporate time into

the analysis but not necessarily to the fullest extent possible.

146

The dynamic nature of the analytical model used in this study
gives it certain advantages over a static model. Due to the fact
there is an assumed time lag between the use of inputs and harvest
of products, prices and yield cannot be expected to be known with
certainty. Thus, the model incorporates stochastic elements in-
volving a supposedly realistic distribution of values in an implicit
recognition of the influence of time lags. The recognition of time
as an element of production is explicit in the division of labor
requirements and restraints by quarters. This, however, leads to
one of the limitations of this study's model which was the failure
to divide the firm's annual supply of capital and its annual capital
requirements into subperiods. Forcing the firm to synchronize the
inflow and outflow of capital within a year is a realistic require-
ment that could result in a different set of optimum production
decisions, particularly in the case where dairying is not the major
enterprise. This subdivision of the capital flows was not available
in Simfarm, and it was omitted because of the difficulty of inserting
such a routine. However, its inclusion may be more critical when
the firm's operation consists entirely of enterprises that do not
result in revenue flows at close, regular intervals as dairying does.

A second probable limitation was inherent in the consumption
function built into the model. It resulted in consumption levels
that in retrospect appear to be much too low given the income level
of the operator. This is particularly true in the later years of the
study when income levels were quite high. Apparently what happened
is that the model was extended to firms of a size outside the range
over which the included consumption was appropriate. This, however,

is an important factor in any growth model since it directly affects

147

the supply of capital available for growth purposes. If the con-
sumption level in this study was, indeed, too low, then it would
have overestimated the capital available for growth purposes and
would have permitted the achievement of too much growth.

A third limitation of this model is that the linear program-
ming routine does not optimize with respect to investment decisions.
It optimizes only with respect to production decisions which means
it yields the maximum level of growth possible with optimum pro-
duction decisions given a set of investment decisions. However,
the impact of this shortcoming is blunted by the use of strategies
since the number of investment alternatives relating to the choice
of assets and terms of acquisition is reduced.

There is a fourth limitation present in the singularity of
the included strategies. An alternative is for a firm to follow
some combination of the pure strategies due to the possibility that
different strategies may be appropriate at various stages of the
growth process. There is, however, a large number of possible
combinations. Only a small number could be included in this study
and the more general knowledge to be gained from the inclusion of
pure strategies was considered to have wider application.

A fifth limitation of the study concerned the handling of
the managerial factor. Two levels of management were distinguished
with regard to the productive capacity of the firm, but this only
concerned the technical capabilities of the manager. This represents
a giant step away from the complete neglect of management in static
models except for the assumption that it is adequate. However, it
does ignore other important aSpects of management such as handling

finances, labor, and uncertainty.

148

Implications for Future Research

When combined into a single model, simulation and linear pro-
gramming have a complementary relationship as the existence Of the
other solution enhances the value of the one under consideration.
This is due to the contrast of the realistic nature of the simulator
solution with the optimal nature of the linear programming solution.
When realistic situations are to be diagnosed for the purpose of
prescribing corrective measures to facilitate improvements, the
availability of an Optimum solution for the situation is invalu-
able. A programming model as simple as the one included in this
study can indicate needed changes in enterprise levels and even
changes in organization. A more inclusive programming model could
prescribe investment decisions in addition to production decisions.
When attempting to evaluate Optimal solutions for such characteristics
as applicability and workability, the availability of a realistic
solution could give the researcher a better feel regarding the use-
fulness Of his optimal solution and as to the implementation of the
findings.

Since all calculations for both simulators and linear pro-
gramming models can be done on high speed computers, very little extra
effort is required in combining the two models so as to Obtain both
types of solutions. The computer must be given the additional
instructions necessary to isolate the required input data in the
first model and to put it in a useable form for the second model.
Once these instructions are programmed, only the input data for the
first model must be provided to Obtain both realistic and optimal

solutions for every situation programmed. It must be admitted,

149

however, that it is probably much easier and less costly to add a
linear programming routine to a simulator since standard optimizing
programs are available. These generally require only a few modifica-
tions to ensure compatibility with the dimensions of the particular
input matrix to make them Operational. 0n the other hand, designing
a simulator is an undertaking of such magnitude that it would
probably not be economical to design one just to complement a linear
programming model unless they were to receive extensive use.

