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This is to certify that the

thesis entitled
A MULTIPLE OUTPUT TRANSLOG COST FUNCTION

ESTIMATION OF ACADEMIC LABOR SERVICES

presented by

William Dale King

has been accepted towards fulfillment
of the requirements for

Ph .0. degree in Economics

 

Major professor

Date November IO, I980

 

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© Copyright by
William Dale King
1980

A MULTIPLE OUTPUT TRANSLOG COST FUNCTION ESTIMATION

OF ACADEMIC LABOR SERVICES

BY

William Dale King

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

1980

ABSTRACT

A MULTIPLE OUTPUT TRANSLOG COST FUNCTION ESTIMATION
OF ACADEMIC LABOR SERVICES

BY

William Dale King

This study addresses several questions concerning the
structure of costs in higher education using a multiple out-
put model. The objectives are: l) to analyze the demand
for academic labor services consisting of tenured faculty,
non-tenured faculty, and graduate assistants, 2) to analyze
the supply of outputs of higher education consisting of under-
graduate instruction, graduate instruction, and research, and
3) to test for the existance of separability, homogeneity of
outputs, constant returns to scale, and a Cobb-Douglas
structure to costs in higher education.

These objectives require estimation of production
relations without placing a priori constraints on the elas-
ticities of substitution among the academic labor services
and the outputs. Thus, a translog cost function is specified
as a quadratic approximation to the production process. It
is from these estimates of this cost function that the
appropriate elasticities of demand, marginal cost, and sub-
stitution are derived. In addition, a system of direct
demand equations for the academic labor services is also
solved simultaneously to provide results to compare with the
transloq cost function.

Estimation is based on the underlying assumption that

William Dale King
technology is similar across all departments included at
Michigan State University and leads to the following conclu-
sions. Among the academic labor services, all are substitutes
in production. The non-tenured faculty and graduate assist-
ants are the easiest substitutes. The tenured faculty and
non-tenured faculty are less substitutable with the tenured
faculty and graduate assistants having the least substituta-
bility. The elasticities of demand for the inputs are all
negative and sufficiently small to indicate all are inelastic
in demand.

Estimates of the elasticity of substitution for the
outputs indicate all are easy substitutes. The easiest sub-
stitution is between undergraduate instruction and research.
Research and graduate instruction are less substitutable with
graduate and undergraduate instruction having the least
substitutability. In addition, increasing returns to scale
exist for all outputs with research and undergraduate
instruction having the greatest returns and graduate instruc-
tion having the least.

Finally, the evidence did not suggest that any constraints
on the translog cost function are appropriate. The tests of
separability, homogeneity of outputs, constant returns to
scale, and a Cobb-Douglas form produced results that were
significantly different from the unrestricted translog model.
The direct demand model was found to contain symmetry in the

cross-price elasticities and homogeneity of the outputs.

To my wife, Nancy, and my family

ii

ACKNOWLEDGEMENTS

I wish to express my sincere gratitude to Dr. Daniel
Hamermesh, my thesis advisor, for his invaluable advice, en-
couragement and guidance, kindness, and understanding during
the difficult time when this study was being undertaken. A
special debt is owed to Dr. John Henderson for his many years
of friendship and counseling. Dr. Byron Brown and
Dr. Cynthia Rence have also earned my gratitude for their
ideas, suggestions, and criticisms which improved this thesis
considerably.

I wish to thank Dr. Thomas Freeman for his concern and
continued financial support through the Office of Institutional
Research. It is inconceivable that this thesis would have
reached a point of completion without his assistance. Others
in the Office of Institutional Research deserve my appreciation.
They are: Dr. William Rosenthal, Dr. William Gunn, and
Mr. Lynn Peltier.

I must also extend my sincere appreciation to Marion-
Jennette for her patience and diligence while typing the
drafts of this thesis. The final manuscript was typed by
Sandy Bolton. Her careful and expedient typing is greatly
appreciated.

My greatest debt is owed to my wife, Nancy, who

iii

sacrificed much and encouraged me at every stap. Members
of my family I would like to thank for their moral support
through the years are my mother, Wahneta, and my brother,
Richard. Other family members deserving of my appreciation

are Dorothy, Marcia, Alice, Pam, and Chuck.

iv

LIST OF

Chapter

I.

II.

III.

TABLE OF CONTENTS

TABLE 8 O O O O O O O O O O O O O O O O O 0

INTRODUCTION 0 O O O O O O O O O O O O O O
The Nature of Academic Labor Services . .

Two Analytical Approaches . . . . . . . .

THEORETICAL FRAMEWORK . . . . . . . . . .
Introduction . . . . . . . . . . . . . . .

The Approach to the Specification of Joint
Production . . . . . . . . . . . . .

The Joint Product Cost Function —- The
General Form . . . . . . . . . . . .

The Joint Product Cost Function -- Share
Equations . . . . . . . . . . . . . .

The Joint Product Cost Function -- First-
and Second-Order Conditions . . . . .

The Joint Product Cost Function -- The
Constraints . . . . . . . . . . . . .

The Joint Product Cost Function -- The
Elasticities of Substitution, Demand,
and Marginal Cost . . . . . . . . . .

Conclusion . . . . . . . . . . . . . . . .

MODEL SPECIFICATION AND DATA . . . . . . .
Introduction . . . . . . . . . . . . . . .

Defining and Measuring the Outputs . . . .

Page

viii

12

12

13

21

25

28

29

32

35

37
37
41

Chapter Page
III. (CONTINUED)

Defining and Measuring the Inputs and

Cost of Inputs . . . . . . . . . . . . . . 45

IV. MODEL ESTIMATION . . . . . . . . . . . . . . . . 50

Introduction . . . . . . . . . . . . . . . . . . 50

Direct Demand Constraints . . . . . . . . . . . 50

Direct Demand Estimates -- The Inputs . . . . . 53

Direct Demand Estimates -- The Outputs . . . . . 58

Direct Demand Estimates -- The Three Year
Rate of Adjustment . . . . . . . . . . . . 64

The Joint Cost Function Equations and
Tests of the Constraints . . . . . . . . . 70

The Joint Product Cost Function Estimates --
The Inputs . . . . . . . . . . . . . . . . 81

The Joint Cost Function -- The Outputs . . . . . 85

Conclusions . . . . . . . . . . . . . . . . . . 90

V. MODEL SIMULATIONS . . . . . . . . . . . . . . . 92
Introduction . . . . . . . . . . . . . . . . . . 92
Declining Undergraduate Enrollments . . . . . . 93

Special "Catch-Up" Salary Increases to
the Faculty . . . . . . . . . . . . . . . . 98

Increasing Research Outputs . . . . . . . . . . 101

VI. POLICY IMPLICATIONS AND CONCLUSIONS . . . . . . 105
Overall Perspective of Analysis . . . . . . . . 105

Future Research . . . . . . . . . . . . . . . . 109

vi

Page

APPENDICES

A. LIST OF DEPARTMENTS INCLUDED AND DELETED
F ROM THE DATA 0 O O O O O O O O O O O O O O 1 l 3
B 0 MODEL DATA 0 O O O O O O O O O O O O O O 0 O O O l 1 6

BIBLIOGMPHY O C O O O C O C O O O C O C O C O C O O O .

vii

LIST OF TABLES
Table Page

4.1 Direct Demand Analysis: Chi-Square Test of
Restrictions . . . . . . . . . . . . . . . . 52

4.2 Direct Demand Estimates: Price Coefficients . . . 54
4.3 Direct Demand Estimates: Output Coefficients . . 59

4.4 Direct Demand Estimates: Model Coefficients
With Lagged Instructional Variables,
Included and Excluded, 1977-78 Data With
Homogeneity and Symmetry Constraints . . . . 67

4.5 Joint Cost Function: Log of the Likelihood
Functions . . . . . . . . . . . . . . . . . . 72

4.6 Parameter Estimates for the Joint Translog
Cost Function: 1977-78 Data and Four
Share Equations Only . . . . . . . . . . . . 75

4.7 Joint Cost Function: Test Statistics for
Restricted Models, 1977-78 Data - Four
Share Equations Only . . . . . . . . . . . . 79

4.8 Joint Cost Function: Estimates of Elasticities,
1977-78 Data 0 o o o o o o o o o o o o o o o 82

4.9 Joint Cost Function: Estimates of Output
ElaStiCitieS, 1977-78 Data 0 a o o o o o o o 87

viii

"I must candidly admit that I do not know what
the elasticity of supply of resources to the
educational sector is or how easy it is to
switch resources in the educational sector
from teaching to research (at least at the
margin where the switch counts). The substi-
tutability of resources within the sector
depends on the production function for the
various outputs produced by the sector."

(Nerlove, 1972)

ix

CHAPTER I

INTRODUCTION

Regardless of how optimistically one would like to view
the future, there is little doubt that enrollments in higher
education will decline sharply over the next decade. The
cost of not knowing the substitutability of resources will
continue to rise as administrators and faculty try to
restructure their institutions to meet these changing cir-
cumstances.

Empirical estimates of the elasticities of substitution
among the faculty and graduate assistants, for example, are
important in determining the impact upon a university when
reduced enrollments necessitate cutbacks in the teaching
staff. Administrators have many options available. They
could adopt programs to promote early retirement for the
tenured faculty, lengthen the time period necessary for
faculty members to gain tenure, or eliminate graduate
assistantships in specific programs. Currently, very little
is known about how each of these employment policies will
affect the overall teaching and research aspects of a
university. It may be true that many provosts, deans, or
department Chairpersons have some intuitive notion of how

their institutions can adapt to the declines of the future,

2
but it is doubtful that anyone has a clear grasp of the
system of higher education as a whole (Nerlove, 1972).

There are several ways one might go about modeling the
structure of higher education. Each approach implies a
different assumption about the process being examined. There
are two that are relevant to the study presented here. The
first approach assumes that an instructional department at
one university is faced with the same production function as
similar departments at other universities. The other
approach assumes that although each department within a
university may face a slightly different production function,
the differences are not great enough to overshadow the
valuable information that can be provided to the central
administration of the university. The latter approach is
the direction taken by this study. This is not to say that
one is absolutely preferable to the other, but that both can
provide a unique perspective on a rather complicated produc-
tion process.

It appears to be reasonable, based on the above assump-
tions, to build a model that makes use of data relating to a
particular discipline across many universities. Obviously,
the generating of student credit hours for an Economics
Department is more closely related to the production process
at other Economics Departments than it is to, say, the
production process applicable to the science or agriculture
departments within that university. This relationship would

exist for most disciplines of higher education. Research

3
facilities, laboratory equipment, and the size of lectures,
all vary widely from department to department or college to
college within a university. However appealing the cross-
university approachrmay be, there are two serious problems
that arise when building a model on this basis. The first
problem is that it is extremely difficult to gather all of
the data necessary for the model. Most universities compile
data on student credit hours and the number of tenured
faculty. This data could be collected with only minimal dif-
ficulty. On the other hand, research output and full-time
equivalent employment for temporary faculty are not collected
at most universities, thus requiring rough approximations and
guesswork on the part of the model builder. Second, there
would be some question as to whether the data were completely
consistent and compiled according to a uniform set of
definitions across all universities. This would be espe—
cially true for measuring research output and graduate
student credit hours. At this point, this approach for
modeling higher education would be inordinately expensive if
one were to collect enough data that would be suitable for
analysis.

The use of data within one university and across dis-
ciplines also deserves careful examination. The problems
with the above approach do not exist when the data are
collected from a carefully defined set of reports at one
university. Michigan State University collects all of the

necessary data required to make this analysis feasible. The

4
data are compiled according to one uniform set of definitions
and can be considered reliable for the years being studied.
These reports are all available in several forms from the
Office of Institutional Research. Using this approach re-
quires that we assume that all disciplines and departments
within the university are facing the same production function.
This assumption is, indeed, very strong since we do not know,
and are unable to test, the extent to which it is true.
Violating this assumption will affect the estimates of the
model in two important ways. First, it can contribute
significantly to the inability of the model to satisfy the
first- and second-order conditions necessary for a cost
function to be well behaved. Not satisfying the first- and
second-order conditions would lead us to believe that the
departments of the university are not making decisions based
on cost minimization. However, this can be an erroneous
conclusion because it does not rule out the possibility that
the departments are truly cost minimizers but acting accord-
ing to a different production function. Thus, we could
reject the model for not properly estimating the cost
function when, in fact, there may be more than one. The
second difficulty arises in the estimates of elasticities
presented in a later chapter. In the one instance where the
estimated cost function is well-behaved, approximately one-
half of the coefficients are not significantly different
from zero. This implies that the elasticity estimates using

these coefficients may not be reliable.

5

Obviously, it would strengthen the analysis considerably
if the model could account for the differences in the struc-
ture of production across departments. It is unfortunate
that this cannot be done and we must suggest this as a
direction for future investigation. Since the purpose of
this study is to provide the central administration with
university-wide policy proposals, it is necessary to assume
only one production function exists for all of the depart-
ments within the university. The differences applicable to
any one department from the single (hypothetical) production
function being created here will appear in the error term of
the specific regression equations. The role of the error
term will be two-fold in this study. It will contain the
information on the distance certain departments are from
their production frontiers and will also be a measure of the
inadequacy of specifying an entire university's output with

one production function.

The Nature of Academic Labor Services

It is necessary, for the purposes of comparison, to
state explicitly what we regard as an intuitive understand-
ing of the workings of the university and the process of
providing instruction and research. The outputs we include
in our model are undergraduate teaching, graduate teaching,
and research by department. The inputs we measure are three
types of academic labor services defined as the number of

full-time equivalent tenured faculty, non-tenured faculty

6
including tenure stream and temporary faculty,1 and graduate
assistants by department. We believe the non-tenured and
tenured faculty to be substitutes in all three outputs of
undergraduate instruction, graduate instruction, and research.
The non-tenured faculty are at the beginning of their aca-
demic careers and therefore may be more interested in
scholarly publication and graduate instruction but, never-
theless, the tenured and non-tenured faculty share depart-
mental responsibilities for producing all of the outputs.
The difference between these two labor services is only in
the degree that they are substitutes.

Graduate assistants, on the other hand, play a different
role in the production process because they are both inputs
and outputs. It becomes important here to separate the
three outputs and discuss each one separately. In under—
graduate teaching, we feel the graduate assistants are
fairly good substitutes for both types of faculty. There are
two reasons for this. The first is that graduate assistants
frequently act as instructors for classes without requiring
supervision by any faculty member. Second, if student
demand for freshman and sophomore classes increases rapidly,
class sizes can be increased and more graduate assistants
may be hired to assist the faculty member teaching the

class. Rather than hiring a temporary faculty member to

 

Less than 10 percent of the departments in the
university have temporary faculty that are more than 25
percent of the total number of non-tenured faculty.

7
maintain the same class size with more sections taught, most
departments may, instead, hire more graduate assistants

with larger classes. Thus, although the graduate assistants
are working under the supervision of a faculty member and
might be considered to be a complement to the faculty, they
are actually substitutes.

With respect to research, we believe graduate assistants
are complements to both types of faculty. This is because
they produce very little research separate from the faculty.
Further, we feel that the faculty can attract graduate
assistants to provide much of the "leg work" of their
research activity, although the data are not available to
prove this. It is for this reason that the graduate assist-
ants would be expected to be complements with the faculty.

We believe graduate assistants do not make any signifi-
cant contribution to graduate instruction. Although there
might be some support by graduate assistants to the faculty,
we do not know its size. Therefore, we will assume it to be
negligible, and expect to find that graduate assistants are
only slight substitutes with both types of faculty with
respect to graduate teaching. However, this does not mean
that a correlation does not exist between the size of a
graduate program and the number of graduate assistantships
offered by the department. In fact, the number of graduate
students taught by departments was found to be a significant

predictor of the number of graduate assistants

8
employed.2 There is an additional connection between the
graduate program and the number of graduate assistants. The
salary paid graduate assistants not only reimburses them for
services performed, but also represents a stipend for their
enrollment in the graduate program. There is not Sufficient
data available to determine how graduate assistants divide
their working hours between assisting faculty members and
providing unsupervised undergraduate instruction. This makes
it difficult to determine whether the substitutability
between graduate assistants and the faculty in undergraduate
and graduate instruction overshadows the complementarity in
research. We will assume that it does. This is because we
believe the percentage of all of the graduate assistants'
time spent on instruction is greater than that spent on
research. Again, these relationships reflect a tentative a
priori understanding of the structure of academic labor
services in higher education and will be used in the analysis
to provide a basis for comparing the estimates of the model

presented in Chapter IV.

 

‘ 2 In the demand equations, to be discussed in Chapter IV,
we discovered that graduate student credit hours was a signi-
ficant variable in predicting the number of graduate assistant
appointments. It is estimated from direct demand equations
that a 10% increase in graduate instruction will cause approx-
imately a 3% increase in graduate assistant employment (See
Table 4.3).

9

Two Analytical Approaches

 

There are two analytical approaches to the study of
higher education presented in this study. The first method
of analysis is through a system of demand equations with
each equation representing the demand for each input. The
second method is a multiple output cost function estimation
where the substitutability of the inputs can be examined in
a joint production framework. This will produce not only
demand elasticities for the inputs but, also, elasticities
of substitution and the supply elasticities of the outputs.

This study concentrates only on what are referred to as
"academic labor services" or those individuals employed in
instructional departments and holding faculty rank or a
graduate assistant appointment. This seemingly narrow ap-
proach is justified on practical grounds. First, the costs
related to the operation of a college or university that are
not devoted to faculty or graduate assistant salaries are
extremely difficult to associate with any one department.
Many different departments share the same facilities such as
classrooms, laboratories, and libraries. In addition, a
major goal of academic administrators (provosts, deans, and
Chairpersons) is to optimize the mix of their academic labor
services with all other expenditures assumed to be of
secondary importance.

Within the examination of higher education at the depart-
mental level this study's objectives are: l) to test the

applicability of a priori restrictions of homogeneity,

10
separability, and a Cobb-Douglas form, 2) to estimate the
demand elasticities and cross-price elasticities of academic
labor services, 3) to estimate the supply elasticities of
outputs. These objectives, once achieved, can assist in the
discussion of changing the structure or composition of
academic labor services in higher education consisting of
tenured faculty, non-tenured faculty, and graduate assistants.
The outputs will consist of undergraduate instruction,
graduate instruction, and research.

Chapter II provides the theoretical framework on which
the direct demand analysis and joint cost function analyses
are based. Both analyses are developed with their necessary
assumptions and testable restrictions. The methods of esti-
mation and determination of elasticities derived are also
presented in this chapter.

In Chapter III, special attention is paid to how the
inputs and outputs of higher education are specified. This
chapter also elaborates upon many of the problems that must
be overcome in order to make it possible to adapt the avail-
able data to a model of the academic labor services of higher
education.

Chapter IV provides the actual estimates from the system
of demand equations and the translog cost function. The
various elasticities are presented along with the applica-
bility of the translog cost function and the restrictions of
homogeneity of the outputs, separability, and the joint

product Cobb-Douglas functional form.

11

It is possible to apply the various elasticities derived
from both methods to answer specific policy questions. Some
of these questions will be formulated and answered in
Chapter V. The issues that can be addressed relate to the
decline of undergraduate enrollments, continuation of certain
graduate programs, and projecting the impact of salary in-
creases on the employment of labor services.

Chapter VI summarizes the conclusions and draws the
relevant policy implications toward higher education based on
the findings of the models. The findings indicate that it
would be appropriate for a university in times of decline, to
reduce its non-tenured faculty level first, with graduate
assistants supporting their teaching loads and the tenured

faculty providing the research.

CHAPTER II

THEORETICAL FRAMEWORK

Introduction

 

The structure of higher education can be studied from
two rather different perspectives. The first, which will be
referred to as the "Direct Demand Analysis," looks at the
structure as a system of simultaneous demand equations for
each factor input. The second perspective, termed the
"Joint Product Cost Function,” considers the underlying cost
function directly and from it the demand equations for the
factor inputs are derived.

The interpretation of the demand for academic labor
services will be based on these two perspectives. Both
methods are included in this study because each contains
advantages and disadvantages. The direct demand analysis
provides a simple, straightforward approach unencumbered by
long mathematical expressions or abstract functional designs.
It is less attractive because it does not allow us to derive
the elasticities of substitution of the factor inputs or
provide an insight into the jointness of outputs. These are
serious disadvantages since it is the existence of the joint-
ness of the outputs that makes the study of higher education
an interesting economic and econometric problem and the

12

l3
motivation for this research. The direct demand analysis is
nonetheless important to this study for two reasons. First,
it does provide estimates of demand elasticities and scale
economies that are useful for comparison with the estimates
derived from the joint product cost function; and, second,
it provides some measure of how well higher education con-
forms to the principles of microeconomic theory.

