A NEW PRODUCTGROWTHMODELFORCONSUMER
DURABLES
- FRANKM. BASS
INSTITUTE FOR RESEARCH
IN THE BEHAVIORAL, ECONOMIC,
AND MANAGEMENTSCIENCES
INSTITUTE PAPER
NO. 175
HERMAN C. KRANNERT GRADUATE SCHOOL
of
INDUSTRIAL ADMINISTRATION
PURDU E UNIVERSITY
;
.---
PURDUE UNIVERSITY
KRANNERT SCHOOLOF INDUSTRIALADMINISTRATIONINSTITUTE PAPER SERIES
Copies of the following papers may be>obtained by writing to The Editor, Institute Paper Series, School of Industrial Administration,
Purdue University,
Lafayette, Indiana.
An asterisk (*) after the title indicates that the
supply has been exhausted, though copies may occasionally
be obtained by writing directly to the author. The
symbol, #, indicates that the paper has been subsequently
published, and is available in either the Institute
Series or published version.
1964
65.
66.
67.
68.
Charles W. Howe, PROCESS AND PRODUCTION FUNCTIONS FOR INLAND WATERWAY TRANSPORTATION.*
Donald B. Rice, PRODUCT LINE SELECTION AND DISCRETE OPTIMIZING.*
William Starbuck, ORGANIZATIONAL GROWTH AND DEVELOPMENT.#*
Cliff Lloyd, ON THE FALSIFIABILITY
OF TRADITIONAL DEMAND THEORY.#*
69.
70.
Vernon L. Smith, EXPERIMENTAL AUCTION MARKETS AND THE WALRASIAN HYPOTHESIS.#*
Yasusuke Murakami, BALANCED GROWTH UNDER EXOGENOUS LABOR GROWTH. "
71.
72.
Paul De Schutter, AN AP PRAISAL OF A FEW EXAMPLES OF CONTEMPORARY
James P. Streamo, TESTING ECONOMETRIC MODELS.*
73.
Karl E. Weick, LABORATORY
74.
75.
James Quirk and Richard Ruppert, QUALITATIVE ECONOMICS AND THE STABILITY OF EQUILIBRIUM.#*
Vernon L. Smith, ON PRODUCTION FUNCTIONS OF CONSTANT ELAST)cITY OF SUBSTITUTION.
76.
Hugo Sonnenschein,
CHOICE SPACE.
77.
Charles W. Howe, MODELS OF A. BARGELlNE:
TRANSPORTATION. *
78.
R. L. Basmann, ON PREDICTIVE
FOOD IN THE U.S.*
79.
Thomas Joseph Muench, CONSISTENCY OF LEAST SQUARE ESTIMATORS OF COEFFICIENTS
STOCHASTIC DIFFERENCE
EQUA TIONS.*
80.
81.
82.
Peter Jason Kalman, THEORY OF CHOICE WHEN PRICES ENTER THE UTILITY FUNCTION.
Yasusuke Murakami, BALANCED GROWTH UNDER EXOGENOUS LABOR GROWTH: 11*
George Horwich, AN INTEGRA TED ANAL YSIS OF AGGREGA TE SUPPL Y AND DEMAND.*
83.
Peter Jason
84.
85.
86.
87.
Peter Jason Kalman, PROFESSOR PEARCE'S ASSUMPTIONS AND THE NONEXISTENCE OF A UTILITY
Richard E. Walton, THEORY OF CONFLICT IN LA TERAL ORGANIZATIONAL RELA TlONSHIPS.*
Richard E, Walton and Robert B, McKersie, ATTITUDE CHANGE IN INTERGROUP RELA TlONS.*
William H. Starbuck, MATHEMA TICS AND ORGANIZA TION THEORY.#*
ECONOMETRIC ANAL YSIS.*
EXPERIMENTA TION WITH ORGANIZA TIONS.*
THE RELA TIONSHIP BETWEEN TRANSITIVE
PREFERENCE
AND THE STRUCTURE
OF THE
AN ANALYSIS OF RETURNS TO SCALE IN INLAND WATERWAY
TESTING OF A SIMUL TANEOUS EQUATIONS MODEL: THE RETAIL MARKET FOR
Kalman, A CLASS OF UTILITY
Kalman, THE EXISTENCE
IN EXPLOSIVE
"
FUNCTIONS ADMITTING TYRNI'S HOMOGENEOUS SAVING FUNCTION.
88.
Peter Jason
89.
Vernon L. Smith, BIDDING THEORY AND THE TR'EASURY BILL AUCTION: DOES PRICE DISCRIMINATION INCREASE
BILL PRICES?#
90.
Yasusuke
91.
Nancy Lou Schwartz, ECONOMIC TRANSPORTATION
ERENCE TO INLAND WATERWA Y TRANSPORT.
92.
93.
J. M. Dutton and R. E. Walton, INTERDEPARTMENTAL
CONFLICT AND COOPERATION: TWO CONTRASTING STUDIES.*
R. E. Walton, J.M. Dutton, H. G. Fitch, A STUDY OF CONFLICT IN THE PROCESS, STRUCTURE AND ATTITUDES OF
LATERAL RELATIONSHIPS. #*
Murakami,
OF A GLOBALLY
FORMAL STRUCTURE
DIFFERENTIABLE
FUNCTION.,
DEMAND FUNCTION.
OF MAJORITY DECISION.
FLEET
COMPOSITION AND SCHEDULING,
94.
Edgar A. Pessemier,
95.
96.
Richard E. Walton, TWO STRA TEGIES OF SOCIAL CHANGE AND THEIR DILEMMAS.#*
John J. Sherwood, SELF IDENTITY AND THE SOCIAL ENVIRONMENT.#*
97.
Michael J. Driver, A STRUCTURAL
SIMULA TION.
98.
George Horwich,
99.
Vernon L. Smith, DISCRIMINATION VS. COMPETITION
AND MARKET BEHAVIOR.*
WITH SPECIAL
REF-
PRODUCT POLlCY.#
1965
ANALYSIS OF AGGRESSION, STRESS, AND PERSONALITY
TIGHT MONEY, MONETARY RESTRAINT,
AND THE PRICE LEVEL.#*
IN SEALED BID AUCTION MARKETS: A STUDY IN INDIVIDUAL
100.
John J. Sherwood,
101.
Keith V. Smith, CLASSIFICATION
102.
James Streamo, ANOTHER LOOK AT THE RETAIL FOOD MARKET IN THE UNITED STATES: 1942-1959
ECONOMETRIC MODEL).
Yo Fukuba, DYNAMIC NETWORK FLOWS.
103.
104.
AUTHORITARIANISM
IN AN INTER-NATION
AND MORAL REALlSM.#*
OF INVESTMENT SECURITIES
R. L. Basmann, ON THE EMPIRICAL
'INTERDEPENDENT'
MODELS. "
TESTABILITY
OF 'EXPLICIT
USING MUL TIPLE
DISCRIMINANT ANALYSIS.