For purposes of studying growth, a model combining simulation
with some variation of the linear programming technique would appear
to always offer the advantage of the contrast of realism versus
Optimization. This is true whether the Objective is to evaluate
growth strategies or the more tactical type decisions regarding pro-
duction and level of investment that occur with greater frequency.
For purposes of comparing strategies only, an appropriate combina-
tion might be multiperiod programming and simulation operated
independently except for the initial situation and the rules of in-
vestments as dictated by the strategy. For purposes of evaluating
the tactical type decisions made before and during each production
period, more appropriate programming techniques would be recursive
programming or a single year Optimizing model of the type used in
this study. The choice would depend on whether the simulator or
the programming model was used to maintain continuity of the firm
over the length Of the study. The two crucial considerations for
studying tactical decisions in a growth study is that one technique
be used to carry the assets of the firm over to the next production
Period and that the decision process be sequential. Based on these

criteria, either recursive programming solutions could be simulated

150

each production period or simulation solutions could be optimized
each period as was done in this study. Combining the two techniques
would appear to place no additional restrictions on the use of the
primary model--the one used to establish continuity of operation~-
and offers the advantages of contrasting solutions--realism versus
Optimality--in assessing any one solution.

Regardless of the technique used, there are several aspects
of farm firm growth that deserve further study. One is the growth
potential of firms Operating under management possessing an excep-
tional level of competency in any one or some combination of a number
of areas--technical knowledge, financial management, labor manage-
ment, marketing expertise, etc. Related questions would involve a
determination of how such management could be attracted into
agriculture, of what would be the impact upon the organization of
agriculture, and of whether such changes, if any, would be desir-
able from the point of view Of present producers and/or society in
general.

Secondly, the issue as to what is the best strategy to follow
in achieving growth is still not settled. The conclusion of this
study that renting-in land is one of the least desirable means ofex-
pansionthscompletely counter to the findings of some other studies.
Future studies should make a determination as to the crucialness of
a strategy possessing the capability to withstand adverse conditions
and as to the appropriateness of rented land having lower yields.
These were the two primary reasons that the strategy of renting-in
land received an unfavorable judgment in this study.

There are a third and fourth aspect that deserve brief mention.

There were indications that additional information in the form of

151

improved predictions of market and yield conditions leading to more
nearly Optimum decision making could increase the net cash income of
firms. An economic analysis Of the provision of the required informa-
tion could be a worthwhile undertaking. There were also indications
that the occurrence of a series of near perfect yield conditions

would allow a firm to attain a size quite a bit larger than it would
achieve, on the average under stochastic conditions. An economic
analysis of the provision of these near perfect conditions by arti-

ficial means would appear to be a possible worthwhile venture.

Summary of Analysis

The analysis presented in this chapter attempted to effect
an interpretation of the results of the four computer phases pre-
sented in the preceding chapter in accordance with the objectives
of the study. The objectives dealt with (1) the loss of net income
and potential growth from nonoptimal decision making, (2) the
determination of the relative strengths and weaknesses of alternative
growth strategies, (3) the comparison of two levels of managerial
ability, and (4) the measurement of the effect of stochastic variables.
The four strategies consisted of a vertical strategy and three
variations of the lateral strategy. The two included levels of
managerial ability were designated as above average and exceptional--
the two groups thought most likely to achieve growth.

The effect of incorrect production decisions was found to be
quite large for all four strategies and both levels of managerial
ability totalling, in every case, between $100,000 and $200,000 for
a 15 year period. This was true deSpite the fact that a real effort

was made to simulate realistic combinations of enterprises. The

152

gain in net income under the linear programming solution was primarily
due to two sources. One was combining the included enterprises at
different levels. The second was renting-out a large proportion of
the land in reflecting the low level of profitability Of all crops

in comparison to rent levels. The introduction of a new commodity,
field beans, was reSponsible for a smaller part of the net income
increase in the optimum solution.

There were two causal factors that resulted in the incprrect
decision--lack of knowledge and misuse of available knowledge. Of
these, misuse of available information was responsible for major
portion of the economic loss as it accounted for 87 percent of the
loss incurred over a five year period. The remaining 13 percent was
accounted-for by imperfect knowledge in the form of stochastically
determined variables.

