Citation

## Material Information

Title:
An Entrepreneurial discretion model theory and implementation
Creator:
McLaughlin, Frank Sherman, 1936-
Publication Date:
1967
Language:
English
Physical Description:
viii, 214 leaves. : ill. ; 28 cm.

## Subjects

Subjects / Keywords:
Assets ( jstor )
Balance sheets ( jstor )
Entrepreneurs ( jstor )
Linear programming ( jstor )
Mathematics ( jstor )
Net income ( jstor )
Optimal solutions ( jstor )
Prices ( jstor )
Production functions ( jstor )
Dissertations, Academic -- Management -- UF ( lcsh )
Industrial management -- Mathematical models ( lcsh )
Management thesis Ph. D ( lcsh )
Operations research ( lcsh )
City of Lakeland ( local )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

## Notes

Thesis:
Thesis -- University of Florida.
Bibliography:
Bibliography: leaves 207-212.
Also available on World Wide Web
General Note:
Manuscript copy.
General Note:
Vita.

## Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
022047560 ( AlephBibNum )
13435851 ( OCLC )
ACY4535 ( NOTIS )

Full Text

AN ENTREPRENEURIAL DISCRETION MODEL:

THEORY AND IMPLEMENTATION

By
FRANK SHERMAN MCLAUGHLIN, JR.

A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA
August, 1967

ACKNOWLEDGMENTS

The author would have never been in a position

assistance, advice, and help from many people. Unfortu-

nately, it is impossible to list, in this short space, all

of those whom the author would like to thank. It is only

possible to say, that for all this kindness, the author

is exceedingly grateful.

Special thanks should go to three groups of people

who played an especially significant role in the prepa-

ration of this dissertation. The members of the author's

supervisory committee, Dr. W. V. Wilmot, Jr. (Chairman),

Dr. E. L. Jackson, Dr. R. L. Lassiter, and Dr. M. E. Thomas,

gave invaluable assistance. Mr. James W. Sikes, President

of Florida Tile Industries, Inc., and other members of

management at Florida Tile provided resources, assistance,

and information without which this document could not have

been written. Mrs. Carolyn Lyons assisted the author in

many ways, .ost particularly in the final preparation of

this dissertation.

Page

ACKNOWLEDGMENTS . . . . . . . . .. ii

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

LIST OF FIGURES . . . . . . . ... iii

Section

I. INTRODUCTION . . . . . . . . 1

Plan of This Study . .. . ... 1
Basic Definitions and Aesumption . . 4

II. A SIMPLE PORTRAYAL OF THE FIRM: THE
TRADITIONAL APPROACH . . . . 11

The Objective Function . . . . .. 11
The Production Function . . . .. 12
The Entrepreneurial Solution . . .. 14
Concepts from Economic Theory .. ... 16
Optimizing Relationships in the
Entrepreneurial Solution . . ... 19

III. THE QUESTION OF MULTIPLE OBJECTIVES . ... 24

A Review of the Question ......... 24
The Relationship to Psychological
Theories . . . . . . . . 28
The Effect of Satisficing Constraints 35
Function . . . . . . . . 38

IV. THE FIRM AND ITS MARKETS . . . . . 41

A Discussion of the Basic Assumot ion . 41
Oligcpoly and Price Stability. . . . 43
Sales Constraints in the Porvrayal of
the Firm . . . . . . . . 46

iii

Section Page

V. A RESTATEMENT OF THE PORTRAYAL OF THE
FIRM . . . . . . . . . 48

A Revised Entrepreneurial Solution . . 49
Ramifications of the Revised
Entrepreneurial Solution . . . . 50

VI. THE ENTREPRENEUR AND THE ENTREPRENEURIAL
PROCESS . . . . . . . ... 52

The Entrepreneur . . . . . .. 52
The Entrepreneurial Process . . . 54
The Iterative Nature of the Entrepre-
neurial Process . . . . ... 60

VII. A REEVALUATION OF THE PRODUCTION FUNCTION . 64

The Concept of a Process . . . .. 65
Processes and the Production Function . 69
Processes and the Objective Funcvion . 70

VIII. THE RELATIONSHIP BETWEEN THE PORTRAYAL OF
THE FIRM AND MATHEMATICAL PROGRAtMING . 72

The General Programming Problem ... . 72
Linear Programming . . . . . . 73
Linear Prograr.ming and the Portrayal
of the Firm . . . . . . . 75
The Simplex Process . . . . . 76

IX. THE PORTRAYAL OF THE FIRM: AN ACCOUNTING
VERSION . . . . . . . . 81

The Accountant's Balance Sheet . . .. 82
Business Transactions . . ... . 86
Business Income .. . . . . . 93

X. THE PORTRAYAL OF THE FIRM: A MODIFIED
ACCOUNTING VERSION . .. . . . 97

The Entrepreneurial Balance Sheet . . 97
A Modified Concept of Processes... 1.01
A Modified Form of Business Income . .. 106

Section

XI. THE PORTRAYAL OF THE FIRM: A PARTIAL
MATHEMATICAL FORMULATION . . . .

Survival Constraints . . . . .
Satisfactory Profit Constraints . .
Sales Constraints . . . . . .
Direct Production Constraints ..
Corporate Image Constraints . . .
Review and Summary . . . . . .

XII. IMPLEMENTATION: THE PORTRAYAL OF THE FIRM

The Firm Chosen for the Implementing
Study . . . . . . . .
Data Collection and Presentation . .

XIII. IMPLEMENTATION: A COMPARISON OF AN ACTUAL
AND AN OPTIMAL ENTREPRENEURIAL
SOLUTION . . . . . . . .

The Two Solutions . . . . .
Duality Theory . . . . . .
Comparison of the Actual and Optimal
Solutions . ... .
Economic Activity in the Mono-periodic
Period Chosen for Analysis . . .
The Opportunity Costs of Excluded
Alternatives . . . . . .

XIV. COMMENTS OF THE PRESENTATION ..

The Model Presented . . . . .
Modifications of the Model Presented .

A SELECTED BIBLIOGRAPHY . . . . . . .

Page

.110

. 112
. 116
. 119
. 120
S123
. 124

. 127

. 127
. 128

. 165

. 165
. 172

. 188

S 196

. 197

200

200
202

. 207

BIOGRAPHICAL SKETCH . . .. .

. .
. .

. . . . 213

LIST OF TABLES

Table

1.

2.

3.

Hypothetical Balance Sheet . . .

Hypothetical Process Illustrations .

Hypothetical Entrepreneurial Balance

Sheet

Page

. 87

. 90

. 102

4. Hypothetical Entrepreneurial Process
Illustrations . . . . . . ... 103

5. Beginning of Period Entrepreneurial
Balance Sheet . . . . . . . 129

6. Key to Process Numbers . . . . ... 132

7. Manufacturing Processes . .. . . . 135

8. Selling Processes . . . . . . 142

9. Purchasing Processes . . . .. . . 145

10. Finance Processes . . . .... .. .... .. 146

11. General and Administrative Processes .. . 150

12. Constraints Defining the Entrepreneurial
Sphere of Discretion . . . . .. 153

13. Actual Entrepreneurial Solution . . .. .166

14. Actual End of Period Entrepreneurial
Balance Sheet . .. . . . . . 169

15. Optimal Entrepreneurial Solution . . .. 173

16. Optimal End of Period Entrepreneurial
Balance Sheet . . . . . . . 176

17. Optimal Dual Variables Associated with
Constraints Defining the Entrepre-
neurial Sphere of Discretion . . . 182

LIST OF TABLES--Continued

Page

Net Contribution Values Associated with
Manufacturing and Selling Processes . . 184

Profit Losses in Subproblem I . . ... 191

Profit Losses in Subproblem II . . ... 192

Profit Losses in Subproblem III . . .. .194

Profit Losses in Subproblem IV ....... 195

Optimal Dual Variables Associated with
Processes Omitted from the Optimal
Entrepreneurial Solution . . . ... 198

vii

Table

18.

19.

20.

21.

22.

23.

LIST OF FIGURES

Figure Page

1. Schematic Representation of the
Entrepreneurial Process . . . .. 63

2. Schematic Representation of the Sirrplex
Method for Solution of Linear
Programming Problems . . . ... .79

viii

SECTION I

INTRODUCTION

There are many ways of describing a business firm.

So.e descriptions are very simple, others extremely complex.

The simplest portrayal of a business firm consists of

three parts; an entrepreneur, an objective function, and

a production function. There are three major parts of

this study. The first part is primarily concerned with

modifying the simple portrayal of the firm in order to

obtain a more realistic and workable model. The second

part provides the background into which the portrayal

should be set. The last part is an implementing section

and is presented to show that the developed portrayal is

realistic and is workable.

Plan of This Study

The first part of this study reviews the simple

portrayal of the firm, and,then, using a stepwise procedure,

modifies this simple portrayal until a more realistic and

more workable model is obtained. Emphasis is placed upon

the entrepreneur and the entrepreneurial process. The

portrayal, therefore, is a management portrayal.

A major deficiency in the simple three-part por-

trayal is that it contains a single objective which the

- 1 -

- 2 -

firm strives to optimize. Most firms have many objectives.

This study follows the thoughts of Simon (1959) that most

objectives are "satisficing" rather than "optimizing" ob-

jectives. Furthermore, there seems to be a relationship

between corporate objectives and the hierarchy of needs

which serve as motivators of human action. Section III is

offered to illustrate how the simple firm portrayal can be

modified to incorporate these multiple objectives of the

firm.

The simple portrayal of the firm is often criticized

for its assumptions about the markets in which the firm

operates, and for its assumption about the prices the firm

pays for input factors and the prices the firm receives for

its outputs. Section IV questions these assumptions, and

attempts to determine which assumptions are sufficiently

realistic to be included in a workable portrayal, and which

assumptions must be modified. The necessary modifications

are made and are incorporated into the developing portrayal.

As noted earlier, emphasis is placed upon developing

a management portrayal of the firm. The simple portrayal

includes an "omniscient power" which manipulates the vari--

ables in the production function and the objective function

is an optimal manner. In order for the portrayal to be

more correct, a more realistic concept of an entrepreneur

must be presented. Section VI presents a concept of the

- 3 -

entrepreneur and the entrepreneurial process which is more

realistic and workable, and which fits well into the de-

veloping portrayal of the firm.

The production function is the last part of the

simple portrayal of the firm to be modified. Section VII

redefines the production function, giving consideration

to the entrepreneurial process presented in Section VI,

the multiple objectives considered in Section III, and the

marketing considerations of Section IV. This modified

concept of a production function is more realistic than

the concept of a production function used in the simple

portrayal of the firm. This modified concept also fits

well into the developing portrayal of the firm.

The next four sections are concerned with the

background into which the portrayal should be set.

Section VIII emphasizes the relationship between mathe-

matical programming and the modified picture of the firm.

Section IX and Section X show hcw the portrayal can be

set into a modified accounting framework. These sections

also show the compatibility of the modified accounting

framework, the modified portrayal of the firm, and mathe-

matical programming. Section XI is concerned wiLh a

partial theoretical formulation of the portrayal in terms

of the concepts previously presented.

- 4 -

Although this dissertation is primarily concerned

with the conceptual presentation, it was thought that

significance would be added to the presentation if an

implementing study was made. The remaining part of this

study is devoted to this implementing study. Section XII

describes the firm using the concepts presented in the

study. Section XIII compares an actual and an optimal

entrepreneurial solution. Section XIV is primarily de-

voted to review, summary, and general comments.

Basic Definitions and Assumptions

Before beginning the main work in this study, it

would probably be wise to introduce some basic definitions

and assumptions. Many definitions and many assumptions

will be modified later. Attempts will also be made to

justify some assumptions made here. For the moment, the

made. We must begin somewhere, and this is how we choose

to begin.

Production may be defined as the process of

combining and coordinating materials and resources in the

creation of some valuable good or service. We do not

limit the definition of production to the purely technical

process of turning raw materials into finished products.

Rather we accept such functions as accounting, sales and

- 5 -

personnel administration to be integral parts of the pro-

duction process. Our definition is not so broad, however,

as to include intangible items such as corporate image or

community relations.

Any production process will consist of two parts,

the inputs and the outputs. The output of a production

process may be thought of as aggregates or sums of physical

materials or resources. These materials and resources are

the inputs or factor services of the production process.

Thus production converts inputs into outputs. The term

input and output must be envisioned with reference to the

process, since a good or service which is an output from

one production process may be the input to another. The

inputs and outputs of the production process should be

thought of as time flows of physical quantities. They may

be hours of labor, kilowatts of electricity, or tons of

fertilizer per year. The production process represents

the transformation of input flows into ouput flows.

Economic theorists generally concern themselves

with two types of productive services; those which vary

with output and those which do not vary with the amount of

output produced. These two types of services are generally

referred to as variable and fixed factors of production.

Raw materials and direct labor are often examples of

variable factors, while the services of a building may be

thought of as a fixed factor.

The distinguishing characteristic between fixed

and variable factors is not the technical feasibility of

varying the factor, but r t.r it is hl degree of vari-

ability of costs associated with utilizing this factor.

Direct labor is normally thought of as being a variable

cost; however if a guaranteed work week contract is in

effect, direct labor may well be a fixed factor of pro-

duction. To begin with, we shall assume that the firm

possesses some factors of production which are fixed in

quantity. The cost of these factors does not vary with

the amount of output. We shall assume that the firm also

utilizes some variable factors of production. The cost of

these factors will vary with output.

In practice, a sharp dividing line seldom exists

between fixed and variable productive services. Fixed

services are generally only fixed within some limits of

output variation. When output increases beyond these

limits, some so-called fixed productive services may have

to be increased, while some may remain fixed.

We shall define the term business firm to be a

single productive unit. It may have many inputs and many

outputs, but there must be some interrelationship between

the inputs and the outputs. The firm is a total economic

- 7 -

unit under the control of just one "power." We shall call

this "power" the entrepreneur. Thus the entrepreneur

manages the business firm. The firm is the total economic

unit over which the entrepreneur has financial control.

It is the unit for which he calculates his profit and his

loss. For our purposes, there is no need to distinguish

between management and ownership. We can assume that the

entrepreneur is both the manager and the owner.

Another assumption made is that the firm's pro-

duction activity is arranged so that production in one

time period is independent of the production in preceding

and subsequent periods. The assumption is that the firm

is interested in the activity of only one time period and

that this activity is determined exclusively by conditions

prevailing in that period and is independent of any other

set of conditions. Following Carlson (1956), we shall

refer to this as mono-periodic production. Mono-periodic

production implies that production starts on a given date

and ends at another date when the output is sold on the

market. The time interval between the two dates represents

the period under consideration.

In reality, it is impossible for a firm to arrange

its operations so that production in one time period is

independent of conditions in preceding and subsequent

periods. The assumption of a mono-periodic production

- 8 -

period is, however, used extensively in economic literature

to illustrate the optimizing procedures of a business firm.

It should be remembered that such procedures are actually

concer-:ed with suboptimization rather than optimi""tion,

ev .. though they are often rezrre t-o as in this suzay)

as optimizing techniques. A true optimizing procedure

would have to consider conditions prevailing in the period

under consideration as well as conditions in preceding and

subsequent periods.

Demand conditions for final goods and services

inform the entrepreneur about products that can be sold

on the market. To the entrepreneur, demand appears as a

series of possible price-quantity combinations which depend

on prevailing market conditions and the firm's position in

the market. To begin, we shall assume that the demand

condition faced by the firm is essentially that of pure

competition. The price a firm receives for any outpuz has

been predetermined by market forces. This price must be

accepted by the firm as a predetermined parameter. It is

not a variable which can be manipulated by the entrepreneur.

Pure competition implies that a firm may sell as

much as it wants of any given product at the predetermined

price. Later we shall modify this assumption. As we shall

show later, the assumption of a predetermined price is not

- 9 -

a great departure from reality. The assumption that the

firm may sell an infinite quantity is, however, a major

departure from reality and must be modified later.

The supply of productive services, like the demand,

will appear to the entrepreneur as a series of price-

quantity combinations. For our purposes, however, we will

again assume conditions which are essentially those of

pure competition. The firm cannot influence the price by

the quantity it takes. The factor prices are predetermined.

Fixed factors of production are in the possession of the

entrepreneur at the beginning of the mono-periodic pro-

duction period. The cost of these factors is, in effect,

sunk and cannot be varied.

The technical knowledge of the firm will be assumed

to be fixed. Technical knowledge informs the entrepreneur

of how a given output can be produced. Quite often there

will be many (perhaps an infinite number) ways of combining

inputs to obtain a desired output. It is the awareness of

these different possible combinations which is known as

technical knowledge or state of technology. It is this

degree of awareness that is assumed not to change during

the mono-periodic production period.

Finally, let us assume that the entrepreneur would

like to maximize his total net return for the period under

consideration. The validity of this assumption is highly

- 10 -

questionable. Most entrepreneurs however, seem to maneuver

toward some goal. The assumption that they tend to opti-

mize their profit position gives us a good place to start.

It will be modified later.

In optimizing, the entrepreneur must concern himself

with two broad types of problems. The first type is the

purely technical problem of production. This type of

problems pertains to the state of technology. It is

concerned with the quantitative relation between inputs

and outputs. The second type of problems are cost problems

of production. These problems assume a given state of

technical knowledge. They are concerned with the relation

between the costs of different inputs and the value of

different outputs. It is with this second type of problem

that we will be primarily concerned in this study.

SECTION II

A SIMPLE PORTRAYAL OF THE FIRM: THE TRADITIONAL APPROACH

The simplest portrayal of a business firm consists

of three parts: an entrepreneur, an objective function,

and a production function. The entrepreneur is assumed to

be the sole manager and proprietor of the business firm.

The entrepreneur makes all decisions in the firm. Thus he

manipulates the variables in the objective function and

the production function in an attempt to achieve some

objective. This objective is normally assumed to be

profit maximization.

The Objective Function

The term objective function has made its way into

economic and management literature primarily by the route

of mathematical programming. The concept implies that a

predetermined objective (for example, profit maximization)

does exist. Furthermore, it assumes that the entrepreneur

is fully aware of certain conditions such as demand for

final products and supply of factor services. Unfortunately

in problems involving more than a few aspects of the

managing of a complex organization, it becomes most diffi-

cult to describe the objective function. As the complexity

- 11 -

- 12 -

of the organization grows, and as multiple goals are taken

into account, the so called objective function becomes more

and more subjective and less quantitative.

If we use the simplified conditions assumed in

Section I, we can easily represent the firm's objective

function mathematically,

n m
P= p.x. w.y. S.
i=1 1 j=1

This is the firm's objective function--the function

which the entrepreneur would like to maximize. It is also

the firm's profit function, thus the implication that the

firm would like to maximize profits. pi is the constant

price at which output i can be sold. w. is the constant
3
price at which input j can be bought. yi represents the

extent of utilization of input j and xi represents the

level or rate at which output i is produced. S represents

the fixed or sunk costs which must be paid by the firm

regardless of the rate of output.

The Production Function

We have assumed that a firm possesses a given amount

of certain fixed factors of production. These factors,

together with the state of technology, impose a set of

technical relations which govern the possible transformation

- 13 -

of inputs into outputs. This relationship is the firm's

production function.
1
The production func-cion may be conveniently

expressed in mathematical form, writing output as a

function of input,
Xl x2 X = G(Y1' Y2' Ym)
F(xl, x2, . n x) G(yl, y' ym .

The production function is always defined in

relation to a given set of fixed factors of production.

Furthermore the production function is defined to yield

the maximum product obtainable from any specific combi-

nations of input factors, given an existing state of

technology.

It is best to visualize the production function as

defining a number of constraints within which the firm

must operate. As such, the production function is a

boundary relationship which indicates the present limits

of the firm's production possibilities. This relationship

states that a firm cannot achieve a higher rate of output

without using more inpu-s, and that fewer inputs cannot be

used without decreasing the rate of output. The production

function indicates the manner in which the firm can substi-

tute inputs without varying the amount of output, and also

An alternate representation of the production
function is given by

x = G.(y Y i = I, .. n.
i. Gi "2

the w, in which the firm can substitute one output for

another without altering its total usage of inut. h

produc-ion function represents only technically efficient

operations by the firm. If a firm is not operating on its

production function, then by shifting its operations to the

production function, it can produce its present output

with a smaller volume of inputs, it can use its present

inputs to produce a larger volume of one or more outputs.

If a firm wants to maximize profits, its operating possi-

bilities are constrained to points on the production

function.

The Entrepreneurial Solution

To complete our simple picture of the firm, it is

only necessary to show how the entrepreneur will attempt

to manipulate the variables under his control so as to

obtain the maximum amount of profit which the constraints

of the production function will allow.

Mathematically, the problem is easily solved using

the Lagrange multiplier technique for solutions to con-

strained maximization problems. In practice, as we shall

see later, the problem is never so easy. Nevertheless, we

shall proceed with the mathematical solution for two

reasons. First, it should provide the entrepreneur with

an indication as to how to maximize. It should point him

in the right direction. Second, we will be able to define

r.-re c r y iL:Z relanionship between -.is ct,:..2zation

_oble,.. and scme concepts of tradition-l economic theory.
9
The Lar ange function mc.y be expressed as

L = E- S + AF(x, ..., xn
i=i =1 J

G(y1' Y ) ] .

Invoking the necessary conditions for a maximum, we find,

L/C x = Pi + X(5F/x.) = i = . n,

L/o y; = w. A(G/y_) 0 = 0, j = m,
J
6L/6 = F(x, . ., x ) = G(yi, . ., Y ).

Rearranging the above equations, we obtain,

(8F/Ax)/p 1 = ). ., = (F/3xn)/ = .

= (6G/Yl1)/w = ., = (oG/y.J)/wm

= -i/A.

t.'e have m + n + 1 independent equations in m + n + 1

unknowns. Theoretically, this system of equations can be

solved for vhe values of the va-iables which maximize the

firm's profit position. It is implicitly assumed that the

maximum value of P is not less than -S. If P is less

2The implicit assumption here is that the functions
? and G are continuous and differentiable.

- JL: -

than -5, thLen the optimal solution for the firm would -e

to shut down its operations, therefore making P = -S.

he nmaihematical solution to the sta-ed problem

nice, but in its mathematical form it does little to describe

what relation shps the entrepreneur will strive to obain-

in his quest for optimization. before attempting to de-

scribe these relationships, it would probably be wise to

introduce some concepts from economic theory.

Concepts from Economic Theory

The law of diminishing returns is < frequently

quoted general economic principle. The law states that as

equal increments of one input are added, while other inputs

are held at a constant level, -hen beyond some point the

resulting increments of output will decrease, i.e., the

Urgcin-l product will diminish. The law ahols equally well

when a nurmer of variable factors are increased in their

-most optimum proportions while other factors are held at a

fixed level.

The law of diminishing returns assumes a given state

of technical knowledge. It says nothing about the effect

It is important to point out here that S, the fixed
or overhead cosus of the firm, should only be used in de-
iermaning whether the firm should operate or shu- down.
Beyond this, S plays no part in the production decisions
of a firm which s'lls in a competitiv-- market.

- -O -

- 17 -

of adding units of any one input factor, holding the other

factors constant, when the technological processes are also

being changed. Also, there must be at least one fixed

factor of production. The law of diminishing returns

does not apply to a process in which all factors are

variable. It also must be possible to vary the pro-

portions in which the different input factors are combined.

The law of diminishing returns is an empirical generali-

zation. In most production processes which we can observe

in the real world the law of diminishing returns seems to

hold.

The law of diminishing returns implies the existence

of diminishing returns in some parts of the production

function. It does not, however, rule out the possibility

of having increasing returns in other areas of the pro-

duction function. When the ratio of variable factors to

fixed factors is small, it is quite possible to be in a

region of increasing marginal returns. As the proportion

of variable factors is increased in relation to the fixed

factors, we would expect to enter eventually a region of

decreasing marginal returns. The proportion of variable

factors could be increased to such an extent that total

returns may actually diminish. It is obvious from the

above discussion that the necessary conditions for a maximum

are not also sufficient conditions. In order to insure that

- 18 -

a point obtained by the use of these equations is indeed

a maximum, second order conditions must be investigated.

Excellent discussions of second order conditions are given

by Hancock (1960), Hadley (1964), and Gue and Thomas (to

be published).

Marginal product, value of the marginal product,

marginal cost, marginal rate of product transformation,

and marginal rate of substitution are terms which also

abound in economic literature. We shall define aG/Zyj,

as the marginal product of input j. oG/ay. can be in-

terpreted as an index of the marginal increase in total

output resulting from a small increase in input j.

5F/ox can best be interpreted as an index of the

marginal increase in inputs required to produce a small

increase of output i. From these definitions, it is easy

to show that -X(iG/y.j) is the value of the marginal

product resulting from a change in any one input.

n
TR(total revenue) = p.x.,
i=l
n
dTR = Z p.dx.,
i=l
n m
i (8F/xi.)dxi = ( 3G/5y )dyj,
i=l 1 1

dyk = 0, if k j,

_1 n
dy1 = ( G/ yj) i (5F/i x )dx ,
> i=l

- 19 -

_1 n
dyj = (G/yyj) E (p /A)dx ,
i=l
n n
dTR/dy = [ Z pidxi/ E Pidxi] (-X)(aG/8y ),
i=l i=l

dTR/dyj = X(GG/8yj).

Likewise, X(6F/8x.) is the marginal cost resulting

from a change in any one output. We shall define the

marginal rate of substitution as the rate at which one

input can be substituted for another while maintaining all

outputs and all other inputs at a constant level. Thus,

the marginal rate of substitution between inputs k and t

may be defined mathematically as dyk/dyt. The marginal

rate of product transformation is the rate at which one

output may be substituted for another, while maintaining

all inputs and all other outputs at a constant level.

Using these definitions and the mathematical relationships

previously derived, we can make several statements about

the inputs to our optimal production process.

Optimizing Relationships in the
Entrepreneurial Solution

The entrepreneur will attempt to operate so that

the marginal product of the last unit of money spent of

each input will be equal for every input,

(G/yl)/1 = ..., (SG/yj)wj = .

(G/a ym)/wm

- 20 -

The entrepreneur will attempt to utilize all inputs

in such a manner that the value of their marginal product

equals their market price,

X(-G/ayj) = wj, j = .., m.

The entrepreneur will attempt to operate in such a

way that the marginal rate of substitution between every

pair of inputs, holding all other inputs and outputs

constant, is numerically equal to the inverse ratio of

the input prices,

IdYk/dytj = wt/wk' all k, t,

This is shown below.

n m
E (aF/ix.)dx = 7 (G/y.j)dy.,
i=l 1 j=l

dyj = 0, j k k, t,

dx. = 0, i = . .,n.
1

(aG/ yk)dyk + (5G/8yt)dyt = 0,

(aG/aYt)/(sG/ yk) = dyk/dyt,

(OG/Syt)/(SG/8yk) = wt/wk'

Syk/d Ytj = wt/wk.

Following the same line of analysis as above, we

can make the following statements about outputs in our

optimal production process.

- 21 -

The entrepreneur will attempt to produce each

output in such a manner that its selling price equals its

marginal cost,

X(aF/ax.) = pi, i = 1, .., n.

The entrepreneur will attempt to operate in such

a way that the rate of product transformation between

every pair of outputs, holding all other outputs and

inputs constant, is numerically equal to the inverse

ratio of their prices,

Idyk/dyti = pt/pk'

Again following the same line of analysis, we can

make the following statements about the relationship

between inputs and outputs.

In the optimal solution, the marginal value re-

ceived from the last unit of input must be equal for every

output,

pl(aF/lxi) = i/(,F/axi)

pn/(F/x n).

In the optimal solution, the rate at which any

input should be transformed into any output, holding all

other inputs and outputs constant, is equal to the inverse

ratio of their prices,

- 22 -

dxi/dj = w /pi, all i, j.

This is shown below.

(3G/oyj)/(2F/6xi) = w /p ,

dxi/dyj = (5G/Syj)/(9F/8x)

dx./dYj = wj/Pi.

In a few short pages, we have prescribed to the

entrepreneur of our simple firm the procedure which he

should follow in order to obtain the "most" from his

scarce resources. The theory is fine; without it the

entrepreneur would, perhaps, lack the direction in which

.to move. There are, however, two major weaknesses in what

we have done. First we have oversimplified the picture of

our firm. In fact, in our effort to simplify we have made

some questionable assumptions about the firm's behavior.

These will be discussed later. In the second place, theory

alone is not enough. Tools must be developed (and existing

tools must be utilized) to aid the entrepreneur in ob-

taining the most efficient utilization of his scarce

resources.

There is, of course, nothing new about the preceding

analysis. This is the type of analysis that classical

economist have traditionally used to describe the firm.

It has often been criticized because it tends to be more

o= a :.....tive description rather un an .pem;.n

tccl. In defense, iz should be noted that the classical

cconcmisns did not greatly concern themselves with the

implemcnwation of the theory they had developed. The

economist accepted the produci-on function as a description

of the technological condition of production, and they

accepted no direct responsibility for deriving it. The

problem of efficiency was generally thoughtof as falling

into the domain of the scientist or engineer.

A primary aim of economic theorists has been to

understand business behavior rather than to make recom-

aendations to business men. Economic theory, in effect,

describes what a rational individual, who is well versed

in decision-making, would do in his economic activities.

The assumption of an optimal production function is

important to the economist becauzo it helps him understand

the behavior of business men, consumers, and other members

of the economy. Business knowledge and experience does

allow buyers and sellers to arrive at decisions which come

close co being optimal. Furthermore, competition often

eliminates firms whose decision-making is consistently

poor. Thus, the assumption of an optimal production function

is somewhat valid, and to the extent that it is valid,

-coromic theory serves as a relatively good description

ol economic behavior.

- 23 -

SECTION III

THE QUESTION OF MULTIPLE OBJECTIVES

Perhaps the most important criticism of our simple

picture of the firm is that a typical firm does not possess

just one objective function, but instead has many purposes

and goals. In fact, if one goal could be selected as the

paramount objective it is sometimes questioned if this

goal would be profit maximization.

A Review of the Question

Baumol (1959) insists that consulting experience

has shown him that firms attempt to maximize sales subject

to a profit constraint. He believes that firms will

attempt to sell as much (in terms of monetary revenue) as

possible as long as a reasonable profit is made. Shubik

(196], p. 360) in a survey of twenty-five large corpo-

rations notes that such terms as "fair share, fair return,

investment" are often stated as company objectives.

Shubik (1961, p. 366) notes that a firm may often

make a statement such as, "we wish to maximize profits and

market share." It is quite possible that these two items

may be negatively correlated through the effect of

- 24 -

- 25 -

independent variables. In this case, the cost of sales

effort necessary to increase market shares may decrease

profits. In some situations, however, the correlation

between the factors which control the values of the stated

goals of the firm may be sufficiently close to unity so

that the maximization of one value maximizes the value of

another (to a good approximation).

Peter Drucker (1954, p. 46) claims that "the

guiding principle of business economics is not the maxi-

mization of profits; it is the avoidance of loss." To

carry this reasoning one step further, survival of the

firm must be considered as a paramount objective. The

firm, as a social and economic organization, like may

other organisms, has a compelling urge to survive. The

motive to survive is probably more fundamental than the

profit motive; it is implicit in most decisions within

the firm. In the long run a firm that survives will make

a positive profit. However, a firm that maximizes profits

might not survive. Obviously, sufficiently large losses

will bankrupt a firm. It is also possible to be a profit-

able firm, but because of inadequate liquidity, etc., not

to survive. Thus the goal of survival may take precedence

over all other objectives of the firm. In the short run,

all positive profit may have to be sacrificed to permit

survival.

- 26 -

Many entrepreneurs believe the key to survival lies

in sound financial management. Financial management in-

cludes a variety of goals which can be generalized by

stating that the financial requirements of all possible

future conditions of the firm should be met adequately.

No firm can realize this objective completely; to

prepare for one contingency adequately often limits a

firm's ability to meet other situations. For instance,

the relative amount of debt and equity financing should be

determined on the basis of the worst possible earnings

position which can reasonably be expected within the firm's

economic horizon.

Some of the major types of financial limitations

would be the maximum amount of short-term or long-term

debt, the minimum ratio of current assets to fixed assets,

the maximum amount of inventory or receivables in relation

to sales, and the minimum level of working capital.

In addition to these basic relationships, financial

management makes use of a wide variety of comparisons and

ratios between the major components of the balance sheet

and income statement. All these financial yardsticks can

be applied as constraints in the solution of any nonfi-

nancial problem of the firm.

Occasionally, in the short run, a financial ob-

jective may take precedence over all other objectives.

- 27 -

The liquidity position of the firm can be of prime importance

and at times might be crucial. While cash is the only truly

liquid asset, most firms regard receivables as liquid

assets. The firm might want to maximize cash and receiva-

bles as a percentage of other total assets. Other fi-

nancial ratios or relationships might be optimized in a

similar manner.

The creation and maintenance of corporate images

plays an important role in the modern firm. Several types

of images are of significance. Ultimately, all decisions

result from some sort of image in the mind of the decision-

maker. However, this image is partially a reflection of

what the decision-maker thinks is the image of his firm

and its products that is held by various other groups.