The joint product cost function, on the other hand,
easily produces the elasticities of substitution, demand,
and marginal cost but also contains disadvantages in the
empirical estimation of the model. In this model,there are
27 independent variables. The large number of coefficients
to be estimated increases the likelihood that many coeffi-
cients will be insignificant. Since the elasticities of
substitution, demand, and marginal cost are estimated from
insignificant coefficients, the major disadvantage with this

approach is the unreliable estimates of these coefficients.

The Approach to the Specification of Joint Production

 

The process of producing higher education can be
examined through the estimation of either a production
function or cost function. Estimating a production function
requires specifying the inputs in terms of quantities while
a cost function uses inputs prices. The general production

function of the model is:
f(Yl,Y2,...,Ym,Xl,X2,...,Xn) = 0 (2.1)

where the Y's represent the outputs and the X's represent

14
the inputs (Hall, 1973: Brown et al., 1979).
Applying this general form to our higher education

problem we have:

f(Y Y Y,L

U'G’R 'L L

K,E,M) = 0 (2.2)

T N' A'

where YU' Y Y are the outputs of undergraduate and

G' R
graduate education and research respectively. The academic
labor services are defined as tenured faculty (LT), non-
tenured faculty (LN), and graduate assistance (LA). The
other inputs relate to capital (K), other employment (E),
and materials, supplies and services (M). Since this study
is only concerned with the substitution among the types of
academic labor services, all of the other inputs can be
expressed as elements within the subset Xi'l

Typically, this general function is developed further
to gain more insight into the specific relationships under
study. Hudson and Jorgensen (1974), Griffin (1977), Fuss
(1977), and Brown et al. (1979), are popular examples of
models making use of an aggregator function.

Applying the use of aggregator functions to higher
education, we can create a production function that permits
us to examine only the outputs and the academic labor ser-

vices. Writing the general functional form in a form that

will permit us to examine only the outputs and the academic

 

1 This is consistent with the terminology developed in
Hasenkamp (1976).

15

labor services, we have:

f(h(YU,YG,YR,LT,LN,LA), k(X,...Xe)) = 0 (2.3)

where functions h and k, are referred to as aggregators.

Writing the production function in this form implies the
existence of weak separability between the outputs and
academic labor inputs, h(-), and the non-academic inputs,
k(°).

Weak separability means that the marginal rates of sub-
stitution between elements within an aggregator are indepen-
dent of the quantities demanded of elements outside the
aggregator. For example, the cost-minimizing choice of the
academic labor mix is independent of either the mix or level
of capital, other employment, or materials (Berndt and
Christensen, 1973).

Imposing separability provides two important results.
First, only under the existence of separability do aggregate
functions exist. Second, the existence of aggregates which
are homothetic in their components implies an underlying
two-stage optimization procedure: optimize the mix of com-
ponents within each aggregate and then optimize the mix of
the aggregates.

It is important that we assume separability exists in
order to reduce our model from all of the inputs and outputs
of higher education to only those inputs (and outputs) that
we feel are important to the decision-making processes. The

constraint of separability does agree, generally, with what

16
we find in how employment decisions are made. Additionally,
the separability constraint justifies the separate construc-
tion of a sub-model into only the academic labor and output

components expressed as:

f(h(YU,Y Y LT,L

G. R. LAM = o (2.4)

N'
and is the structural basis for this study (Fuss, 1977).

The translog function used in this study is assumed to
be a good second-order approximation to an unknown function
and not the "exact" function (Fuss, 1977).2 More recently,
Brown et al. (1979), were able to test the constraint of
separability between multiple inputs and multiple outputs.
Their test will be incorporated into this study. However,
the existence of separability between any non-academic labor
input and the outputs can only be assumed and cannot be proven
due to the non-labor inputs being excluded from the sub-model
(and not included in the data).

In this section we establish the specific direct demand
equations from the general functional form developed above.
In addition, the model is also modified to the existence of
the constraints of homogeneity, symmetry, and constant returns
to scale. Having derived the general functional form as
stated in equation (2.4) above, the relevant demand equa-

tions are a transformation of this form. Demand for each

 

2 Denny and Fuss (1977) present a comprehensive discus-

sion of an exact versus an approximate production function.

17
type of academic labor service is a function not only of the
price of that input but also the price of the other labor

inputs and the outputs:

r'
ll

LT(PT,P 'PA'Y

N U'YG'YR)

L = LN(PT,P PA,YU,Y (2.5)

N' G'YR)

LA = LA(PT,PN,PA,YU,YG,YR)

where P P and P represent the full-time equivalent

T' N' A
salaries of the tenured faculty, non-tenured faculty, and
graduate assistants respectively.

Expressing all of the variables as logarithms, the un-
restricted model has the input quantities as the dependent
variable with the dependent variables consisting of the
input prices and the output quantities.

The explicit equations to be estimated in the Unre-

stricted Direct Demand model are:

RnL =A +BlflnPT+B

T 1 RnP +B RnPA+C

2 N 3 lnY +C RnY +C RnY +e

l U 2 G 3 R 1

lnLN=A2+B RnP +B EDP +3

4 T 5 N 6£nPA+C

4RnYU+C52nYG+C65LnYR+e2 (2.6)

InL =A +B RnP +B RnP +B

A 3 7 T 8 N 9RnPA+C72nY +C finY +C RnY +e

U 8 G 9 R 3

where the lnL's are the logarithms of the quantities of the
inputs of tenured faculty (T), non-tenured faculty (N), and
graduate assistants (A); and the RnP's are the logarithms of
the prices of inputs T, N, and A. The outputs (Y's) are
defined as undergraduate student credit hours (U), graduate

student credit hours (G), and research (R). The coefficients

18
denoted by B's or C's represent the elasticities of the
prices and outputs, respectively.

The constraints of homogeneity of input prices, symmetry
of cross price elasticities, and constant returns to scale
are all possible conditions that can be imposed. Linear
homogeneity of a production function implies that when the
quantities of all the inputs employed are increased by some
proportion, say doubled, then output will also be doubled.
Given that linear homogeneity exists in a production process,
then it can be said the model is homogeneous of degree zero
with respect to input price. That is to say -- the relative
quantities or quantity ratios of the factor inputs used in
the production process are determined solely by relative
prices (or price ratios). If all input prices were to
double, there would be no change in the relative quantities
of the inputs employed. This condition can be represented by
setting the sum of the coefficients on prices equal to zero
in each equation which will place three restrictions on the
model.

The demand equations, with the constraint of homogeneity,

become:

lnLT— Bl£n(PT/PA)+szn(PN/PA)+CanY +C IInYG +C’ RnY +e

A1+ U 2 3 R 1

RnLN=A2+B4£n(PT/PA)+B5£n(PN/PA)+C4£nYU+C5£nYG +C62nYR +e e2 (2.7)

lnLA =A3+B7 £n(P T/PA )+B8 ILn(PN /PA )+C7 lnY +C’ RnYG

U 8 +C95LnYR +e’

3

The remaining parameters are determined from the linear homo-

geneity constraint:

19

B3 = -(B1 + B2)
B6 = -(B4 + BS) (2.8)
B5 = -(B7 + BB)

Constant returns to scale can be imposed by setting the
sum of the coefficients on the outputs equal to one. This
can be done easily, with exactly the same procedure used
for the homogeneity constraint, and will result in a total
of six restrictions. When we impose constant returns to

scale, the model becomes:

RnL =A"

T 1+Bi2n(PT/PA)+B'2'ILn(PN/PA)+C’1'5Ln(YU/YR)+C'2'£n(YG/YR)+ei

RnLN=A3+BZ£n(PT/PA)+Bg£n(PN/PA)+CZ£n(YU/YR)+Cg£n(YG/YR)+e5 (2.9)
RHLA=A§+B;£n(PT/PA)+B§£n(PN/PA)+C3£n(YU/YR)+C§£n(YG/YR)+e§

The coefficients Bi are determined in the same manner as

before, and the coefficients Cj are found with the following

equations:
C3 = 1 - (C1 + C5)
C6 = l - (C2 + cg) (2.10)
C3 = l - (c; + cg)

The final constraint that can be placed on the direct
demand model is symmetry of the cross price elasticities.

This can be defined as:

35?.nLi.= 32nL.

EInPj SlnP. (2'11)

1

20
This implies a reciprocal relationship of the corresponding
coefficients on "other prices" in the demand equations. For
example, the coefficient on PA in the demand equation LT must

be equal to the coefficient P in the demand equation L

T A'
This will place three restrictions on the model stated as:

_ I "I III "I "I "I II I"
RnLT —AfWBl£nPT +BZRnPN +B3£nPA+C1£nYU +C2£nYG+C32nYR+el

ILnL =A"‘+B"'ILnP +B"‘ILnP +B"'ILnP +C"'ILnY +C"'ILnY +C"'£nY +e'"

N 2 2 T 5 N 6 A 4 U 5 G 6 R 2 (2°12)

= u m m m m m m m
RnLA A5W83£nPT+BGLnPN+BgfinPA+C7LnYU+C82nYG+C9£nYR+e3

The combination of symmetry and homogeneity will place
six restrictions on the model. The Direct Demand equations

to be estimated become:

ZnL =A*

* * * *
T 1+BiRn(PT/PA)+B22n(PN/PA)+Ci2nYU+C RnY +c lnY +9

2 G 3 R 1

=* * 'k * 'k 'k *
RnL A2+B2£n(PT/PA)+B4£n(PN/PA)+C4£nY +C RnY +C RnY +e (2.13)

N U 5 G 6 R 2

=* * 'k * *
ILnLA A3+C7£nYU+C8RnYG+C9£nYR+e3

with the remaining parameters determined from the following

equations:
* = - *
B3 (B1 + B5)
B6 (B3 + B4) (2.14)
* = 'k * 'k

In conclusion, these four restrictive models will be
tested against the unrestricted model to determine the most
appropriate set of constraints to represent the production

process of higher education.

21

The Joint Product Cost Function -- The General Form

As stated by Christensen and Green (1976), recent appli-
cation of duality theory to problems in economics has
resulted in many useful results for the study of production
and cost relationship. (An extensive review of the litera-
ture is contained in Diewert (1974).) A fundamental result
is that, given certain regularity conditions to be stated
later, for every production function there is a cost function
that is dual to it. Thus, the structure of production can be
studied empirically through the use of either a production
function or a cost function.

It is commonly accepted in the literature that the
choice between a cost function or production function should
be made on the economic characteristics of the market to be
analyzed. It is thought that if prices are exogenous, a cost
function is the best approach; and, if prices are endogenous, a
production function model is preferable (Grant, 1979).

Berndt and Wood (1975) suggest that, "At the level of an
individual firm it may be reasonable to assume that the
supply of inputs is perfectly elastic and, therefore, the
input prices are fixed." It is for this reason that we have
chosen to estimate a joint cost function with the assumption
of exogenous prices. However, there is an economic issue
regarding whether factor prices are truly exogenous even when
a production function is estimated. If the factor prices

are endogenous, or P = P(Y), then even under constant returns

to scale, the cost function is C(Y,P) = C(Y,P(Y)) and not

22
C(Y,P) = Y x C(P) as is commonly assumed. The consequence
of assuming that factor prices are not exogenous and there-
fore not constant to the firm is that an underlying supply
curve for each factor must be specified. In practice, this
is not usually done. Most models make use of production
function estimates that were derived through the first-order
conditions in Cobb-Douglas and CBS functions or factor share
equations as in translog estimation. Thus, the data points
represent points where the price ratio equals the marginal
rate of transformation. The price ratio, in turn, requires
prices to be determined outside the model and must be exo-
genous. Therefore, the point to be expressed here is that,
regardless of whether a cost or production function is
explicitly used in the study, both make use of exogenous
prices if first-order conditions or share equations are
used.

It has been shown by Hall (1973) that for every joint
production function (similar to equation 2.4 above) there
exists a joint cost function that is dual to it. We can,
therefore, write our model in terms of a unique joint cost

function as:

Proving this transformation requires the use of the Shephard-
Uzawa-McFadden-Duality Theorem for Joint Cost Functions.

Briefly, this theorem states that, if it is assumed that the

transformation function f(Y,X) has a strictly convex input

23
structure (to rule out perfect substitutes or perfect comple-
ments), then there exists a unique joint cost function that
is dual to the transformation function. Further, the cost
function must be positive, linear, homogeneous, non-
decreasing, and concave in factor prices. Finally, the cost
function must obey Shephard's lemma, which states that the
vector of cost minimizing factor inputs is equal to the
vector of derivatives of the cost function with respect to
factor prices. (A proof of this theorem exists in McFadden
(1973)).

As stated in the introduction, this study will illustrate
how the translog function proposed by Christensen et a1.
(1973) can be used to represent a joint cost function. The
translog is a second-order approximation to a general
functional form. It will permit the testing of assumptions
on the structure of cost in higher education such as the
separability between the input and the outputs and the homo—
geneity of outputs along with determining the Allen-Uzawa
Elasticities of Substitution (Berndt & Christensen, 1973a
and Denny and Fuss, 1977). The translog form places no a
priori restrictions on the substitution possibilities among
the inputs.

The general form of the translog cost function is as

follows:

24

m n

£nC = A + 2 AiILnYi + Z B.£nP.
i=1 j=1 3 3

n

XDi.£nYilnY.
1 j=l 3

+ 8

i

"MB

(2.16)
m n
+ % Z 2 Gi.2nPi£nP.
i=1 j=1 3 3
m n
+ Z Z Ri.£nYi£nP.
i=1 j=1 3
where Ao represent the state of technological knowledge,
A., B., D.., G.., and R.. are the technologically determined
1 j 13 13 13
cost parameters of the first-and second-order parameters.
Additionally, the D.. = D.. and the G.. = G.. but the
13 31 13 31
Rij # Rji are imposed as a symmetry condition (for further
discussion see Berndt and Christensen, 1973b). The expres—
sion in (2.16) has one neutral parameter (A0), n + m first-
order parameters (Ai'Bj)' and (m+1)(m/2) + (n+l)(n/2) + mn
second-order parameters where m is the number of outputs and
n is the number of inputs.

The application of the assumption of homogeneity of
input prices as described by Brown (1979) for the multipro—
duct cost function implies:

n n

m
2 B. = 1 Z G.. = 0 X

1 Ri. = o (2.17)
1 3 i=1 3 i=1 3

The derivation of these restrictions is contained in
Christensen et a1. (1973). They imply that as input prices

rise by a fixed percentage, total cost will rise by that same

25
percentage. The second-order terms are forced to sum to
zero in order to negate any effect they might have on total
cost. This will leave the Bj to exert the only impact on
total cost as input prices change and maintain the economic
meaning of homoqeneity. This assumption, along with the
condition of symmetry, reduces the number of free parameters
to (m+n+1)(m+n)/2.

Relating the general format to the specific cost func-
tion under study, we can thus modify the unrestricted case
of the translog cost function for higher education to include
the constraints of symmetry and homogeneity in input prices
with perfectly competitive factor markets.

The joint cost function of academic labor services con-
tains a total of 34 independent parameters. There are one
neutral, 6 first-order, and 27 second-order parameters to be
determined. The symmetry condition eliminates 6 parameters
while the homogeneity of input prices permits the number of
free parameters to be reduced by an additional 7. Thus, the

number of free parameters to be estimated in the model is 21.

The Joint Product Cost Function —- Share Equations

 

In order to estimate the parameters of (2.16) above, we
can employ the simple method of ordinary least squares. How-
ever, additional information is available, which will result
in improved efficiency of estimation. Shephard's lemma
assures us that there is a set of factor demand equations

which can be derived from the joint cost function. In

26
logarithmic form, Shephard's lemma can be written:
3£nC __ 3C .._1 = j j = Sj

afinP. - 3P. C C
J 3

where Sj is the share of input j in total cost. For the
joint translog function in (2.16), this yields the following
three equations representing the input shares of each of the

factors:

ST = BT + 1ElGinLnPi + JIgleTSLnYJ
n m

SN = BN + iilGiNfinPi + jile fian (2.18)
n m

SA = BA + iilGiAinPi + jileAfian

(where i = T,N,A, and j = U,G,R)

Additionally, we can improve the efficiency of the
estimates of the model by using the information contained in
the outputs (Hall, 1973 and Burgess, 1974). However, in
order to take advantage of this information we must first
add an additional assumption to the model. We must assume
that perfect competition also exists in the output market.
It is difficult to imagine instruction and research among
the departments of a university as having a homogeneous
product. An argument can be made that this condition is not
appropriate since instruction or research in business and
engineering, for example, is a far different product than

that being offered in music or history. However, we must

27
accept these difficulties in the output market in order to
gain the needed efficiency in the model. Thus,we can define
the output shares as being equal to the percentage change in
total cost that occurs with a percentage change in an output

produced or:

Y. P.Y.

l 1
C Mi (2.19)

8£nC ___ 3C __1___
C

ainYi BYi

 

 

where Mi is the share of output i of total cost. This pro-

duces the following three additional equations:

m n
MU = AU + jEleunan + iilRuiznPi
m n
MG = AG + jileGQan + iEIRGiJLnPi (2.20)
m n
MR = AR + jileRian + iElRRiRnPi

(where j = U,G,R and i = T,N,A)

These applications of Shephard's lemma and perfect com-
petition produce six equations in addition to the joint cost
function without the addition of any unknown parameters. By
specifying that the seven equations have joint normal addi-
tive disturbances, the method of maximum likelihood can be
used to estimate the unknown parameters. Although the cost
function could be estimated in isolation from the cost share
equations, it is clearly more efficient to estimate the para-
meters with the six share equations included in the system.

Actually, only four equations can be used in the regression

28
model since one equation of both the output and input shares

is linearly dependent on the other two.

The Joint Product Cost Function --
First- and Second-Order Conditions

 

As previously stated, the translog is a second-order
approximation to a general functional form. It is necessary
for this approximation to meet several regularity conditions
for us to maintain the belief that it is a reasonable
representation of the true (and unknown) cost function of a
university's academic labor services. First, each fitted
input share and output share must be greater than zero and
less than one at every data point. A model that predicts
inputs (and outputs) that contribute negatively or greater
than 100 percent to total cost (total revenue) is without
meaning. Second, it is necessary for a function to have a
strictly convex input structure as stated in the Duality
Theorem above. Following the procedure employed by Grant
(1979), from Allen (1938), we can test the convexity condi-
tions by computing determinants of the bordered Hessian

matrix.

F.
O C 0 . Hl O C O Hn 7
C 0 ij 0
H = Hi Hii . (2.21)
. H. . . .
1:1
H O O 0 O O O OH
_ n nn_J

 

 

where Hi = Mi' Hii = Oii' and Hij = Oij

It then remains to demonstrate that the determinants of this
matrix are negative semi-definite at each data point. The
translog specification of the partial A-UES has no a priori
constraints. Rather, the elasticities are allowed to vary
with the share equations. In the instances where these
first- and second-order conditions are met, the relevant
elasticities will be assumed to reflect accurately the

structure of the academic labor costs in higher education.

The Joint Product Cost Function -- The Constraints

 

This section is designed to identify the specific form
of the joint product cost function including the constraints
of: i) homogeneity of output prices, ii) separability,

iii) constant returns to scale, iv) homogeneity and separa-
bility, and v) the Cobb-Douglas form.

Separability between the inputs and outputs implies
that the transformation function can be written with an
aggregator function to represent output as a single variable.

It is assumed the transformation function can be written as:

f(YU,Y ,YR) = g(LT,L LA) (2.22)

G N'

The dual cost function to (2.22) above would be:
= * *
c k(h (YU'YG’YR)'.g (PT'PN'PA)) (2.23)

The restrictiveness of separability illustrated by (2.23)

30
implies that the relative marginal costs for any two outputs
are independent of input prices (Brown, 1979). Thus, the
existence of separable input and output functions states that
the specific mix of outputs produced is not affected by the
mix of inputs used and vice versa. (Despite this restrictive-
ness, the separable form of the transformation function was
commonly accepted in empirical studies as recently as
Hasenkamp's (1976) treatise.) The test of the separability
of the outputs can be incorporated into the model with the
addition of the constraint that the ratio of marginal costs
of any two outputs will not be affected by a change in the
price of any factor input. For the translog form this
implies that:

m
. D

3[(A. +
1 1

n
1RijflnPi)/Ak + j .Ran + E RkiRnPi)]

kj i

utflB

n
Di.£nY. + 2
3:1 3 i= 1

 

BinP2

o (2.24)

This rather complicated partial derivative is equivalent to
setting the Rij = 0 for all i's and j's in the cost function.
Since there are m(n-l) free Rjj' equation (2.24) places six
additional restrictions on the previously unrestricted model.3
Another important step in this analysis is to test

whether, given a fixed percentage increase in all of the out-

puts, total costs rise by that percentage. This constraint

 

3 Except for linear homogeneity of input prices.

31
is known as the homogeneity of outputs.. We can incorporate

it into the model with the following equalities:

m m
2 D! c = o and Z: R. l = 0 (2025)
i=1 13 i=1 13

where i = U, G, and R; k = U, G, and R; and j = T, N, and A.
These conditions have the effect of isolating the impact of
all increases on total cost to be solely determined by
coefficients on the first-order parameters, namely AU, AG,
AR' This assumption will place five additional restrictions

on the unrestricted model. Only two of the conditions in

m n

2 R.. = 0 are independent since 2 R.. = O has already been
._ ij ._ 1]
3—1 1-1
imposed by the assumption of linear homogeneity in factor

prices (Brown et al., 1979). In addition, by further assum-

m
ing the 2 Aj = 1, the cost function can be tested for con-
i=1

stant returns to scale.

