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ABSTRACT

RESOURCE ALLOCATION IN HIGHER EDUCATION:
A STUDY OF UNIVERSITY COSTS

 

BY

Philip Edward Austin

The demand for educational services on the university
level has increased greatly in recent years and every indica-
tion is that the trend will continue. It is also likely that
the demand for these educational services will increase at a
faster rate than the supply, the major limitation on supply
being the budget constraint. This situation makes it impera—
tive that decision makers in institutions of higher learning
allocate their limited resources in the most efficient manner
so as to provide for the attainment of institutional objec—

,W]tives. In order to make intelligent decisions with regard to

155.“: “I u.
figthe allgéation of scarce resources, they must know what courses

    
 

of action will accomplish institutional objectives and the.
economic costs that will be incurred as a result of the imple—
mentation of each course of action. The purpose of this study
was to provide a basis for obtaining the cost information
needed to make sound decisions in the process of allocating

educational resources.

 

 

Philip Edward Austin

The costs which must be included in an economic analy-
sis were discussed as well as the conceptual framework within
which constrained choice problems are solved. Consumer indif—
ference theory was used to demonstrate the method of choosing
the point of optimum allocation when resources are limited
and wants are insatiable. The isoquant approach to production
theory and its application to long—run educational resource
allocation problems was reviewed. The opportunity cost princi—
ple was outlined and applied to educational costing problems.

Based on these economic principles, a method of deter-
mining the costs incurred by the College of Education, Michigan
State University, in the production of academic degrees was
developed. The total cost of the degree programs of the 180
students in the sample was found by summing five component
cost categories: (1) instructional costs, (2) faculty support
costs, (3) research costs, (4) space costs, and (5) administra—
tive costs.

The total costs of producing a degree in each of the
several degree programs in the sample were presented. On the
average, the costs incurred by the College of Education in
producing a Ph.D. degree ($1399) were about twice the costs
incurred in the production of either a B.A. degree ($653) or

M.A. degree ($652). When degree cost variations within each

 

 

 

 

Philip Edward Austin
level were considered, these generalizations lost much of their
meaning. The cost ranges within each level were as follows:

(1) B.A. — $431, (2) M.A. — $278, and (3) Ph.D. — $326.

These total degree costs were used as the dependent
variable in the multivariate regression analysis which was the
statistical technique used to test the hypothesis. The hypothe—
sis stated that the following factors were statistically sig-
nificant at the 5 percent level in explaining differences in
degree program costs in the College of Education, Michigan
State University: (1) class size, (2) level of study, (3)
curriculum, (4) number of College of Education student credit
hours in the degree program, and (5) ratio of graduate to total
student credit hours in the degree program. The null hypothe—
sis was used in the statistical tests and was rejected. That
is, the above factors were found to be statistically significant
at the 5 percent level.

The regression equation revealed that, in response to
an increase in class size of one student, degree costs, on the
average, decrease by $3.40. Also, degree costs increase $10,
on the average, with each additional College of Education credit
hour in the degree program. Policy implications such as the

reduction of course duplication were discussed.

 

 

 

 

AMA hr;

Philip Edward Austin

Operating under the assumption that no economies of
scale were available to the College of Education and that the
budget was constant, the degree costs derived in the study
were used to show the cost of one degree program in terms of
others. For example, on the M.A. level, it was shown that to
increase the level of degree production in the area of Student
Personnel Work, at the expense of Agricultural Education,
requires a reduction of six student positions in the latter

area for every increase of four in the former.

 

 

 

 

 

 

 

 

 

 

 

 

 

RESOURCE ALLOCATION IN HIGHER EDUCATION:

A STUDY OF UNIVERSITY COSTS

by

Philip Edward Austin

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Economics

1969

 

 

 

 

 

C) Copyright by J
PHILIP EDWARD AUSTIN

1969

 

 

 

 

 

 

 

ACKNOWLEDGEMENTS

Sincere appreciation is extended to Dr. John P.
Henderson for his guidance and advice not only during
the writing of this dissertation, but throughout the
entire period of my graduate study.

Special thanks are also extended to Dr. Lester V.
Manderscheid and Dr. James E. Heald for reviewing parts

of the manuscript and offering many substantive suggestions.

PEA

ii

fflm ‘i.:e_--r;::<; ...A, V7 _

Chapter

II

III

IV

V

TABLE OF CONTENTS

INTRODUCTION 1
General Objective of the Study
Hypothesis of the Study
Sources of Data

REVIEW OF LITERATURE 8
Classification of Academic Data
Methods of Cost Analysis
Computer Programming and Educational
Costs
Cost Utility Analysis in Education

ECONOMIC THEORY AND EDUCATIONAL COSTS 31
Educational Resource Allocation
Efficient Resource Use

DERIVATION OF EDUCATIONAL DEGREE COSTS 44
Costs to be Included
Measurement of Costs
Determining Educational Costs
Instructional Costs
Faculty Support Costs
Research Costs
Space Costs
Administrative Costs
STATISTICAL ANALYSIS 59
College of Education Degree Costs
Regression Analysis
Level of Study and Curriculum Variables

Summary

iv
Chapter
VI SUMMARY AND IMPLICATIONS
Summary
Implications
BIBLIOGRAPHY

APPENDICES

90

 

LIST OF FIGURES

Iterations in the Program Budgeting
Process. . . . . . . . . . . . . . . 34

Production Possibility Curve . . . . . 36
Optimal Allocation of Resources. . . . 39

Isoquant and Set of Three Isocost
Lines. . . . . . . . . . . . . . . . 41

Regression Equation Residuals Plotted
Against Average Class Size Variable,
Degree Program Cost Study, College
of Education, Michigan State University,
1969 . . . . . . . . . . . . . . . . 7O

Regression Equation Residuals Plotted
Against Student Credit Hours Variable,
Degree Program Cost Study, College of
Education, Michigan State University,
1969 . . . . . . . . . . . . . . . . 7l

Regression Equation Residuals Plotted
Against Total Cost Variable, Degree
Program Cost Study, College of
Education, Michigan State University,
1969 . . . . . . . . . . . . . . . . 72

LIST OF TABLES

Table Page

1. Secretary—Faculty Ratios (Sec/Fac),
Average Annual Professorial and
Secretarial Equipment Costs (Eq/Prof
and Eq/Sec), Office Space Allocations,
Number of Full—Time Equivalent General
Fund Faculty Members (FTEF), Supplies
and Services Expenditures Per Full—
Time Equivalent General Fund Faculty
Member (SS/FTEF), and Secretarial
Salaries Per Full—Time Equivalent
Faculty Member (Sec Sal/FTEF) by
Department, College of Education,
Academic Year, 1967-68 . . . . . . . 51

2. Average Ten—Month Salary Figures, by
Department and Rank, College of
Education, Michigan State University,
1967-68. . . . . . . . . . . . . . . 55

3. Administrative Expenses: Undergraduate
Student Affairs Office (UGSAO), Gradu-
ate Student Affairs Office (GSAO), and
Dean's Office; Student Credit Hours:
Graduate, Undergraduate, and Total;
Administrative Costs per Student Credit
Hour: Graduate, Undergraduate, Overall;
College of Education, Michigan State
University, Academic Year 1967-68. . 57

 

4. Space, Administrative, Faculty Support,
Instructional, Research, and Total
Costs, in Dollars and Percent of
Total, by Academic Level, College of
Education, Michigan State University,
1967—68. . . . . . . . . . . . . . . 60

j Vi ,7

 

 

 

 

Table

5. Space, Administrative, Faculty Support,
Instructional, Research, and Total
Degree Costs, in Dollars and Percent
of Total, by Level and Curriculum,
College of Education, Michigan State
University, 1967—68. . . . . . . . .

6. Student Credit Hours (SCH), Class Size,
Total Cost, and Regression Residuals,
by Student Observation, Degree Program
Cost Study, College of Education,
Michigan State University, 1967—68 .

7. Matrix of t Values Generated by Tests
for Significant Differences at 5
Percent Level, by Combinations of
Degree Programs, Degree Program Cost
Study, College of Education, Michigan
State University, January 1969 . . .

 

63

65

79

 

 

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CHAPTER I

INTRODUCTION

Educators are becoming increasingly concerned with

the rising costs of educational programs on the university

 

level. As the demand for higher education continues to
grow, in many cases at a faster rate than resource appro—
priations, it is evident that given the quality of a pro—
gram, the costs of providing that program must be minimized
if the maximum number of students are to be educated. In
order to arrive at reliable cost/benefit decisions, adminis—
trators obviously must be aware of the relative costs of the

various programs provided by their institutions. Decision

 

makers in higher education, as well as all taxpaying
citizens who are interested in attaining the most efficient
allocation of educational resources, are looking to econo—
mists for alternatives to be used as foundations for educa-
tional policy decisions.

The study of educational costs should not be taken

as an indication that economic factors alone are the principal

 

determinants of educational resource allocation. Intelli—
gent educational decisions will always be based on the
nature of education and of educational institutions. To
achieve efficiency in institutions of higher learning,
economy must be consistent with the institutional environ—
ment necessary for academic interaction. The primary
responsibility of higher education is to increase the store
of knowledge, both in terms of quantity and in terms of
breadth of distribution. The costs incurred in discharging
this responsibility are small relative to the value to
society. Obviously, some very high cost programs might be
considered of high value and not only continued, but
expanded. This does not preclude the necessity on the

part of the administrators for being aware of the cost of
such programs. There might be instances where a cost
analysis would suggest the desirability of the contraction,

or the termination, of a particular course of study. For

 

example, a continuum could be constructed arranging all of
an institution's programs in decreasing order of educational
importance, and a second list could be constructed arrang-
ing programs according to a decreasing order of magnitude

‘in terms of cost. If the least important program from an
educational standpoint (a value judgment imposed by profes—

sional personnel) were the most costly, the continuation of

 

such a program might be called into question.

   

 

 

Previous research in this area has not, in general,
been adequately precise to be of great value to university
decision makers. Much of the work has taken the form of
dividing the total number of student credit hours by the
appropriate university or departmental expenditure to
arrive at a cost per student credit hour. Comparisons were
then made among departments or colleges of one university,
or among many universities.1

The value of interinstitutional comparisons is quite
obviously limited by variations among the several institu—
tions such as the content of course offerings of similar
departments, institutional goals and objectives, and
accounting procedures. Colleges and universities are
diverse operations. The goals and objectives of a small,
private liberal arts college, and the functions it performs
can be quite different from those of a large state univer—
sity. Even if they are committed to the same goals, the

methods they use to classify financial and academic data

 

lThree recent studies of this general form are:
(1) California and Western Conference Cost and Statistical
Study. (New York: Fund for the Advancement of Education,
1960) (2) Ralph Nelson Calkins, The Unit Costs 9f Programs
in_Higher Education. (Ann Arbor: University Microfilms,
1963) and (3) Unit Cost Study: Instruction and Departmental
Research. (Lansing, Mich.: Michigan Council of State
College Presidents, August, 1966).

 

 

 

 

 

 

 

 

might vary. Different institutions might also be operating
on different cost schedules or at different points on the
same schedule. All of these factors limit severely the
usefulness and applicability of interinstitutional cost
comparisons.

To a lesser extent, objections can be raised about
making cost comparisons in a single institution where all
accounting and registration procedures are identical. In
this case there will still be differences in departmental
goals and objectives which will be reflected in the average
student credit hour production per faculty member. For
example, one department might be largely committed to edu—
cating graduate students and conducting research, while
the faculty of another might perceive their responsibility
to be one of providing educational resources for under-
graduates. The student credit hour production per full-
time equivalent faculty member in the former would most
often be significantly lower than the latter; this differ—
ence would have a corresponding effect on the average cost
per student credit hour in the departments.

In addition to the problems of data homogeneity,
it must be emphasized that unit costs themselves have
limitations. They reflect a situation in which a given

number of students are consuming a given amount of

 

w?” 5'? ~—~ ' ' " \*--—~ T1

 

educational resources, at a given price at a point in time.
A change in the educational production function or any of
the inputs, regardless of size, might change the relative
unit costs entirely. Also, higher costs per unit of
educational output can mean greater inefficiency, greater
quality, or simply reflect the desire of administrators
to allocate more resources to one program than to others.
In spite of their limitations, unit costs can be
of great assistance to administrators if they are aware of
the assumptions under which the costs are derived and use
them accordingly. However, even if the cost information
is completely accurate and administrators use the figures
only to the extent of their reliability, unit costs alone
do not provide enough information to be of assistance in
making some types of decisions. For example, assume there
are a number of degree programs that will accomplish a
particular goal or set of goals in an institution. Addition—
ally, due to a limited resource base, only one program can
be offered. If all programs are equally effective in
accomplishing institutional goals or objectives, and there
are no rigidities such as tenured faculty members in one
area, the relative costs would be the major criterion used

in deciding upon which will be offered. In this case, the

 

 

 

 

 

cost of the entire program of study is the relevant figure

for decision making.