These groups include customers, employees, competitors,

stockholders, suppliers, government officials, and the

general public. Decisions result not from the actual

images held by these groups but by what managers think

these images are. The reaction of management to the

images of various groups is not a passive one because it

is generally recognized that a firm's actions can and do

influence these images.

Depending upon the group involved, various types

of images may be considered desirable by a firm. A

desirable consumer image might include such aspects as

- 28 -

service, quality of products, fairness of price, leadership

and innovation. The image held by competitors would in-

volve fair dealing, efficiency, leadership in volume of

sales, etc.

The entire problem of image creation is complicated

by the fact that the existence of a characteristic does

not necessarily create an image of it nor does an image

insure the presence of the elements involved. Actual

service may not create a consumer image of service. The

image of economy in a product may best be created not by

a low price per unit but rather by a package that appears

to give more units for a given price.

The Relationship to Psychological Theories

Simon (1959) gives one of the best explanations of

multiple objectives. To Simon, the critical assumption is

that the firm does wish to maximize. Simon argues that

the firm may not wish to maximize, but may simply want to

earn a return that is regarded as satisfactory. In his

analysis, Simon draws heavily from the field of psychology.

He notes that while satiation plays no role in economic

theory, it does enter rather predominantly into the

treatment of motivation theory in psychology. In most

psychological theories, the motive to act stems from

drives, and action terminates when the drive is satisfied.

- 29 -

Moreover, the condition for satisfying a drive is not

necessarily fixed, but may be specified by an aspiration

level that itself may adjust upward and downward on the

basis of experience.

To better understand this concept of multiple goal

formulation, it is best to draw upon the field of psychology,

rather than the field of economics. Business firms are run

by men, therefore we would expect an analogy between

corporate goals and human goals.

Mastow's hierarchy

A. H. Maslow (1954) lists five types of human needs

which are arranged in a hierarchy from lower levels to

higher levels. They are:

1. Physiological needs, such as hunger, thirst,
and sex.

2. Safety needs, such as security, stability, and
order.

3. Belongingness and love needs, such as needs
for affection, affiliation, and identification.

4. Esteem needs, such as needs for prestige,
success, and self respect.

5. Need for self-actualization.

The ordering of these needs is significant in two

ways. It is the order in which they tend to appear in the

normal development of the person and also the order in

which they tend to be satisfied.

- 30 -

The individual attempts first to satisfy his physio-

logical needs. Once these are relatively well satisfied,

then higher order needs emerge and begin to dominate the

individual. When these are in turn satisfied, again new

(and still higher) needs emerge, and so on. This is what

Maslow meant by saying that the basic human needs are

organized into a hierarchy of relative prepotency. The

individual is dominated and his behavior organized only

by the unsatisfied needs. Thus, man lives by bread alone--

when there is no bread. But man's desires change when

there is plenty of bread and his stomach is chronically

filled. A brief summary of the needs are given below.

Physiological needs.--Although it is impossible to

make a complete list of physiological needs, certainly

they would include hunger, thirst, sleep, sex, and body

homeostasis.

Undoubtedly these physiological needs are the most

prepotent of all needs. To the human being who is missing

everything in life in an extreme fashion, it is most

likely that the major motivation would be physiological

needs rather than any other. A person who is lacking in

1Homeostasis refers to the body's automatic efforts
to maintain a constant, normal state of the blood stream.
Thus, if the body lacks some chemical, the individual will
tend to develop a specific appetite or hunger for that
food.

- 31 -

food, safety, love, and esteem would probably hunger for

food more strongly than for anything else. If all the

needs are unsatisfied, and the individual is dominated by

the physiological needs, then all other needs may simply

become non-existent or simply become pushed into the

background. As Maslow (1954, p. 82) has said, "For the

man who is extremely and dangerously hungry, no other

interests exist but food. He dreams food, he remembers

food, he thinks about food, he perceives only food, and

he wants only food."

Safety needs.--If the physiological needs are

relatively well satisfied, there then emerges a new set

of needs, which are roughly characterized as safety needs.

All that has been said of the physiological needs is

equally true, although in a less degree, of these desires.

The individual may equally well be wholly dominated by

them. Most adults in our society are safe enough from

wild animals, extremes of temperature, criminal assault,

etc. Therefore, in a very real sense, man no longer has

any safety needs as true motivators. We can, however,

perceive the existence of safety needs in such phenomena

as formation of labor unions, job tenure, and insurance.

As we will note later, safety needs do seem to have some

effect in corporate goal formulation.

- 32 -

Love needs.--If both the physiological and the

safety needs are fairly well satisfied, there will emerge

the love and affection needs, and the whole cycle will

repeat itself. The person will now feel keenly about the

absence of friends, or a wife, or children. He will

hunger for affectionate relationships with people in

general, or for a place in his group, and he will strive

with great intensity to achieve this goal.

Esteem needs.--All people in our society have a

need or desire for a stable, firmly based, usually high

evaluation of themselves, for self-respect, self-esteem

and for the esteem of others. These needs may be classi-

fied into two subsidiary sets. First, there are the

desires for strength, achievement, adequacy, competence,

confidence, freedom, and independence. Second, there are

the desires for reputation, prestige, status, dominance,

recognition, attention, appreciation, and importance.

Need for self-actualization.--Even if all the above

needs are satisfied, discontent and restlessness will de-

velop unless an individual is doing what he is fitted for.

This need we may call self-actualization. It refers to

man's desire for self-fulfillment, namely, to the tendency

for him to become actualized in what he is potentially.

The specific form that these needs will take will of course

vary from individual to individual. The clear emergence of

- 33 -

these needs, however, usually rests upon prior satisfaction

of the physiological, safety, love, and esteem needs.

The above discussion may have given the impression

that these five sets of needs are arranged in such terms

that when one need is satisfied, then another need emerges.

This might lead to the false impression that a need must

be fully satisfied before the next need emerges. In

reality, most members of our society are partially satis-

fied and partially unsatisfied in all of their basic needs

at the same time. A more realistic description of the

hierarchy would be in terms of decreasing percentage of

satisfaction as we go up the hierarchy. Perhaps an average

member of society is satisfied 90% in his physiological

needs, 75% in his safety needs, and 50% in his love needs,

35% in his self-esteem needs, and 15% in his self-actuali-

zation needs. The emergence of a new need is seldom a

sudden phenomenon, but rather a gradual emergence. For

example, if need A is satisfied only 10%, then need B may

not be visible at all. However as need A becomes satisfied

40%, then need B may emerge 5%, etc.

One difficulty in the formulation of the need

hierarchy is that needs are often not what they seem to

be. A person who thinks he is hungry may actually be

seeking more comfort or dependence. Conversely, it is

possible to satisfy the hunger need in part by other

- 34 -

activities such as drinking water or smoking cigarettes.

As another example, there are supposed to be people (Morgan,

1961) who seek self-esteem for the sake of love rather

than for self-esteem itself. This sometimes apparent

reversal of the hierarchy does not, however, diminish the

value of the concept for our purpose.

Maslow's hierarchy and the firm's goals

It is easy to see that there is an analogy between

Maslow's hierarchy and the multiple goals of the firm.

The analogy, however, is difficult to formalize. Certainly

there is a hierarchy of corporate goals, but the determi-

nation of the hierarchy is difficult.

Certainly the survival needs of the firm would be

in the lowest possible set of the hierarchy. Unless, and

until the firm can be sure of surviving it is unlikely

that management will concern itself greatly with corporate

images, etc. To paraphrase Maslow, a firm which is short

of cash will probably dream cash, think about cash, perceive

cash, and want only cash.

Maslow's safety needs are primarily evidenced in

corporations as insurance contracts, engineering specifi-

cations, etc. It can be argued, however, that safety needs

are responsible for the tendency toward consolidation, and

for apparent price stability in certain industries. This

latter concept will be considered again in the next section.

- 35 -

Corporate love needs and esteem needs vary, but

typical needs are obvious to most people. Each individual

could produce his own list of great length. Let us just

say that, in general, these needs are human needs which

are projected through the edifice of the business firm.

The business firm conception of self-actualization

needs is again open to many interpretations. Maslow (1954)

indicated that the need for self-actualization is a need

for an individual to do what he can do best, and to do

that in the best way he can. In business language, this

is not far from the economist's concept of profit maxi-

mization.

The Effect of Satisficing Constraints

If we are to explain business behavior in terms of

this psychological theory, we must expect the firm's goals

not to be formulated in terms of maximization, but rather

in terms of attaining a certain level or rate of profit,

holding a certain share of the market or maintaining a

certain level of sales. Firms would try to "satisfice"

rather than to maximize.

If we use this theory, then it is obvious that we

have removed the objective function from our picture of

the firm. In its place we have added a series of additional

constraints which the firm must satisfy. The objective

- 36 -

function could, of course, be thought of as being a function

of the constraint equations.2 Conceptually, however, it is

more convenient to think of the firm as an organism which

seeks a feasible solution (one that satisfies the con-

straints) to the problem with only lower order constraints

attached. Once this feasible solution is attained, the

firm will add the constraints from the next level of the

hierarchy and search for a solution which satisfies all

constraints. The process then will be repeated until all

constraints are attached.

Let us assume that a firm has no objective function

and that it is seeking a feasible solution with "all con-

straints attached." There are three possible results.

First there might be a unique solution toward which the

firm will proceed. The probability of this, however, is

almost zero. Second, it is possible that the "satisficing"

constraints placed upon the firm by itself are inconsistent.

Thus there is no action the firm can take which will

satisfy all constraints. The third possibility is that

there will be a range or set of activities which will

satisfy all constraints. With no objective function, it

must be assumed that any combination of activities which

Some economists refer to this as the firm's
utility function.

- 37 -

satisfies all of the constraint equations would be equally

desirable. The last two possibilities are quite relevant

to reality.

In the case of inconsistency, the firm has no

feasible alternative. Its only course of action is to

violate (drop or reevaluate) some of the constraints. In

general, the firm will violate those constraints which

are associated with goals in the higher hierarchy levels.

It will continue to violate these constraints until a

feasible solution is obtained.

The second possibility, that there is a range of

activities which the firm considers as satisfactory is,

in reality, ridiculous. Any entrepreneur will state that

his firm is always trying to do better, always attempting

to achieve optimality. Certainly we must place the ob-

jective function back into our picture. The question

remains, what is the firm trying to optimize?

Shubik (1961, p. 368) handles the problem this way.

He says, suppose a firm states that 'it wishes to maximize

profits, maintain growth, and treat employees and

stockholders fairly." The statement contains no evalu-

ation of the worth of fulfillment of the different aims

and does not indicate the interrelationships that may

exist among them. If, as is invariably the case, an over-

all valuation of a utility function for the many features

- 38 -

of corporate aims does not exist, we have to devise methods

to give operational meaning to them. In Shubik's example

we can select one feature and assume that the firm wishes

to maximize it subject to the boundary conditions which

require that the other corporate aims meet certain specifi-

cations. Thus, we can represent the firm as:

Maximizing profits subject to maintaining a
specific growth program, dividend rate and em-
ployment policy which will satisfy stockholders
and employees sufficiently that they do not act
to change our environment (Shubick, 1961, p. 368).

Alternatively, if the dominant interest of the

firm is to take care of its employees, its goals raay be

stated:

Maximizing disbursement to employees subject to
maintaining a specific growth pattern and dividend
policy which will satisfy stockholders (Shubik,
1961, p. 368).

Thus Shubik would have us keep an objective function

The objective function would represent the dominant goal

of the firm. The constraints would represent those ob-

jectives which the firm is intent on satisfying.

An Assumption About the Objective Function

In our picture of the firm we will continue to use

profit maximization as the objective function of the firm.

We do this for three reasons. First, it is a logical

- 39 -

extension of Maslow's theory. According to Maslow, after

all other needs are reasonably well satisfied, the self-

actualization need will dominate the actions of the indi-

vidual. We have shown that there is an analogy between

self-actualization in the individual and profit maxi-

mization in the firm.

For the second reason, we follow Joan Robinson

(1953, p. 590) who said,

Meanwhile I am inclined to retort to those who
grouse about the assumption that the entrepreneur's
aim is to maximize profits in the immortal words of
Old Bill: "If you know of a better 'ole, go to it."

The figure of speech is apt (Ashley, 1961, p. 96) for the

cartoon of Old Bill shows him in a hole which appears to

be the target of artillery fire from all directions. Per-

haps, if he had scampered away, he might have found a

place where he could have dug himself a better hole; his

horizon was limited.

Or finally we could follow Professor Scitovsky

(1959, p. 59) who said, "We have a vested interest

maintaining this assumption--it makes economic analysis

so much easier."

A business firm, however, will not be content

with using profit just in the objective function. The

basic problem is that the distinction between constraints

and goals tend to blur. If a firm operates to maximize

porius sul. act to inviolable cons rains, it car. be argued

that fulfilling the constraining conditions is more im-

yortan- to the firm than is the function to be maximized.

A business firm will want to insure that other objectives

do not cake precedence over a satisfactory profit. Ini

could be accomplished by including a satisfactory profit

requirement as part of the system of constraints, it is

reasonable to expect, however, th-t the entrepreneur will

be aware of the value of the objective function and can

de-cermine if this value satisfies any minimum profit

requirements he might' have. 'The imposition of a satis-

factory profit constraint would therefore be redundant.

Before leaving this subject of multiple goals, it

shll b noted that any prb s exist in the intifi-

cation of goals. Some possible goals. e os can be defined

preciasel and lend themselves to measurement. These

include such things as market shares, profits, sales,

and balance shee- homeostasis.-

Other goals, perhaps no less important to the firm.

such as power, survival, socially responsible behavior,

etc., can not be defined so precisely and elude efforts

toward measurement.

Balance s:. at homeostasis is a concept borrowed
from biology. i refers to the firm's att=-pt to intain
certain balance sneet ratios at a predetermined level.

SECTION IV

THE FIRM AND ITS MARKETS

A second major criticism of our portrayal of the

We have essentially assumed pure competition in the demand

for final products. Furthermore, we have assumed that the

firm, by its own actions, cannot affect the price of its

inputs. Here we are using Chamberlin's (1948, p. 6)

definition of pure competition, that is "competition un-

alloyed with monopoly elements." The sole requirements

of Chamberlain's definition is that no participant has

any degree of control over price. Control over price is

essentially eliminated when:

1. There are a large number of participants--
enough to insure that any one participant's
influence is negligible.

2. Products must be perfectly homogeneous.

A Discussion of the Basic Assumption

The assumption of a constant price in the factor

market does not concern us to a great extent, primarily

because the assumption conforms closely to reality. Even

firms which control a large percentage of a final product

market (perhaps even a monopolist) do not tend to be a

- 41 -

- 42 -

large enough user of input factors so that their actions

materially affect the price of these factors.

The assumption of pure competition in the output

market is of more concern to us. These conditions are

approached in some industries such as agriculture. In

general, however, this assumption does not conform to

reality.

The market structure assumption is not, per se, of

prime importance to this study. What is important, is the

assumption of a constant price for final products during

the mono-periodic production period.

Although pure competition exists in only a few

places in our economy, the assumption of a constant price

for the period under consideration is not a great departure

from reality.

Oxenfeldt (1951, p. 191) notes the following:

Probably the best reason for using a constant price
assumption is that evidence supports Hall and Hitch
who studied the price policies of thirty-six firms
in England and concluded that "changes in price are
frequently very costly, a nuisance to salesmen, and
are disliked by merchants and consumers."

Oxenfeldt (1951, p. 189) also points out that large

firms such as Sears, Roebuck and Company, and Montgomery

Ward are able to publish a retail catalog where prices are

constant for periods of up to a year. Joel Dean (1951,

p. 457) notes that "its [price rigidity] existence should

be recognized."

- 43 -

Although the theoretical reasons for this apparent

price stability are not known, a study of oligopoly theory

probably sheds the most light on the subject.

Oligopoly and Price Stability

The dominant market in the American economy is

oligopoly (Chamberlin, 1950). Oligopolistic markets are

characterized by fewness of sellers, restricted entry, and

mutual interdependence. Furthermore, prices in oligopoly

markets are usually quite stable. Although the reason

for this price stability is not known with certainty, it

is often attributed to such things as collusion, price

leadership, or fear of competitive reactions. An analogy

could easily be drawn between the reasons for price

stability in oligopolistic markets and human safety needs

as postulated by Maslow (1954) and discussed in Section III.

The kinked demand curve

Some economists have used the kinked demand curve

to explain this price stability. The oligopolist's demand

curve is viewed as having a kink at the point of the

prevailing price. The basic assumption is that if you

raise price, your competitors will not. If you lower

price, however, competitors will tend to follow. Thus the

demand curve is thought to be relatively elastic at prices

- 44 -

above the kink, and relatively inelastic at prices below

the kink. The distinguishing feature of this demand curve

is that it is not differentiable at the kink. There is a

"gap" between the value of the left hand derivative and

the value of the right hand derivative. This results in a

discontinuity of the traditional marginal revenue curve.

The curve, therefore, explains stability in spite of

variations among the marginal cost curves of different

firms in the industry. The kinked demand curve is con-

sistent with profit maximization and the traditional

assumption that the firm equates marginal revenue and

marginal cost. The kinked demand curve analysis is

limited, however, because it does not explain how the

prevailing price is reached. The works of Bain, Andrews,

and Fellner do, however, shed light on this problem.

Price determination

Bain (1949) insists that oligopolistic firms will

set price so as to discourage potential competitors from

entering the industry. Thus they are really setting prices

so as to maximize long run profits. Bain defines a "limit

price" as being the highest conrmon price which the es-

tablished firms in the industry believe they can change

without encouraging at least one new entry into the industry.

Andrews' (1949) theory is based on the "full cost

principle." He believes that firms select their prices on

- 45 -

the basis of direct costs plus a standard profit margin to

cover overhead expenses. Andrews refers to this price as

a "right price." Any variance from this price by the firm

will not be profitable. He believes, as does Bain (1949),

that a price which is higher than the right price will

induce rivals into the industry and eventually cut profits.

Prices lower than the right price will not be profitable

because the "rightness" of the price results from it repre-

senting full costs.

Fellner (1960) uses a bargaining approach to analyze

oligopoly prices. He believes that stable prices in oli-

gopoly are the resultant of a type of intraindustry

bargaining which is similar to bargaining in a bilateral

monopoly. Fellner does not imply that actual negotiations

must take place in order to have bargaining. Fellner

(1960, p. 54) states that "spontaneous coordination" arises

because oligopolistic situations are bargaining situations.

"They involve two or more participants who know that what

they do affects the policies of others, just as the action

of others affects them." In such cases a range is es-

tablished within which a given price tends to emerge.

The absolute limits of this range are set by zero profits

for any of the firms. Between these zero profit points

lies the bargaining range. The price which is set within

- 46 -

this range will depend on the relative bargaining strengths

of firms in the industry.

Bain's "limit price," Andrews' "right price," and

Fellner's "bargaining price," help to explain the level of

the kink in the kinked demand curve. The important thing

for us here, however, is not how the kink got where it is,

but rather that price stability does seem to be a fact.

Sales Constraints in the Portrayal of the Firm

The kinked demand curve implies both a unique price

and a unique output. If the firm were aware of this unique

output, then it would be easy to incorporate this value

into our picture. As was the case with our multiple goals,

we could simply add a constraint which required that a

given amount of the product in question be sold. For the

typical firm, the constraint will not take the form of a

strict equality constraint. The firm normally reacts to

expected demand. It will usually have in mind an amount

of any product which it feels it can sell. The firm will

normally plan to sell any amount up to this maximum figure.

Thus the sales constraints will generally take the form of

"less than" inequality constraints.1

In some cases a firm will feel as though it must
produce a minimum amount of a certain product in order to
maintain a corporate image, customer good will, etc. These
types of constraints are generally considered as multiple
goal constraints rather than sales constraints.

47 -

The preceding discussion was not meant to imply

that demand estimation should always be abandoned and

replaced by a "right price" and a sales constraint. The

introduction of these concepts does, however, serve to

focus our picture of the firm.

SECTION V

A RESTATEMENT OF THE PORTRAYAL OF THE FIRM

In our portrayal of the firm we now have an objective

(profit) function, a production function, and a set of con-

straints. These constraints represent alternative goals

of the enterprise that must be satisfied as well as sales

limitations which must be considered.

The major question to be answered now is: what

effect will the addition of these constraints have on the

optimal solution derived earlier? Let us make the heroic

assumption that these constraints can be quantified, and

further that they can be expressed either as functions of

the input variables alone, or as functions of the output

variables alone. Actually, these assumptions are quite

valid for the marketing constraints. These constraints

will generally take the form that some function of the

output variables is less than a constant. The assumption

that all goals of the firm can be quantified has been

discussed before and is indeed heroic. To the extent that

they can be quantified, however, these goals will generally

be a function of either input variables or output variables

and not of both. With these assumptions made, we can again

solve our constrained maximization problem.

- 48 -

- 49 -

A Revised Entrepreneurial Solution

For the sake of mathematical convenience, we will

let A represent the set of indices of the constraints

associated with the output variables. B will represent

the set of indices of the constraints associated with

input variables. Furthermore we shall assume that all

constraints (except the production function) are "less

than" inequality constraints. Any constraint not in this

form can easily be converted by multiplying through by -1.

We can now form our new Lagrange function.

n m
L = p.x. Z wlyj S + X1[F (x, ., Xn)
i=l j==

GI(Y' ". Ym)]

+ E X [F(xiI .. ., x ) + u2 b ]
.r r n r r

+ [sGs (Y1 ., ym) + u2 bs
seB

The necessary conditions for a maximum are:

L/8xi = p. + X (5F/x.) + E X (1 /'xi = 0,
1 r + i r r i
reA

i = . ., n,

L/y. = wj 1(5G/3Y) +s B s(s /o Yj) = 0,

50 -

aL/al = F(xI, .., xn) = G((y, ", Ym) '

aL/8Xr hr(xl' r xn) br] 0, rEA,

L/Xs s[Gsy1' ., ym) bs] = 0, sEB,

Ar < 0, rEA,

A < 0: seB,

F (xI, . ., xn) < br, reA

Gs(' 1 Y ) < bs, cEB.

Ramifications of the Revised Entrepreneurial Solution

Our primary purpose in stating the necessary

conditions for a maximum is to show that we have now lost

the neat and simple expressions we had previously pre-

scribed to the entrepreneur. In his search for opti-

mization, he cannot depend on neat slogans such as

"utilize all inputs in such a manner that the value of

their marginal product equals their market price." Thus,

if the economist is going to aid the entrepreneur, he

must search for simpler, and more efficient tools.

Before leaving this analysis, we should review

several things we have learned from the imposition of

picture can only decrease (or not change) the absolute

amount of profits involved in the optimal solution.

- 51 -

Although this is a mathematical fact, it may come as a

surprise to some entrepreneurs who insist that the mainte-

nance of some goal such as market share is essential in

maximizing profits.

If the optimal solution could be obtained mathe-

matically, the Lagrange multipliers would represent the

opportunity costs of maintaining an objective or a sales

constraint at a given level. Thus if a numerical value

could be obtained for any Lagrange multiplier, then the

entrepreneur could estimate the value of altering the

associated constraint requirement by an incremental unit.

For example, if the Lagrange multiplier associated with a

given sales constraint is zero, then any additional sales

effort spent on this output would constitute a wasted

resource.

Let us also recognize that there may be no solution

to the Lagrange equation. Mathematically we might say

that the constraints are inconsistent. Practically we

would say that the firm has too many goals and it simply

cannot satisfy them all. It is also possible to have a

solution to the Lagrange equation which does not meet the

minimum profit requirements of the entrepreneur. In these

cases it becomes the duty of the entrepreneur to reevaluate

the constraints of the firm and to choose one or more to

be modified so that a satisfactory solution may be reached.

SECTION VI

THE ENTREPRENEUR AND THE ENTREPRENEURIAL PROCESS

Throughout the first portion of this study we have

said quite a bit about the entrepreneur without describing

who he was or what he did. This section will attempt to

define more clearly the concepts of the entrepreneur and

the entrepreneurial process.

The Entrepreneur

The entrepreneur is a manager. He manages the

instrument for the transformation of the services of

persons and things into completed products. The basic

structural unit in an enterprise can be termed as a

group. A group is a combination of two or more indi-

viduals jointly contributing specialized services which

are coordinated to the attainment of a firm's objectives.

A complex is a combination of two or more groups jointly

contributing specialized services which are coordinated

to the attainment of an objective of the firm. A complex

differs from the group in two respects. First, the basic

units of a complex are groups rather than individuals;

We are borrowing our definitions from Barnard
(1938).

- 52 -

- 53 -

second, the specialized services contributed to a complex

are the services of member groups and not directly of

individuals. The business firm is the resultant of the

combination of individuals into groups, of groups into

complexes, of subordinate complexes into superior complexes,

and finally into the supreme complex which is the business

firm.

Each group and each complex is headed by a manager.

These managers are responsible for coordinating the services

contributed by the units comprising the groups or complexes

which they head. The managers of groups manage the indi-

viduals who comprise the groups. The managers of complexes

comprised of groups do not directly manage the individuals

comprising the groups but only do so indirectly by managing

the managers who head those groups. The managers themselves

are combined into managerial groups; thus the managers of

a combination of groups together with the managers of a

complex comprising these groups may be referred to as a

managerial group. The same may be said for the managers of

subordinate complexes and the manager of the superior

complex comprising these subordinate complexes. Indi-

viduals who are managers are therefore members of two

units--the unit which they head and a managerial unit.

This fact relates the managerial superstructure to the

structure of groups and complexes and makes possible an

- 54 -

integral whole. This integral, coordinated, pluralistic

whole we will call the entrepreneur. It is the entrepre-

neur's job to optimize. As we stated earlier, economic

theorists have not been greatly concerned with how the

entrepreneur optimizes.

The Entrepreneurial Process

The twentieth century has seen the rise of another

group of analysts, often called management theorists, who

are interested in how the entrepreneur optimizes. In

fact, that is their whole reason for existence. The

approaches taken by management theorists are quite varied.

One approach is to divide the entrepreneur's job into

managerial functions. Koontz and O'Donnell (1959) state

that it is the job of the entrepreneur to plan, organize,

staff, and control the business firm. Through these

managerial functions, the entrepreneur should coordinate

the activities of the firm in such a manner as to best

achieve the objectives of the firm.

There is another approach taken by some management

theorists. This approach holds that the entrepreneur

utilizes his available assets, by operating certain

activities in a way which will best achieve some prede-

termined objective. The various activities of the firm

include such things as manufacturing, selling, personnel

ac_. n. _ir c--c accoun-i-ng, 'c ; ncc -. s

,iabi_itis are negative asse-. include such thi-s a;

land, p- nt, euipment, inventory, accounts receivable,

etc. This second approach is more applicable to this stacy

and is the one we shall employ.

D .cisi ,. makingg

iLhgh different mnagermCent theorists hcve

difr~-ren basic mrezhods of viewing a firm, r:.ost theorists

acree that the tecnnique of tdcision-making pervades the

r-or-.ance of the entrepreneur. Kcontz and O'Donnell

(13S-) note that in order to plan, organize, direct, or

ccntrcl, the entrepreneur r;ust make decisions which affect

tnh operations of the firm.

:ay-nes and ..assie (1lSl) note that entrepreneurs

select among possible activities, and then decide how much

emphasis to place on the selected activities. Thus, we

mav think of the entrepreneur as a decision-mak.er. :e

v. generally strive to make those decisions which are in

scee sene optimal.

Etymologically, "to decide" means "to cut off."

_n i-s present u.age it suggests the coming to a conclusion.

1_ ". resuppoes previous consideration of a matter causing

cub-t, wavering debate, or controversy and impli- the

ariving at a mor.- or lezs logical cc--cLusion ta.,. .r-n,.

doubu, adcbhe, etc., to ant cnJ Vebstsr t., 1-.-2, 1-.2 .

- 56 -

Decision-making involves a conscious choice or

selection of one alternative from among a group of two or

more alternatives. In making a decision, an individual

must become aware of the relevant alternatives, define

them, and evaluate them as a basis for choice. Tannenbaum

(1950) defines the following steps in the decision-making

process.

Awareness of alternatives.--Before making a decision,

an entrepreneur should become aware of all alternatives

which are relevant to the decision to be made. This, of

course, is seldom possible. Often an entrepreneur must

depend upon his own limited experience and information.

Memory of these is often sketchy and incomplete. It is

possible for an entrepreneur to discover relevant alterna-

tives through investigation or by tapping the knowledge of

others. This process is, of course, excessively time

consuming and does not guarantee complete coverage of all

alternatives. For these reasons, it is exceedingly

doubtful if most decisions are based upon awareness of

all relevant alternatives.

Definition of alternatives.--Once the entrepreneur

is aware of alternatives, he must next define each of them.

Ideally, this definition involves a determination of all

the consequences related to each alternative under con-

sideration. This, of course, can never be fully achieved.

- 57 -

The consequences of various alternatives lie in the future

and therefore must be anticipated. Whenever the future is

anticipated, uncertainty is present. Uncertainty is present

because a decision-maker never has the knowledge to make

it possible to accurately determine the nature of the

consequences which will follow upon his choice of a given

alternative, assuming all other related elements remain

constant. In addition, all other related elements will

probably not remain constant.

Evaluation of alternatives.--After an entrepreneur

has become aware of certain alternatives and consequences

associated with these alternatives, he must make a choice

among them, that is, he must make a decision.

There are two basic types of decisions any indi-

vidual must make. Some of these decisions (a small pro-

portion) relate to the individual's system of values.

They determine his ultimate ends. All other decisions

are directly or indirectly related to means for the

attainment of these ultimate ends. In choosing among

alternatives, an entrepreneur will attempt to make a

selection, within the limits of his knowledge, which will

maximize results (the degree of attainment of the relevant

end) at a given cost or which will attain given results at

the lowest cost. Thus, the individual has a criterion to

guide his choice. This 'criterion is similar to the

- 58 -

economist's concept of an opportunity cost. Joel Dean (1951)

defines opportunity costs as profits foregone because of the

exclusion of a particular alternative. An entrepreneur can

very seldom place a dollar value on the opportunity cost of

any alternative. iNevertheless, the decision-making process

must take place in this framework. Obviously, the oppor-

tunity cost of an alternative which is presently being used

is zero. There can be no foregone profit associated with

an alternative which is being used. In order for any

alternative to be valuable, it must have a positive oppor-

tunity cost. In other words, the firm must be foregoing

something of value by not utilizing the foregone alternative.

The rational entrepreneur, in the decision-making process,

will choose that alternative which has the highest oppor-

tunity cost. The opportunity cost of each alternative is

relative to the chosen alternative. If the entrepreneur

chooses the most profitable alternative, then the oppor-

tunity costs of all excluded alternatives must become

negative. The implication being that since the best

alternative is not among the excluded set, a selection of

an element of this set would reduce the entrepreneur's

profits.

The entrepreneurial sphere of discretion

With respect to any given problem which requires a

decision, the entrepreneur (any-individual) may have many

- 59 -

z .. ._..'. alerna-ves among which -o c.cos<. following

T nn<,nbum (1S50), we shall define an entrepreneur's

s here of discretion as the set of all feasible alcerna-

uivcs. The factors which restrict, restrain, or limit the

exercise of discretion to available alternatives are

referred to as "constraints." Decision-making, then, is

judgment exercised within constraints.

l'a7 I ana sepe II decisions

Tannenbaum describes two basic zypes of decisions

any individual must make. Some decisions (usually a small

minority) relate to the individual's system of values.

They ca-ermine his ultimate ends. All cuher decisions are

directly related or indirectly related to means for the

attainment of these ultimate ends. It is important for us

to make a distinction between these two types of decision.

We shal refer to the type of decisions which relate to an

individual's system of values as type I decisions. Those

decisions which relate to the means for the atcainmen. of

the ultimate ends will be defined as type II decisions.

i is important to realize that type I decisions"

The distinction between type I and type II
decisions t-nds to be rela-cie. In Section I, we noted
.t .y optimizing procedure -hat incorporates the
assu.:ption of a mono-periodic production period is
actually a subcptimizing procedure. Business firms

serae as conscra_-ts upon all uype II cecisio.s. 1_, _or

example, the entrepreneur decides (makes a type I decision)

he wants to sell a certain minimum quantity of a particular

product, then this limits or constrains the type II de-

cisicns he can make in an effort to maximize his objective

function.

It is also possible that the decision-maker can

make such a variety of type I decisions that there are no

uype II alternatives which will satisfy all type I de-

cision=. In this case, the entrepreneur must reevaluate

his type I decisions, and alter one or more of them so

that a feasible solution can be found.

The Iterative Nature of the EntrepreneuriaZ Process

Litchfield (i956) nozes that the entrepreneurial

\.c-inistrative) process is a cycle of action which in-

cludes decision-making, programming, and reappraising.

Certainly an entrepreneur is not an ormniscient individual.

