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Full text of "Dynamics of price elasticity and the product life cycle : an empirical study"

7f 



WORKING PAPER 
ALFRED P. SLOAN SCHOOL OF MANAGEMENT 



DYNAMICS OF PRICE ELASTICITY 
AND THE PRODUCT LIFE CYCLE - AN EMPIRICAL STUDY* 



Hermann Simon 



** 



WP 1035-78 



November 1978 



MASSACHUSETTS 

INSTITUTE OF TECHNOLOGY 

50 MEMORIAL DRIVE 

CAMBRIDGE, MASSACHUSETTS 02139 



DYNAMICS OF PRICE ELASTICITY 
AND THE PRODUCT LIFE CYCLE - AN EMPIRICAL STUDY* 



Hermann Simon 



** 



WP 1035-78 November 1978 



The author gratefully acknowledges the helpful comments of 
Horst Albach, Helmut Bruse (University of Bonn), Alain Bultez 
(EIASM Brussels), and Alvin J. Silk (M.I.T.). 



** Assistant Professor of Management Science 
University of Bonn, and 

Visiting Fellow, Sloan School of Management, 
Massachusetts Institute of Technology 



ABSTRACT 

The author presents a product life cycle model which incorporates 
carryover-effects and obsolescence and allows for time-varying price 
responses. An empirical study of 35 products reveals typical changes 
in price elasticity over the product life cycle and casts doubt upon 
the hypotheses prevailing in the marketing literature. Some important 
implications for strategic pricing and anti-trust issues are being 
discussed. 



13 LOIS 



- 1 



INTRODUCTION 



In the marketing literature it has frequently been alleged that marketing 
strategy should vary over the product life cycle (Kotler 1971, Lambin 1970, 
Levitt 1965, Wasson 1974, sec also Dhalla and Yuspeh 1976). Such allegations 
presuppose a certain knowledge on the efficiency of various marketing instruments 
at different stages of the life cycle. In fact, very little is known about this 
issue. In support of the allegations, reference is usually made to Mickwitz 
(Kotler 1971, p. 62; Lambin 1970, p. 15; Parsons 1975) who - back in 1959 - pre- 
sented some theoretical considerations on the changes in marketing elasticities 
over the life cycle, but did not give any empirical evidence of his hypotheses. 

Too often no clear distinction between the life cycle of a particular product 
and the life cycle of a whole product class has been made, two exceptions being 
the studies of Polli and Cook (1969) and Dhalla and Yuspeh (1976). The present 
study is clearly confined to single products, no conclusions on whole product 
classes will be drawn. Throughout the paper, the term product life cycle (PLC) 

denotes the time series q. ,,..., q. T of quantities sol d of a particular pro- 
duct or brand i. The PLC-concept is not understood as an ideal -type model. 

We focus on price and on the changes in price elasticity over time. According 
to Mickwitz (1959) and his followers price elasticity increases over the first 
three stages of the PLC (introduction, growth, maturity) and decreases during 
the stage of decline. 

The first part of this hypothesis seems to be supported by some findings of 
diffusion research according to which early adopters of new products typically 
have higher incomes and pay less attention to price than later adopters do 
(Robertson 1967, Rogers 1968). The hypothesis is also confirmed by a General 
Motors study on the price elasticity of automobile demand for the years 1919 
- 38 to which Dean (1950, p. 227) refers. One should note, however, that both 
the diffusion studies and the GM study are concerned with product classes and 



2 ~ 



do not read,,, allow conclusions for single products or brands. 
AS for single products , a great many empi>ica, tests of dynamic sales respons, 
functus have been conducted, almost al, of which are, however, related to 
-"*..** Clarke (,„, reviewed about 70 of these stuoies, further review, 
can be found in Parsons and Schultz (1976) and Dh.ll. (1978). 

Relatively few studies include nrirc **=„,, , 

'ciuoe price as an explanatory variable (Telser 1962 

Umbin ,970, Houston .„d Weiss ,974, Wildt ,974, Lambin.Naert.and Bultez ,97, 
-riarty ,975, Lambin ,97S, Pr.sad ,d Ping ,g 76 , A „ of these studjes ^ 
—invariant price response or price elasticity coefficients .nd, therefore 
do not per.it .ny conclusive inference on the cb.nges in price response or 
Pnce elasticity over the PLC. The o„,y models which Include time-varying 
sales responses are ,i mi ted to advertising issues (8eckwith ,9,:, P ar sons ,975 
Wildt ,976, Winer ,976, Erickson ,977). 

««* (,977a,b, has presented a mo del in which price elasticity varies with i 

aspect to the advertising expenditure, but nevertheless is const.nt with 

respect to tin*. A dec re.se in the magnitude of price elasticity over «- is 

Produced in the well-known competitive simulation mode, of Kotler (,965, This 

-de,, however, can bard,y be tested e m pirica„y and yie,ds - due to the fact 

that price elasticity approaches the zero level - stratemV » „ • 

levei strategic recommendations 

which cannot be considered as reasmvhia. «.■ • 

as reasonable; this is shown in Simon (1978). 

This short survey, thus, leads to the conclusion Mat „„ • • 

uie conclusion that no convincing empirical 

or theoretical evidence nf th a ~i».. 

evidence of the changes in price elasticity over the PLC and 

of the marketing efficiency of price at different stages of the PLC is available 



THE DATA 

Data on prices and quantities sold of 43 products (brands) on 7 different 
markets were available for this study. All data are of most recent origin 
(all after 1970) and refer to the West German market. They were supplied by 
large German corporations on a confidential basis so that the product identi- 
ties cannot be revealed. The most important data characteristics are given 
in table 1. 

INSERT TABLE 1 HERE 

All products represent frequently purchased branded items. On each market, 
products at different stages of their individual PLC's are represented. All 
markets had been established before the period under investigation so that our 
analysis applies and is limited to products which are introduced onto markets 
with existing substitutes, it does not apply to generically new products. We 
are not aware of any single study which includes a greater number of products. 