General Objective of the Study

This study is undertaken with the general objective
of developing a model which will provide administrators of
institutions of higher learning with the data needed to
make decisions concerning resource allocations. More
specifically, it will provide degree program cost figures
for the College of Education, Michigan State University,
and identify some major factors responsible for cost vari-
ations among programs. It is a part of a wider study being
conducted by the Planning and Development Office of the
College in which all existing programs being offered by
departments and institutes will be examined with respect
to objectives value and cost. In short, the purpose of
the study is to provide a basis for evaluating alternative
allocation policies under the assumption that the College
of Education has a range of values and changing objectives,
but a fixed resource base that provides a very important

constraint.

Hypothesis 2: the Study
The hypothesis of the study is that the following

factors are statistically significant at the 5 percent

 

 

 

 

level in explaining differences in degree program costs
in the College of Education, Michigan State University:
(1) class size, (2) level of study, (3) curriculum, (4)
number of College of Education student credit hours in
the degree program, and (5) ratio of graduate to total
College of Education student credit hours in the degree
program. To conduct the statistical tests, the null
hypothesis is constructed. The null hypothesis states
that the five factors listed above are not statistically
significant at the five percent level in explaining differ—
ences in degree program costs. The hypothesis and the
appropriate statistical tests are discussed in detail

in Chapter V.

Sources gf_2ata

Data were obtained from the College of Education
Office of the Dean, the Office of Institutional Research,
and the Graduate and Undergraduate Student Affairs Offices
of the College of Education, all of Michigan State
University. Other data, as necessary, were collected from

the several department chairmen and institute directors.

 

 

 

 

 

 

 

CHAPTER II

REVIEW OF LITERATURE

The economics of education is a relatively wide area
of academic inquiry. Such diverse research topics as deter—
mining the role of education in economic development, measur—
ing the economic return to education, determining the demand
for educational services, and discovering efficient methods
of allocating educational resources on the institutional
level have all been included in the category of the economics
of education. This generic classification can be divided
into macro and micro subcategories, with the first three
of the above four categories being included in the macro
section. It is to this category that economists have directed
most of their research efforts in recent years.

The literature on the micro or institutional level
(usually concerned with resource allocation problems) has
increased in recent years, but many conceptual and method~
Ological questions remain to be solved. The literature
which is of particular relevance will be reviewed in this

8

 

 

 

 

 

 

9

chapter. The general areas to be considered are as follows:
(1) the classification of academic data, (2) methods of edu-
cational cost analysis, (3) computer programming and educa—

tional costs, and (4) cost-utility analysis in education.

Classification p£_Academic Data

A cost analysis has many aspects. Subsequent to the
statementof the problem, terms must be defined. That is,
before engaging in an analysis of resource allocations, the
economist must decide in what units the various inputs and
outputs of the educational process are to be measured. A
recent National Science Foundation study was designed to:

...devise and test systems of measuring and

reporting activities in colleges and univer—

sities so that such institutions would be

enabled to maintain records adequate both ‘

for their own purposes and for reporting to

the various agencies which stand in need of
this type of data.

 

1Systems for Measuring and Reporting the Resources
and Activities pf Colleges gpg_Universities, National Science
Foundation, NSF — 67-15 (Washington, D.C.: U.S. Government
Printing Office, July 1967), p. 5. Some other publications
in this area that have been widely used by various institutions
of higher learning over the past four decades are as follows:
(1) Edwin E. Stevens and Edward C. Elliott, Unit Costs pf
Higher Education (New York: Macmillan and Company, 1925);
(2) National Committee on Standard Reports for Institutions
of Higher Education, Financial Reports Egg Colleges 32g
Universities (Chicago: University of Chicago Press, 1935);
(3) National Committee on the Preparation of a Manual on
College and University Business Administration, College gpg
University Business Administration (Washington, D.C.: Center

 

 

 

10

The NSF researchers recognized that the activities
of academic personnel have traditionally been categorized in
terms of teaching, research, and public and professional
activities. Additional categories sometimes included are
administration and student services. From their study of
basic personnel data items, however, several new categories
were established.

The new categories were concerned with the over—
lapping of two traditional categories (teaching and research),
and with creative activity in the arts and humanities as
opposed to creative activity in scientific research. Many
professors suggested a need for a category to cover research
activity when the research was part of the educational
process. When a professor is conducting a research project
with a graduate student he is engaged in both teaching and
research. To represent the role of the professor in this
type of research and teaching activity, the category of

”Teaching—Research” was established.

 

fpr Applied Research in Education, 1952 [Vol. I/ and 1955
[Vol. 13/);(4) California 32g Western Conference Cost apd
Statistical Study (Berkeley: University of California
Printing Department, 1960); and (5) American Association
of Collegiate Registrars and Admissions Officers, Handbook
pf Data and Definitions pp_Education (Chicago: University

 

 

of Chicago Press, 1962).

 

 

 

11

A separate category was also needed to cover
"creative activity” in non-scientific disciplines when such
activity could not be appropriately designated as research.
The production of a play is quite a different activity from
the clinical testing of a drug, and the time allocation
reports should reflect these differences. To fill this
need, the "Creative Activity in Art and Scholarship” cate—
gory was devised. Once this classification was established,
a category parallel to that of teaching-research was estab—
lished. The new category was labeled ”Teaching Through
Creative Art and Scholarship" and defined as follows: "That
kind of creative activity which is carried on with one or
more apprentices for whom this involvement is part of their
formal educational program."2

The study resulted in a list of ten major categories
which, taken collectively, represent the full professional
life of the academic—professional person. This list includes:
(1) teaching, (2) research, (3) teaching-research, (4) creative
activity in art and scholarship, (5) teaching through creative
activity in art and scholarship, (6) public service, (7)
administration, (8) formal personal education, (9) intra—
university activities, and (10) other extra—university

activities.

 

2Ibid., pp. 73—74.

 

 

 

 

 

 

 

 

12

While this set of categories is quite complete, an
Operational problem.exists. It would be very difficult to
generate enough interest among faculty members to cause them
to become acquainted with the categories, or to record the
allocation of their time, on a regular basis, among the
categories. Also, in general, as a group of data is sub—
divided to a greater extent, there is a tendency for those
using the data to place more reliance in its authenticity.
To the extent that the more precise classifications are
accurate, they are more helpful to decision makers, but it
must be remembered that the chance of classifying the alloca—
tion of one‘s time incorrectly increases as the number of

categories increases.

Methods g: Egg: Analysis

Costs can be expressed in many forms. Some of the
common units of presentation are cost per student credit
hour, cost per course taught, cost per academic program,
cost per full—time equivalent student, and expenditures
by department. In a thesis completed at Purdue University,3
a unique approach to educational costs was taken. The
product of higher education was considered to be unquantifi-

able. Therefore, rather than assigning costs directly to

 

3Harry Hamel Hirschl, Some Economic Considerations and
gpPr0cedure for 3 University Cost Study, M.S. Thesis (Lafayette:
Department of Economics, Purdue University, 1965).

 

 

 

 

 

 

 

01>. h..- (i it)

13

the product, they were assigned to a quantity that represents
the product. The quantity used in the study was the class,
defined as the meeting of students and teacher. The final
figure presented as the unit of comparison was the average
expense per student by academic level and field of study.
The total cost of offering each course was distributed over
the student body on the basis of the composition of the
class. For example, the number of sophomore students major—
ing in electrical engineering would be allocated 20 percent
of the total costs of a given class if ten out of the fifty
students in the class Were in this category. This cost is
derived for each category of student for each class. These
figures are then summed, and this figure divided by the num—
ber of students in the appropriate category. This average
expense per student minus the average fees collected per
student represent the average net cost per student in each
category to the State of Indiana.

One of the fundamental differences between the
Indiana study and the present thesis lies in the educational
product or service being measured. In the former study,
costs per student were calculated by level of study and
academic area. In the latter study, the total costs involved
in the process of degree production are considered to be

the relevant units of measurement. To carry out a cost

 

 

 

14

benefit analysis of several degree programs, the total costs
of each must be known. The Indiana study did not provide
the information needed for this type of analysis while the
present study does.

A recent U. S. Office of Education study4 considered
the costs and returns of only doctoral programs in four
academic disciplines. Separate rates of return were calcu-
lated for different employment possibilities open to bachelor
degree holders in the four areas and, on the assumption that
an individual's contribution to output is reflected by these
rates of return, they were used as "earnings foregone"
estimates, and included as opportunity costs in the total
cost of education figures.

The sample from which the cost data were obtained
was composed of eleven universities known to have varying
qualities of cost data and accounting records. Since inter—
institutional data were used and only doctoral programs were
considered, the general applicability of the conclusions is
limited. Also, even though it is one of the most impressive
of the recent studies in the economics of education, the

cost analysis section had some limitations. The costing

 

4 . .
Irene Butter, Economics pf Graduate Education: 53
Exploratory Study, U. S. Office of Education Cooperative
Research Project No. 2852 (Ann Arbor: Department of

Economics: University of Michigan, 1966).

 

 

 

 

 

 

15

procedure which was used implied that the cost per student

credit hour of all courses was equal.

 

The following costs were considered in the analysis:
(1) instructional costs consisting of graduate faculty
salaries, staff benefits, departmental supplies, equip-
ment, and clerical costs, (2) research costs, (3) costs of
physical facilities, (4) administrative costs, including
both general university and departmental administration,
(5) library costs, and (6) Opportunity costs. The total
costs were divided by the number of student credit hours
produced by each department to arrive at a cost per student
credit hour. The number of student credit hours in the course
taking phase of the academic program of each discipline was
multiplied by one cost per student credit hour figure for
each university and the research credit hours were multi—
plied by another. This method ignores the fact that a
relatively large class taught by a relatively low paid

professor will produce lower cost student credit hours than

 

a relatively small class with a relatively high-salaried
professor. Since only doctoral programs were considered,
the criticism is less valid than if the procedure were used
in the present study where degree programs of all levels
are analyzed. The deficiency does not exist in the present

study because, rather than determining an average cost for

 

 

 

16

course credit hours and another average cost for research
credit hours, the cost per credit hour was calculated for
each course taught in the College of Education, Michigan
State University, during the academic year 1967—68. The
total costs for the appropriate courses were then summed
to determine the degree cost of each student in the sample.
A more detailed account of the procedure will be presented
in Chapter Iv,

Butter found that the average costs of training
Ph.D. students in sociology and English were less than
one—half of the average costs of training doctoral students
in physics and zoology. The cost levels of physics and
zoology were quite close to each other, while English was
less than sociology. When the opportunity costs referred
to above were added, the relative cost positions changed:
the difference between zoology and physics increased, but
the difference between the average costs of the natural
sciences on the one hand, and of sociology and English on
the other, decreased. The changes in the relative cost
positions when opportunity costs were included resulted
primarily from the differences in the number of years
required to complete the doctorate in the four fields.

It was also found that at the 5 percent level no

significant differences existed in the total cost of the Ph.D.

 

 

17

between departments of the public and private universities
in each discipline. Economies of scale measured by the
number of graduate students enrolled in the department
appeared to exist in physics and sociology, but not in
English. The difference in theeconomies of scale observed
in the sciences and English is probably generated by the
larger equipment expenditures of the fixed cost variety
required in the sciences. As more students are added to

a given plant, capacity utilization increases and the costs
per student decrease. The faculty—student ratio was not a
statistically significant factor, but average faculty sala—
ries accounted for 70 percent and 91 percent of the variance
in average total costs in zoology and sociology, respec—
tively, when all other variables were held constant.

Average faculty salary played only a minor role in explain—
ing cost variations in physics. Analyses of variance indi-
cated that at the 5 percent level, the average costs of the
research phase in physics and zoology are significantly
higher than the correSponding costs in sociology and English.
No significant differences were found at the 5 percent level
in the cost of the research phase between departments in
public universities and the same departments in private
universities. The differences in the costs of the research

phase of the degree programs are generated primarily by the

 

 

 

 

18
varying laboratory and space requirements of the four
disciplines.