He cannot immediately see the consequences of all his

actions, thus the cyclical process. Typically, the problem

h-ve long-run goals and objectives. The requirements and
objectives of the firm for a give". mono-periodic production
period can not be set in isolation. Consideration must be
g-ven to zhe effect of these decisions upon the long-run
position of the firm. Thus, short-run requirements are
usually made with the aim of achieving long-run objectives.
The type I decisions of a short-run model may be the type
I decisions for a long-run model.

- O0 -

- 61 -

faced by an entrepreneur is not that of finding a completely

new solution, but rather improving on an existing solution.

He then evaluates the opportunity costs of the excluded

alternatives and checks to see if a better solution is

possible. If a better solution is possible, he then

selects the best alternative and incorporates it into his

solution, checks the new solution for feasibility, and

then programs the new solution (puts it into operation).

He then repeats the cycle. If the entrepreneur ever

reaches a point where all of the excluded alternatives

have non-positive opportunity costs, he can assume that

he can do no better.

Let us define more precisely what we mean by a

managerial or entrepreneurial solution. An entrepreneur

chooses among feasible alternatives. Typically he does

no-c choose one alternative to the exclusion of all others.

He more likely will choose a small set of alternatives

from among a large set. Furthermore, some of the chosen

alternatives will receive more emphasis than others. It

is convenient to think of alternatives in the excluded set

as receiving no emphasis.

Thus the set of feasible alternatives, together

with the amount of emphasis each is receiving at a particular

time, determine the entrepreneur's solution or program.

62 -

We may combine the thoughts of Tannenbaum and

Litchfield to define an entrepreneurial process. This

process is illustrated schematically in Figure 1. Let us

note that the previously defined concept of an "activity"

can easily fit into the framework of Tannenbaum's "al-

ternative."

- 63 -

Evaluate Opportunity Costs
of Excluded Alternatives

Are All Opportunity '(Yes)
Costs Non-Positive?

___ (No)

Is There Evidence of (Ye,
Possible Misformulation
(No)

Select Alternative With
Highest Opportunity Cost
(Type II Decision)

Insure Feasibility
of New Program

Reprogram L

FIGURE I--SCHEMATIC REPRESENTATION OF THE
ENTREPRENEURIAL PROCESS

SECTION VII

A REEVALUATION OF THE PRODUCTION FUNCTION

In our analysis up to this point, we assumed the

production function to be given. We did not concern our-

selves with how this function was derived, but only used

this function to characterize the optimum production

alternatives when considered in relation to the markets

in which the firm must buy and sell, and the multiple goals

of the firm. Historically, this has been the position

taken by economic theorists. This conventional theory is

often justified on the grounds that the analysis of the

firm is but one step in the analysis of economic markets.

Suppose, however, that we are interested in the

firm per se. Suppose we are interested in aiding manage-

ment in determining how to solve its optimization problem.

We cannot now assume that the derivation of the production

function is irrelevant. Instead we must examine more

function.

The choice variables in the traditional production

function are generally conceived as time rates of con-

sumption of various inputs and time rates of production

of various outputs. The choices of production and

- 64 -

- 65 -

consumption are, of course, dependent, otherwise output

would be chosen very large and input very small.

Business firms are operated by entrepreneurs.

Entrepreneurs are human. We must accept the fact that

they do not possess perfect knowledge and therefore are

not fully aware of the firm's production function. What

then, do entrepreneurs do? We have stated that entrepre-

neurs are primarily decision-makers. Following Tannenbaum,

we have defined decision-making as a choice among feasible

alternatives. Thus we can see that the concept of the

traditional production function is really not relevant to

the modern firm. Normally, the choice is among various

feasible alternatives. These feasible alternatives may be

thought of as "different ways of doing things." Each

alternative implies its own characteristic pattern of

input and output rates.

The Concept of a Process

The decisions made by the firm do not deal directly

with levels of input and output but are more concerned with

the: choices among technically feasible processe-. We shall

define a process as a "way of doing something." A process

is a set of ratios among rates of consumption of various

inputs and rates of production of various outputs. Thus

a firm makes a choice among a number of processes.

- 66 -

The firm is not restricted to the use of only one

process. It can normally utilize several processes

simultaneously. Furthermore we shall assume that most

processes can be operated at a range of levels. By level

of a process we mean the time rate of consumption of all

inputs and the time rate of production of all its outputs

in the same proportion.1

When we were discussing the entrepreneurial process

we noted that the entrepreneur normally chooses a small set

of alternatives from among a large set. Furthermore we

Implicitly we have assumed linearity. Initial
thought was to include an appendix to justify this as-
sumption. This was not done for three reasons. First,
there are many articles and books in the economic litera-
ture which illustrate examples of the application of
linear models to economic problems. For example, see
Bowman and Fetter (1959). Second, the entrepreneurial
model presented in later sections of this study is formu-
lated in terms of "balance sheet accounts" and "business
transactions." For the most part, it is obviously linear.
Third, in the implementing part of this study effort was
be the case. The concept of linear programming will be
discussed in subsequent sections. It should be pointed
out here, however, that the phenomenon of decreasing
marginal returns is encountered in a linear progranaming
analysis of the firm. Baurol (1959, pp. 270--274) and Wu
and Kwang (1960) give a comprehensive comparison of di-
minishing productivity in the traditional economic analysis
and diminishing productivity in the linear programming
analysis. Baumol (1959, p. 281) states, ". . the ordi-
nary law of diminishing returns is compatible with linear
programming, i.e., the marginal yield to increased use may
decline, provided the employment of other factors remains
unchanged, .. but the decreases characteristically
occur in discontinuous jumps."

- 67 -

stated that some of the chosen alternatives will receive

more emphasis than others, and that alternatives in the

excluded set could be thought of as receiving no emphasis.

Thus the set of feasible alternatives, together with the

amount of emphasis each is receiving, define the entre-

preneur's solution or program.

We can now be more specific and say that the

entrepreneur selects a small set of processes from among

a large set. The level of a process corresponds closely

to the degree of emphasis. All processes in the excluded

set can be thought of as being utilized at a zero level.

Thus the set of processes, together with their level of

utilization, define the entrepreneur's solution or program.

A process can represent any activity within the

firm. It may represent sales effort, personnel relations,

research and development or anything else a firm might do.

The definition of a process implies something more specific

than an activity undertaken by the firm. It is the way or

the method that a firm undertakes an activity.

One of the most common activities of a firm is

that of manufacturing a product. It is essential, however,

to distinguish between a product and a process. A product

is an economic good or service which is sold on the market

for a particular price. A process is a way of manufacturing

a particular product. Normally there will be a number of

- 68 -

technically feasible processes which will produce the same

product. The same is true for most other activities under-

taken by the firm. Thus, the number of processes will

always be greater than or equal to the number of activities.

It is possible in some cases to have a large number of

processes for a given product. Usually, the number of

processes available is small. We shall assume that the

entrepreneur is free to utilize several process simul-

taneously so long as he does not violate his sphere of

discretion.

We have stated that there is a constant price

associated with each input and each output. Since a

process is a set of ratios among rates of consumption of

various inputs and rates of production of various outputs,

it must be true that associated with each process is a

value which we shall call the net contribution to profit

and overhead. Net contribution represents the difference

ditional cost incurred by the utilization of one additional

unit of any given process. Under our assumption of

linearity, net contribution is a constant and is inde-

pendent of the level of utilization of any process. It

would be incorrect to refer to this new parameter as

profit. The firm does incur a certain amount of fixed

- 69 -

costs (which may be called overhead) and technically profits

are not obtained until the net contribution is greater than

Since a firm will normally employ several processes,

it follows that the firm's total consumption of resources

and total production of outputs will be the sum of the

quantities of factors consumed by the various processes

and the sum of the products created by the various processes.

A change in the quantity or proportion of inputs consumed

or outputs produced can only result from a change in the

levels at which the various processes are operated. The

firm cannot alter directly the quantities of inputs or

outputs, but can only change these factors indirectly by
2
means of changes in the level of various processes. It

should be the goal of the entrepreneur to choose those

levels cf the various processes which will maximize his

own objectives while at the same time not violate his

sphere of discretion.

Processes and the Production Function

The introduction of the concept of a process has

forced us to reexamine the traditional production function.

The typical entrepreneur is not aware of an "optimal"

We shall assume that all processes must be oper-
ated at non-negative levels.

- 70 -

production function on which he must operate. He is much

more aware of the limitations or constraints on his

selection of processes. The entrepreneur has available

certain fixed and variable factors of production. The

entrepreneur uses these inputs (by operating processes)

to create outputs. In doing so, the entrepreneur selects

among various alternative processes. He is not free to

operate any process at any level. He is constrained by

the availability of certain factors of production. We

shall call these constraints the direct production con-

straints.

We shall refer to all other constraints placed

upon the entrepreneur as indirect production constraints.

The direct and indirect production constraints together

define the entrepreneur's sphere of discretion.

We have now redefined our production function.

Instead of the continuous production function of the

traditional economists, we have a production function

that consists of two parts; a set of processes, and a

sphere of discretion.

Processes and the Objective Function

The introduction of the concept of a process has

also forced us to reformulate our objective function in

terms of processes. This is easily done mathematically

as follows:

- 71 -

n
P = c.x. S.
i=l 1 1

x. represents the level at which process i is

utilized in any solution. c. represents the net contri-

bution of a unit of process i. S represents the fixed or

sunk costs which must be paid by the firm regardless of

the rate of output. It is the duty of the entrepreneur

to select those processes and operate them at the correct

level to maximize this objective function.

SECTION VIII

THE RELATIONSHIP BETWEEN THE PORTRAYAL OF THE
FIRM AND MATHEMATICAL PROGRAMMING

Mathematically, any problem which seeks to maximize

(or minimize) a numerical function of one or more variables

(or functions) when the variables can be independent or

related in some way through the specification of certain

constraints may be referred to as an optimization problem.

The methods of differential calculus have long been applied

to optimization problems in the theory of the firm. In

fact, traditional economic theory of the firm is framed

in the methods of differential calculus.

In the last twenty years there has been a large

growth of interest in a new class of optimizing problems,

referred to as programming problems, which are usually

not amenable to solution by classical methods of calculus.

The General Programming Problem

The general programming problem can be formulated

in the following way. The objective is to determine

values for n variables xl, x2, . which satisfy

the m inequalities or equations

g (x x2, . ., ){<, =, }bj, j = 1, . ., m,
2n j

- 72 -

- 73 -

and in addition, maximize (or minimize) the objective

function

z = f(xl, x2, . ., xn)

The constraints are assumed to be specific functions, and

the b. are assumed to be known constants. One and only

one of the signs {<, =, >} holds for each constraint, but

the sign may vary from one constraint to another. The

values of m and n need not be related in any way. m can

be equal to, less than, or greater than n. Usually, some

or all of the variables are restricted to be non-negative.

Linear Programming

The rinil n..pe-tus for the growth of interest in

programming problems csme in 1947 (Hadley, 1964, p. 14)

when George Dantzig devised the simplex algorithm for

solving the general linear prcgra7mming problem. If,

n
g (xl, x2, . ., xn) = a3x j = 1. ., m,
i=1

f(x ', x2' "., xn) i l ii'

where a.. and c are known constants, the progra-ming
3.12- .
problem is said to be linear provided that there are no

other restrictions except perhaps the requirement that

some or all of the variables rimst be non-negative.

- 74 -

Usually in the formulation of the general linear programming

problem, it is specified that each variable must be non-

negative, i.e.,

x. > 0, i = 1, . ., n.
1-

This form is most convenient when making numerical calcu-

lations. Thus a linear programming problem seeks to

determine non-negative values of the n variables xl, x2,

S. ., x, which satisfy the m constraints

n
i aj..x {<, =, >}b., j = 1, . ., m,
i=1 -

and which optimize the linear function

n
z = E cx..
=l

It is often convenient to express the general

linear programming problem in vector form, i.e.,

max z = cx,

n
s.t. E a.x.{ =, >}b.
i1 1 2.
i=l

c and x are n component vectors and may be represented as

C = (c c2, . ., Cn),

x = [xl, x2, . ., Xn]

c is generally referred to as the price vector and x as

the program vector.

- 75 -

a. and b are m component vectors and may be repre-

sented as

ai = [ali' a2i', ., ami],

b = [bl, b ., bm].

The a. are called activity vectors and b is generally

referred to as the requirements vector.

Linear Programming and the Portrayal of the Firm

The typical linear programming formulation is

almost identical to our modified picture of the firm.

The objective function is the linear programming formu-

lation does not contain the term -S. In other words,

there is no provision for fixed or sunk costs in the linear

programming model. It has been emphasized, however, that

fixed costs are relevant only to the decision of whether

to operate the firm or shut it down.

The linear programming activity vector is identical

to our concept of a process. It is a set of ratios among

rates of consumption of various inputs and rate of pro-

duction of various outputs. The linear programming de-

cision variables are identical to our concept of level of

a process. The program vector (vector of decision vari-

ables) is identical to our concept of an entrepreneurial

solution. The prices in the linear programming formulation

- 76 -

correspond to our net contribution values. The linear

programming constraints define our entrepreneur's sphere

of discretion.

The Simplex Process

The formal method of solution of linear program-

ming problems is not, per se, of great interest here.

It is interesting to note, however, the similarity

between the iterative mathematical solution process of

linear programming and the entrepreneurial process as

outlined by Tannenbaum and Litchfie.ld, and discussed in

Section VI.

The simplex method for the solution to linear

programming :problems is an iterative procedure which

reaches an optimal solution in a finite number of steps

or provides an indication that there is an unbounded

solution. If th. problem has an optimal solution, the

optimuwt value of z must be finite. Let us assume that

"An unbounded solution indicates a problem in which
the value of tne objective function can be made infinitely
large. Such solutions are not expected in the real world
and generally indicate a misfcrmulation of the problem.
As Gue and ThcmaFs 'to e published) have said, ". .. if
the reader is awv:are of a profit ma'.:iriization problem
where the objective function grows without bound, he
is requested to w-.rite the authors immediately with the
details of the problema."

- 77 -

the linear programming problem has been converted to the

standard form,2

max z = cx,

n
s.t. a x. = b,
i=li

x > 0.

The two following theorems can easily be proved (Hadley,

1964, p. 31).

1. If the problem has an optimal solution, at
least one basic3 feasible solution will be
optji al.

2. If we have a basic feasible solution which is
not optimal, it is possible to reach an opti-
mal basic solution in a finite number of steps
by changing just one of the basic variables
at each step, or to obtain ultimately an
indication of an unbounded solution.

2For maathematical convenience, it is advisable to
convert inequalities into qualities. This is done by the.
addition of slack and surplus variables. Stack variables
are introduced into "less than" inequalities and represent
the difference between the maximum available resource, bj.
and the amount actually used. Surplus variables are
introduced in-o "greater than" inequalities and represent
the amount by which a minimum requirement, b is exceeded.
It is also usually convenient to have all components of
the requirements vector positive. If necessary, this can
easily be accomplished by multiplying a constraint
equation by -1.

A basic solution is a solution that has no more
than m variables different from zero where m represents
the number of constraints.

- 78 -

The simplex method begins with an initial basic

feasible solution. It then computes the opportunity costs4

for all vectors (process) not in the basis. If all ex-

cluded alternatives (vectors not in the basis) have non-

positive opportunity costs, the simplex method concludes

that the present solution is optimal. If one or more of

the excluded alternatives have a positive opportunity

cost, the simplex method checks for the possibility of a

misformulated. problem (urnbcnded soj utior). If there is

no incd..cation of ar. unbcunded solution, the simplex method

chooses the excluded alternative with the largestoppor-

tunrity cost to erter thz. basis. Ths simplex method then

selects a process to be rerAcved in .uch a way as to insure

feasibility of the new solution. The procedure is then

repeated until an optimal solut-.on is reached.

There are many cases where the simplex method must

begin with a solution which contains artificial processes.

The simplex method then follows.v an iterative procedure to

remove the artificial vectors and thereby obtain a real

basic feasible solution. In some cases this will not be

possible. The simplex procedure will. indicate when a

problem is formulated so that no feasible solution may be

found. A flow chart of the simplex process is shown in

Figure 2.

A
-Actually the simplex method computes an approxi-
mation to the opportunity cost.

- 79 -

Formulate Problem

i Obtain Artificial Solution

Is There a Real (N
Feasible Solution?

_(Y__es
Obtain Initial Real
Basic Feasible Solution

Reconsider

o)

'I,, ^________
__ Compute Opportunity Costs of
All Excluded Alternatives
--__ -__ -^ -- _

Are All Opportunity ,J Yes)
Costs Non-Positive?

(No)
Is There Evidence of an Yes Unbounded
< Unbounded Solution? Solution

.(No)

Select Alternative Witn
Highest Opportunity Cost

Insure Feasibility

Reprogram So:

FIGURE 2--SCHEMATIC REPRESENTATION OF THE SIMPLEX
METHOD FOR SOLUTION OF LINEAR PROGRAMMING
PROBLEMS

timal
lution

- 80 -

Notice the similarity between the flow chart of the

simplex method and the flow chart of the entrepreneurial

process as shown in Figure 1.

The type II decisions of the entrepreneur correspond

closely to the selection of basis vectors in the simplex

method. The entrepreneur's type I decisions are reflected

in two places in the linear programming process. First in

the selection of the objective function, and second in the

selection of some components of the requirements vector.

SECTION IX

THE PORTRAYAL OF THE FIRM: AN ACCOUNTING VERSION

The typical linear programming problem is normally

formulated in such a way as to obtain computational ef-

ficiency in solving the optimizing problem under consider-

ation. If we are to focus more sharply our picture of the

firm, however, we should (for the purpose of this study)

concern ourselves less with mathematical (computational)

efficiency and more with the concepts used by an entre-

preneur in operating his business. Previously we have

stated that one view of management theory suggests that

the entrepreneur utilizes his available assets, by

operating processes, in a way which will best achieve

some predetermined objective. We stated that the various

processes of the firm include such things as manufacturing,

selling, personnel administration, accounting, ard finance.

We also noted that the assets (liabilities are negative

assets) include such things as land, plant, equipment,

inventory, accounts receivable, etc. Now we would like to

be more specific about our concepts of assets and lia-

bilities, and introduce other terms such as balance sheet,

net income, business transaction, and double-entry bookkeeping.

In short, we want to borrow some terr',s from the accountant.

- 81 -

- 82 -

Accounting furnishes a good part of the data used by manage-

ment in making decisions and directing operations. One

branch of accounting, administrative or managerial ac-

counting, is based upon the concept of accounting as a

method of management or as a tool by which managerial

effectiveness is enhanced. Thus, entrepreneurs tend to

think in an accounting framework, and the accountants are

more and more tending to utilize a framework which enhances

managerial effectiveness. We will not be content to use

the accountant's framework entirely, however, but we must

modify it to some extent so that it will correspond more

closely to our picture of the firm.

The Accountant's Balance Sheet

First let us look at a simplified version of the

accountant's balance sheet. The balance sheet contains an

inventory of the several kinds of assets to which the firm

has title and the liabilities which the firm has incurred.

Traditional accounting statement generally report assets

and liabilities at their cash value. The cash balance is

perhaps the most precise valuation on the balance sheet.

It is important mainly with respect to what can be done

with it rather than the absolute amount held at balance

sheet time. Other assets, like receivables and securities,

are reported at an exact amount expected to be realized as

- 83 -

the business continues normal operations; this amount may

be cost or a value less than cost. Inventories are held

for ultimate sale, so the dollar valuation of inventory

is the number of cost dollars expected to be recovered

from future sales. Dollars tied up in plant and facilities

must likewise be recovered as revenue dollars; the balance

sheet reflects the dollars of original outlay not yet so

recovered. Offset against these costs not yet realized

is a list of claims that must be satisfied in the future.

These, of course, are the liabilities of the firm.

Balance sheet accounts

In order to make better comparisons and judgments,

the accountant classifies the information on the balance

sheet. He groups like things together, starting with a

basic division of financial elements into assets and

liabilities, and then proceeds with common subgroups. A

few subclassifications commonly found in a balance sheet

are discussed below.

Current assets are those resources now available,

claims for payments of cash in the near future, investment

in marketable securities, and goods which are expected to

be converted to cash as a result of normal operations in

the near future. Conversion of assets is a primary

objective of management. The accountant, therefore,

attempts to report then at realizable value. Accounts

- 84 -

receivable are reviewed with the idea of reporting only

those which appear to be collectable. If expected real-

ization on inventories has fallen below historical cost,

the accounting valuation is reduced to reflect as accu-

rately as possible the probable recovery. The current

asset classification is subdivided in many ways depending

on the situation. Three subclassifications found on most

balance sheets, however, are cash, accounts receivable,

and inventory. The general inventory classification may

be divided into finished goods inventory and raw materials

inventory.

Fixed assets include both tangible property and

intangible rights which will be used for a number of

periods, or from which some benefit will be derived for

a comparatively long time. Fixed tangible assets are

sometimes grouped together into one item, plant and

equipment. More often, however, descriptive titles are

used for each type of tangible assets. Land, buildings,

and equipment are three comn.,on subclassifications found

on most balance sheets. Use is the key to classification

of fixed assets.

The accounting procedure for fixed assets provides

for some portion of cost to be deducted from the income of

each period and charged to the particular asset. The

remainder of cost appears on the balance sheet as the

- 85 -

accountant's valuation of the asset, a valuation which has

no necessary relation to the current market value of the

asset. Because this assignment of cost to periods is a

matter of judgment, the original cost of fixed assets as

well as the accumulated cost charged off are usually

separately reported on the balance sheet (or in a supporting

statement).

The assumption is usually made that the firm will

endure longer than any particular asset. The entire cost,

therefore, of all fixed assets (but no more than cost) will

be charged against the revenue of some period (or against

revenues from the sales of the asset). In a sense fixed

assets may be thought of as being reported at realizable

value, just as current assets are, but the term of real-

ization is much longer and may involve a number of future

Current liabilities are those debts which mature

in the near future and whose liquidation requires the

expenditure of current assets. In the case of both

assets and liabilities, "current" normally refers to the

next operating cycle. Accounts payable to trade creditors,

notes payable to financial institutions, accrued wages,

accrued taxes, etc., make up the current liabilities.

Fixed liabilities, sometimes called long-term debt,

are those liabilities which nature sometime in the future

- 86 -

(beyond the current period). That part of long-term debt

which falls due within the current period is normally

reclassified as a current liability unless some provision

has been made to repay (or refund) the debt without a drain

on current assets.

Owner's equity is normally reported without regard

to individual owners but classified by nature and source

of capital. Capital invested by the owners is reported

under two headings: par or stated value of the shares

issued is reported as capital stock, the excess of the

investment over par or stated value of the shares is

reported as paid-in or capital surplus. The increase in

equity resulting from profitable operations and not

distributed to stockholders is reported as retained

earnings.

A typical balance sheet is shown in Table 1.

Next let us consider the concept of a business

transaction. When the business firm enters into a trans-

action with other entities, the kind of property owned,

or the amount and nature of debts or money obligations,

or the owners' equity is changed. A transaction is an

exchange of things having monetary value. Many trans-

actions involve an outside party, but transactions can

- 87 -

TABLE 1--HYPOTHETICAL BALANCE SHEET

Account
Number Account Name Valuation

101
102
103
104

121
122
122a
123
123a

Total liabilities:

Current assets:
Cash
Accounts receivable
Inventory (finished goods)
Inventory (raw materials)

Fixed assets:
Land
Building
Accumulated depreciation
Equipment
Accumulated depreciation

Total assets:

Current liabilities:
Accounts payable
Accrued wages
Accrued taxes

Long-term debt:
Bonds payable

Stockholders' equity:
Common stock
Retained earnings

Balance

20,000
100,000
100,000
60,000
280,000

50,000
100,000
(40,000)
122,000
(60,000)
172,000

452,000

50,000
10,000
4,000
64,000

100,000
100,000

240,000
48,000
288,000

452,000

201
202
203

22]

301
302

Source: See Section IX, The Accountant's
Sheet, for source and explanation of data.

--

- 88 -

occur solely within the firm. Any transaction affects two

or more accounting elements within the firm. For our

purposes, the minimum necessary requirements for a trans-

action is that it requires a "double-entry" by the firm's

accountant. A proprietor's investment of money in the

business, for example, is a transaction between the firm

and the owner. The effect on the firm is to increase its

assets and its capital by the same amount. The consumption

of fuel oil in the office furnace is likewise a transaction.

Its effect is to diminish the assets of the firm and

substitute an expense of equal amount. The sale of a

product is still another transaction. Its effect might

be to increase accounts receivable and reduce finished

goods inventory by the same amount. A transaction of

"collection" might then decrease accounts receivable and

increase cash.

We have noted that any transaction affects two or

more accounting elements (or simply accounts) within the

firm. The balance sheet entries previously defined are

accounting elements. The most important objective of

accounting, from a financial viewpoint, is the measurement

of business income or profit. This purpose requires-that

revenues (incomes) and costs (expenses) be accounted for.

Revenue accounts are broken down to show nature of revenue

(sales, interest, etc.), source of revenue by product, or

- 89 -

to any other extent which may be useful to management.

Cost accounts are usually separated by nature of expendi-

ture.

Process illustrations

Table 2 illustrates the concept of a transaction

(although not in the nice debit and credit form normally

used by accountants). Six typical transactions are

illustrated as follows:

1. Manufacturing of one unit of a product. The
firm converts raw materials, equipment (per-
unit depreciation is assumed), and labor into
finished goods inventory. Inventory is valued
at cost, therefore final goods inventory is
increased by $70. Raw material inventory is decreased by$40, and the value of fixed
equipment is decreased by $5. The firm has also incurred labor expenses of$25 (which
have not yet been paid).

2. Selling one unit of product. The firm has sold
a unit of finished goods inventory for $100 on credit. Accounts receivable have increased by$100, final goods inventory has been decreased
by $70. The firm has received$100 of revenue
from sales and the cost of goods sold was $70. 3. Collection. The firm has converted accounts receivable into cash. 4. Payments. The firm has paid the wages for part of the labor it utilized in production. 5. Purchases. The firm has purchased (for cash) additional raw materials so that additional product can be made. For convenience, the chart of accounts in Table 2 has been abbreviated. - 90 - 00 o r- r- I H 00 LI I I U-IJ 0rd 4 d 4- Hd 0 0 >C) C) C OJ 4->1 () .)Q -4 St0- 'd C)- o0 u 03 4<0 n r-I C(Nn q CN o 0 00 C). (N r-i r- -A r-! H-- HNHH H rA HNC r4 --I .0 "- i:1 c C) ,- 0 C, NNl N c M n -V I L) LO Q) C) aCa () 0 >> Cj 0 (3 4- cno - 91 - 6. General and administrative expense. The firm has paid for general and administrative ex- penses which it used throughout the period under consideration. The concept of a transaction is very similar to the concept of a process previously defined, and may be thought of as such. It is a set of ratios among rates of con- sumption of various inputs and rates of production of various outputs. Indeed, we would like to think of a process in terms of a financial transaction. We have noted that processes are the alternatives from which entrepreneurs must choose in the decision-making process, and as Brown (1958, p. 101) has said, "All (business) decisions are financial decisions." Brown justifies his statement this way: All decisions are financial, either because they directly affect the expenditure of money, or because they indirectly affect expenditures by consuming or disposing of effort, facilities, or material, all of which cost money. A decision to improve toilet and locker facilities nmy begin from a proper concern for the health and comfort of employees, but it requires an expenditure, and every expenditure af- fects the earnings of the enterprise. All decisions are financial because you cannot conceive of one that does not affect, in one way or another, and in some degree, the earnings of the enterprise. . to these decisions, the engineer, the pro- duction man, the merchandiser, and perhaps others, must all contribute. What they contribute are facts-- the facts that each is skilled to obtain. To the facts so contributed, moreover, someone must apply reason--intelligence--so as to give them their proper weight, evaluate them, and relate them properly to each other. This is the material--the foundation--of decision. This is the financial approach. - 92 - . each of these men has a primary operating function, but each must approach that function with a financial viewpoint because his decision will af- fect the earnings of the enterprise. In that sense, each is a financial man. Let us assume that the ratios shown in Table 2 represent the respective processes when they are being operated at the unit level. For example, if process 4 is operated at a level of 10, the finished goods inventory will be increased by$700, raw materials inventory will