The data show enough variation to admit an examination of the dynamic relation- 
ships between prices and sales. The managers concerned with the products con- 
sider price (besides quality which remained unchanged over the period under 
investigation) as the most important marketing variable. 

Even in the case of the detergents, the absence of non-price data 
doesn't seem to be too serious a problem. This is in particular true for 
advertising data due to two reasons. On the one hand, advertising is 
much less important in Germany than in the U.S.; this is mainly due to 
strict limitations of TV-advertising (only 20 min. per weekday, no adv. on 
Sundays and holidays; in 1977 the advertising budget of Procter & Gamble (USA) 
alone amounted to 93.8% of the total amount spent on TV-adv. in Germany). 



- 4 



On the other hand, the managers hold that advertising spending for detergents 
is rather evenly distributed over the year and hasn't changed much over the 
period under investigation, so that the impact of advertising is likely to be 
adequately reflected in the constant term of the sales function. 

MODEL SPECIFICATION 

The empirically tested dynamic sales response models usually have the form 

1i,t = a l +a 2 Vt-1 +f(p i,t' Pi,t } (1 > 

where q. . product i's sales in period t (either units or market share) 

p.; t product i's price in period t 

p. t some weighted average price of products competing with 
1,1. 

product i in period t 
f(») price response function 
a-. , ao parameters 

The sales and price variables are either in natural or in logarithmic 

dimension. Typically all functional relationships in (1) are assumed to be 

time-invariant. Hence, for constant prices and |a 2 ! < 1, function (1) can only 

describe the approach of q. . towards an equilibrium level of sales. The 

1 1* 

dynamics of (1) do not allow for a representation of a life cycle curve with 
an ascending and a descending branch if prices remain unchanged. Moreover, the 
time-invariant price response presupposed in this function must be considered 
as a very restrictive assumption. 

Within the last few years a number of advertising models which allow for time- 
varying coefficients f both advertising and the lagged sales variable, the 
so called "carry-over effect", have been proposed (Beckwith 1972, Parsons 1975, 
Wildt 1976, Winer 1976). The results of these few studies as to the carry-over 






effect are not unequivocal- Parsons (1975), for instance, presupposed 
an increase in the carry-over effect over time and Wildt (1976) investigated 
industry sales and not product sales. The results of Beckwith (1972) and 
Winer (1976) both ofwhom studied the Lydia Pinkham data indicate a downward 
tendency of the carry-over effect. Product life cycle theory indeed suggests 
that the abilitiy of a product to retain its customers from period to period 
should decrease in the course of time due to the introduction of new competit- 
ive products which, in a dynamic market, are likely to be superior either tech- 
nologically or "psychologically" (fashion, taste etc.). The erosion or 
"obsolescence" of the old products and the diffusion of the new products, how- 
ever, occur gradually and not immediately. It seems reasonable to assume an 
exponential pattern of the decrease in the carry-over in order to account for 
this phenomenon. 

Thus, we obtain for the non-price terms in (1), for which we write A. . 

i , t 

Al: A 1§t - a 1 + a 2 .q. jt _ 1 . (l^^i ( 2) 

where < a 3 < 1 can be interpreted as'rate of obsolescence' and t. denotes the 
period of introduction of product i. For t=t. we have A. .=8,, hence a, repre- 
sents product i's initial demand potential. 

The results of Winer (1976) indicate that not only the carry-over effect but 
also the initial demand potential may be subject to the obsolescence phenome- 
non. Assuming the same rate a 3 we obtain as an alternative model to (2) 

A2: A. )t = (a^a^.^) (l-a/^l (3) 

It should be noted that Al and A2 include the function with constant parameters 
as a special case where ao=0. 

A great variety of possible life cycle curves can be represented by means of 
these simple functions. This flexibility is highly important since empirical 



PLC's tend to have very different shapes (Cox 1967, Polli and Cook 1969, Wasson 
1974, Dhalla and Yuspeh 1976). Figure 1 gives an illustration of this flexi- 
bility [f (.)-<>]. 

INSERT FIGURE 1 HERE 

Some of the products under investigation show seasonal sales patterns which are 
due to season-related diseases in the case of the drugs and to certain habits 
of German housewives in the case of the detergents (draperies etc. are typically 
laundered in spring and fall). Both managerial experience and visual inspection 
of the sales curves indicated that only two types of seasonal patterns existed 
so that one dummy variable D. = {0,1} is sufficient to account for the 
seasonalities. Adding the seasonal term to Al and A2 respectively we obtain. 

A3: A. jt = a x + d.D t + a 2 q^^l-ag)*"*! (4) 

A4: A i)t = ( 3l + d-D t + a 2 q 1>t>1 ) (l-a 3 ) t " t i (5) 

In a few cases, a further version A5 which is equal to Al with a-, =0 has been 

tested. 

It seems reasonable to assume that product i's sales depend both on the absolute 

level of its price p. . and on the differential between p. t and the prices of 

competing products. 

In the absence of evidence to the contrary, we hypothesize and test a linear 

relationship between q. . and the absolute price p. .. 

B i,t = b -Pi,t < 6) 

As to the sales effect of the price differential we adopt a hypothesis which 
was first proposed by Gutenberg (1955, 1976) and has found wide acceptance in 
the European marketing literature. According to this hypothesis a relatively 
small price differential is assumed to have an underproportional sales effect, 
whereas a relatively great price differential is assumed to produce an over- 



7 - 



proportional sales response. This hypothesis- is based on the experience that 
only very few customers are likely to switch from their accustomed brand to 
another brand if the price differential changes by e.g. 1% or 2% only, whereas 
the number of brand switchers typically grows overproportionally when the 
price differential increases for instance to 20% or 30%. 

A nonlinear relationship of this type can be represented by a sinh-function 
(sinus hyperbolicus, Albach 1973). We consider two versions of sales response 
to price differentials, the first being 

CI: C. )t = cj-sinh ( ^ Ap i>t ) (7) 

where Ap. = (p n - t -p.- + )/P,- t is the price differential, 

Y m. .p. . is the market share (m. .) 
i»t " ._, ,, n weighted average price of 
3?i J ' products competing with i, 

c, ,C2 are parameters. 