The California and Western Conference Cost and

 

Statistical Study,5 published in 1960, gave support to

 

many theories of educational costs which had either never
been tested or the evidence supporting them was very limited.
The data for the study were collected from ten colleges and
universities and included all persons who were paid from

an instructional budget. Expenditures were allocated to
three levels of instruction: (1) lower-division under—
graduate, (2) upper-division undergraduate, and (3) gradu—
ate. Total instructional costs within each department were
divided by the number of student credit hours produced by
that department to arrive at costs per student credit hour.
Therefore, in the sense that the data were not disaggregated
to the individual course level, the results suffer from the
same deficiency as those of the Butter study. Additionally,
since only instructional costs were considered, the useful—
ness of the results is restricted. As was indicated above,
an attempt has been made to remedy these deficiencies in the

present study.

 

5California and Western Conference Cost and Statis—
tical Study, op. cit.

 

 

 

19

Analysis of the results indicated (1) significant
variation in unit costs among institutions within subject
fields, (2) the unit costs of graduate instruction were
significantly higher than those of upper-level which was
higher than the costs of lower-level instruction, and (3)
high or low unit costs were not peculiar to specific sub—
ject fields, but were the result of a combination of fac—
tors which affect the costs of organized classes. The last
of the three findings is contrary to Butter's conclusion
that curriculum has an influence on the behavior of unit
costs. The results of the present study, to be reported
in Chapter V, support Butter's conclusion. A possible
explanation for the different results reported by the
California group is that they considered only instructional
costs. In the institutions studied in the California study,
the most important factor explaining variations in unit
costs is the ratio of students to staff in the particular
subject field. The effect of changes in the ratio on edu—
cational quality was not considered.

The researchers concluded that no generalized state—
ment could be made with regard to the effect of enrollment
changes on unit costs. Also, among the institutions studied,
it was found that high faculty salaries are not necessarily

associated with high costs per student. Other factors, such

 

20
as size of class, faculty assignment, and teaching expendi-
tures other than faculty salaries influenced costs per
student more than did the level of academic salaries. A
policy conclusion drawn from this finding was that it was
quite possible for an institution to raise its faculty
compensation without causing an increase in per student
costs. It was predicted that the increasing costs of
higher education will continue partially in response to the
broadening of curricula which is made necessary by scien—
tific and technological progress. Theoretically, unit
costs would be minimized if all students followed the same
curriculum, since only the minimum number of courses would
have to be offered. A policy conclusion to be drawn is
that the number of courses offered by any given university
subunit should be the minimum level necessary to achieve
institutional goals and keep pace with scientific and tech—

nological progress.

Computer Programming and Educational Costs

 

In making administrative decisions, university
officials should have at their disposal tools as s0phisti~
cated and precise as those used by their counterparts in
the business world. One of the most widely used recent

developments in this area is the simulation model.

 

 

 

 

 

21
Computers have been used for some time in decision making
in the business world, but their use in universities has
been largely restricted to payroll, registration, and other
simple data reduction activities. Within the last few years
several separate research projects have been conducted which
have attempted to apply simulation analysis to university
operations. Two of the most relevant studies will be
reviewed.

Models are simply abstractions from the real world
and, to the extent that they reflect reality, they can be
used to simulate the behavior of the real world. The model
becomes to the administrator what the laboratory is to the
engineer; he is able to test alternatives before making a
decision and anticipate problems rather than face unexpec—
ted crises. The analyst can vary the inputs of a system
and note the effects on cost and output prior to deciding
which of the systems is the most desirable. Obviously,
before these comparisons can be made, all of the costs,
alternative processes and output measures have to be worked

out. In this sense, the methodologies and conceptual frame—

 

works develOped in many of the recent simulation studies are
similar to those used in the present study.
One of the most complete studies in this area was

Sponsored by the National Science Foundation and carried out

 

 

 

22
by the Division of Engineering Research at Michigan State
University.6 The model developed by the research group was
a mathematical description of the way a university utilizes
its resources in production. The resources were categorized
as personnel, space, and equipment while the products were
identified as developed manpower, research, and public or
technical services. The purpose was to provide a basis for
evaluating alternative allocation policies. No attempt
was made to define the goals of higher education or to

determine optimum allocation policies.

6Herman Koenig, et. al., “A Systems Approach to
Higher Education," Interim Report No. 3, Project C—396,
National Science Foundation (East Lansing: Division of
Engineering Research, Michigan State University, 1966);
Rita Zemach, "A State—Space Model for Resource Allocation
in Higher Educationfi'Technical Report (East Lansing:
Division of Engineering Research, Michigan State University,
1967); and Herman Koenig and Martin Keeney, "A Prototype
Planning and Resource Allocation Program for Higher
Education,“ paper presented at the Symposium on the Opera-
tions Analysis of Education, U. S. Office of Education,
Washington, D.C., November 19—22, 1967. Some related
publications of a more general nature are: J. A. Kershaw
and R. N. McKean, Systems Analysis gpg Education, Memorandum
RM-2473—FF (Santa Monica, California: The Rand Corporation,
1959); Richard W. Judy and Jack B. Levine, §.§§E Tool for
Educational Agpinistrators, The Commission on the Financing
of Higher Education (Toronto: University of Toronto Press,

 

.—-—.——-——-—__

9f pg Urban School District (Philadelphia: Management
Science Center, University of Pennsylvania Press, 1967).

 

 

 

 

 

 

 

 

23

The model consisted of sets of equations which
described the relationship of resources to production and
the associated costs of production. The model was composed
of several sectors, each of which was related to a specific
operation of the university. The characteristics of each
sector were modeled independently, then the model of their
interrelationship was developed.

The input—output relationships of the model were
obtained from actual university data. Since some of the
variables, such as the imputed value of manpower output
were not directly measureable, the model could not be
validated by observation. It was assumed that if those
parameters, which depend on human behavior, accurately
reflected the collective behavior of students and adminis—
trators, the validity of the non—measurable values was
implied. Other parameters were based directly on university
records, and were valid to the extent the data base was
valid.

The data used in the cost analysis are of special
concern here. To arrive at the institutional costs for
any given quarter, it was necessary to know the total faculty
time devoted to each course and the total number of students,

as well as the salary of each faculty member. The final

 

 

 

 

24

figure presented was the instructional cost (i.e., faculty
salaries) per student credit hour by student field and level.

The major problem encountered in the cost analysis
portion of the study was in the defining of terms. For
example, the faculty time expenditure categories of instruc—
tion, research, and administration were not clearly defined,
so the data collected frOm the several departments were not
homogeneous. The researchers attempted to remove this
deficiency by making a series of recommendations with regard
to future data gathering procedures. They outlined a cen—
tralized and mechanized record system that would (1) supply
day—to-day operational data, (2) provide a data base for
model building, and (3) serve as a part of the general
university data base. The information would be stored on
magnetic tape and would be segmented into four subdivisions,
determined on the basis of type of data and frequency of use.
A central office would be in charge of all data gathering
activities to insure not only efficiency but also homogeneity.

7 also con—

A group of researchers at Tulane University
struCted a simulation model which, in many respects, was

similar to the NSF work at Michigan State University.

 

7Peter A. Fermin, Seymour 8. Goodman, Thomas E.

Henricks, and James J. Linn, University Cost Structure and
Behavior (New Orleans, La: Department of Economics, Tulane
University, 1967).

 

E
r

 

 

 

 

25

The Tulane study began with a careful examination
of the nature of a university, its goals and objectives,
and the relationship of these goals and objectives to the
behavior of costs. Using data from several unidentified
public and private institutions, historical cost behavior
was analyzed. Relationships between expense categories
and various university functions such as library, food
services, housing, student activities, and physical plant

were studied.

On the basis of empirical data, a model was construc—

ted to simulate the behavior of university costs. The
basic framework of the model was a.seven part conception
of the following university functions: (1) teaching, (2)
administration, (3) research, (4) professional activities,
(5) community service, (6) supporting activities, and (7)
student activities. The simulation model facilitated com-
parative analyses of interdepartmental costs and was used
to predict future costs. On the basis of five years of
historical data, the model would predict cost levels and

behavior for the four subsequent years.

Some of the important and obvious conclusions reached

by the Tulane researchers were: (1) enrollment is the best
available predictor of the aggregate level of university

costs, (2) the most important element of university costs

 

 

 

 

 

26
is salaries. Salary payments, however, represent different
proportions of total departmental expenditures, and this
proportion varies with the discipline which the department
represents. In those departments which require few physical
facilities or laboratories, salaries are the dominant——
almost exclusive--expenditure. Alternatively, in the
physical sciences salary payments, obviously, constitute a

smaller proportion of total instructional expenses; (3) the

 

assumptions that the unit cost of instruction increases with
the level of instruction in the undergraduate program, and
that unit costs of instructing graduate students are higher
than the units of instructing undergraduates, were confirmed
by the study. This simply reflects the patterns of academic
effort which typically call for smaller section sizes and

higher ranking professors for higher level courses.

Cost Utility Analysis £3 Education

 

As was pointed out in the introduction, the results
of the present study are to be used as part of the data base
for a cost/utility analysis of the College of Education,
Michigan State University. Most of the recent work in the

cost/utility analysis area has been related to government

 

 

 

 

 

27

activities, particularly the Defense Department.8 The
basic principles, however, apply to analyses of educational
institutions as well.

Cost/utility analysis refers to the systematic
examination of alternative courses of action which might
be taken to achieve specified goals for a given time
period. Many factors must be considered in evaluating the

alternatives, but two are of special importance: (1) the

economic costs incurred in providing each of the alterna-
tives, and (2) the benefits or utility available from each
alternative. It is assumed in the present study that the
several degree programs offered by the College of Education
are alternative methods of achieving stated college objec—
tives. It is the purpose of the study to calculate the

amount of economic resources consumed in the process of

8Charles J. Hitch and Roland McKean, The Economics

2: Defense £p_ppp Nuclear Agp (Cambridge: Harvard University
Press, 1960); RolanélMcKean, Efficiency ip_Government Through
Systems Analysis (New York: John Wiley and Sons, 1958);
David Novick, Program Budgeting ;p_ppg Department p: Defense,
RM—4210-RC (Santa Monica, Cal: The Rand Corporation, 1964);
Arthur Smithies, A_Conceptua1 Framework Egg pp; Program
Budget, RM—4271-RC (Santa Monica, Cal: The Rand Corporation,
1964)7J. String, A Model fpp PrOjecting Costs pg Space
Exploration, P—3119 (Santa Monica, Cal.: The Rand Corpora—
tion, 1965); J.D. McCullough, Cost Analysis jg; Planning
Programming—Budgeting—Cost—Benefit Studies, P—3479 (Santa
Monica, Cal.: The Rand Corporation, 1966).

 

 

 

   

28

providing each alternative so the administrators and faculty
members of the College will be better equipped to make intel—
ligent resource allocation decisions. The primary purpose
of cost/utility analysis is not to make the decision, but
to improve the judgment and intuition of the decision makers.
Most problems involve political, sociological and psycho—
logical considerations that cannot be measured and included
in the analysis in quantitative form. Therefore, human
judgment is still an important aspect of the decision—making
process.

Fisher9 lists a series of important guidelines to
be followed when carrying out a cost/utility analysis. The
most important is the prOper structuring of the problem and
design of the analysis. It is in the design stage that most
cost/utility studies either become hOpeless or cross the
most crucial barrier to success. The problem must be struc—
tured so the right questions are being asked and only the
relevant aspects of the environment are considered in the
analysis, One group of costs which have been either omitted
entirely or incorrectly measured in most previous educational

cost studies is the one pertaining to space and physical

 

9

G. H. Fisher, The Role g: Cost/Utility Analysis i2
Program Budgeting, RM—4279—RC (Santa Monica, Cal.: The
Rand Corporation, pp. 8—16, 1964).

 

 

 

 

 

 

 

 

29
facilities. Some researchers, apparently assuming that
capital account expenditures are sunk and should not be
considered when making allocation decisions, have implicitly
assumed the cost of building space to be zero by analyzing
only operating costs. Others, realizing that the construc—
tion of physical facilities consumes resources, have amortized
construction costs over a given number of years. Neither
of these methods is acceptable in an economic analysis since
opportunity costs are not considered. That is, the relevant
costs of a given building are those incurred as a result of
not devoting the space to alternative uses. The method
used to handle these problems in the present study is dis—
cussed in Chapters III and IV.