The last constraint useful in this analysis is equivalent
to transforming the generalized translog function into a
Cobb-Douglas multiple output cost function. Conveniently,
the translog cost function reduces to a Cobb-Douglas cost
function by setting all second-order parameters equal to

zero. Stated algebraically:

D.. = 0, G.. = 0, and R.. = O for all i and j. (2.26)
13 13 1]

These constraints cause the cost function to be reduced to

only six non-zero terms, which are the intercept, the three

32
output terms, and the two input price terms. (The third

input price was previously dropped with the homogeneity of

n
prices constraint which forced the 2 Bi = 1). It is thus an
i=1

even more restrictive case than the combined constraints of
output homogeneity and separability.

In summary, there are five constraints that can be
imposed on the unrestricted model. First, homogeneity in
the outputs assumes total cost will change by the same percen-
tage as the outputs. Second, separability assumes the
general transformation function can be written with an
aggregator function for the outputs and inputs separately.
Third, homogeneity and separability can be imposed together.
Fourth, the model can be constrained to include constant
returns to scale. Fifth, the model can be constrained to

represent a Cobb-Douglas multiple output function.

The Joint Product Cost Function -- The Elasticities of
Substitution, Demand, and Marginal Cost

 

The usefulness of determining the Allen (l938)-Uzawa
(1962) partial elasticities of substitution (A-UES) is that
they summarize the ease with which one input can be substi-
tuted for another without changing any of the outputs or
input prices. In other words, the elasticity of substitution
determines the proportion of quantities of one input that
can be traded for another by movement along the isoquant.

A large elasticity of substitution indicates that one input

can be easily substituted for another while an elasticity

33
that is close to zero implies that the two inputs are very
poor substitutes. Negative elasticities of substitution
imply the inputs are complements.

Uzawa (1962) provides the complete derivation of the
Allen partial elasticities of substitution adapted to cost
function estimation. Briefly, the general form of the
elasticity of substitution (0) becomes:

CJC..
1

= J
Oij Cicj (2.27)

 

where C is the cost function, Ci and Cj representing partial
derivative with respect to P1 and Pj respectively, and Cij is
a second partial derivative for i # j.

The A-UES have been adapted to the translog cost
function by many economists such as Christensen and Greene
(1976), Berndt and Wood (1975) and (1979), Humphrey and
Moroney (1975), Anderson (1979), and Griffin (1977). The

form of the elasticities are:

 

 

.. + 5.5
0.. = 11~ 1 J
13 Sisj
(2.28)
G.. + S.(S. - l)
_ ll 1 J.
011 ‘ 2
Si

where Si and Sj are the factor shares and Gij and Gii are the
coefficients of the cross products of the factors. Obviously,

from this definition, symmetry must exist between the

elasticities, o. c

. ... These definitions do not change
13 31

for the multiple output case but, due to the content of share

34
equations, the elasticities are expanded so that each oij
is a function not only of the level of each input price but
also the level of each output. In Chapter IV, we provide
estimates evaluated at the mean of the actual shares of the
six elasticities of substitution.

Another statistic important in an analysis of the
structure of production is the input demand elasticity.
This permits consideration of how the quantity of one factor
demanded will change with respect to a change in its price
or that of another factor. Cross-price elasticities and
own-price elasticities are respectively:

ij j ij (2 29)

It can be seen that, since Eij is a function of only the
factor share of the jth factor, then Eij # Eji'

The joint cost function in an analysis of production
can be used to study substitution elasticities among the
outputs. The calculations are identical although the defini-
tions are the inverse of those applied to the inputs. This
is due to the independent variables of the cost function
consisting of exogenous output quantities and input prices.
It is for this reason that the inverse of the elasticity of
substitution for the outputs is defined as the percentage
change in the output price ratio occurring from a percentage
change in the ratio of the output quantities produced. Thus

the inverse elasticities of substitution of the outputs are

35

defined as:

 

 

D.. +M.M.
n.. = 13 3*3
13 MiMj
(2.30)
D.. + M.(M.-l)
_ 11 1 1
and n.. -
11 M.2
1

It should, therefore, be remembered that a high value for
"ij would indicate that a small change in outputs would cause
a large change in output prices, or that the outputs are not
easily substitutable.

The "ii can be used to determine the marginal cost

elasticities and the inverse of the cross price elasticities

for the outputs. These elasticities are defined as:

alnPi
Bij = "37716)? = Mjnij
(2.31)
BRnPi
and Bii = m; = ”N511

As with the inputs, all output elasticities will also be

evaluated at their means.

Conclusion

 

It is possible to estimate the parameters of both models
through the use of ordinary least squares regression. How-
ever, there are several desirable properties of regression
analysis that cannot be sacrificed in the interests of simpli-

city. The most important of these is the ability to measure

36
the applicability of the previously mentioned restrictions
on the models.

The statistical technique implemented is the Iterated
Zellner Efficient Estimation (IZEF) method. Kmenta and
Gilbert (1968) have demonstrated that the parameters
estimated through IZEF are identical to those that would be
produced through a maximum likelihood procedure for all
samples. Ruble (1969) proved the computational equivalence
of the two methods. The equivalence of the methods is
important since the IZEF will produce the estimates, but the
methodology for testing the applicability of the additional

constraints is based on maximum likelihood estimation.

CHAPTER III

MODEL SPECIFICATION AND DATA

Introduction

 

Although the study of the structure and organization
of resources in higher education may appear to be a fruitful
area for quantitative research,very little empirical analy-
sis has taken place. To be sure, the discipline of higher
education administration has produced multitudinous publica-
tions in this field. However, these studies have been very
limited in their approach. Typically, they attempt to deal
only with measuring the concepts of productivity and effi-
ciency. O'Neill (1976), Wallhaus (1975), McGuckin and
Winkler (1979), and James (1978) are representative examples
of this vast body of literature. In most cases, the studies
define productivity along the lines of some measure of unit
cost such as dollars of expenditures per student credit hour
produced or the student faculty ratio for specific depart-
ments or the university as a whole. These measures of unit
cost are then compared to the unit costs of other univer-
sities which serve as a scale of performance to determine
productivity.

There is one study by Verry and Layard (1975) that
deserves special consideration because it is the only study

37

38

that estimates cost functions for university research and
teaching. Their approach differs from that presented here
in three major aspects. First, they attempt to estimate a
total cost function for a group of British universities in
total rather than across instructional departments. Second,
they are not concerned with the substitutability among the
types of academic labor services. (Teachers' salaries are
included only as one component of total cost.) Third,
research is incorporated into their model as an independent
variable and is computed as teachers' time devoted to
research rather than an actual measure of output such as
journal articles produced. Thus research, an output, is
treated as if it were a labor input.

The problems associated with applying economic theory
to higher education are best explained in the following

statement by James (1978).

"Ideally, in examining questions of produc-
tivity and technology, we would like some index
of the learning and increased earning potential
imparted by different instructional modes, but
these data are generally not available. The pre-
valence of nonprice rationing, the lack of con-
sumer information, and the possibility of
externalities mean that market price cannot be
taken as;an indicator of marginal social value in
higher education. A mechanism for separating the
contribution of student time and characteristics
and interactions from other inputs has not yet
been devised. Teaching quality might, in prin-
ciple, be approximated by comparing 'before and
after' test scores, but these have not been widely
adopted. As a result, teaching output has been
measured simply in terms of student credit hours
or degree candidates of various sorts, abstract-
ing from the quality dimension, by most of the
studies referred to in this paper.

"The situation is even worse with respect to

39

basic university research which, typically, is

not sold on the market at all. Not only are we

lacking a subjective quality index, we do not

even have a crude quantity index, such as num-

bers of articles and books, for most disciplines

and years. Therefore, quantification of re-

search productivity has rarely been attempted,

and most studies simply look at the input side

of the picture."

We must agree that many of the problems are, indeed, formid-
able. The lack of a well-defined marketplace where price

and quantity are uniquely determined for every instructional
department and every output is not easily solved. However,
the use of student credit hours (SCH) as a measure of
instructional output remains as the only quantitative measure
of a department's teaching load.

The issue of quality can, at best, be minimized by
assuming that all of the instructional departments within a
university attempt to maintain a level of quality in instruc-
tion research that is consistent within the reputation of the
university as a whole. Naturally, there are departments
that can be considered to be out-lyers to the university's
overall reputation. However, without a marketplace to
differentiate the departments' outputs, any decisions
regarding quality becomes arbitrary. The problem with
reporting research output has been solved (although the
quality issue is still present). Michigan State University
does have fairly accurate records of all journal articles
and book publications by the faculty. There is a problem

specifying this output because a research article or book is

credited to a department only for the year of publication

40
and not the year the research was actually performed. We
have addressed this issue by assuming that a department will
record its publications in the calendar year following an
academic year. For example, the publications for the
calendar year, 1978, were assigned to the academic year,
1977-78.

Among the additional difficulties that have faced
researchers of the structure of higher education has been the
lack of accurate employment records. It has not been until
recently that universities have kept faculty records on a
full-time equivalency basis. Previously, records on
temporary and part-time faculty were recorded only on a
headcount basis. Since the percentage distribution of full—
time and part-time faculty is not identical across all
departments of a university, erroneous results would be
produced. At Michigan State University, complete full-time
equivalent information for all faculty members exists for
only two years -— 1977-78, and 1978-79. Although data exist
for the other variables in prior years, it is of little use
without accurate full-time equivalencies.

Additionally, the data for both years include only those
departments that produced all three outputs. A department
reporting a zero for any one output has been dropped from
the sample. This is because all outputs (and inputs) are
in logarithmic form. Beyond the teaching of students and
research, faculty are also expected to participate in public

service. Those departments that are considered to have

41
public service as a major output have also been excluded
from the sample data.

Appendix A is a listing of which departments are included
in the data along with a brief explanation for excluding
specific departments. The departments that have been included
were chosen to represent a group as similar as possible with
respect to both their efficiency and the quality of the out-
puts. The data are a two-year cross section of sixty-one
instructional departments at Michigan State University for
the academic years 1977-78, and 1978-79. It would have been
preferable to estimate the model over a much longer period
of time, say, five to ten years. However, as stated above,
the data were simply not available. The source of all data
used is the Office of Institutional Research, Michigan State

University.

Defining and Measuring the Outputs

 

The definition and measurement of a unit of output in
higher education is a controversial issue. Agreement does
not even exist on the precise function of education. Does
education produce more qualified individuals or is it nothing
more than a screening process? The first function implies
that through education an individual's skills are changed,
while the second function implies that schools do nothing
more than identify the most able individuals in the society.
The latter has been the subject of both theoretical treatment

(Spence, 1973) and empirical treatment (Taubman and Wales,

42
1973 and 1974). The differences between the two social
functions of education should, theoretically, affect the
specification of quality within a model.

Besides not knowing exactly how education should be
measured, there is the additional problem of measuring the
quality of education. One approach is to measure some change
that has occurred in students due to their exposure to the
faculty and graduate assistants. This is feasible for
instruction, since students could be tested at the end of
each term, but it would be impossible to measure the change
in total human knowledge based on a single piece of research.
Another approach would be to create some arbitrary index of
performance to specify the differences in quality, much as
one would "grade" the quality of meat or the horsepower of
an engine. It is conceivable that an index could be created
for research articles; however, any index that would be used
would be costly to compile or extremely artibrary (such as
asking department chairpersons to judge the quality of their
faculty's research). It would also be possible theoretically
to index the quality of instruction based on the earnings of
graduates. However, this is not possible since it would be
difficult to determine which portion of a graduate's salary
could be attributed to the specific departments within the
university (O'Neill, 1976).

Thus, although we can understand the problems of measure-
ment, we cannot entirely solve them in this study. The out-

puts of each instructional department are defined as

43
undergraduate student credit hours (YU), graduate student
credit hours (YG), and research (YR), (discussed below).
Nerlove (1972) describes these as being the relevant outputs
produced by the higher education sector. This study will
differ from the concepts established by Nerlove in two major
aspects. The first is that he classifies research into one
of two categories -- basic and applied -- and, further, that
graduate education and basic research are perfect compli-
ments. Since the data used in this study do not draw any
distinction between basic and applied research, these points
cannot be considered.

The undergraduate and graduate student credit hours are
three-term academic year totals on a course level basis rather
than a student level basis. In other words, if a graduate
student majoring in chemical engineering were to take an
undergraduate class in economics, his student credit hours
would be reported by the Department of Economics in under-
graduate student credit hours. The graduate student credit
hours include, besides classroom instruction, all doctoral
dissertation research credits assigned to that department.
Research is defined for the purposes of this study as only
the publication of refereed journal articles and books
(all other types of publications being ignored). Setting
the relative value of one book equivalent to four journal
articles and three co-authored books is, admittedly,
arbitrary. This ratio represents nothing more than the

average of the ratios used by many other authors (Hugine,

44
1978). Folger and Bayer (1966) describe the use of one
weighting method of publications over another by stating,
"none of the researchers had an objective or empirical basis
for their choice of weights and several admit to subjectivity
of the weighting system employed."
The means and variances for each output variable over

both years are:

 

 

. variance %
mean variance mean
Undergraduate SCH (YU)
per department 9585 798 8%
Graduate SCH (YG)
per department 1631 1554 95%
Research units (YR)
per department 33 37 112%

Comparing the means and variances above, we find that
research has greatest variance relative to its mean (112%).
This is followed by graduate SCH (95%) and undergraduate SCH
a distant third (8%). Although these large variances are
understandable and to be expected, a serious difficulty
arises in interpreting the results. The conclusions drawn
from the analysis of the production process of higher educa-
tion is based on various elasticities evaluated at the means
of the variables. The statistical technique used to estimate
the model's coefficients provides a confidence interval over
the entire range of the data. As we move away from the mean

we find that the interval increases in width which implies

45

less accuracy in predicting total cost. Therefore, the
model's estimates will become more unreliable the farther a
particular department's outputs are from the mean of that out-
put.

Obviously, from a statistical perspective, it is
desirable to have variables with sizable variance; however,
it does tend to weaken the analysis based on the means. It
shall be left to future studies with more refined data to
estimate the substitutions of the inputs evaluated away from

the mean.

Defining and Measuring the Inputs and Cost of Inputs

 

For the purpose of estimating substitution among the
professional labor services of a university, it is necessary
to identify and measure these labor inputs on a full-time
equivalency basis. This method assumes one full-time equiva-
lent appointment to be forty-hours per week from September 15th
to June 15th, without adjustment for vacations or sick leave.
In a technical sense, it would be more appropriate to use an
annual salary equivalent to an hourly wage rate multiplied
by hours actually worked. This would provide a closer
relationship between the wages paid for work actually per-
formed and the amount of output produced from that work.
However, as described by Blackburn (1974) the collecting of
data on the quantity of each labor input used in the produc-
tion process would be extremely difficult and almost

certainly meaningless. There exists a basic inability to

46
distinguish between leisure activities and professional
development. If an historian is reading a biography, he is
engaged in both leisure and academic pursuits. When a
sociologist scans a newspaper, he is inevitably applying
what he reads to either his classroom discussions or his
scholarly investigations. Free time and work time are often
hard to distinguish in the academic professions. It is for
this reason that nine-month academic year salaries are used
as proxies for a specific price paid for a unit of work.

The faculty salaries reported are assigned to each
department on the basis of where the credit hours were pro-
duced rather than the administrative department of faculty
members. For example, if a professor of economics were to
teach a class in the Department of Labor and Industrial
Relations, the professor's salary would be assigned to Labor
and Industrial Relations rather than Economics. This cross-
ing over between departments does not exist for graduate
assistants; therefore, their salaries are assigned to their
administrative unit of record. This permits a matched assoc-
iation of student credit hours produced with the faculty
member's salary. However, the research publications of the
faculty are assigned to only the department paying the
largest proportion of faculty member's salary. The method
of reporting research by Michigan State University does not
permit prorating research across several departments.

Again, we mention that the category of non-tenured

faculty includes the tenure stream and temporary faculty.

47
The tenure stream faculty are hired with the understanding
that if they make reasonable progress in their profession,
they will be granted tenure at some date in the future,
usually six years, at Michigan State University. The tempo-
rary faculty are hired only to fill temporary shortages in
teaching positions and are assumed not to contribute to the
research output of the instructional department. Combining
these two types of labor services into one input becomes
an important consideration when the policy implications are
stated in Chapter VI.

Graduate assistants are not appointed on a ten-month
basis at Michigan State University but, rather, on a three-
terms-per-year basis. The salaries recorded for graduate
assistants, therefore, represent the sum of the three terms
adjusted to a forty-hours-per-week full-time equivalency
basis.

As stated above, two years of data are included in the
sample. The 1977-78 year's data has been increased by seven
percent to reflect the average increase in faculty salaries
between the years 1977-78 and 1978-79. Individuals receiving
salary increases greater or less than seven percent are
assumed to have some change in their productivity reflected
in this difference.

The means and variances of the inputs and related data

are:

48

 

 

 

. variance %

mean variance mean
Total cost $674,260 $482,110 71%
Tenured Faculty Cost 407,200 305,457 75%
Non-Tenured Faculty Cost 140,703 115,743 82%
Graduate Assistant Cost 126,356 137,013 108%
Price-Tenured Faculty (PT) 26,331 2,462 9%
Price-Non-Tenured Faculty (PN) 16,613 2,382 14%
Price-Graduate Assistants (PA) 9,585 798 8%

We find in these statistics very little that is unexpected;
however, there are two points worth noting. Graduate
assistants' salaries have the smallest variance as a percen-
tage of the mean. This is understandable when we consider
that their salaries constitute both compensation for services
and a stipend to maintain enrollment in a graduate program.
Thus, with all graduate students having the same tuition and
fee structure, we would expect this portion of their salaries
to be the same across all departments. Another reason for
the small.variance is that departments have less flexibility
and smaller salary ranges for graduate assistants than for
the faculty. If there is anything surprising about the above
average salaries, it is that the variance of non-tenured
faculty salaries is not larger. However, this can be
explained by remembering that this is not a variance of all
non-tenured faculty salaries but only the variance of average
non-tenured faculty salaries across departments. It is not

for this study to explain the variations in salaries of

49
individuals. This is left for the numerous studies currently
available. It is only important here to note the differences

across departments.

CHAPTER IV

MODEL ESTIMATION

Introduction

 

This chapter presents the results of both the Direct De-
mand Analysis and the Joint Cost Function Analysis in estimating
the demand for the inputs to higher education. The results
that will be discussed are: 1) the factor demand elasticities
for both models, 2) the elasticity of supply for both models,

3) the applicability of model restrictions, such as homo-
geneity, constant return to scale, symmetry,separability,and
the Cobb-Douglas restrictions, 4) the "goodness of fit" of the
estimated joint cost function, and 5) the Allen-Uzawa elasti-
cities of substitution for the inputs and outputs (derived

only from the joint cost function model).

Direct Demand Constraints

The model was estimated for each year of data with five
sets of restrictions imposed. In each case, IZEF estimation

was performed with every variable regressed in logarithmic form.1

 

The computer programming used the Time Series Processor
(TSP) Version 2.8 statistical package and was run on the CDC
750 computer at Michigan State University.

50

51
Table 4.1 shows the applicable Chi-Square test results for
the various restrictions.

The 1977-78 data reflect both homogeneity of input
prices and homogeneity with symmetry of the cross price elas-
ticities, while the 1978-79 data can be appropriately
specified with only the symmetry constraint.