The four types of strategies included in this study were found
to possess a great deal of individuality. No single strategy was
superior under both of the tests to which they were subjected. The
vertical strategy was the most resilient in the face Of adversity
but permitted the achievement of a small amount of growth (less than
two-thirds) relative to two of the other strategies. The weakest
all-around strategy was expansion by renting land as it was always
the first to succumb to adverse conditions and was also relatively
weak in the amount of growth allowed.

Expansion by way of purchasing land was found to be the best
means by which a firm could achieve growth. This was due to leader-
ship in achieving growth and demonstrations of strength in with-
standing adverse conditions. Also, it was concluded that the lower

the level of downpayment, the better the firm's performance under

153

both measures.

With regard to the two included levels of managerial competency,
that designated as above average was able to achieve growth only at
a rather moderate rate. On the other hand, that level of managerial
ability designated as exceptional was able to achieve growth at a
rather fantastic rate. The firms under exceptional management also
demonstrated superior strength in the face of adversity.

Another aspect that came to light was that given a bundle of
assets and a set of production decisions, variations in stochastic
elements had very little effect on the growth of a firm during a
one-year period. Yield was found to have a cumulative effect over
time but not a very large one on the average. It appeared that the
acquisition of land was the biggest factor in determining the in-
crease in size. This is, Of course, consistent with the findings
that a land contract offers certain advantages over other strategies
because it allows more land to be controlled and that imperfect
knowledge accounted for only a small prOportion of the income fore-

gone under incorrect decisions.

154

References

 

According to Telfarm data, southern Michigan dairy farmers follow
a somewhat rigid cropping pattern with corn being the predominant
crop. It is followed in importance by hay and small grain with
perhaps a small amount of soybeans. For more information see
Telfarm Business Analysis Summary Egr Southern Dairy General,
1261, Agricultural Economics Report No. 104, Michigan State
University, 1968.

Martin, J.R. and J.S. Plaxico. Polyperiod Analysis of growth
and Capital Accumulation of Farms n t e Ro ling Plains 2f
leghgmg_gng_1gx§§, Agricultural Experiment Station Technical

Bulletin NO. 1381, Department of Agricultural Economics,
Oklahoma State University, Stillwater.

Lins, D.A. "An Empirical Comparison of Simulation and Recursive
Linear Programming Firm Growth Models," Ag. Econ. Res., 1969,
21:7-12.

In support of this finding is the fact that the 46 state winners
in 1969 of the Outstanding Young Farmers program Sponsored by
the U.S. Jaycees and Central Soya had been farming an average

of 9.8 years; started with assets that averaged $28,723; and had
current assets averaging $309,744. They had likewise increased
their average net worth from $7,537 to $200,447. (source:

Farm Journal, July 1969).

CHAPTER VII

Summary and Conclusions

Growth of the farm firm has been, and is projected to be,

a continuous trend confronting farm firm operators. Since most of
the causal factors tend to be industry-wide, a large portion of farm
Operators are affected and find it necessary to expand their opera-
tion. With this situation in mind, the objectives of this study
were to measure the effects Of incorrect production decisions, to
make a comparison Of four alternative growth strategies and two
levels of managerial ability, and to determine the impact of the
various stochastic elements on the achievement of growth. A model
which consisted of a simulator and a linear programming routine was
used to analyze a size category of dairy farms common throughout
southern Michigan, the 35 to 40 cow herd size.

The major portion of this study was based on eight synthesized
frim situations, one for each of four strategies operating under
each of two levels of managerial ability. The four strategies
included a vertical strategy and three lateral strategies. The
three lateral strategies were (1) renting land, (2) purchasing land
with a land contract, and (3) purchasing land with a mortgage. The
two levels Of managerial ability were both better than average
farmers who were regarded as being the group most likely to

successfully achieve growth.