In the version CI the price response is time-invariant. The second version 
to be tested is based on the assumption that the sales response on a price 
differential is proportional to the total market demand hitherto effective. 

C2: C. t = c x sinh (c 2 AP i>t ) q^ (8) 

where n 

q. , = I q. . , is the total market demand in t-1 . 

The version C2 meets in particular the requirement of Parsons and Schultz 
(1976, p. 158) that a time-varying response should rather be explained by 
marketing variables than merely by time. 

The terms A, . , B. . , and C. t can be linked either additively or multiplicative- 
ly. We hold that a multiplicative linkage is less appropriate in our case since 



it implies that the price response, i.e. the derivative 8q. + /9p 1 - t , develops 
proportionally with the non-price term A. . so that the price response would 
be affected by the obsolescence effect in the same way as the carry-over 
effect. This would, in fact, amount to a predetermination of the question 
to be investigated. Therefore, the assumption of independence between the 
non-price influences and the price influences is made so that a linear 
function is obtained. 

<i,t =A i,t +B i,t +C i,t +u i,t < 9 > 

where A. . is either Al , ,A5; C. . is either CI or C2; and u. t is the 

error term. 

In anticipation of the detailed regression results we note here that 
the influence of the absolute price, b-p. . , did not prove significant for 
any of the products. This result coincides very well with the managerial 
opinion that primary demand for the products under investigation has not been 
affected by changes in the absolute price levels (since 1970). This applies 
both to the detergents and to the pharmaceuticals. 

Due to this outcome, we can confine subsequent attention to A. . and 

C. .. The solid line in figure 2 gives a graphical illustration of the price 

response function (with A, .=1, B. .=0, c,=.l, c 2 =10, p. .=1) 

INSERT FIGURE 2 HERE 

The price elasticity denotes the percentage change in sales induced by an 
incremental (or 1%-) change in price and is mathematically defined as 

e i,t = 9 Vt /3p i,t ' p i,t /q i,t < 10) 

For the two versions CI and C2 of our price response function we obtain 



9 - 



CI 



P i,t 



e i t = ~ c l c 2 cosh ( c 2 Ap i t^ '~ ( 1] ) 



C2: 



q i,t p i,t 



e i>t = - Cl c 2 cosh(c 2 Ap i>t )^^l (12) 



'i,t K i,t 

The equations (10) - (12) show that the dimensions of prices and quantitities 
are eliminated when e^ t is computed. Hence, price elasticity is a dimension- 
less measure of price response and can readily be compared for different products. 

The proposed price response function and its price elasticity have the follow- 
ing properties: 

(1) The function gives economically reasonable values within a certain inter- 
val only. It doesn't make any sense to compute the expected sales effect of 

an arbitrarily large price differential (e.g. 1000SQ by means of this function. 
According to Kotler (1971) this property applies to most marketing response 
functions. 

(2) The magnitude of price elasticity increases for increasing positive and 
negative deviations of p. . from p. . ; this is a necessary consequence of 

our basic assumption that sales response increases overproportionally with Ap. t 

I * w • 

The price elasticity values are given by the dotted line in figure 2. 

(3) The function allows for any development of price elasticity over time; 
£; t may decrease, increase , remain constant, or develop irregularly over 
time. Some examples which give evidence of this flexibility are depicted in 
figure 3 (the parameter values can be found in table 2). 

INSERT FIGURE 3 HERE 

(4) Since the absolute price level has turned out to have no significant 

influence on sales, the direct price elasticity e. . , the cross-price 

l tt 

C - - 

elasticity e. . = 3q. ./ap. . • p. ./q. ., and the respective market share 



10 



elasticities have the same magnitude. Therefore, we need not distinguish 
between direct and cross elasticities (though they have different signs) 
and can confine ourselves to the discussion of their common magnitude. 

REGRESSION RESULTS 

Since market shares do not necessarily show a PLC-pattern (e.g. if market 
sales and product sales develop proportionally-^ m. .=const.) sales units were 
considered as the more appropriate dependent variable for our purpose. 

The different versions of (9) are nonlinear with respect to the obsolescence 
parameter a 3 and the price parameter c 2< Therefore, the nonlinear least squares 
estimation technique of the TSP-program (a Gauss-Newton algorithm) was applied. 
The results of these estimations, however, proved highly unsatisfactory due to 
the following reasons (ranked according to their importance): 

- though convergence was achieved in most cases the coefficients were almost 
invariably insignificant. 

- the rate of obsolescence a 3 often had a negative sign which is economically 
unreasonable since it implies an unlimited growth of the carry-over effect. 

- in about 20% of the cases no convergence was achieved. 

These results suggested to attempt a different approach in which a 3 and c 2 
were prefixed so that the sales function became linear in the remaining para- 
meters and ordinary least squares (OLSQ) estimation procedures could be applied. 

The search for the obsolescence parameter a 3 was limited to the interval (0, .1) 
since a 3 can reasonably be assumed not to exceed .1 for the given data inter- 
vals (quarters and bimonths). 

A similarly apparent interval for reasonable values of c 2 is not available. For 
a given Ap. ^, this parameter determines the magnitude of the argument of sinh and 



11 



thereby, the degree of nonlinearity of price response. One can easily realize 
this relationship in figure 2 by considering Ap^ t as given and c 2 as variable. 
For |c 2 Ap i t | <1, sinh is almost linear; for |c 2 Ap i t | > 1, sinh becomes 
increasingly nonlinear. Thus, by prefixing different values of c 2 we can 
account for different degrees of nonlinearity in the sales response to price 
differentials. 

In the estimations we usually prefixed three values in the following way 
(x- denotes the maximal magnitude of Ap. . over all periods) 



case 


value 


range of 


maximum 


competitive price effect 




of c 2 


argument 
of sinh 


of sinh 


(shape of sinh within range) 


1 


c 2 =l/x i 


-1 +1 


1.17 


quasi-linear (proportional) 


2 


c 2 =2/x i 


-2 +2 


3.62 


medium nonlinear 


3 


c 2 =3/x i 


-3 +3 


10.01 


highly nonlinear 



In this way, both a quasi-linear and various nonlinear patterns of sales 
response to price differentials were admitted. In a few cases, where the 
results indicated that smaller or greater values of c 2 would improve the 
estimation some additional prefixations of c 2 were tested. 