(TESTING AN
CAUSAL CHAINS' AGAINST THE CLASS OF
A NEW PRODUCT GROWTH MODEL FOR CONSUMER DtJRABLES
BY
FRANK M. BASS
PAPER NO. 175
JUNE 1967
INSTITUTE FOR RESEARCH
IN THE BEHAVIORAL, ECONOMIC
AND MANAGEMENT
SCIENCES
HERMANC. KR.A!rnERTGRADUATESCHOOL
OF
INDUSTRIAL ADMINISTRATION
PURDUE UNIVERSITY
LAFAYETTE, INDIANA
A New Product
Growth
Model
Frank
Krannert
Graduate
For Consumer
Durables*
M. Bass
School
of Industrial
Purdue
University
Administration
A growth model for the timing of initial purchase of new products is
developed and tested empirically against data for eleven consumer durables.
The basic assumption of the model is that the timing of a consumer's initial
purchase is related to the number of previous buyers.
A behavioral rationale
for the model is offered in terms of innovative and imitative behavior.
The
model yields good predictions
of the sales peak and the timing of the peak
when applied to historical data.
A long-range forecast is developed for the
sales of color television sets.
The concern
initial
purchase
work presented
however,
range
here
between
to apply
classes
of products
for new brands
and Woodlock
[2],
or new products
The growth
reflected
by growth patterns
to a peak
and then level
*
to the growth
new classes
[1], Fourt
asymptote.
1
The empirical
with consumer
"new" generic
of a theory
of timing
aspects
durables.l
as opposed
of the
The theory,
of initial purchases
of products.
of
of a broad
Thus we draw a
to new brands
or
of older products.
Haines
models
products.
deal primarily
of distinctive
new models
is the development
of new consumer
is intended
distinction
same
of this paper
See the addendum
model
and others have
which
postulated
similar
suggests
here,
exponential
however,
to that shown in Figure
off at some magnitude
for analysis
suggested
lower
growth
growth to
is best
1.
Sales grow
than the peak.
of two non-durables.
Same of the basic ideas in this paper were originally suggested to
me by Peter Frevert, now of the University of Kansas.
Thomas H.
Bruhn, Gordon Constable, and Murray Silverman provided programming
and computational
assistance.
2
The stabilizing
effect
ment purchasing
component
component.
is accounted
of sales
We shall be concerned
Sales
for by the relative
and the decline
here
growth of the replace-
of the initial purchase
only with the timing
of initi~l purchase.
..
Time
Figure 1
.Growth of a New Product
Long-range
best.
Some things,
theoretical
have
the assumptions
concepts
emerging
differs
growth
application
are similar
a rationale
in epidemology.
in certain
respects
on new product
on the log-normal
in that the behavioral
models
[3J Behav-
to the theoretical
adoption
and diffusion,
[7J, [8J The model
distribution
assumptions
The
for long-range
from the contagion
well as to some learning models.
based
game, at
to guess than others.
here provides
in the literature
from models
models
sales is a guessing
stems mathematically
such widespread
iorally,
[4J, [5J, [6Jas
may be easier
presented
The theory
found
of new product
however,
framework
forecasting.
which
forecasting
[9J and other
are explicit.
3
'Ihe Theory of Adoption and Diffusion
The theory
by a social
is largely
the premises
follows
will
of other
individuals
decide
formulation
This
We shall
expect
the following
as
of the
refer
the first
classes
to these
adopters
of adopters
(3) Early Majority,
classification
are
(4) Late
is based upon the timing
are influenced
social
system,
presented
(5) above and define
vators,
are influenced
in the
system.
two and one-half
venturesome
When we say that
by other
of the theory
independently
system.
ordinarily
adopters
through
as being
which
of
groups.
of the theory
as the first
easy to separate
In the discussion
(2) Early Adopters,
of the
social
This
[4]
not always
an innovation
with the number of previous
members of the
by Rogers.
the major ideas
in a social
We might
from innovators,
adopters
purchase
to adopt
In the literature,
th~ pressures
or new products
of adoption.
by the various
Apart
innovators.
conclusions.
and (5) Laggards.
adoption
described
from the
(1) Innovators,
.
Majority,
later
is therefore
as innovators.
specified:
tion.by
It
individuals
to be innovators.
of new ideas
at length
be made to outline
to the timing
Some individuals
decisions
literary.
of the theory
an attempt
apply
and diffusion
system has been discussed
discussion
they
of the adoption
here
the pressure
adopters.
we shall
them as imit_e.tors.
timing
percent
defines
they
members of the
aggregate
innovators,
They also
system,
groups
(2)
unlike
inno-
by the decisions
are not influenced
social
for
In the mathematical
of the adopters.
and daring.
of adop-
increasing
Imitators,
of adoption
Rogers
in the timing
of other
rather
arbitrarily,
Innovators
interact
with other
in the timing
we mean that
are
of
the pressure
for
4
adoption,
for this group,
process.
In fact,
In applying
consumer
quite
does not increase
the opposite
the theory
product,
of initial purchase
the following
precise
initial purchase
~
~
linear
!!.
p +.9.
m yeT),
buyers.
function
where
Since
~ ~ ~ !i!given ~ ~
Y(O) = 0, the constant
=°
in the social
system.
time
used
and its magnitude
to measure
time,
in which
the pressures
operating
In the section
be formulated
to initial
element
Rogers
which
in terms
purchase.
the fraction
follows,
as a likelihood.
The product
as the number
model
therefore
Thus, p( T) =
of previous
of innovators
depend upon the
to select a unit of measure
the basic
of a continuous
We shall
of the model
~
of an initial
the importance
of all ad?pters
them.
on imitators
buyers.
p is the probability
it is possible
defines
The probability that
and yeT) is the number
reflects
assumption
purchasehas
yet
.
,
previoUs
Since the parameters
such that p reflects
the sense
~
number
p and .9.
m are constants
purchase at T
scale
~ ~
of a new
and basic
which, hopefully, characterizes the literary theory:
~
of the adoption
may be true.
to the timing
we formulate
with the growth
who are innovators
in
.9.
m times yeT) reflects
of previous
assumption
buyers
increases.
of the theory'will
and a density
refer
for
function
of time
to the linear probability
5
Assumptions and the Model
The following
a)
purchases
fundamental
assumptions
Over the period
characterize
of interest
there will be mini tial
of the product.
b)
The likelihood
of purchase
at time T given
purchase has yet been made is i~~tT)
::
likelihood of purchase at T and F(T)
= S Of(t)
fore sales at T
The
being
the buying
of their
bought
the product,
buyers.
already
+ q J o~
for these
the important
timing
previous
dt,
where
that
and F(O)
T
('
dt J [ m
assumptions
initial
distinction
motive.
purchase
while
Innovators
by the number
imitators
Imitators
between
= O.
