Download Applying the SAS System in Undergraduate Managerial Economics: A General Approach

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Applying the SAS® System in Undergraduate Managerial Economics:
A General Approac h
Seid M. Zekavat, Loyola Marymount University, los Angeles
The third step is the employment of a suitable decision
science technique. Tools and techniques of analysis used in
decision sciences as related to business and economics include
statistical estimation, and optimization. It is at this stage where
regression analysis Is used. Model-building. statistical estimation,
and prediction play essential roles in this phase of management
decision problems. Model building means writing a model or a
mathematical fundion which will provide a good fit to a set of
demand, produdion, or cost data. (Terry Sincich, A Second
Course in Business Statistics: Regression Analysis). A carefully
determined model is expeded 10 give good estimates of the
mean and prediction values of dependent variable for given
values of independent variables.
INTRODUCTION
Undergraduate managerial economics is designed 10 present those
aspectS of economic analysis which are most relevant to students
of business administration. It provides a comprehensive application
of economic theory and methodology to managerial decision
making with emphasis on the concept of optimization. This
concept refers 10 "the process of balandng benefits against the
costs and doing the best within the limits of what is possible."
(Michael Parkin. Microeconomics, 1994). In a narrower sense as it
applies 10 managerial economics, optimization is "the process of
efficiently arriving at the best possible solution 10 a given
(management) problem.• (Marie Hirshey and James L. Pappas,
Managerial Economics, 1993).
The founh step is the application of the appropriate SAS
procedures 10 obtain the optimal algebraic and graphic solutions
to the problem.
At Loyola Marymount University, managerial economics is
not a required course. The course, however, attraCIS a number of
top senior students from both the School of Business
Administration and the Department of Economics each semester.
From the oral and written comments expressed by the students
who have taken the course, it appears that students find
managerial economics useful, worthwhile and necessary
knowledge to acquire.
APPLICATION OF THE SAS SYSTEM
Often the complexity and the size of data which represent a
firm's produdion, cost and revenue information do not lend
themselves to an easy way of finding the most suitable model for
the data. Fonunately, SAS offers several simple procedures
which would assist the researcher 10 choose from among the
most appropriate alternatives.
The background required for the course consists of an
adequate knowledge of college math and calculus, intermediate
macroeconomics, and basic statistics. By the time students of
business and economics reach the senior level, it is expected that
they have acquired adequate skills in using the compuler as a tool
to make quantitative analysis of business data.
P..OC Stepwise. This procedure, which is also known as
Stepwise Regression, performs a screening task, It would include
the important independent variables in the model and screen out
those that are not important. Stepwise regression provides a
systematic approach to building a model with a large number of
independent variables. Without this approach the interpretation
of multi-variable interadions and highei'Order polynomials of
square terms or cubic terms would be very tedious.
METHODOLOGY
Undergraduate managerial economics is treated as a case
study course. Bebe assigning management case problems 10
students, however, a lecture on fundamental principles of
economic analysis is given. Once the relevant basic economic
relations are explained, the students are taught how to apply the
tools and techniques of optimization for the purpose of finding the
best course of action.
This process first fits all possible one-variable (simple
regression) models. If the independent variable xl included in
the model shows to be highly signifiCallt, the procedure declares
it the best one-v.~riable predldor of the dependent variable, y.
Stepwise regression now begins to search through the remaining
independent variables for the best twOo¥ariable model. It
continues to check the third, and the founh independent
variable. As each new independent variable is added 10 the
model, its significance in terms of its relationship to the
dependent variable y is shown.
The first step is to identify the management decision problem
in the case. Is it related to output and price, produdion
techniques, selection of advertising media and the intensity of
prodUd or service exposure to the market, labor hiring. or
investment and financing!
PROC REG. By definition, PROC REG is the SAS procedure
which performs the simple or multiple regression analysis. The
PROC REG command, however, must be followed by a model
equation seleded for the case under study. The model simply
calfs for the dependent y to regress upon the independent
variable(s). The output from the PROC RECi includes, for the
most pan, an analysis of variance (ANOVAl table from which
one can readily deled the extent of the relationship of
The second step is to choose the appropriale economic
concept as the framework of analysis. Each area in the first step
outlined above will then be explained by its matching economic
concepts. Here pertinent analyses of demand and elasticity,
prodUdion and costs, and various market structureS in terms of the
intensity of competition or the lack thereof are focused on and
seleded.