Comparing the data for both years provides some indica-
tion of why the estimates in the direct demand analysis and
the joint product cost function (to be discussed later) are
so different across the two years (see Appendix B). The
cause of the difference is the variable for research (YR) and
this appears to be the major cause of the different results.
There is very little difference in the factor prices after
the 1977-78 has been adjusted for inflation at a rate of 7
percent. The reporting of student credit hours for under-
graduate and graduate instruction are not much different
between the years with only minor exceptions such as Bio-
physics, Crop and Soil Sciences, and Packaging. Research,
on the other hand, is considerably different for many
departments between the two years. The Department of
Psychology, for example, dropped in publications from 126 in
1977-78, to 65 in 1978-79, while the Department of Crop and
Soil Sciences increased its research output from 42 to 159.
If we group the departments with the greatest reported
changes together, we find they are concentrated in the
Colleges of Agriculture and Natural Resources, Arts and

Letters, and, to a lesser extent, Natural Science. One

52

Table 4.1: Direct demand analysis: Chi-Square test of
restrictions.

 

 

 

 

Restrictions Chi-Square

1977-78 Data (Degrees of Freedom) Test
Homogeneity 3 5.0
Symmetry 3 18.0*
Homogeneity and Symmetry 6 10.8
Constant Returns to Scale 6 80.4*
1978-79 Data

Homogeneity 3 13.2*
Symmetry 3 6.6
Homogeneity and Symmetry 6 22.6*
Constant Returns to Scale 6 88.0*

* Significantly different from zero at a = .01.

53
possible explanation could be that the research occurring in
the Colleges of Natural Science and Agriculture and Natural
Resources is more directed toward scientific experimentation
which requires long periods of testing and data collection in
laboratories. Thus, we reason that this would cause the
research to be highly variable in these colleges. We would
expect these year-to-year differences to be minimal when the
data are aggregated to the departmental level but apparently
they are not. Whatever the actual or assumed cause of the
wide variation in publications from year to year, there is
no doubt that the ability of the model to replicate the
structure of academic labor services would be improved with
better specification of research output. Pooling data over
a period of several years would reduce the model's sensitivity
to research cycles. This cannot be done now because only two

years of data are currently available.

Direct Demand Estimates -- The Inputs

The estimates for the structure of higher education,
although not consistent, can provide valuable insight into
the production process. Rather than discuss the wide range
of results presented by each model, we will concentrate on
the most restrictive case that is applicable to the system,
the 1977—78 data with homogeneity of input prices and
symmetry of cross price elasticities.

Table 4.2 presents the regression estimates and the

applicable constraints. The elasticities of demand for the

54

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55
three types of labor services are all negative and sufficiently
large in size so that demand may be described as highly
elastic (ET = -l.15, EN = -1.28, EA
the demand equations the amount demanded for each input was

= -4.01). Recall that in

a function of input prices and the output quantities.
Therefore, a 1 percent increase in tenured faculty salaries,
for example, would cause a 1.15 percent decrease in the number
of tenured faculty employed. The relative sizes of the
estimates indicate that the input with the greatest elasticity
is graduate assistant employment. These individuals have not
had the time or experience in their discipline to establish

a reputation and could be considered to be in a competitive
market with all graduate students for their assistantships.
Tenured faculty, on the other hand, have more years experience,
and have established areas of experitise that makes the

demand for their services far more unique. Thus, we see
nation-wide searches carried out by departments interested in
filling tenured faculty vacancies while the same departments
choose their new graduate assistants from the applications
received annually with very little solicitation. In terms

of economic theory, the tenured faculty have (successfully)
differentiated their product of labor services more effectively
than either the non-tenured faculty or graduate assistants.
The non-tenured faculty have also provided more differentia-
tion of their product than graduate assistants since they

have completed a doctoral program and, in most cases, have

specialized in several areas within their discipline.

56

Because of the large standard errors, the cross price
elasticities do not provide estimates from which clear
implications can be drawn. As expected, graduate assistants
are easy substitutes for both the tenured faculty (ETA = 1.94)
and the non-tenured faculty (ENA = 2.07) because we had
assumed in Chapter I that the substitution would be greater
than complementarity. These results indicate that a l per-
cent change in the salaries of either of the two faculty
categories will cause approximately a 2 percent increase in
the number of graduate assistants employed and tell us that
administrators are quite willing to employ graduate assistants
if the salaries of the faculty rise sharply. The explanation
for these results is that the graduate assistants' contribu-
tion to undergraduate instruction rather than research or
graduate instruction cause the substitution with the faculty.
As stated in Chapter I, the apparent reason for these find-
ings is the unsupervised instruction by graduate assistants
and the use of large lectures with one faculty member and
several graduate assistants to replace hiring more faculty
members. Obviously, the same argument applies to the high
cross price elasticity between the non-tenured faculty and
graduate assistants.

The other cross-price elasticity between tenured and

non-tenured faculty (E = -.79) is contrary to what we

TN
expected. We expected that the non-tenured faculty, consist-
ing of both temporary and tenure stream employees, could be

easily substituted for tenured faculty since the

57
responsibilities of instruction and research are generally
shared. However, this inconsistency can be explained by
considering the importance of research to the non-tenured
faculty. Most of these individuals are attempting to advance
their careers in their profession (and gain tenure). How-
ever, as we stated in Chapter III, the variable "research
output" does contain some misspecification due to time lags
in reporting publication. Therefore, we find it reasonable
to conclude that the misspecification of research is the
cause for the non—tenured faculty to appear as substitutes
for graduate assistants and complements to the tenured
faculty. There is one possible explanation for the comple-
mentarity between the tenured and non-tenured faculty. It
must be assumed that, with respect to instruction, both
graduate and undergraduate are substitutes and, therefore,
any complementarity that exists must occur within research.
We can argue that the role of the tenured faculty in research
is one of generating their own projects along with providing
assistance to the non-tenured faculty in attaining research
grants and developing proposals for research topic. Thus,
although the tenured faculty may or may not provide much
assistance to the non-tenured faculty, the tenured faculty
may play a very important role in supporting the non-tenured
faculty research. Although the non-tenured faculty may do
all of the data collection, development of analysis, and
writing the research articles, it is the professional sophis-

tication of the tenured faculty that initially generates the

58
design and feasibility of project. It is difficult to
estimate which of the two explanations above contributes
most to the complementarity; however, it does seem that
together they overshadow the effects of substitution related

to instruction.

Direct Demand Estimates -- The Outputs

The direct demand analysis also provides estimates of
the returns to scale appearing in Table 4.3. These results
are much more consistent across all of the model restrictions
and for both years of data than were the estimates of price
elasticities. Returning to the constrained model of homo-
geneity of input prices and symmetry of the cross-price
elasticities, the sum of the output coefficients for tenured
and non-tenured faculty and graduate assistants are .60, .43,
and .91 respectively. Increasing each output simultaneously
by some fixed percentage, say 1 percent, will cause a less
than one percent increase in employment for all three types
of labor services. The largest increase in employment occurs
with the graduate assistants. This can be explained by the
argument that graduate assistants, in general, contribute to
the outputs only as support personnel to the faculty. Thus
as faculty teaching loads increase and the average class
size increases, there would be more graduate assistants
employed and assigned to each faculty member. The output
of the faculty appears greater, implying greater scale

economies while the graduate assistants exhibit far smaller

59

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61
scale economies.
Additionally, we should note that in the demand for
graduate assistants the coefficient on graduate instruction
(Y

G = .18) is more than three times greater than the coeffi—

cient on undergraduate instruction, Y .05, as shown in

U _
Table 4.3. It is not reasonable that increasing graduate
instruction would gau§g_an increase in the number of graduate
assistants since we assumed their contribution to graduate
teaching was negligible. It is more likely that the strong
correlation is due to the dual role graduate assistants play
in the production process as inputs and as contributors to
the output of graduate instruction. Increasing the size of a
graduate program would require increasing the number of
assistants available since the assistantships are partially

a stipend to induce students into starting the graduate pro-
gram. Therefore, the larger graduate programs invariably
provide more graduate assistantships. There is another aspect
to the correlation between graduate instruction and graduate
assistants that should be discussed. A department that is
experiencing a sizable increase in the demand for its under-
graduate programs will hire graduate assistants to do the
teaching. Increasing the number of graduate assistantships
will, in turn, increase the size of the graduate program.
Thus, we see an increase in the undergraduate program has

the spill-over effect of increasing the graduate program
simultaneously. Conversely, when undergraduate enrollments

decline, we can expect the graduate programs at colleges and

62
universities to also decline. We also see from Table 4.3
that if all of the outputs were to rise by the same propor-
tion, say 10 percent, there would be a greater increase in
the demand for tenured faculty (6.0 percent) than in the
demand for non-tenured faculty (4.3 percent). We could argue
that increasing the outputs would require a greater increase
in the demand for the non-tenured faculty than tenured
faculty because the non-tenured faculty are in their prime
research and publishing years and increased research would
significantly increase the demand for their services. How-
ever, the coefficient on research (YR = .16) in the non-
tenured faculty demand equation is approximately one-half
that of the corresponding coefficient (YR = .33) in the
tenured faculty equation. Again, this appears to be another
form of the misspecification of research causing the estimates
related to the non—tenured faculty to be unreasonable.

If we add the coefficients for each output variable
across the three demand equations, we have the following
estimates of the total impact of each output on employment
(using the 1977-78 data and the constraints of homogeneity

and symmetry from Table 4.3).

YU = .32
YG = .45
YR = 1.17

These statistics imply that, if each output is increased by

the same percentage, total employment will be increased by

63
the smallest percentage from undergraduate instruction with
much larger increases from graduate instruction and a still
larger increase in employment from research. These results
reflect the ability of departments to increase instruction
through the use of large lecture halls and televised instruc-
tion. Graduate instruction is found to have roughly the same
effect on the employment of both types of faculty as under-
graduate instruction. This result implies that it is
possible, from the supply side of the output market, to adapt
some of the scale economies such as large lectures and
televised instruction used in undergraduate teaching to
graduate programs. However, it is unlikely that graduate
enrollments (the demand side) are large enough to make this
feasible. The employment diseconomies associated with
research can be explained when we look at lnY in each of

R
the three equations.

 

 

Demand Equation £nYR
Tenured Faculty .33
Non-Tenured Faculty .16
Graduate Assistants .68

From the above table we see the greatest increase in demand
occurs with graduate assistants. It is possible that the
total cost of research can decline as departments shift
their labor resources to research since the cost of an
additional graduate assistant is cheaper than a faculty

member. The graduate assistants then provide their services

64
for reviewing the literature, data collection, and any
computer programming that might be necessary. These laborious
and time consuming tasks are no longer the responsibility of
the faculty member, thus making his or her time more valuable

and requiring less of an increase in faculty employment.

Direct Demand Estimates -- The Three Year Rate of Adjustment

 

It is also important in the study of higher education to
gain some understanding of how departments adjust their in-
puts to some optimal level when there is an exogenous change
in the outputs. The analysis up to this point has assumed
that each department is capable of adjusting its inputs
instantaneously at the beginning of each academic year.
Obviously, this is not possible for most, if any, depart-
ments. For the purposes of further developing this study,
we assume that the departments at Michigan State University
base their employment decisions only on the instruction and
research in the current year and differences between the
amount of current instruction,kxfifliundergraduate and graduate,
and level of instruction three years prior. The direct
demand analysis can be adapted to include consideration of
the adjustment process through the addition of two terms in
each regression equation. The theoretical form of these
equations with the constraints of symmetry and homogeneity

(adapted from equation 2.13) are:

65

lnLT = A1+Blzn(PT/PA)+len(PN/PA)+Cl£nYU+CZ£nYG+C3£nYR
+Dl(£nYU-£nYU_3)+D2(£nYG-inYG_3)+El+el
RnLN = £2+§22n(pT/pA)+£42n(pN/pA)+842nYU+ESInYG+862nYG (4.1)
+D3(£nYU-£nYU_3)+D4(finYG-anG_3)+E2+e2
9,nLA = A3+C7anU+CBRnYG+C9£nYR+D5(anU-nnYU_3)+D6(lnYG-lnYG_3)
+£3.23
where 82 = -(Bl + 82)
£6 = -(§4 + £5)
and 89 — -(B7 + 88)
and YU-3 and YG-3 are the lagged output variables of under-

graduate and graduate instruction respectively. These regres-
sion equations can be altered slightly to produce a system of
equations that will reduce the number of calculations necessary

in deriving the coefficients. The actual regression equations

are:
£nLT = Al+81£n(PT/PA)+Ezln(PN/PA)+El2nYU+E2£nYG+C3£nYR
-Dl£nYU_3-D22nYG_3+El+el
2nLN = A2+82£n(PT/PA)+B4£n(PN/PA)+E32nYU+E42nYG+C6£nYR (4.2)
-D32nYU_3-D42nYG_3+E2+e2
2nLA = A3+E5£nYU+E6£nYG+C9anR-DslnYU_3-D62nYG_3+E3+e3
where: E1 = (Cl - D1) E4 = (C4 - D4)
E2 = (82 ’ ”2’ E5 = (as ‘ Ds)

66

E3 = (C3 ‘ ”3’ E6 = (C6 ’ D6)

The coefficients Dj are defined as the estimates of the
rate of change in the demand for a particular labor input
based on the exogenous change in an instructional output.
For example, if undergraduate instruction were to be 1 per-
cent greater in the academic year 1977-78, than in 1974-75,
the coefficient Dl would estimate the percentage change in
demand for tenured faculty. If Dl were very small in value
and not statistically significant, this may indicate that
the departments can instantaneously adjust the number of
tenured faculty employed. Although this may appear to be a
reasonable conclusion, it is obviously wrong. It is far
more reasonable to believe that, if D1 is insignificant, it
is due to the adjustment in the demand for tenured faculty
being greater (or less) than three years. No one believes
that every department within the university can instantane—
ously adjust any of the three types of academic labor
services. Rather, it is a shortcoming of the model since it
cannot accurately determine the appropriate time lag required
for adjustment. The coefficients on the current level of
output (E1) is the sum of both the long-term equilibrium
effects of current changes on the demand for particular
input and the three-year rate of adjustment.

Table 4.4 shows all of the coefficients estimated from
the system of equations in (4.2). Included in this table,
for purposes of comparison, are the estimates of the same

model discussed previously (equation 2.13) with the lagged

67

Table 4.4: Direct demand estimates: Model coefficients
with lagged instructional variables, included
-and excluded, 1977-78 data with homogeneity and
symmetry constraints (t-test statistics in
parentheses).

Model Model
Including Excluding
Lagged Variables Lagged Variables

 

 

Dependent Variable: Number
of Tenured Faculty Employ-

ed Coefficient on:

( .58)

Price of Tenured Faculty (Bl) -l.13 -1.15
A (1.97) (1.99)
Price of Non-Tenured (B2) — .76 - .79
Faculty A (1.72) (1.78)
Price of Graduate Assist- (B3) 1.90 1.94
ants (3.44) (5.37)
Undergraduate SCH (E1) .14 .16
(1.77) (2.15)
Graduate SCH (E2) .11 .11
A (1.38) (1.43)
Research (C3) .32 .33
(4.66) (4.84)
Lagged Undergraduate SCH (D1) - .05 N/A
( .67)
Lagged Graduate SCH (D2) - .004 N/A
( .04)
Dependent Variable: Number
of Non-Tenured Faculty
Employed Coefficient on:
Price of Tenured Faculty (B2) - .76 - .79
A (1.72) (1.78)
Price of Non-Tenured (B4) -l.18 -1.28
Faculty A (1.65) (1.83)
Price of Graduate Assist- (86) 1.94 2.07
ants (2.66) (4.27)
Undergraduate SCH (E3) .07 .11
( .56) ( .93)
Graduate SCH (E4) .18 .16
A (1.52) (1.38)
Research (C6) .14 .16
(1.37) (1.52)
Lagged Undergraduate SCH (D3) - .10 N/A
( .85)
Lagged Graduate SCH (D4) .07 N/A

68
Table 4.4: Continued.
Model

Including
Lagged Variables

Model

Excluding
Lagged Variables

 

Dependent Variable: Number
of Graduate Assistants
Employed Coefficient on:

Price of Tenured Faculty (B3) 1.90
A (3.44)

Price of Non-Tenured (B6) 1.94
Faculty A (2.66)
Price of Graduate Assist- (B9) -3.85
ants (4.01)
Undergraduate SCH (E5) .14
(1.37)

Graduate SCH (E6) .09
A ( .83)

Research (C9) .74
(8.42)

Lagged Undergraduate SCH (D5) .28
(2.72)

Lagged Graduate SCH (D6) - .26

(2.60)

 

1.94
(5.37)
2.07
(4.27)
-4.01
(5.27)
.05

.18
(1.65)
.68
(7.43)
N/A

N/A

69
instructional variables excluded. In this table, we see very
little difference in the estimates of the demand for tenured
and non-tenured faculty. The lagged variable terms (YU_3 and
YG-3) are very small and not significant at the a = .05
level. Only in the demand for graduate assistants equation

are both of the lagged variables on instruction (D and D6)

5
significant.

Overall, the estimates of the direct demand equations,
modified to include estimates of the rate of adjustment,
are quite reasonable because the only significant lagged
variables appear in the demand for graduate assistants
equation. We can assume that adjustment in the demand for
tenured and non-tenured faculty is not three years but
probably a greater period of time. Departments can easily
make changes to the number of graduate assistants employed
since they are only hired on a year to year basis with the
average length of a graduate program being three years.
Many non-tenured faculty are in the tenure stream and are
assumed, for planning purposes, to have continuing employ-
ment which would imply an adjustment longer than three years.
Changes in the demand for the tenured faculty would be
assumed to require the greatest time since normal attrition
and lengthy nation-wide searches are typically necessary for
changes in tenure faculty employment.

Returning to the demand for graduate assistants, the
changes in the non-lagged coefficients are negligible. How-

ever, the estimates of the rate of adjustment do provide

70
some unusual results. This would imply that, when the
graduate and undergraduate program is growing over a three-
year period, the demand for graduate assistants would
increase. The reasons for this are obvious. As undergraduate
instruction increases, class sizes would increase and more
graduate assistants would be employed to assist the faculty.
This is consistent with the model's estimates with DS equal
to .28. We previously discussed a positive correlation
between the size of a graduate program and the number of
graduate assistant appointments; therefore, we would expect
to find an increasing graduate program would increase the
demand for graduate assistants. However, the estimate of
the rate of adjustment in the demand for graduate assistants
from changes in the graduate program is negative (D6 = -.26).
This implies that increasing the size of a graduate program
causes a decline in the demand for graduate assistants.
One possible explanation of why this coefficient should be
negative is that the use of a three-year lagged variable on

graduate instruction is not appropriate.

The Joint Cost Function Equations and Tests of the Constraints

 

In this approach to modeling the structure of higher
education, we first estimate the underlying cost function
parameters. These, in turn, are used to derive the elasti-
cities of substitution, output supply, and factor demand.
However, before our conclusions can be drawn regarding the

production process, the exact specification of the cost

71
function model must first be determined. Recall from Chapter
II that there is a cost function and four possible share
equations that can be included in the regression model. Thus
there are four possible methods for specifying the model.
Each method produces all of the parameter estimates necessary

for analysis. The four methods are:

l. The cost function only;

2. The cost function and two input share equations;

3. The cost function and two input and two output
share equations; and

4. The two input and the two output share equations

only.

The choice of which of the above four is "best" is made from
two requirements: 1) which set of equations maximizes the
likelihood function; and 2) which set of estimates satisfies
the first- and second-order conditions.

Table 4.5 contains the values of the logarithmic likeli-
hood functions for each of the four methods for both 1977-78
and 1978-79. In the two years under study, the likelihood
function is maximized when the system of regression equations
consists only of the four share equations (method 4 above).

Next the conditions of monotonicity and convexity must

3C BC

be checked. Monoton1c1ty ex1sts 1f 55; and 3?;

are greater

than zero. An equivalent condition is that every Mj and

Si is greater than zero and less than one. The convexity

condition, as previously stated, is satisfied if the Hessian

72

Table 4.5: Joint cost function: Log of the likelihood
functions.

 

 

 

Regression Model 1977-78 Data 1978-79 Data
Four Share Equations only 218.5* 228.8
Cost Function only .41 7.4

Cost Function
and four Share Equations 188.6 190.9

Cost Function
and two Input Share Equations 98.5 103.4

* Denotes positive shares for both inputs and outputs and
that the second order condition is reasonably satisfied.

73

matrix is negative semi-definite. These regularity condi-
tions were tested for each year and each set of equation
systems. The results were less than encouraging. The
conditions were reasonably met only with the four share
equations (excluding the cost function) and for only the
1977-78 data year. In this set of regression equations the
conditions were tested using both fitted factor shares and
actual factor shares. When fitted input and output shares
were used, the regularity conditions were satisfied for 50
to 592 departments. The actual input and output shares met
the regularity conditions for 40 out of the 59 departments.
In the other possible systems of regression equations where
the first—order conditions are met, none of the regularity
conditions were met. In the set of equations where the
fitted shares were acceptable, the determinants of the
bordered Hessian matrix were of the wrong sign. The inability
of the model to produce acceptable results was also evident
in the 1978-79 data. None of the four possible systems of
regression equations could produce results that were con-
sistent with the conditions of convexity for a well-behaved
cost function.