- j OS(t)
There-
dt ]
.
are summarized:
"innovators"
an ihnovator
and an
are not influenced
of people
are influenced
"learn,"
no
is the
f(T)
Initial purchases of the product are made by
"imitators,"
imitator
rationale
p T+ q F(T)
Ts(t )
= SeT) = mr(T) = [ p
behavioral
a)
and
the model:
who have
by the number
in some sense,
in the
already
of
from those who have
bought.
b)
The importance
of innovators
will be greater
at first but
will diminish monotonically with time.
c)
q as the
We shall refer
coefficient
Since f(T)
F
=p
= [p
= (q
+ (q-p
dF) F
- pe
- (T +
q (1 + e-(T
of innovation
and
of imitation.
in order to find F(T)
dT
to.p as the coefficient
-q
+ q F(T)]
[1
we must
F2.
- F(T)]
solve
=P
this non-linear
The solution is:
C) (p + q) )
+ C) (p + q))
.
+ (q
- p)
F(T)
- q [F(T)]2,
differen~ial
equation:
6
Since
F(O)
-c _
1
= 0,
the integration
- I' + q Ln (qjp)
constant
and F(T) = (1
-
e
- (p
_I
=
(I'
e
+ q)2
-
(I'
+ q) T
p.
(I'
(qjpe
To find the time
at which
,
+ q)
T
+.
1)2
the sales
-(1"+ q) T
+ q) T)
(I'+ q) T
+
1)
( Y./pe
f(T)
may be evaluated:
and
rate reaches
its peak,
we differentiate
-(I'+ q) T
e
1)
S' = m
- I'
T
(qjpe
1)3
Thus, T* = - I' .~ q Ln(p/q) .= I' ~ q Ln(qjp) and if an interiormaximum
exists, .q > p.
The solution is depicted graphically in Figure 2 and 3.
SeT)
SeT)
T
T*
Figure 2
Growth Rate
(q>
1')
T
Figure 3
Growth Rate
(q "S 1')
S,
7
T
We note that S( T*)
Since
for
= m(p
successful
ordinarily
+ q)2
new products
be much larger
is approximately
to purchase,
than
one-half
E(T),
and Y(T*)
m.
the coefficient
;~
also
In estimating
data
model is:
SeT)
the parameters
we use the following
ST ~ sales
where:
period T-l.
-qjm:
-mc
Then q
= q,
analogue:
that
sales
the expected
time
- qjm Y2 (T).
(q - p) yeT)
ST
T-1
=a
~1
+ bYT
_
time series
1 + c~
= cumulative
St
pm, b estimates
_ 1
'sales
and c m + bm + a
T
= 2,3...
through
Jb2c2 -
+
-b-
2
'
q-p, and c estimates
= p.
- p = -mc -aim = b,
and the parameters
of innovation,
and m from discrete
at T, and YT _ 1: t
aim
will
Analogue
= pm +
p,q,
Since a estimates
of imitation
.
The Discrete
The basic
= m(q2q'
- p)
S(t ) dt
coefficient
We note
~ Ln~
is
the
=J°
= 0, or m =
p, q, and m are identified.
4ca
If we write S(YT _ 1)
dS
and differentiate
with
respect
to YT _ l'
dyT
T-
= b + 2cYT _ l'
1
-b m(q - p)
Setting
this
equal
b2
b2
a-2C+4C=
to 0, Y*
T
m(p + q)2
4q
a function
of time
cumulative
sales.
=
coincides
-
1
S( T*)
= 2c =
.
Therefore,
were developed
to test
using
the model,
annual
the maximum value
with the maximum value
Regression
In order
= Y(T*), and ST(y*T - 1 ) =
2q
time
of S as a function
of
Analysis
regression
series
of S as
data
estimates
for
eleven
of the parameters
different
consumer
8
durables.
The period
only those
intervals
tance.
of analysis
in which
Table 1 displays
The data appear
are reasonably
model.
4,
5,
For every
product
studied
of the time path
of the peaks
are largely
explainable
and booms
apparent
in the years
was not a factor
with the model.
estimates
equation
of impor-
The R2 values
seem reasonable
for three of the products
the regression
of growth
a very
the timing
is especially
case to include
for the
and 6 show the actual values of sales and the values
by the regression
provides
in every
results.
to be in g~od agreement
high and the parameter
Figures
equation
repeat purchasing
the regression
predicted
trend
was restricted
good
very
equation
well.
In addition,
fit with respect
in Figure
of sharp
of short-term
5,
where
deviations
the general
the regression
to both the magnitude
for all of the products.
in terms
describes
analyzed.
Deviations
from trend
income variations.
it is easy to identify
from trend.
and
This
recessions
Table I
Growth
Product
Period
Covered
Model
Regression
~
Results
~
~
3,
,
For
Eleven
Consumer
Durable
~
R2
(,,,-7,J
c~-
Products
~
~
A
c
"7ii\
.
m
3
- ,
p
q
Electric
Refrigerators
1920-1940
104.67
.21305
- .053913
.903
1.164
6.142
-2.548
40,001
.0026167
.21566
Home
Freezers
1946-1961
308.12
.15298
-.071868
.742
4.195
4.769
-3.619
21,973
.018119
.17110
2,696.2
.22317
-.025957
.576
3.312
3.724
-3.167
96,717
.027877
.25105
.919
3.593
8.089
-6.451
5,793
.017103
.29695
Black and White
Television
1946-1961
Water
1949-1961
.10256
.27925
Room Air
Conditioners
1946-1961
175.69
.40820
-.24777
.911
1.915
8.317
-6.034
16,895
.010399
.41861
Clothes Dryer
1948-1961
259.67
.33968
-.23647
.896
2.941
7.427
-5.701
15,092
.017206
.35688
I.awnmowers
1948-1961
410.98
.32871
-
.075506
.932
1.935
7.408
-4.740
44,751
.0091837
.33790
Electric Bed
Coverings
1949-1961
450.04
.23800
--031842
.976
3.522
6.820
-1.826
76,589
.005876
.24387
1948-1961.
1,008.2
.28435
-.051242
.883
3.109
6.186
-4.353
58,838
.017135
.30145
Steam Irons
1949-1960
1,594.7
.29928
-.058875
.828
3.649
5.288
-4.318
55,696
.028632
.32791
Record
1952-1961
.62931
-.29817
.899
1. 911
5.194
-3.718
21,937
.024796
.65410
Softeners
Power
-512.59
Automatic
Coffee
Makers
Players
543.94
Data Sources:
Economic
Almanac,
Electrical
Statistical
Merchandising,
Abstracts
of the U.S.,
and Electrica1JMerchaDd1Sing
~.
\0
.
10
.
.
en
IJ.J
...J
«en
.
.
.
.
20
o
1947
1949
-
.
1951
.
1953
1955
ACTUAL
PREDICTED
1957
1959
YEAR
Figure
4
Actual
(Room
Sales
and Sales
Air Conditioners)
Predicted
by Regression
Equation
1961
11
1200
110
1000
900
(/)
-c
c:
0
I.
(/) 8001
::J
0
.
I
.c
b
en
LLI
...J
«en
60
500
-
.
ACTUAL
PREDICTED
400
1947
1949
1951
1953
1955
1957
1959
YEAR
Figure
5
Actual
(Home
Sales and Sales
Freezers)
Predicted
by Regression
Equation
1961
12
8000
7000
6000
.....-.-
5000
.
c::
c
(/)
:I
4000
...