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fRAMEWORK OF EcONOMIC ANALYSIS
dependent variable to those of the independent variables. The
bottom half of the table contains the estimates of the parameters of
1be regression equation such as the intercept, or constant term, and
coeflidents(s) of independent variables and t-5!alistics together with
standard error of estimates.
The decision problem in this case is one of output and
price. Assuming that the company seeks profit maximization.
determination of the optimal number of razors to produce per
week and the unit price to charge would be the prime objec!ive
in this case. To adlleve this we use the familiar technique of
equating marginal cost to marginal revenue func:lions and
solving for the quantity. This is an optimal quantity. In relation
to EZ Razor, marginal cost may be defined as the cost of
producins an additional unit of razor. Marginal revenue is the
revenue that is associated with the sale of the same additional
razor. Marginal cost and marginal revenue functions are
determined by taking the derivatives of TR and TC equations
(ModelS), respectively. This will take us to the third step,
namely, selecting the right model for TR and TC data.
PROC CORR. Conelation procedure is also used for a better
understanding of the more complex regression analyses in
managerial economics. PROC CORR computes correlation
coefficients between all pairs of variables included in the model.
Conelation coeffk:ient shows the strength of a relationship that
exists between two variables. It is a number ranging between - 1
to 0 for an inverse relationship and 0 to + 1 for a direct
relationship. A positive correlation indicates that as values of one
variable increase, values of the (](her variables tend to increase. A
negative correlation coefficient shows that as the value of one
variable goes up the other goes down. An insignificant linear
relationship becomes apparent when a small or zero coefficient of
correlation is obtained.
USE OF SAS TO CHOOSE APPROPRIATE TR AND TC
EQUATIONS
A HYPOTHEnCAL MANAGERIAL CAsE STUDY
To begin resolving this management optimization case, we
first need to develop the most suitable equations for the total
costs and IO(al revenue data. PROC PLOT of the data provides a
good guidance in selecting the appropriate models.
The type of case study problems used in the managerial
economics course are somewhat complex. The solution of such
case stud"aes requires a good knowledge of macroeconomics, basic
statistics and a fairly strong math background. They also demand a
thorough understanding of the geometric relations among IO(als,
marginals, and averages. Knowledge and skills in these areas have
proven to be prerequisites to a successful use of the optimization
techniques and profit maximization procedutes. To minimize such
a complexity, a simplified version of a hypothetical case study
problem is treated here. The SAS approach to this hypothetical
management case involves statistical analysis of the short run costs
and revenue for the EZ Razor Company. The purpose of analyzing
this data is to determine the optimum level of weekly razor
production and the price per unit of razor to be charged in order
to make the largest possible profit.
PROC PLOT. Figure I presents the plot of the TR and TC
data.
Figure I
PROC PLOT of TR ('r'l and TC
10000 •
tSOO •
tooo •
1500 •
1000 •
7500 •
7000 •
1500 •
The Data. Our hypothetical data include 16 weekly
obsetvatlons on razor Olllput (in thousands of units) and total cost
and total revenue (in dollars) for the last six months period. The
original data is presented in Table L TO(al costs include overhead
and variable costs of production. Variable costs cover payments to
all the material and services requited to produce weekly razors.
For simplicity, the theory of least cost combination of factors of
production and their allocation are kept out of this analysis.
IDOl •
$500.
- ·-·
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A simple visual scan of the scattered diagram shown in
Figure I suggests a second order linear regression func:lion for TR
and a third order polynomial regression func:lion for TC. They
can be written as:
c.aso
5,751
a.soo
TR - a + bQ + cQ' and TC - a + bQ + cQ' + dQ'.
5,001
7,000
c,so1
1,.251
5,250
1.000
1,100
7,500
•c
••
1000 +
7.001
4,250
4,500
·c
•
••
•• •
•
• • • •• •
c
2500.
2000 +
1500 •
........ (II
s.uo
c
•
•
• • ••
•
1100 •
1100 +
.......
7.000
1,250
•
stOO +
4500.
4100 •
Table 1:
Weekly Production, Total Cost and Total Revenue
EZ Razor Company
OIICpu.t.
('c')
PROC REG. The SAS regression procedure provides the
ANOVA tables for these equations. Estimates of the rcgres.<ion
coefficients, the coeilicient of correlation, the F and t statistics
and the measure of the extent of the relationship between the Q
terms and dependent variables CTR or TCI are shown
systematically. Tables II and Ill show these parameters for TR
and TC.