be decreased by $400, etc. Mathematical notation It is convenient at this point to reintroduce some mathematical notation. Suppose we assign a number j to each of the firm's accounts and assume that i takes on integer values from 1 to w*. We will then group the accounts so that as j varies as shown below, the following type of accounts will be assigned the number represented by j. Current assets 1 5 j < P* Fixed assets p* + 1 i j 5 q* Current liabilities q* + 1 < j < r* Long-term debt r* + 1 < j < s* Owners' equity s* + 1 < j < t* Revenues t* + 1 < j < u* Expenses u* + 1 < j < w* 1 < p* < q* < r* < S* < t* < u* < w% Full Text PAGE 1 AN ENTREPRENEURIAL DISCRETION MODEL: THEORY AND IMPLEMENTATION By FRANK SHERMAN MCLAUGHLIN, JR. A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PAKTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA August, 1967 PAGE 2 ACKNOWLEDGMENTS The author would hava never been in a position to begin, or complete this docuinent if he had not received assistance, advice, and help from iriimy people. Unfortunately, it is irapossible to list, in this short space, all of those whora the author would like to thank. It is only possible to say, that for a].l this k.indness, the author is exceedingly grateful. Special thanks should go to three groups of people who played an especially significant role in the preparation of this dissertation. The inarnber^ of the author's supervisory coii'iaittee , Dr. W. V. Wilmot, Jr. (Chairman), Dr. E. L. Jackson, Dr. R. L, Lassiter, and Dr M. E. Thcma; gave invaluable assistance. Mr. James VJ. Sikes, President of Florida Tile Industries, Inc., and other members of management at Florida Tile provided resources, assistance, and information without which tiiis doccument could not have hee.n written. Mrs. Carolyn Lyons assisted the author i.n many v;ays , most particularly in the firal preparation of this dissertation. PAGE 3 TABLE OF CONTENTS Page ACKNOWLEDGMENTS ..... ... ii LIST OF TABLES vi LIST OF FIGURES viii Sec Lion I. INTRODUCTION . 1 'flan of This Study 1 Bast J Definition.'; and Aesump tione .... 4 II. A SIMPLE PORTFiAYAL OF THE FIRM: THE TRADITIONAL APPROACH 11 The OhQeative Function 11 Th?, Production Function 12 The Ent-:>eTpx^sneuvia'L Solution 14 Concepts from Economic Theory 16 C-ptimizing Relationships in the Entrepveneurio.l Solution 19 III. THE QUESTION OF MULTIPLE OBJECTIVES 24 A. Review of the Question 24 The Relationship to Fsycholog ioo.l Theories 28 The Effect of Satisficing Constraints . , 35 A.n Assumption .About the OhQsctive FuAiction 38 IV. THE FIR-M AND ITS MARKETS 41 A Uisoussion of the Basic Assimvtion ... 41 Oligopoly and Price Stability 4 3 Sales Constraints in the Porvrayal of the Firm 4 6 PAGE 4 TABLE OF CONTENTS' -Con tinii^^a Section Page V. A RESTATEMENT OF THE PORTRAYAL OF THE FII^I 48 A Re-vised EntvQ-preneurial Solution .... 49 Ramifications of the Revised Entrepreneurial Solution 50 VI. THE ENTREPRENEUR JiND THE ENTREPRENEURIAL PROCESS ..... 52 The Entrepreneur 52 The Entrepreneurial Process 54 The Iterative Nature of the Entrepreneurial Process 60 VII. A REEVALUATION OF THE PRODUCTION FUNCTION . . 64 The Concept of a Process 65 Processes and the Production Function . . 69 Processes and the Cbjecv-ive Function ... 70 VIII. THE RELATIONSHIP BETWEEN THE PORTP^^YAL OF THE FIRD4 AND K^THEI'lATICAL PR0GRAMI4ING . . 7 2 The General Programming Problem 7 2 Linear Prcgraw.ming 73 Linear Pi'ogramming and the Portrayal of the Firm 7 5 The Simplex Process 76 IX. THE PORTPA.YAL OF THE FIRM: AN ACCOUNTING VERSION 8 J. The Accountant ' s Balance Sheet ...... 82 Business Transactions . 86 Business Income ' 9 3 X. THE PORTRAYAL CF THE FIRM: A MODIFIED ACCOUNTING VERSION .... 97 The Entrepreneurial Balance Sheet .... 97 /i Modified Concept of Processes 101 A Modified Form of Business Income .... 106 PAGE 5 TABLE OF CONTENTS Â— Continued Section Page XI. THE PORTRfvYAL OF THE FIRM: A PARTIAL MATHEMATICAL FORMULATION 110 Survival Constraints 112 Satisfactory Profit Constraints 116 Sales Constraints 119 Direct Production Constraints 120 Corporate Image Constraints 12 3 Review and Summary 124 XII. IMPLEMENTATION: THE PORTRAYAL OF THE FIFuM . 127 The Firm Chosen for tr.e Implementing Study 127 Data Collection and Presentation 12 8 XIII. IMPLEMENTATION: A COMPARISON OF AN ACTUAL AND AN OPTIMAL ENTREPRENEURIAL SOLUTION 165 The Two Solutions 165 Duality Theory 172 Com.parison of the Actual and Optimal Solutions 188 Economic Activity in the Mono-periodic Period Chosen for Analysis 196 The Opportunity Costs of Excluded. Alternatives ....... 197 XIV. COM.MENTS OF THE PRESENTATION , 2 00 The Model Presented 200 Modifications of the Model Presented . . . 202 A SELECTED BIBLIOGRAPHY 2 07 BIOGPAPHICAL SKETCH 213 PAGE 6 LIST OF TABLES Table Page 1. Hypothetical Balance Sheet S7 2. Hypothetical Process Illustrations . 90 3. Hypothetical Entrepreneurial Balance Sheet , . 102 4. Hypothetical Entrepreneurial Process Illustrations 103 5. Beginning of Period Entrepreneurial Balance Sheet ..... 129 6. Key to Process Numbers 132 ?. Manufacturing Processes . 135 8. Selling Processes 142 9. Purchasing Processes 145 10. Finance Processes 146 11. General and Administrative Processes ..... 150 12. Constraints Defining the Entrepreneurial Sphere of Discretion ........... 153 13. Actual Entrepreneurial Solution 166 14. Actual End of Period EntrepiÂ€nour_al Balance Sheet 16 9 15. Optimal Entrepreneurial Solution 173 16. Optimal End of Period Lntreprcneurial Balance Sheet 176 17. Optimal Dual Variables Associated with Constraints Defining the Entrepreneurial Sphere of Discretion 182 PAGE 7 LIST OF TABLES Â— Continued Table Page 18. Net Contribution Values Associated with Manufacturing and Selling Processes .... 184 19. Profit Losses in Subproblera I 191 20. Profit Losses in Subproblem II 192 21. Profit Losses in Subproblem III 194 22. Profit Losses in Subproblem IV 155 23. Optimal Dual Variables Associated with Processes Omitted from the Optimal Entrepreneurial Solution 198 PAGE 8 LIST OF FIGURES Figure Page 1. Schematic Representation of the Entrepreneurial Process , . . . 63 2. Schematic Representation of the Siirplsx Method for Solution of Linear Programming Problems 79 PAGE 9 SECTION I INTRODUCTION There are many ways of describing a business firm. Sorae d~;scriptions are very simple, others extremely complex. The simiplest portrayal of a business firm consisus of three parts; an entrepreneur, an objective function , and a production function. There are three major pares of this study. The first part is primarily concerned with modifying the simple portrayal of the firm in order to obtain a more realistic and workable m^odel. The second part provides the background into which the portrayal should be set. The last part is an im.plementing section and is presented to show that the developed portrayal is realistic and is workable. Flan of This Study The first part of this study reviews the simple portrayal of the firm, and, then, using a stepwise procedure, modifies this simple portrayal until a more realistic and more workable model is obtained. Emphasis is placed upon the entrepreneur and the entrepreneurial process. The portrayal, therefore, is a managem.ent portrayal. A major deficiency in the simple three-part portrayal is t] PAGE 10 2 firm strives to optimize. Most fir^ns have many objectives. This study follows the thoughts of Simon (1959) that most objectives are "satisf icing" rather than ''optimizing" objectives. Furthermore, there seems to be a relationship between corporate objectives and the hierarchy of needs which serve as motivators of hum.an action. Section III is offered to illustrate hov/ the simple firm po]:trayal can be modified to incorporate these mulriple objectives of the firm. The simple portrayal of the firm is often criticized for its assumptions about the markets in which the firm operates, and for its assumption about the prices the firm pays for input factors and the prices the firm receives for its outputs. Section IV questions these assumptions, and attempts to determine which assumptions are sufficiently realistic to be included in a v/orkable portrayal, and which assumptions must be modified. The necessary modifications are made and are incorporated into the developing portrayal. As noted earlier, emphasis is placed upon developing a managem.ent portrayal of the firm. The simple portrayal includes an "omniscient power" which manipulates the variables in the production function and the objective function is an optimal manner. In order for the portrayal to be more correct, a more realistic concept of an entrepreneur must be presented. Section VI presents a concept of the PAGE 11 3 entrepreneur and the entrepreneurial process which is more realistic and workable, 5.nd which fits v/el2 into the developing portrayal of the firm. The production function is the last part of the simple portrayal of the firm to be modified. Section VII redefines the production function, giving consideration to the entrepreneurial process presented in Section VI, the multiple objectives considered in Section III, and the marketing considerations of Section IV. This modified concept of a production function is more realistic than the concept cf a production function used m the simple portrayal of the firm. This modified concept also fits well into the developing portrayal of the firm.. The next four sections are concerned with the background into v;hich the portrayal should be set. Section VIII emphasizes the relationship between m.athematical prograrrLTP.ing and che modified picture of the firm. Section IX and Section X show hew the portrayal can be set into a modified accounting framcv/crk. These sections also show the compatibility of tne modified accounting framev.'ork, the modified portrayal of the firm, and mathen'laticcx programming. Section XI is concerned wiLh a partial tneoretical formulation of the. portrayal in cerms of the concepts previously presented. PAGE 12 4 Although this dissertation is primarily concerned with the conceptual presentation, it was thought that significance would be added to the presentation if an implementing study was made. The remaining part of this study is devoted to this implementing study. Section XII describes the firm using the concepts presented in the study. Section XIII compares an actual and an optimal entrepreneurial solution. Section XIV is primarily devoted to review, summary, and general comments, Basic Definiticns aiid Assumptions Before beginning the main work in this study, it would probably be v/ise to introduce some basic definitions and assumptions. Many definitions and many assumptions will be modified later. Attempts will also be made to justify some assumptions made here. For the moment, the rec-ider i.s asked to accept the definitions and assumptions made. V^e must begin som.ewhere. and this is how we choose to begin. Produation may be defined as the process of cortib'ining and coordinating m.aterials and resources in the creat.ion of some valuable good or service. We do not limit the definition of production to the purely technical process of turning raw materials into finished products. Rather we accept such functions as accounting, sales and PAGE 13 5 personnel administration to be integral parts of the production process. Our definition is not so broad, however, as to include intangible items such as corporate image or community relations. Any production process will consist of two parts, the inputs and the outputs. The output of a production process may be thought of as aggregates or sums of physical materials or resources. The.<^e materials and resources are the inputs or factor services of the production process. Thus production converts inputs into outputs. The term input and output must be envisioned with reference to the process, since a good or service which is an output from one production process may be the input to another. The inputs and outputs of the production process should be thought of as time flows of physical quantities. They may be hours of labor, kilowatts of electricity, or tons of fertilizer per year. The production process represents the transformation of input flows into ouput flows. Economic theorists generally concern themselves with two types of productive services; those which vary with output and those which do not vary with the amount of output produced. These two types of services are generally referred to as variable and fixed factors of production. Raw materials and direct labor are often examples of PAGE 14 6 variable factors, while the services of a building may be thought of as a fixed factor. The distinguishing characteristic between fixed and variable factors is not the technical feasibility of varying the factor, but r^th^r it is chc degree of variability of costs associated with utilizing this factor. Direct labor is normally thought of as being a variable cost; however if a guaranteed work week, contract is in effect, direct labor may well be a fixed factor of production. To begin with, we shall assume that the firm possesses some factors of production which are fixed in quantity. The cost of these factors does not vary with the amount of output. We shall assume that the firm also utilizes some variable factors of production. The cost of these factors will vary with output. In practice, a sharp dividing line seldom exists between fixed and variable productive services. Fixed services are generally only fixed within some limits of output variation. When output increases beyond these limits, some so-called fixed productive services may have to be increased, while some may remiain fixed. We shall define the term business firm to be a single productive unit. It m.ay have m.any inputs and many outputs, but there must be scm.e interrelationship between the inputs and the outpurs . The firm is a total economic PAGE 15 unit under the control of just one "pov/er." We shall call this "pov/er" the sntrepi'eneuv . Thus the entrepreneur manages the business firm. The firm is the total economic unit over which the entrepreneur has financial control. It is the unit for v/hich he calculates his profit and his loss. For our purposes, there is no need to distinguish between management and ownership. We can assume that the entrepreneur is both the m.anager and the owner. Another assumption made is that the firm's production activity is arranged so that production in one time period is independent of the production in preceding and subsequent periods. The assumption is that the firrfi is interested in the activity of only one time period and that this activity is determined exclusively by conditions prevailing in that period and is independent of any otherset of conditions. Follov\?ing Carlson (1956), we shall refer to this as r.iono-peri-odic production . iMono-periodic prodaction imp.lies that production starts on a given date and ends at another date v/hen the output is sold on the market. The time interval between the two dates represent.the period under consideration. In reality, it is impossible for a firm to arrange its operations so that production in one tirae period is independent of conditions in preceding and subsequent perj.ods. The assumiption of a mono-periodic production PAGE 16 period is, however, used extensively in economic literature to illustrate the optiir.izing procedures of a business firra. It should be remerriDered that such procedures are actually concerned wixih suboptiir.ization rather than optiraisation , even though they are often rererrea uo ^as in this suuay) as optimizing techniques. A true optimizing procedure would have to consider conditions prevailing in the period under consideration as well as conditions in preceding and subsequent periods. Demand conditions for final goods and services inform the entrepreneur about products that can be sold on the market. To the entrepreneur, demand appears as a series of possible price-quantity combinations which depend on prevailing market conditions and the firm's position in the market. To begin, we shall assume that the demand condition faced by the firm, is essentially that of pure competition. The price a firmi receives for any output has been predetermined by market forces. This price must be accepted by the firm, as a predetermined parameter. It is not a variable which can be manipulated by the entrepreneur. Pure com.petition im.plies that a firm may sell as much as it wants of any given product at the predetermined price. Later we shall m.odify this assum.ption. As we shall show later, the assum.ption of a predetermined price is not PAGE 17 9 a great departure from reality. The assumption that the firm may sell an infinite quantity is, hov/ever , a major departure from reality and must be modified later. The supply of productive services, like the demand, will appear to the entrepreneur as a series of pricequantity combinations. For our purposes, however, we will again assume conditions which are essentially those of pure com.petition. The firm cannot influence the price by the quantity it takes. The factor prices are predetermined. Fixed factors of production are in the possession of the entrepreneur at the beginning of the mono-periodic production period. The cost of these factors is, in effect, sunk and cannot be varied. The technical knowledge of the firm will be assum.ed to be fixed. Technical knowledge informs the entrepreneur of how a given output can be produced. Quite often there will be many (perhaps an infinite number) v;ays of combining inputs to obtain a desired output. It is the av/areness of these different possible combinations which is known as technical knowledge or state of technology. It is this degree of awareness that is assumed not to change during the mono-periodic production period. Finally, let us assume that the entrepreneur would like to maximize his total net return for the period under consideration. The validity of this assumption is highly PAGE 18 10 questionable. Most entrepreneurs however, seem to maneuver toward some goal. The assuniption that they tend to optimize their profit position gives us a good place to start. It will be modified later. In optimizing, the entrepreneur must concern himself with two broad types of problems. The first type is the purely technical problem of production. This type of problems pertains to the state of technology. It is concerned v/i.th the quantitative relation between inputs and outputs. The second type of problems are cost problems of production. These problems assume a given state cf technical knov/lcdge. They are concerned v;ith the relation betv.'een the costs of different inputs and the value of different outputs. It is with this second type of problem that we will be prim.arily concerned in this study. PAGE 19 SECTION II A SIMPLE PORTRAYAL OF THE FIRM: THE TRADITIONAL APPROACH The simplest portrayal of a busiriess firm consists of three parts: an entrepreneur, an objective function, and a production function. The entrepreneur is assumed to be the sole manager and proprietor of the business firm. The entrepreneur makes all decisions in the firm. Thus he manipulates the variables in the objective function and the production function in an attempt to achieve soniC objective. This objective is normally assumed to be profit maximization. The Objective Funotion The term objective function has made its way into economic and management literature primarily by the route of mathematical programming. The concept implies that a predetermined objective (for example, profit raaximization) does exist. Furthermore, it assumes that the entrepreneur is fully aware of certain conditions such as demand for final products and supply of factor services. Unfortunately in problems involving more than a few aspects of the managing of a complex organization, it becomes most difficult to describe the objective function. As the complexity 11 PAGE 20 12 of the organization grows, and as multiple goals are taken into account, the so called objective function becomes more and more subjective and less quantitative. If we use the simplified conditions assumed in Section I, we can easily represent the firm's objective function mathematically, n m P= Zp.x. Zw.y.-S. i=l ^ ^ j = l ^^ This is the firm's objective f unction--the function which the entrepreneur would like to maximize. It is also the firm's profit function, thus the implication that the firm would like to maximize profits. p. is the constant price at which output i can be sold. w. is the constant price at which input j can be bought. y. represents the extent of utilization of input j and x. represents the level or rate at v/hich output i is produced. S represents the fixed or sunk costs which must be paid by the firm regardless of the rate of output. The Production Function We have assumed that a firm possesses a given amount of certain fixed factors of production. These factors, together with the state of technology, impose a set of technical relations which govern the possible transformation PAGE 21 13 of inputs into ouuputs. This relationship is the firm's production function. The production funcuion may be convenien-cly expressed in mathematical form, writing output as a function of input, -"^^1' -^2 ^n' = ^^^1' ^2' Â• Â• Â•' VThe production function is always defined in relation to a given set of fixed factors of production. Furthermore -che production function is defined to yield the maximum product obtainable from any specific combinations of input factors, given an existing state of technology. It is best to visualize the production function as defining a number of constraints within which the firm must operate. As such, the produccion function is a boundary relationship which indicates the present lim.its of the firm's production possibilo-ties . This relationship states that a firm cannot achieve a higher rate of output without using more inpurs , and that fewer inputs cannot be used without decreasing the rate of output. The production function indicates the manner in which the firm can substitute inputs without varying the amount of output, and also ^An alternate representation of the production )n is given by G.. (y, v., . . ., yÂ„) , PAGE 22 the way in which the firm can substitute one output for another without altering its total usage of inputs. The production function represents only technically efficient operations by the firm. If a firni is not operating on its production function, then by shifting its operations to the production function, it can produce its present output with a srr>aller volume of inputs , it can use its present inputs to produce a larger volume of one or more outputs. If a firm wants to maximize profits, its operating possibilities are constrained to points on the production function. The EntTepreneui-'ial Solution To complete our simple picture of the firm, it is only necessary to show how the entrepreneur will attempt to manipulate the variables under his control so as to obtain the maximum am.ount of profit v;hich the cons-crainus of the production function will allow. Xathem.atically , the problem is easily solved using the Lagrange multiplier technique for solutions to constrained maximdzation problem.s . In practice, as we shall see later, the problem is never so easy. Nevertheless, we shall proceed with the miathemiatical solution for two reasons. First, it should provide the entrepreneur with an indication as to how to maximize. It should point him in the right direction. Second, we will be able to define PAGE 23 15 more clearly the relationship between this opti?aization problem and sorae concepts of traditional economic theory. The Lagrange runction may be expressed as n m L = I p X, I v/^y^ Â£ -r alFCXw . . Â•/ ^-Â„) G(y^ y^_^)]. Invoking the necessary conditions for a maximum, we find. BL/c x^ = Pi + X(3F/Sx^) =G, i = l, ...,n, BL/o V . = w. X(oG/cy.) =3, j = l, . . .,ir., J J J SL/oA = ?(x^, . . ., xÂ„) = G(y^, . . ' f Y^) ' Rearranging the above equations, we obtain, (d?/ox^)/p^ = . . ., = (o?/ox^Â„^)/p^ = . . ., = (oG/ay, )/w^= . . ., = (oG/oy.Â„)/w_^ = 1/X. We have m -in + 1 independent equations in m + n + 1 unknowns. Theoretically, this system of equations can be solved for the values of the variables which maximize the firm's profit position. It is implicitly assumed that the maxim>um. value of P is not less than -S. If P is less 2 Â•rhe implicit assumption here is that the functions F and G are continuous and dif ferentiable . PAGE 24 tr.an -B, ;_n.en the optiir.al solution'^ for che firiri v;ould be to shut down irs operations, therefore making P = -Â£. The matheniatical solu-cion to the sta-ced problem i. nice, but in its ir.atheraatical form it does little to describs what relationships the entrepreneur v;ill strive to obtain in his quest for optimization. Before attempting to describe these relationships , it would probably be v.'ise to introduce some concepts from, econom.ic theory. Concepts from Economic Theory The lau of diminishing returns is a frequently quoted general econom.ic principle. The law states that as equal increm.ants of one input are added, while other inputs are held at a constant level, then beyond some point the resulting increm.ents of output will decrease, i.e., the miarginal product will dim.inish. The law holds equally well when a numier of variable facrors are increased in their most optimum proportions while other factors are held at a fixed level. The law of dim.inishing returns assumes a given state of technical knowledge. It says nothing about the effect 3j-t is im.portant to point out here that S, the fixed or overhead costs of the firm, should only be used in determining whether the firm should operate or shut down. Beyond this, S plays no part in the production decisions of a firm which sells in a com;oetitivo market. PAGE 25 17 of adding units of any one input factor, holding the other f actors constant, when the technological processes are also being changed. Also, there must be at least one fixed facT^or of production. The law of diminishing returns does not apply to a process in which all factors are variable. It also must be possible to vary the proportions in which the different input factors are combined. The law of diminishing returns is an empirical generalization. In most production processes v/hich we can observe in the real v/orld the law of diminishing returns seems to hold. The law of diminishing returns implies the existence of diminishing returns in some parts of the production function. It does not, however, rule out the possibility of leaving increasing returns in other areas of the production function. When the ratio of variable factors to fixed factors is small, it is quite possible to be in a region of increasing marginal returns. As the proportion of variable factors is increased in relation to the fixed factors, we would expect to enter eventually a region of decreasing marginal returns. The proportion cf variable factors could be increased to such an extent that total returns raay actually diminish. It is obvious from the above discussion that the necessary conditions for a maxim.um are not also sufficient conditions. In ord^r to insure that PAGE 26 a point obtained by the use of these equations is indeed a maximum, second order conditions must be investigated. Excellent discussions of second order conditions are given by Hancock (1960), Hadley (1964), and Gue and Thomas (to be published) . Marginal "product ^ valm of the marginal product ^ marginal cost, marginal rate of product transformation, and marginal rate of substitution are terms which also abound in economic literature. We shall define dG/cy., as the marginal product of input j. OG/oy. can be interpreted as an index of the marginal increase in total output resulting from a small increase in input j . dF/ox. can best be interpreted as an index of the marginal increase in inputs required to produce a sm.all increase of output i. From these definitions, it is easy to show that -X(c;G/'dy.) is the value of the m.arginal product resulting from a change in any one input. n TR(total revenue) = T, p^.x., i=l " n dTR = L p.dx. , n m Z (dF/ox. )dx. = I (oG/Â£y.)dv. i-1 ^ ^ j-1 ^ ^ dy^^ = 0, if k ?-' j, _i I'l dy. = (SG/Sy.) Z OF/Sx.)dx., 3 i-1 ^ ^ PAGE 27 19 dy. = (SG/^y ) E (p /X)dx. , -Â• -^ i-1 ^ ^ n n dTR/dy. = [ Z p . dx . / E p . dx . ] {-X ) ( dG/oy . ) , ^ i-1 -^ ^ i-1 ^ ^ J dTR/dy . X ( SG/S y . ) . Likev.'iEe, X ( ijF/a x . ) is the marginal cost resu] ting from a change in any one output. We shall define the m.arginal rate of substitution as the rate at which one input can be substituted for another while maintaining all outputs and all other inputs at a constant leve]. . Thus, the marginal rate of substitution betv/een inputs k and t may be defined mathem.atically as dy,/dy . The marginal rate of product transformation is the rate at which one output may be substituted for another, wlxile maintaining all inputs and all other outputs at a constant level. Using these definitions and the mathematical relationships previously derived, we can make several statements about the inputs to our optimal production process. Optimizing Relationships in the Entrepreneurial Solution The entrepreneur v.'ill attempt to operate so that the marginal product of the last unit of m.oney spent of each input will be equal for every input, (BG/3yj)A.'^ . . ., (9G/by.)w. . (6G/dy^)/w^. PAGE 28 20 The entrepreneur will attempt to utilize all inputs in such a manner that the value of their marginal product equals their market price, A(SG/6y.) w. , j = 1, . . ., m. The entrepreneur will attempt to operate in such a way that the marginal rate of substitution between every pair of inputs, holding al] other inputs and outputs constant, is numerically equal to the inverse ratio of the input prices, |dy^/dy^| = w^/Wj^, all k, t, This is shown below. n I (SF/ox i-1 ' PAGE 29 21 The entrepreneur will attempt to produce each output in such a manner that its selling price equals its marginal cost, X(SF/dx^) = p^, i = 1, . . , , n. The entrepreneur will attempt to operate in such a way that the rate of product transf orniation between every pair of outputs, holding all other outputs and inputs constant, is numerically equal to the inverse ratio of their prices, Idy^^/dy^l = P,./F^. Again following the same line of analysis, v/e can make the following statements aboui the relationship between inputs and outputs. In the optimal solution, the marginal value received from the last unit of input must be equal for every output, p^(aF/Bx^) . . ., p^/OF/dx^) . . ., py (oF/dx^) . In the optimal solution, the rate ar which any input should be transformed in-co any output, holdi.ng all other inputs and outputs constant, is equal to the inverse ratio of their prices, PAGE 30 22 dx^/dy. w^/p^, all i, j. This is shov/n below. dx^/dy^ = OG/ay.)/(3F/dx^), dx^/dy^ = w^/p^. In a few short pages, we have prescribed to the entrepreneur of our simple firm the procedure which he should follow in order to obtain the '"rnosffrom his scarce resources. The theory is fine; without it the entrepreneur would, perhaps, l?ck the direction in which .to move. There are, however, two major weaknesses in wPiat we have done. First we have oversimplified the picture of our firm. In fact, in our effort to simplify we have made some questionable assumptions about the firm's behavior. These will be discussed later. In the second place, theory alone is not enough. Tools mv;st be developed (and existing tools must be utilized) to aid the entrepreneur in obtaining the most efficient utilization of his scarce resources . There is, of course, nothing new about the preceding analysis. This is the type of analysis that classical econom.ist have traditionally used to describe the firm. It has often been criticized because it tends to be more PAGE 31 of a narrative description rather than an iraplemanting tool. In defense, it should be noted that the classical economists did not greatly concern ther:.selves with the in-.plementation of the theory they had developed. '2he economist accepted the production function as a description of the technological condition of production, and they accepted no direct responsibility for deriving it. The problem of efficiency was generally thought of as falling into the domain of the scientist or engineer. A primary aim of economic theorists has been to understand business behavior rather than to make recommendations to business men. Economiic theory, in effect, describes what a rational individual, who is well versed in decision-making, would do in his economic activities. -'^.e assum.ption of an optimal production function is im.portant to the economist because it helps him understand the behavior of business men, consumers, and other members of the economy. Business knowledge and experience does allov7 buyers and sellers to arrive at decisions v/hich come close to being optimal. Furthermore, competition often eliminates firm>s whose decision-making is consistently poor. Thus, the assumption of an optimal producuicn functioi is somewhat valid, and to the extent that it is valid, economic theory serves as a relatively good description of economic behavior. PAGE 32 SECTION III THE QUESTION OF MULTIPLE OBJECTIVES Perhaps the most important criticism of our simple picture of the firm is that a typical firm does not possess just one objective function, but instead has many purposes and goals. In fact, if one goal could be selected as the paramount objective it is sometim.es questioned if this goal would be profit maximization. A Review of the Question Baumol (1959) insists that consulting experience has shown him that firms attempt to maximize sales subject to a profit constraint. He believes that firms will attempt to sell as much (in term;of monetary revenue) as possible as long as a reasonable profit is made. Shubik (196J. , p. 360) in a survey of tv/enty-five large corporations notes that such terms as "fair share, fair return, equitable wages, fair treatment, and proper return to investmiOnt" are often stated as company objectives. Shubik (1961, p. 366) notes that a firm, may often m.ake a statem.ent such as, "we wish, to maximize profits and market share." It is quite possible that these two items may be negatively correlated through the effect of 24 PAGE 33 25 independent variables. In this case, the cost of sales effort necessary to increase market shares may decrease profits. In some situations, however, the correlation between the factors which control the values of the stated goals of the firm may be sufficiently close to unity so that the maximization of one value maximizes the value of another (to a good approximation) . Peter Drucker (1954, p. 46) claims that "the guiding principle of business economics is not the maximi'-iation of profits; it is the avoidance of loss." To carry this reasoning one step further, survival of the firm must be considered as a paramount objective. The firm, as a social and economic organization, like may other organism.s, has a compelling urge to survive. The motive to survive is probably more fundam.ental than the profit motive; it is implicit in most decisions v/ithj.n the firRL. In the long run a firm, that survives will make a positive profit. However, a firm that maxim.izes profits might not survive. Obviously, sufficiently large losses will bankrupt a firm. It is also possible to be a profitable firm, but becouse of inadequate liquidity, etc., not to survive. Thus the goal of survival may take precedence over all other objectives of the firm. In the short run, all positive profit may have to be sacrificed to permit survival . PAGE 34 26 Many entrepreneurs believe the key to survival lies in sound financial management. Financial management includes a variety of goals which can be generalized by stating that the financial requirem.ents of all possible future conditions of the firm should be met adequately. No firm can realize this objective completely; to prepare for one contingency adequately often limits a firm's ability to meet other situations. For instance, the relative amount of debt and equity financing should be determined on the basis of the worst possible earnings position which can reasonably be expected within the firm's economic horizon. Some of the major types of financial limitations would be the maximumi am.ount of short-term or long-term debt, the minimum ratio of current assets to fixed assets, the maximum amount of inventory or receivables in relation to sales, and the minimum level of working capital. In addition to these basic relationships, fin^ncial management makes use of a wide variety of com.parisons and ratios between the major components of the balance sheet and income statement. All these financial yardsticks can be applied as constraints in the solution of any nonfi.nancial problem, of the firm. Occasionally, in the short run, a financial objective may take precedence over all other objectives. PAGE 35 27 The liquidity position of the firm can be of prime importance and at times might be crucial. Whij.e cash is the only truly liquid asset, most firms regard receivables as liquid assets. The firm might want to maximize cash and receivables as a percentage of other total assets. Other financial ratios or relationships might be optimized in a sim.ilar manner. The creation and maintenance of corporate images plays an important role in the modern firm. Several types of images are of significance. Ultimately, all decisions result from some sort of image in the mind of the decisionmaker. However, this iraage is partially a reflection of what the decision-maker thinks is the image of his firm and its products that is held by various other groups. These groups include customers, employees, competitors, stockholders, suppliers, governm.ent officials, and the general public. Decisions result not from the actual images held by these groups but by what managers think these iniages are. The reaction of management to the images of various groups is not a passive one because it is generally recognized that a firm.'s actions can and do influence these images. Depending upon the group involved, varxous types of images may be considered desirable by a firm. A desirabJ.e consumer image might include such aspects as PAGE 36 28 service, quality of products, fairness of price, leadership and innovation. The image held by competitors v/ould involve fair dealing, efficiency, leadership in volum.e of sales, etc. The entire problem of image creation is complicated by the fact that the existence of a characteristic dees not necessarily create an image of it nor docs an image insure the presence of the elements in\;olved. Actual service may not create a consumer image of service. The image of economy in a product may best be created not by a low price per unit but rather by a package that appears to give more units for a given price. The Relationship to Psychologiaal Theories Simon (1959) gives one of the best explanations of multiple objectives. To Simon, the critical assumption is that tne firm does wish to maximize. Simon argues that the firm may not wish to maximize, but may simply want to earn a return that is regarded as satisfactory. In his analysis, Simon draws heavily from the field of psychology. He notes that while satiation plays no role in economic theory, it does enter rather predominantly into the trÂ€:atment of motivation theory in psychology. In most psychological theories, the m.otive to act stems from drives, and action terminates when the drive is satisfied. PAGE 37 29 Moreover, the condition for satisfying a drive is not necessarily fixed, but may be specified by an aspiration level that itself may adjust upward and downward on the basis of experience. To better understand this concept of multiple goal formulation, it is best to draw upon the field of psychology, rather than the field of economics. Business firms are run by men, therefore we would expect an analogy between corporate goals and human goals. Ma&low's hievarahy A. K. Maslow (1954) lists five types of human needs which are arranged in a hierarchy from lower levels to higher levels. They are: 1. Physiological needs, such as hunger, thirst, and sex. 2. Safety needs, such as security, stability, and order . 3. Belongingness and love needs, such as needs for affection, affiliation, and identification. 4. Esteeia needs, such as needs for prestige, success, and self respect. 5. Meed for self-actualization. The ordering of these needs is significant in two ways. It is the order i l\ which they tend to appear in the normal developm.ent of the person and also the order in which they tend to be satisfied. PAGE 38 30 The individual attempts first to satisfy his physiological needs. Once these are relatively well satisfied, then higher order needs emerge and begin to dominate the individual. When these are in turn satisfied, again new (and still higher) needs emerge, and so on. This is what Mas low meant by saying that the basic human needs are organized into a hierarchy of relative prepotency. The individual is dominated and his behavior organized only by the unsatisfied needs. Thus, man lives by bread alone-when there is no bread. But man's desires change when there is plenty of bread and his stomach is chronically filled. A brief summary of the needs are given belov;. Physiological needs. Â— Although it is impor.sible to make a complete list of physiological needs, certainly they would include hunger, thirst, sleep, sex, and body homeostasis . Undoubtedly these physiological needs are the most prepotent of all needs. To the human being who is missing everything in life in an extreme fashion, it is most likely that the major motivation would be physiological needs rather than any other. A person who is lacking in Homeostasis refers to the body's automatic efforts to maintain a constant, normal state of the blood stream. Thus, if the body lacks some chem.ical, the individual will tend to develop a specific appetite or hunger for that food. PAGE 39 31 food, safety, love, and esteem would probably hunger for food more strongly than for anything else. If all the needs are unsatisfied, and the individual is dominated by the physiological needs, then all other needs may simply become non-existent or simply become pushed into the background. As Maslow (1954, p. 82) has said, "For the man who is extremely and dangerously hungry, no other interests exist but food. He dreams food, he rememl;>ers food, he thinks about food, he perceives only food, and he v;ants only food." Safety needs .--If the physiological needs are relatively v/ell satisfied, there then emerges a new set of needs, which are roughly characterized as safety needs, All tiiat has been said of the physiological needs is equally true, although in a less degree, of these desires The individual may oquaJ.ly v;ell be wholly dom.inated by them. Most adults in our society are safe enough from wild animals, extremes of temperature, crim.inal assault, etc. Therefore, in a very real sense, man no longer has any safety needs as true m.otivators. We can, however, perceive the existence of safety needs in such phenomena as formation of labor unions, job tenure, and insurance. As we will note later, safety needs do seem to have seme effect in corporate goal formulation. PAGE 40 32 Love needs. Â— If both the physiological and the safety needs are fairly well satisfied, there vv'ill emerge the love and affection needs, and the whole cycle v/ill repeat itself. The person will now feel keenly about the absence of friends, or a wife, or children. He will hunger for affectionate relationships witli people in general, or for a place in his group, and he will strive with great intensity to achieve this goal. Esteem needs. Â— All people in our society have e need or desire for a stable, firmly based, usually high evaluation of tliemselves , for self -respeci: , self-esteem and for the esteem of others. These needs nay be classified into two subsidiary sets. First, there are the desires for strength, achievement, adequacy, competence, confidence, freedom., and independence. ^.econd, tliare are the desires for reputation, prestige, status, domincinco, recognition, attention, appreciation, and importance. Need for self -actualization . Â— Even if all the above needs are satisfied, discontent and restlessness will develop unless an individual is doing what he is fitted for. This need we may call self-actuali::ation . It refers to man's desire for self-fulfillment, namely, to the tendency for him> to become actualized in what he is potentially. The specific form, that these needs will take will of course vary from individual to individual. The clear emergence of PAGE 41 33 these needs, hov.'cver, usually rests upon prior satisfaction of the physiological, safety, love, and esteem needs. The above discussion may have given the impression that these five sets of needs are arranged in such terms that when one need is satisfied, then another need emerges. This might lead to the false impression that a need must be fully satisfied before the next need emerges. In reality, most members of our society are partially satisfied and partially unsatisfied in all of their basic needs at the same time. A more realistic descriptj.on of the hierarchy v;ould be in terms of decreasing percentage of satisfaction as we go up the hierarchy. Perhaps an average member of society is satisfied 90% in his pliysiological needs, 75% in his safety needs, and 50% in his love needs, 35% in his self-esteem needs, and 15% in his self-actualization needs. The em.ergence of a new need is seldom, a sudden phenomenon, but rather a gradual emergence. For example, if need A is satis fie:d only 10%, then need B may not be visible at all. However as need A becomes satisfied 40%, then need B may emerge 5%, etc. One difficulty in the formulation of the need hierarchy is that needs arc often not v;hat they seem to be, A person who thinks he is hungry may actually be seeking more comfort or dependence. Conversely, i.t is possible to satisfy the hunger need in part by other PAGE 42 34 activities such as drinking water or smoking cigaretts. As another example, there are supposed to be people (Morgan, 1961) who seek self-esteem for the sake of love rather than for self-esteem itself. This sometimes apparent reversal of the hierarchy does not, however, diminish the value of the concept for our purpose. Maslow's hieravohy and the firm's goals It is easy to see that there is an analogy between Maslow's hierarchy and the multiple goals of the firm. The analogy, however, is difficult to formalize. Certainly there is a hierarchy of corporate gof.ls, but the derermination of the hierarchy is difficult. Certainly the survival needs of the firm would be in the lowest possible set of the hierarchy. UnJess, and until the firm can be sure of surviving it is unlikely that management will concern itself greatly v:ith corporate images, etc. To paraphrase Maslov;, a firm which is short of cash will probably dream cash, think about cash, perceive cash, and want only cash. Maslow's safety needs are primarily evidenced in corporations as insurance contracts, engineering specifications, etc. It can be argued, however, that safety needs are responsible for the tendency toward consolidation, and for apparent price stability in certain industries. This latter concept v^ill be considered again in the next section. PAGE 43 35 Corporate love needs and esteem needs vary, but typical needs are obvious to most people. Each individual could produce his own list of great lengtVi. Let us just say that, in general, these needs are human needs which are projected through the edifice of the business firm. The business firm conception of self-actualization needs is again open to many interpretations. Maslow (1954) indicated that the need for self-actualization is a need for an individual to do what he can do best, and to do that in the best way he can. In business language, this is not far from, the economist's concept of profit maximization. The Effect of Satis fioing Constr'aints If we are to explain business behavior in terms of this psychological theory, we m.ust expect the firm's goals not to be formulated in terms of maximization, but rather in terms of attaining a certain level or rate of profit, holding a certain share of the market or maintaining a certain level of sales. Firms would try to "satisf ice" rather than to maximize. If we use this theory, then it is obvious that we have removed the objective function from our picture of the firm. In its place we have added a series of addj.tional constraints v;hich the firm must satisfy. The objective PAGE 44 36 function could, of course, be thought of as being a functioi of the constraint equations. Conceptually, however, it is more convenient to think of the firm as an organism which seeks a feasible solution (one that satisfies the constraints) to the problem with only lower order constraints attached. Once this feasible solution is attained, the firm will add tb.e constraints from the next level of the hierarchy and search for a solution which satisfies all constraints. The process then will be repeated until all constraints are attached. Let us assume that a firm has no objective function and that it is seeking a feasible solution with "all constraints attached." There are three possible results. First there might be a unique solution toward which the firm v/ill proceed. The probability of this, however, is almost zero. Second, it is possible that the "satisf icing" constraints placed upon the firm by itself are inconsistent. Tnus there is no action the firm can take which will satisfy all constraints. I'he third possibility is that there will be a range or set of activities v/hich will satisfy all constraints. With nc objective function, it must be assumed that any combination of activities which Some economists refer to this as the firm's utxlxty function. PAGE 45 37 satisfies all of the constraint equations would be equally desirable. The last two possibilities are quite relevant to reality. In the case of inconsistency, the firm has no feasible alternative. Its only course of action is to violate (drop or reevaluate) some of the constraints. In general, the firm will violate those constraints which are associated with goals in the higher hierarchy levels. It will continue to violate these constraints until a feasible solution is obtained. The second possibility, that there is a range of activities v;hich the firm, considers as satisfactory is, in reality, ridiculous. Any entrepreneur will state that his firm is always trying to do better, always attempting to achieve optimality. Certainly we must p] ace the objective function back into our picture. The question remains, what is the firm trying to optimize? Shubik (1961, p. 368) handles the problem this way, He says, suppose a firm states that ''it wishes to laaximize profits, m.aintain growth, and treat employees and stockholders fairly." The statement contains no evaluation of the ;;orth of fulfillment of tre different aims and does not indicate the interrelationships that may exi.st among them. If, as is invariably the case, an overall valuation of a utility function for the many features PAGE 46 38 of corporate aims does not exist, v;e have to devise methods to give operational meaning to them. In Shubik's example we can select one feature and assume that the firm wishes to maximize it subject to the boundary conditions which require that the other corporate aims meet certain specifications. Thus, we can represent the firm as: Maximizing profits subject to maintaining a -^ specific growth program, dividend rate and employment policy which v;ill satisfy stockholders and employees sufficiently that they do not act to change our environment (Shubick, 1961, p, 368), Alternatively, if the dominant interest of the firm is to take care of its employees, its goals may be stated: Maximizing disbursement to employees subject i:o maintaining a specific grov/th pattern and dividend policy which will satisfy stockholders (Shubik, 1961, p. 368) . Thus Shubik would have us keep an objective fu.ncricn in the picture and, in addition, add a set of constraints. The objective function would represent the dominant goal of the firm. The constraints would represent those objectives which the firir. is intent on satisfying. An Assumption About the Objective Funation In our picture of the firm wa will continue to use profit maximization as the objective function of the firra. We do this for three reasons. First, it is a logical PAGE 47 39 extension of Maslow's theory. According to Maslov;, ^fter all other needs are reasonably well satisfied, the selfactualization need will dominate the actions of the individual. We have shown that there is an analogy between self-actualization in the individual and profit maximization in the firm. For the second reason, we follow Joan Robinson (1953, p. 590) who said, Meanwhile I am inclined to retort to those v;ho grouse about the assumption that the entrepreneur's aim is to maximize profits in the imip.ortal words of Old Bill: "If you knov/ of a better 'ole, go to it." The figure of speech is apt (Ashley, 1961, p. 96) for the cartoon of Old Bill shows him in a hole which appears to be the target of artillery fire from all directions. Perhaps, if he had scampered away, he might have found a p].ace where he could have dug himself a better hole; his horizon was limited. Or finally we could follov; Professor Scitovsky (1959, p. 59) who said, "We have a vested interest maintaining this assumiption--it makes economic analvsis so much easier." A business firm, however, will not be content with using profit just in the objective function. The basic problem is that the distinction between constraints and goals tend to blur. If a firm operates to maximize PAGE 48 4 profits subject to inviolable constraints, it can be argued that fulfilling the constraining conditions is rr>cre ir:.portam:: to the firiu than is the function to be maximised. A business firm will want to insure that other objectives do not zake precedence over a satisfactory profit. This could be accomplished by including a satisfactory profit requirement as part of the system of constraints. Ic is reasonable to expect, however, that the entrepreneur will be aware of the value of the objective function and can determine if this value satisfies any minimum profit requirements he might have. The im.position of a satisfactory profit constraint would therefore be redundant. Before leaving this subject of multiple goals, it should be noted that m^any problems exist in the identification of goals. Som.e possible goals can be defined precisely and lend therriselves to measurement. These include such things as market shares, profits, sales, and balance sheet hom.eostasis . "^ Other goals, perhaps no less im.portant to -che firm, such as power, survival, socially responsible behavior, e-cc, can not be defined so precisely and elude efforts toward measurement. Balance sheet homeostasis is a concept borrov/ed from biology. It refers to the firiTi's attempt to maintain certain balance sheet ratios at a predetermined level. PAGE 49 SECTION IV THE FIRM AND ITS MARKETS A second major criticism of our portrayal of the firm concerns the assumptions m.ade about supply and demand. We have essentially assumed pure competition in the demand for final products. Furthermore, we have assumed that the firm, by its own actions, cannot affect the price of its inputs. Here we are using Chamberlin's (1948, p. 6) definition of pure competition, that is "competition unalloyed with monopoly elements." The sole requirements of Chamberlain's definition is that no participant has any degree of control over price. Control over price is essentially eliminated v,,'hen: 1. There are a large number of participants-enouyh to insure that any one participant's influence is negligible. 