.......-
-
CJ)
3000
«CJ)
.
.-
.
.
r-
2000
-
1000
1947
1949
1951
1953
ACTUAL'
.
PREDICTED
1955
1957
1959
YEAR
Figure 6
Actual
(Black
Sales and Sales Predicted
& White Television)
by Regression
Equation
1961
13
Model
The performance
Performance
of the regression
equation
relative
to actual
sales
is a
,
relatively
comparison
test
weak test of the modei.tsperformance
since it amounts
of the regression
with the data.
is the performance
ling parameter
provides
peak
for the eleven
period
the comparison
timing
products
"forecast"
~
for the first
period
over a long-range
values,
in the
model,
2
of
the regression
with which
It is clear from
of the-
studied.
it would
interval
I as that
good predictions
for all eleven products
the accuracy
time period
time.
2 that the model provides
to determine
sales
Table
of time of peak and magnitude
S(O) = pm, we identify
or exceed
of the peaks
the parameter
basic
prediction
estimates.
studied.
in Table
and magnitude
In order
equal
;E9st
with time as the vari3ble and control~
from the regression
to the model
sales
shown
model
of the model's
according
in which
estimates
of the basic
as determined
a comparison
Since,
to
values
equation
to an .~
A much stronger
have been possible
with prior
p.stimates of the parameters
knowledge
of
were substituted
c - (p + q) T
S(T)
(p + q)
+
/pe
(q
arid sales
estimates
generated
for each of the products
in the intervals shown in Table
fit to the data.
a good description
trend
being
and actual
Even
3.
sharp, but ephemeral.
sales
curves
In most cases the model provides a good
in the few instances
of the general
for three
for each year indicated
trend
of low 1'2 values,
of the sales
Figures
7,
8,
the model provides
curve, the deviations
and 9 illustrate
of the products.
from
the predicted
14
Table 2
Comparison
Product
of Predicted Time and Ma~tude
of Peak with Actual
for Eleven Consumer Durable Products
qjp
Predicted
Actual Time
of Peak*
Time
of Peak
Values
Predicted Magnitude, of Peak, "
2
, ,. "1
T*
p+q
Home
Freezers
'
'
82.4
Peak
S(T*) =
Ln(qjp)
(106)
Electric
Refrigerators
Actual
Magni tude
20.1
q
(106)
**
2.20
**
13
1.2
1.2
..'
9.4
11.6
9.0
7.8
7
7.5
7.8
16.7
8.9
9
.5
.5
.
Black &
White
Televisior
Water
Softeners
Room Air
Condi..
..,
"
tioners
40.2
8.6
7
1.8
1.7
Clothes
Dryer
20.7
8.1
:1
1.5
1.5
Power
Lawnmowers
36.7
10.3
11
4.0
4.2
Electric
Bed
Coverings
41.6
14.9
14
4.8
4.5
10
4.8
4.9
7
5.5
5.9
5
3.8
3.7
"
Automatic
Coffee
Makers
18.1
,-
9.0
Steam
Irons
11.4
6.8
Record
Players
26.3
4.8
I
*Time period one ASAdefined
as that period
equal or exceed p m for the first time.
**Interrupted
by war.
6 ,,'.-,
x 10 Uriits;
Prewar
peak
for which
sales
in year 16 (1940) at 2.6
'
of
15
4500
4000
3500
----.
~c 3000
c
U)
::J
o
.s::.
...
'--'
2500
.
(J)
~
«
2000
.
(J)
.
1500
-
.
1000
500
19~9
1951
1953
1955
ACTUAL
PRED
1957
1CTED
1959
YEAR
Figure
7
Actual Sales and Sales
(Power Lawnrnowers)
Predicted
by Model
1961
16
1600
1400
1200
......-.
fn
-c
c:
C
fn
1
r
.
L
I
.
I
000
0
.s=
.
0
en
800
IJJ
-I
<t 600
en
-
.
400
1954
1956
ACTUAL
PREDICTED
1958
YEAR
Figure
8
Actual
Sales and
(Clothes
Dryers)
Sales
Predicted
by Model
1960
17
8000
7000
f/)
"'C
C
C
~
6000
o
.s::;
+-,.
en 5000
ILl
...J
.
«
.
.
en 4000
3000
-
1949
Figure
1951
9
Actual
(Black
1953
1955
YEAR
.
ACTUAL
PRED CTED
1
1957
Sales and Sales Predicted
& White Television)
1959
by Model
1961
1$
It would
agreement
eppear
fair
to conclude
with the roodel.
and verified,
'l"hemodel
He may now claim
set out to explore.
for purposes
has,
is, however,
are two cases
the no-data
ask:
worth
considering
is it easier
or easier
to guess
to answer
this question,
to guess
the parameters
in general,
of the potential
to guess
at m, the size of the market,
curve
of
the
model
In order
case,
mate
since
there
occurs
skepticism,
variations
useful
develop
is possible
vations
be
as
by means
a test
of
in the three
will be made
here
that for some
guesses
of the parameters.
motives
should make it possible
other
the
values
than the model
in terms
of p and q,
observations
the parameter
observations.
of
possibilities
In prin-
of these obserwith some
are very sensitive
applying
data
some kind of esti-
should be viewed
Before
forecast.
in the limited
if the first
estimates
the
set sales.
to be estimated,
suggested
of the parameters
credibility
for color television
Any such estimate
since
No attempt
of this forecast
the forecasting
only three
curve for the new product
by a;:b'0nsideration ofbu:.yiJilg
motives;.. If
a forecast
at T = O.
however,
be useful
of these possibilities
and of the relative
are three parameters
with
the sales
and the buying
determined
to illustrate
we shall
ciple,
market
the implications
might
For either
to make plausible
is to be determined
in this paper,
we
forecasting:
but it does seem likely
Analysis
the sales
will this knowledge
of the model?
it would be possible
guess being
the phenomenon
in long-range
case.
products
the latter
"tested"
Forecasting
case and the limited-data
one may well
about
good
forecasting?
Long-Range
There
then, in some sense, been
to know something
The question
of long-range
that the data are in generally
estimates
to small
obtained
from
19
Table 3
Forecasting
Accuracy
Product
of the Model
for Eleven
Period
Consumer
of Forecast
Durable
Products
2
r
Electric
Refrigerators
1926-1940
.762
Home Freezers
1947-1961
.473
Black & White
Television
1949 -1961
.077*
.
1950-1961
.920
Room Air
Conditioners
1950-1961
.900
Clothes
Dryers
1950-1961
.858
Lawnmowers
1949 -1961
.898
1950-1961
.934
1951-1961
.690
1950-1961
.730
1953-1958
.953
Water
Power
Softeners
Electric
.
Bed
Coverings
Automatic
Makers
Steam
Record
Coffee
Irons
Players
*The low "explained" variance for this product is
accounted for by extreme deviation from trend in
two periods.
Actually, the model provide s a
fairly good description of the growth rate, as
indicatedin Figure9.
20
a limited
number
be closely
of observations,
the plausibility
of these estimates
scrutinized.