3.000
•. ,so
't,SOO
C,250
,,750
1,100
t.100
7,500
7,250
5.300
5,250
..250
4,250
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One can easily note that rtZ (c;oeflicient of detennination)
increases as the models lake the forms most suitable to the Razor
2
Company's data. R indicates signific:anc:e of the relalionship of
the independent variables to the dependent variable. The size of
the Mean Square Error also declines. The Sltonger the
relationship, the smaller the MSE.
Table II
Analysis of Variance Dependent Variable: TR
-......
-1
C-.l
.......
.........
--.. ........
........
.....
••
•
••
:as•a:n.n.uT
lSOSU:l. Cttl
3ttl740l ••••
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··-
••~cera.c.l•t
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g.
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cu.,,...
o.to:u.
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Pu...cer-0
o.tTUOU l
PE'ab ..
11'1
o.nsa
0.715
12.258
•11.111
4J,U3ti3 94
-13.:130!11 2
for the sake of compari son, the summa.y process of the
step entry of independent variables made by PROC
by
step
STEPWISE into the t01a1 revenue and total costs functions is
shown above. The standard error and the t value for each added
Q variable are also shown. Our choice ol the best fitted models
to the data is confirmed by the Stepwise procedure•
..
HS.121l U1t
UO,l5'721 3
1
1
1
0.0101
0.1100
R•aqu.ut
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-··
rvalue
111.21
1"1'71101 1-"t
152401.tl4 14o
Now that the most suitable models are selected for both TR
and TC, we are able to superimpose the TR and TC regression
lines we found in the PROC STEPWISE tables (IV and V). This is
shown in Figure II.
0.0001.
0.0001
Table Ill
Analysis of Variance Dependent Variable: TC
......
_,
......
c 'Z'Cit.l
••
•••••
ucnna .u
_,.,.,
1
1
1
1
Q
g:
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-
1000 •
7500 •
o.tnt
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)41.211"
7000 •
GSOO •
11000 •
O.t40'1
ssoo •
5000 •
4500 ..
4000 •
~t•nd..cn
.....
•• t'. . .l:ft'
ll~i.Mt.e
liDI.tltJ U
405,71347 7
-:ll.SU2 lt
0.313101
tit. 410.2 • &·&4.740 ... ll.:ZQI'
ln:::
0,0001
.J.2UOS.1 ttt.l
51161Ut .l15
C.'l.
VU110le
- ·- .......
...
........0.
--..
........
Figure II
Plot of TR ('r'l and TC ('c')
and the Fitted Regression Lines
't for
HO~
, .. .cer-0
1411.410 44H
Ut.l2J't1 UO
a.saotu n
1.Z7C
2.0H
0.2154
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JSOO +
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....•
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zooo ..
1500 •
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o.oozo
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'IC' • 110? • 4055.1Q .. :UI4Q" •••
.
........_......... -.......................................................................
.....0 ...... .... _
11
•ul,ZOZ42132:l,4.0<141
Other funaions, such as maginal revenue (MR). marginal
cost (MQ, a\ierage reYenue (ARI, and average cost lAO, are
needed to detennine the optimum levels of Razor production
quantity and price. Taking the derivatives of the TR and TC
funaions, we obtain MR and MC functions respectively. Figure
Ill shows the plot of MR and MC of EZ Razor Co.
The Analysis of Variance Tables indic:31e significant relationships
between TOial Revenue and the Q variables. Likewise a significant
strength between TC and the Q terms is evident. Nevertheless, it is
instructive to use PROC STEPWISE in search for the most suitable
n
model applicable to the data. The results of the STEPWISE regressio
are summarized below:
Table IV
Summaty of PROC STEPWISE for Dependent Variable TR
-...........
..-·•
Oil_.....
"0 ..
515 •
550 •
S2S•
SOD •
4'15 •
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10,441
J,l,
4.ZS •
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•so •
lU •.U
'
IIC. 405,,., -
....
o.n
O.lZl
'I'll
Figure Ill
PROC PLOT of MR ('r'l and MC ('c')
.....
Q--
Seep 1
a-
u.:zQ'
.. CO.t11
uo.:z • '"·"•o
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:150 •
12$ •
300 •
.... .
....
250 •
200 •
11S •
150.