Building the model is another important step and,
again, Fisher emphasizes that only the most relevant data
be included. As the amount of data considered increases,
the model becomes more unmanageable. The fundamental
purposes of the model are: (1) to develop a meaningful
set of relations among objectives, (2) to develop alterna—
tive methods of arriving at those objectives, (3) to esti—
mate the costs of the alternatives, and (4) to estimate
the utility functions of the alternatives. Finally, there

is the testing of the validity of the model which is quite

 

 

 

3O
often a difficult task. Fisher suggests10 the analyst should
attempt to answer whether: (1) the model describes the
known facts and situations reasonably well, (2) when the
principle parameters involved are varied, the results remain
consistent and plausible, (3) the model can handle special
cases where there is already some indication as to what the
outcome should be, and (4) it can assign causes to known

effects.

M

10
Ibid., pp. 14-15.

 

 

 

 

 

 

CHAPTER III

ECONOMIC THEORY AND EDUCATIONAL COSTS

Educational Resource Allocation

The efficient allocation of scarce resources is one
of the central problems of microeconomics. As Robbins has
written, microeconomics "...is concerned with that aspect
of behavior which arises from the scarcity of means to

"1 If the attainment of one set of

achieve given ends.
ends involves the sacrifice of others, the problem has an
economic aspect, an opportunity cost element. Clearly,
then, the allocation of educational resources is a problem
which deserves the attention of economists.

Resources allocation within educational institutions
is a unique problem because, unlike business firms in the
private sector, there are no built in mechanisms which lead

to efficiency. In universities, for example, no profit

motive exists and promotions, salary increases, desirable

 

1Lionel Robbins, The Nature and Significance pfi
Economic Science, 2nd Edition (London: Macmillan and
Company, 1952).

 

31

 

 

 

 

 

 

 

32
appointments, and prestige do not depend on the accumulation
of profits. In short, the tendency of inefficient firms to

be forced out of the market simply is not a characteristic

of the state— —supported higher education industry in the

United States.» This characteristic makes the existence of

non—market efficiency criteria all the more important.

Efficient Resource Use

 

The term efficiency as used in this thesis refers
to the situation in which the production of one output
cannot be increased without decreasing the production of

another output, given the size of the budget. In other

 

words, it is impossible to increase one output without either
increasing the quantity of inputs or decreasing an alterna-
tive output. Maximizing output given the budget constraint
is equivalent to minimizing cost given the level of output,
if the size of either the gain or the cost is the same in
the two methods. The former analysis was chosen for this
study because the problem facing the College of Education
Iis to maximize educational services given the constraint of
the annual budget. Either the quantity of educational
services given quality, or the quality of educational
services given quantity, can be maximized in this case,

but not in both. Similarly, it is impossible to simultane—

ously maximize gain and minimize cost. In comparing two

 

 

33
courses of action, X and Y, alternative X might produce
a higher output at a lower cost than alternative Y, but
this will not hold true when course of action X is compared
with all other alternatives. Maximum gain is infinity and
minimum cost is zero, a combination that is not attainable.
To reach a specified goal, many alternatives may exist,
each of them requiring resources. Since the resources are
limited and the goals and alternatives are not, a choice
mustbe made.

Budget allocation under constrained choice may be
viewed as the process of choosing methods for channeling
limited resources into alternative areas of use. In the
process of funding programs which will lead to the attain—
ment of long-run institutional objectives, the decision
maker is faced with the situation in which there are more
competing demands for resources than there are resources
available. Classical economic theory provides a framework
for making such a choice: under competitive conditions,
market processes are adjusted by the constrained choices
of consumers.

Figure l is a graphical example of the analytical
process in which the resources of a university would be
distributed under conditions of constrained choice. Each

radial line represents a different program area and the

 

 

 

 

 

D I: D a D =4 Total avanlabb resources
A

l
g } = Funding of manor program areas

Figure l. Iterations in the Program Budgeting Proaess

Source: Harry Williams, Planning for Effective Resource
Allocation £p_Universities (Washington, D.C.z American
Council on Education, 1967). p. 5.

 

 

 

 

 

 

 

35

 

length of the line segments within the closed figures
represents the level of funding allocated for the particu—
lar program. The areas enclosed by the three sets of lines
in this example are constant, representing a fixed quantity
of resources. Therefore, increasing the resources allocated
to one program (moving out along one of the radial lines),
decreases the resources available for other program areas.
Alternatively, moving toward the center on one of the radial
lines releases resources for use in other areas.

To make an intelligent selection, the relative
costs of the alternative courses of action must be known.
The real cost of any alternative is whatever must be
foregone to adopt that alternative. The cost is the
sacrificed alternative opportunity; therefore, the sacri—
ficed alternatives may be called the "opportunity costs"
of the chosen course of action.

The application of this concept to education can
be demonstrated quite clearly by the use of indifference
curve analysis. Assume that a certain college goal or
objective can be accomplished by training and graduating
a specified number of students of a given quality on the
B.A. level in two curriculum areas: Area A and Area B.
The problem facing the decision makers is to determine

how resources should be allocated between these two

 

 

 

 

 

36

programs. A production possibility curve can be construc—

ted representing the maximum number of students who can be
trained in Area A and the maximum number that can be trained

in Area B, given the budget constraint. The X intercept rep—
resents the number of students who could be trained if all
resources were devoted to Area A. A corresponding relation-
ship exists for the Y intercept and Area B students. Any
point on the curve that connects these two points is efficient
in the sense that no increase in the output of students in one
area can be realized unless either the output of students in
the other area is decreased or the input base is expanded.
Any points lying
below and to the
left of the produc-

tion possibility

Area B

curve are obviously
not efficient, given
the existing

budget, but are

feasible. That

Number of Students

is, they are at

attainable. Any

 

 

Number of Students Area A point above and
Figure 2. Production Possibility Curve to the right 0f

the curve is

 

 

 

37

infeasible or not attainable. The locus of efficient points,
therefore, is the boundary between feasible and infeasible
points.

The concept of opportunity cost is quite apparent
in this example. The real cost of training X number of
students in Area A is the sacrifice that must be made in
the training of students in Area B. The gains that could

have been obtained by using the resources in Area B are

what have to be given up or sacrificed when the resources
are devoted to Area A.

Any point on the production possibility curve
represents technical efficiency. The curve is a locus of
efficient alternatives, but technical efficiency is not
a sufficient condition for reaching an economic optimum.
At the one extreme there will be no students graduated
in Area A, while at the other extreme there will be
no students graduated in Area B. To determine which of
these extremes, or combination of students from the two
areas, will be chosen the preferences of the decision ,
makers (or those to whom the decision makers are answer—
able) must be known.

The course of action which is chosen should maxi—
mize “quantities" such as the satisfaction of an individual,

the profits of a firm, the well—being of a group, or the

 

 

 

38
educational services of a school. In education, the goals
or objectives are usually defined by answering questions
such as what knowledge and skills should be develOped, and
when, where, how, by whom, and for whom. In other words,
in a given period of time, what kind of education should
be offered for how many students. In the case of the
example cited above, after these questions have been
answered, various combinations of students in the two areas
that will be equally acceptable to the decision makers
are determined and plotted on a graph. This locus of
points is an indifference curve.

Any combination of the two outputs on a given
curve represents equal utility, so there is indifference
as to which point is chosen. The slopes of the indiffer—
ence curves indicate the rate at which the decision
makers are willing to trade one output for another. The
more of one output that is given up, the more valuable it
becomes, and more of the other good is needed to substitute
for one unit of it. Two assumptions underlying indiffer—
ence theory are (l) the consumer finds both commodities
desirable (this ensures a negative slope to the curves and,
as between two indifference curves, ensures the higher one
is preferred because it contains as much X and more Y, or

as much Y and more X), and (2) the commodities are

 

 

 

Area B

Number of Students

39
continuously divisible (this assumption ensures that the
curves will be continuous and not a series of discrete
points).2

An infinite number of indifference curves will
theoretically exist in any graphical space but only one
point of one curve will be tangent to the production
possibility curve, assuming convexity to the origin over
the relevant ranges of the whole set of indifference curves,
and concavity to the origin over the relevant range of the
production possibility curve. The point of tangency between
the two curves
is the optimum
point, and is
the combination
that will be

b chosen.

 

III

2George J.
Stigler, The
Theory 2f Price
I (New York: The
MacMillan Company,
1966), pp. 50—51.

II

 

 

 

a1
Number of Students Area A
Figure 3. Optimal Allocation of Resources.

 

 

 

 

 

In the case of Figure 3, the optimum combination

is represented by point A (al students in Area A and b1
students in Area B). As indicated above, the equilibrium
point must be in a feasible area so all indifference

curves above II are irrelevant given the existing produc—
tion constraint. No indifference curve below II would be
chosen, such as Curve I which crosses the production
possibility curve at point B, because by moving toward
point A a higher level of utility is achieved. That is,

by moving on the production possibility curve toward point
A, positions on higher level indifference curves are
attained. At the point of tangency, the marginal rate

of substitution (the rate at which the decision makers

Egg willing to substitute A for B) is equal to the marginal
rate of transformation (the rate at which they ggfl_substi—
tute A for B). Unless this point is reached, it is possible
to change the allocation of resources so as to achieve a
higher level of utility.

Indifference curve analysis is helpful in concep—

 

tualizing the process of determining the amounts of each
of two products to be produced. The isoquant approach

to production theory is helpful in conceptualizing the

 

process of determining what combination of resources will

produce a given output in the most efficient manner.

 

 

 

 

 

 

Resource B

41

An isoquant is a locus of points representing
different combinations of two inputs with which a given
amount of product can be produced. At each point on
Isoquant I in Figure 4 total product is the same, just
as on a given indifference curve total utility is the
same. At point X, al units of Resource A and b1 units
of Resource B are required to produce the output. The
slope of the isoquant between any two of its points is
equal to the ratio of the marginal products of A and B.

Isocost lines (such as CC, DD, and BE in Figure 4)
show the various combinations of inputs that can be pur-

chased for a
specific outlay,
y given the prices
of the inputs.
If the level

of output to be

 

produced has been
determined, the
problem is to com-
bine resources in

the most efficient

 

 

 

a E D C
Resource A
Figure 4. Isoquant and Set of Three
Isocost Lines.

manner so as to

 

 

 

 

 

42

minimize the cost of producing the output. The problem
can be solved graphically by the isoquant—isocost approach.
The cost level represented by BE in Figure 4 is not feasible
because output level I cannot be produced by any combination
of inputs available for this outlay. Cost level CC is
possible but will not be chosen because by moving from
either Point Y or Point Z to Point X, the same level of
output can be obtained at a lower cost. The optimum
combination of resources is given by the point of tangency
between the isocost curve and the isoquant. At this point,
the marginal rate of technical substitution of A for B
equals the ratio of the price of A to the price of B.
That is, the last dollar spent on one input yields the same
marginal product as the last dollar spent on the other
input.

Since appropriations for productive resources
(faculty salaries, supplies and services, and equipment)
in institutional subunits of Michigan State University
cannot be shifted from one account to another, the appli—
cability of this analysis in the short run is limited.
However, to the extent that budget officials allow changes
at the beginning of each fiscal year in the proportion of the
total budget accounted for by the various accounts, this

analysis is valid for long run resource allocation decisions.

 

 

 

 

43

Assume a given number of students can be presented
a certain amount of academic material by any one of several
combinations of faculty members and computers. An isoquant
can be constructed reflecting these combinations, and an
isocost curve can be drawn indicating the relative costs of
these factors of production. The point at which these two
curves are tangent represents that combination of faculty
members and computers which can present the material to the
students in the most efficient or least-cost manner.
Similar problems can be handled involving the trade—off
values between other sets of factors of production such
as faculty members and graduate assistants.

The methods used in Chapter IV to determine the
costs of degree programs and the implications drawn in
Chapter VI are based on the theoretical concepts outlined

in this Chapter.

 

 

 

 

CHAPTER IV

DERIVATION OF EDUCATIONAL DEGREE COSTS

The justification for an economist devoting his
efforts to educational resource allocation problems was
established in the last chapter. In order to make this
type of analysis, the costs of the various educational
programs must be determined. Being a part of the overall
economic problem, therefore, the development of a method
of costing educational programs is also an area germane
to economic research.

The initial problem is to determine what costs are
to be included in the analysis, and the units in which the

costs are to be presented.

Qg§5§_§g be Included

All costs — both direct and indirect — that are
incurred at any point in time as a result of implementing
a given course of action are to be included in the analysis.

If a cost will be incurred at some point in the future as

44

 

 

 

 

 

 

45
a result of adopting an alternative or course of action,
it must be considered.