2, Products m.ust be perfectly homogeneous. /. Discussion of the Basic Assumption The assum.ption of a constai'it price in the factor market does not concern us to a great extent, primarily because the assumption conforms closely to reality. Even firms v;hich control a large percentage of a final product market (perhaps even a monopolist) do not tend to be a 41 PAGE 50 42 large enough user of input factors so that their actions materially affect the price of these factors. The assumption of pure competition in the output market is of more concern to us. These conditions are approached in some industries such as agriculture. In general, hov/ever, this assumption does not conform to reality. The market structure assumption is not, per se, of prime importance to this study. What is im.portant, is the assumption of a constant price for final products during the mono-periodic production period. Althougli pure competition exists in only a fev; places in our economy, the assumption of a constant price for the period under consideration is not a great departure from, reality. Oxenfeldt (1951, p. 191) notes the follov/ing: Probably the best reason for using a constant price assumption is that evidence supports Kail and Hitch who studied the price policies of thirtysix firms in England and concluded that "changes in price are frequently very costly, a nuisance to salesmen, and are disliked by merchants and consumers." Oxenfeldt (1951, p. 189) also points out that large firms such as Scars, Roebuck and Company, and Montgomery Ward are able to publish a retail catalog where prices are constant for periods of up to a year. Joel Dean (1951, p. 457) notes that "its [price rigidity] existence should be recognized." PAGE 51 43 Although the theoretical reasons for this apparent price stability are not known, a study of oligopoly theory probably sheds the most light on the subject. Oligopoly and Price Stability The dominant market in the American econom.y is oligopoly (Chamberlin, 1950) . Oligopolistic markets are characterized by fewness of sellers, restricted entry, and mutual interdependence. Furthermore, prices in oligopoly markets are usually quite stable. Although the reason for this price stability is not known with certainty, ix: is often attributed to such things as collusion, price leadership, or fear of competitive reactions. An analogy could easily be drawn between the reasons for price stability in oligopolistic markets and human safety needs as postulated by Maslow (1954) and discussed in Section III The kinked demand curve Some economists have used the kinked demand curve to explain this price stability. The oligopolist's demand curve is viewed as having a kink at the point of the prevailing price. The basic assumption is that if you raise price, your com.petitors will not. If ycu lower price, however, competitors will tend to follow. Thus the demand curve is thought to be relatively elastic at prices PAGE 52 above the kink, and relatively inelastic at prices below the kink. The distinguishing feature of this demand curve is that it is not dif f erentiable at the kink. There is a "gap" between the value of the left hand derivative and the value of the right hand derivative. This results in a discontinuity of the traditi.onal marginal revenue curve. The curve, therefore, explains stability in spite of variations among the marginal cost curves of different firms in the industry. The kinked dem.and curve is consistent v/ith profit maximization and the traditional assumption that the firm equates marginal revenue and marginal cost. The kinked demand curve analysis is limited, however, because it does not explain how the prevailing price is reached. The works of Bain, Andrev/s , and Fellner do, hov/ever, shed light on this problem. Price determination Bain (1949) insists that oligopolistic firms will set price so as to discourage potential competitors from entering the industry. Thus they are really setting prices so as to m.aximize long run profits. Bain defines a "limit price"' as being the highest co^ar.on price which the established firms in the industry believe they can change without encouraging at least one new entry into the industry. Andrews' (1949) theory is based on the "full cost principle." Ha believes that firms select their prices on PAGE 53 45 the basis of direct costs plus a standard profit margin to cover overhead expenses. Andrews refers to this price as a "right prj.ce." Any variance from this price by the firm will not be profitable. He believes, as does Bain (1949), that a price which is higher than the right price will induce rivals into the industry and eventually cut profits. Prices lower than the right price will not be profitable because the "rightness" of the price results from it representing full costs. Fellner (1960) uses a bargaining approach to analyze oligopoly prices. He believes that stable prices in oligopoly are the resultant of a type of intraindustry bargaining which is similar to bargaining in a biJ.ateral monopoly.. Fellner does not imply that actual negotiations must take place in order to have bargaining. Fellner (1360, p. 54) states that "spontaneous coordination'" arises because oligopo.listic situations are bargaining situations. "They involve two or more participants who know that what they do affects the policies of others, just as the action of others affects them." In such Ccises a range is established vv'ithi.n which a given price tends to emerge. The absolute limits of this range are set by zero profits for any of the firms. Between these zero profit points lies the bargaining range. The price which is set within PAGE 54 46 this range will depend on the relative bargc.ininc strengths of firms in the industry. Bain's "limit price," Andrews' "right price," and Fellner's "bargaining price," help to explain the level of the kink in the kinked demand curve. The important thing for us here, hov/ever, is not how the kink got where it is, but rather that price stability does seem to be a fact. Sales Constvaints in tne Portrayal cf the Firm The kinked demand curve implies both a unique price and a unique output. If the firm were aware of this unique output, then it would be easy to incorporate this value into our picture. As was the case with cur multiple goals, we could sim.ply add a constraint which required that a given amount of tlic product in question be sold. For the typical firm, the constraint will not take the form of a strict equality constraint. The firm normally reacts to expected demand. Iw will usually have in mind an amount of any product which it feels it can sell. The firm v;ill normally plan to sell any amount up ro this maximum figure. Thus the sa]es constraints will generally take the forni of "less than" inequality constraints . In some cases a firm v.^lll feel as though it m^ust produce a minimum amount of a certain product in order to maintain a corporate image, customer good will, etc. These types of constraints are generally considered as multiple goal constraints rather than sales constraints. PAGE 55 47 The preceding discussion was not meant to imply that demand estimation should always be abandoned and replaced by a "right price" and a sales constraint. The introduction of these concepts does, however, serve to focus our picture of the firm. PAGE 56 SECTION V A RESTATEMENT OF THE PORTRAYAL OF THE FIRM In our portrayal of the firm we now have an objective (profit) function, a production function, and a set of constraints. These constraints represent alternative goals of the enterprise that must be satisfied as well as sales limitations which must be considered. The major question to be answered now is: what effect will the addition of these constraints have on the optimal solution derived earlier? Let us m.ake the heroic assumption that these constraints can be quantified, and further that they can be expressed either as functions of the input variables alone, or as functions of the output va.riables alone. Actually, these assumptions are quite valid for rhe mar.keting constraints. These constraints will generally take the form that scm.e function of the output variables is less than a constant. The assumption that all goals of the firm can be quantified has been discussed before and is indeed heroic. To the extent that they can be quantified, however, these goals will generally be a function of either input variables or output variables and not of both. Vvith these assumptions made, v/e can again solve our constrained maximization problem. 48 PAGE 57 49 A Revised Entrepreneurial Solution For the sake of mathematical convenience, v.'e will let A represent the set of indices of the constraints associated with the output variables. B will represent the set of indices of the constraints associated with jnput variables. Furthermore we shall assume that all constrai.nts (except the production function) are "less than" inequality constraints. Any constraint not. in this form can easily be converted by multiplying through by -1. We can now form our new Lagrange function. n E w.y . S + A, [F, (x , i = l ^ ^ -^ L = T. p^x^ _E w y S + A^ [F.^^ (x-j^ , . . Â• , x^) 1=1 ^l^^l V + E A^[F^(x^, . . ., x^) + uj b^] reh ' seB The necessary conditi.ons for a maximum are: oL/dx. = p. + A.f3F/dx.) + E A (oF /Sx. = 0, X 1 1 X ^^^ r r 1 i = 1, . . . , n. SL/Sy. =-w. A,(aG/c)v.) + E A (bG /& y . ) = , ^ 3 -^ 3 seB ^ ^ ^ j = 1, . . . , m, PAGE 58 50 SL/SA-L F(x^, . . . PAGE 59 51 Although this is a mathematical fact, it may come as a surprise to some entrepreneurs who insist that the maintenance of some goal such as market share is essential in maximizing profits. If the optimal solution could be obtained mathematically, the Lagrange multipliers would represent the opportunity costs of maintaining an objective or a sales constraint at a given level. Thus if a numerical value could be obtained for any Lagrange multiplier, then the entrepreneur could estimate the value of altering the associated constraint requirement by an incremental unit. For example, if the Lagrange multiplier associated \;i th a given sales constraint is zero, then any additional sales effort spent on this output Vs^ould constitute a wasted resource . Let us also recognize that there may be no soJution to the Lagrange equation. Mathematically we might say that the constraints are inconsistent. Practically v;e vrould say that the firm has too many goals and it simply cannot satisfy them all. It is also possible to have a solution to the Lagrange equation which does not meet the minimum profit requirements of the entrepreneur. In these cases it becomes the duty of the entrepreneur to reevaluate the constraints of the firm and to choose one or more to be m.odified so that a satisfactory solution may be reached. PAGE 60 SECTION VI THE ENTRTiPRENEUR AND THE ENTREPRENEURIAL PROCESS Throughout the first portion of this study we have said quite a bit about the entrepreneur without describing who he was or what he did. This section will attempt to define more clearly the concepts of the entrepreneur and the entrepreneurial process. The Entrepreneur The entrepreneur is a manager. He manages the business firm. A business firm may be viev;ed as an instrument for the transformation of the services cf persons and things into completed products. The basic structural unit in an enterprise can be termed as a group. A group is a combination of two or m.ore individuals jointly contributing specialized services which are coordinated to the attainment of a firm's objectives. A complex is a combination of two or mere groups jointly contributing specialii^ed services which are coordinated to the attainment cf an objective of the firm. A complex differs from the group in tvs^o respects. First, the basic units of a complex are groups rather than individuals; (1938) We are borrowing our definitions from Barnard 52 PAGE 61 53 second, the specialized services contributed to a complex are the services of member groups and not directly of individuals. The business firm is the resultant of the combination of individuals into groups, of groups into complexes, of subordinate complexes into superior complexes, and finally into the supreme complex which is the business firm. Each group and each complex is headed by a manager. These managers are responsible for coordinating the services contributed by the units comprising the groups or complexes which they head. The managers of groups manage the individuals who comprise the groups. The managers of complexes comprised of groups do not directly manage the individuals comprising the groups but only do so indirectly by raanaging the managers v/ho head those groups. The managers themselves are combined into managerial groups; thus the managers of a combination of groups together with the managers of a complex comprising these groups may be referred to as a managerial group. The same may be said for the managers of subordinate complexes and the manager of the superior complex com.prising these subordinate complexes. Individu-als v/ho are managers are therefore m.embers of two units--the unit v/hich they head and a managerial unit. This fact reflates the managerial superstructure to the srructure of groups and coraplexes and makes possible an PAGE 62 54 integral whole. This integral, coordinated, pluralistic v/hole we will call the entrepreneur. It is the entrepreneur's job to optimize. As we stated earlier, economic theorists have not been greatly concerned with how the entrepreneur optiniizes. The Entrepreneurial Process The twentieth century has seen the rise of another group of analysts, often called management theorists, who are interested in how the entrepreneur optimizes. In fact, that is their whole reason for existence. The approaches taken by management theorists are quite varied. One approach is to divide the entrepreneur's job into managerial functions. Koontz and O'Donnell (1959) state that it is the job of tlie entrepreneur to plan, organize, staff, and control the business firm. Through these managerial functions, the entrepreneur should coordinate the activities of the firm in such a manner as to best achieve the objectives of the firm. There is another approach taken by some management theorists. This approach holds that the entrepreneur utilizes his available assets, by operating certain activities in a way v/hich will best achieve some predetermiined objective. The various activities of the firm include such things as manufacturing, selling, personnel PAGE 63 adiTiinistration, accounting, and finance. The assats (liabilities are negative assets) include such things as land, plant, equipment, inventory, accounts receivable, . etc. This second approach is nore applicable to this study and is the one we shall enploy. D 3 c i s i on-making Although different ir.anagement theorists have different basic irie-chods of viewing a firm, niost theorists agree that the technique of decision-making pervades the performance of the entrepreneur. Kcontz and O'Donnell (195S) note -chat in order to plan, organize, direct, or control, the entrepreneur must make decisions which affect the operations of the firm. Haynes and Massie (19 61) note that entrepreneurs select among possible ac-civities, and then decide hov; much emphasis to place on the selected activities. Thus, v/e may think of the entrepreneur as a decision-miaker . He will generally strive to make those decisions v/hich are in sor.e sense cptimial . Stym.ologically , "to decide" m.eans "to cut off." In i-cs present usage it suggests the com.ing to a conclusion. Ii: "presupposes previous consideration of a m.atter causing doubt, wavering debate, or controversy and im.plies the arriving at a more or less logical conclusion that brings doubt, debate, etc., to an end" {Wsbstsr ' Sj 1S42, p. l>-i2; . PAGE 64 56 Decision-making involves a conscious choice or selection of one alternative from among a group of tv;o or more alternatives. In making a decision, an individual must become av;are of the relevant alternatives, define them, and evaluate them as a basis for choice. Tannenbaum (1950) defines the following steps in the decision-making process. Awareness of alternatives . Â— Before making a decision, an entrepreneur should become aware of all alternatives v/hich are relevant to the decision to be made. This, of course, is seldom possible. Often an entrepreneur must depend upon his own limited experience and information. Memory of these is often sketchy and incomplete. It is possible for an entrepreneur to discover relevant alternatives through investigation or by tapping the knowledge of others. This process is, of course, excessively tim.e consuming and does not guarantee complete coverage of all alternatives. For these reasons, it is exceedingly doubtful if most decisions are based upon awareness of all relevant alternatives. Definition of alternatives . Â— Once the entrepreneur is aware of a].ternatives , he must next define each of them. Ideally, this definition involves a determination of all the consequences related to each alternative under consideration. This, of course, can never be fully achieved. PAGE 65 57 The consequences of various alternatives J ie in the future and therefore must be anticipated. Whenever the future is anticipated, uncertainty is present. Uncertainty is present because a decision-maker never has the knowledge to make it possible to accurately determine the nature of the consequences which will follov; upon his choice of a given alternative, assuming all other related elements remain constant. In addition, all other related elements will probably not remain constant. Evaluation of alternatives .--Atter an entrepreneur has become aware of certain alternatives and consequences associated with these alternatives, he must make a choice among them, that is, he must make a decision. There are two basic types of decisions any individual must make. Some of these decisions (a small proportion) relate to the individual's system of values. Tliey determine his ultimate ends. All other decisions are directly or indirectly related to m.eans for the attainmient of these ultimate ends. In choosing among alternatives, an entrepreneur will attempt to make a selection, v/ithin th.e limits of his knowledge, which will maximize results (the degree of attainment of the relevant end) at a given cost or which will attain given results at the lowest cost. Thus, the individual has a criterion to guide his choice. This criterion is similar to the PAGE 66 58 economist's concept of an opportvmjty cost. Joel Dean (1951) defines opportunity costs as profits foregone because of the exclusion of a particular alternative. An entrepreneur can very seldom place a dollar value on the opportunity cost of any alternative. Nevertheless, the decision-making process must take place in this f ramev/ork . Oi-jviously, the opportunity cost of an alternntive v/hich is presently being used is zero. There can be no foregone profit associated 'v/ith an alternative vvhich is being used. In order for any altcrnati.ve to be valuable, it must have a positive opportunity cost. In other words, the firm must be foregoing so;i\ething of value by not utilizing the foregone alternative. The rational entrepreneur, in the decision-making process, will choose that alternative whi.ch has the highest opportunity cost. The opportunity cost of each alternative is relative to the chosen alternative. If the entrepreneur chooses the most profitable alternative, then the opportunity costs of all excluded alternatives must become negative. The i.mi.ilication being that since the best alternative is not among the excluded set, a selection of an eJeraent of this set v/ould reduce the entrepreneur's profits. The entre'pi'eneurial sphere of discretion With respect to any given problem which requires a decision, the entrepreneur (any-individual) may have m.any PAGE 67 59 feasible alternatives among which to choose. Following Tannenbaum (1950), v/e shall define an entrepreneur's sphere of discretion as the set of all feasible alternatives. The factors which restrict, restrain, or limit the exercise of discretion to available alternatives are referred to as "constraints." Decision-making, then, is judgment exercised within constraints. Type I and type II deoisions Tannenbaum describes two basic types of decisions any individual must make. Some decisions (usually a sm^all miinority) relate to the individual's system of values. They determine his ultimate ends. All other decisions are directly related or indirectly related to m.eans for the attainment of these ultimate ends. It is important for us to make a distinction between these two types of decisions. V;e shall refer to the type of decisions which relate to an individual's system of values as type I decisions. Those decisions which relate to the means for the attainment of the ultimate ends will be defined as type II decisions. It is imporuant to realize that type I decisions must be made first. Once they are made, they effectively The distinction between type I and type II decisions tends to be relative. In Section I, we noted that any optimizing procedure that incorporates the assum.ption of a iriono-periodic production period is actually a subcptimizing procedure. Business firms PAGE 68 60 serve as constraints upon all type II decisions. If, for example, the entrepreneur decides (:nakes a type I decision) he wants to sell a certain mininuir. quantity of a particular product, -chen this liiriits or constrains the type II decisions he can make in an effort to ir.axi:ai2e his objective function. It is also possible that the decision-maker can make such a variety of type I decisions that there are no type II alternatives which will satisfy all type I decisions. In this case, the entrepreneur must reevaluate his type I decisions, and alter one or more of them so that a feasible solution can be found. The Iterative Nature of the Entrepreneurial Process Litchfield (1556) notes that the entrepreneurial (administrative) process is a cycle of action which includes decision-making, programming, and reappraising. Certainly an entrepreneur is not: an omniscient individual. He cannot iirjr.ediately see the consequences of all his actions, thus the cyclical process. Typically, the problem have long-run goals and objectives. The requirements and objectives of the firm for a given m.ono-per iodic production period can not be set in isolation. Consideration m.ust be given to the effect of these decisions upon the long-run position of the firmi. Thus, short-run requiremients are usually made with the aim of achieving long-run objectives. The type I decisions of a short-run model may be the type II decisions for a long-run miodel. PAGE 69 61 faced by an entrepreneur is not that of finding a completely new solution, but rather improving on an existing solution. Thus an entrepreneur may start with a feasible solution. He then evaluates the opportunity costs of the excluded alternatives and checks to see if a better solution is possible. If a better solution is possible, he then selects the best alternative and incorporates it into his solution, checks the new solution for feasibility, and then programs the new solution (puts it into operation) . He then repeats the cycle. If the entrepreneur ever reaches a point where all of the excluded alternativeo have non-positive opportunity costs, he can assume that he can do no better. Let us define more precisely what we mean by a managerial or entrepreneurial solution. An entrepreneur chooses among feasible alternatives. Typically he does not choose one alternative to the exclusion of all otliers. He more likely v;ill choose a small set of alternatives from among a large set. Furthermore, some of the chosen alternatives will receive m.ore emphasis than others. It is conveniei:t to think of alternatives in the excluded set as receiving no emphasis. Thus the set of feasible alternatives, together with the amount of e-npbas:s i:i3ch is receiving at a particula: tihie, determine the entrepreneur's solution or program. PAGE 70 62 We may combine the thoughts of Tannenbaum and Litchfield to define an entrepreneurial process. This process is illustrated schematically in Figure 1. Let us note that the previously defined concept of an "activity" can easily fit into the framework of Tannenbaum 's "alternative . " PAGE 71 63 I Consider I M the Problem y ake Type I D ecisions > r Recons [__ F/^a lu ^'C ate Constraints < I Z] Is ThGre a Feasible Solution? . .. vl (Yes) j Prograni Fe a s i ble Solution (No) .1 Evaluate Opportunity Costs '1 of Excluded Alternatives Are All Opportunity Costs NonPositive? I (N o) i-derj Is There Evidence of Possible Misformulation (No; Select A.lternative With Highest Opportunity Cos (lype II Decision) [ Insure Feasibi3.ity of Nev,' Program czmii Reproqram J __.} Optimal ^ Solution FIGURE 1--SCHEMATIC REPRESENTATION OF THE ENTRF.PRENEURIAL PROCESS PAGE 72 SECTION VII A RI;EVALUATI0N of the rRODUCTION FUNCTION In our analysis up to this point, we assumed the production function to be given. We did not concern ourselves with hov; this function was derived, but only used this function to characterize the optimum production alternatives v^hen considered in relation to the markets in v.'hich the firm must buy and sell, and the multiple goals of the firm. Historically, this has been the position taken by economic theorists. This conventional theory is often justified on the grounds that the analysis of the firm i.s but one step i.n the analysis of economic markets. Suppose, however, that we are interested in the firm per se. Suppose we are interested in aiding manageraent in determining how to solve its optimization pjroblem. We cannot now assume that the derivation of the production function is irrelevant. Instead we must examine more critically the traditional assum.ptions about the production function. The choice variables in the traditional production function are generally conceived as time rates of consumption of various inputs and time rates of production of various outputs. The choices of production and 64 - PAGE 73 65 consumption are, of course, dependent, otherwise output would be chosen very large and input very small. Business firms are operated by entrepreneurs. Entrepreneurs are human. We must accept the fact that they do not possess perfect knowledge and therefore are not fully aware of the firm's production function. What then, do entrepreneurs do? We have stated that entrepreneurs are primarily decision-makers. Following Tannenbaum>, we have defined decision-making as a choice among feasible alternatives. Thus we can see that the concept of the traditional production function is really not relevant to the modern firm. Normally, the choice is among various feasible alternatives. These feasible alternatives may be thought of as "different -ways of doing things." Each alternative implies its ov;n characteristic pattern of input and output rates. The. Concept of a Process The decisions made by the firr.i do not deal directly with levelr cf input and output but are more concerned with the choices c.xnong technically feasible proc;esse-3. We shall define a process as a "way of doing something." A process is a set of ratios among rates of consumiption of various inputs and rates of production of various outputs. Thus a firm makes a choice among a nun\b>er of processes. PAGE 74 66 The firm is not restricted to the use of only one process. It can normally utilize several processes simultaneously. Furthermore we shall assume that most processes can be operated at a range of levels. By level of a process we mean the time rate of consumption of all inputs and the time rate of production of all its outputs in the same proportion. When v;e were discussing the entrepreneurial process we noted that the entrepreneur normally chooses a small set of alternatives from among a large set. Furthermore we ImpJ.icitly we have assumed linearity. Initial thought v/as to include an appendix to justify this aseumption. This was not done for three reasons. First, there are many articles and books in the economic literature which illustrate examples of the application of linear models to economic problem.s . For example, see Bowman and Fetter (1959) . Second, the entrepreneurial model presented in later sections of this study is formulated in terms of "balance sheet accounts" and "business transactions." For the most part, it is obviously linear. Third, in the implementing part of this study effort was made to determine if this assumption had any detrimental effects on the implementing model. This was not found to be the case. The concept of linear programming will be discussed in subsequent sections. It should be pointed out here, hov'ever, that the phenomenon of decreasing marginal returns is encountered in a linear prograirjuing analysis of the firm, Bauraol (1959, pp. 270-274) and Wu and Kwang (1960) give a comprehensive comparison of diminishing productivity in the traditional economic analysis and diminishing productivity in the linear prograniming analysis. Baumol (1959, p. 231) states, "... the ordinary law of diminishing returns is compatible with linear programming, i.e., the marginal yield to increased use may decline, provided the employment of other factors remains unchanged, . . . but the decreases characteristically occur in discontinuous jumps." PAGE 75 67 stated that some of the chosen alternatives will receive more emphasis than others, and that alternatives in the excluded set could be thought of as receiving no emphasis. Thus the set of feasible alternatives, together with the amount of emphasis each is receiving, define the entrepreneur's solution or program. We can now be more specific and say that the entrepreneur selects a small set of processes from among a large set. The level of a process corresponds closely to the degree of emphasis. All processes in the excluded set can be thought of as being utilized at a zero level. Thus the set of processes, together with their level of utilizatd.on, define the entrepreneur's solution or program. A process can represent any activity within the firm. It may represent sales effort, personnel relations, research and development or anything else a firm might do. The definition of a process implies something more specific than an activity undertaken by the firm. It is the way or the method that a firm undertakes an activity. One of the most common activities of a firm is that of manufacturing a product. It is essential, hov;ever, to distinguish between a product and a process. A product is an economic good or service which is sold en the market for a particular price. A process is a way of manufacturing a particular product. Normally there will be a nurabcr of PAGE 76 68 technically feasible processes which will produce the sarae product. The same is true for most other activities undertaken by the firm. Thus, the number of processes will always be greater than or equal to the number of activities. It is possible in some cases to have a large number of processes for a given product. Usually, the number of processes available is small . We shall assume that the entrepreneur is free to utilize several process simultaneously so long as he does not violate his sphere of discretion. We have stated that there is a constant price associated w.i th each input and each output. Since a process is a set of ratios among rates of consumption of various inputs and rates of production of various outputs, it m.ust be true that associated with each process is a value which we shall call the net contribution to profit and overhead. Net contribution represents the difference between the additional revenue recei.ved by and the additional cost incurred by the utilization of one additional unit of any given process. Under cur assumption of linearity, net contribution is a constant and is independent of the level of utilization of any process. Ir would be incorrect to refer to this new parameter as profit. The firm does incur a certain amount of fixed PAGE 77 69 costs (v;hich may be called overhead) and technically profits are not obtained until the net contribution is greater than overhead. Since a firm will normally employ several processes, it follows that the firm's total consumption of resources and total production of outputs will be the sum of the quantities of factors consumed by the various processes and the sum of the products created by the various processes. A change in the quantity or proportion of inputs consumed or outputs produced can only result from a change in the levels at which the various processes are operated. The f:rm cannot aJter directly the quantities of inputs or outputs, but can only change these factors indirectly by 2 means of changes in the level of various processes. It should be the goal of the entrepreneur to choose those levels cf the various processes which will maxim.ize his own objectives while at the same time not violate his sphere of discretion. Proiicsses and the Froduotion Function The introduct-i on of the concept of a process has forced us to reexamine the traditional production function. The typical entrepreneur is not aware of an "optimal" 2 We shall assume that all processes must be operated at non-negative levels. PAGE 78 70 production function on which he must operate. He is much more av/are of the limitations or constraints on his selection of processes. The entrepreneur has available certain fixed and variable factors of production. The entrepreneur uses these inputs (by operating processes) to create outputs. In doing so, the entrepreneur selects among vai-ious alternative processes. He is not free to operate any process at any level. He is constrained by the availability of certain factors of productioi. We shall call these constraints the direct production constraints . We shall refer to all other ccnstrai.nts placed upon the entrepreneur as indirect production constraints . The direct and indirect production constraints together define the entrepreneur's sphere of discretion. We have nov; redefined our production function. Instead of the continuous production function of the traditional economists, we have a production function that consists of two parts; a set of processes, and a sphere of discretion. Processes and the Objective Function The introduction of the concept of a process has a].so forced us to reforxmulate our objective function in terras of processes. This is easily done mathematically as follov/s: PAGE 79 71 n Z ex. S. i=l 1 1 X. represents the level at which process i is utilized in any solution. c represents the net contribution of a unit of process i. S represents the fixed or sunk costs which must be paid by the firm regardless of the rate of output. It is the duty of the entrepreneur to select those processes and operate them at the correct level to maximize this objective function. PAGE 80 SECTION VIII THE RELATIONSHIP BETWEEN THE PORTRAYAL OF THE FIRM AND MATHEMATICP.L PROGRAMMING Mathematically, any problem v;hich seeks to maximize (or minimize) a numerical function of one or more variabJ.es (or functions) when the variables can be independent or related in some way through the specification of certain constraints may be referred to as an optimiJiation problem. The methods of differential calculus have long been applied to optimization problems in the theory of the firm. In fact, traditional economic theory of the firm is framed in the ir.Gthcds of di f f erentj.al cc-.lculus. In the last twenty years there has been a large growth of interest in a new class of optimizing problems;, referred to as progreirj^.ii.ng problems, which are usually not amenable to solution by classical methods of calculus. The C-eneval Programming Problem The general prograpiTang problem can be formulated in the following way. The objective is to determine values for n variables x , x,^ , . . ., x^ which satisfy the m inequalities or equations g^ (x-, , X , . . ., X ){<, =, >}b. , i ^ 1, . . ., m, J a^ n J ~ 72 - PAGE 81 73 and in addition, maximize (or minimize) the objective function The constraints are assumed to be specific functions, and the b. are assumed to be knov;n constants. One and only 3 one of the signs {<, =, >} holds for each constraint, but the sign may vary from one constraint to another. The values of m. and n need not be related in any way. m can be equal to, less than, or greater than n. Usually, some or all of the variables are restricted to be non-negative. Linear' 'Progranirnir.g The xe.'il iuperus for th^, gro'-'th of interest in prograiviming probl.ems c?me in 1947 (Hndley, 1964, p. 14) when George Dant:-ig devised the simplex algorithm for solving the general linear prcgraiiLniing problem. If, n g . (x, , X . . . , X ) Z a . . X . , j 1 .... , ^j 1' 2' n' ^^^ 32 i' -" n f(x,, x~, . . ., X ) Z C.X., 1 2 ' ' n Â•i:=i i ^ where a., and c are knov/n constants, the progrannvii ng problem js said to be linear provided that there are no other restrictions except perhaps the requirement that some or all of the variables must be non-negative. PAGE 82 74 Usually in the formulation of the genera], linear programip.ing problem, it is specified that each variable must be nonnegative , i .8. , X. >0, i=l, . . .,n. This form is most convenient v/hen making nujnerical calculations. Thus a linear programJTiing problem seeks to determine ncn-negative values of the n variables x^ , x^, . . ., X , which satisfy the m constraints n Z a..x.{<, =, >}b., j = 1, . . ./in, i-1 3^ ^ 3 and which optimize the linear function n z = Z c . x . . i=l ^ ^ It is often convenient to express the general linear programming problem in vector form, i.e., max z cXj n s.t. i: a .X, {<, =, >}h. i-1 ^ ~ e and x are n component vectors and may be represented as ^ (c^i' c., . . ., c^), X = [x^, x^, . . ., x^J. e is generally referred to as the price vector and .r as the program vector. PAGE 83 75 aand h are m component vectors and may be representea as '^li' ^2i %il' t^' "2 VThe a. are called activity vectors and h is generally referred to as the requirements vector. Lineo.y Frogramming and the Portrayal of tke Firm The typical linear programming formulation is almost identical to our m.odified picture of the firm. The objective function is the linear programming formulation does not contain the term -S. In other words, there is no provision for fixed or sun]; costs in the linear programming model. It has been emphasized, hov/ever, that fixed costs are relevant only to the decision of whether to operate the firm or shut it down. The linear programming activity vector is identical tc our concept of a process. It is a set of ratios among rates of consumption of various i npv.ts and rate of production of various outputs. The linear programming decision variables are identical to our concept of level of a process. The program vector (vector of decision variables) is identi':.-.! to our concept of an entrepreneurial solution. The prices in the linear programming formulation PAGE 84 76 correspond to our net contribution values. The linear prograiaraing constraints define cur entrepreneur's sphere of discretion. The Simplex Process The forinal metinod of solution of ].inear programming problems is not, per se, of great interest here. It is interesring to note, however, the similarity between the iterative mathematical solution process of linear programming and the entrepreneurial process as outlined by Tannansaum and Litchfield, and discussed in Section VI . The simplex method for the solution to linear programm.ing problems is an ittirative procedure v.'hich reaches an optimal soJuti.on in a finite number of steps or provides an indication that tl^ere is an unbounded solution. If the problem has an optimal solution, the optim.ut.i value of z must be finite,. Let us assum.e that An unbounded solution indicates a p.roblem in which the value of the objectj.ve function can be made infinitely large. Such solutions are not exv.ected in the real world and generally indicate a misf crmulation of the problem. As Gue and Thomas {to be published) have said, ". . .if the reader is avrare of a piofit :?.axir>iization pioblem where the objective function grows v/ithcut bound, he is requested to vvrite the authors iiTLmediately with the details of the troblem, " PAGE 85 77 the linear progranuiiing problem has been converted to the stand-nrd forra, max z =Â• oXj n E. t. Z a X . b, i=l ^ ^ X > . The tvro follov/ing theorems can easily be proved (tiadley, 1964, p. 31) . 1. If the problem has an optimal solution, at least one basic3 feasible solution ;vill be optimal . 2. If we have a basic feasible solution which is not optimal, it is possible to reach an optimal basic solution in a finite nuiriber of step; by changing just one of the basic varial^les at each step, or to obtain ultimately an indicatior. of an unbounded solution. convert inequalities into equalities. This is done, by the addition of slack and surplus variables. Slack vaviahles are introduced into "less than" inequalities and represent the difference betv/een the maximuiTi available resource, b'. and rhe amount actually used. Surplus vai-iables are introduced inxio "greater than" inequalities and represent the amount by which a minimum requirement, bj , is exceeded, It is also usually convenient to have all components of the requirements vector positive. If necessary, this can easily be acconplished by multiplying a constraint equation by -1. A basic solution is a solution thar has no m.ore than m variables different from zero where m represents the number of constraints. PAGE 86 78 The simplex method begins v;ith an initial basic feasible solution. It then computes the opportunity costs for all vectors (process) not in the basis. If all excluded alternailves (vectors not in the basis) have nonpositive opportunity costs, the simplex method concludes tliat the present solution i.s optiiaal. If one or more of the excluded alternatives have a positive opportunity cost., the simplex method checks for the poscibility of a misforifiulated problem (anbcundod soJutior'). If there is no incl.i.catior-. of ar. u^ibcunded solution, the simplex method chooses the excluded alterr.r.tive v.'ith the largest oppor_tunity cob't to enter the basis. The simp].ex mcvhiod then selects a proce.i..?, to be rcT.icved m such a vay as to insure feasibility of the new solution.. The procedure is then repeated until an optimal solution is reached. There are many cases -vhere the simcplex m.ethod m.ust begin wit'n a solution v/hich contains artificial processes. The siiuplex method then follo/,'s a.v). iterative procedure to remove the artificial vectc's and thereby obtain a real ba.sic feasible solution. In some cases this v.'ill not be possii'le. Tne simplex procedure wij..l i.ndicate v;hen a probJ.er.i is formulated so that no feasible solution may be found. A flov; chart of i.he simplex process is shown in 5\icfure 2. Actually the simplex metriod cornpiites an approximation to the opportunity cost. PAGE 87 79 Formulate Prohleiri Obtain Artificial Solution 3 Is There a Real Feasj.ble Solution? II_(Yesi_ (No) Obtain Initia]. Real Basic Feasible Solution Coinpute Opportunity Costs of All Excluded Alternatives Are All Opportunity Costs Non-I'ositive? " T" (No) s There Evidence of an Unbounded Solution? j: Reconsider Select Alternative Highest Opportun r" T ve witn ity Cost j Insure Fe a s i bil ity D nbounded j olution Un Sol Reprogran'i :z:r"~ L Â— .jF Optimdl FIGURE 2 Â— SCKEI4ATIC REPRESENTATION OF THE SIMPLEX METHOD FOR SOLUTION OF LINEAR PROGRAMI^iING PROBLEMS PAGE 88 80 Notice the similarity between the flovj chart of the simplex method and the flov^/ chart of the entrepreneurial process as shown in Figure 1. The type II decisions of the entrepreneur correspond closely to the selection of basis vectors in the simplex method. The entrepreneur's type I decisions are reflected in two places in the linear programming process. First in the selection of the objective function, and second in the selection of some components of the requirements vector. PAGE 89 SECTION IX THE PORTRAYAL OF THE FIRM: AN ACCOUNTING VERSION The typical linear programming problem is normally formulated in such a way as to obtain computational efficiency in solving the optimizing problem under consideratj.on. If we are to focus more sharply our picture of the firm, hov/ever, we should (for the purpose of this study) concern ourselves less v;ith mathematical (computational) efficiency and m.ore with the concepts used by an entrepreneur in operating his business. Previously we have stated that one view of management theory suggests that the entrepreneur utilizes his available assets, by operating processes, in a way which v/ill best achieve some predetermined objective. We stated that the various processes of the firm include such things as manufacturing, selling, personnel administration, accounting, and finance. We also noted that the assets (liabilities are negative assets) include such thi.ngs as land, plaiit, equipment, inventory, accounts receivable, etc. Nov/ wo would like to be more specific about our concepts of assets and liabilities, and introduce other terms such a-s balance sheet, net income, business transaction, and double-entry bookkeeping, In short, we want to borrow some terras from the accountant. 81 PAGE 90 82 Accounting furnishes a good part of the data used by management in making decisions and directing operations. One branch of accounting, administrati^ve or managerial accounting, is based upon the concept of accounting as a method of managem.ent or as a tool by which managerial effectiveness is enhanced. Thas, entrepreneurs tend to think in an accounting framework, and the accountants are more and more tending to utilize a framework which enhances managerial effectiveness. We will not be content -co use the accountant's fraraev/ork entirely, however, but v;e must modify it to some extent so that it will correspond more closely to our picture of the firm. The Accountant's Balance Sheet First let us look at a simplified version of the accountant's balance sheet. The balance sheet contains an inventory of the several kinds of assets to v;hich the firm has title and the liabilities which the firm has incurred. Traditional accounting statement generally report assets and liabilities at their cash value. The cash balance is perhaps the most precise valuation on the balance sheet. It is important mainly with respect to what can be done with it rather than the absolute amount held at balance sheet time. Other assets, like receivables and securities, are reported at an exact amount expected to be realized as PAGE 91 83 the business continues normal operations; this amount m.ay be cost or ci value less than cost. Inventories are held for ultimate sale, sc the dollar valuation of inventory is the number of cost dollars expected to be recovered from future sales. Dollars tied up in plant and facilities must likev/ise be recovered as revenue dollars; the balance sheet reflects the dollars of original outlay not yet so recovered. Offset against these costs not yet realized is a list of claim.s that must be satisfied in the future. These, of course, are the liabilities of the firm. Balance sheet acaounts In order to make better comparisons and judgments, the accountan.t classifies the information on the balance sheet. He groups like things together, starting with a basic division of financial elements into assets and liabilities, and then proceeds with common subgroups. A fev/ subclassif ications commonly found in a balance sheet are discussed belov/. Cur-i'P.nt assets are those resources now available, claims for payments of cash in the near future,, investment in marketable securities, and goods which are expected to be converted to cash as a result of normal operations in the near future. Conversion of assets is a primary objective of management. The accountant, therefore, attem'its to recort then at realizable value. Accounts PAGE 92 !4 receivable are reviev/ed with the idea of reporting only those v/hich appear to be collectable. If expected realization on inventories has fallen below historical cost, the accounting valuation is reduced to reflect as accurately as possible the probable recovery. The current asset classification is subdivided in many ways depending on the situation. Three subclassif ications fecund on most balance sheets, however, are cash, accounts receivable , and inventoi.-'ij . The general inventory classification m.ay be divided into finished goods inventory and rav/ materials inventory. Fixed assets include both tangible property and intangible rights v;hich v.'iJl be used for a numl:)er of periods, or from which some benefit will be derived for a comparatively long time. Fixed tftngible assets are sometimes grouped together into one item, plant and equipment . More often, however, descriptive titles are used for each type of tangible assets. Land, buildings , and equipment are three comj'-on subclassif ications found on m.ost balance sheets. Use is the key to classification of fixed assets. The accounting procedure for fixed assets provides for some portion of cost to be deducted from the income of each period and charged to tlie particular asset. The remainder of cost appears on the balance sheet as the PAGE 93 accountant's valuation of the asset, a valuation which has no necessary relation to the current market value of the asset. Because this assignraent of cost to periods is a matter of judgment, the origina] cost of fixed assets as well as the accumulated cost charged off are usually separately reported on the balance sheet (or in a supporting stateraent) . The assumption is usually made that the firm will endure longer than any particular asset. The entire cost, therefore, of all fixed assets (but no more than cost) will be charged against the revenue of some period (or against revenues from the sales of the asset) . In a sense fixed assets may be thought of as being reported at realizable value, just as current assets are, but the term of realization is much longer and may involve a num.ber of future periods instead of just one. Current liabilities are those debts which mature in the near future and whose liquidation requires the expenditure of current assets. In the case of both assets and liabilities, "current" normally refers to the next operating cycle. Accounts paijahle to trade creditors, notes payable to financial institutions, accrued wages ^ aocvued taxes, etc, make up the current liabilities. Fixed liabilities J sometimes called long-term debt, are those liabilities v/hich rr.ature sometime in the future PAGE 94 86 (beyond the current period) . That part of long-term debt which falls due within the current period is normally reclassified as a current liability unless some provision has been made to repay (or refund) the debt without a drain on current assets. Owner's equity is normally reported without regard to individual owners but classified by nature and source of capital. Capital invested by the owners is reported under two headings: par or stated value of the shares issued is reported as capital stocky the excess of the investment over par or stated value of the shares is ^reported as paid-in or capital surplus. The increase in equity resulting from profitable operations and not distributed to stockholders is reported as retained ear?iings . A typical balance sheet is shown in Table 1. Business Transactions Next let us consider the concept of a business transaction. When the business firm enters into a transaction with other entities, the kind of property ov/ned , or the amount and nature of debts or money obligatj ons , or the owners' equity is changed. A transaction is an exchange of things having monetary value. Many transactions involve an outside party, but transactions can PAGE 95 87 TABLE l--HyPOTIlETICAL BALANCE SHEET Account Mumber Account Name Valuation 101 102 103 104 Current assets: Cash Accounts receivable Inventory (finished goods] Inventory (raw materials) 20,000 100,000 100,000 60,0 00 280,000 121 122 12 2a 123 123a Fixed assets: Land Building Accumulated depreciation Equipm.ent Accumulated depreciation 50,000 100,000 (40,000) 122,000 (60,000) 172,000 Total assets 452,000 201 202 203 Current liabilities; Accounts payable Accrued wages Accrued taxes 50,000 10,000 4,000 64,000 22] Long-term debt: Bonds payable 100,000 100,000 301 302 Stockiiolders ' equity Comip.on stock Retained earnings Total liabilities: 452,000 Source: See Section IX, The Anoountant ' s Balance Sheet, for source and explanation of data. PAGE 96 88 occur solely within the firm. Any transaction affects tv/o or more accounting elements within the firm. For our purposes, the minimum necessary requirements for a transaction is that it requires a "double-entry" by the firm's accountant. A proprietor's investment of money in the business, for exam.ple, is a transaction betv/een the firm and the owner. The effect on the firm is to increase its assets and its capital by the same amount. The consumf-tion of fuel oil in the office furnace is likewise a transaction Its effect is to diminish the assets of the firm and substitute an expense of equal amount. The sale of a product is still another transaction. Its effect might be to increase accounts receivable and reduce finished goods inventory by the same amount. A transaction of "collection" m.ight then decrease accounts receivable and increase cash. We have noted that any transaction affects two or more accounting elements (or simply accounts) within the firm. The balance sheet entries previously defined are accounting elements. The most important objective of accounting, from a financial viewpoint, is the measurem.ent of business income or profit. This purpose requires that revenues (incomes) and costs (expenses) be accounted for. Revenue accounts are broken down to show nature of revenue (sales, interest, etc.), source of revenue by product, or PAGE 97 to any other extent which may be useful to raanagement. Cost accounts are usually separated by nature of expenditure . Process illustrations Table 2 illustrates the concept of a transaction (although not in the nice debit and credit form normally used by accountants) . Six. typical transactions are illustrated as foJ.lows: 1. Manufacturing of one unit of a product. The firru converts raw materials, equipment (perunit depreciation is assumed) , and labor into finished goods inventory. Inventory is valued at cost, therefore final goods inventory is increased by$70. Raw material inventory is decreased by $4 0, and the value of fixed equipment is decreased by$5. The firm has also incurred labor expenses of $25 (which have not yet been paid) . 2. Selling one unit of product. The firm has sold a unit of finished goods inventory for$100 on credit. Accounts receivable have increased by $100, final goods inventory has been decreased by$70. The firm has received $100 of revenue fi"om. sales and the cost of goods sold was$7 0. 3. Collection. The firm has converted accounts receivable into cash. 4. Fayments . The firm has paid the wages for part of the labor it utilized in productj.on. 5. Purchases . The firm has purchased (for cash) additional raw materials so that additional product can be m.ade. For convenience, the chart of accounts in Table 2 has been abbreviated.