125 •
100 •
..•
Table V
Summary of PROC STEPWISE for Dependent Variable: TC
,•
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:
The quantity at which MC and MR inlenec t is the optimal
number ol razors that would lead to the highest level of profits.
As the above graph indic:ates, each additional unit of razor
• 1101 • 4H • •21.MQ' • o.6Q'
1200J
3,03
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Table VII
Analysis of Variance Dependent Variable: AC
that unit (MQ, but only up 10 the 21st unit where both MR and
MC begin 10 break even. Beyond this intersection quantity the cost
of each unit exceeds the revenue from the same uniL It stands 10
reason that the acc:umulated marginal profits would reach the
maximum at the quantity where the intersec:tion of MR and MC
takes place. This quantity is the optimal number olrazors which
would bring: the maximum profiL In order 10 determine the
volume of this quantity, MC and MR functions are equated and
solved for Q:
-....
.....
-1·
C-.>
-
Ya.l'i..W.e
oa
315 •
c
c
300 ..
275 •
250.
225 ..
c
••
200 •
...
115 +
150 •
125.
0.0001
o.tn•
o.t300
.....
.. ...- ....
hc..cu aet.t..«••
2? • SOTOtl31
1.311041•4
O.hn42C.T
'f for IUh
2&.1H
-13.4,0
11.114
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11'1
o.DOD1
O.DOOl
O.DOU
The optimal price charged per thousand each week is
approximately $341.50. This can be obtained by substituting 21.45
for Q in the average revenue functions:
AR - P - 644.74 - 13.23 (21.45)
..
r
-
~--
Adj .....
l"·'"
......
AC- 664.5 - 32.14Q + 0.53Q'
101 •
575•
!150.
• ••
•r
c
•
•
, .....
The AC !'unction, according 10 the above Analysis of
Variance, is:
Figure IV
PROC PLOT ol AR ('r'J and AC ('c')
4ZS +
hCJARa
•J2.l&J2SI
0.5213'71
0
IV.
450 +
IIF
Ut.:tOlSt
1.10142
114.41CSZT
AR and AC are derived through the process of averaging the
TR and TC data. PROC PlOT of AR and AC is presented in Figure
500.
21
--
'o"o.un
JCO .. .)O'IT
UOUO.)T4&'
121'7 .D510T
lUCD7.GII4
11.!117&
Using the quadratic equation the optimal quantity of razors is
21.45 (1,000) units per week.
525•
23
c.v.
MR - MC: 644.74-26.46Q - 405.76-43.1Q + 1.2Q'.
... .
....
....... .
-
.,• ......
_...
.........
In the same manner the average cost can be detennined for
this optimum level ol output by subslituting 21.45 for Q in the AC
functions:
•
.. • •• •• • •• ••
•
c
r
•
c
•c
•
AC - 664.5 - 32.14 (21.45} + 0.53 (21.45)2
110 •
••
25.
0.
.................................
.................................................
.................................................
d
U
40
U
n
H
U
H
U
U
I
4
0
50.
Thus AC is $203.75. Figure V illustrates the graphic relation
of the AC and AR.
FigureV
AR and AC estimates are obtained by using PROC REG. The
PROC PlOT of AR ('r'J and AC ('c')
results are provided in Tables V and VI. The optimal quantity of
21.45 (1,000) per week can lead us 10 the optimal price 10 be
charged for largest possible profit.
.... .
100 •
550 •
525 •
500 •
4'75 •
450 •
Table VI
425 •
coo •
Analysis of Variance Dependent Variable: AR
31$.
350 •
.......
-
......
DP
.....
-1
,,.,. ,..,41
...51"-Slf!S.O
25
C TOCal
RoocMD
14.1'7211
Dep Mean
21C.12U3
S.12'J't4
c.v.
325 •
3100 •
......
44«11.40"2
1
24
r valve
2015-344
444C:ll.40,t2
llft'IIICIIft
Q
••
1
•
h:rat~eCIH'
bci-te
"4.?U.10l
-U.23
.......
1?5 •
150.
...
121.
0.0001
1.00 •
•••
215.27335
.......
.-...
l.lt94ll41
0.3UO!H4
0 •
0.,.10
M:l R·•'l
T
tar
BO:
Pu'...CU'.O
...,
....,
7C.TCI.
-
............... --·-. U-- ...... J·-----·-- --·-- .... -·- .......: 1.................
....................................
II044<11
. 2•
IUUZO
6
0
'·""
a--.an
Paz'~ltDt.i..CH
V.riabla
....... ..