Some assets, such as a classroom building, are

 

likely to be inherited from the past. These are sunk
costs and are not relevant in comparisons of alternative
methods, of accomplishing objectives, unless they have
value in other present or future uses. That is, the_

use of these assets might involve opportunity costs, and
make it necessary to forego opportunities of using them

to reach other objectives. For example, the building
space that would be used for classrooms in one plan might
be used in another plan as storage space. If this is the
case, the net value of the space for storage is an oppor—
tunity cost that should be included in the costs of the
program requiring the space for classrooms. The essential
point is that the value of the Space as classrooms is not
related to the historical construction cost of the build-
ing. The only costs and benefits of interest to the
economic analyst in comparing alternatives are future
costs and benefits. As was implied above, this assumes
that the opportunity costs associated with using inherited

assets are included in the "future costs" category.

 

 

 

 

 

46

 

Measurement pf Costs

 

If the decision makers are to determine policies
which achieve a certain objective at minimum cost, they
must consider the costs that provide the real constraint.
For example, if only one input is the real constraint,
the costs of all alternative courses of action should be
expressed in terms of that one input. If several individual
inputs are limited, costs should be expressed in terms of
those inputs. If there is a general monetary constraint
with no limits on the various inputs, costs should be
expressed in dollars. Dollar costs indicate what must be
given up in order to adopt a particular policy. The
prices of different items show the rates at which they
can be substituted for one another. Admittedly, the dollar
costs measure real sacrifices accurately only to the extent
that they accurately reflect the relative scarcity of
resources. There is, however, no close substitute for
the use of dollar costs in this study. Costs in terms of
professorial expertise and numbers of secretaries could
be very misleading. To say that a BA degree in one area
costs so many professors, secretaries, and equipment does
not say how these resources can be traded off to produce

an MA in the same field. Expressing the relative values

 

47

in terms of dollars facilitates better comparisons, there-
fore, aids in planning future trade—offs.

Another reason for using dollars as the basic
unit of measurement in this study is that the annual
college budget is expressed in dollar terms; also, no
significant inelasticities exist in educational resource
markets. As was pointed out above, one exception to this
might be the existence of tenured faculty members in an
academic area or field of study which is to be dropped

from the College program.

Determininngducational Costs

 

The goal of this study is to determine and compare
the costs (and the factors that affect them) of programs
that are already in operation rather than programs that
are in the planning stage of development. This reduces
the element of uncertainty in the figures which are derived,
since they are based on experience, not judgments of what
might happen. The research methods used are the same,
however, whether the analysis is of the planning variety
or of the re—evaluation variety.

The total costs incurred in the production of a
series of degree programs are the ultimate figures to be

derived. Since the purpose of the study is to provide a

 

 

 

 

 

48

decision making tool for the administrators of a college
with a fixed resource base, only costs internal to the
college will be considered. Other costs, such as those
incurred by the university administration and foregone
student earnings, are parts of the total social cost of
educating the students, but should have no direct effect
on resource allocation within the college. These costs
should enter the analysis at higher decision—making levels
such as the Board of Trustees and the State Legislature.

It is assumed throughout this study that no College
of Education student credit hours were produced on a con—
tributed basis, that is, taught by a professor who was
not paid by the College of Education for his services.
An example of this situation is a university administrator
teaching a course for the Department of Administration
and Higher Education but not receiving a salary for
teaching. This also applies to the direction of doctoral
dissertation research where the advisor might actually
be contributing his time because it is on an overload
basis. The results of the study, therefore, will indicate
the costs that would be incurred by the College of Education
if it had to pay for all courses taught with a College of

Education title.

 

 

 

 

 

 

49

 

Each of the departments in the College of Education
offers a degree program on one or more of four different
levels: (1) bachelors, (2) masters, (3) educational
specialist, and (4) doctorate. In some departments more
than one program of study is offered at each level; the
Department of Secondary Education and Curriculum offers
programs in both Secondary Education and Curriculum.
Eighteen of these programs (three on the bachelors level,

ten on the masters level, and five on the doctoral level)

 

were selected for this study on the basis of the availa—
bility of transcripts. A sample of ten recent graduates
in each area was selected from a stratified population
on a systematic basis.

The cost of each individual degree was determined
by summing the following component categories: (1) instruc—
tional costs, (2) faculty support costs, (3) research costs,
(4) space costs and (5) administrative costs. The deriva-

tion of the costs in each of these categories is discussed

 

below.

Instructional Costs
The instructional costs of each course offered by
the College of Education during the academic year 1967-68

were determined by dividing the appropriate faculty

 

 

 

 

 

SO

salaries by twelve under the assumption that each

faculty member receives four (4) assignments per academic
quarter, and teaching one course is equivalent to one
assignment.l This quotient was divided by the number of
students in the class to arrive at the cost per student.
The class size and faculty salary figures were based on
the academic year 1967-68 since the data were available
for this period, and the assumption was that variations
over time are negligible. The class size, faculty salary,
and instructional cost per student credit hour figures

for each course taught in the College of Education (exclud—
ing the Department of Health, Physical Education, and
Recreation) during the 1967—68 academic year are presented
in Appendix A. If the course was taught more than once
during this period, the class sizes and professorial
salaries are averages. Since identifying the course
numbers could reveal the salaries of individual faculty
members, the courses are coded. The costs per student
for the appropriate courses were summed to arrive at the
total instructional cost for the degree. Algebraically,
instructional costs for each degree were derived as in

equation (1):

 

1The salaries of those faculty members who are
employed on a twelve—month basis were adjusted to a ten-
month base.

 

 

51
(1) n
1c . Z (75%;?)
i = 1
Where: IC = Instructional costs

FS = Faculty salary

8 Number of students in the course

N = Number of College of Education courses
in program of study

 

Faculty Support Costs
The costs of supporting services, such as equipment,
secretarial, office space, and supplies and services (see

Table l) were aggregated for each department and allocated

Table 1. Secretary—Faculty Ratios (Sec/Fac), Average Annual
Professorial and Secretarial Equipment Costs (Eq/Prof and
Eq/Sec), Office Space Allocations, Number of Full-Time Equi-
valent General Fund Faculty Members (FTEF). Supplies and
Services Expenditures Per Full—Time Equivalent General Fund
Faculty Member (SS/FTEF), and Secretarial Salaries Per Full-
Time Equivalent Faculty Member (Sec Sal/FTEF) by Department,
College of Education, Academic Year 1967-68

 

 

 

Eq/ Eq/ Office 55/ Sec Sal/
Department Sec/ Prof* Sec* Space FTEF FTEF FTEF
Fac i§l_ (§) 5Q.Ft (S) (S)
Counseling .3 470 742 3911 25 112 1638
Administration .5 470 742 3142 16 112 2952
Secondary .2 470 742 3902 38 112 961
Elementary .16 470 742 3410 41 112 804

 

*Communication with members of the College of Education Office

of Administrative services indicated the following average
equipment allocation per professor: l desk - $155; 2 chairs —
$95; 2 files - $114; 2 bookcases - $106. The average equipment
allocation per secretary is as follows: 1 desk — $160; 1 chair _
$50; 1 typewriter — $430; 1 file - $57; and l stencil file — $45.
These costs were amortized over five years.

Source: Office of the Dean and Office of Administrative Services,
College of Education, Michigan State University, January 1969.

 

52

 

among the full—time equivalent faculty members in each
department. These faculty support figures were converted
to a cost per student per course basis and summed to arrive
at a supporting services cost per degree by the following
method.

Secretarial equipment and salary expenditures were
multiplied by the secretary—faculty ratio in each depart—
ment to determine what proportion should be allocated to
each professor.2 The number of square feet of building
space allowed each department was divided by the number
of full-time equivalent general fund faculty members to
arrive at a space allocation per professor figure. This
figure was multiplied by $5, the estimated rental cost per
square foot to determine the costs of providing office
space per professor. Since the variation in supplies and
services expenditures among departments is negligible,
the total supplies and services costs of the College were
divided by the number of full—time equivalent general fund

faculty members in the College to provide a supplies and

 

services cost figure per faculty member. The assumption
is that all professors in a given department are provided

with equal amounts of equipment, secretarial services,

 

2The secretary—faculty ratio for each department
was determined by dividing the number of departmental sec—
retaries by the number of departmental full-time equivalent
general fund faculty members.

 

I‘—

 

53

 

office space, and supplies and services. Also, continuing
to operate under the assumption that each professor receives
four assignments during each of the three academic quarters,
one-twelfth of each of the above figures was divided by the
number of students in the course under consideration.

Algebraically, this process is described in equation (2):

 

n
(2) PE (SE)(S£F) + (Sa1)(s§F)
FSC: Z (12)(S) (12)(S) (12)(S)
i = 1
(DOS + DFTEGFF)($5) +
(12)(S)
ss -
i (CFTEGFF) ] * E12)(sfl
L
Where: FSC = Faculty Support Costs

PE = Average annual equipment costs
per professor
S = Number of students in the course
SE = Average annual equipment costs
per secretary
S/F = Secretary—faculty ratio
DOS = Departmental office space allocation
(square feet)
DFTEGFF = Number of departmental full—time
equivalent general fund faculty
members
Annual College supplies and
services expenditures
CFTEGFF = Number of College full—time equiva—
, lent general fund faculty members
Sal = Average departmental secretary
salaries
n = Number of College of Education
courses in program of study

SS

 

 

 

 

 

54

Research ggsgs

The costs of the research phase of the doctoral
programs were derived by dividing one—twelfth of the
average annual faculty salary in the appropriate department
by four, under the assumption that the direction of four
completed dissertations during any academic quarter is
equivalent to the teaching of one course. In equation

form the process is as follows:

FS

RC = (12) (4)

Where: RC = Research costs of degree
FS = Annual faculty salary

The average departmental salary figures used in the calcu—
lations were as follows: (1) Administration and Higher
Education - $11,141, (2) Counseling, Personnel Services
and Educational Psychology — $12,007, (3) Elementary and
Special Education — $11,675, and (4) Secondary Education
and Curriculum — $11,231. These averages were derived

from the six highest academic ranks listed in Table 2.

Space Costs

The determination of classroom space costs is a
case where the opportunity cost principle is quite apparent.
The historical costs of classroom buildings have no rele—

vance. The costs of the space should be considered only

 

 

 

 

55

 

 

 

Table 2. Average Ten—Month Salary Figures, by Department
and Rank, College of Education, Michigan State University,
1967—68
Counseling,
Administration Personnel Elementary Secondary
Rank and Higher Services & and Education
Education Educational Special and
Psychology Education Curriculum
Professor 16,498 15,914 14,858 14,800
Associate
Professor 12,596 13,175 12,193 12,088
Assistant
Professor 9,920 10,540 11,593 11,155
Instructor 5,550 —- 8,533 8,516
Specialist -- -— 11,200 9,600
Lecturer —- 8,400 -- —-
Assistant
Instructor 4,200 4,305 4,165 4,200
Graduate
Assistant 3,150 2,889 2,873 3,129
Clerical 4,650 4,084 3,986 4,093
Source: Office of the Dean, College of Education, Michigan

State University, January 1969

to the extent that the space has value in alternative uses.

The annual rental values of comparable space in the Lansing—

East Lansing area is the closest approximation of the econ—

omic costs incurred in the use of space.

On the basis of

discussions with members of the Michigan State University

 

56

Office of Space Utilization, it was assumed that the average
size of a "classroom student station” was 13 square feet,
which would rent commercially at $5 per square foot. It
was further assumed that the average student station pro-
vides 1200 hours of service per year (30 hours per week
for forty weeks at 100 percent of capacity). The normal
three hour course will consume 30 hours per term or 2.5
percent of the annual space service. Therefore, $1.62
was charged as a space cost to each student in each three
hour course taught in a classroom. To arrive at space
costs (SC) per degree, this figure was multiplied by the

number of three hour courses taken by the student.