The inadequacy of the data to satisfy the necessary

conditions for analysis is, in general, due to the changing

 

2 Two additional departments were dropped from the 1977-

78 data due to zeros appearing in their output values. See
Appendix A for a listing of the included departments for each
year's data.

74

of sign of several of the many insignificant variables in-
volved in calculations. In Table 4.6, we see the number of
coefficients significant at the a = .05 level ranges from a
low of 8 to a high of 15 out of a possible 29 coefficients.
The instability of the coefficients affects the model in
two ways. First, in the cases where all of the shares are
not in the regression system, it produces fitted shares that
are not acceptable. A model with these results is of little
value since, for example, it is not possible for under-
graduate SCH to contribute to total revenue by more than 100
percent and research cannot contribute to revenue by some
negative amount. Thus without reasonable factor shares, the
estimates of the elasticities are not valid. Second, in
those cases where the fitted shares were acceptable, the
second-order conditions were not met. This was due primarily
to the estimates of the own-elasticities of substitution,

Gii + si(si - l)

def1ned as Oii = S 2 where the Gii were pos1t1ve

J.

 

although not significantly different from zero. There is
another problem with the model when the Oii are estimated to
be positive. Since the demand elasticities, defined as:

BinYi

E11 = alnP. = 51°11 (4'3)

 

are a function of the Oii and the always positive Si' an

estimated value of a 011 greater than zero will cause a

positively sloped demand curve. Obviously, this result is

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76

 

 

 

 

 

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77

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78
not feasible in the context of microeconomic theory since it
implies an increasing marginal rate of factor substitution.
That is, the estimated cost function is not well-behaved.

Fortunately, the conditions of a maximized likelihood
function and satisfactory first- and second-order conditions
are met simultaneously for the year 1977-78. This occurs
when the system of regression equations consists of only the
four share equations. Table 4.6 presents the maximum likeli-
hood estimates of the unrestricted translog joint cost func-
tion and four restricted specifications of homogeneity,
separability, homogeneity and separability, and Cobb-Douglas
form.

Table 4.7 presents the Chi-Square test statistics for
each of the four restrictive cases. As shown by this table,
none of the restrictive forms are applicable, although homo-
geneity of outputs is barely rejected. The analysis of the
structure of the academic labor services of higher education
will, therefore, be based solely on the 1977-78 data year and
the unrestricted model of four share equations.3 The dis-
cussion of the direct demand analysis involving the consider-
able differences in the reported research output between the
two years is also applicable to the joint cost function. It
appears, from Appendix B, that the research output share does
not change significantly between the two years; however,

there is a large change in the research publications. This,

 

Except for linear homogeneity in factor prices.

79

 

 

 

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.mHmCOE mmuoHuumwu Mom moHumHumum puma “COHHOCCH umoo uCH0h uh.v mHnt

80

again, may be due to the problem of having only two years of
data and the highly variable nature of research projects.

There are two coefficients in the unrestricted model
that cause some concern. The values of AU and AG are less
than zero. This indicates that as undergraduate and graduate
instruction increases, total cost will decline. The sign of
the coefficient on graduate instruction (RnYG = -.019) is of
lesser importance since the t—statistic indicates that this
variable is highly insignificant. However, the coefficient

of £nY of -.349 is significant at the a = .05 level. From.

U
a theoretical standpoint, there is no reason why this should
occur. The only rational explanation must come from the fact
that there are 27 independent variables in the system which
burden the model and cause this estimate to occur. With
respect to the first-order input variables, all three_
coefficients are positive, and two of the three are signifi-
cant. These results show that the model does reflect
positive marginal costs. The second-order cross product
terms have coefficients that are, at best, obscure in mean-
ing. Therefore, it is preferable to base the analysis on

the elasticities derived from these coefficients. Estimates
of the demand, supply, and substitution elasticities are

evaluated at the mean of observations over all departments

in the sample.

81

The Joint Product Cost Function Estimates -- The Inputs

Table 4.8 summarizes the demand, cross-price, and sub-
stitution elasticities for each of the inputs. The elastici-
ties of substitution are all positive and in agreement with
what we expected. The easiest substitution is between

graduate assistants and non-tenured faculty (0 .886).

NA =
Next is the substitution elasticity between tenured and non-
tenured faculty, ONT = .87, with the weakest substitution,

0 = .276, occurring, as expected, between tenured faculty

AT
and graduate assistants. The input elasticities of substi-
tution are of special importance because they imply a
structure for the academic labor services that is consistent
with what we had assumed in Chapter I. If we believe these
estimates are reliable, we must be careful in interpreting

the results because several implications are possible.
Graduate assistants, for example, are fairly easily substitut-

able with the non-tenured faculty (0 .886). We could,

NA=
incorrectly, interpret this to mean that the non-tenured
faculty must be providing services that are in most respects
similar to those of graduate assistants. Therefore, it can
be concluded that the contribution to research by the non-
tenured faculty must be minimal. However, we believe that
these results may be unreliable because the data do not
accurately specify the research output, which is important
to the tenured and non-tenured faculty. Additionally,

recall that the category of non-tenured faculty was defined

to include temporary and tenure stream faculty members. If

82

Table 4.8: Joint cost function: Estimates of elasticities,
1977-78 data.

 

 

 

Part A. Input Elasticities of Substitution
CNN = -l.97 UNA = .886
0AA = —2.09 ONT = .487
OTT = - .260 OAT = .276
Part B. Demand Elasticities
ETT = -.16
ENN = -.44
EAA = -.36
Part C. Cross Price Elasticities
ETN = .109 ETA = .048 ENA = .155
ENT = .293 EAT = .166 EAN = .198

NOTE: These elasticities are derived from coefficients
estimated from the share equations (2.18 and 2.20).

83
the non-tenured faculty were to include only the temporary
faculty, we would believe these results to be more reasonable.
This point can be restated from another perspective when we
look at the substitution possibilities between the tenured

faculty and graduate assistants (0 .276), and between

AT =

the tenured and non-tenured faculty (0 .487). As ex-

NT =

pected, is very low, which implies that they are not

OAT
very good substitutes.

The demand elasticities in Part B, Table 4.8, are consis-
tently negative and all imply highly inelastic demand curves.
These extremely low estimates of elasticity (ETT = -.16,

ENN = -.44, EAA = .-36) are some cause for concern Since
the difference is caused by the coefficients needed to
estimate the own-elasticity of substitution of the inputs.
G

The coefficients G are all found to have t-

TT' NN' GAA
statistics less than one. It would appear that, given these
results, the inelastic demand for the inputs is due to the
inability of the rather burdened joint cost function to
produce significant coefficients. Nevertheless, the model is
capable of reasonably meeting all of the conditions of a
well-behaved cost function and producing downward sloping
demand curves. The fact that the slope is unusually steep

is unfortunate Inn: not expected. If we were to interpret
these results as if they were statistically reliable, we would

draw conclusions opposite to those from the direct demand

analysis. These results indicate that the departments are

84

not concerned with prices paid but only quantities of each
type of labor they need (since the supply curve is assumed
to be perfectly elastic -- it determines factor prices).
Additionally, the inelastic demand curve implies each input
is uniquely differentiated from the other inputs and does
not have a close substitute. This obviously contradicts
the rather high elasticity of substitution estimated for
graduate assistants and the non-tenured faculty.

The cross-price elasticity appearing in Table 4.8 and

equation 2.30 is defined as:

alnY.
1

 

As shown by the above definition, the cross-price elasticity
is a function of the elasticity of substitution weighted by
the factor share. Since we know all of the factor shares
are less than one and positive in value, we can see that all
of the information contained in the cross-price elasticity is
also contained in the elasticity of substitution. Therefore,
it would be redundant to discuss the underlying structure
again. However, there are two points that should be noted.
First, because the tenured faculty receive almost 60 percent
of the total costs (see Chapter III), we see that they are
least affected by changes in the prices of the other two
inputs (ETN = .109 and ETA = .048). It is reasonable to

assume that, when the relative prices of the inputs change,

the employment of the tenured faculty will change least.

85
Second, since the non-tenured faculty were found to be fairly
easy substitutes for both the tenured faculty and graduate
assistants, the non-tenured would be more susceptible to

changes in employment due to changes in relative prices.

The Joint Cost Function -- The Outputs

 

The joint translog cost function described in equation
(2.16) does not differentiate between inputs and outputs
within its structure. Thus, it is only a mechanical proce-
dure for adapting the definitions used in determining the
input elasticities to the outputs. Table 4.8 reports each
of the output elasticities as they have been defined in
Chapter II, evaluated at the means of the input variables.

A major difficulty is that of trying to gain a practical
understanding of the inverse of the elasticity of substitu-
tion as it relates to the process of higher education.4
This term 1:; defined as the percentage change that will occur
in relative shadow output prices based on percentage
relative change in the output quantities produced. This
definition implies that a university administrator, dean, or

chairperson adjusts the price of the output to be supplied

 

4 The inverse elasticity of substitution can be made

more understandable if we divide it into one. This will
change the estimates into the more familiar elasticity of
substitution. We should note that there is no true economic
meaning to these transformed elasticities, since they imply
output prices as exogeneous which, in this case, is not an
assumption of the model.

86
based on the quantity required as determined by perfectly
inelastic demand for the output. This simply is not the
case and, in fact, presents a serious problem in attempting
to draw conclusions, especially conclusions about the relative
value of the outputs. This is not to say the inverse
elasticities of substitution are important. Table 4.9 shows
that undergraduate instruction and research are the most
easily substitutable (n = .188). They are followed by

UR

graduate SCH and research (HGR = .696) and least but, never-
theless, still highly substitutable are graduate and under-
graduate SCH (HUG = .779).

It is somewhat surprising that undergraduate instruction
and research are the easiest substitutes. However, it does
have an understandable interpretation. We would have
assumed graduate and undergraduate instruction to have the
highest estimate of the elasticity of substitution because
the non-tenured and tenured faculty share in the teaching
responsibilities of both levels. This ease of substitution
does not seem to be present in the data because the non--
tenured faculty were more easily substituted for the graduate
assistants than they were for the tenured faculty. On the
other hand, we can believe that the graduate assistants can
be reassigned quite easily between teaching and research. It
is apparent, therefore, that the cause of the low estimate

of (and strong substitution) is due to the ease with

"UR

which graduate assistants can be reassigned. The two remain-

ing elasticities of substitution involving graduate

87

Table 4.9: Joint cost function: Estimates of output
elasticities, 1977—78 data.

Part A. Inverse Output Elasticities of Substitution

 

 

 

"UU = - .62 HUG = .779
"GG = -2.28 NUR = .188
“RR = - .71 "GR = .696
Part B. Marginal Cost Elasticities
BUU = -.257
BGG = -.468
BRR = -.267
Part C. Inverse Output Cross Price Elasticities
BGR = .30 BGU = .323 BRU = .078
BRG = .16 BUG = .16 BUR = .071

NOTE: These elasticities are derived from the coefficients
estimated from the share equation (2.18 and 2.20).

88
instruction ("GR = .696 and HUG = .779) are roughly equivalent.
Their values indicate that graduate instruction is easily
substitutable for either research or undergraduate instruc-
tion. This implies that the tenured and non-tenured faculty
can also be easily reassigned since we have assumed that
graduate assistants do not contribute to graduate instruction
and, therefore, are not included in these estimates.

The estimates of the marginal cost elasticities5 provide
results that do follow closely with what would be expected to
occur in higher education and the results of the direct
demand analysis. The marginal cost elasticities for all three
outputs are negative. These results imply increasing returns
to scale. The greatest economies are related to graduate

instruction (B = -.47). This would indicate that, by

GG
increasing the quantities of the outputs by some equal per-
centage, the greatest decrease in price will be associated
with graduate SCH. This result is due primarily to the ease
with which both undergraduate instruction and research can
be substituted for graduate instruction. Thus, a slight
increase in quantity will be accompanied by shifting the
faculty away from either research or undergraduate instruc-
tion.

It is somewhat surprising that undergraduate instruction

(BUU = -.26) does not have the greatest returns to scale as

 

5 The marginal cost elasticity can also be considered to

be the inverse of the supply elasticity.

89
estimated in the direct demand analysis. Comparing the
estimates from the direct demand analysis and the joint cost
function analysis, we find conflicting results. Recall that
in the direct demand analysis undergraduate instruction had
the least effect on employment and greatest returns to scale
while in the joint product cost function, graduate instruc-
tion has the greatest scale economies. If outputs can be
increased with less than proportional increases in total
employment, we can assume that the underlying supply curve
relating price and quantity of the output is downward slop-
ing. The apparent conflict between which type of instruction
has the greatest economies of scale may be explained as a
problem related to the aggregation of the data. In certain
disciplines, such as Economics, Chemistry, or English litera-
ture, there may indeed be large economies of scale in the
introductory classes. However, the data within the model
represent total undergraduate instruction including many
upper level classes that cannot take advantage of televised
instruction or large lecture halls. This is due to a lack
of sufficient demand for the output or the method of instruc—
tion, such as sophisticated laboratory equipment. Thus,
when all of the undergraduate student credit hours are aggre-
gated at the departmental level, much of the scale economies
within a department's undergraduate program may be lost in
the process. It appears that the conflicting estimates are
due primarily to the statistical methods of estimating the

model rather than something inherent in the structure of

90
higher education. Nevertheless, it remains that based on
the estimates of the joint cost function, the greatest
economies of scale are attributed to the graduate instruc-
tion.
Research is also found to have economies of scale

(B = -.27) to roughly the same degree as undergraduate

RR
instruction. This could be explained as synergistic effect
within the faculty. As the size of the departments increase,
there is also an increase in the professional interaction of
the faculty within a department. The increased interaction
will increase the possibility for individuals with the same
areas of expertise to collaborate. It is from this collabora-
tion that the ideas are developed which ultimately lead to
research projects.

The inverse cross-price elasticities of the outputs
add significantly to the analysis since they are only the
inverse elasticities of substitution weighted by the output

share. The implications have been discussed above and it

would be redundant to state them again.

Conclusions

 

Based on a synthesis of the estimates derived from the
direct demand analysis and the joint cost function analysis,
the following conclusions will be restated. Obviously, this
is a rather heavy-handed approach, but is necessary to
narrow the focus of discussion from which the policy implica-

tions will be drawn.

91

First, the demand function for tenured faculty, non-
tenured faculty, and graduate assistants, are all inelastic
and negatively sloped. Second, there is little or no sub—
stitution between tenured faculty and graduate assistants,
while graduate assistants are easily substitutable with the
non-tenured faculty. Also, the tenured and non-tenured
faculty are only moderately substitutable for each other.
These conclusions are drawn primarily from the joint cost
function analysis with some, but not complete, agreement
with the results of the direct demand analysis.

On the output side, it appears that there is considerable
agreement between both methods. There is strong evidence of
increasing returns to scale. The marginal cost elasticities
of the outputs are slightly negative, which implies a down-
ward sloping, long-run supply curve. This is corroborated by

the output coefficients in the direct demand analysis.

CHAPTER V

MODEL SIMULATIONS

Introduction

 

We can apply the estimates derived from the two models
to some of the major issues currently facing administrators
in institutions of higher education. The period of the
1980's is expected to be one of substantial change in how
colleges and universities provide services to the society as
a whole and individual students in particular. Among the
issues that will cause serious difficulties to higher educa-
tion are the projected decline in the available pool of
college-age men and women and the continued reduction in the
financial support for higher education by state government.
In 1970, higher education received 17.0 percent of the State
of Michigan's general fund budget. State support has
declined steadily from that time to the point where less
than 14 percent of the State's general fund budget supports
higher education. A continued decline has implications for
future fiscal planning. While the simulations presented in
this chapter cannot eliminate all of the uncertainty of the
future, they might shed some light on an area that has pre-
viously been unexplored.

The conclusions of the following sections are based only

92

93
on the 1977-78 data because the estimated cost function was
well-behaved for only that year. In addition, the estimated
coefficients are evaluated only at the means of the independent
variables. Thus, if a department has unusually low research
output (like Family and Child Sciences, for example) the
analysis will indicate substitutions of the inputs that may
not be applicable.

It is possible that many institutions of higher educa-
tion will be faced with non-marginal changes that cannot be
estimated within the context of this model. This is because
we have assumed a fixed structure to the production process.
The decline in enrollments could be so significant that some
administrators would be forced to restructure their institu-
tions more than just beyond the slight changes to the level
of employment of the academic labor services as suggested by
the estimates of this model. The restructuring could include
eliminating certain degree programs, consolidating depart-

ments or colleges, or closing the institution entirely.

Declining Undergraduate Enrollments

The most crucial issue of the next decade confronting
higher education is how a university can maintain the quality
of its product during a period of declining enrollments and
revenues. Although measures of quality are not directly
included in this study, a university that cannot adjust its
faculty to meet the needs of the future will find itself more

concerned with survival rather than maintaining quality.

94

Naturally, the effects of declining enrollments will not be
equally felt across all colleges and universities. The
forecasted decline can be considered within the context of
this study with two possible policy alternatives available
to administrators. First, there is the possibility of main—
taining salaries and letting the reduction in undergraduate
instruction lead to a reduction in the number of faculty and
graduate assistants employed. Second, there may be a desire
not to decrease employment but to simply produce more of
another output, namely research. Each of these two possibili-
ties can be analyzed within the framework of the direct demand
analysis.1 The predicted changes determined from this model
on employment and research are not meant to be d3 fagtg
changes that would occur at all institutions but only provide
some additional information for determining employment policies.

The implications of the first alternative can be found
by simply reading the coefficients on the undergraduate
instruction variable, YU, from each of the three demand
equations (see Table 4.3). Each coefficient tells us the
percentage change employment that would occur from a percen-
tage change in undergraduate instruction. Thus, we find a

10 percent decline in Y will cause: i) the demand for the

U
tenured faculty to fall by 1.6 percent, ii) the demand for the

non-tenured faculty to decline by 1.1 percent, and iii) the

 

l The constraints of homogeneity and symmetry are imposed
for the year 1977-78 only.

95
demand for graduate assistants to decrease by .5%. These
results suggest that graduate assistants would be least
affected by a teaching cutback. We intuitively know just
the opposite would probably occur, in the short run. This
is because less teaching would reduce the size of classes and
the number of sections taught for each course. Almost
certainly, we would find that the number of graduate assistants
needed would rapidly decrease while, at least temporarily,
the demand for the faculty would remain unchanged. However,
from a long run perspective these results are reasonable.
They suggest that the faculty, both tenured and non-tenured,
would have a decline in the demand for their services as
departments reduce their faculty in an attempt to gain
flexibility. They would then permit the number of graduate
assistants to fluctuate only on a short run basis filling
temporary openings.

The second alternative assumes that the demand for each
type of labor service is unchanged and the faculty and
graduate assistants devote more time to research as teaching
loads are reduced due to a lack of students. Although it is
not precisely correct to say that the decline in instruction
caused an increase in research, we can look at the two
relevant coefficients (YU and YR) as offsetting one another
to maintain the level of factor demand. The calculations
necessary can be reduced to a simple ratio of the coefficient
on YU over the coefficient on Y to determine the required

R

percentage increase in research.

96

The relevant values from Table 4.3 are:

 

Ratio
Demand Equation 33L. 3%: (YD/YR)
Tenured faculty .16 .33 .48
Non-tenured faculty .11 .16 .69
Graduate assistants .05 .68 .07

If undergraduate instruction were to decline 10 percent, a

4.8 percent offsetting increase would be necessary in research
publications for the demand of the tenured faculty to remain
unchanged. The demand for the non-tenured faculty would
remain constant if the department's research were to rise by
6.9 percent, while the demand for graduate assistants would
require only a .7 percent increase in research to offset the
decline in undergraduate instruction. These results indi-
cate that demand can be maintained for all three labor ser-
vices with less than a 10 percent increase in research. As
discussed in Chapter IV, this is due primarily to changes in
research having a significantly greater effect on factor
demand than undergraduate instruction. Thus, we see that a
small percentage increase in research will offset proportion-
ately larger declines in undergraduate instruction. This is
especially true for the demand for graduate assistants when
the increase in research would only need to be .7 percent.
Because the coefficient on YR in the graduate assistant demand
equation is 6.8, we can conclude from this coefficient that
increasing research output would increase the demand for

graduate assistants by a larger percentage than the increase

97
in the demand for either type of faculty. If a department
were to shift its academic labor services to the production
of research, there would need to be a greater number of
graduate assistants assigned to each faculty member than
would be required in the production of instruction. The
graduate assistants would provide the "legwork" of research
such as reviewing the literature or collecting data. It is
for this reason that the decline in undergraduate instruction
can be easily offset by increasing research to maintain the
demand for graduate assistants. The tenured and non-tenured
faculty can then become more productive with the reassigning
of graduate assistants from instruction to research and,
consequently, research must rise by a greater percentage to
maintain the level of their demand.