T-l
In substituting
continuous
model,
there
are several
Thus,
the proper
,T
~ St in the
t=o
a certain
probability
formulation
analogue
for!
Set) dt in the
Vo
was introduced.
This bias is mitigated
but can be crucial when there
of the discrete
model,
2
when
are only a few.
if ST = SeT) is:
ST =
yeT)
T =1
distribution
~
discrete
1 + ck (T) YT _ l' where k(T) = y--
_
for which~
x-l
= 0,
bias
observations,
2
a + bk(T) YT
F(O)
should
a)
f(x)
In particular,
f(t) = l/k F(x)o
= l/k
We note that for any
.
[F (x + 1) = F(x)J, and b)
these two properties
hold for the
t=O
exponential distribution.
x=l
Therefore, for this distribution ~
t=O
~() =
ko
The
f(t)
density function f(T) in the growth model developed in this paper is approx-
imately exponentialin characterwhen
[F.
(T +~)
-
apx
therefore
Then
write:
~t
m = l~t,
different
values
F
(T)]an~.=
apx
ST
=a
+ b'YT
_'1£q_1
q = .~1)
and p
1'1
and T are small
0
(p + q)
(
[e p
+
.
Forsmallvaluesof T we
)
q
- 1]
2
1 + ct~ _ l' Where b'
~. pI
_
=~.
of p + q has been
k
apx(T) = !
ThUs, f
The
value
calculated
= kb,
and c'
=k
Of'(k for each of several
and appears
in Table 40
C.
j
"
I
b'~'
-i
)
-'1/ j ,
-, -
~
=);;--
.. Ji
~I
d;;
---1
.'
.~
i
-- b J
-
'
..---
i,
Z.
J b -4~t.f
.
~
--
c..,'
" -.- x;.,
(j
~I
f)
J
,
'::
.
q
~
'76 ~. 4(1-1 i;)b
4(J-I- ~)6 ~ -. 97? +(=-0
--..-
q
.0
-; ,
~1,~
fl:.'11)?--f.~ (l+l,Jt
,~(l~~}
21
4
Table
Calculated
Values
O:f~k
and (p + q)
(p + q)
.85
.81
.77
.73
.69
.65
.61
-3
.4
.5
.6
.7
.8
.9
On the basis
Table
4:
I
o:f the relationship
Ik = .97 - ·4 (p
.
.
q'/p' =
p,
\ve turn
data
are
-~
d
qf
an
p
- q'
q
+ q), q
=
betweeny,k and (p + q) indicated
'f~I.'t!
=~
= , ..L I,
.97
(,
qI
..L 1 Ie. \
~
I
,
in
wheree
=
.97 p'.
1 +
now to the :forecast
.4
( 1 + e )p'
o:f color
teleVision
set. sales.
..The :folloWing
available:
(Millions
Sales
o:f Units)
Year
.7
1.35
2.50
Solving
the :following
So
system
o:f equations:
= .7 = a
= 1.35 = a + .7 b' + .49 c'
S2 = 2.50 = a + 2.05 b' + 4.20 c',
a' = .7, b' = .954, c' = -.0374,
Sl
we :find:
m' = 26.2, q' = .96, pi = ,0267,
q = .67, p = .018, m = 37.4.
.,
22
Table 5
Forecast
of Color Television
Sales
Year
Sales
these
parameter
model to generate
10.
The projected
cast
differs
pany's
values
appear
the series
plausible,
of estimates
peak occurs
department
has estimated
between
7 and 8 million
units.
reality
of actual
and one's
whether
or not the
sales
forecast
they have been used in the basic
of sales
in 1968 at around
somewhat from some industry
research
(millions)
1.35
2.5
4.1
5.8
6.7
6.3
4.7
1964
1965
1966
1967
1968
1969
1970
Since
1966-1970
shown in Table 5 and Figure
7 million
forecasts.
that
The forecast
personal
sales
speaks
units.
At this
will
writing,
one com-
"top out" iri1967
for itself
criterion
This fore-
at
and the ultimate
of "goodness"
will
determine
was a good one.
7
"
6
..........
to
s::
0
5
""
",
"
'ri
4
'B
........
to
Q)
M
cd
(J)
3
2
1
1964
66
68
Projected
Figu;re 10
Sales-Color Television
70
23
While
derived
this
forecast
from data,
sibility
was objectively
it is also based
of the parameters.
to small variations
the importance
upon
determined
a subjective
Since the parameter
in the observations
of the plausibility
in the sense that it was
judgment
estimates
of the plau-
are very sensitive
when there are only a few observations,
test
cannot be overemphasized.
Conclusion
The growth model
developed
purchase
of new products
purchase
at any time
is related
is a behavioral
rationale
There
exponential
In this
respect
Data
estimates
model
growth
viewpoint,
predictions
process
rationale
from other
the central
of both
Insofar
of new product
for long-range
to the number
to a peak
new product
are in,good
analysis
and magnitude
adoption,
implies
when used in conjunction
of sales.
decay.
Parameter
with the
From a planning
forecasting
for the products
contributes
buyers.
with the model.
of the sales peak.
the model
forecasting.
The model
of
growth models.
in long-range
of these variables
as the model
of previous
and then exponential
agreement
of the growth
interest
of initial
that the probability
for this assumption.
durables
of the timing
applied.
linearly
from regression
probably
for the timing
upon an assumption
purchases
good descriptions
good predictions
been
it differs
derived
provide
is based
of initial
for consumer
in this paper
The model
to which
to an understanding
may be useful
lies
in
provides
it has
of the
in providing
a
24
24
18
15
-'
W
> 12
.
W
..J
09
06
-
.
.
ACTUAL
PREDI CTED
.
03
01
02
03
04
05
07
06
09
08
TIME PERIODS
Figure
11
Actual
Model
Number Adopting
(Weed Spray)
and Number
Predicted
-
by
10
22.5
25
20.
.
1'7.5
15.0
.
12.51
J
W
>
W
.
J IQO
'7. 51
5.0
.".
2.51
.
01
02
03
TIME
Figure
12
Actual
Model
04
ACTUAL
PREDICTED
05
06
07
PERIODS
Number Adopting
(New Drug)
and Number
Predicted
by
08
26
ADDENDUM
Survey
The adoption
paper
were
patterns
inferred
from
was not a significant
analysis.
Published
products--a
on the timing
analyzed
of sales during
of some interest,
on survey
and panel
of the weed
in the main body
the time period
classes
methods
Information
,spray ,~d'from
covered by the
to examine
the dynamics
with non-sales
are available
was obtained
were
cumulative
slightly
from
distribution
sources.
for two
physi:cians..on,the timing
The data are shown below in Table 6.
by reading
data
from farmers
of'adoption of the new drug.
obtained
of the
that repeat purchasing
therefore,
product
and a new drug.
of adoption
Adoption
on the premise
for additional
data based
weed spray
for applicances
component
process
Non-Appliance
sales data
It is a matter
of the adoption
Data,
graphs
These
data
and therefore
are
inaccurate.