155

156

The effect Of incorrect production decisions, as measured by
variation in net income, was found to be quite large. This was true
even though an attempt was made to simulate realistic combinations
of enterprises. The increases in net income had two sources of
causation. One was decisions that were incorrect with regard to the
assumed decision criterion, expected net cash incomes. The other
was the stochastic variables. The incorrect decisiomwere the
primary causal factor as they accounted for 87 percent Of the in-
come foregone through nonoptimal decisions in one five year test
period. The occurrence of these incorrect decisions in actuality
could be due to the farmers' failure to properly utilize their
information and/or to the fact that they do not have adequate in-
formation. In either event, there exists the possibility of a rather
substantial payoff for ensuring that more nearly Optimal decisions
are made where optimal is defined in terms of maximizing expected
net cash income.

The linear programming solutions differed from the simulator
solutions primarily in terms of two activities to which it allocated
land. One was the persistent renting-out of a portion Of the land
under the control of the farmer. In reality Operators probably tend
to rent-out either all or none of their land. This all-or-nothing
action would appear to be based on the assumption that assets have
perfectly elastic supply curves. With the recognition Of the fact
that the land controlled by the firm is perfectly divisible, assets
can then be combined in fixed proportions within a limited range.

An additional assumption Of constant returns to scale, results in
constant values of marginal products. Combine this constant value

of marginal product with a constant imputed opportunity cost for

157

land and the use of land does become an all-or-nothing situation.
However, allowing the supply curve for one or more inputs to become
upward sloping eliminates the all-or-nothing situation. If the
Supply curves for hired labor and capital are, indeed, upward
sloping as in the model of this study, it would appear that farmers
may have to consider the alternative of renting-out a portion of
their land to achieve the goal of profit maximization.

The second organizational change was the inclusion of field
beans in a large proportion of the optimum solutions; however, this
crop generally occupied no more than 10 to 15 percent of the land.
Given the relatively small acreage devoted to the crops in con-
junction with the fact it requires a specific type of soil, about
all that can be said is that the individual farmer should consider
field beans as being among his alternatives.

The analysis of the four types of strategies was divided
into two parts: (1) what is the potential for growth under each
strategy? and (2) what is the relative strength of the various
strategies under adverse conditions? No single strategy was
superior under both tests. The vertical strategy was the most
resilient in the face of adversity but permitted the achievement
of a small amount of growth relative to two of the other strategies.
The weakest all-around strategy was expansion by renting land under
a long term contract as it was always the first firm to succumb
to adverse conditions and was also relatively weak in the amount of
growth allowed. Due to its leadership in achieving growth and
demonstrations of strength in withstanding adverse conditions,
expanding laterally by means of a land contract arrangement was

found to be the best all-around strategy. Based on the findings

158

of this study, purchasing land under a contract offers certain
advantages to farmers if such an arrangement is available. With

its small down payment, it offers the possibility of either acquiring
control of additional quantities of land or of releasing additional
funds for other uses. It does, however, present the imprudent
Operator with a means to finance ruins through too much indebtedness.
On the other hand, with reasonable use, it offers the opportunity

to acquire additional resources beyond what could be purchased with
larger down payments which can be especially important in the case

of those assets subject to capital gains.

There is nothing original about an attempt to compare the
growth potential of alternative growth strategies. On the other
hand, the evaluation of the ability of firms operating under a
particular strategy to withstand adverse conditions has not been
widely done. It can be concluded from the study that there is a
wide variation between strategies with regard to this characteristic,
and it would appear that this aSpect would deserve a great deal of
consideration from an operator planning to commit large sums of
money to growth. It is certainly not beyond the realm of possibility
that future technological innovations could result in substantial
outward shifts in the supply curve for agricultural commodities.
Also, the development of substitutes or drastic changes in govern-
ment policy are possibilities constantly facing agriculture. Any
of these three factors, and perhaps others, could put agricultural
producers through the "wringer" for a lengthy period of time as part
of an adjustment process that would likely see a number of operations

fail. Operators planning to invest several hundred thousand dollars

159

would in all likelihood want to reduce the risk of failure and thus
should be made aware of the variations in the risk associated with
the different strategies.

With regard to the two included levels of managerial competency,
that designated as above average was able to achieve growth only at
a rather moderate rate. On the other hand, the exceptional level of
management achieved growth at a rate that can only be described as
bordering on phenomenal. The fact that this utterly fantastic rate
of growth was achieved under stochastic market and yield conditions
would seem to increase the incredulity of the results. However, the
finding that this level of managerial ability is able to prosper
under unfavorable conditions that could lead to bankruptcy for the
majority of farmers would tend to support the conclusions about
growth rates.