The above estimates indicate that the tenured faculty would
have the greatest decrease in demand with graduate assistants
having the least. In practice, this would not occur at
least in the short run. Administrators would prefer, instead,
to first eliminate the graduate assistants up to the point
where it becomes detrimental to their graduate programs with
a decline in their undergraduate programs. At that point,
adjustments, either in salary or demand, would next occur
with the non-tenured faculty. The reasons for this are
beyond the ability of the model to take into account such as
preserving the prestige of the university or the political
influence of the tenured faculty in preserving their positions

at the expense of the non-tenured faculty and graduate

98

assistants.

Special "Catch-Up" Salary Increases to the Faculty

An issue that is currently confronting many institutions
is that of a university finding that the salaries paid its
faculty are considerably less than faculty salaries at
similar institutions. Michigan State University, for example,
is continually ranked near the bottom of the Big Ten in the
salaries paid to full professors. In an attempt to correct
the situation, the university administrators recently
instituted a 2 percent across-the-board salary increase to
faculty members. The raise was not given to graduate assist-
ants. We can ask, "How will raising faculty salaries (PT and
PN) by 2 percent affect the level of demand for all three
types of academic labor services?" The joint product cost
function estimates will again be used because they provide
the more reliable estimates of the cross-price elasticities
(as reported in Table 4.8).

It is a trivial matter to determine the impact of the 2
percent salary increase for the faculty after the price and
cross-price elasticities have been estimated. With respect
to the tenured faculty, we find only a slight decrease in

demand of .32 percent (E = -.16) due to increasing their

TN

salary 2 percent along with an offsetting increase in demand
because of the non-tenured faculty also receiving a 2 percent

increase (from the cross-price elasticity (E .109)). Thus,

TN:

the net effect is an extremely small decrease in demand for

99

the tenured faculty of .10 percent. These results indicate
that the change in demand for the tenured faculty is negli-
gible which is reasonable since it was not the intention of
the administration to reduce demand (or employment) of the
faculty but only to offer additional compensation to those
currently employed.

The net effect on demand for the non-tenured faculty is
more than twice that of the tenured faculty at .29 percent.
This is caused by a .88 percent decrease in demand due to

the increase in non-tenured faculty salaries (E .44).

NN =
This is offset by an increase in demand of .59 percent caused
by the increase in tenured faculty salaries. These results,
although greater than for the tenured faculty, are consistent
with the policy of not significantly affecting demand but
still providing for salary adjustments. The 2 percent in-
crease may not be sufficiently large to restore salary level
to match those of the peer group institutions; however, it
does acknowledge an area of deficiency that the administration
is attempting to correct.

If we look at the demand for graduate assistants, we
see an overall increase of .73 percent. This increase arises
from the substitutability of both types of faculty with
graduate assistants found in our results. The increase in
demand can be divided into two roughly equal shares caused
by the salary increases attributed to the tenured and non-

tenured faculty. Although the substitution of graduate

assistants is greater with the non—tenured faculty than the

100
tenured faculty, the tenured faculty share is much larger.
The implications of this are that, although the graduate
assistants are more easily substitutable with the non-
tenured faculty, the demand for their services is much more
sensitive to changes in the salary paid the tenured faculty.
This is because the tenured faculty receive a much greater
share of total cost which causes large changes in the demand
for graduate assistants with only slight changes in the
salaries paid the tenured faculty. Nevertheless, the 2 per-
cent salary increase should be considered to have only a
minimal effect on the demand for graduate assistants.

The major result of this hypothetical exercise is that
the decline in the demand for the non-tenured faculty is
more than twice that of the tenured faculty. These results
can be explained by the somewhat unexpected estimates of
the elasticities of substitution discussed in Chapter IV.
Although both types of faculty received the same salary in-
creases, the tenured faculty's contribution to research and
graduate instruction was such that neither the non-tenured
faculty nor graduate assistants could be easily substituted
for them. On the other hand, graduate assistants were
estimated to easily substitute for the non-tenured faculty.
Therefore, it could be concluded, if the salaries of both
types of faculty were to increase by the same amount, the
administration would be more willing to reduce the number of
non-tenured faculty and increase the number of graduate

assistant appointments. Obviously, these results are

101

distorted by the misspecification of the research output.

Increasing Research Outputs

 

It is not difficult to imagine a situation where the
university administration would, in anticipation of declining
enrollments, wish to establish a reputation as a research
oriented institution. This decision to increase the research
productivity of the faculty would help to minimize the
potentially disastrous effect of the reduced number of
students. Increasing the number of research publications
would raise the reputation of the institution and, in turn,
make it more competitive in attracting more research grants
from both private and governmental sources in future years.
This reasoning on the surface, appears to be a viable approach
to the future. However, in order to produce more research,
the academic labor services must be shifted away from under-
graduate and graduate instruction. Thus, the effects of
increasing research will cause the relative value of all three
outputs to change. The relative changes in the values of the
outputs will determine whether the policy of greater research
output will be desirable.

The joint product cost function is the only model that
provides the necessary inverse cross-price elasticities to
analyze the implications of this hypothetical policy. If
we assume a 10 percent increase in research this will lower

the relative value of research by 2.7% (B = 6.267 from

RR

Table 4.9). An increase in the quantity supplied at a lower

102

value is due to the increasing returns to scale discussed
in Chapter IV. In addition, there will also be an increase
in the value of instruction due to the substitutability of
the outputs. As more labor services are directed toward
producing research, less will be devoted to undergraduate and
graduate instruction. Since both types of instruction were
also estimated to have increasing returns to scale, we would
expect their relative values to rise. In fact, the model
estimates that the value of undergraduate instruction would
rise .71 percent while a much larger increase would occur in
the relative value of graduate instruction at 3.0 percent.

The implication of these results is that graduate
assistants, assigned to support the faculty as graders and
proctors for large classes, would be reassigned to faculty
research projects. This would cause the departments to reduce
their average class size and offer more sections. This
would make the relative value of undergraduate instruction
rise. However, we estimated the rise in graduate instruction
to be more than three times that of undergraduate instruction.
Therefore, the faculty providing graduate instruction would
be reassigned to undergraduate instruction to restore the
lost scale economies. Thus, the relative value of graduate
instruction rises because there are fewer teaching faculty
in graduate instruction. The relative value of research falls
because there are more graduate assistants providing support
such as data collection and reviewing the literature for the

research oriented faculty.

103

Although this story is plausible and provides an explana-
tion to the estimates, there are other possibilities that are
just as plausible. The tenured and non-tenured faculty could
be reassigned to research and away from undergraduate instruc—
tion while graduate assistants could be used more in under-
graduate instruction without supervision. This would raise
the price of undergraduate instruction because more sections
with fewer students in each section would be needed which
agrees with our results. With more faculty members devoting
their time to research, there would be a synergistic effect
that would generate more ideas and, hopefully, more publica-
tions while reducing the value of each research unit. The
graduate program would also have a reduction in its teaching
faculty. This would, in many instances, require the closing
of sections and the curtailing of course offerings and, in
turn, raise the relative value of the output. Another
possible method of transferring the labor services from
instruction to research would be to simply move the tenured
and non-tenured faculty and graduate assistants in the same
proportion that they exist within the current teaching
structure. For example, if there are four graduate assistants
for every faculty member teaching an undergraduate course,
then reassigning that faculty member to research would also
imply reassigning the four graduate assistants to research
activities. The graduate teaching faculty members that do
not have graduate assistants assigned to them would also be

assigned to research without any corresponding transfer of

104

graduate assistants. Thus, there would be a larger increase
in the price of graduate instruction because every individual
transferred would require increasing substantially the work-
load burden of the remaining graduate teaching faculty.
Undergraduate instruction would have much less of a price
increase because the workload increase would be spread among
the graduate assistants having to grade more papers or proctor
larger classes. The faculty members transferred to research
would be able to enjoy the same efficiency they had when
teaching because their graduate assistants would still pro-
.vide support for their research activities.

Regardless of which method is used to increase the number
of research publications of the department, we would find
that the largest price increase would be for graduate instruc-
tion. The increase in relative value of undergraduate

instruction at .7 percent is negligible.

CHAPTER VI

POLICY IMPLICATIONS AND CONCLUSIONS

Overall Perspective of Analysis.

 

In Chapter I, we stated that this study was motivated
by an impending decline in higher education enrollments.
Therefore, the implications for higher education administra-
tive policy should only be considered within the context of
declining enrollments. The nation's colleges and universities
have shown themselves to be quite capable of administering
increasing enrollments, as seen by the rapid expansion in
higher education in the 1960's, but it is far more difficult
to retrench and cut back inputs than it is to grow.

Before the policy implications of this study can be
developed, a very important distinction must be made. One
of the inputs of the academic labor service was classified as
"non-tenured faculty." This input, in actuality, consists
of two inputs. One group is temporary faculty, or those
individuals who are appointed only on a year-to-year basis,
and the other is those faculty members who are in the
"tenure stream" but who do not yet have continuing tenure.
This distinction between temporary and tenure stream appoint—
ments of the non-tenured faculty is an important option
available to administrators. Thus, in order to relate the

105

106
conclusions of this study to administrative policy, it will
be stated whether a change should occur through changes in
the number of temporary or tenure stream appointments. In
addition, there are several institutional constraints that
also affect administrative policy and should be explicitly
stated. One option available to reduce the number of tenured
faculty is through programs and policies affecting the supply
side of the market such as offering sizable cash bonuses
for early retirement. In this analysis, we concluded that,
for the most part, policies directed at the demand for tenured
faculty would have little effect on substantially reducing
employment. This is because of the inelastic demand for the
tenured faculty in the joint product cost function. Thus,
normal attrition will be the only factor causing the number
of tenured faculty to decline.

It can be imagined that an administrator, faced with
projection of a sharp downturn in enrollment, might take a
very conservative approach in setting employment policies
for the faculty and graduate assistants. As stated in Chapter
I, it was previously assumed without the benefit of the
conclusions of this study that the tenured and non—tenured
faculty would be easy substitutes. In addition, we assumed
that graduate assistants were substitutes with both types of
faculty. Given these assumptions, an administrator would
want to minimize his future employment and financial obliga-
tions and keep as much budget flexibility as possible. This

reasoning would lead him to conclude the best policy would be

107
one of replacing all tenured faculty positions with temporary
faculty or graduate assistants. Thus, when a faculty member
retires or resigns, his or her replacement would be hired on
a temporary year-to-year basis as either a non-tenured
faculty member or graduate assistant.

Based on the results presented in this study, this would
not be the most productive cost-minimizing policy to follow.
First, we showed that graduate assistants are easy substitutes
with the non-tenured faculty and weak substitutes with the
tenured faculty. Also, the non-tenured faculty and tenured
faculty were found to be substitutes but much less than was
expected. These results (ignoring misspecification of the
variables) imply that the tenured faculty cannot be easily
replaced by the temporary faculty on a one-for-one basis
without affecting the ability of the departments to produce
their outputs. Instead, it would be better to maintain the
number of faculty positions and reduce the number of non-
tenured faculty. The decline in non-tenured employment
could then be offset by increasing the number of graduate
assistantships. The concern for maintaining flexible budget-
ary obligations would be substantially reduced because of the
ease with which departments could make adjustments to the
number of graduate assistants they have employed. It may
be necessary, if student enrollments decline drastically, to
reduce employment in all three types of labor services. How-
ever, based on the estimates of this study, the non-tenured

faculty should have the greatest percentage decrease in

108
employment.

The reasons for maintaining the tenured and tenure stream
faculty while decreasing the temporary faculty are quite
plausible despite the misspecification of the model variables.
Recall that there were increasing returns to scale for all
outputs with research being an easy substitute with graduate
and undergraduate instruction. In addition, it is assumed
that most of the research is produced by the tenured or
tenure stream faculty with the temporary faculty mostly in-
volved in undergraduate instruction. If undergraduate enroll-
ments are reduced by, say, 15 percent then total employment
of the academic labor services devoted to undergraduate
instruction must be reduced by more than 15 percent. The
tenured and tenure stream faculty could be easily shifted
away from instruction and into research. The temporary
faculty would be reduced with graduate assistants providing
the necessary support to fill temporary shortages that would
then consist of mostly those individuals who are in the
tenure stream. This policy would not affect the ability of
the university to attract quality individuals since being
hired would, to some degree, be an offer of tenure at some
time in the future.

There is an additional advantage to this general employ-
ment policy that deserves special consideration. The continued
support of graduate assistantships will benefit the department
by maintaining the graduate instruction program. From the

direct demand analysis, we stated there was a strong

109
correlation between the size of the graduate program and the
number of graduate assistants employed. By reducing the size
of the temporary faculty and replacing them with graduate
assistants, the department will also be supporting its
graduate program and maintaining the teaching loads of the
graduate teaching faculty. If the departments were forced to
eliminate graduate assistant appointments this would cer-
tainly cause graduate enrollments to decline which, in turn,
would reduce the demand for the services of the tenured and
tenure stream faculty. It is this correlation of the number
of graduate assistants employed affecting the level of demand
for the other labor services through generating student

credit hours.

Future Research

 

There are four areas in this study that would add con-
siderably to our understanding of the academic labor markets
of higher education. As stated in Chapter III, very little
research has been done in this area and the list below is
not intended to be all-inclusive. It is, however, necessary
to focus upon those areas of this study where the underlying
assumptions, although necessary, may not be applicable.

First, it would be useful to gain an understanding of
the process of how instructional departments adjust their
mix of labor services to reach their optimal level. This
study assumed that all departments were operating at their

most efficient level through their ability to adjust all

110
inputs instantaneously. Some study was done with the direct
demand analysis model using only a three year lag period.
However, this was inadequate to fully explain the process of
the changing demand for tenured and non-tenured faculty
caused by exogenous changes in the level of the outputs.
Knowing the rate at which departments adjust their labor
services would be a valuable tool in setting policy. Depart-
ments that are experiencing large changes in enrollments would
then have guidelines to follow in making the transition to a
new level of output demand.

The second area of further study should involve question-
ing whether the instructional departments actually do operate
at their optimal level. This would require designing a
methodology that determines the true production possibilities
frontier and tests whether a unit is operating at that level.
The study of optimality also would involve defining the
appropriate general functional form of production. The
translog cost function was adapted to meet the purposes of
this study. This is not the only possible production function
that can be applied to joint product procesSes. Further
investigation could involve use of other general functions
that might be more appropriate than the translog.

Third, a major obstacle to drawing meaningful conclusions
from the estimates of the elasticities was the misspecifica-
tion of the research output. Since this is the first study
to treat research publication as an output, it does add to

better identifying the process of higher education but must

111
be improved to be useful. The highly cyclical nature of
research and the long time periods involved from beginning to
end were not adequately dealt with by using only two years
of data. Using more years pooled across all departments
might improve the model's ability to estimate a well-behaved
cost function (if, in fact, a well—behaved cost function
exists). It may be appropriate to include other types of
professional accomplishments within the variable research.
Rather than just refereed journal articles and books,
delivered paper or non-refereed articles could also be in-
cluded since they do represent an investment of time on the
part of the faculty.

Fourth, we believe some of the estimates of the input
elasticities of substitution were affected by defining the
non-tenured faculty to include tenure stream and temporary
faculty. It would be useful to know if the model presented
here would provide different estimates if the three types of
academic labor services were defined as i) tenured and tenure
stream faculty, ii) temporary faculty, and iii) graduate
assistants. It is possible that the estimated cost function
may be well-behaved and meet the first- and second-order
conditions satisfactorily when the inputs are defined in
this form.

This study was designed for the purpose of identifying
the substitutions of academic labor services within the con-
text of a general joint product cost function. It has ful-

filled that goal although it appears to have raised more

112
questions regarding the structure of higher education than
it answered. Nevertheless, it does provide an initial under-
standing of how faculty and graduate assistants combine to

produce the outputs of instruction and research.

APPENDICES

APPENDIX A

LIST OF DEPARTMENTS INCLUDED AND DELETED FROM THE DATA

Agriculture and Natural Resources

Arts

Agricultural Economics
Agricultural Engineering
Animal Husbandry

Crop and Soil Science
Dairy Science

Fisheries & Wildlife
Forestry

Horticulture

Packaging

Poultry Sciences

Parks & Recreation Resources
Resource Development

and Letters

English Language Center

Art

English

German & Russian Languages

Linguistics, Oriental and African
Languages

Romance Languages

History

Music

Philosophy

Religious Studies

Theatre

Business

Accounting & Financial Administration

Business Law and Office Administration

Economics

Hotel Management

Management

Marketing and Transportation
Administration

113

 

1977-78 1978-79
x x
x x
x x
x x
x x
x x
x x
x x
x x
x x
x x
x x
D x
C C
x x
x x
x x
x x'
C C
x x
C C
C C
x x
x x
x x
x x
x x
x x

114

1977-78 1978-79

 

Communication Arts & Sciences

Advertising x x
Audiology & Speech Science x x
Communication x x
Journalism x x
Telecommunication x x
Education
Administration & Higher Education A A
Counseling & Personnel Services A A
Elementary & Special Education A A
Secondary Education A A
Student Teaching A A
Health and Physical Recreation A A
Engineering
Chemical Engineering x x
Civil & Sanitary Engineering x x
Electrical Engineering and Systems
Science x x
Computer Science x x
Mechanical Engineering x x
Metallurgy, Mechanical and Materials
Science x x
Human Ecology
Human Nutrition & Foods x x
Family and Child Science x x
Family Ecology x x
Human Environment and Design x x
Natural Science
Astronomy x D
Biochemistry x x
Biophysics x x
Botany and Plant Pathology x x
Chemistry x x
Entomology x x
Geology x x
Mathematics x x
Microbiology and Public Health C C
Nursing C C
Physiology C C
Physics x x
Statistics x x
Zoology x x

115

1977-78 1978-79

 

Social Science

Labor and Industrial Relations B B
Anthropology x x
Geography x x
Criminal Justice x x
Political Science x x
Psychology x x
Social Work x x
Sociology x x
Urban Planning & Landscape Archi-
tecture x x
University College
American Thought and Language D D
Humanities D D
Natural Science D D
Social Science D D
Justin Morrill D D
James Madison x x
Lyman Briggs D x
Urban Development
Racial and Ethnic Studies D D
Urban and Metropolitan Studies x x
Human Medicine C C
Osteopathic Medicine C C
Veterinary Medicine C C

KEY:

Department included in the sample.

Non-traditional departments; data cannot be assigned
to department directly.

Public service is major output.

Clinical departments where research cannot be
defined in terms of books and journal articles.

One output or input is zero.