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so 'O -H

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II 6. General and administrative expense. The firm has paid for general and administrative expenses which it used throughout the period under consideration. The concept of a transaction is very similar to the concept of a process previously defined, and may be thought of as such. It is a set of ratios among rates of consiomption of ve.rious inputs and rates of production of various outputs. Indeed, we v/ould like to think of a process in terms of a financial transaction. We have noted that processes are the alternatives from which entrepreneurs must choose in the decision-making process, and as Brown (1958, p. 101) has said, "All (business) decisions are financial decisions." Brown justifies his statement this way: All decisions are financial, either because they directly affect the expenditure of money, or because they indirectly affect expenditures by consuming or disposing of effort, facilities, or material, all of which cost money. A decision to improve toilet and locker facilities ms-y begin frorn a proper concern for the health and comfort of employees, but it requires an expenditure, and every expenditure affects the earnings of the enterprise. All decisions are financial because you cannot conceive of one that does not affect, in one way or another, and in som.e degree, the earnings of the enterprise. . . . to these decisions, the engineer, the production man, the merchandiser, and perhaps others, must all contribute. What they contribute are facts Â— the facts that each is skilled to obtain. To the facts so contributed, moreover, someone must apply reason--intel] igence Â— so as to give them their proper weight, evaluate them, and relate them properly to each other. This is the material-the foundation--of decision. This is the financial approach .

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92 . . . each of these men has a primary operating function, but each must approach that function with a financial viewpoint because his decision will affect the earnings of the enterprise. In that sense, eacli is a financial man. Let us assume that the ratios shown in Table 2 represent the respective processes when they are being operated at the unit level. For example, if process 4 is operated at a level of 10, the finished goods inventory v;ill be increased by $700, raw materials inventory v/iil be decreased by$400, etc. Mathematical notation It is convenient at this point to reintroduce: soicie mathematical notd;tion. Suppose we assign a number j to each of the firm's accounts and assume that j takes on integer va.lues from 1 to w* . VJe will then group tiie accounts so that as j varies as shown below, the folJ.owing type of accounts will be assigned the nuri'ber represented by j. Currerit assets ^ 1 J .1 P* Fixed assets p* + 1 < j < q* Current liabilities 9* + 1 < J 1 ^* Long-term debt r*-i-l
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93 Let us also assume that there are n processes and we will let i be the index of process numbers so that 1 < i < n. Let X. represent the level of utilization of process i, and x, the program vector be X = [x^, x^, . . . , x^] . a., v/ill represent the net effect on the "i"th account by utilizing process i at a unit level. Any process can be represented by the process vector The process matrix yl ^ , v/ill then be We will utilize this notation after we have considered another concept utilized by the entrepreneur. Business Income Let us briefly investigate a simplified example of a typical income statement of a firm. The income statement is a suiiimary of the changes in equity which result either from trai:isactions betv/cen the owner and the firm or from transactions entered into by the firm for profit. Net income is the difference between realized revenues and expired costs for the period under consideration. The

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94 simplest arrangement of an income statement is a tv;o-part summary with all revenues reported first and then all expired costs deducted. Mathematically, net income can be represented in two forms; Form I, U^sc) d^ = net income. d' -

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of a^. d^ is likewise identical to d'' except that it also contains only the first t* components. ,2 ~ \~,2 -.2 a2 Â• ^1= Ki' ^k -^i^' J3 . [d3, d3, . . ., d3j, d' td^ d^ d^, Net income may now be expressed as {A^x)'^dK Rearranging, we find X A'^ a^ = net income. T Let z represent net income and let c be an n coiiiponent vector so that -T ' T A^ d^ c . Thus, z = ex ~ net income. We have nov/ expressed net income in the form of the linear programming objective function. Under our assumption of profit maximization, this is the entrepreneur's objective function. Suppose v;e let ^' be a t* component vector representing the exact amount in each of the t* balance sheets

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96 accounts at the beginning of the period. y'^ would be a t* component column vector representing the balance sheet accounts at the end of the period. Let us define y to equal a'^-x. y represents the net changes (during the period) in all balance sheet accounts except the owners' equity account. It does not reflect the entry of closing net income into owners' equity. Although this may seem abstruse here, it v/ill serve to illustrate concepts used later in this study.

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SECTION X THE PORTRAYAL OF THE FIRM: A MODIFIED ACCOUNTING VERSION The preceding section of this study has tended to be more of a financial or '"bookkeeping" picture of the fi.rm. It did not particularly help us understand the concept of entrepreneurial discretion under constraint. In order to gain a better picture of this process, v/e must modify our concepts of balance sheets, income statements, and business transactions. The Entrepreneur-ial Balance Sheet First let us consider the balance sheet. In order to allov/ for entrepreneurial discretion, the major asset cJ.assif ic^.tions on our balance sheet should now be variable and rionvariable assets, rather than current and fixed assets. Likev.nse, the liabilities should be divided into variable and non-variable liabilities . The key to dif:tingui shing between variable assets and non-variable assets is the type of entrepreneurial discretion involved iri utilizing the asset. For variable assets, the entrepreneur has a range of discretion in 97

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98 deciding how (in what way) an asset should be used and hov/ much" (in terms of quantity or value) of the asset to be utilized. For non-variable assets, the entrepreneur still must decide how the asset is to be utilized, but he has a gi.ven quantity available for utilization v/hether he uses it or not. Variable assets in our new balance sheet correspond closely to the current assets of our old balance sheet; they give us little concern. It should be remembered, however, that entrepreneurial discretion is the key to our new balance sheet. Sufficient subclassif icaticn should be done to allow for a full range of entrepreneurial discretion. For example, if several products are being manufactured, an account for the finished goods inventory of each product should be listed, instead of combining the total inventory into one account. Non-variable assets arc of more concern to us. Traditional balance sheets stair.e the value of fixed assets in terms of dollars. This, however, is not the ma^or concern of the entrepreneur as he plans his operations It is true that some of the variable assets are committed to mieet non-discretionary expenses such as raxes, guaranteed wage payments, etc., but tne entrepreneur does have som.e latitude in the extent of utilization of variable assets.

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99 for the next mono-periodic production period. He is more concerned with what can be done with the available assets than he is with the accountant's evaluation of them. There are some assets (perhaps the land of on which his factory operates, or even the factory building itself) which do not enter into the management decision process for the period under consideration. These assets might be omitted from our balance sheet without loss of effectiveness. To better understand this concept of non-variable assets, let us introduce the concept of a control unit (center). Most managers, instead of viewing the factory as one big operation, cut the fabricating activity up into control centers. These control units can be one asset, or a group of assets working as a unit. The distinguishing characteristic of a control unit is that it operates as an entity. In regards to production, it represents an uninterrupted process flow. Any m.aterial which enters a controj unit cannot be removed until it has undergone all operations and services offered by that control center. In a sense, there is no entrepreneurial discretion Vv'ithin a. control center. Consider a tile manufacturing operation. If a firm has only one mixer, one press, and one furnace, then the firm may be thought of as having only one control center. Suppose, however, that the firm has two mixers, two presses, and t\/o furnaces,ana that the mixers may

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100 feed either press, and each press may feed either of the tv;o furnaces. The firm must now be thought of as having six control units. Services under a guaranteed contract must also be considered as non-variable assets. If the firm, has a contract guaranteeing a thirty hour workweek for some or all of its employees, then this must be considered as a non-variable asset. This amount of .labor is available to the entrepreneur whether he uses it or not. Guarantees for other services such as a minimuia amount of electrj.city or water should likev/ise be considered as non-variable assets . The important consideration with non-variable assets is the amount available during the period. Consideration must be given to the fact that the units of measurement differ from asset to asset. The simplest method of handling these differences is to convert all availability to a percentage basis. TJormally, 100% of each fixed asset will be available in each mono-periodic production period. There will be times, however, when less than 100% (a machine needs repair) of a non-variable cisset is available. The distinction betv/een variable and non-variable liabilities should, as in the case of the assets, be made with respect to the entrepreneurial discretion involved.

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J 01 Accrued wages, accounts payable, etc., are considered to be variable liabilities because they vary as the result of management decisions made about the opera tiois of the period. The important consideration with variable liabilities is, as was the case wJ.th variable assets,to provide enough subclassif ication to insure entrepreneurial discretion. Most firms, however, do have raany items whicli can be considered as non-variable liabilities. The firm usually has a given tax bill to pay (or accrue) during each period. The sam.e thing would hold true for saJ.arics, guaranteed wages, and other items which the firm is committed to pay regardless of the operations during the laono-periodic production period. Since some entrepreneurial decisions are based upon the effect of the chosen alternatives upon traditional balance sheet accounts, it is convenient to include these in the entrepreneurial discretion balance sheet. A typical entrepreneurial discretion balance siieet is shown in Table 3. A Modified Concept of Prooesaes Let us next consider the concept of process Ctransaction) . Our new concept of a process is almost identical to the previous one. Table 4 illustrates several transactioi

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102 TABLE 3Â— HYPOTHETICAL ENTREPRENEURIAL BALANCE SHEET Account Number Account Name Variable assets: 101 Cash 102 Accounts receivable Inventory (finished goods) 103 Product alpha 104 Product beta Inventory (raw materials) 105 Material omega 106 Material zeta Value of fixed assets 201 Land 202 Buildings 203 Equipment Non-variable assets: 301 Control unit A 302 Control unit B 303 Control unit C 304 Guaranteed labor 305 Other guarantees Variable liabilities: 401 Accounts payable 402 Accrued wages 403 Other accruals Long-term debt: 501 Bonds payable Stockholders' equity 601 Common stock 602 Retained earnings Non-variable liabilities: 701 Guaranteed wages 7 02 General and administrative Valuation

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103 4J C U G XJ r-i CO I I

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104 -

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105 Process I represents the production of one unit of product "alpha" by a particular method. This process produces $70 of "alpha" inventory . It utilizes$30 of "omega" inventory, $10 of "zeta" inventory, 1% of the total capacity of cost unit A, 8% of the total capacity of cost unit B, and 2% of the labor V7hich is under a 2 guciranteed contract. Notice that the accrued wages account is not affected. The firm has utilized a fixed asset (guaranteed labor) instead of acquiring a variable liability (wage payments) . Prooess 2 is another method of producing$7 of "alpha" inventory. It utilizes different perceritages of the firm's fixed assets than does process one. Process 2 is identical to process one excep-c that it does not utilize any of the pre-paid labor. Instead, it uses discretionary laoor ; labor which can be purchased or not purchased. It is obvious that process three will never be utilized as long as the entrepreneur is free to utilize more of process one. Processes 4 through 8 are very similar to the traditio2~ial accounting transactions. Process 4 represents 2 The assumption witli non-variable assets (for exeauple, cost unit A) is that there is 100% availability at the beginning of the period and that process one reduces (thus the minus sign) this availability by 1%.

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106 the selling of a unit of "alpha" inventory on credit. Prooess 5 represents the conversion of accounts receivable into cash. Process 6 represents the action of paying wages. Process 7 and p-rocess 8 represent the purchasing (for cash) of "oiiiega" and "zeta" inventories respectively. Process 9 represents the payiTients of guaranteed wages and process 10 represents the payiiients for general and administrative expenses used throughout the period. Process II accounts for the depreciation of fixed assets during the period (timeperiod depreciation is assumed) . A Modified Form of Business Income Let us assume that we have w accounts on our nev7 balance sheet. Suppose v;e again assign a number j to each of the firm's accounts and assume that j takes on integer values from 1 to w. We v.'ill then group the accounts so that as j varies as shown below, the following type of accounts v;ill be assigned the nuir.ber represented by j . Variable assets 1 < Value of fixed assets p -t 1 < j < q Availabi.lity of fixed assets q + 1 < j Variable liabilities r r 1 ;Â• Value of long-term debt s + 1 < ^ Valuation of ov/ners' equity t + 1 < j < u Fixed liabilities u + 1 < j

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107 Let us also assume that there are n processes and we v/j.ll let i again be the index of process nuniber so that 1 < i < n. Let X. represent the level of utilization of process i, and X, the program vector, be ^ = f^l' ^2 ^n^a^ . will represent the net effect on the "j"th account by utilizing the process i at a unit level. Any process can then be represented by a process vector a / "i ^ f^li' ^2i \'i^The process matrix A v/ill then be /. (a, , a^^ , , . . , o: ) . Suppose v/e define a new w component column vector d"* so that 1 /! W d^

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108 The accountant's version of net income is now represented by (.4:c) d^ ~ z ~ net income. Let o /.^'c^S 7. = ex. This, however, is not the function which the entrepreneur v/ould like to optimize. Suppose we define another w component column vector d^ so that d~' = [d5, d^, . . . , d^J , d5 1, d^ = 0, ~1, d^ = J d5 = -; j = 1, . . J == P + 1/ j = r + 1, j = s + 1, j = u + 1, let Now consider the function Ux)'^d^ = z, a -Ad-', I w. This is the function the entrepreneur would like to maximize The reason it is preferred is that it either does not consider, or "washes out" actions v.'hich are forced upon the

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109 entrepreneur and thus effectively only considers those actions which are associated with entrepreneurial discreation. Let us again let y'^ be a w component column vector of balance sheet accounts at the beginning of the period and 1/2 be a w component vector of balance sheet accounts at the end of the period. y = Ax represents the change in balance sheet accounts during the period .