Administrative Costs

College administrative costs were allocated to
the various courses on the basis of student credit hour
production. All salaries and other expenses incurred by
the three offices were included in the final cost figures
and are presented in Table 3. The expenses of the Dean's
Office were allocated over all student credit hours pro—
duced by the College, while the expenses of the Graduate
Student Affairs Office and the Undergraduate Student Affairs
Office were charged off to graduate and undergraduate

Students, respectively, on the basis of student credit

 

 

57

Table 3. Administrative Expenses: Undergraduate Student
Affairs Office (UGSAO), Graduate Student Affairs Office
(GSAO), and Dean's Office; Student Credit Hours: Graduate,
Undergraduate, and Total; Administrative Costs per Student
Credit Hour: Graduate, Undergraduate, Overall; College of
Education, Michigan State University, '
Academic Year 1967—68

 

 

Office Total Expenses Student Credit Hours Cost/SCH
UGSAO $ 67,660 130,920 $ .51
GSAO 42,029 36,743 1.14
Dean‘s Office 149,186 167,663 .89

 

Source: Office of the Dean, College of Education, Michigan
State University, January 1959.

hours consumed. This method of deriving administrative costs

for a given degree can be represented algebraically as follows:

 

 

ACG = GSAO expenses + Dean's expenses X SCH
Grad. SCH C of E Total SCH

ACU = UGSAO expenses + Dean s expenses X SCH
UG SCH C of E Total SCH

Where: ACG = Administrative costs (Graduate students)

AC = Administrative costs (Undergraduate students)
GSAO expenses = Total academic year expenses incurred by the
Graduate Student Affairs Office
Grad. SCH = Total number of graduate student credit hours
produced during academic year
Dean's expenses = Total expenses incurred by Dean's Office

during academic year
C of E Total SCH = Total student credit hours produced by
College of Education during academic year
UGSAO expenses = Total academic year expenses incurred by the
Undergraduate Student Affairs Office
UGSCH = Total number of undergraduate student credit
hours produced during academic year
SCH = College of Education student credit hours
in student's program

 

58
Most degree candidates take courses
College of Education. No cost figures were
these costs were external to the College of

Therefore, the total cost to the College of

outside the
imputed since
Education.

Education for

any given degree is the sum of the above five categories,

that is: TC = IC + FSC + RC + SC + AC.

Where: TC = Total Degree Costs
IC = Instructional Costs

FSC = Faculty Support Costs
RC = Research Costs
SC = Space Costs

AC = Administrative Costs

The cost calculation method presented in this

Chapter was used to determine the cost of each of the

programs in the sample (Appendix B). These

degree costs

were used as dependent variables in the regression analysis

which is discussed in the next chapter.

 

CHAPTER V

STATISTICAL ANALYSIS

The method used to derive the costs of the degree
programs in the College of Education was presented in the
last Chapter. In this Chapter, the total costs (and com—
ponent costs) of the programs are presented along with

the statistical analysis used to test the hypothesis.

College pf_Education Degree Costs

To say that, on the average, the cost of degree
programs offered by the College of Education is §_number
of dollars would be highly misleading and meaningless due
to the wide variety of degree program offerings, and
variations in their costs. The programs must be disag—
gregated with respect to level of study if the cost figures
are to have any significance, and further subdivided by
curriculum to achieve a greater level of precision.

Table 4 presents the average total cost of degree

programs on the three levels under consideration.

59

 

60

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61

As might be expected, the total cost of the doctorate
is the highest of the three programs, being over twice the
cost of either of the other two degree categories. The
percentage of total costs accounted for by instruction
drops by about 17 percent (13 or 14 percentage points) when
moving from the B.A. and M.A. levels to the Ph.D. level
(from 78 percent and 77 percent for the B.A. and M.A.,
respectively, to 64 percent for the Ph.D.).

The change in percentage accounted for by instruc—
tion is generated primarily by the addition of the research
costs category which, on the doctoral level, accounts for
17 percent. The Faculty Support Costs category appears to
be an increasingly important cost component as the level
of study increases. The trend in faculty support costs
is largely the result of the typically smaller class size
on the graduate level where the support costs per faculty
member for the course under consideration are allocated
over a smaller number of students. There is an inverse
relation between the level of study and the percentage of
total costs accounted for by administrative costs. Since
administrative costs were calculated on the basis of the
number of student credit hours in the degree program, the
relation between administrative expenses and the proportion

of total costs is explained by the larger number of College

 

62
of Education student credit hours in the typical under-
graduate program.

Within each program level, variations in cost
exist (see Table 5). On the B.A. level, the total cost
of a degree in Special Education, on the average, is
substantially higher than either of the other two
curricula. Two degree candidate requirements in the
Special Education program explain the high costs: (1) a
series of high—cost courses, and (2) 15 credit hours of
in-field student teaching over the normal certification
requirement. Total costs of the individual degrees among
the several curricula on the M.A. level range from $527
(Agricultural Education) to $805 (College Personnel Work).
On the doctoral level, the range of costs of the various
degree programs is $326 (Educational Administration —

$1,561 to Curriculum - $1,235).

Regression Analysis

 

To determine if the cost differences among the
degree programs on the three levels and the several curricula
are statistically significant, and to isolate the factors
that explain the variations, the data were subjected to
step—wise multivariate regression analysis. The use of

this technique in making statistical inferences implies

 

 

 

 

 

 

 

63

 

 

 

 

 

 

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64

the following assumptions with regard to the residuals:1
(1) they are clustered around a rectilinear (not curved)
plane, (2) they are independent of each other, (3) they
are uniform in their scatter and, for the small samples,
(4) they are normally distributed.2 A simple method of
checking the fulfillment of these assumptions is to plot
the residuals against the variables. Three variables
(Number of College of Education Student Credit Hours,
Average Class Size, and Total Degree Costs) were plotted
against the residuals. Observation of Table 6 and Figures
4, 5, and 6 indicates approximately uniform scatter over
the range of the variables under consideration, and there
is no evidence of curvilinearity. Therefore, it can be
concluded that the assumptions of linearity and homoscedas—
ticity have been fulfilled.

Multiple regression analysis measures the joint
effect of a specified number of variables on an independent

variable. The multiple regression equation represents the

 

l

The residual (z = Y—Yc) gives the variation in
degree costs not explained by the multiple regression
equation.

2William A. Spurr and Charles P. Bonini, Statistical
Analysis for Business Decisions. (Homewood, 111.: Richard
D. Irwin, Inc., 1967).

 

 

 

65

Table 6. Student Credit Hours (SCH), Class Size, Total Cost,
and Regression Residuals, by Student Observation,
Degree Program Cost Study, College of Education,
Michigan State University, 1969

Observation SCH. Class Size Total Cost Residual
1 45 150 496 118.61
2 59 119 643 15.41
3 49 133 461 —13.89
4 58 131 583 6.22
5 55 130 551 16.17
6 86 103 742 —3l9.42
7 57 130 574 4.76
8 58 131 583 6.22
9 58 116 652 25.28

10 47 172 419 110.89
11 84 79 985 — 3.04
12 84 100 807 —111.13
13 78 111 843 26.65
14 89 77 974 —75.01
15 79 119 812 11.43
16 87 97 995 34.29
17 79 112 844 20.12
18 80 106 910 55.28
19 86 90 1048 74.85
20 82 106 893 —33.43
21 58 157 457 —20.52
22 59 164 539 73.92
23 60 107 591 —74.71
24 46 157 419 71.81
25 57 126 519 —50.86
26 49 145 447 27.2/
27 54 128 505 —25.62
28 46 157 419 71.81
29 50 146 435 7.74
31 39 27 620 — 1.69
32 42 36 552 —54.55
34 42 38 526 —38.37
35 37 28 542 -54.64
36 39 27 620 23.67
37 42 35 670 77.87
38 48 35 637 5.08
39 39 39 673 —68.14

 

 

66

 

Observation SCH Class Size Total Cost Residual
41 21 26 623 113.40
42 31 33 428 —120.92
43 25 38 444 -23.10
44 32 32 510 — 7.44
45 21 3 300 -111.44
46 32 32 512 -15.59
47 35 27 710 97.65
48 25 28 444 —56.40
49 34 37 612 66.64
50 34 20 682 57.21
51 34 21 863 155.55
52 30 32 610 8.00
53 36 32 708 15.45
54 34 31 645 -51.98
55 33 29 632 -60.78
56 34 31 645 —29.14
57 31 30 635 - 9.89
58 33 36 635 -11.63
59 37 35 634 -82.25
60 42 29 842 66.68
61 31 32 541 1.33
62 36 29 680 93.80
63 33 32 541 -20.38
64 31 30 541 — 5.32
65 38 30 423 -88.73
66 34 26 631 38.77
67 36 41 470 -33.10
68 33 32 541 — 5.16
69 36 29 698 94.04
70 33 39 440 —75.24
71 33 39 429 —16.35
72 45 36 591 - 4.82
73 30 37 450 35.64
74 45 36 591 33.23
75 42 41 428 —118.59
76 45 34 702 99.51
77 42 35 666 114.65
78 42 38 590 53.71
79 39 40 557 24.43
80 45 39 543 —42.84
81 3O 23 621 -67.65
82 51 25 898 61.49
84 34 30 527 —l38.66
85 45 29 837 33.38

Observation

67

Class Size

Total Cost

563
744
897
771
846

Residual

~110.27

16.25
265.98

13.84

48.72
—108.15
— 8.30
—9l.ll
—100.77
-77.86
—107.86
—l31.11
-143.10
—114.00
—27.19

—90.49

82.58
10.63
55.79
—42.21
—70.41
~19.60
88.59
43.20
142.20
73.65
23.88
53.49
77.73
38.72
77.30

 

 

 

 

 

 

 

 

Observation

68

Class Size

Total Cost

1292
1072
1292
1019
1250
1102
1078
1426
1339
1464
1518
1641
1391
1104
1208
1559
1246
1188

1438
1575
1575
1388
1723
1409

Residual

—29.87
—165.34
8.18
-222.40
—47.70
—218.84

113.08

—34.90

 

Observation

176

69

Class Size

Total Cost

1448
1402
1458
1402
1409

Residual

—44.42
—12.64

98.53
-12.64
—34.90

 

 

RESIDUAL

200

180

I60

140

120

-120

-160

'160

 

 

Figure 5.

Regression Eduation Residuals Plotted Against Average

.
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0
.
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Class Size

Class Size Variable. Degree Program Cost Study, College

of Education. Michigan State University, 1969.

 

 

I35 IWAL

 

 

200
o v
180
160
1100 .
120
o e
e . .
100 .
so ' ‘
n a . . : . . .
60 ‘ .
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o o .
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.120 , ' .
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'160 '
-180
in o n o to b in ‘ o T

Figure 6.

 

Student Credit Hours

Regression Equation Residuals Plotted Against Student
Credit Hours Variable, Degree Program Cost Study,
College of Education, Michigan State Univeraity, 1969.

 

130

160

140

120

80

60

40

-120

olbo

-160

-180

 

72

 

Figure 7.

Regression Equation Residuals Plotted Against Total
Cost Variable, Degree Program Cost Study, College
of Education, Michigan State University, 1969.

 

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I
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O
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o .. .. .
o. .. '
o o ‘ ° . o
O O
O
s
.. . .0.
e o.
. o e
. ' e I
. ' o. n. :
. o
O .0. 0
e. o. ' o
. e 0 .
..e: o .
e o ' . °
0 C. o
.0 e ' . '
e 0 ° . .
e o
000‘ o .
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O. at. e 0 c .7.
. u
0.
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o e
e
. e e
e n
_ O
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o . e
o
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W O O O O O 0 fl
ssosoogosossss
.3 an up r~ no o~ —* 0V 6° <9 U5 so r~

.4 an ed —4 .4 r4 ed ,ed
Total Coot

 

 

73

influence exerted simultaneously by the independent vari-
ables on the dependent variable. In stepwise regression
analysis, the independent variables enter the regression
equation in the order of ability to reduce the unexplained
error sum of squares of the dependent variable. The inde—
pendent variable which causes the greatest reduction will
enter the equation first, the variable causing the next
greatest reduction enters second, and so forth until all
variables which have a statistically significant effect on
the dependent variable have entered the equation.3

The regression equation was of the general form

YC = a + lel + b2x2 + ... + bnxn

In the terminal step of this analysis (Appendix D)

the appropriate regression and standard error coefficients

were as follows: YC = 421.7 — 377.6 x1 + 202.5 x2 + 136.7 X6 +

(110.9) (117.5) (32.9)

149.3 x + 211.5 x + 164.7 X10 + 146.1 X + 66.3 x12 +
(26.4) (23.8) (32.9) (33.6) (26.3)
10.0 xl3 _ 3.4 x14 + 2.9 x15 R2 = .941

(0.8) (0.7) (1.1)

 

3"Statistically significant” as used here means that
differences of the magnitude obtained would be expected to
occur only rarely if no difference existed in the population.
In some cases, statistically significant differences might be
found with no corresponding economic significance. An analysis
indicating that two different varieties of wheat have statis-
tically significant differences in yield (even at an alpha
level of less than one percent) has no economic significance
if the difference in average yield is one pound per hundred

 

74

Where: YC = Cost of degree

x1 = M.A.

x2 = Ph.D.