Table
6
Adoption Data for Two New Products
Time Period
1
2
3
4
5
6
7
8
9
2,4-D Weed Spray
Number Adopting
13.32
16.28
20.72
23.68
19.24
17.76
10.36
8.88
5.92
New Drug
Number
Adopting
18.75
21.25
22.50
5.00
6.25
8.75
3.75
2.50
Sources: Rogers, E. M., Diffusion of Innovations
(New York: The ~ee Press, 1962). p:- 109.
Coleman, James, Menzel, Herbert, and Katz, Elihu,
"Social Processes in Physicians Adoption of a New
Drug," in Frank, R. E. Kuehn, A.A., and Massy, W. F.,
~
Marketing
AnalksiS
Quantitative
Te'chniques
(Homewood: Richard
D. Irwin,
1962) po
2 1
,
The results of the regression analysis are summarized in Table
Figures
11 and 12.
The
density
function
of time
to initial
purchase
again unimodel and the model adequately describes the data.
Table
Parameter
Estimates
Parameters
a
b
c
m
q
P2
R2
r
For
a Weed
spray
Weed spray
8.04387
.44472
-.00346
144.1
.4998
.0558
.953
.958
7
and
a New
Drug
New D
17.81431
.189229
-.003277
107.07
.35086
.16638
.827
.791
7 and
is
28I
References
1.
Haines, G. H., Jr.,
"A Theory of Market Behavior After Innovation,"
Management Science',
No.4,
Vol. lO, July,
1964.
2.
Fourt, L., A. and WoodlQck, J. W., "Ea:r~y Prediction
for New Grocery Products,"
Journal of Marketing,
October, 1960.
3.
Bartlett,
4.
Rogers,
5 . King,
M. S.. Stochastic
E. M., Piffusionof
Population
6.
Katz, E. and Lazarsfeld,
7.
Rashevsky, N., Mathematical
University Press, 1959
1955.
Inflttence,
An Overview,"
(
New Yor~:
The Free Press,
Chicago:
The
"
Bush, R. R. and, Mostel;Ler, F., Stochastic Models for Learning, New
York:
9.
1962.
Conference of the
of Social Behavior,
,
8.
The Free Press,
in Marketing:
1966 Fall
Chicago, 1966.
F., Personal
Biolo~
New York:
Research
Technology and Marketing,
American Marketing Association,
of Market Success
No.2, Vol. 26,
Models in Ecolo
Innov)tt:ions,
C" W., "AQ.option and Diffusion
in Science,
.
Wiley, 1955.
Bain, A. D., The Growth of Television Owners:Q.ipin the United Kingdom,
A Lognormal Model, Cambridge;: The University Press, 19
10,
Dernburg , T., F ., "Consumer Response to Innovation:
Television,"
in
Studies in Household Economic Behavior, Yale Studies in'Economics,
Vol. 9, New Haven, Connecticut:
Yale, 1958.
'
..
.
11... Massy, W. F., "Innovation and Market Penetration,:'
Ph,D. Thesis,
Massachusetts Institute
of Technology, 1960, Cambr1dge, Massachusetts.
l2.
Mansfield, E., "Techno1.ogical Change and the Rate of Imitation,"
Econometrica, No.4, Vol. 29, October, 1961.
13.
Pessemier, E. A., .NewProduc,t Decisions,
McGraw-Hill, 19
An Anal
roach, New York:
APPENDIX
C
;_J~L.:::;PllliDICTION ANALYSIS-REGRESSIONCOEFFICIENTS
DIMENSION TITLE (80), S ( 50) , IDNUM(50) , ACTSAL(50 )
DATADOLLAR,/lH$,lHb
1 READ(5, 100) TITLE
WRITE(6,101) TITLE
-
/
SENT=BLANK
READ(5,102) A,B,C,N
0=(~B-SQRT(B**2-4.*A*C»/(2.*
P-A/O
Q=-O*C
K=l
MM=O
DO
C)
7 I=l,N
T=FLOAT(I)
.
S(K)=(0*(P+Q)*(EXP«-P-Q*T)/«Q(.P*EXP«-P-Q)*T)+1.)**2»
IF(SENT .EQ.DOLLAR)
GO TO
6
READ(5,103) IDNUM(K),ACTSAL(K),SENT
MM=K
6 IF(K.EQ.l.AND.ACTSAL(K) .LT.A) GO TO 7
K=K+l
7 CONTINUE
WRITE(6,104) O,P,Q
WRITE( 6,105)
DO 8 I=l,MM
WRITE(6,106)
I, IDNUM(I),S(I),ACTSAL(I)
8 CONTINUE
NN=MM+l
IDNUMP=IDNUM(MM)
K=K-l
DO 9 I=NN,K
IDNUMP=IDNUMP+l
WRI~(6,107)
I,IDNUMP,S(I)
9 CONTINUE
SUMSQD=O
.0
SUM=O.O
SUMSQ=O
.0
DO 10 I=l,MM
SUMSQ=SUMSQ+(S(I)-ACTSAL(I»**2
10 SUM=SUM+ACTSAL(I)
DO 11 I=l,MM
11 SUMSQD=SUMSQD+(ACTSAL(I)-(SUM/FLOAT(MM»
)**2
RSQ-l.
-
(SUMSQ/SUMSQD)
WRm:(6,lOB)
RSQ
GO TO 1
100 FORMAT(80Al)
101 FORMAT(lHl,19R PRODUCTANALYZED. , 80Al)
102 FORMAT(3F20.8,12)
103 FORMAT(14,FI0.3,65X,Al)
104 FORMAT(lH ,13H COEFFICIENTS,10X,4R M= ,FI0.3,10X,4H
P= ,F12.8,10X,
l4R Q= ,F12.8///)
105 FORMAT(iH ,13H SALES PERIOD, lOX, 5R YEAA,lOX, lOR EST-SALES, lOX, lOR
lACT-SALES ),
106 FORMAT(lH ,llX,'12,llX,1~,llX,F9.3,1+X,F9.3)
107 FORMAT(lH ,llX;12,llX,14,llX,F9.3)
108
FORMAT(lH ,13R
END
$DATA
R S~ARED
.
= ,F7.5),
29
30
[FORTRAN IV LANGUAGE]
SALES ESTIMATIONANALYSIS
- REGRESSIONCOEFFICIENTS
Problem:
Given regression
parameters
Calculate:
m, 15, q
where:
M=
p
q
Then:
S(T)
A, B, C for a PRODUCT
= Aim
= -mc
2
= m(p+q)
p
[(qfp)
where T = 1, N
St
= Actual
S(l)
= 1st
period
f
Print
Time periods
sales
Predicted
E-(P+q)T
E-(p+q)T+J.]::?
of perdiction
t
in time periods
for
which
sales
= 1,
n
S > A
t
(S(T) - St)2
Output:
1)
PARAMETERSM, P, Q and NAMEOF PRODUCT
2)
St Actual
where
3)
St
Sales,
-
where t goes from 1st
sales
per:i,od
.
A to n
S(T) Predicted
.
4)
and t,
>
Sales,
and T time period,
>
1
sa eS.,perJ.od where St - A
2
R term
with
1 the
first
31
I
IDENTIFICATIONCARD
Col.