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SECTION XI THE P0RTR,2iYAL OF THE FIRM: A PARTIAL MATHEMATICAL FORMULATION We have shovm that T r {Ax) d'' = ex 7. is the objective function of the firm. Nov let us brxefly reconsider the entrepreneur's sphere of discretion. The constraints which define the entrepreneur's sphere of discretion will often be formulated from the entrepreneurial balance sheet. The balance sheet itself, hcv/ever , is not per se a constraint or set of constraints. The constraints must be formed from the balance sheet. We will often want to formulate a constraint in terms of an end of period baleince sheet account, or in terms of net change in a balance sheet account during a period. Since i/^ is assumed to be knov/r. , and since the follov,'ing relationships hold, y^ ^ \i '-^ yr , yl + y . y2, j'-j ^J ^3 y -' Ax , n i=l J]. I 110 -

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Ill it is irrelevant whether we express the constraints in terns of ij components or y^ components because constraints expressed in terms of one can alv.-ays be converted to the other. For our purposes, it will normally be convenient to express constraints in terms of y components. Let us introduce a new vector c, which will be defined so that n z i=l Z a . . X . . Thus, e^ = (a.^, a.^, . . ., a .^) , ^k = (^kl' ^k2' Â• Â• Â•' ^kn^There i s no previously defined relationship between j and k. The relationship v/hich does exist for any particular problem will be dependent only on the problem formulation. There will also be occasions when we would like to formulate a constraint directly in terms of a process or processes instead of in term.s of balance sheet accounts. (The balance sheet account constraints were indirectly formed in terms of processes.) We m.ay, for example, want to insure that process j. is operated at less than or equal to a certain level, or that process 2 plus process 3 equals zero, etc. e^ for these constraints may be formed from these equations by letting the "i"th component of e, equal the coefficient of the "i"th process in the constraint equation. For processes

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112 not considered in the constraint equation, the corresponding component of e, will be zero. In general a constraint will be formulated so that some combination of processes is required to be less than, greater than, or equal to a predetermined constant, A typical constraint will take the forii^ of V ^^' ^' ^^\There are many possible types of constraint formulations for a typical firm. It V7ould probably be unv/ise to spend a great amount of effort here on mathematical .formulation of constraints. It would, however, be wise to select a few types of constraints which are coramon to most firms; show how these can be formulated mathematically, and show that the formulation corresponds to the form previously described. Survival constraints, minimura profit constraints, corporate image constraints, sales constraints, and direction production constraints are considered below. Survival Constraints' Earlier, we noted that the firm, has a compelling urge to survive. Furtheriaore a firm which raaxiTnizes profj.ts might not survive because of inadequate liquidity, etc. Therefore many firms put financial constraints upon

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113 their operations. These constraints often take the form cf ratios among two or more types of asset and liability accounts, ye wj.ll consider tv;o typical ratios here,, the current ratio and the liquidity ratio. Current ratio constraint One of the simplest balance sheet ratios used by a firm, is known as the current ratio. It is a simple ratio of current assets to current liabilities. The current ratio is the most widely known analytical percentage in financial management. It is not too accurate, and it can be manipulated easily by management. The current ratio reports, in percentage, the shrinkage that can occur in conversion of current assets to cash before becoming unable to pay off current liabilities. It is often believed tnat the current ratio should be maintained at a value v.'hich is greater than or equal to some constant such as two. Let us define a current asset vector f^ , a current liability vector f'^ , and a current rat j.o vector /^ . All will be v; component coluum vectors and /^ will equal /^ -2/-^, i.e., /3 = y-l _ 2/2 . The co!p.ponents of f^ will vary as follows: f^ 1, j 1, . . ., p, f ^ =^ 0, j = p + 1, . . . , w.

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114 The components of f'^ will vary as follows: f^ 0, j 1, . . ., r, fj 1, j = r + 1, . . ... s, f^ j = s + 1, . . ., w. The current ratio constraint can be expressed as CA/CL > 2, CA 2CL > 0, rn P CA fl-" i,Ax) + I Y^ , j = l 3 CL f'Ux) -r Z yl j=r+l ^ m P s CA 2CL = f^ Ux) + I y\ ~ 2 I y^. > j = l ^ j=r-fl ^ E y^ 2 E y^ = K (known constant j=l ^ j-r+1 ^ ^ ), P {Ax) > Kt /3 z a.x > K , i-1 ^ ^ I J^'^a.x, > K i-1 ^ Â• ^ ^k^ i K^ = b^, ^r, (/''^a^. /'^a. /'%)Â•

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215 Liquidity of assets constraint Liquidity of assets is an important consideration in any firm and at times a firm might choose to make decisions so that its quick assets (cash and receivables) will be at least a certain (for exam.ple, 2 5%) percent of total assets. Suppose we let y^ represent cash and y| represent receivables. f^ v;ill be the quick asset vector and f^ will represent the total asset vector. f'^ will represent the liquidity ratio vector. f^ = f'* .25f^. The components of f^ will vary as folJows: f^ 1, j = .1, 2, f^ = 0, j = 3, . . ., w. The components of f^ will vary as follows: f^ = 1, j = 1, . . ., q, f ^ =Â• , j = q + 1 , , . . , v; . The liquidity constraint can be foxmulated as follows: QA > .2 5TA, T 2 QA f'^UAx) 4 Z yl j-1 rn g TA ^f^^ iAx) + I y] , j = l

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116 QA -.25TA = f^ iAx) + Z y^. .25 E y^ j--l ^ j = l ^ 2 q E y^. .25 E y^ = K^ (known constant) j = l -T j = l ^ QA > .25TA == f^''^ U--C) > K^, J/--". Satisfactory Profit Constraints Earlier in this study we noted that the entrepreneur should always be aware of the value of the objective function to insure that other objectives do not take precedence over the making of a satisfactory profj.t. It was noted that a miniiP.uiQ profit constraint could be formulated, but the inclusion of this requirement into the set of constraints would probably be redundant. This is certainly true if the entrepreneur expresses his minimum profit requirement as an absolute value. There are cases, however, where it V70uld be advisable to include in the set of constraj.nts , a requirement for a minim.um return on sales, or on operating assets.

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117 Return on sales Let t be the sales vector, ' = (^1' 4 ^r^t. equals the value received for operating a selling process at a unit leve] . t. v?ill equal zero for all processes which are not selling processes. Z t.x. = total sales, i^l ^ ^ E ex. = net .income. i^l ^ ^ Â•Let us assume that a firm would like for net income to be greater than or equal to 5% of total sales. NI > .05TS, NI .05TX > 0, n n I ex. .05 E t.x. > 0, i=l ' ^ i==l ^ ^ L (c. ,05t.)x. > i^-1 ^ ^ ^ % ^^^1 -^^h^ ^^n ~ -'''-'^u^^ Return on operating assets Next let us consider return of operating assets. Assume thaL the firm, would like net incom.e to be greater

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than or equa]. to 1% of operating assets. Let f'' be the operating assets vector, and d.^ as previously defined is the net income vector. /^ v;ill be the return on operating assets vector. /S = J^ .01/7, f? = 1, j = 1, . . ., q, f? = 0, j = q + 1, . . ., w, f {Ax) + Z y. = operating assets, J-1 d^ KAx) = z = net income, NI > .OlOA, NI .OlOA > 0, d}"^ {Ax) -.01/7(^1^^) = .01 E y^. > 0, .0], E y": K. (known constant), d""^^ {Ax) .^\f {Ax) > K^, /8 _,^,.x. > K^ E /Â« a,.x. > K^ ^k =" ^^'^'^1' f''''^2' Â• Â• Â•' -^''^^n^'

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119 Sales Constraints Sales constraints are easily for;aulated mathematically. We will consider here three types of sales constraints which v/e shall call simple sales constraints, total sales constraints, and complementary product constraints. Simple S3i].es constraints state that no more than a given amount of a certain product may be sold during the period under consideration. Since we have a process for each selling activity, the constraint will take the form that the corresponding process must be less than or equal to som.e predetermJ.ned constant. X, < K. (known constant) t Â— Â•k 6 k ' i t , i 7^ t. Total sales constraints are extensions of simple sales constraints. A firm may be manufacturing three products and decide that total sales cannot exceed a given amcvjnt . X, + X < K (knov/n constant) , D c / ^k'

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120 e^^ =1, i = a, b, c, e^^ 0, i 7^ a, b, c. Complementary product constraints arise when a firm manufactures two products which must be sold in a given ratio. The classic example is left shoes and right shoes. For each ]eft shoe sold there must be a right shoe sold. Suppose a firm must sell twice as much of one product as another. ^-a

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121 converted to the othei . In reality, most of the constraint: concerning variable assets or variable liabilities will be first expressed in terms of z/^ components and then, for convenience, must be converted to terms of y com.ponents. A^

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12; ^j ^\o y] \v. Non-variable asset constraints are almost always expressed in terras of y components. To be more specific the total amount of a non-variab].e assoc utilized v/ill usually be constrained to be less than 10C%. y. < 100, n I a . .X. < 10 ^ b, , i=l 31 ^ k e^x < 100, ^k -^""yi.' ^j2' ' Â• Â•' ^jn^Non-variable liabilities are normally constrained to be zero (or a certain specific value) at the close of the period. In general, the total amount of any nonvariable liability must be paid dur.ing the peri.od so that the non-variable liability account on the entrepreneurial balance sheet must equal zero at the end of t}ie period. y\ 0, y^ + y^ = 0, J J y. .. yl z. b, , E a . . X . =-b, ,

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123 Corporate Image Constraints Earlier in this study v/e noted that the creation and maintenance of corporate images plays an important role in the modern firm. Ultimately, all decisions result from some sort of image in the mind of the decision-maker. The important consideration with corporate image constraints is what act, or what decisions, will project the correct corporate image to the group involved. These groups include customers, employees, competitors, stockholders, suppliers, government officials and the ge;ieral public. Decisions result not from the actual images held by these groups, but by what acts management thinks will project the correct image. The proJi-ilem of image creation is complicated by the fact that the existence of a characteristic does not necessarily create an image of it, nor does an image insure the presence of the characteristics involved. Thus management is constrained by their belief in what v;j.ll create the proper image, rather than by the image itself. Depending upon the group involved, various types of images raay be considered desirable by a firm. In most

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124 cases, however, corporate image constraints wij. 1 take the form of one of the other types of constraints presented. Constraints which might project a desirable image to the general public would include the maintenance of a minimum total sales volume, m.aintenance of a minimum sales volume in some particular product line, or a minimum contribution to charitable and civic activities. Stockholders may require a minimum return to invested capital. Government officials may frown on an excessive profit. Employees may be better satisfied if a certain level of contribution is made to a profit sharing program. The corporate image constraints v/ill vary greatly from firm to firm, but in general the formulation of the constraints will be similar to the formulation of other types of constraints. For this reason, no attempt v.'ill be made here to formulate typical corporate image constraints . Review and Surrimary The entrepreneur's sphere of discretion will be defined by a series of constraints of the form Let us assume that there are m such constraints and tliat the entrepreneur's sphere of discretion is the

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125 set. of points which satisfies aJ.l la of the constraint equations. If all the constraint equations are converted to equality constraints, the entrepreneur's sphere of discretion can easily be converted to matrix form. Ex = h. The object of the restatement is to avoid some of the j.nequalities which resulted from economic analysis but which a?-e ciwkvard m.athem.atically . This conversion is easily accompJished by the addition of slack and surplus processes. Each slack ?nd surplus process vector will have a zero for each com.ponent except for the component corresponding to the process for which it v/as intended to convert from an ineqi;.ality to an equality. This component will norraally have a unit value. The exact interpretation of these slack and surplus processes will vary, but in general a slack process v;ill represent the amount by which the program under consideration fails to satisfy the corresponding constraint as a strict equality, and a surplus process will represent the amount by which the program exceeds the minimum requirements of the corresponding constraint. The firm is run by the entrepreneur. The entrepreneur is not one mari , but a number of men who compose a management structure of groups and complexes; a

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126 pluralistic whole. The entrepreneur, in carrying out the function of management, is prim.arily a decision-maker. An ultimate task of the entrepreneur is to select among alternatives v/hich have varying opportunity costs. In this task, the entrepreneur will strive to select that alternative, or that set of alternatives which will optimize som.e predetermined objective. The entrepreneur is not free, however, to choose any set of alternatives. He must always select an alternative or set of alternative; which is v;ithin his sphere of discretion. Mathematically, the entrepreneur would like to se].ect a program, x, that v.'ill make his entrepreneurial discretion income, z = ox, as large as possible, subject to the lim.itations or constraints imposed. Succinctly, the problem is to find a program, x, which satisfies Ex = h, X > 0, and which makes as large as possible.

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SECTION XII IMPLEMENTATION: THE PORTRJ^YAL OF THE FIRM This section actempis to xormu-late, in terras of the concepts previously presented, t?ie problem faced by one entrepreneur in a typical mono-periodic production period. The Firm Chosen for the Implementing Study A wall tj le manufacturing plant v;as chosen for Â•che implementation part of this study. There were two primary reasons for this choice. First, and perhaps most important, management \;as interested in the project and was extremely cooperative rn p:,-oviding the records, interviews, and ether informati.on from which the data presented in this section were obtained. Second, the orgar.ization of the firm and the types of problems faced by management serve well to illustrate the concepts previously presented, The particular firm used for this implementation is one of the six largest firms in the ceramic tile manufacturing industry. It is a multiproduct , singleplant firm. The firm is run by a very progressive management team which has led the firm through a period 127 -

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12i of rapid growth. For the past six years, the firm has experienced the most rapid growth in the industry. Data Collection and Presentation The data presented in this section v;ere obtained frora an extensive analysis of the firm's accounting, production and sales records, and from. interviev;s with management personnel. The compilation of this data was one of the most difficul.t and time consuming aspects of this study. Table 5 represents an actual entrepreneurial .balance sheet for the firm at the beginning of a particular mono-periodic production period. Table 6 lists the various process alternatives available to the entrepreneur. Tables 7 through 11 m.athematically describe (in vector form) the available processes. Table 12 lists the constraints v/hxch define the entrepreneur's sphere of discretion.

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129 TABLE 5---BEGINNING OF PERIOD ENTREPRENEURIAL BALANCE SHEET Account

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130 TABLE 5 Â— Continued Account Number Account Name Va.luation 305 Machine score 420 306 Machine press 420 307 Straight-line number four 420 308 Straight-line number five 420 309 Spray 420 310 Hand spray 420 311 Kiln 420 312 Grading 420 Variable liabilities: 401 Notes payable 966,000 402 Accounts payable 464,949 403 Accrued salaries and wages 64,301 404 Accrued taxes 236,667 405 Miscellaneous accruals 51,410 Long-term debt: 501 Bonds payable 1,479,398 Stockholders equity: 601 Comimon stock 3 4 0,980 602 Excess over par 752,72? 603 Retained earnings 1,825,275 Total liabilities 6^18X/_70 2 Non-variable liabilities: Finance 701 Dividends payable 702 Profit sharing contribution 703 Interest expense 704 Personal and prcper::y tax 705 Planned purchases General and administrative 751 Sales division 752 Warehousing and distribution 753 Finance division 754 Executive division 755 Industrial relations 756 Expansion and diversification 5,4 46

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131 TABLE 5 Â— Continued Account NuiTiber Account Name 757 Research and development 758 Maintenance 759 General factory expenses 760 Engineering supervision 761 Transportation division 762 Quality control 763 Engineering services Valuation

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-132 TABLE 6--KEy TO PROCESS NUMBERS Process Number Descripcion 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 Manuf actur ing : Bright 4-3/8; method 1 Bright 4-3/8; method 2 Bright 4-3/8; method 3 Bright 4-3/8; method 4 Bright 4-3/8; method 5 Bright trim; method 1 Bright trim; method 2 Matte 4-3/8; method 1 Matte 4-3/8; method 2 Matte 4-3/8; method 3 Matte 4-3/8; method 4 Matte 4-3/8; method 5 Matte triru; method 1 Matte trim; method 2 Dapple 4-1/4; method 1 Dapple 4-1/4; method 2 Dapple 4-1/4; method 3 Dapple trim; method 1 Dapple trim; method 2 Crystal 4-3/8; method 1 Crystal 4-3/S; method 2 Crystal 4-3/8; method 3 Crystal 4-3/3; method 4 Crystal trim; method 1 Crystal trim; method 2 Hex 3; method 1 Hex 3; method 2 Hex 6; m.ethod 1 Hex 6 ; method 2 Scored ware Scored trim; method 1. Scored trim; method 2 Sills Six by six 40 41 42 jelling : Bright 4-3/8 Bright triiTi Matte 4-3/8

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133 TABLE 6 Â— Continued Process Nuraber Description 4 3 Matte trim 44 Dapple 4-1/4 45 Dapple trim 46 Crystal 4-3/8 47 Crystal trim 4 8 Hex 3 49 Hex 6 5 Scored ware 51 Scored trim 52 Sills 53 Six by six Purchasing : 54 Body material 55 Glaze material 56 Packing material 57 Mechanical stores 58 Die parts 59 Refractory supplies Finance : 60 Reduction of accounts receivable 61 Reduction of accounts payable 62 Reduction of notes payable 63 Payment of wages 64 Reduction of miscellaneous accruals 65 Transfer of long term debt 66 Dividend payments 67 Contribution to profit sharing 6 8 Interest expense 59 Interest earned 70 Income tax accruals 71 Income tax payments 72 Plant depreciation--buildings 73 Plant depreciation Â— equipment 74 Plant depreciation--other 75 Personal and property tax--accrijals 7 6 Personal and property t3X--payments 7 7 Machinery pu.rchases 78 Charitable and civic

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134 TABLE 6 Â— Continued Process Number Description Genera], and administrative: 80 Sales division 81 Warehousing and distribution 82 Finance division 83 Executive division 84 Industrial relations 85 Expansion and diversification 86 Research and development 87 Maintenance 88 General factory 89 Engineering supervision 90 Transportation 91 Quality control 92 Engd.neering services 93 Advertising Source: See Section XII, Data Collection and Presentation^, for source and explanation of data.

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136 o o o o o o c o o o o o O LTi (N (Â— I O og O iH (Tv CTi -^ Â«^ in CO o o in CN o o i-l ,-i y.D M o o ro rs] I I o o o o o o O O O CO o o CO O fN rH r^ rO O M CTi C^ ^ LD 1111(1 in rH in tH

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137 o o o o o o o o 00 MD rv] r~-

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138 o o o o o o o o o o o o 00 r-fN oj LD o in ro o in r^ o o o o

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139 C O O O O O rs cTi o lO vn r00 o r^ r^ M iH I I I I I I I ^ O (N UO * O M VÂ£) n O CN CN

PAGE 148

140 O O O O O O VO o o o o o o r\j CO a\ CN >^ CO OD r-\ o i^ 0-, CO n CO o rCM I I I I I ! I o o o o o o o o o o o o 00 r^ LO o CO cr> fo o CO CO o m I I I I I t o o o o o o o o o o o o CO M LO n CO CM a U O .q o Â« o 3 rq r^ CO CO ui vD o o o o o o o o o o o o CO iH U-) "^ O LD f-1 rvj o o o o o o o o o o o o o o o o o o CO r^ LO r O '^ ^' rrr-i r-{ I I I I I I CO Ti o .Â— { r^j o") IÂ— 1 og ro ^' rn \jD r^ CO o-> o rH MrHcvjcNoirM ooooooooor-1,-1 iH r-l Â— i 1Â— 1 M iH m rn ro n n ro ro <^) C-] rr, ro

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144 O b O 1:5 o

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145 O r> I --H CM ro 00 a\ O r-i CN ro rH ^^j I o o o pH ,h r^i oj oj r-i o cj I r-\ -; n-! ^H _H ,-H ^-^ M M Â»} ^ 1) ra O 4-' o o

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PAGE 158

150 O rxj .-I M O -Q o e K ! r -1 c\i ro ^ o o o c> CN r-i r\tH csj ro --r LD >Â£i 1-CO oi o r-i oj ro lT; in lD ui L ) in in u' lo o '-y vd ^ r-rr^ i--r~ rrr^ r[^ r-~ r-r-

PAGE 159

151 o r-{ n o ^ .H r-; ro ^LTi o o o o o ^ TJ.-1 'J. ^ rH (N OT ^ LT! iXi r^ 03 CTi O rH C^J ro lD lO lD lO L/> lO iD lT) lT) 'X) ^ vO >X) rrrrrrr-r-~ r-~ rr^ ir-

PAGE 160

152 00 n O O f1 3^ i-H CN (^; -^ C3 O O O CM rsi CM -H (N ro ^ LO o o o o o ^-' ^ ^ ^J1 ^^ iH CN ro "^j' L") ^T! r^ CO 0~^ O iH CN r^") Ln LO LO LT) LO :r) lO ;r) Li 1^ VÂ£) MD ;Â£) r^ r~r^ C-rr^ r-rr-^ 1^ ^~ r^ r-^

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153 TABLE 12--C0NSTRAINTS DEFINING THE ENTREPRENEURIAL SPHERE OF DISCRETION Constraint Number Constraint Description Direct production constraints 101 .f^-ioii^-. ^ ^^'^51 102 -E a,^, .X. < 2,60' j._, lOli 1 103 Z ax. < 41,204 i=l ]04 -I a_.,.x. < 58,796 ,_, 102i X 105 1 a,^,.x. < 20,347 106 -Z a ^2^x. < 21,653 i-1 107 Z ^^104 i^i -Â• 1'7'5'^^ 108 -Z a^, . .x. < 32,428 i.l 104^ ^ 109 Z a, ,,^ .X. < 2,283

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154 TABLE 12-Continued Constraint Number Constraint Descriptior 110 -I ^105i^i 27,717 i=l 111 J^^lOGi-i <^'258 112 -E a^Q^.x. < 10,742 1=1 ~ 113 .^^107i^i ^ 2'^'' x=l 114 -Z a.-Q^^x^ < 11,545 i=l 115 I ^1081^1 ^ ^'^^'' 1=1 216 -f^^lOSi^i ^ ^'-'^^ 117 .^-109.--i 1 ^'Â°^2 i=i n 118 -I a^Q^^x^ < 958 i=l n 119 I a-,,^.x. < 365

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124 128 155 TABLE 12 Â— Continued Constraint Number Constraint Description 120 T^/llOd^i < -958 1-1 121 Z a,T, X. < 506 n 122 -Z a,T, .X. < 1,494 i=l 1-^-^ ^ -Â• 123 Z aTTÂ„.x. < 83S 1=^1 11^^ ^ ^]1 ., .X. < 9,16 2 2i 1 125 Z a,,^.x. < 4,599 126 -Z a, , -, .X. < 15,4 01 . , 113:. 1 i=l 127 Z a^^,.x. :: 668 1=1 -Z a, , , .X. < 5,332 i=l ^-'^ ' 129 Z a^T.;-. < 3,096

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156 TABLE 12~-Co7^tinued Constraint Number Constraint Description 130 -E a^^^^x. < 1,904 131 Z a^T^.x. < 453 Â± 1 b J. 1 Â— 132 -f.^llGi^i ^ ^'^'' n n i=l n y. 133 L a .X < 1,194 i-1 -'''Â•^ n 134 -I a ,^.v_. < 806 i=l -^-^'^ "135 Z a-,,g.x. < 1,877 136 -I a,,Â„.x. < 18,123 i-1 ^-^^^ Â•" 137 iil'-llSi^i " ^-^'^'' 138 -;^^119i^i 28,832 139 .f^^l20i^i -^ 2.356

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14 3 157 TABLE 12 Â— Continued Constraint Nuiaber Constraint Description 140 -f^^l20i^-i ^ ^^^ 141 Z a^2ii^i < 25,842 1=1 142 -E a .-, .X. < 4,153 i=l ^'-^^ ^ n E a^,Â„.x, < 15,161 144 -Z a^Â„Â„.x. < 4,839 1=1 ^^^^ ^ 145 Z a3_23iX, < 10,990 1=1 146 -Z a^ .X. < 10 1=1 ^ ^ 147 -^^^3011^1 ^ '^-' 148 -Z a_,Â„^.x. < 420 149 -;^^303i-^i '^20

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158 TABLE 12 Â— Continued Constraint Number Constraint Description 150 -f^^304i^i < 4^0 151 ~l a^^,^ .X. < 420 15 2 :^.^306i^^i ^ 4^^ 153 -!,-307i^i < ^-20 154 -Z a,Â„. .X. < .^, 30 8x 1 420 155 -Z_^a3Q,^x. < 420 156 -f^-310i-i ^ ''' 157 Â• L a _, , , . X i=l 3].li" i 420 :^-3i2i-i :: ^2Â° 1=1 159 .^ a4,3.x. < 34,000 1-1

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159 TABLE 12-Â— Continued Constraint Nuiuber Constraint Description 16C -I a,., .X. < 66,000 4011 1 i-1 161 Z a^Q2i^i 2^'Â°51 i=l 162 -Z a,02iX, < 64,949 i=l 163 Z ax < 5,699 i=l 164 :^^403i^i ^ ^'^'-^^1 1=1 165 E a^^ . .X. < 63,333 . _ -, 4 4 1 1 166 :^^404i>''i < 56,667 1=1 167 Z a.Â„^.x, < 18,590 . _ , 4 5 a 1 ' 168 -^.^405i>'i '^I'^l" 169 :^^7011.^i 1=1

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160 TABLE 12 Â— Continued Constraint Number Constraint Description 170 -f^^02i^i ^'^Â°^ 171 -I a^Q3.x. =^ 22,761 i-1 172 :fl"704i-i = ^'^^^ 173 -Z a^Â„^.x. = 54,883 n 174 -I. a^p, .X. = 21,398 175 -Z a^^Â„ .X. = 18,629 i=l '^-^^ ^ 176 -E a,. .X. = 16,563 177 -? ^7541^1 = 1^'5^Â° i-1 178 -Z a^., X. = 20,038 179 -Z a_^,.x. ^5,446 .^3_ 756.1 X

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2C2 161 TABLE 12 Â— Continued Constraint Number Constraint Description 180 -Z a_,Â„.x. 5,949 i=l ^^'" ^ 181 -I a^^g.x. :. 9,607 i-1 182 -2 a^^Â„.x. = 23,519 i==l ^^5x J. 183 -I a^,Â„.x. 7,056 184 -Z a^,. .X. = 16,527 i=l ^^^^ ^ 185 -Z a^,,,.x. -4,953 i.l 76^1 1 186 -Z aÂ„,,.x. 6,397 j_..l /633. X Sales constraints; 201 x^Q < 1,000.0 Â•-^^'^40 -^41 i ^ 203 -Â•12>-M0 Â•Â• ^41 ^ Â° 204 x^2 5 ^^-O

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162 TABLE \2Â— Continued Constraint Number Constraint Description 205 206 -Â•1^^42 + ^43 ^ Â° 207 x^^ < 96.0 208 .09x^4 ^45 1 Â° 209 --12x44 + x^3 < 210 x,^ < 64.0 211 .14x4g x^^ < 212 .16x4^ -r x^^ :: 213 x^g < 45.0 214 x^g < 25.5 215 x^Q < 39.0 216 .OSX3Q x^^ < 217 -.lOx^^ + x.^ < 218 X52 5 2*^-219 X33 < 2,0

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Constraint Number 163 TABLE 12--Continued Constraint Description Survival constraints: i-1 1 1 302 y /-e^a.x. < 618,170 1=1 ^ ^ n 303 I (c^ .04t. ) > 50,000 i=l 304 Z (fS'a.x. > 30,908 Corporate image constraints: 401 x^Q > 500.0 4 02 403 x^4 > 40.0 404 X.. > 40.0 46 [05 406 x^.Q > 20.0 407 x-Â„ > 4.3 / o 408 Xg3 > 14.0

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164 TABLE 3_2 Â— Continued Constraint Number Constraint Description 505 Marginal constraints: 501 x^Â„ = 0.0 502 503 Xg^ == 0.0 04 x^g = 4.086 506 x^j_ = 40.401 507 x^2 = 38.937 508 509 x^. =0.66 74 510 x^, = 0.0 7b Source: See Section XII, Do.ta Collection anc Vresentation^ tor source and explanation of data.

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SECTION XIII IMPLEMENTATION: A COMPARISON OF AN ACTUAL 7vND AN OPTIMAL ENTREPPJ;:NEURIAL SOLUTION Although this study is primarily concerned with a conceptual presentation rather than with any calculations which might result from the entrepreneurial model, it was thought that significance v/ould be added to the conceptual presentation if an optimal solution was calculated and compared to the firm's actual operations during a particular mono-periodic production peri.od. The Two Solutions The actual solution Table 13 presents the actual operations of the firm during a particular mono-periodic production period. Table 14 presents the end of period entrepreneurial balance s:ieet which resulted from this actua] solution. Before tax net income for the period is represented by rhe difference betv.'een total assets and total liabilities in the end of period entrepreneur ial balance sheet. Actual before tax net income for this particular period amounted to $5 7,843. 16! PAGE 174 166 TABLE 13 Â— ACTUAL ENTREPRENEURIAL SOLUTION Process PAGE 175 1G7 TABLE 13Â— Continued Process Value 30 31 32 33 34 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 34. PAGE 176 161 TABLE 13Â— Continued Process Value 64 13.576 65 0.000 66 0.000 67 6.680 68 22.761 69 4.086 70 0.000 71 40.401 72 38,937 73 IS. 267 74 0.660 75 8.8G5 76 0.000 77 54.888 78 4.300 80 84.827 81 131.220 82 90.930 83 64.050 84 139.950 85 201.920 85 112.623 87 86.037 88 S3. 951 89 104.000 90 175. G33 91 105.579 92 105.200 93 14.000 Source: See Section XIII, Tke actual solutioii^ tox source and explanation of data PAGE 177 169 TABLE 14--ACTUAL END OF PERIOD ENTREPRENEURIAL BALANCE SHEET Account Number Account Name Valuation Variable assets: 101 Cash 226,444 -i^02 Accounts receivable 762,685 103 Prepaid expenses 21,653 Inventory (finished goods) 104 Bright 4-3/8 290,357 105 Bright trim 321,881 lOG Matte 4-3/8 42,510 107 Matte trim 54,295 108 Dapple 4-1/4 37,453 109 Dapple trim 42,144 1^0 Crystal 4-3/8 32,753 ill Crystal trim 71,770 112 Hex 3 34,154 113 Hex 6 44,83 ll^j Scored ware 78,291 3 1'5 Scored trim 88,095 llf' Sills 26,569 117 Six by six 18,882 Inventory (raw materials) 118 Body material 97,815 115 Glaze material 181,263 1^0 Packing material 27,94 9 121 Mechanical stores 154,120 122 Die parts 63,550 123 Refractory supplies 70,024 Value of fixed assets 201 Land 378,281 202 Buildings 378,281 203 Equipment 2,138,909 2 04 Other 43,726 Total asset value: 6,198 ,372 Non -variable assets: 301 Glaze preparation 229 302 Hand score 396 303 Straight-] ine number one 7 304 Â£traight-3.ine number tv.'o 149 PAGE 178 170 TABLE 14 Â— Continued Account PAGE 179 171 TABLE 14 Â— Continued Account Number Account Naine Valuation 758 Maintenance 759 General factory 760 Engineering supervision 761 Transportation 762 Quality control 763 Engineering rervices Source: See Section XIII, The actual solution_ for source and explanation of data. PAGE 180 172 The optimal solution The optimal solution was calculated by using a standard linear programmi.ng procedure. The problem v.'as solved on an IBM 709 computer using the C-E-I-R LP/90 program. Table 15 presents the optimal solution. Table 16 presents the end of period entrepreneurial balance sheet which would have resulted if this optimal solution had actually been put into operation. Net income for tliis optimal program is$95,775. Before analyzing the differences in the two solutions, i.t would probably be v.'ise to introduce another concept from the theory of linear programming. This concept is duality theory. Duality theory will help us analyze the differences betvjeen the actual and the optimal solutions. Duality Thaovy The dual problem Given any linear programming probleui (which may be referred to as the primal problem) : max z Â— ex ^ B.t. Ex < b, X > O3 there is another linear programming problem, cal]ed the dual, vmich can be represented as:

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17; TABLE 15--0PTIMAL ENTREPRENEURIAL SOLUTION Process Value 1 418.4333 2 541.237 3 210.617 4 0.000 5 0.000 6 147.113 7 0.000 8 57.558 9 0.000 10 0.000 11 0.000 12 0.000 13 14.04 3 14 0.000 15 101.206 16 0.000 17 0.000 18 25.579 19 0.000 20 65.246 21 O.OCC 22 000 23 0.000 24 10.936 25 0.000 26 4 7.00y 27 0.000 28 36.450 29 0.000

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174 TABLE 15 Â— Continued Process Value 30 26.305 31 5.952 32 0.000 33 29.410 34 4.596 40 1,100.000 41 143.000 42 53.000 43 7.950 44 96.000 45 11.520 46 64.000 47 10.240 48 45.000 49 25.500 50 39.000 51 3.900 52 28.500 53 2.000 54 106.162 55 33.923 56 17.311 57 44.084 5S 23.303 59 8.661 60 800.549 61 473.756 62 O.OCO 63 223.730 64 60.971

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175 TABLE IS Â— Continued Process Value 65 66 67 68 69 70 71 72 73 74 75 !0 0.000 0.000 6.8 00 22.751 4.086 0.000 40.401 38.937 15.267 0.660 8.865 7^ 0.000 '^"7 54.888 ^S 4.300 84.822 Si 131.217 8^ ' 90.930 83 64.050 84 139.950 85 201.928 8^ 1.12.628 86.038 93.951 89 103.994 90 175.632 9J 105.585 92 105.196 93 14.000 Source: See Section XIII, The optimal iolution^ for source and explanation of data.

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176 TABLE 16Â— OPTIMAL END OF PERIOD ENTREPRENEURIAL BALANCE SHEET Account

PAGE 185

177 TABLE 16 Â— Continued Account

PAGE 186

178 TABLE 16 Â— Continued Account KuirJjer Account Name Valuation 758 Maintenance 759 General factory 760 Engineering supervision 761 Transportation 762 Quality control 763 Engineering services Source: See Section XIII, The optimal solution, for source and explanation of data.