This strength in the face of adversity was due primarily to
the greater profitability of the firm under more normal operating
conditions. In fact, the firms possessing exceptional management
were so successful under the Stochastic conditions that they
accumulated cash at a faster rate than they could realistically
expect to utilize it in acquiring assets within the price range
included in the simulator. This conclusion is based on the assump-
tion that the Supply curve for land facing a firm would tend to be
rather inelastic in the Short run. The result is that the firm
would usually have proportionately lower debt commitments and more
liquid portfolios of assets that allow it to successfully endure

conditions of adversity.

160

The finding with regard to the impact of exceptional managerial
ability is especially noteworthy because it pinpoints an important
force in agricultural production. However, this Study merely scratches
the surface with regard to the supply and the characteristics of this
element of production. As pointed out earlier, it definitely deserves
additional research.

Another point that came under investigation was the impact of
variations in stochastic elements on the growth possibilities of a
firm. The conclusion was that given a bundle of assets and a set
of production decisions, variations in Stochastic elements had very
little effect on the growth of a firm during a one-year period. Of
all the stochastic influences, it appeared that land purchasing was
the biggest factor in determining the increase in size. This means
that the failure to acquire land, whether due to its unavailability
at certain times or to the failure or inability to submit an adequate
bid, can be critical to the growth prospects of a firm.

The conclusion reached regarding the rather small impact of
the stochastic element associated with commodity prices and yields
is consistent with the earlier finding that the stochastic elements
accounted for only a relatively small proportion of the economic
loss associated with nonoptimal solutions. Also, the conclusion
about the impact on firm size of the various outcomes of a Stochastic
determination of land acquisitions reinforces the finding that a
land contract Offers certain advantages because it allows more land

to be controlled.

Appendix A

Simfarm Transmittal Form

Appendix Table A. l.

161

Simfarm Transmittal Form

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

leave
blank
Name: (16 letters or less) T2-3 (Tl)
T Management Decisions Proposed
Plan
4. Farm Number to Buy: (Circle one) 1 2 3
If farm.was_purchased before this year
5. Farm number to sell: (Circle one) 1 2 3
go. of 40 acre units ...
6. To buy: Class I land
7. Class II land
8. Ingggll: Class 1 land
9. Class II land
10. To rent: Class I land
Class II land
Class III land
Land Purchase Bid Per Acre:
11. Class I land $
12. Class II land $
13. Class III land $
Real Estate Down Payment: CZ)
141 5% or 10% or 15% 20% or 25% or 30% %
Land Contract Mortgage
Years to Amortize Real Estate L23“?
15. 10 or 15 or 20 or 25 yrs.
16. Crop Technology: Circle one A B C
Crop Rotation Number by Land Class
1 C-C-C-C-C 7. C-C-O-H-H Class I land
17. 2 C-FB-C-C-FB 8. C-FB-C-OJW (Rotations 1-12) No.
3 C-SB-C-C-SB 9. C-SB-C-O-W Class II land
18. 4. C-C-FB-FB-W 10. C-C-C-O4W (Rotations 6-12) No.
5 C-C-SB-SB-W ll. H-H-H-H-H Class III land
19. 6 C-O-H-H-H 12. Cash rent (Rotations 11-12) No..___.__.—
C I Corn 0 I Oats W I Wheat H I Hay
SBI Soybeans FB I Fieldbeans
20. Livestock Technology Level: (Circle one) A B C
(Cannot be changed after lst. year without
selling breeding Stock)

 

 

 

 

 

162

Appendix Table A. 1. --Continued

 

21. Dairngows: Number to buy this year
22. % to sell per year after first
(at least 16%)

23. Beef Cows: Number to buy this year ._______.

24. % to sell per year after first
(at least 16%)

25. Bred Gilts: Number to buy this year _________
26. Sell all sows? Yes No

How Pigs Born Will Be Sold: (Circle code)
27. 1. As Feeder Pigs 2. As Market Hogs 1