1
2,3
4-6
7-10
11
12-14
15
16-18
19-20
21-72
$
.m
blanks
account number assigned by Computer Sci.
*
time estimate1
*
page output estimate1
**
name .! any other information
II
CONTROL CARDS2
A.
Col. 1
!
2-8
9-15
16-20
EXECUTE
blanks
PO'FFET
(or)
B.
!
Col. 1
2-8
9-15
16-20
EXECUTE
blanks
C.
Col. 1
2-6
!
D.
Col. 1
!
2-6
7
8
1
2
If8
page
If 9
page
or less
estimate
IBFTC
;;-raDk
SPARCE
data sets
(010)
or more data sets
estimate
are
used time
estimate
are use~ time estimate
2 min (002)
5 min (005)
(050)
If 8 or less Data sets are used punch control
deck under category "P"
If 9 or more data sets are used punch control
submi t deck under category "A".
card A and submit
cards B, C.,D and
32
III
DATA CARDS
A.
TITLE CARD
Name of product to be analyzed is punched on this card
Col 1-30 may be used with any data to define name.
B.
COEFFICIENTS.AND LIMIT CARD
Co1.
Co1.
Co1.
Co1.
1-20
21-40
41-60
61-62
VALUE OF COEFFICIENT A
VALUEOF COEFFICIENT B
VALUE OF COEFFICIENT C
MAXIMUM
NUMBEROF SALES PERIODS FOR WHICH
PREDICTION WILL BE MADE (N ~ 50)
Values of A,B,C may be numbers whose total length each is 19 or less
digi ts with 8 or less digits to right of decimal point.
Decimal Point
must be punched.
N is a two digit
number between 01-50.
Decimal Point ~
E.2!~ punched.
C. ACTUAL
SALES CARD(S)
Col.
1-4
Co1.
5-14
IDENTIFICATION NUMBERFOR SALES VALUE
(ALL four digits punched (0001»
VALUEOF ACTUALSALES FOR PARl'ICULARIDENTIFICATION
NUMBER
Valu~ of Actual sales may have up to 9 digits or less, with
3 or less digits to right of decimal point.
Decimal point
~ 'be punched.
Col.
80
A
!
acter
blank
or
!
in Col 80 signals the end of a data set.
This charmust be punched on the Last ACTUAL SALES CARD for
~given~set.
-
---
The number of ACRTALSALES CARDS must not exceed 50 and
must be less
than
equ'BI""'tO N (Specified
in data
card
B)
33
IV
ORDER OF CARDS
1-
2.
3.
Data
Deck
~:
U.
IDENTIFICATION CARD
CONTROL CARD(S)
SALES PREDICTION ANALYSIS
TITLE CARD (A)
-
PROGRAMDECK
COEFFICIENTSANDLIMIT CARD (B)
ACTUAL SALES CARD(S )
(C)
[WITH! IN COL80 OF LAST CARD]
Items 4-6 may be repeated any number of times if more than one data
set is used. See Notes (1) and (2) for proper control cards and
job category.
.
PURDUEUNIVERSITY
KRANNERT SCHOOLOF INDUSTRIAL ADMINISTRATIONINSTITUTE PAPER SERIES
(Continued from inside front cover)
106.
Michael J. Driver and Siegfried A. Streufert, THE "GENERAL INCONGRUITY ADAPTATION
AN ANAL YSIS AND INTEGRA TION OF COGNITIVE APPROACHES TO MOTIVA TION.
William H. Starbuck, THE HETEROSCEDASTIC NORMAL.
105.
AND SELF-IDENTITY
(GIAL) HYPOTHESIS:
THEORY.*
107.
John J. Sherwood and John R. P. French,
108.
Richard
109.
Stanley Reiter and Donald B. Rice, DISCRETE OPTIMIZING SOLUTION PROCEDURES FOR LINEAR AND NONLINEAR
INTEGER PROGRAMMING PROBLEMS.#
110.
111.
John J. Sherwood, SELF-REPORT
AND PROJECTIVE MEASURES OF ACHIEVEMENT AND AFFILIATION.#*
Ronald Kochems, AN APPLICATION OF MUL TIPLE DISCRIMINANT ANAL YSIS.
112.
113.
114.
John A. Shaw, THE THEORY OF CONSUMER RATIONING, PARETO OPTIMALlTY, AND THE U.S.S.R.
R. K. James, W. H. Starbuck and D. C. King, A STUDY OF PERFORMANCE IN A BUSINESS GAME _ REPORT 1.
Michael J. Driver, Purdue University, and Siegfried Streufert, Rutgers-The
State University, TH E GEN ERAL INCONGRUI TY
ADAPTATION LEVEL (GIAL) HYPOTHESIS: AN ANALYSIS AND INTEGRATION OF COGNITIVE APPROACHES TO
MOTIVATION.
E. Walton and Robert B. McKersie,
SELF-ACTUALIZATION
LEVEL"
BEHAVIORAL DILEMMAS IN MIXED MOTIVE DECISION-MAKING.#
115. Frank M. Bass and Ronald T. Lonsdale, AN EXPLORATION OF LINEAR PROGRAMMINGIN MEDIA SELECTION. *
Frank M. Bass, THE DYNAMICSOF MARKET SHARE BEHAVIOR.
116.
117.
118.
W. H. Starbuck
and F. M. Bass,
A HEWPRODUCT CONTEXT.*
AN EXPERIMENTAL
STUDY OF RISK-TAKING AND THE VALUE OF INFORMA TION IN
.
John R. P. French, Jr., John J. Sherwood and David L. Bradford,
ING CONFERENCE. #*
SOME ASPECTS
CHANGE IN SELF-IDENTITY
IN A MANAGEMENT TRAIN-
OF THE ECONOMICS OF A COMPUTER SYSTEM STUDY.
119.
R. A. Layton,
120.
121.
Walter Sikes, AN ANAL YS1SOF SOMEOUTCOMESOF HUMANRELATIONSLABORATORY TRAINING.
Charles W. King, COMMUNICATING WITH THE INNOVATOR IN THE FASHION ADOPTION PROCESS. #*
122.
R. A. Layton, A "SEARCH
POVERTY STUDIES.
123.
Charles
124.
Robert V. Horton, THE DUALITY
125.
Clarke C. Johnson
126.
Lawrence
AND ESTIMATION"
R. Keen, A NOTE ON KONDRATIEFF
SAMPLING PROCEDURE, WITH APPLICATIONS
IN AUDITING AND
CYCLES IN PREWAR JAPAN.
IN NATURE OF OFFERINGS OF ADDITIONAL
COMMON STOCK BY MEANS OF "RIGHTS".
1966
127.