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179 u > 0. Primal-dual relationships There are several interesting relationships betv;een the primal and the dual probleras. These relationships are given below and can easily be proved (Hadley, 13 62, pp. 224242). 1. If the primal problem has an optimal solution, then the dual also has an optimal solution. 2. If Â£ is a feasible solution to the priraal, and w is a feasible solution to the dual such that ox = b'^w , then x is an optimal solution to the primal and w is an optimal solution to the dual. 3. If a slack or surplus variable x-^j^-; , which has ceen added to the "j" primal constraint, appears in an optimal basic solution, then for the corresponding optimal solution to the dual, the "j"th dual variable is zero, that is Wj = 0. 4. If the variable Xj_ appears in an optimal basic solution to the primal problem, then in the corresponding optimal solution to the dual , the "i"th dual constraint holds as a strict equality, that is, the dual slack or surplus variable w , . = . m+i Eoor.orr.ic intarpretation of the dual variables First let us consider the physical dimensions of the variable in our problem. The dimensions of the variables v.will be units of seme process operated per period. The dimensions of the b. vary depending upon the

PAGE 188

180 concerned constraint, but, in general, they represent units of resource j available in a given raono-periodic production period. The a., have the dimensions of units of resource j per unit of process i. The dimensions of c. are dollars per unit; of process i. a..w. must have the dimensions of dollars per unit of process i. But since the dimensions of a., are units of resource j per unit of process i, it must be true that the w. have the dimensions of dollars per unit of resource j . To each resource j there corresponds a dual variable v; . which, by its dimensions, is a value to be associated with one unit of resource j. The dual variables are sometimes referred to as shadow prices or imputed values of the resources. This valuation is an opportunity cost valuation. If it v/ere possible to increase or decrease the amount of available resource j by one unit without changing the dual solution, then profit would be increased or decreased by w , . Of course, if b. were actually changed to b. + 1, the profit would not, in general inci'ease by w. because the entire optimal solution changes. Nevertheless, v; . can be interpreted as the hz/cih.. Thus v;hen z is being maximized, w. is a measure of the rate of 3 change of z with respect to b^ . If any resource is not fully utilized in an optimal solution, z v/ill not change

PAGE 189

181 if the aval] ability of the resource is changed slightly. Thus, the dual variable associated with this resource should be zero. Table 17 lists the values of the dual variables associated with the constraints defining the entrepreneurial sphere of discretion. The value of the dual variable is zero for eacli associated constraint v;hich is not satisfied as a strict equality. Dual variables wrth a zero valuation have been omitted froni Table 17. In order to better illustrate this duality concept, let us choose some typical constraints and illustrate more completely tlie significance of the dual variables. Illustrations of duo.l variables Direct production cons traints . --Constraints 1 through 186 are direct production constraints. The dimensions of b . , j = 147, . . ., 158, are percent of weekly capacity f>vailable. Consider constraint 149. The associated dual variable has a value cf 28.7371. Thus a 1% increase in weekly capacity should yield an increase in net income of $28.74. An increase of 1% would allow the utilization of process 1 to increase by 1.29 (This allows 1.29 additional units of bright wall tile to be run en straight-line number one, which is the PAGE 190 182 TABLE 17 Â— OPTIIvlAL DUAL VARIABLES ASSOCIATED WITH CONSTR/VINTS DEFINING THE ENTREPRENEURIAL SPHERE OF DISCRETION Dual Variable Constraint Valuation 107 0.1672 109 0.4580 111 0.1967 113 0.3993 115 0.2500 117 0.3836 119 0.2140 121 0.4662 123 0.2417 125 0.2826 128 0.2691 129 0.6393 131 0.3922 133 0.3650 149 28.7371 150 28.7371 201 216.9130 203 740.1000 204 232.7950 206 677.3000 207 287.2560 209 1,021.3000 210 345.4800 212 811.8000 213 281.7000 214 226.6600 215 94.3600 217 1,074.6000 218 480.2000 219 456.8000 Source: See Section XIII, Eoonornio interpretation of the dual variables , for source and ey.planation of data. PAGE 191 183 more efficient straight-line.) which provides for a net contribution to profit of$82.86. 1.29 less units of process 3 (production of bright wall tile on straight-line number four, the less efficient straight-line) would therefore be utilized. This would decrease net income by $54.12, The marginal value of this resource and hence the value of the dual variable is$82.86 minus $54.12 which is$2 8.74. The dimensions of b . , j 1 , . . .,14 6, and j 159, . . . ,. 186 are net change in dollar valuation of balance sheet accounts. Notice that the associated dual variables are all zero except for those associated with the final goods inventory constraints. Consider constraint ill, which is associated with the m.aximum amount of matte wall tile inventory in terms of dollar valuation. The associated dual variable has a value of 0.1967 which indicates that an increase in the inventory limit of $1.00 woujd add$0.20 of net income to the firm. This is easily verified. A unit increase in b,,, would allow an additiorial 0.00362 units of matte wall tile to be produced. These uni.ts would be prodirced on straightline number one (process 8) , However since straight-line ^The per unit contribution of any process can be obtained by c? = /Tj**. por convenience, the net contribution cf the manufacturing and selling processes are given in Table 18.

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184 TABLE 18Â— NET CONTRIBUTION VALUES ASSOCIATED WITH MANUFACTURING AND SELLING PROCESSES Net Contribution Process Values 1 64.10 2 64.10 3 41.80 4 41.80 5 37.70 6 254.20 7 24 4.2 8 76. GO 9 76.6 10 51.50 11 51.50 12 45.4 13 226.10 14 220.80 15 71.80 16 71.80 17 65.40 18 219,40 19 209.40 20 85.00 21 85.00 22 56.70 23 56.70 24 3 3 8.90 25 323.40 26 100.80

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185 TABLE 18 Â— Continued Net Contribution Process Values 27 20.10 28 118,70 29 100,60 30 -113.00 31 964.70 32 961.20 33 155.30 34 167.90 40 78.90 41 485.90 42 76.90 43 450.90 44 92.90 45 801.90 46 152.90 47 472.90 48 180.90 49 107.90 50 99.90 51 109.90 52 284.90 53 284.90 Source: See Section XIII, Illustrations of dual vai-iables 3 for source and explanation of data.

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186 nui.'ber one is presently being utilized at full capacity, 0,00362 units of bright v;all tile must be shifted from straight-line number one (process 1) to straight-line number four (process ?) . Thus the dual variable should be 0.00362 tim.es the sum of the net contributions of process 3 and process 8 minus the net contrib\it ion of process 1 ; Wj^^-, = .00362(76.60 + 41.80 64.10) = 0.1967. This procedure points to one of the big disadvantages of a mono-periodic production period model. The greater the volume of any product manufactured, the less v;ill be the per unit overhead associated with the product. Thus, the model will believe it can create income by utilizing fixed capacity. The optimal solution will therefore contain as much inventory as the constraints will allov/. In our problem, the limiting constraints are the inventory constraints. In other problems it could be a different constraint such as a limit on production facilities. In reality, this disad\'antage of tVie model is not so great. If the problem is formulated correctly, it is reasonable to expect the entrepreneur to utilize as much of his fixed assets as possible, and therefore prepare for future m.ono-periodic production periods where excess capacity might not be available.

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187 It is interesting Lo note that the dua3 variables associated with non-variable liability constraints are zero. It is certainly true that an increase or decrease in these constraints would change the net income for the period. Non-variable liabilities, however, are beyond the control of entrepreneurial discretion. The corresponding dual variables have a zero vaJ.uation, This is as it should be. Sales constvaints . --Sales constraints are of tv.'o types; those which set limits on the amount of primary product which can be sold, and those which limit the ratios of primary products sold to trim sold. Consider constraint 204. The associated dual variable has a va] ue of 232.7950. If b^^. is increased by one unit, this will allov; process 42 and process 8 to be increased by one unit, and v/ill allow process 43 and process 13 to be increased by 0.15 units . In order to allov; process 8 to be increased by one unit, one unit of bright wall tile must be shifted from straight-line number one to straight-line number four (process 1 to process 3). Thus, = c^^ + Cg + .15(c^ = 76.90 -[76.60 + .15(450.90 -)Â• 226.40) 64.10 + 41.80, 232.795.

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188 Now consider constraint 2 03 which limits the ratio of bright trim sold to bright wall tile sold. If bÂ„Â„^ is i.ncreased by one unit, this will allov/ process 41 and process 6 to increase by one unit and therefore add $740.10 to net income.$740.10 is, of course, the value of the dual variable. Remaining constraints . --It should be noted that the value of the dual variables associated v/ith all the remaining constraints are zero. Thus, nothing can be gained by changing the corresponding b value by an incremental unit. Compar ison of the Actual and the Optir/ial Solutions Before comparing the optimal and actual solutions, two facts should be noted. Our actual aolution violates constraint 217 by 0.379 units, thus indicating a slight problem, misf ormulation. However the discrepancy is net considered to be serious and therefore is ignored. Except for this one exception in the actua], solution, both solutions satisfy all constraints. The firm's actions are therefore dominated by the highest order goal in the firm's hierarchy of goals. Ilius, the firn.'s actions are dominated by the profit motive. Second, we should note that there are alternative optima in the optimal solution. For example, if process 60 (reduction of accounts receivable)

PAGE 197

189 held been operated at a slightly lower level, all constraints would still be satisfied, and the value of the objective function would not have changed. An entrepreneur, presented v-ith an optimal solution, V70uld probably question what accounted for the difference in net income betv/een the actual solution and the optimal solution. This is the approach v.'e shall take in comparing the two solutions. To aid us in our comparison we shall utilize the value of the dual variables. Earlier, however, v/e noted that if b. is cictually changed by one unit, z might not actually change by w. because the v/hole optimal solution may change. Therefore in utilizing the dual variables, we must insure that we only utilize them over an appropriate range. For this reason, v;e have broken the analysis into four subproblems . Siibpr-oblem I Subproblem I is concerned primarily with efficient production schedulir.g. In subproblein I, all processes, except p3:oduction processes, are constrained to have the same value as the corresponding value in the actual solution. Fur '^hermore, the total amount of each product manufactured is constrained to equaJ the amount manufactured in the actual solution. In effect, this problem

PAGE 198

.90 minimizes the cost of manufacturing the output of the actual solution. A sunmiary of the results is given in Table 19, The solution of subproblem I tells management to utilize the more efficient straight-lines to the fullest possible extent. The amount of bright wall which cannot be made on the more efficient straicht-lines (because of capacity lim.i tations) should be made on straight-line number three. The total savings from this shifting of production amounts to $4,773. Subprobleni II Subproblem II is concerned with ratio sales constraints. Management felt that they could sell a volume of trim which was equal to or less than a given percentag; of primary product. Except for the case previously mentioned, the failure to satisfy these constraints as strict equalities cost the firm m.oney . A summary of the profit losses is given in Table 20. The total profit loss amounts to$3,881. Subproblem III Subproblem III is concerned with the profit loss which resulted from the failure to sell as much primary product as management felt it was possible to sell. It should be remembered that the value of the dual variables

PAGE 199

191 TABLE 19--P.R0FIT LOSSES IN SUBPROBLEM I

PAGE 200

192 TABLE 2 0--PRCFIT LOSSES IN SUBPROBLEM II Constraint

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193 takes into account all related changes v/hich must be made. It therefore considers such things as production changes which must be made, and the effect upon sales of complementary products. A summary of the profit losses is given in Table 21. The total profit loss amounts to $10,201. Suhprohtem IV Subproblcm IV considers the net incoirie loss which results from, the failure to satisfy inventory constraints as strict equalities. As discussed before, the question of whether this is an actual income loss is highly questionable. Nevertheless, if the problem has been "formulated, correctly, it must be assumed that there is some value in ut.ilising the excess capacity. A summary of the profit losses is given it? Table 22. Total profit loss amounts to$19,077. Svirrmary of subprobletns The sum of the profit losses from subproblems I through IV amounts to $37,932, When this value is added to$57,84 3, which is the net income for the actual solution, the result is $95,775 which is the net income for the optimal solution. PAGE 202 194 TABLE 21--PR0FIT LOSSES IN SU3PR0BLEM III Constraint PAGE 203 195 TABLE 22 Â— PROFIT LOSSES IN SUBPROBLEM IV PAGE 204 196 Economio Activity in the Mono --periodic Period Chosen for Analysis Monetary conditions in the United States during the particular mono-periodic production period chosen for analysis could be described by the phrase, "tight money." Interests rates on mortgages were high. This might account for the fact that demand for houses and building materials was low. Our firm, therefore, was operating at considerably belov/ capacity. This fact made it much easier for us to analyze the differences betv/een the optimal and actual solutions. In a period of high economic activity, the problem would have been much m>cre difficult and v.'ould have required more subproblems . This type of analysis, however, v/ould be m.uch more valiiable to a firm if the ana]-ysis were made on a period in which there was a high rate of economic activity. In our problem, the dual variables were easy to calculate and illustrate. In fact, the value of the dual variables probably could have been obtained without any type of fon.ial programming technique. In a period of high econoa,,ic activity, the number of dependent relationships would be greatly increased, and the value of the dual variables would be much more difficult to estimate. The model presented could have been formulated in much miore detail. Both the number of processes and the PAGE 205 197 number of balance sheet components could have been increased. More constraints could have been imposed, and more dependent relationships between tlie process could have been formulated. Such an extension of the raodel might be valuable. For our purposes, however, it seemed as though more could he gained by moderate aggregation. For one reason, the concepts could be illustrated better. The Opportunitij Costs of Excluded Alternatives Since we have introduced the concept of dual variables, we should probably point out that another intejrpretation of them is that they are the negative of the opportunity costs of the excluded alternatives. In Section VI , when we were discussing the entrepreneurial process, we noted that the entrepreneur should always choose that alternative with the highest opportunity cost. FurtJiermore , we said that if an entrepreneur ever reaches a point in the entrepreneurial process v;here the opportunity costs of all excluded alternatives are non-positive, theii he can do no better. Table 2 3 lists the dual variables in a slight.ly different form than Table 17. In Table 23, tne dual variables are associated with the excluded alternatives. All dual variables are non-negative therefore all opportunity costs are non-positive. Consider the dual PAGE 206 19! TABLE 2 3--OPTIM?vL DUAL VARIABLES ASSOCIATED WITH PROCESSES OMITTED FROM THE OPTIMAL ENTREPRENEURIAL SOLUTION PAGE 207 199 variable associated with process 10. If this process were operated at a unit leve]. , net income would be increased by$51.50. However one unit of process 8 must be removed at a cost of $76.60. This would allow process 1 to be increased by one unit with a resulting net contribution of$64.10, One unit of process 3 must then be removed at a cost of $41.80. The net result is Â£ cost of$2.80. The values of the dual variables given in Table 13 are the negative of the opportunity costs associated with the slack or surplus variables which were originally introduced to convert a] .1 inequalities constraints to equality constraints. The opportunity costs of some excluded alternatives cire zero. Thus, at least an incremental unit of these processes could be uti.lized without changing the value of the optima.! solution. This simply points to the fact that we do have alternative optima in the optimal solution.

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SECTION XIV COI^iMENTS ON THE PRESENTATION The iriajor work of this study is cor.ple-ce. Perhaps, however, we should briefly review the purpose of the presentation of the raodel and then show that the ir.odel presented ir.ay serve as a basis for the forniulation of more efficient and more operational models. The Modal Fresented It is obvious that the entrepreneurial model presented is not an efficient problem-solving model. Tne intent was not to develop an efficient mathematical model, but rather to set the portrayal of the entire firm into a prograriUT.ing fram.ework. Mathematicians and operations researchers have m.ade rapid progress in using the tools of quantitative analysis re aid managemen-c in solving particular problems of the firm. It is significant, however, that managem.ent theorists have made less use of the inherent qualities of mathematical programming to advance the theory of the firm. Koontz and O'Donnell (195 9, p. 527) state the following about the methods of operations research. 200

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201 . . . operations research is essentially the application of scientific method to problems. As such, it is not nev, since attempts have long been m^ade to approach business and managem.ent problems scientifically. But v;hat does have an element of novelty, is the orderliness and completeness of the approach to business problems v;hich operations researchers have attempted to develop. They have placed emphasis on defining the problem and the goals, on carefully collecting and evaluating the facts, on developing and testing hypotheses from the myriad of facts bearing on a problem, on determining relationships between these facts, on developing and checking predictions based on these hypotheses, and on devising measures by which the effectiveness of a course of action leading toward a goal can be evaluated. Thus the essential methods of operations research may be sunimarized as: 1. The emphasis on goals in a problem area and the development of effectiveness in determining whether a solution shows promise of attaining the goal. For example, if the goal is profit, the measure of effectiveness may be the rate of return on investment, and every proposed solution will arrange the variables and parameters involved so that the end result can be weighed against this measure. 2. The attempt to incorporate all the parameters bearing on a problem, or at least those which appear to be important to its solution, in an analysis. 3. The emphasis on models Â— the logical representation of a problem. These may, of course, be simple or complex . 4. The attempt to quantify the parameters in a problem to the extent possible, since only quantifiable data can be inserted into a model to yield a finite result or value for prediction. 5. Th.e a-utempt to supplement quantifiable data v;ith such usable mathem.atical and statistical limits as the probabilities in a situation, thus making the mathematical and computing problem workable v/ithin a small, and relatively insignificant, margin of error .

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202 These features should be valuable to the managetnent theorist in his attempt to improve the portrayal of the firm. It is primarily j,n this light that this study is offered. Modifications of the Model Presented We have noted that this study was not primarily concerned with efficient mathems-tical models which would aid the entrepreneur in obtaining solutions to particular problems. Nevertheless, it v/ould be worthwhile briefly tc show how the entrepreneurial m;odel presented could be /jsed as the basis for deriving m.athematica]. models which would be of operational value to che firn; . A brief discussion of model modifications is given below. Profitability of product lines The profitabilities of various product lines were obtained from our simple entrepreneurial model. The profitability factors of product lines in the imiplementing sL.udy are represented by the dual variable values in subproblen III, Section XIII. Thch^T' data are obviously valuable, on a routine basis, for such purposes as aiding sales personnel to determirte the degree of emphasis to be placed upon various product lines. They are aJ.so valuable for special

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203 programs, such as determining if a price concession can be made for an exceptional, very large order. The value of the model would be greatly enhanced if it were expanded to distinguish among product line sales by geographic location, territory, or distributor. Let us consider a model wb.ich is expanded to include product line sales by territory. The dual problem then indicates the profitability factors of product lines in each territory. The expanded model would include a selling process for each product in each territory. Additional sales constraints would also have to be formulated, but the value of the increase in information should far outweigh the cost of the model expansion. Consider the case where a distributor asks for a special price for a very large order. The inclusion of a process for this potential order into the expanded model would allow the firm to determine not only the total profitability of the order, but also the profitability of this process at various levels of utilization. In making such a determination, the firm's analyst would have to give careful consideration to the value of the associated dur^l variable, and to the ranges over which a This does not imply that the firm chosen for the implementing study maintained a policy of granting price concessions in exceptional cases. This example is chosen for illustrative purposes only.

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204 particular dual variable value holds. There are, of course, many other uses of an expanded sales model. The example given v/as chosen for illustrative purposes only. VJhenever such a model is used, the laodel considers all dependent adjustments that must be made in the firm's operations. The number of dependent relationships can often be so large, that a good estimate of prof ital)ility factors can only be obtained by some type of programming technique . Pi-'oduction scheduling Subproblem I, Section XIII, solved the problem of efficient product line scheduling. Once the quantities of tiie products to be manufactured v/ei-e determined, the production scheduling problem was dependent only on the various production processes available, and the capacity limitations of productive resources. If a firm scheduled its manufacturing activities at given intervals (once a week, for example) then a much sim.pler m.odel could be used for this production scheduling. In the "reduced-capacity" period chose;: for our implementing study, the production scheduling problem is not large and probal^ly does not require the use of any programming technique. However as economic activity increases, and the number of dependent relationships increase, the production scheduling problem

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205 becomes more difficult and the vtilue of a programming technique is greatly increased. The dual variable associated with the capacity limitations of the simple production scheduliiig model are the marginal values of the productive resources. VJith proper interpretation, these dual variables can be extremely valuable in determining the value of increasing the capacity of some fixed production facility. Again, the estimation of these dual values, and the determ.ination of the range over which these vaD.ues hold, may be easily obtained for the simple case, but become much more difficult to obtain as the complexity of the problem increases . A simple production model V'/culd also aid in the evaluation of new production alternatives as they are being developed. These nev; alternatives can not be eveiluared in isolation, but must be considered in relation to all dependent changes which must be made in the firm's operations. The evaluation of the total effect upon the firm of any nev; production alternative may be extremely difficult without the aid of a programming technique which considers the many dependent relationships involved. Multi-plant firms An expanded version of the model presented v/ould be extremely valuable for a multiplant firm. In such a model.

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206 separate processes must be included for raanuf acturing alternatives at each plant location. Selling processes would include the transportation costs from a particular plant to a particu].ar distributor. A solution to an expanded model of this type would give proper con-^idetation to both the efficiency of various manufacturing a].ternatives and the transportation coses involved. The associated dual variables, which represent the marginal values of constraint limitations, would likewise consider the many dependent relationships involved. In a multiplant arrangement, the number of dependent relationships would be so great that it would be almost impossible to "guess" an optimal solution, or to "e5;timate" the marginal values of resources unless some type of programming technique v;as used. In sam;-aary, it ce>.n be said that the value of this type of programiming increases with the complexity of the problem and the number of dependent relationships involved. The implicit assiimption is, of course, that a reasonable model can be formulated.

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A SELECTED BIBLIOGRAPHY Books, Periodicals J and Public Documents Ashburne, Jim G. and C. Aubrey Smith. 196 0. Financial and Administrative Accounting . Nev; York: McGrawHill Book Co:i\pany, Inc. Bain, Joe S. 1946. Pricing, Distribution, and Employment. New York: Henry Kolt and Company. Barnard, Chester I. 1938. T?ie Functions of the Executive . Cambridge: Harvard University Press. Baumol, William J. 1959. Business Behavior, Value and. Groiiith. New York: The MacMillan Company. . 1961. Economic Theory and Operations Recearch. "Englewood Cliffs, New Jersey: Prentice-Kail, Inc. Bello-.-.-s, Roger and Thomas Gilson. 1962. Executive Skills. Englewocd Cliffs, New Jersey: Prentice-Hall, Inc. Bierman, Harold, Lawrence E. Fourakcr, and Robert K. Jaedicke. 1961. Quantitative Analysis for Business Decisions . Hom.ev;ood , Illinois: Richard D. Irwin, Inc. BlodgcLt, R'ilph Hamilton. 1959. Our Expanding Economy. New Yor]:: Holt, Rinehart, and Winston. Bov/raan, Edward K. and Robert B. Fetter. 1959. Analysis of Indus trial Operations . Homev'ood, Illinois: Richard D. Irv:in, Inc. . 19G1. Analysis for Production Management, Homev.\5od, Illinois: Richard D. Irwin, Inc. C-E-I-R, Inc. 1963. LF/90 Usage Manual. 2nd ed . Wasbinoton , D. C. Carlso:i, Sune. 1956. A Study on the Pure Theory of Pvodv.oticm. New York': Kelly and Millman. ;07

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208 Chaiuberlin, Edward H. 1948. The Theory of Monopoliotia Competition. Cambridge: Harvard University Press. Cohen, Kalman J. and Richard M. Cyret. 1965. Theoi-'y of the Firm: Resource Allocation in a Market Economu . Englewood Cliffs, New Jersey: PrenticeHall, Inc. Coppock, Joseph D. 1959. Economics of the Business Firm. New York: McGraw-Hill Book Company, Inc. Curtis, A. E. and J. H. Cooper. 1961. Mathematics of Accounting . Englev;ood Cliffs, New Jersey: Prentice-Hall, Inc. Dean, Joel. 1951. Managerial Economics . Eng] ev^ood Cliffs, New Jersey: Prentice-Hall, Inc. Dev/ey, Richard and VJ. J. Humber. 1966. An Introduction to Social Psychology . New York: The MacMillan Company . Dor f man, Robert, Paul A. Samuelson, and Robert M. Solow. 1958. Linear Programming and Economic Analysis . New York: McGraw-Hill Book Company, Inc. Drucker, P. F. 1954. The Practice of Management. New York: Harper and Brothers. Due, John F. 1956. Intermediate Economic Analysis . Homewood, Illinois: Richard D, Irwin, Inc. Enrick, Norbert Lloyd. 1965. Management Operations Research. Nev; York: Holt, Rinehart, and Winston. Felln.'i> , William John. 1960. Competition Among the Few. New York. A. M. Kelly, Inc. Florida Tile Industries, Inc. 1966. 19 6 S Annual Report. Lakeland, Florida . 1967. 1966 Annual Report. Lakeland, Florida. . 1965. A Decade of Progress . Lakeland,. Florida. 1963. This h'e Believe. Lakeland, Florida.

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209 Gala, David. 1960. The Theory of Linear Economic Models. Nev/ York: McGraw-Hill Book Ccvipany, Inc. Que, R. L. and M. E. Thorp.as. To be published. MathematioaZ Methods of Operations Research. Kadley, G. 1963. Linear Algebra. Reading/ Massachusetts: Addison-Wesley Publishing Company, Inc. . 19S2. Linear 'Programming . Reading, Massachuse-cts : Addison-Wesley Publishing Company , Inc . 1SS4. Nonlinear and Dynamic Programming . Reading, Massachusetts: Addison-Wesley Publishing Company, Inc. Hancock, Harris. 1950. Theory of Maxima and Minima. New York : Dover Publications . Haynes, William Warren. 1963. Managerial Econom.ics . Homewood, Illinois: The Dorsey Press, Inc. Vt. ynes, W. and J. L. Massie. 1961. Management: Analysis^ Concepts^ and Cases. Englewood Cliffs, New Jersey: Prentice-Kail, Inc. Henderson, James M. and Richard E. Quandt. 195S. Microeconomic Theory. New York; McGraw-Hill Book Company , Inc . Hilgard, Earnest R. 1957. Introduction to Psye'nology . New York: Harcourt, Brace and World, Inc. Johnson, Robert W. 1959. Financial Management. Boston: Allyn and Bacon, Inc. Koontz, Harold and Cyril O'Donnell. 1959. Principles of Management. 2nd ed. New York: McGraw-Hill Book Company, Inc. Lindsay, Franklin A. 1963. il/ew Techniques for Management Decision Making. New York: McGraw-Hill Book Com.pany , Inc . Maslow, A. H. 1954. Motivation and Personality . New York: Harper and Brothers. Mattessich, Richard. 1964. Accounting and Analytical Methods. ?Iom.ewood , Illinois: Richard D. Irwin, Inc.

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210 Morgan, Clifford T. 1961. Introduction to Psychology . 2nd ed. New York: McGraw-Kill Book Company', Inc. Oxenfeldt, Alfred R. 1951. Industrial Pricing and Market Practices . New York: Prenbice-Hall , Inc. Robinson, Joan. 1933. The Economics of Imperfect Competition. London: MacMJ.llan and Company, Ltd . Scoville, Hiram T. and C. A. Moyer . 1940. Fundamentals of Accounting . Boston: D. C. Heath and Corapany. Stigler, George. 1946. The Theory of Price. New York: The MacMillan Company. Webster ' s Dictionary of Synonyms . 1942. Springfield, Massachusetts: G. and C. Merriam Co. Articles Andrews, P. W. S. 1949. "A Reconstruction of the Theory of the Individual Business," Oxford Economic Papers, Vol. I, No. 1 (January, 1949), pp. 54-89. Ashley, C. A. 1961. "Maximization of Profit," Canadian Journal of Economics and Political Scieyice , Vol. 27, No. 1 (February, 1961), pp. 91-97. Bain, Joe S. 1949. "A Note on Pricing i.n Monopoly and Oligopoly," American Economic Review, Vol. XXIX, No. l" (March, 1949), pp. 448-464. . 1948. "Price and Production Policies," in A Survey of Contemporary Economics . H. S. Ellis, ed. Homewood, Illinois: Richard D. Irwin, Inc. pp. 129-173. Brown, Alvj.n. 1958. "All Decisions are Financial," in Selected Readings in Management. F. A. Schull, ed. Homev70od , Illinois: Richard D. Irv;in, Inc. pp. 100-102. Chamberlin, Edward H. 1950. "Product Heterogenity and Public Policy," Americayi Economic Revieu), Vol. XL, No. 2 (May, 1950), pp. 101-103.

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211 Fellner, William John. 1950. "Collusiorx and Its Limits Under Oligopoly," AmeTican Economic Review ^ Vol. XL, No. 2 (May, 1950), pp. 54-62. Florida Tile Industries, Inc. 19 65. "The Process," Ceramic Chatter j, Vol. 3, No. 3 (SeptemÂ±>er, 1965) , pp. 3-7. Galbraith, John K. 1948. "Monopoly and the Concentration of Economic Power," in A Survey of Contemporary Economics. H. S. Ellis, ed. Komewood, Illinois: Richard D. Irv.'in, Inc. pp. S 9-12 8. Lamberton, D. M. 19 60. "Alternative Profit Criteria," Th.e Quarterly Journal of Econom.ics^ Vol. LXXIV, No. 4 (November, 1960), pp. 635-640. Litchfield, Edv7ard H. 1956. "Ivotes on a General Theory of Administration," Administrative Science Quarterly^ Vol. I, No. 2 (June, 1956), pp. 1-29. Phillips, Almarin. 1961. "Operations Research and the Theory of the Firm," Southern Economic ^Journal ^ Vol. XXVIII, No. 1 (July, 1951), pp. 357-371. Robinson, Joan. 1953. "Imperfect Competition Revisited," Economic Journal:, Vol. 63, No. 3 (September, 1953) , pp. 579-593. SciuOVdky, T. 1959. "A Note of Profit Maximization and its Implications," Review of Economic Studies^ Vol. XI, No. 4 (Winter, 1959), pp. 57-60. Shubik, Martin. 1961. "Objectives Functions and Models of Corporate Optimization," The Quarterly Journal of Economics, Vol. LXXV, No. 3 (August, 1961) , pp. 345-375. Simon, Herbert A. 1959. "Theories of Decision Making in Economics and Behaviorial Science," The American Economic Review , Vol. XLIX^ No, 3 .(June, 19591, pp. 252-283. Tannenbaum., Robert. 1949. "The Manager Concept: A Rational Synthesis," Journal of Business:, Vol. XXII, No. 2 (April, 1949), pp. 225-2-^0. . 125 0. "Managerial Decision-Making," Jourr,^'. :>; Business, Vol.' XXIII, No. 1 (January, 1950), po. 23-29.

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212 Tatnall, R. Francis. 1966. "Florida Tile Industries, Inc.," Ceramic Age, Vol. 7, No. 3 (June, 1966), pp. 41-46. Vvilcox, C. 19!30. "Ov. the Alledged Ubiquity of Oligopoly, Amevican Eooyiomic Review, Papers and Proceedings, Vol. XL, No. 2 (May, 1950), pp. 67-73. Wu, Yuan-li and Chirg-v.'en Kwang. 1960. "An Analytical and Graphical Compai'ison of Marginal Analysis and Mathematical Programming in the Theory of the Firm, " in Linear Programming and the Theory of the Firm. K. E. Boulding and VJ. A. Spivey, eds. New York: The MacMillan Company, Inc.

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BIOGRAPHICAL SKETCH Frank Sherman McLaughlin, Jr., was born on NoveipJ.Der 22, 1936 in Lake Wales, Florida. He attended public schools in Lake Wales and graduated fro'n Lake Wales High School in 1954, After graduating from high school, the author enrolled in Vanderbilt University. He was awarded the degree of Bachelor of Engineering cum laude in 1958. From 1958 until 1961 he served in t}>e United States Navy aboard a destroyer in the A.tlantic Fleet. On discharge from r.iilitary service he entered the Graduate School at tlie University of Florida and received the MBA degree in 1962. He V7as then employed by Owens-Illinois as a chemical enc'Dnoer to v;ork i.n their pulp and paperboard mill in Jacksonville, Florida. He remained with this firm until 1565. In 19 65 the autlior received a Ford Foundation Fellowship in Economics and Business Administration and. returned to the University of Florida to work toward the Doctor of Philosophy Degree. 'I:)r.(i author completed all roquii-em.ents for the Ph.D. wi.tJi a major in Economics and Business Administration in August, 3 967. He has accepted " 213

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214 an appointment as an Assistant Professor of Business Administration at the University of Richmond starting in September, 1967.

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This dissertation v;as prepared under the direction of the chairmiin of the candidate's supervisory conmiittee and has been approved by all merabers of that committee. It was submitted to the Dean of the College of Business Adrainistration and to the Graduate Council, and was approved as partial fulfil] raent of the requirements for the degree of Doctor of Philosophy. August 12, 1967 .x^^ Dean, College of Business Administration Dean, Graduate School S up e V V 5, . s o r y C o n"im i 1 1 e e : Chairman, W. V. Wdliaot, Jr M. E. Thomc;f;

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