28. Feeder Pigs: No. to buy this year

29. Feede; Steers: NO. to buy this year

Down payment on Livestock Bought: (Z)
30. Cows or gilts: 40 or 60 or 100
Feeder Pigs or Steers: CZ)

 

 

 

 

 

 

 

 

31. 0 10 20 40 60 100
Machinery Down Payment
32. 10 20 40 60 100
Non-Farm Investment
33. Class I Investment: 3 to Buy $
34. $ to Sell $
35. Class II Investment: $ to Buy $
36. $ to Sell $
37. Class III Investment: $ to Buy $
$ to Sell 3
For SIMFARM administrator use only
1. Years for this plan to be iterated: years
(Years I 1 unless otherwise indicated)
2. Model will be ...
Deterministic ‘QR Stochastic
with with
RSND I 0 -3 < RSND < +3
RSND I -3
RSND I +3

(Model will be Stochastic unless otherwise indicated)

 

Appendix B

Simfarm Output Form

163

Appendix Table B. l. Simfarm Output Form

 

 

 

Simfarm Prices Received Market Year 2
FIRST SECOND THIRD FOURTH

COMMODITY QUARTER QUARTER QUARTER. QUARTER
Corn (bu.) 1.02 1.08 1.12 0.98*
Oats (bu.) 0.67 0.67 0.63* 0.63
Wheat (bu.) (1.66 1.65 l.66* 1.61
Soybeans (bu.) 2.45 2.60 2.62 2.28*
Fieldbeans (bu.) 3.83 3.90 4.01* 3.38
Hay (ton) 19.97 18.56 18.84* 19.17
Hogs (cwt.) 18.60 19.53 20.77 18.83*
Milk (cwt.) 4.92 4.64* 4.94 5.05
Fat Cattle (cwt.) 25.03 25.73* 26.66 26.15
Feeder Steers (400 lbs.) 109.92 119.59 116.17* 117.20
Feeder Pigs (40 lbs.) 12.97 12.62* 13.27 14.14
Cull Diary Cows (head) 112.21 178.68 198.83 186.23
Cull Beef Cows (head) 112.21 178.68 198.83 186.23
Diary Calves (head) 11.20 18.52 23.18 21.92
Land Rent

Class I (acre) 31.72

Class II (acre) 27.72

Class III (acre) 9.72
Nonfarm Income

Class I ($1) 0.14

Class II ($1) 0.08

Class 111 ($1) 0.04
RSND -l.30 0.42 1.42 -2.17

164

Appendix Table B. 1. -- Continued

 

PR1 CES PAID MARKET

 

CROP COSTS PER ACRE

 

CROP I595. LAND I LAND II LAND III
CORN A 54.92 43 42

OORN B 50.51 38.82

(DRN C 45.72 34.22

0ATS A 21.39 19.70

OATS B 18.68 16.98

OATS C 15.97 14.28

WHEAT A 37.37 32.74

WHEAT 8 33.62 28.93

WHEAT c 29.84 25.18

SOYBEANS A 28.40 24.58

SOYBEANS 8 25.86 22.04

SOYBEANS C 23.31 19.50

FLDEEANS A 50.10 43.42

FlDBEANS B 45.64 38.97

FlDBEANS c 41.12 34.51

C SILACE A 56.79 43.34

C SILAGE 8 51.41 37.96

C SILAGE C 46.03 32.59

HAY A 42.45 36.37 18.14
HAY 8 36.37 30.30 12.08
HAY c 30.30 24.23 6.00

LAND PRICE PER ACRE AND LAND RENT PER ACRE

LAND PRICE FOR CLASS 1 $ 305.80
LAND PRICE FOR CLASS 2 $ 281.74
LAND PRICE FOR CLASS 3 $ 142.66
LAND RENT FOR CLASS 1 $ 27.42
LAND RENT FOR CLASS 2 $ 26.75
LAND RENT FOR CLASS 3 $ 8.18

LIVESTOCK (DSTS WHICH ARE ADJUSTED ANNUALLY

BEEF cow COSTS TECH. A - $ 205.11 TECH. B - s 187.32
FEEDER CATTLE COSTS/HEAD - $ 116.17

PURCHASE PRICE OF BRED CILTS - $ 65.10

PURCHASE PRICE OF FEEDER PICS PER HEAD = $ 12.62

165

 

 

 

 

 

 

 

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Appendix C

Linear Programing Matrix

167

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S imfarm Support ing Data

Appendix Table D.