X6 = Business and Distributive Education
x8 = Guidance and Personnel Services

x9 = Educational Administration
xlo = Student Personnel Work

xll = Educational Psychology

x12 = Curriculum
xl3 = Number of College of Education Student
Credit Hours
X14 = Average Class Size
x15 = Ratio of Graduate to Total College of
Education Student Credit Hours
The regression coefficients are interpreted in the
normal manner. For example, the equation states that, on
the average, the degree costs will increase by ten dollars
with each additional College of Education student credit
hour in the program (x13) and decrease by $3.40, on the
average, as the average class size (x14) increases by one
student. The policy implications of the regression coef—
ficients are discussed in Chapter VI.
The regression equation was significant in explain—

ing variations in total costs at this point with an F value

of 243.39. The multiple correlation coefficient was .970;

 

acres. Alternatively, a difference of ten bushels per acre
might have economic significance even though it was not stat-
istically significant at a given alpha level. The term
"significant” when used in this thesis, refers to Vstatistical
significance." (See Lester V. Manderscheid, 52 Introduction
to Statistical Hypothesis Testing} East Lansing: Department
of Agricultural Economics, Michigan State University, 1964,

p. 29)

 

 

‘71—.-. .

75

 

therefore, an R2 value of .94 was obtained. That is, 94
percent of the variation in total degree costs is explained
by the regression equation. The number of College of
Education student credit hours, the ratio of graduate to
total student credit hours, and the average claSS size were
found to have statistically significant effects on the costs
of degree programs (t values of 11.3113, - 4.7838, and
2.4049, respectively).

The first variable to enter the equation was number
two, the dummy variable4 for the doctoral level of study.
The multiple correlation coefficient was .902, so 81 percent
of the variation in degree program costs was explained
by the Ph.D. level of study when it was the only independent
variable considered. The number of College of Education
student credit hours was the second variable to enter the
equation. These two variables explained 85 percent of the
variation in degree costs. Class size was the third
, variable to enter and, when the three were considered
together, they explained 88 percent of the variation in
cost.

4Dummy variables are often used to represent quali—
tative variables in regression analysis. In this thesis,
level of study and curriculum were represented by dummy

variables with the B.A. level and Elementary Education being
the variables which were dropped.

 

 

 

76

 

Level of Study and Curriculum Variables

It must be emphasized that contradictions may exist
between the whole and the parts in a statistical analysis.
As indicated above, the differences in degree costs between
the doctoral level and the B.A. level are statistically
significant. It does not follow that level of study, in
general, is a statistically significant factor affecting
degree program costs. To determine if level of study and
curriculum were statistically significant cost factors,
the following test was used:5

ESSl — E852 /d.f.

 

ESSl /d.f.

Where: ESSl = Error Sum of Squares of the regres-
sion equation including dummy vari—
ables for level and curriculum.

E882 = Error Sum of Squares of regression
equation excluding dummy variables
of factor under consideration (i.e.,
either level or curriculum).

d.f. = degrees of freedom

In testing for the significance of level of study,

the null and alternative hypotheses were as follows:

HO: B1 = B2 = 0 (level has no effect)
HA: Bl # B2 # 0 (level has an effect)
5

J. Johnston, Econometric Methods (New York: McGraw-
Hill, Inc., 1963), Pp. 136-137.

 

77

Similarly, the null and alternative hypotheses for
testing the significance of curriculum differences were as
follows:

HO: B3 = B4 = Bn = 0 (curriculum has no effect)

HA: B3 # B4 ¢ Bn f 0 (curriculum has an effect)

An F value of 391.0 was found in testing for the
effects of level differences on cost, and an F value of
11.6 was found when testing for the effects of curriculum
differences on cost. Both of these values were significant
at the 5 percent level; therefore, the null hypothesis was
rejected in both cases. That is, both the level of study
and curriculum have a statistically significant effect on

degree program costs.

 

As indicated ab0ve, dummy variables were used to
isolate the effects of level of study and curriculum on
total cost. Both the M.A. and Ph.D. variables were found
to be significant at the 5 percent level. This indicates
that there was a statistically significant difference in
cost between the B.A. level and the M.A. level, and also
between the B.A. level and the Ph.D_ level, but no informa—
tion about the relationship between the M.A. and Ph.D. was
available. To arrive at an approximation of this relation—
ship, a modified Student t test was used. It was an approxi—

mation in the sense that no account was taken of covariance

 

 

78

in the equation, so problems of transitivity might arise.

The test was of the following form:

 

b — b
t _ l 2
— 2 2
S + S
b
1 b2
where: b = regression coefficient
S = standard error

A t value of 3.6 was obtained indicating that a
statistically significant difference probably exists between
M.A. and Ph.D. program costs at the 5 percent level.

The following curriculum variables were included
in the regression equation's eleventh step: Business and
Distributive Education, Guidance and Personnel Services,
Educational Administration, Student Personnel Work,
Educational Psychology, and Curriculum. The t values of
each of these variables were significant, indicating that
the costs of providing degrees in these areas were signi—
ficantly different from the cost of a degree in Elementary
Education. To determine if differences of statistical
significance existed between sets of these variables, the ‘
t test described above was applied.

The results of the t test are contained in Table 7
At the 5 percent level, the cost differences between the
following sets of degrees were found to be significant:

(1) Educational Administration — Business and Distributive

 

79

Education, (2) Curriculum - Business and Distributive
Education, (3) Educational Administration - Guidance and
Personnel Services, (4) Curriculum - Guidance and Personnel
Services, (5) Curriculum - Educational Administration,

(6) Curriculum — Student Personnel Work, and (7) Curriculum —
Educational Psychology.

Table 7. Matrix of t Values Generated by Tests for Signifi—
cant Differences at 5 percent Level, by Combinations of

Degree Programs, Degree Program Cost Study, College of
Education, Michigan State University, January 1969.

 

Bus & Dist Guid Student
Department Education & Pers. Ed Admin Pers. Ed. Psych

Guidance &
Personnel .30

Educational

 

Administration 1.85 1.77

Student

Personnel .63 .38 1.12

Educational

Psychology .22 .07 1.58 .40
Curriculum 1.70 2.24 4.14 2.35 1.90
Summary

The general conclusion of this chapter is that the
null hypothesis of the thesis was rejected. That is, it

was concluded that the following factors were statistically

significant at the 5 percent level in explaining differences

 

80

in degree program costs in the College of Education, Michigan
State University: (1) class size, (2) level of study, (3)
curriculum, (4) number of College of Education student credit
hours in the degree program, and (5) ratio of graduate to
total College of Education student credit hours in the
degree program.

The policy implications of the degree costs and
statistical findings presented in this Chapter are discussed

in detail in Chapter VI.

 

 

 

CHAPTER VI

SUMMARY AND IMPLICATIONS

In recent years, the demand for educational services
on the university level has increased greatly and every
indication is that the trend will continue. Additionally,
it is likely that the demand for these educational services
will increase at a faster rate than the supply, the major
limitation on supply being the budget constraint. Faced
with this economic problem, decision makers in institutions
of higher learning must allocate their limited resources
as efficiently as possible to provide for the attainment
of feasible institutional objectives. In order to make
intelligent decisions with regard to the allocation of
scarce resources, they must know the alternative courses
of action that will accomplish institutional objectives,
and the economic costs involved in providing each
alternative.

The purpose of this study was to provide a basis

for obtaining the cost information needed to make sound,

81

 

82

 

economic decisions in the process of allocating educational

resources .

Summary

The relevant literature in the area of educational
costs was reviewed in Chapter II. This review indicated
that most of the previous researchers in this area had
either simply divided total expenditures by some unit of
educational output or disaggregated the cost data into
such general categories that the final unit cost figures
were relatively meaningless. In most cases, the costs
were simply accounting data that did not reflect the value
of resources in terms of alternative uses. The present
study attempted to remedy this deficiency.

The costs which must be included in an economic
analysis were outlined in Chapter III along with the
conceptual framework within which constrained choice
problems are solved. Consumer indifference theory was
uSed to demonstrate the method of choosing the point of
optimum allocation when resources are limited and wants
are insatiable. The isoquant approach to production theory
and its application to long run educational resource allo—
cation was reviewed. The opportunity cost principle was

outlined and applied to educational costing problems.

 

 

 

 

83

Based on the economic principles outlined in Chapter

 

III, the method of determining the costs of educational
programs in the College of Education was presented in
Chapter IV. The types of costs to be included in an econ—
omic analysis as well as the units in which the costs
should be measured were determined before the actual cost—
ing method was developed. All costs (regardless of the
point in time at which they were incurred) that result

from adopting a particular course of action must be
included. Since the supply function of educational inputs
faced by the individual college appears to have relatively
few bottlenecks, the major limitation on expanded resource
use is the annual budget. Therefore, the dollar was chosen
as the unit of measurement in which costs would be pre—
sented. The total cost of each degree was found by summing
five component cost categories: (1) instructional costs,
(2) faculty support costs, (3) research costs, (4) space
costs, and (5) administrative costs.

The total costs (and component costs) of the
several degree programs in the sample were presented in
Chapter V along with the statistical analysis used to test
the hypothesis. On the average, the cost incurred by the
College of Education in producing a Ph.D. degree ($1399)

was about twice the cost incurred in the production of

 

 

 

84

   

either a B.A. degree ($653) or M.A. degree ($652). When
degree cost variations within each level were considered,
however, these generalizations lost much of their meaning.
The cost of an average B.A. degree in Special Education
($910) was almost twice that of a B.A. degree in Elementary
Education ($479), and $105 more than the most costly degree
on the M.A. level. The cost ranges within each level of
study were as follows: (1) B.A. - $431, (2) M.A. - $278,
and (3) Ph.D. — $326.

The hypothesis was that the following factors were
statistically significant at the five percent level in
explaining degree program cost differences in the College
of Education: (1) class size, (2) program level (i.e.,
B.A., M.A., Ph.D.), (3) curriculum, (4) number of College
of Education student credit hours in the degree program,
and (5) the ratio of graduate to total student credit
hours in the degree program. Each of these factors was
found to be statistically significant in explaining cost

differences at the five percent level, so the null hypothe—

 

sis was rejected.

Implications

It was pointed out in Chapter V that a difference
exists between statistical significance and economic sig-

nificance. From an economic point of view, a knowledge of

IIIII[::::_____________________________1

 

85
differences in costs is necessary to determine which alter—
natives must be given up in order to achieve an objective
with other alternatives. The costs derived in this study
should be useful to the administrators in making decisions
such as determining the number of students to be admitted
to degree programs on each of the four levels in each of
the curriculum areas. In making decisions of this type,
the marginal cost per degree is the relevant cost to be
considered. The costs derived in this study were average
costs; however, operating under the assumption that no
scale economies or diseconomies will result from changing
the number of students in a given program with quality
constant, average costs may be used. This substitution is
possible because a horizontal average cost curve is equal.
to the curve marginal to it at each level of output.
Communication with Dr. Floyd Reeves, a pioneer researcher
in the field of educational costs, indicated that no con—
clusive research results have been published with regard
to economies of scale in subunits of institutions of
higher learning. Based on his experience, however, he
suggested that in the range of operation, very few scale
economies are available to an institutional subunit such
as the College of Education, if the quality of educational

services are held constant. If the student—teacher ratio,

 

 

 

 

 

 

l
I.
r:

 

 

 

 

 

 

86

average class size, the quality of faculty, the physical
facilities, and supporting services are held constant, the
per unit cost changes resulting from institutional size
changes should be minimal. This would not necessarily
be the case for the entire university due to large expendi-
tures of the sunk cost variety. Some examples of expenditures
in this category are those for extracurricular activities,
health services, police services, and university administration.
The quality constant condition is of major importance
to the assumption of constant costs. If additional students
are handled by increasing class size with no corresponding
increase in faculty, administrators, or supporting facilities,
economies of class size would obviously cause decreases in
instructional costs. The regression equation presented in
Chapter V reveals that, on the average, degree costs decrease
by $3.40 in response to an increase in class size of one
student. Therefore, to the extent that the minimization of
costs is one of the primary goals of the College, there
would be an incentive to increase the size of classes. For I
the purpose of comparing the costs of degree programs in
this study, however, the assumption is that the decision
makers are able to overcome this incentive and maintain

the size of any given class at a constant level.

 

 

 

 

 

87

The regression equation also indicated that, on
the average, costs increased $10 for each additional
College of Education credit hour in the degree program.
An obvious cost—reducing administrative action would be
to cause a decrease in the ratio of College of Education
student credit hours to total student credit hours in
the average program of study. This action could be
implemented without changing the number of degrees pro—
duced in any given academic area or reducing the number
of student credit hours required for graduation by
eliminating courses which are similar to courses pre-
sented by other colleges in the University. It would
seem that unnecessary duplication might exist in areas
such as psychology, sociology, and statistics. Certainly
some courses relating specifically to educational research
methods, for example, are not only desirable, but necessary
for a well—balanced, complete degree program. The courses
which should be considered for elimination are those in
which general principles are covered, and are already
being adequately handled by a department of another
college. As indicated in Chapter I, many factors other
than those of an economic nature enter into decisions of
this type, but it is imperative that administrators be
aware of the effect that the luxury of course duplication
has on degree costs.