0 (am 33%

APPENDIX B

MODEL DATA

116

Hm
hm

mHH
mm
mH
hm
mmH
mm
om
0v

 

Ame Coumwmmm

mmm
mmn
vvv

omMH
mam
mOH
MNNN

vmVH
mmm
huh
Hmm
HhHH
whoH
mhmH
hhm
mmmH
omOH
HNm
hHhN

 

AowV CoHuoCHumCH
mumsmmuu

hmmMH

wamm
hmHNH
mmhm

vamN
vah
ommv
mmNHm

mHmm
mvoH
momm
HHhm
mMNOH
vmmn
mmmm
¢HN¢
mmGNH
«mom
ommb
Nmmm

 

ADNV CoHuoCHumCH
mumspmumummCD

 

mmHuHquso usmuso

mmmHHm CmE>H mo mmmHHou

mmmmCmCmH HmOHmmmHU w moCmEom
hCQomOHHCm
mommsmCmH
CmoHHmm pCm HmquHHO .moHumHCmCHH
muoumHm
CmHmmCm w CmEHmO
umquU mmmsmCmH CmHHoCm
CmHHmCm

mnmuumq mCm

HCGEQOHm>mo mousomwm
mmoCmHom muuHCom
COHHmmuomm w mxnmm
mCHmmxomm

mHCuHCoHuHom

muummuom

mMHHmHHz a mmHHmCmHm
moCmHom wuHmo

woCmHom HHom mCm mouu
humCmnmCm HmEHC<
mCHHmmCHmCm HmHCuHCoHHm<
mOHEOCoom HmHCuHCOHHmC

mand

mmoHCOmwm
Hmusumz mCm mHCuHCoHH04 Ho mmeHou

 

mhlmbmH

117

NH

mm
mm

HH
mm
5H

mm
mH
mH

mm

mm

Hom

mow
HOHN
mmb
mmHH
mmh

mum
mHm
m¢vm
hHmH
5mm

mmmm
vam
mmm

NHmv
th

mvmv

mmmOH

mwhHH
mhhHH
HHooN
mhmm
hmom

mmmm
Homm
mehN
momm
mommH

mmmmm
NHth
hmeH

vamm
mmvNH

mvomv

moCmHom mHmHHmumz
pCm HmoHCmComz .meCHHmumz
mCHHmmCHmCm HmUHCmComz
mCHHmmCHmCm HmoHHuomHm
mOCmHom HmquEoo
mCHHmmCHmCm HH>HU
mCHHmmCHmCm HmOHEmCO

mCHHmmCHmCm

COHumoHCCEEoomHmB
EmHHmCHCon
mCOHumOHCCEEoo
comwmm a amoHOHmsm
mCHmHuHm>mm

mHHAN COfiUflUHQDEEOU

mCHummez
UCmEmmmCmS
quEmmmsz
COHuCuHumCH a quHCmummm .Hmuom
moHEOCoom
CoHumHumHCHEmm
monmo w 3mg mmmCHmsm
COHumHumHCHEmC
HmHOCmCHm w mCHuCCoooC

mmmCHmsm

 

 

 

Ame Coumwmmm AOHV COHuOCHmeH ADHV COHuosuumCH
mumsmmuu mumsmmumummCD

 

mmHuHquCO usmuso

118

m mmmm men xnoz HmHoom
mm mmhm mmon smoHonommm
mm mmom mmomm monHom HmOHuHHom
hm wHOH mmovH mammumomw
«H Hmom mmmmH moHumsn HmaHsHuo
5H mva nmva mmoHomouzucm

moCmHom HmHoom
mm HwVH mmHNH mmOHooN
mH mHmH OONMH muHHHanoum w mOHumHumum
MhH HomH mmmmm monhcm
m mom om~m mchnsz
am meow HmHNOH moHumsmsumz
Hm 4mm HQHG mmoHomo
om mmoH amvm mmOHosouam
mOH mHmv mmwmm muumHEmCU
MOH mmma «map amoHonumm acMHm a acouom
MH mmm vvv mOHmhnm0Hm
HHH ohmv «wow muumHsmCUOHm
m Hm mmmm wmoHouumm a msocouumm

moCmHom Hmusumz

m as HammH comemz magma mo mmmaaoo
m mmq mmNHH acmeaouH>cm :mssm
mm mva hmmMH GUCmHom moom
ma man «was mmoHoom mHHsmm
N Hmwa NNNH mocmHom UHHno mam maHemm

mmOHoom CmECm

 

 

 

Ame Conmmmwm AOMV CoHuoCHumCH ADMV CoHuUCHumCH
mumsmmuo mumsmmumnmmCD

 

mmHuHquso usmuso

119

HH
Hm

NH

Nv
om
5H
hm
mm
Nv
mm
5H

mH

 

Am

HV

Coummmmm

NNm
mvwm

NmmH
mHm
bhh
mm
NhHH
OHw
H¢HH
0mm
NomH
Hmm
huh
HNMN

m5

0mm
mmhm

 

AowV :oHuoauumcH
mumdmmuw

NNmm

OHmvm

moHv
momm
hhhm
mowv
mmmm
Hwom
vwhh
vmhq
oovv
wmvw
mmmh
mmbm

Nmmv

moom

mhomH

 

ADHV coHuosuumaH
mumsmmumummCD

 

mmHuHquCo usmuso

CMflmmDm w GMEHOU
smHqum

muwuumq mCm muum

quEmon>mo mOHCOmwm
mmoCmHom muuHCom
CoHummHomm a mxumm
mCvaxomm
.mHCuHCUHuHom

muummuom

mMHHmHHS w mmHHmCmHm
moCmHom mHHma

woCmHom HHom mCm monu
mumCmnmsm HmEHCm
mCHummCHmCm HmusuHCoHumm
moHEOCoom HmHCuHCoHHmm

monCommm
Hmuspmz mCm mnsuHCOHHmm mo mmmHHoo

mhlhhmH

mmHmCum CmuHHomonuwz m Cmnus
quEmon>mQ CmQHD mo mmmHHou

mCHCCmHm CmnHD
mmOHOHoom

AmmCCHuCooV moCmHom HmHoom

120

NH mmoa «mam mcHummchcm HH>Ho
OH mum Homm mCHHmmCHmCm HmoHEwCU
mCHHmmCHmCm
m mvm mums COHumoHCsEEoomHmB
m owe ommh EmHHmCCCOU
mm mvom mmmvm mCoHumoHCCEEoo
H Gmom vam nommmm a mmoHonnm
m wvw HomNH mCHmHuum>p¢
mpum COHumOHCCEEou
mm «Has Gamma mcHuwxumz
mm Hmon MHHHN acmsmmmcmz
a cam mHHvH unmammmcmz
COHusuHumCH w quusmummm .Hmuom
vm Nmmv Nommm moHEOCoom
m mew mmmHH COHumuumHCHEmC
monmo w 3mH mmmCHmCm
vH mhvv mmmmv CoHpmHumHCHEmC
HmHOCmCHm a mCHquoooC
mmeHmCm
hm vmm whovm mommCmCmH HmonmmHU a GUCmEom
m omm thHH anmomoHHCm
m «mm Hhhm mwmmsmCmH
CmoHHmC mCm HmpCmHHo .mOHumHsmCHH
om GGMH mvhmm muoumHm

AUQDQHUCOOV mHmHUmn—H USN muzu<

 

 

 

AmNV Coummmmm AomV CoHuoCuumCH ADMV CoHuoCHumCH
mumzmmuw mumsmmumummCD

 

mmHuHquCO usmuao

121

mm vth HmHmH mmoHooN
mH mHHH vmmmH muHHHnmboum w moHumHumum
mom mva mmwmm monmnm
H Hmm onH mchusz
mm H¢h~ thHOH moHumeCumz
HN «mm mHmo smoaomo
no mmm momv mmOHoEoqu
mNH thm mwomm mHumHEmCU
om oHnH vans smoHonumm acmHm a scouom
om Hmm th mon%CQ0Hm
vb ommm cums muansmnoon
moCmHom Hmusumz
n omm OHth quECouH>Cm CmECm
oHH GOHN Hmqu mOCmHom moom
m mam Hmmv smoaoom CHHsmm
m mmva cosh mocmflom HHHno mam AHHsmm
mmoHoom CmEom
m omm when moCmHom mHmHHmumz
mCm HmoHCmComz .mmHsHHmumz
mH vmh mnvm mCHHmmCHmCm HmOHCmComE
mm mmmm ommOH mcHumqumcm HmoHuuomHm
o Hmm mommH mocmHom Amundsoo

AmmsCHuCooV mCHHmmCHmCm

 

 

 

ACMV Coumwmmm AUHV COHuosuumCH ADMV COHuoCHumCH
mumsmmuw mumsmmumummCD

 

mmHuHquCO usmuso

122

NH

vN
vH
mNH
mv
mN
NN
VH

 

Ame Coumwmwm

5N

HMHH
mmmw
hmmm
mmmH
OMMH
ONmN
NONH
mHNH

 

AOMV COHuosuumCH
mumsmmuw

HNvm

wHNm

MOHmH
¢¢mh

ONHNo
hammN
wHNMH
mmth
HNmNH

 

ADHV COHuUCHumCH
mumsmmumummCD

 

meuHquCO usauno

mepsum CmuHHomouuwz a CmQHD
“CmEmon>mo CmnHD mo mmmHHou

mCHCCmHm CmnHD
mmoHOHoom

xuog HmHoom
mmoHocommm
woCmHom HmoHuHHom
hammumomw

moHuan HmCHEHHU
wmoHomousqu

moCmHom HmHoom

123

 

 

 

mecca mHHHH onmmm mmmHHm amasq mo mmeHoo
vam HmmmH mmmmm mmmmsmcmq HmonmmHo a mocmsom
«Hem ommva Hm¢m~ manomoaanm

OVHm omHvH ommHm mmmmsmcmq

CmoHHmC mCm HmucmHHo .moHumHCmCHH
mmvm Hmmmfl mmmwm NuoumHm
mva HmHvH «mmmm cmHmmsm a cmsumo
onmm moomfi mmmmH umuamo mmmsmcma gmHHmcm
mmmm mmmma Hwnvm :mHHmcm

mumunmfl Ucm muud
«oma MHmmH ovmmm unmemon>ma mousommm
«Ham HmooH mmmmm mwocmHom NHuHsom
comm mman monm cOHummuomm a mxumm
ommm mavom mhamm mcflmmxomm
qwma moonH «mmmm musuHsOHunom
mHmm mHomH mmHnm Nuummnom
ommm mmmHH Hmmmm mmHHmHHz a mmHumanm
mmHm mmvnH mmmam mucmHom muHmo
mmHOH Haqu mommm mocmHom HHom mam mono
Gmmm mHmGH mqmnm mumcmnmsm Hmchm
movHH mnvma Hanna maHummcHoam amusuasoHuma
mama Hmva mmmom moHeocoom HausuHsUHuma

meHDOmwm
Hmusumz pCm mHCuHCoHHom mo womHHoo
AmmV mumamm .m>< AzaV Nunamm .m>¢ AemV mumamm .m>< maumnma
mquumHmmC muHComm NUHComm
mumsmmuw mmHCCmBICoz UmHCCmB

 

mmoHHm quCH

124

thOH

vHMOH
vmeH
NQFOH
ONMOH
wmmOH

ommm
Noam
ommm
wmmm
mwvm

omhm
vhmm
moom

ombm
mva

mmmm

HvaH

Hhth
mmmmH
mhhmH
thmH
mvmmH

NNNvH
omeH
thmH
wmme
HVth

mmNHN
om¢NN
NthH

mman
oommH

HmONN

MHmmN

ovth
whmmN
mHHbN
HoomN
hNHmN

NmmmN
mmmmm
HHmmN
thhN
oomom

Mmem
womwN
NmmmN

NmONm
chth

MMHmN

mOCmHom mHmHumumz
UCm HmoHCmComz .mmHCHHmumz
mCHHmeHmCm HmoHCmCowz
mCHHmmCHmCm HmoHHuome
moCmHom HmquEoo
mCHmeCHmCm HH>HU
mCHHmmCHmCm HmoHEmCU

mCHHmmCHmCm

COHumoHCCEEoomHmB
EmHHmCHCOb
mCOHumoHCCEEou
Commmm w mmoHOHmsm
mCHmHuum>m¢

muwhfi GOflHMUHCHHEEOU

mCHummez
quEmmmsz
pCmEmmmsz
CoHDCUHumCH w quHCmumwm .kuom
moHEOCoom
COHumHumHCHEUC
mOHmwo a 3mm mmmCHmCm
COHumHumHCHEmm
HmHoCmCHm a mCHquoood

mmmCHmCm

 

 

 

AmmV Numamm .m>m Asz mumHmm,.m>m AamV mumawm .m><
mquumHmm< muHComm wuHComm
mumsmmuw mmHCCmBICoz mmHsCmB

 

mmoHum usmCH

125

acca ammam Hmcaa xuoz maaooa
aaca mamam comcm aaoHoaoama
amma aamam ammaa mocmmoa HaoHuHmoa
avca mmamm aaaam anoauaomo
aaaa aaaam ocaam momuasc HammeHuo
aaacm amama aaaaa aaoHoooucuca

mocmfiom HmHOOm
aama aaaam momma aa0mooa
amaa Hmaam cocoa auHHHnanoua a moHumHuaum
cmaa aacam omaaa moamanm
oamam macaa aaaca acmmusz
maccm aacmm aaama moauasmcumz
caaa momma aamam aaomomo
cmaa ccamH cmmaa aaomoeoucm
ochH mmaam macaa auumHEmno
mama amamm comma aaoHonuaa ucmma a acouom
coma aaccm aaaaa moamaoooaa
mama aaaam maaaa auuamsmnooma
cmaa caaaH mmacm aaoHouumm a aeocouumm

monHom HmHCumz

amca aaamm acmca coaacaz magma mo mamHmoo
amaa aaaam amama acmscoua>cm omega
amaa amamm mmama moamaoa coca
mama amcam ammaa aaoHoom amaema
coma maaam aamaa moammoa cmmgo cam mmmeaa

wmoHoom CmECm

 

 

 

AaaV auaaaa .a>a AzaV anamaa .a>a AaaV summaa .a>a
mquumHmmC wuHComm wuHComm
mumsmmuw mmuCCmBICoz mmHCCwE

 

mmoHHm quCH

126

«new
momm

vvmm
mmmm
OHmm
mmmb
mHmm
omom
owmm
mHmm
omvm
NHom
NHmm
ohmm

NmBOH

NOHm
wmmm

ommVH
NOOMH

mmOMH
MvaH
thmH
ooo>H
mmmvH
mome
OONmH
mmmmH
vaVH
mmmmH
mmva
OHth

mman

Hmth
NmmvH

mm¢oN
mHNMN

Homvm
mmmwm
mmomN
MNme
hoovN
MvaN
meMN
mNmVN
mmme
Nova
mmnmm
HmomN

HohMN

vmmmm
ommmN

 

CmHmmsm a CmEumo
anmacm

muwuumq mCm muum

UCmEmon>mo mouCOmmm
mwonHom anuHsom
COHummHowm a mxumm
mCHmmxomm

mHCuHCoHuHom

muummuom

meHmHHB a mmHHmCmHm
woCmHom muHmo

moCmHom HHom mCm mono
wnmCmnmsm HmEHC4
mCHummCHmCm HmHCuHCoHHmC
moHEOCoom HmHCuHCoHHmC

mmOHCOmmm
Hmusumz mCm wHCpHCOHHmC mo mmeHou

mhlhan

mmHmCum CmuHHomouumz a CmQHD
quEmon>mo CmnHD mo mmmHHoo

mCHCCmHm CmQHD
hmoHOHoom

AmmCCHUCooV moCmHom HmHoom

AaaV anamam .a>4 AzaV anamaa .a>< AaaV anamaa .a>a
mquumHmmm wuHComm muHComm
wumsmmuu mmuCCwBICoz mousta

 

mmOHum quCH

127

womm
monm

omHm
ovom
meOH
NMHm
NNvm

mmwm
mme
owmm

thm
owmm

NNmm

«mom
comm
omom

momm

ONMhH
omomH

mmHvH
hmmmH
MONmH
mmBMH
hmmmH

Nwth
thON
omhmH

hmmmH
oommH

hmHON

NHmMH
thvH
omme

mvaH

mVHmN
HNcmN

ovaN
ommNN
mmhvm
HthN
mmmmm

vvwom
mhth
mmwhN

oommN
ONNmN

mmth

mmvNN
NNwHN
NNmON

mmmNN

 

 

mCHHmeHmCm HH>HU
mCHHmmCHmCm HmOHEwCU

mCHHmmCHmCm

COHumoHCCEEoomHmB
EmHHmCH50b
mCOHumoHCCEEou
Commmm w mmoHOHmCC
mCHmHuHm>mm

muu< CoHumoHCCEEoo
mCHumxumz

quEwmmsz
quEwmmsz

CoHuCuHumCH a quHCmummm .Hmuom

moHEOCoom
COHHmuumHCHEm<

monmo a 3mg mmmCHmCm
COHumHumHCHEm<

HmHoCmCHm a mCHuCCooo<

mmmCHmsm

mommCmCmH HmOHmmmHU a woCmEom

aaaomoaaaa
mmmmCmCmH

CmOHuwm mCm HmquHHO .moHumHCmCHH

wuoumHm

AmmCCHUCooV mumuumq mCm muum

AmmV auamam .a>< AzoV summam .a>¢ AHmV anmmmm .a>«
mquumHmmm muHsomm wuHsomm
mumsmmuw mmuCCmBICoz mmHCCmB

 

mmoHHm uCQCH

128

aaaa maamm mamam aaomoON
cama ammom cmamm NDHHHnanoum a moHumHuaum
caaa aaaam oacam momamza
cmmmm mmamm aamam aaHmusz
mmma cammH aocam aoHuasmcuaz
amma caaam maaam aaomomo
cama aaHmH cmamm aaomosoucm
oHaa aaamH mmmam auumHsmno
amaa amccH oaamm aaoHosuam ucmHo a acouom
acaa acamm amamm mommaomoma
aaaa aoamm aaacm NuumHsmnoon
wocmflom HMHDMGZ
acaa amaaH aaHHm ucmscoua>am cassm
amoa mmaam maamm moamHom coca
aama comma maamm aaoHoom mmmsam
acma ochH oaomm wocmHom oHHno mam NHHsam
mmoHoom CmEC:
maaa maoam oomom mocmHom mmamumuaz
mCm HmoHCmComz .hmHCHHmumz
cmccm aaaam aamam acmummcmaqm maomcasomz
maaa mamcm mammm acHummCHacm HmoHuuumHm
ommcH camaH aHaam mocmHom “musmsoo

AmmCCHuCooV mCHummCHmcm

 

 

AaaV auamaa .a>< AzaV amamaa .a>a AeoV amamaa .a>a
mquumHmm< muHComm wuHsomm
mumsmmuw mmuCCoBICoz mmuCCmB

 

monum quCH

129

mHmm

wmmm
Nehm
OONm
mhmm
OHmm
vam
ommm
mem

 

Ad

mV aanmm .m>¢
mquumHmmC
mumsmmuo

mmva

mvnhH
bmmoH
HvaH
mNmmH
«NmMH
hmwMH
v¢obH
mummH

homNN

movmm
vmmVN
NNovN
ommmN
thvm
mommN
vacN
mmmmm

 

 

Asz auamam .a>¢
wuHComm
mmHCCwBICoz

AeaV amamam .a>a
wuHoomh
mmuCCma

 

mmoHHm quCH

mmHmsum CmuHHomouumz a CmQHD
quEmon>mo CmQuD mo mmmHHoo

mCHCCmHm CmnHD
mmoHOHoom

xuoz HmHoom
mmoHOCommm
woCmHom HmOHuHHom
mammhmomw

OOHUme HmCHEHHU
hmOHOQOHCUCC

moCmHom HmHoom

130

OOOOHN.

ooomoH.
oooomN.
ooommH.

ooomHm.
OOONHH.
ooommo.
ooomNH.

0005mm.
ooommw.
ooomom.
OOONHN.
OOOMHh.
ooommm.
oooomm.
OOOHom.
ooommw.
ooommm.
ooohmm.
ooomow.

Asz
Coummmmm

OQONOO.

vvaNH.
ommHhH.
mNhHHN.

ommva.
ohmHON.
VHmNHH.
ommmmH.

HHMMNN.
omhmmN.
ommmmm.
vath.
mmmmao.
mmthN.
om¢mmm.
HmHHNH.
HooomN.
mommHH.
mNmMHN.
mNmo¢H.

Aon
mumspmuw

omwhmh.

omvah.
0Nmmmm.
NhNomm.

omooom.
vammm.
wmomom.
ovomHh.

mmwmho.
ovawN.
OvamN.
momowm.
N¢HHmH.
NHmomo.
ommHmH.
coonno.
mmmmHH.
NmHmmN.
ooomNN.
QOOHmo.