171

1. Prices Received

 

 

COMI‘DD ITY UN IT PO RANGE
1. Corn Bu. $ 1.00 .09
2. Oats Bu. .62 .04
3. Wheat Bu. 1.70 .06
4. Soybeans Bu. 2.21 .07
5. Field Beans Bu. 3.87 .23
6. Hay Ton 19.50 1.21
7. Milk th. 4.15 .52

Appendix Table D. 2.

172

Crop Yields

 

 

 

LAND YIELD AND RANGE

CROP CLASS TECH A TECH B
Corn (bu.) I 108 _+_ 24 100 i 24
Corn (bu.) II 88 i 24 80 i 24
Oats (bu.) I 80 1- 24 72 i 24
Oats (bu.) II 75 i 24 67 i 24
Wheat (bu.) I 46 1- 18 42 i 18
Wheat (bu.) II 41 1 18 37 1 18
Soybeans (bu.) I 28 i 9 26 i 9
Soybeans (bu.) II 25 1 9 23 i 9
Field beans (bu.) I 28 i 9 26 i 9
Field beans (bu.) II 25 i 9 23 i 9
Hay (T.) I 4.5 1 1 5 4.0 i 1 5
Hay (T.) 11 4 0 i 1.5 3 5 i 1.5
Hay (T.) 111 3011.5 2 5:1 5

173

Appendix Table D. 3. Input Prices

E

 

ITEM PRICE RANGE

Land Price: Class I/acre $320 i $27
Class II/acre 275 _-I_- 27

Class III/acre 150 j; 29

lend Rent: Class I/acre 29 i- 3
Class II/acre 26 i- 3

Class III/acre 9 i 3

Crop Cost Per Acre

Crop

 

Corn

Corn

Oats

Oats

Wheat
Wheat
Soybeans
Soybeans ‘
Field beans
Field beans
Hay

Hay

Hay

Land Class

I

II

I

II

I

II

I

II

I

II

I

II

111

Tech A

 

$57.30

45.30
22.32
20.55
38.99
34.16
29.63
25.65
52.27
45.38
44.29
37.95

18.93

Tech B

 

$52.70
40.50
19.49
17.72
35.03
30.19
26.98
23.00
47.62
40.66
37.95
31.02

12.60

174

Appendix Table D. 4. Livestock Rules

 

 

ITEM TECH A TECH B
Initial dairy cow costs $425 $350
*Feed costs per cow & replacements 320 302
*Other dairy costs per cow 45 35

Equipment requirements are determined by the whole number (rounded
up) of livestock units defined as 10 dairy cows. Equipment
requirements have been met if the dollar valuation is not less

than $500 per unit. Adjustments are made automatically.

Milk production (sold) per cow
a. in first year: Tech A: 14000 lbs.'i 2250
Tech B: 11000 lbs. 1 2250
b. in subsequent years:
last year's ave. production +'(0 to 600) leading
to a maximum of 17300 and 14300 for technologies

A and B reSpectively.

Dairy calves
a. born per cow: .9‘: .75

b. Proportion of calves sold (males): .51: .375

*Subject to annual adjustment by index of prices.

Appendix Table D. 5.

175

Labor Requirements by Enterprise1

 

 

 

SIZE

ENTERPRISE (ACRES)
50 75 100 150 200 250 300 400 500
Corn 8.7 7.8 7.3 6.6 6.2 5.8 5.6 5.2 4.9
Oats 6.8 5.9 5.3 4.6 4.2 3.9 3.6 3.3 3.1
Wheat 6.4 5.7 5.1 4.5 4.1 3.8 3.6 3.3 3.0
Soybeans 7.6 6.6 6.0 5.2 4.7 4.4 4.1 3.7 3.4
Field beans 6.3 5.3 4.6 3.9 3.4 3.1 2.9 2.6 2.3
Hay 12.7 12.0 11.5 10.9 10.5 10.2 10.0 9.6 9.3

(HEAD)
20 30 40 50 75 100 150 200 300
Dairy 108 92 83 76 65 58 50 44 38

 

1Expressed as hours per unit and varies with size

BIBLIOGRAPHY

BIBLIOGRAPHY
Books

Heady, E. 0. and W. Candler. Linear Programming Methods, Ames:
The Iowa State University Press, 1958.