EII:;______________________________

 

 

88

 

If the decision makers in the College of Education
decide that the production of degrees in one academic area
should be expanded, the production of degrees in another
area (or areas) will have to be reduced assuming a con—

stant budget.1

The cost figures derived in the present
study provide information regarding what benefits (degrees)
have to be sacrificed in one academic area to receive

a given level of benefits (degrees) in another area. If
it is determined that more students in the area of Student
Personnel Work are to be admitted to the Master's degree
program, and the additional resources required to expand
the degree program are to be obtained by reducing the
level of degree production in Agricultural Education on the
M.A. level, the data presented in Chapter V indicate that
for every six student positions removed from agricultural
education, about four can be added to the Student

Personnel Work degree program without additional resources.

Relations of this type can be made between and among all

 

of the degrees for which costs were calculated.

1Personnel in the College of Education are engaged

in resource consuming activities other than teaching such
as research and public services. In this study only degree
programs are considered, but the same analysis would apply
in allocating resources among a number of activities.

 

 

 

 

 

89

 

As indicated in previous chapters, one of the goals
of this thesis was to remedy some of the deficiencies found
in previous educational cost studies. To the extent that
the costs derived in these studies have been inaccurate
and have been used in the decision—making process, they
might have led to the misallocation of resources. Resource
misallocation occurred in the sense that inaccurate and
imprecise cost figures do not reflect the true economic
value of factors of production, and when inaccurate values
are assigned to resources, maximum efficiency is impossible.
It is only when an educational institution combines its

resources in the most efficient manner that a given number

 

of students can be provided a certain quality education at
a minimum cost. Stated alternatively, it is only when
resources are combined in the most efficient manner that
the maximum number of students can be provided a certain
quality of education at a given cost.

The contention is not that the present study has

eliminated all of the problems encountered in measuring

 

educational costs and, therefore, provided educational
decision makers with the data necessary to obtain optimal
resource allocation positions. It is hoped, however, that
the methods developed will permit a movement toward the
optimum solution, and provide the basis for future research

which will allow further movements toward optimality.

 

 

 

 

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APPENDICES

Appendix A. Average Class Size, Average Annual (Ten Month)
Professorial Salary, Average Professorial Salary Per Course,
and Instructional Cost Per Student by Course, College of
Education, Michigan State University,

Academic Year 1967—68

 

Salary ($)

 

 

Coded Average Instructional
Course Class Average Allocated Cost Per
Number Size Annual to thls St d nt

Course %$?
A 78 8,533 711 9.21
B 22 6,000 500 22.71
C 24 12,088 1007 41.94
12,088 + 12*
D 500 12,518 + 3 1007 + 4172 10.35
E 20 3,129 1043 52.14
F 46 13,175 1098 23.86
G 110 12,500 1041 9.50
H 97 11,500 958 11.26
I 34 11,231 936 27.51
J 17 12,088 1007 59.22
K 13 11,593 966 74.28
L 46 10, 540 878 19. 08
M 39 12,007 1000 25.62
N 13 11,500 958 73.68
0 44 11,675 973 22.11
P 21 6,000 500 23.79
Q 27 6,000 500 18.51
R 27 11,675 973 41.10
S 103 11,231 936 9.09
T ‘ 20 12,088 1007 50.34
U 112 12,000 1000 30.00
V 37 13,000 1083 29.25
W 99 15,914 1326 13.38
x 381 151.6451: : :2. 929 + 3881 12.60
Y 34 11,231 936 27.51
Z 32 13,000 1083 33.84
AA 37 11,155 929 27.57
BB 13 13,175 1097 84.36

96

 

 

97

 

 

 

Salary .
Coded Average Average Allocated Instructional
Course Class Annual to this COSt Per
Number Size Course Student
cc 43 12,000 1000 ‘23.25
DD 31 10,540 878 28.32
BE 35 13,500 1125 32.13
FF 13 12,596 1049 80.70
GG 22 12,007 1000 45.45
HH 28 14,800 1233 44.00
11 27 14,800 1233 45.66
JJ 20 13,500 1125 56.25
KK 25 11,231 936 37.44
LL 32 11,675 973 30.39
MM 25 11,155 929 37.14
NN 16 14,800 1233 77.07
00 14 9,000 750 53.55
pp 24 14,000 1166 48.57
Q0 93 11,700 975 10.47
RR 23 12,000 1000 43.47
88 20 14,000 1166 58.29
TT 12 6,500 541 45.06
UU 27 13,000 1082 45.72
vv 35 13,000 1082 31.00
ww 13 12,500 1041 80.07
xx 35 2,889 963 34.35
YY 62 12,000 1000 16.11
22 24 11,800 983 40.95
A1 10 12,150 1010 101.98
B1 25 11,500 958 38.31
cl 10 12,500 1040 103.98
D1 12 12,750 1062 88.50
El 7 12,500 1040 148.50
F1 20 13,000 1083 54.12
G1 10 13,000 1083 108.50
H1 12 13,000 1083 90.00
I1 15 12,000 983 65.50

 

*Graduate Assistants' salaries are divided by three
under the assumption that one assignment is received per
academic quarter.

Source: Office of Institutional Research, Michigan State
University, and Office of the Dean, College of Education,
Michigan State University, January 1969.

 

98

 

 

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Appendix D. Printout of Eleven Steps of Stepwise Multiple
Regression Analysis, Degree Program Cost Study,
College of Education, Michigan State University,

 

1969
Step Number 1 Enter Variable 2
Standard Error of Estimate = 160.635

Multiple Correlation Coefficient = 0.902
Goodness of Fit, F ( 1,178 ) = 781.2175
Constant Term = 651.5693

Std Dev
Var Coeff Coeff t Value
2 747.1508 26.7313 27.9503
Step Number 2 Enter Variable 13

Standard Error of Estimate = 147.113
Multiple Correlation Coefficient = 0.919
Goodness of Fit, F ( 2, 177 ) = 483.3261
Constant Term = 447.1672

Std Dev

Var Coeff Coeff t Value
2 741.7893 24.4978 30.2797
13 4.7222 0.7956 ”5.9350
Step Number 3 Enter Variable 14

Standard Error of Estimate = 120.675
Multiple Correlation Coefficient = 0.946
Goodness of Fit, F ( 3, 176) = 507.8908

Constant Term = 404.9010

Std Dev
Var Coeff Coeff t Value
2 642.8428 22.7218 28.2918
13 9.3707 0.8210 11.4125
14 — 2.9858 0.3200 — 9.3302

106

Beta Coeff

0.9024

Beta Coeff

0.8959
0.1756

Beta Coeff

0.7764
0.3484
—0.3063

 

 

 

107

Step Number 4 Enter Variable 9
Standard Error of Estimate = 110.167
Multiple Correlation Coefficient = 0.956
Goodness of Fit, F ( 4,175 ) = 466.0889
Constant Term = 376.0509

Std Dev
Var Coeff Coeff t Value Beta Coeff
2 596.2890 22.1404 26.9321 0.7202
9 144.7795 24.0718 6.0144 0.1455
13 9.7541 0.7522 12.9658 0.3627
14 — 2.9649 0.2921 —10.1477 —0.3042
Step Number 5 Enter Variable 8
Standard Error of Estimate = 106.314
Multiple Correlation Coefficient = 0.959
Goodness of Fit, F ( 5, 174 ) = 403.1676
Constant Term = 384.9497
Std Dev
Var Coeff Coeff t Value Beta Coeff
2 577.9395 21.9252 26.3596 0.6980
8 100.8201 27.0293 3.7300 0.0854
9 169.4817 24.1555 7.0162 0.1703
13 10.0635 0.7307 13.7721 0.3742
14 — 2.8887 0.2826 -10.2184 —0.2964

Step Number 6 Enter Variable 10
Standard Error of Estimate = 102.942
Multiple Correlation Coefficient = 0.962
Goodness of Fit, F ( 6, 173) = 360.4418
Constant Term = 337.7097

Std Dev
Var Coeff Coeff t Value Beta Coeff
2 591.2601 21.5592 27.4248 0.7141
8 110.2506 26.3067 4.1909 0.0934
9 176.6885 23.4774 7.5258 0.1775
10 123.9532 34.9394 3.5476 0.0765
13 9.7998 0.7114 13.7749 0.3644
14 - 2.6663 0.2808 —9.4950 —O.2735

 

 

Step Number 7
Standard Error of Estimate

Multiple Correlation Coefficient

108

Enter Variable 6

Goodness of Fit, F (7,172)
Constant Term =

Coeff

599.2850
106.2115
120.8854
185.0806
137.2834

9.9886
- 2.5686

Step Number 8

313.6789

Std Dev
Coeff

21.1979
34.1972
25.9003
23.0706
34.3668

0.6969

0.2758

100.463

= 0.964

325.7691

t Value

28.2708
3.1058
4.6673
8.0223
3.9946

14.3321

—9.3119

Enter Variable 11

Standard Error of Estimate = 97.904
Multiple Correlation Coefficient = 0.966
Goodness of Fit, F ( 8, 171) = 301.4061
Constant Term = 290.8834
Std Dev
Var Coeff Coeff t Value
2 610.0286 20.9326 29.1425
6 122.3294 33.7096 3.6289
8 132.5016 25.5037 5.1953
9 194.2015 22.6653 8.5682
10 153.3275 33.8695 4.5270
11 106.6365 33.5404 3.1793
13 10.0546 0.6795 14.7969
14 — 2.4246 0.2726 -8.8941

Beta Coeff

0.7238
0.0656
0.1024
0.1860
0.0848
0.3714
—0.2635

Beta Coeff

0.7368
0.0755
0.1122
0.1951
0.0947
0,0658
0.3739
-0.2487

 

 

 

 

109

Step Number 9 Enter Variable 12

Standard Error of Estimate = 95.860
Multiple Correlation Coefficient = 0.967
Goodness of Fit, F ( 9,170) = 280.3919
Constant Term = 253.6898
Std Dev
Var Coeff Coeff t Value Beta Coeff
2 595.7973 21.0777 28.2666 0.7196
6 143.0605 33.7749 4.2356 0.0883
8 159.9924 26.7183 5.9881 0.1355
9 222.5375 24.2576 9.1738 0.2236
10 171.4272 33.7475 5.0796 0.1058
11 126.0691 33.5202 3.7609 0.0778
12 77.2341 26.6976 2.8929 0.0654
13 10.4268 0.6776 15.3867 0.3877
14 — 2.3050 0.2701 —8.5337 -0.2365
Step Number 10 Enter Variable 1

Standard Error of Estimate = 94.578
Multiple Correlation Coefficient = 0.968

Goodness of Fit, F (10, 169) = 259.8017
Constant Term = 530.1026
Std Dev
Var Coeff Coeff t Value Beta Coeff
1 —184.1617 77.5581 — 2.3745 —0.2467
2 411.2477 80.4555 5.1114 0.4967
6 138.3057 33.3835 4.1429 0.0854
8 147.9406 26.8453 5.5108 0.1253
9 219.4546 23.9685 9.1559 0.2205
10 171.4688 33.2963 5.1497 0.1059
11 126.4967 33.0726 3.8248 0.0781
12 66.9675 26.6932 2.5087 0.0567
13 9.2345 0.8361 11.0443 0.3434
14 — 3.8240 0.6930 — 5.5179 -0.3923

 

 

Euty.

Step Number 11
Standard Error of Estimate

Coeff

—377.5770

202.4992
136.6665
149.2520

211.4653,

164.7210
146.0646
66.3350
10.0035
— 3.3843
2.8647

110

Enter Variable 15

421.6934

Std Dev
Coeff

110.9851
117.5971
32.9279
26.4788
23.8687
32.9545
33.6138
26.3246
0.8843
0.7074
1.1911

168)

93.268
Multiple Correlation Coefficient
Goodness of Fit, F ( 11,
Constant Term

= 0.970
243.3946

t Value

— 3.4020
1.7219
4.1504
5.6366
8.8595
4.9984
4.3453
2.5198

11.3113
-4.7838
2.4049

Beta Coeff

—0.5059
0.2445
0.0844
0.1264
0.2125
0.1017
0.0902
0.0562
0.3720

—0.3472
0.2683

 

 

 

 

 

 

 

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