For each product, about 20 - 25 estimations with different combinations of a-. 
and c 2 were run, the total number of regressions amounting to about 5000. The 
detailed results are reported in table 2. 

INSERT TABLE 2 SOMEWHERE HERE 



(Footnote to table 2) 

Column (1) gives the product number (first digit: market, second digit: pro- 
duct). 0LSQ in column (2) means ordinary least squares and C0RC stands for 
the Cochrane-Orcutt iterative technique - a generalized least squares 
method - which was applied when the Durbin-Watson statistic (DW) of the 0LSQ- 



12 - 



estimate fell into the inconclusive range or indicated autocorrelation. This 
enforced criterion has been suggested (Schneeweiss 1974, p. 244) since DW is 
of limited reliability when one of the regressors is the lagged dependent 
variable (Durbin 1970). Durbin's H which would be appropriate in this case 
is not provided in the TSP-program of MIT-Harvard by means of which the 
estimations were made. 

Column (10) gives the introduction periods l. t a negative number indicates 
that the product has been introduced before the period under investigation. 
In the cases marked by an asterisk the true introduction periods were not 
available, and t. was set equal to 1. The numbers in parentheses are the 
t-statistics and a, b, c, and d denote significance at 1%, 5%, 10%, and 25% 
respectively (one tailed test). 
(End of footnote table 2). 

Reasonable results have been obtained for 35 out of the 43 products. A summary 
of the statistical criteria of the regressions is given in table 3. 

INSERT TABLE 3 HERE 

Thus, 82% of the coefficients were significant at 90% or more and 83% of 

2 
the coefficients of determination R exceeded 0.60. These results give strong 

empirical support to the hypotheses underlying our model. Both the PLC-dynamics 

and the competitive price effects appear to be adequately represented. 

PRICE ELASTICITIES 

From the regression equations, we computed price elasticities for all products 
and all periods. For this purpose the actual values of prices and quantities 
were inserted into (11) and (12) respectively. 



- 13 



In order to obtain condensed and comparable measures of the magnitude and the 
development of each product's price elasticity the median i and the average 

growth rate g of each time series e. . , t = t. , ,T were calculated. In 

this case, the median is the appropriate measure of the average magnitude of 
price elasticity since it excludes the influence of outlyers which were not 
infrequent. The average growth rate g is obtained as the geometric mean of 
the time series of elasticity growth rates. Note that the arithmetic mean 
would be inappropriate when applied to growth rates. The values of e and g 
are given in columns (3) and (4) of table 4. 

INSERT TABLE 4 SOMEWHERE HERE 

One readily recognizes from column (3) in table 4 that the elasticity medians 
of the two product groups are considerably different. Almost all of the price 
elasticities of the pharmaceutical products (markets 1 - 4) are smaller than 
(or close to) 1, whereas the values for the detergents without exception are 
greater than 1. This important finding is further clarified in figure 4 
where the distributions of the elasticity medians are depicted, separately 
for the two product groups. Only cases with significant price influence are 
included in figure 4. 

INSERT FIGURE 4 HERE 

The graphical illustration gives even stronger evidence of the differences 
in price response between the two product groups, the medians of the two 
distributions (.44 and 1.88) being significantly different at the 1%-level. 
Both these differences and the absolute magnitudes of price elasticities 
coincide very well with the managerial experience. The results are also in 
good accordance with the findings of other researchers (Telser 1962, 
Lambin 1976). 






- 14 - 

The average growth rates g in column (4) of table 4 indicate that the price 
elasticities have frequently undergone considerable changes over time of both 
positive and negative sign. In order to investigate this issue more deeply 
and to find out whether the changes in price elasticity show characteristic 
linkages with certain PLC-stages, we make two types of comparisons. 

We first compare the elasticity growth rates of those products which were at 
the same PLC-stage (introduction, growth, maturity, or decline) during the 
last quarter or bimonth under investigation. 

In addition to this cross-section comparison we study the magnitudes of price 
elasticity of one and the same product at different stages of this product's 
PLC - Tnis longitudinal comparison is necessarily limited to products whose 
sales curve includes at least two PLC-stages; 30 products belong to this group. 

Both the cross-section and the longitudinal comparisons require a preceding 
classification of the actual sales curves into PLC-stages. It is certainly 
desirable to use objective criteria for this classification. Respective attempts, 
in which growth rates, moving averages of 2, 3, and 4 growth rates, changes in 
signs of growth rates, or the stage identification criteria proposed by Pol 1 i 
and Cook (1969) were used, did, however, not prove useful. Polli and Cook state 
themselves that their criteria "are by no means flawless" and their application 
would, in fact, have led to stage sequences like e.g. maturity-growth-decline- 
maturity. The growth patterns in our sample (and probably empirical growth 
patterns in general) are somewhat different from the regular PLC-schemes usually 
found in marketing textbooks. Positive and negative growth rates or averages of 
growth rates actually occurred at all stages, and the magnitudes of growth rates 
showed enormous irregular variations (see also Dhalla and Yuspeh 1976). 
Therefore, a standardized classification scheme was not considered as appropriate 
and we decided to effect the necessary classification on the basis of a visual 
inspection of the sales curves. The procedure is demonstrated for three of the 



15 



products under investigation in figure 5. 

JNSERT FIGURE 5 HERE 

Though this method may seem somewhat arbitrary we consider it as justified and 
appropriate in this case. On the one hand, the resulting classification is not 
likely to differ significantly from person to person, as discussions of the 
author with both managers and scientists have shown. Even if there are slight 
deviations in the classification they are not likely to affect the results. It 
should also be noted that this way of classification fully corresponds to the 
way in which the manager has to determine at which stage of its PLC a product 
actually is. 