Carson,
and Charles
E. Gearing, INFLUENCES
ON ACADEMIC PERFORMANCE.*
DonaldJunker,
Eugene Rice, Richard Teach, Douglas Tigert, William Urban, EXPERIMENTAL
IN CONSUMERBEHAVIOR: FOUR EXPLORATORY PAPERS. *
Mohamed A. El-Hodiri, OPTIMAL RESOURCE ALLOCA TION OVER TIME1.*
RESEARCH
128. Atsushi Suzuki, A LlN=:AR STATISTICAL MODEL OF AMERICANBUSINESSCYCLES. *
129. Lowell Bassett, Hamid Habibagahi, James Quirk, QUALITA TIVE ECONOMICS
AND MORISHIMAMATRICES.*
130. Philip Ginsberg and David Richardson, SOMEECONOMICAPPLICATIONS OF THE GCL PRINCIPLE OF ESTIMATION.*
131.
132.
C. S. Yan, OPTIMAL INVESTMENT AND TECHNICAL
C. S. Yan, TECHNICAL CHANGE AND INVESTMENT.
PROGRESS.
133.
Philip Burger and Donald B. Rice, INTEGER PROGRAMMING MODELS OF TRANSPORTATION
SYSTEM EXAMPLE.
134.
135.
Mohamed A. El-Hodiri,
Mohamed A. El-Hodiri,
A CALCULUS PROOF OF THE UNBIASEDNESS OF COMPETITIVE
TWO ESSAYS ON DYNAMIC MICRO ECONOMICS.
SYSTEMS _ AN AIRLINE
EQUILIBRIUM.
136. Marc Pilisuk, J. Alan Winter, Reuben Chapman, Neil Haas, HONESTY, DECEIT, AND TIMING IN THE DISPLAY OF
INTENTIONS.#
E. Walton, CONTRASTING
DESIGNS FOR PARTICIPATIVE
SYSTEMS.
137.
Richard
138.
Marc Pilisuk, Paul Skolnick, Kenneth Thomas, Reuben Chapman,
DEVELOPMENT OF COOPERATIVE STRA TEGY. #
139.
John A. Eisele, Robert Burr Porter, Kenneth C. Young, AN INVESTIGATION
AN EXPLANA TION OF THE BEHAVIOR OF ECONOMIC TIME SERIES.
140.
Mogens D. Romer, ELECTRONIC DATA PROCESSINGIN INDUSTRIAL ENTERPRISE.
141.
Mohamed A. El-Hodiri, CONSTRAINED
REVIEW AND GENERALIZATIONS.
142.
143.
Michael J. Driver and Siegfried Streufert, GROUP COMPOSITION, INPUT LOAD AND GROUP INFORMATION PROCESSING.
Edgar A. Pessemier and Richard D. Teach, A SINGLE SUBJECT SCALING MODEL USING JUDGED DISTANCES BETWEEN
PAIRS OF STIMULI.
144.
145.
Harry Schimmler, ON IMPLICATIONS OF PRODUCTIVITY COEFFICIENTS AND EMPIRICAL
Hamid Habibagahi, WALRASIAN STABILITY: QUALITATIVE ECONOMICS.
BOREDOMVS. COGNITIVE REAPPRAISAL IN THE
OF THE RANDOM WALK HYPOTHESIS AS
EXTREMA OF FUNCTIONS OF A FINITE NUMBER OF VARIABLES.
;
RATIOS.
PURDUEUNIVERSITY
KRANNERTSCHOOLOF INDUSTRIALADMINISTRATIONINSTITUTE PAPER SERIES
(Continued
from inside 'back cover)
146.
Edgar A. Pessemier,
147.
148.
Marc Pilisuk, DEPTH, CENTRALITY, AND TOLERANCE IN COGNITIVE CONSISTENCY.#
Michael J. Driver and Siegfried Streufert, THE GENERAL INCONGRUITYADAPTATION LEVEL (GIAL) HYPOTHESIS- II.
MEASURING SOCIAL, SCIENTIFIC
INCONGRUITY MOTIVATION
149.
150.
151.
TO AFFECT,
AND MILITARY
BENEFITS IN A DOLLAR METRIC.
COGNITION, AND ACTIVATION-AROUSAL
THEORY.
Akira Takayama, BEHAVIOR OF THE FIRM UNDER REGULATORY CONSTRAINT:COMMENT.
Keith V. Smith, PORTFOLIO REVISION.
Abraham Tesser, Robert D. Gatewood, Michael Driver, SOME DETERMINANTS OF FEELINGS OF GRATITUDE.
152. S. N. Afriat, ECONOMIC TRANSFORMATION.
153. Edward Ames and Nathan Rosenberg, THE ENFIELD ARSENAL IN THEORY AND HISTORY.
154. Robert Perrucci,
HEROES AND HOPELESSNESS IN A TOTAL INSTITUTION: ANOMIE THEORY APPLIED TO A COLLECTIVE DISTURBANCE.
155. Akira Takayama, REGIONAL ALLOCATION OF INVESTMENT: A FURTHER ANALYSIS.
156.
Cliff Lloyd, R. J. Rohr and Mark Walker, A CALCULUS PROOF OF THE EXISTENCE OF A CONTINUOUS UTILITY
FUNCTION.
1967
157.
Cliff Lloy<!, MONEYTO SPEND AND MONEYTO HOLD.
158. Cliff Lloyd, TWOCLASSICAL MONETARYMODELS.
159. Robert Perrucci, SOCIAL PROCESSES IN PSYCHIATRIC DECISIONS.
160.
161.
S. N. Afriat, PRINCIPLES OF CHOICE AND PREFERENCE.
James M. Holmes, THE PURCHASING POWER PARITY THEORY: IN DEFENSE OF GUSTAV CASSEL AS A MODERN
162.
John M. Dutton and William H. Starbuck,
163.
Akira Takayama,
164.
Frank DeMeyer and Charles
165.
166.
167.
168.
169.
170.
Siegfried
THEORIST.
171.
172.
173.
174.
Streufert
HOW CHARLIE ESTIMATES RUN-TIME.
PER CAPITA CONSUMPTIONAND GROWTH:A FURTHER ANALYSIS.
R. Plott,
and Michael
THE PROBABILITY
J. Driver,
CREATIVITY,
OF A CYCLICAL
COMPLEXITY
MAJORITY.
THEORY AND INCONGRUITY ADAPTATION.
John C. Carlson, THE CLASSROOM ECONOMY: RULES, RESULTS, REFLECTIONS.
Carl R. Adams, AN ACTIVITY
Charles
W.
MODEL OF THE FIRM UNDER RISK.
King and John O. Summers, INTERACTION PATTERNS IN INTERPERSONAL COMMUNICATION.
Vernon L. Smith, TAXES AND SHARE VALUATION IN COMPETITIVE MARKETS.
James M. Holmes, AN ECONOMETRIC TEST OF SOME MOOERN INTERNATIONAL TRADE THEORIES: CANADA 1870-1960.
Akira Takayama and Mohamed EI-Hodiri, PROGRAMMING, PARETO OPTIMUM AND THE EXISTENCE OF
COMPETITIVE EQUILIBRIA.
Marc Pilisuk and Paul Skolnick, INDUCINGTRUST: A TEST OF THE OSGOODPROPOSAL.
S. N. Afriat, REGRESSION AND PROJ ECTION.
Stanley M. Halpin and Marc Pilisuk,
PREDICTION
AND CHOICE IN THE PRISONER'S
DILEMMA.