275 •
Prab ~
ITI
Using the OVERLAY 5AS option, PROC PLOT of the average
revenue, average cost, marginal revenue, and marginal cost,
exhibits the complete graphic illustration of the optimization
process. Figure VI displays this process.
Q.ODOl
0.0
Based on the Parameter estimates above the AR !'unction is:
AR - 644.74 - 13.23Q
4
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Training & User Support
CONCLUSION
Figure VI
PROCPLOTof
Alt: ('d'), AC ('"'), MR ('r') and MC ('c') Overlays
Once the managerial decision problem is identified and the
matching economic concept is chosen, SAS procedures play a
major role in facilitating the solution of the management case
study. In complex management cases where simultaneous solutions of several related problems are essential in successful
business planning and opemion, SAS procedures seem to have
an extremely important role in the practical application of
economic theories.
....
soo •
S?S +
100 ...
475 •
410 ...
425 •
...
Today economic literacy stepS beyond the mere application
of toOls and concepts. It demands more than learning the ways
that these theories and concepts explain the economic
phenomena and the behavior of business entities in the
economy. Economic literac:Y encompasses skillful use of
computer software as an auxiliary rool of applying the
established principles for optimization.
··-----·-- -- ......... ...........1--..................
12112024
..
0
o•
I
The powerful, extensive and expansive SAS software which
plays a pioneering role in statistical software technology can
immensely benefit the practical application of the concepts
which once were considered as pure abslracts.
The maximum profit can be earned with the optimal
production level of 21.45 (1000) EZ Razors and a unit price of
$341.40. As the above graph indicates, the Company's profit
would be $3,055.552 (1000), assuming no changes in the demand
data and cost of production occur.
REFERENa5
Aster, Rick and Seidman, Rhena. Professional SAS Programming
Secrets. 1991. Blue Ridge Summit, PA.: Windcrest Books.
SUMMARY
Dilorio, Frank. SAS Applications Programming: A Cientle
lntrodudion, 1991. BOSton, Massachusetts: PWS-Kent
Publishing Company.
The decision problem considered in this pmsentltion pertains
to the quantity of razor production and the selling price which
ensure the maximum profit. A hypothedcal management case
study is used for managerial economics analysis. The data relevant
to this case are comprised of 16 weekly razor produc:tian quantity
and the lllSPf!(%ive weekly tolaJ cost and total revenue. Total COSIS
include the overhead and variable production COS1S covering both
the implidt and explidt paymentS made for all the factor inputs be
it material at services.
SAS Institute Inc., SAS System for Regression. Second Edition,
1991. Cary, North Carolina: SAS Institute Inc.
SAS Institute Inc., SAS System for Elementary Statistical Analysis.
1987. Cary, North Carolina: SAS Institute Inc.
SAS Institute Inc., SASIETS User's Ciuide. Version 6 Second
Edition. 1993. Cary, North Carolina: SAS Institute, Inc.
The economic themy of profit maximization targetS the
optimal quantity at which marginal revenue equals marginal COSL
Application of this quantity into the average revenue function
solves the per unit price which brings the maximum profit.
SAS Institute Inc., SASISTAT User's Guide. Version 6 Fourth
Edition. 1990. SAS Institute, Inc.: Cary, North Carolina.
The SAS procedures are instrumental in solving this and more
complex management case problems. Although oversimplified, this
PI oposed case study would have been very difficult to resolve
without the use of the related SAS programs. Within the framework
of economic theory and prindples of profit maximization, PROC
PLOT, PROC RECi, and PROC STEPWISE were used to delermine
the most suitable functions for TR and TC, and to derive other
related functions needed to solve the manaserial case study. The
results are summarized in Table VII.
William and Sincich, Terry. A Second Course in
Edition. 1994. Oellen Publishing Company.
Fourth
Statistics,
Mendenhal~
Hirshey, Mark and Pappas, )ames. Managerial Economics,
Seventh Edition. 1993. The Dryden Press.
Parkin, Michael. Microeconomics, SecOnd Edition. 1993.
Addison-Wesley Publishing Company.
Table VIII
Opdmizatlon Summary Chari
EZ Razor Company
O!Himal nutnber of weekly EZ Razor produclion
O!Himal per unit price 111 c:har1e
Averap per unit CXISI of produaion
Maximum possible economic profit
2,145
$0.34
$0.20
2.145 (0.141-$3 00.00
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