To a certain degree, the appropriateness of our classification is confirmed by 
a comparison of the relative average duration of each stage with the frequency 
distribution of stages obtained by Pol 1 i and Cook (1969) for brands. This com- 
parison reveals a considerable conformity. 



Introduction 


Growth 


Maturity 


Decline 


Relative average duration (%) 11.2 


29.2 


33.1 


26.3 


Frequency distribution (%) 

Polli and Cook (1969) n ' a ' 


37 


36 


27 



The results of the cross-sectional and the longitudinal comparisons are 
summarized in table 5 and columns (5) - (12) of table 4 respectively. Table 
5 gives the average growth rates of price elasticity of all products arranged 
according to their PLC-stages during the last quarter or bimonth under investi- 
gation. 

INSERT TABLE 5 HERE 

Some striking characteristics are revealed: 

- the magnitudes of g show a considerable uniformity within the various stages, 

- all signs of g within the growth stage are negative, 

- all signs of g within the decline stage are positive, 



16 - 



- with only two exceptions (5.1 and 7.3) the following relation proves true 

^Growth '" Maturity <s ^Decline 
Thus, we can conclude from the comparison of the price elasticities of various 
products being actually at different stages of their life cycles: 

(1) Changes in price elasticity over the PLC seem to have a rather uniform 
pattern. 

(2) Price elasticity of growth products decreases over time. 

(3) Price elasticity of decline products increases over time. 

(4) The rates of change in price elasticity are not uniform in sign for 
products being at the maturity stage. These rates, however, seem to be 
smaller in magnitude than both the rates of growth products and decline 
products. 

In columns (5) - (12) of table 4 the numbers of quarters or bimonths and 
the elasticity medians of the different PLC-stages are given for each product. 
If we compare for each product the medians of adjacent stages (thus, only 
products with at least two stages are included), the following relationships 
are revealed: 

(1) In 18 out of 19 cases (95%) the relation e Introduction > e Growth is 
confirmed. 

(2) In 10 out of 14 cases (71%) the relation e Growth > e M a t U ritv is confl ' rmed - 

(3) In 8 out of 8 cases (100%) the relation e Matun - ty < decline is conf " irmed - 

The plot of the medians of the various stages further elucidates these findings. 

INSERT FIGURE 6 HERE 
We can summarize our findings as follows: 

An empirical investigation of 35 products gives strong support to the hypo- 
thesis that price elasticity shows typical changes over the product life 
cycle. During the introduction and the growth stage, a considerable decrease 



17 - 



seems to prevail. At the maturity stage, price elasticity typically reaches a 
minimum which is again followed by an increase during the decline stage. 

These empirical findings are in contradiction to the hypotheses prevailing 
in the literature (see introductory section). This contradiction may partially 
be explained by the fact that usually no clear distinction between the 
absolute sales effect of a price change, which is given by the derivative 
3q i t/3P.j t > and the relative sales effect, which is equal to the elasticity 

e i,t = 9q i,t /9p i,t' p i,t /q i,t has been made - 

How can the uniformity of the empirical outcomes be explained in view of 
the fact that the underlying price response function explicitly allows for 
different development patterns and does not constrain the results to be as 
reported. The main reason for the far-reaching uniformity of the elasticity 
developments has to be seen in the changes in q. . (appearing in the 
denominator of the elasticity term) which typically turned o u t to be considerably 
greater than the changes in the derivative and in p. . .both appearing in the numerator 

1 ,u 

of the elasticity term. Thus, in a certain sense the development of the sales 
q. t tends to determine the changes in e. . . Though the derivative 3q. +./8p. + 
typically also increases over the ascending branch of the PLC this increase 
is almost never so great as to neutralize the reciprocal effect of the growth 
in sales. 

IMPLICATIONS 

Since it has been our main objective to measure price elasticity and its changes 
the managerial and anti-trust implications of our findings shall be outlined in 
short only. The results seem in particular important for the optimization of the 
pricing strategy over the life cycle. The optimal pricing strategy is obtained 
by maximizing the sum of the discounted cash flows over the periods t,...,T (the 



18 - 



product index i is subsequently omitted) 

max , = I {p t+T q t+T - C t+T (q t+T )} (l + i)" T (13) 

T=U 

where C(q) is the cost function and i is the discount rate. 

The maximization of (13) requires a hypothesis on the presumable reaction of 
competitors to the firm's price setting. This complex issue cannot be dis- 
cussed in great detail here. It seems, indeed, of minor importance in this 
case since we are interested less in the absolute levels of optimal prices 
than in their developments over time. Whereas the former are certainly 
governed by the competitive reaction pattern the latter are more likely to 
depend on the changes in price elasticity and cross-price elasticity over 
time. 

Therefore, we consider the assumption that the prices of competing products 
are treated as givens and not as functions of p t as not too restrictive 
for our purpose, which as aforementioned is to gain insights into the 
development of optimal prices. 

Under this assumption the differentiation of (13) with respect to p t leads 

to the first order condition 

a _ 3q. T-t 8q. 

% "it + <>V c ;> W t * Mphx - C i +I ) apf 1 d + ')" T = ° (14) 

where C' denotes marginal cost. 

Due to the formulation of A. . in (3) and (4) we obtain the long-run effect 
of a price change in t as the product of the short-run price response, i.e. 
the derivative 9q t /8p t and the cumulative carry-over effect. 

!!!*+!. !ft a X (l r t + T(T-l)/2 (15) 

ap t 3p t a 2 [l a 3> 



19 



Inserting (15) into (14), multiplying by P t /q t » and solving for the optimal 
price pj gives 

"*t ■ TTT <=i " T^T X "WW "S (l-. 3 ) rtH < rt > /2 (Itlf* (, 6 ) 

t t T-l 



Since e. still depends on p t (16) doesn't allow for a straightforward com- 
putation of pi. The equation clarifies, however, the following relations: 

(1) The optimal dynamic price pi is a compound of the optimal static price, 
which is given by the first term in (16) - this is the well-known Amoroso- 
Robinson-Relation - and the present value of the future marginal revenues 
caused by a price change in t. 