Leftwich, R.H. The Price System and Resource Allocation, New
York: Holt, Rinehart and Winston, 1966.

Naylor, T. H., Balintfy, J. L., Burdick, D. S. and K. Chu.
Computer Simulation Techniques, New York: John Wiley & Sons,
Inc., 1966.

Pugh, C. R. The Structure of Southern Farms of the Future,
Proceedings of the two day conference by the Agricultural
Policy Institute held August 1968, North Carolina State
University, Raleigh.

Viner, J. International Trade and Economic Development,
Oxford: Clarendon Press, 1953, p. l.

 

Stockton, R. S. Introduction to Linear Programming, Boston:
Allyn and Bacon, Inc., 1963, p. 34.

 

Articles and Bulletins

Brake, J. R. and M. E. Wirth, Michigan Farm Credit Panel: ‘A
History of Capital Accumulation, Research Report 25, Michigan
State University Experiment Station, East Lansing, 1964.

 

Bailey, W. R., "Necessary Conditions for Growth of the Farm
Business Firm." Agricultural Economic Research, 1967, 19:1-6.

 

Baker, C. 8., "Credit in the Production Organization of the
Firm." Journal of Farm Economics, 1968, 50:507-520.

 

Heidhues, T., "A Recursive Programming Model of Farm Growth
in Northern Germany," Journal Farm Economics, 1966, 48:668-684.

 

Hepp, R. E. and L. H. Brown, Telfarm Business Analysis Summary
for Southern Dairyiceneral, 1967. Agricultural Economics Report
No. 104, Michigan State University, 1968.

 

Hutton, R. F., A Simulation Technique for Makinnganagement
Decisions in Dairy_Farming, Agricultural Economic Report 87,
U.S. Department of Agriculture, Washington, 1966.

 

 

176

177

Irwin, G. D., "A Comparative Review of Some Firm Growth Models,"
Agricultural Economic Research, NO. 3, 1968, 20:82-100.

 

'Lins, D. A., "An Empirical Comparison of Simulation and Re
cursive Linear Programming Firm Growth Models," Agricultural
Economic Research, 1968, 21:7-12.

 

Martin, J. R. and J. S. Plaxico, Polyperiod Analysis of Growth
and Capital Accumulation of Farms in the Rolling_PlainS of
Oklahoma and Texas, Agricultural Experiment Station Technical
Bulletin No. 1381, Department of Agricultural Economics,
Oklahoma State University, Stillwater.

 

 

Orcutt, G. H., "Simulation of Economic Systems," American
Economic Review, 1960, 50:893-907.

 

Patrick, G. F. and L. M. Eisgruber, "The Impact of Managerial
Ability and Capital Structure on Growth of the Farm Firm,"
Journal of Farm Economics, 1968, 50:491-506.

Rosenblueth, A., and N. Wiener, "The Role of Models in Science,"
Philosophy of Science, No. 4, 1945, 12:316-321.

 

Shubik, M., "Simulation of the Industry and the Firm," American
Economic Review, 1960, 50:908-919.

 

Vincent, W. H. and L. J. Connor, An Orientation for Future Farm
Planning and Information Systems, Department of Agricultural
Economics, Michigan State University, Ag. Econ. Misc., 1968-5.

 

Unpublished Sources

Duvick, R. D., Alternative Methods of Financing Growth of
Michigan Dairy Farms, Unpublished Ph.D. thesis, Michigan
State University, East Lansing, 1970.

 

Johnson, 8. R., An Analysis of Some Factors DetermininggFarm
Firm Growth, Unpublished Ph.D. thesis, Texas A & M University,
College Station, 1966.

 

Renborg, Ulf., Growth of the Firm in Relation to Problems of
Factor Acquisition: The Swedish Experience. Paper presented
to WAERC Farm Management Research Committee, Las Vegas, Nevada,
November 7-8, 1967.