 

Aon
mumsmmumnmmCD

 

mmHmCm usmuso

mmmHum CmEMH Ho mmmHHou

mommCmCmH HmonmmHo a moCmEom
asoomoamna
mommCmCmH
CmoHHmm mCm HmquHHo .moHumHsmCHH
mmoumHm
CmHmmom a CmEHmU
HmquU mmmCmCmH CmHHmCm
CmHHmCm

muwuumq mCm

quEmon>mQ moHCOmmm
mmOCmHom huuHCom
CoHummHomm a mxumm
mCHmmxomm

mHCuHCoHuHom

mupmmmom

meHmHHB a mmHHmCmHm
mOCmHom huHmQ

moCmHom HHom mCm mono
mHUCQOCm HmEHCC
mCHummCHmCm HmusuHCoHumC
mOHEOCoom HmuCpHCOHumC

mand

mmoHCOmmm
Hmusumz mCm mHCuHCoHHmC mo mmmHHOU

mhlman

131

ooommm. NmmmmH. mmmth. wOCmHom mHmHHmumz
mCm HmoHCmComz .mmHCHHmuwz

cocaom. maHacm. mmaHam. aonmmchcm HmoHcmzomz
cccamm. macamm. ammmca. acmummcmacm maoauuommm
oooocm. ccmaaH. ccacmm. moamHum amusmsoo
cocaam. mmmaam. aaamma. acmummcaaam Hm>mo
cccamm. caamcm. aamcaa. aammmmcmacm maomsmoo
mCHHmmCHmCm
cccamm. aammmm. omaaac. coauaomcoasoommme
cccamm. ammmcm. aaamaa. gammacmsoo
coccma. cccaam. ccoaca. moomumomasssoo
cccmmm. mmamcm. aamaam. nommoa a maomomosa
cocamm. mammcm. aacoac. aomamuum>ca

mand COHumoHCCEEOU

 

cccaam. acacmm. camaaa. acmumxuaz
cccaam. cmmamm. oaamam. newsmaacmz
occaam. maHmao. maammo. newsmamcas
COHusuHumCH w quHCmummm .Hmuom
occamm. aaamam. mcmHHa. moHaocoom
ooccam. ammcmH. ooamaa. :oHuauuchHsca
wOHmmo w 3mH mmmCHmCm
cocaam. ammcam. maamaa. :OHuauuchHaom
HmHoCmCHm w mCHuCCooom
mmmCHmCm
Aan as 3:
CUHmMmmm mumsmmno mumsmmumummCD

 

mmumsm usmuso

132

ooommm. Noommm. mhmomN. HHOS HmHOOm

cccaam. mamama. amaaam. aaoHosomma
oocamm. ammmmm. caammm. mocomoa HaoHUHmoa
occama. mmmmmm. aaacma. msoamaomo
occmam. maamam. accmma. momumso macHsHuo
oocamm. caaacm. oammam. aaomooounucm

QUCGHUW HMHUOm

cccmma. amaacm. mamaam. aaoHOON
cccmam. maaacm. ammaam. mummmnanoua a aoauamuaua
oocamm. ccammm. ccmama. moamana
occcmm. cmacam. cacamm. acamusz
cccaam. maaaac. amcama. moHuaewauaz
oocamm. aamcmm. occama. aaomomo
ccommm. mmmaam. aaaooa. maoHoeoucm
occama. aaacam. mmmamm. auumHEmno
oocamm. mamoam. maaaam. aaoHocuaa ucama a acopom
ccomma. cacamm. aaammm. mommazooma
cccoma. cmmmmm. oaammc. muuaHEmaoon
occama. caHamH. caacmc. aaoHouumm a aeocouumm

GUfiwHUm HMH5#MZ

cccmam. mamamm. aaamaa. comHoaz magma mo mammmoo
occama. Hamaom. amaamc. unmaaoua>cm mason
cccmcc. amamac. ammmom. wocmHom coca
oocamm. ommmac. caaaam. aaoaoom mmHaaa
oocamm. maamom. acmmmm. mozmmoa cmano can ammeaa

meHoom CmECm

 

1an Aon 1sz

Coummmmm mumsmmuo mumammumummCD

 

mmnmnm usmuso

133

ooomHm.
OOONHH.

ooomNH.
ooonmm.
OOOwa.
ooomom.
OOONHN.
ooomHh.
ooo~mm.
ooovmm.
OOOHmh.
ooommm.
ooovmm.
OOONNV.

ooomhh.

ooommv.
oooomH.

Asz
gonmmwm

mHhmmH.
mmmNmN.

vmommH.
movaH.
NMvaN.
oommmo.
mvmmmo.
mmmmmo.
vamNN.
vmvmmm.
mmmowH.
womva.
mmmmMH.
oomvhN.

mmmNmH.

vmhmvo.
omvmwN.

Aon
mumsmmnw

mmNHNm.
wvmmmm.

mmmwon.
mmmOHH.
mmwMHN.
cosme.
NmmNmm.
vvvaN.
mmmNmo.
mvmhhH.
mmommo.
mmMNqH.
wvawN.
owqmmN.

Noowbo.

mHthv.
omehm.

 

Asz

mumsmmumummCD

 

mmnmnm usmuso

CmHmmsm w CmEHmw
anHaam

mumuumq mCm mumm

quEmon>mo moHCOmmm
mmoCmHom muuHCom
COHummHomm a mxumm
oCHmmxomm

musuHCoHuHom

huumwuom

mmHHmHHB a mmHHmCmHm
moCmHom mHHmQ

moCmHom HHom mCm mono
mupCmnmCm HmEHCC
mCHumeHmCm HmHCuHsoHHm<
wUHEOCoom HmHCuHCOHHmd

mmoHCOmwm
HmHCumz UCm musuHCOHHmm mo mmmHHoo

mhlhbmH

mmHmCum CmuHHomomumz a CmnHD
quEQOHm>mQ CmnuD Ho mmmHHoo

mCHCCmHm CmnHD
hmoHOHoom

AmwsCHuCooV monHom HmHoom

134

occaam. aacamm. cmamca. mamummcHacm HH>Ho

oocamm. cmaaam. caaama. acaumwcmaca maUHEmao
mCHummCHmCm
occaam. mmmmam. aaacaa. coaumomcseaoommma
oocamm. ammaam. mmammm. gammacusoc
ccccma. ccaamm. ccmmca. maomumomcsesoo
oocamm. aaammm. momamm. oommoa a aaomomcoa
oocamm. mamamm. amammc. acmmmuum>o<

MUH¢ COHUMUflCDEEOU

oocamm. acommm. caaaaa. acmumxuaz
occaam. acommm. maacam. pamEmaacaz
occaam. machc. acaamc. newsmaaaaz
CoHuCuHumCH a quHCmummm .Hmuom
oocamm. ammaam. cacoac. moHEocoom
occaam. HcamaH. aacaao. coHumHuchHsom
OUHWMO w 3mg mmwcflmflm
occaam. Hmmmmm. aoamma. :oHumuumHanmm
HmHoCmCHm w mCHquooom
mmmCHmCm
occaaH. cmmmcm. oaaaaa. mmaacacmq HaoHammHo a mocaeoa
ccccmm. cmccmc. oaaama. momoaoamna
cocoom. occaam. ooomam. mmaasaaaq
CmOHuwm mCm HmquHuo .moHumHsmCHH
occaam. acoaaH. cmamma. amoummm

AmmCCHuCooV muwuumq mCm mand

 

Aan $5 $5

Coummmmm mumsmmuw mumsmmumummCD

 

mmumnm udmuso

135

cccmam. aamcmm. mmaaam. acomoom

oocamm. coamam. oamacm. NDHHHnanoma a moHumHumum
occaam. caaamm. cammam. mommmza
occaam. ccmccc. ccamaa. aammmsz
oocamm. cacamm. aammac. mumpasmnuaz
cccmmm. mmmaam. aaacma. aaoHomo
occama. cmmmam. cmammm. aaoHoaoucm
occaam. aamaam. maacma. muummsmoo
ccomma. aaaaam. mmmmmm. aaoHonuaa ucama a acouom
ccccma. ccaacm. ccmcac. momamooOHm
occama. mmmcam. acammc. auummamooomm

OOCGHUm HMHDUMZ

cccmam. mcmamm. amaaaa. unmaaoua>cm omega
ccomca. aamcac. mmammm. moommom coca
occaam. aamaam. amaaam. aaoHoom mameam
occaam. acmaam. aaamam. moammoa ommso can ammeaa

meHoom CmECm

oocamm. omocoN. ooNomm. mOCmHom mHmHnmumz
mCm HmoHCmComz .mmHCHHmumz
cocaom. caamcm. ccmaam. achmmaHacm HmoHcmnomz
oocamm. moaaHm. cmmmom. aaHummCHacm HmoHuuomHm
oooooN. mHmmom. vwmaHm. woCmHom umquEoo

AmmCCHUCOoV mCHmeCHmCm

 

33 ES AczV

noummmmm mumsmmum wumsmmnoummCD

 

mmumnm usmuso

136

oooomv.

oooomH.
ooomom.
ooommH.
oooomm.
ooohvv.
oooHoN.
ooomNm.
oooNNe.

Amy:
Coummmmm

oomMHo.

oOHomN.
«Hmmmm.
mmvwom.
omNva.
moohmH.
MHHmvm.
NMHomm.
mmloH.

Aon
mumsomno

oovomm.

common.
omvvom.
mwmomv.
vohNNm.
mmmmmm.
hmwmmm.
wmmoem.
NHmoow.

 

Aon

mumspmumumeD

 

mwumnm unmuso

mmHmsum CmuHHomoupwz a Cmnuo
quEQOHw>mo Cmnuo mo mmmHHoo

mCHCCmHm Cmnuo
mmOHoHoom

Muoz HmHoom
amoHOCowmm
moCmHom HmoHuHHom
, msmmumomw
onumCh HmCHEHHU
mmoHomousqu

moCmHom HmHoom

137

ovmmmo.

mHHHNN.
omNeoH.
«mmVHH.

mmmmmo.
thNHH.
mNmNHm.
thNNH.

thNMN.
vaMNH.
NommNN.
ommmmo.
thHmN.
vommmH.
«whohm.
ohmoNN.
MVHHmH.
hmoMHN.
MFMHMH.
NhHmmH.

 

AmmV mquumHmmC
mumzmmnw

ommomo.

ovamo.
HmNmNo.
oVvaH.

mhmHmH.
mHooNN.
omwam.
mmooNH.

NmmomN.
NomHoo.
oHHboo.
NmommN.
mthmH.
ommmmo.
mooth.
mNmNmH.
vmqovH.
ohmmmH.
mmommN.
bmonN.

 

AZmV mumsoam
pmHCCwBICoz

mnnmmm.

omm¢mo.
mowohm.
oomomo.

omoMHh.
mmmooo.
NmmMHH.
mmonb.

Hoohmv.
mummHm.
NNmmom.
vaomo.
mthmm.
ommvmh.
mHNomv.
mmvomm.
mommoo.
homHoo.
mNmmmm.
HhBMNm.

 

AamV aumsoam
mmHCCmB

 

mmumnm usmCH

mmmHHm CmEMH mo mmeHou

mommsmCmH HmonmmHU w moCmEom
monomomHna
mmmmCmCmH
CmOHumm mCm HmHCwHHo .moHumHCmCHH
anoumHm
CmHmmCm a CmEHmo
HmquU mmmCmCmH CmHHmCm
CwHHmCm

mumuumH mCm

quEmon>mo wousommm
mmOCmHom wuuHCom
COHummHomm a mxumm
mCHmmxomm

mHCuHCoHuuom

anummuom

meHmHHS a meHmCmHm
moCmHom muHmo

moCmHom HHom mCm mono
wumCmnmCm HmEHC<
mCHHmmCHmCm HmHCuHCOHHm<
moHEOCoom HmHCuHCoHHmm

muum

. mmOHCOmmm
Hmusumz oCm wHCuHCUHHm< mo wmmHHoo

mhlmhmH

138

mvoomH. whomeN. mommNo. moCmHom mHmHkumz
mCm HmoHCmComz .mmHCHHmuwz

moccao. amcmcm. aamoaa. AaCHummcHacm HaOHcasomz
aaammm. caccmH. occama. acHuwmcHacm HaoHuuommm
aaaaac. mamamH. maamam. mocmHom amusmsoo
maamac. mamamm. maaaca. aaaummaaaom HH>Ho
cmamam. acommm. cammmc. acHummchzm HmoHsmCo
OCHHmmCHmCm
acammH. cmcmoH. aHHch. coHpaoHcseaoommme
mamaaH. acamHm. oHcamo. EmHHmcmsoo
aHacam. amaamm. mmmcac. mcoHumoHccssoo
cmammo. maaaam. Ammmca. nommmm a maoHoHcom
amaamm. maamma. acmaam. acmamuum>o<

MUHAN COflflMUHCDEOU

 

 

 

vaHoN. oomHmN. mmmoom. mCHummez
mcoamm. HccaaH. camHoc. newsmaacaz
amacmc. macoca. omcacc. ucmsmmaqmz
CoHuCuHumCH a pCmquummm .Hmuom
oommMH. mHmvHN. oHNHmo. moHEOCoom
bmmmmo. acommm. mmova. COHumHumHCHEmm
monmo a 3mg mmmCHmsm
mmvmvH. HHmmom. omoovm. COHumHumHCHEmm
HmHoCmCHm w mCHuCCooo<
mmmCHmCm
m Z .H.
A mV muamumHmma A mV aumsoaa A mV anacoam
mpmsmmuw mmHCCmBICoz mmHCCmB

 

mmHmCm uCQCH

139

ovomNo. oomhov. vaNom. xHOB HmHOOm

amcaam. aaaamm. cocaom. aaoaosomma
mamaam. maaamm. aaammm. mocmmoa maomummoa
mammcm. aaaacm. maaaaa. asoauaomu
cammmm. cmmaam. aamaaa. momumsc maaHeHHo
mamamm. aamamm. mmccmm. maomooououca

OOCmHom HmHoom

cmaaam. Haaaac. aaamoa. aaoaoom
mamaam. mmaaca. aaamma. mummmnanoua a momuampaua
aammam. mcammm. aoamca. mommana
amacmc. aammaa. ccmamm. aammusz
oocamm. mmccma. Hammam. momumemguaz
maaocm. acommm. mmmama. Noemomo
aoaamm. cHaaom. Haocaa. aaoHosoucm
aacaac. Hcaaam. mamaca. mmuaHEmno
aaaaam. ammaac. aoaama. macaozuaa gamma a acouom
acamam. acaamm. maamca. mommasmon
aaamam. amccmm. acmacm. muumHEmnoomm
ammamc. mHHHaa. cmoacm. aaoHouumm a asocouumm

woCmHom Hmusumz

Haamao. aammam. mmcmam. commons mmeao mo mammmoo
amaamm. ammmmm. maaamm. unmscoum>zm cassm
cmcaam. cmaacm. camaaa. mocmaoa coca
acommm. mamaam. amcama. Naomoom AHHEME
maacam. aammam. caaaaa. mocmmoa ommno com mmHamm

hmoHoom CmECm

 

 

 

AamV mucaumHmmm Asz mumsomm AemV mumsoam
”HMSGMHG gmHflucmBlgoz UmHflwgmB

 

mmumnm quCH

140

mmmhmH.
NmthH.

mHNmHN.
vamHH.
mommoN.
HummHo.
HhvwoN.
HhooHN.
HmNmmm:
mhhmmH.
vamoH.
movoNN.
omomoH.
HHvaH.

vvmmmH.

moomoo.
vaooN.

 

ACmV mquumHmm<
mumsmmuo

mHmHoH.
onmoH.

HmmomH.
MHmHoH.
othvv.
ommHhH.
mNMNMH.
Honmo.
mumMNm.
mmmoom.
hmmomH.
vmvhoH.
hmewN.
thomN.

mmHmON.

mHmvNN.
mmNNoo.

 

AZmV aumsomo
meCCmBICoz

mmqomo.
mvhohh.

Nmmmmm.
vvnmmh.
mvmmvm.
mmooom.
vonmo.
hNhHoh.
ovamN.
MNNmHm.
mmmovh.
NoHooo.
hhHNmm.
hmeom.

oomHmo.

HHHooh.
ooHHmh.

 

AsmV auasomm
mmHsCmB

 

mmumnm quCH

CmHmmsm a CmEHmo
CmHHmCm

mHmflqu UCM m#H4

pCmEmon>wo onCOmmm
mmoCmHom anuHCom
COHummHomm a mxumm
mCHmmxomm

wusuHCoHuHom

muummuom

mMHHmHHS a mmHumCmHm
mOCmHom hnHmo

wOCmHom HHom mCm mono
wnmCmnmCm HmEHCm
mCHHmmCHoCm HmHCuHCoHHmC
moHEOCoom HmHCuHCoHHmC

mmoumommm
Hmmsumz mCm wHCuHCOHHmC mo mmmHHou

mhlhbmH

mmHmspm CmnHHomouuwz a Cmnuo
“CmEQon>wo Cmnno mo mmmHHoo

mCHCCmHm Cmnuo
mmoHOHoom

AUQSCflDGOOV mucwfiom HMHOOW

141

acmcao. Hacaam. amaaaa. aaaummcaacm HH>Ho

cmHmHm. acommm. mcocca. acHummcHacm Hmomsmno
mCHwaCHmCm
omamam. amamac. amammm. :oHuaoHasEEoommma
aammcm. amaamm. mmaaaa. aammmcusoc
omcaam. mmaamm. amamoc. acomuaoaasasoo
aamamm. mmooaa. aamama. commom a aaoHoHosa
mmaaam. acamma. caaamm. acammuum>cm

munm COHumoHCCEEou

amaamm. macacm. aaamma. acmumxuaz
maaamm. Hocamm. oaacao. unwamaaqaz
chHoo. mammoa. acaamm. ucwswaacas
COHuCuHumCH a quHCmummm .Hmuom
mmmHmH. mmOHvH. vmmoNo. moHEOCoom
mNmmoo. mNmmmv. Nvovmv. CoHpmHumHCHEmm
oonmo a 3mH mmmCHmCm
mommON. cmoomH. Hmvmoo. CoHumHumHCHEmm
HmHoCmCHm a mCHuCCooo<
mmeHmCm
NmOhHN. mOHoho. NHmmoo. mommsmCmH HmOHmmmHo a moCmEom
mamaao. mmammc. maaama. anaemommna
mmmNao. NmoooH. Nmmomn. mmmmCmCmH
CmoHumm mCm HmquHHO .moHumHCmCHH
oommOH. ommomH. aNmmoo. muoumHm

AUmCCHuCooV mumuumq pCm mand

 

 

 

ACmV mquumHmmC AZmV muHComm ABmV muHoomm
mpmsmmuo mmHCCmBICoz mmCCCmB

 

mmumnm quCH

142

amaaam. mommac. acmmac. aaoaoom

momHoH. aaaccH. Hacmmc. NDHHHnanoum a mOHumHumum
moaaam. ccmmam. ammmaa. mommaoa
aaacmc. ammamm. aaaamm. acmmusz
camcmm. maacmm. camaac. momuaemnuaz
aaaaam. mmamam. acmama. acomomo
aaaoam. amacmm. aacaoa. maomoaoucm
ammmac. aamamm. aamaca. Annamawoo
mmammm. mmmmmc. cacamm. aaoHoauma ucama a acouoa
cmcmam. mocaam. aamcam. momaasooam
acaamm. amaamm. mmmmmm. Annamamnoomm

moCmHom Hmusumz

aamcac. cmmaaa. mmmacc. unwecoum>cm mason
Hmcmcc. acmacm. macoam. moammoa coca
aaammm. ammmca. aammma. maOHoom mmmeaa
momaam. amammm. mammam. mocamoa cmano can someaa

hmoHoom CmECm

mmaaac. ammmmm. aoaaaa. mocmHom mmaHuwuaz
mCm HmoHCmComz .>musHHmumz
amHaac. acmHmH. mmmcaa. acHumwcmaqm HaoHcanomz
Hmmccm. coaaoo. maomcc. acHummcHacm HaoHuuommm
camcac. amacmH. aaamac. wocmHom mausosoo

AmmsCHuCooV mCHHmmCHmCm

 

 

 

AmmV mquumHmmm Asz muHComm ABmV >UHComm
mumammuo mmHCCwBICoz mmHCCmB

 

mmHmCm usmCH

143

mHoMBN.

OMNmoH.
HmoNhH.
NmmNmo.
omFoMH.
hthNN.
oMFONN.
mommMH.
NmHmHH.

 

A<mV mquumHmmm
mumsmmuw

mthoH.

HNHoom.
hMHNho.
mmoomm.
uwmvmm.
ooMNMN.
quNoH.
oomvvm.
ohmmHm.

 

AZaV anmsoma
mquCmBICoz

Nvmmmm.

mwommm.
Hmemh.
mhmoho.
hmmem.
mommvm.
mHmoHo.
smoon.
mmmHom.

 

AamV aumsoam
meCCmB

 

mmnmnm usmCH

mmHmCum CmuHHomonumz a cmnuo
quEmon>mo Cmnuo mo momHHou

mCHCCmHm CmQHD
mmoHoHoom

xuoz HmHoom
hmoHOCohmm
moCmHom HmoHuHHom
mnmmumomo

moHuan HmCHEHHO
amOHomousuCC

GUCGHUW HMHoom

B IBLIOGRAPHY

BIBLIOGRAPHY

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Barten, A. P., "Maximum Likelihood Estimation of a Complete
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Berndt, E. R., and Christensen, L. R., "The Internal
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Berndt, E. R., and Wood, D. 0., "Technology, Prices, and the
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Blackburn, R. T., ”The Meaning of Work in Academia," in
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Buckles, 8., "Identification of the Causes of Increasing the
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Burgess, D. F., "A Cost Minimization Approach to Import
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Christensen, L., Greene, W., "Economics of Scale in 0.8.
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Christensen, L. R., Jorgensen, D. W., and Lau, L. J.,
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Denny, M., and Fuss, M., "The Use of Approximation Analysis
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Diewert, W. E., "An Application of the Shephard Duality
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Folger, J., and Bayer, A., "Some Correlates of a Citation
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Fuss, M. A., "The Demand for Energy in Canadian Manufacturing:
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Grant, J. H., Substitution Among Labor, Labor and Capital
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Griffin, J. M., "Inter-Fuel Substitution Possibilities: A
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Hall, R. E., "The Specification of Technology with Several
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