(2) If a 2 > 0, < a 3 < 1 , and p. + > C. + , this present value is positive 
and pi is in all periods x < T less than the optimal static price (note that 
this statement doesn't depend on the assumption on competitive reaction). 

(3) If the price elasticity behaves according to our empirical findings 
(depicted in figure 6) then the optimal mark-up factor £4-/(1 + O is relative- 
ly smaller at the introduction and growth stage and relatively greater at the 
maturity stage, it again decreases during the decline stage. 

(4) Both the long-run price effect and the development of price elasticity 
give support to a strategy of the penetration type. One should keep in mind, 
however, that these statements (and our analysis as a whole) apply to pro- 
ducts which enter onto a market with existing substitutes and have to be 
viewed under the limitations of the assumed competitive reaction pattern. The 
assumption of a different pattern may considerable damp (though not eliminate) 
the outlined trend in optimal prices. 

New products which establish a new market or product class and, thus, have 
no substitutes at the time of their introduction are in a completely different 



20 - 



situation and, consequently, different strategic recommendations apply (see 
Simon 1976). 

It should also be mentioned that changes in cost have, of course, the same 
importance for the pricing strategy as the price response factors. If, for 
instance, marginal cost decreases according to the experience curve concept 
(Henderson 1972) the optimal prices need not increase over time since the 
increase in the mark-up factor can be compensated (or even overcompensated) 
by the decrease in marginal cost. 

The optimal pricing strategy for a particular product at a particular time 
depends on the relative magnitudes of the demand and cost factors. Therefore, 
no general recommendation as to which type of strategy is optimal can be 
given, this decision has to be made in each individual case. 

The numerical optimization of the pricing strategy is best achieved by means 
of a branch-and-bound algorithm which optimizes over a finite number of price 
alternatives within a prefixed price range. In figure 7 the optimal pricing 
strategy for product 4.2 of our sample is depicted. The actual price of this 
product remained constant at .71 whereas the price differential Ap. , being 
negative for all t, changed from - 48% at t=l to - 26% at t=10. The firm 
under consideration usually prices its products above the average prices of 
competing products. The competitors presumably expect this behavior and are 
unlikely to react if prices are up to this expectation. 

Therefore, the optimization was run over the interval (.48, .80). The marginal 
cost was assumed to be constant (CI = .20) and an annual discount rate of 
10 was applied, this rate is actually used in investment decisions by the 
producer of the product. The optimization was carried out for a planning 
horizon of 10 quarters or 2 1/2 years. 

INSERT FIGURE 7 HERE 



- 21 



The resulting optimal strategy confirms the conclusion drawn from equation (16) 
The initially prices are considerably lower than the prices in later periods 
(penetration strategy). The fact that the initial prices are also less than 
the actual prices may be an indication that practitioners don't pay sufficient 
attention to the long-run effects of pricing. The present value of profits of 
the optimal strategy exceeds the respective value of the actual strategy by 
33.7%. 

The limitations of such an optimization have, of course, to be observed. Our 
model doesn't incorporate any negative goodwill or sales responses which may 
result from the price increases, the necessity to raise prices several times 
may well prevent managers from setting a low introduction price. Such con- 
siderations can, however, hardly be represented in a quantitative model 
and should have their proper place at the stage of managerial evaluation of 
the optimization results. 

Further implications of our analysis refer to anti-trust issues. The question 
whether price competition is workable or not and whether dominant products 
are subject to substantial competition or not played an important role in a 
number of recent anti-trust cases (both in Germany and in the European 
Community). 

The discussions on these points have regularly been characterized by a lack 
of objective information. The methods described in this article represent an 
appropriate tool for the measurement of competitive intensity and interde- 
pendences under dynamic conditions. Albach (1977) used similar tools to 
determine the relevant market for pharmaceutical products and to measure the 
effectiveness of competition. He also extended the concept of the dynamic 
cross-price elasticity by estimating partial cross-price elasticities between 
single products or product groups. In this way an objective assessment of 
a product's competitive position on a dynamic market seems attainable. 



22 - 



SUMMARY 



A dynamic sales model which incorporates the product life cycle concept and 
time-varying price responses has been presented. The model is of a very 
general nature and includes both time-invariant and time-varying carry-over 
effects as well as quasi -linear and nonlinear patterns of sales response to 
price differentials. 

An empirical study of 35 products reveals typical changes in price elasticity 
over the life cycle and gives support to the conclusion that the magnitude 
of price elasticity decreases over the introduction and growth stage, reaches 
its minimum at the maturity stage, and again increases during the decline 
stage. 

Though the analysis is subject to limitations (e.g. relatively short periods 
under investigation, many products included only 2 or 3 PLC-stages) the results 
cast heavy doubts upon the hypotheses prevailing in the marketing literature. 
They also call for further research for different product classes. 

The findings seem to indicate the optimal ity of a penetration type strategy 
for products which are introduced onto markets with existing substitutes. 
Further implications are related to anti-trust issues. 



23 - 



TABLE 1: DATA CHARACTERISTICS 



Market 


Product 
Class 


Number of 
Products 


Share of total 
market repre- 
sented in last 
period 


Maximal 
number of 
observa- 
tions 


basis for 
price 
compari- 
son 


period 
length 


1 


Pharma- 


8 


70.2 % 


24 


weight 


quarter 


9 


ceutical 

ii 


6 


83.0 % 


24 


daily dose 


quarter 


3 


• ii 


6 


84.9 % 


24 


daily dose 


quarter 


4 


h 


8 


82.2 % 


24 


daily dose 


quarter 


5 


Detergent 


5 


69.7 % 


18 


weight 


bimonth 


6 


H 


5 


55.5 % 


18 


package 


bimonth 


7 


Household 
Cleanser 


5 


65.3 % 


14 


weight 


bimonth 



Pro- 
duct 


Es t ima- 
t ion 
Method 


Func- 
t i on 
Type 


absolute 
term 

a l 


season 

dummy 

d 


reten- 
tion 
ra te 

a 2 


obso- 
les- 
cence 

a 3 


price d 
t i on e 

c l 


?v \ a - 
ffect 

c 2 


period of 
intro- 
duction 
t 


R 2 


DW 


1.1 


OLSQ 


A3/C2 


69o . 

(i.;?) D 


447 
(2.57) a 


85 a 
(4.67) a 


.03 


■ 15 a 

(3.53) a 


2.28 





.7604 


2.07 


1.2 


CORC 


A3/C2 


32.3 
(1.07) 


76 a 
(3.!5) a 


125 a 
(5.54) a 


.07 


.0012 
(.138) 


2.48 


10 


.7104 


2.08 


1.3 


CORC 


A3/C1 


144 
(3.84) a 


19 H 

( .87)° 


1.18 

(5.16) a 


.05 


12.77 

(3.33) a 


8.05 


5 


.4372 


1.86 


1.4 


OLSQ 


A1/C2 


67 a 
(3.33) a 


- 


.426 
(1.83) c 


.04 


.0125 
(l.B4) C 


2.34 


15 


.7357 


2.63 


1.5 


0L5Q 


A3/C2 


5.9 
(.45) 


16. 3 d 
(145)° 


.626 

(5.19) d 


.01 


.0099 
(2.63)° 


3.53 


18 


.9718 


2.73 


1.7 


OLSQ 


A3/C2 


181 . 
(2.62)° 


121 a 
(3.10)° 


98 a 

(3.71) a 


.06 


.0026 

(1.46) C 


2.02 


13 


.7260 


2.08 


2.1 


OLSQ 


A1/C2 


466 
(3.98) a 


- 


1.06 
(13.43) 


.01 


.001 
(1.81 ) c 


9.42 


19 


.9934 


2.15 


2.2 


OLSQ 


A3/C1 


641 
(1.74)" 


221 . 
(2.40)° 


132 a 
(14.72) a 


.01 


808.6 . 
(1.72) D 


.538 


-16 


.9734 


2.43 


2.3 


OLSQ 


A3/C2 


141 K 

(2.44) D 


201 . 
(2.27) D 


1.22 

(U.29) a 


.001 


.0619 
(1.57) c 


.525 


-16 


.9824 


1.97 


2.4 


CORC 


A3/C2 


4567 
(12.81) 


681 
(9.32) a 


-.307 _, 
(-2.58) a 


.002 


.0702 , 
(.894)° 


.523 


-32 


.7847 


2.21 


2.5 


corc 


A5/C? 


- 


- 


.88 
(1.42) c 


.04 


.131 
(1.50) C 


1.39 


5 


.8376 


1.63 


2.6 


OLSQ 


A3/C2 


64 K 

(2.!9) n 


15? h 
(2.17) D 


.978 
(15.6) a 


.0015 


.0007 
( -65) 


7.06 


12 


.9770 


2.32 


3.2 


CORC 


A1/C2 


19420 
(4.20) a 


- 


.336 . 
(.812)° 


.04 


.002 
(.448) 


7.32 





.9801 


1.79 


3.3 


CORC 


Al/Cl 


7349 
(3.44) a 


- 


.35 
(1.61) 


.004 


1196 . 
(2.05)° 


2.16 


-24 


.6675 


2.01 


3.4 


CORC 


A6/C2 




- 


1.03 , 

i -. * -. . O 
{'■LCI 


.005 


.0007 
(.MS) 


4.85 


11 


.9477 


2.66 


3.6 


CORC 


A5/C2 


- 


- 


.81 

(15.2) a 


.003 


.0013 
(6.45) a 


14.74 


14 


.9131 


1.24 


4.1 


OLSQ 


Al/Cl 


6834 
(4.46) a 


- 


.468 
(6.24) a 


.04 


378 
(2.65) b 


3.35 


17 


.9693 


3.09 


4.2 


OLSQ 


Al/Cl 


936 , 
(2.42) b 




.756 
(3.14) a 


.04 


45.7 
(1.51) c 


6.71 


14 


.8888 


1.01 


4.5 


OLSQ 


A1/C2 


57? 
(.268) 


- 


111 a 

(4.04) a 


.01 


.0224 
(1.66) C 


5.66 


1 


.5074 


2.14 


4.6 


OLSQ 


A1/C2 


9494 
(7.84) a 




39 a 
(4.02) a 


.01 


.083 
(5.01) a 


3.85 


3 


.8594 


1.20 


4.7 


OLSQ 


A1/C2 


1602 . 
(1.79) c 




.564 
(2.91) a 


.01 


.0005 
(.253) 


15.58 


14 


.5215 


2.40 


4.8 


OLSQ 


A1/C2 


2304 a 
(17.1) 




.801 _, 
(11.26) a 


.04 


.007 7 
(1.40)' 


3.45 





.9348 


1.91 


5.1 


OLSQ 


A3/C2 


1160 
(19.08) a 


73 h 
(1.80) D 


-.38 
(-2.81) 3 


.08 


.0104 
(4.11) a 


43.09 


1* 


.6272 


1.56 


5.2 


OLSQ 


Al/Cl 


1142 , 
(9.91) a 


- 


-.136 ,, 
(- -99) d 


.08 


100.2 r 
(1.40) c 


9.02 


1« 


.1102 


1.85 


5.3 


OLSQ 


A3/C2 


1097 . 
(2.15) b 


175 
(2.52) a 


.186 

( .".7) 


.01 


.0006 


44.56 


1* 


.3788 


1.85 


5.4 


CORC 


A3/C2 


782 
(2.92) 


125 
(2.86) a 


.28 . 
(1.12) d 


.045 


.0068 
(1.37) c 


27.70 


1* 


.6356 


1.87 


5.5 


CORC 


A4/C2 


196 a 
(5.00) a 


37 a 
(3.19) a 


.463^ 
(4.09) a 


.045 


.0166 
(15.25) a 


6.65 


1 


.8537 


2.29 


6.1 


OLSQ 


A3/C1 


596 , 
(2.74) a 


92.8 . 
(2.16) b 


.264 
(1.06)° 


.0015 


126.8 . 
(2.06)" 


12.36 


1- 


.5536 


1.28 


6.4 


CORC 


A3/C1 


750 
(3.39) a 


98 
(2.83) a 


.108 
(■45) 


.005 


79.7 
(1-33)° 


16.13 


l m 


.6074 


2.04 


6.5 


OLSQ 


A4/C2 


130 b 
(2.29) R 


32 a 
(4.62) a 


.42 
(175) C 


.015 


.0037 . 
(3.H2) a 


11.26 


!• 


.6772 


2.42 


7.1 


OLSQ 


A1/C2 


1023 b 
(2.06) D 




.63 - 
(3.18) a 


.01 


.0028 r 
(1.72) c 


92.11 


" 1* 


.6192 


1 32 


7.2 


OLSQ 


A1/C2 


445 b 
(2.08) D 


- 


.75 . 
(6.33) a 


.01 


.0169 d 
(1.30)° 


5.32 


5 


.8907 


2.33 


7.3 


OLSQ 


A1/C2 


2396 , 
(3.70) a 




.164 d 
(.976)° 


.0025 


.0927 . 
(4.80) a 


8.85 


1* 


.7709 


1.82 


7.4 


OLSQ 


Al/Cl 


4301 . 
(2.62)° 




• 79 a 
(4.59) a 


.01 


228 . 
(1.48) c 


20.51 


r 


.6777 


1.78 


7.5 


OLSQ 


A1/C2 


1784 
(2.86) a 




.64 
(2.44) b 


.03 


.0494 
(2.02)b 


6.58 


i* 


.6992 


1.87 



25 



TABLE 3: SUMMARY OF STATISTICAL CRITERIA 





Coeffi- 
cients 


Signi 

1 % 


ficant 
5 % 


Coeffic 
10 % 


ients 
25 % 


Equa- 
tions 


<.60 


R 2 
.60 
.70 


.70 

.80 


.80 

.90 


>.90 


n 


118 


57 


23 


17 


9 


35 


6 


8 


6 


5 


10 


% 


100 


48 


20 


14 


8 


100 


17 


23 


17 


14 


29 



TABLE t: PRICE E L A S T 1 CITIES 



- 26 





(1) 
Pro- 
duct 


(?) 
intro- 
duc t ior 
period 


">) /e) a) m m — («j) u\\ M) 

PRICE ELASTICITIES 


TTT5 

price 
influence 
significant 
at (I) 




Tota 

£ 


1 period 
growth 
rate g 


I n tro- 
duc t ion 

n e 


Growth 
n c 


Mat 
n 


uri ty 
c 


Oec 
n 


1 i ne 

c 




1.1 





.37 


2.90 


4 


.33 


7 


.33 


8 


.36 


5 


.46 


1 




1.2 


10 


.15 


-1.54 


2 


.29 


2 


.22 


8 


.11 


3 


.16 


ri.s. 




1.3 


5 


.73 


-11.72 


2 


3.93 


5 


2.79 


12 


.64 






1 




1.4 


15 


.83 


-5.93 






3 


.98 


7 


.66 






10 




1.5 


18 


1.41 


-18.90 


2 


2.34 


5 


1.24 










5 




1.7 


13 


.84 


-15.14 


3 


2.35 


9 


.74 










10 




2.1 


19 


1.26 


-10.39 


2 


1.26 


4 


1.24 










10 




2.2 


-16 


.34 


-9.41 






14 


.53 


10 


.26 






5 




2.3 


-16 


.41 


-4.35 






21 


.43 


3 


.39 






10 




2.4 


-32 


.05 


10. 11 










24 


05 






20 




2.5 


5 


.37 


-12.07 


5 


1.68 


15 


.33 










10 




2.6 


12 


.25 


-19.71 


2 


2.48 


11 


.22 










n.s . 




3.2 





.36 


-5.35 


7 


.73 


17 


.31 










n . s . 




3.3 


-24 


.45 


3.50 










14 


.34 


10 


.62 


5 




3.4 


11 


.14 


-2.14 


2 


.15 


12 


,13 










n.s , 




3.6 


14 


.54 


-12.95 


2 


1 .62 


9 


.54 










1 




4.1 


17 


3.52 


-12.43 


2 


7.11 


6 


3.45 




" 






5 




4.2 


14 


1.09 


-19.89 


2 


6.88 


10 


1.01 










10 




4.5 


1 


.63 


1.14 


3 


.55 


5 


.67 


13 


.63 


3 


.77 


10 




4.6 


3 


.87 


.66 


6 


.89 


10 


.79 


6 


.96 






1 




4.7 


14 


1.03 


-6.24 


1 


34.0 


2 


1.13 


8 


.94 






n.s. 




4.8 





.43 


4,71 






2 


.19 


7 


.41 


14 


.44 


10 




5.1 


1« 


2.85 


-5.50 










18 


2.85 






1 


Li_ 


!• 


1 .22 


1.10 










18 


1 .22 






10 




5.4 


1» 


1.07 


-14.28 


7 


4.81 


11 


.94 










10 




5.5 


1" 


2.22 


4.75 










2 


1.68 | 





?.25 


1 




6.1 


1« 


1 .92 


-1.17 










18 


1.27 j 




■ 




6.4 


1* 


1.83 


-3.34 


7 


2.18 


11 


1 .61 




1 — 

! 




10 




6.5 


1* 


1 .45 


8.76 










11 


1.02 7 


.10 


1 




7.1 


l # 


4.48 


3.77 






5 f 


!.70 


9 


4.40 1 

i 




10 




7.2 


5 


1.82 


-6.59 


2 


3.03 


8 


.76 




i 




15 




7.3 


I* 


4.73 


3.30 






7 -1 


.18 


2 


4.44 ! 5 5 


.27 


1 




7.4 


1« 


1.34 


-1.29 






10 1 


.50 


4 


1.33 




10 


■ 


7.5 


1" 


3.49 


-2.03 






11, 


.95 


3 


2 . 70 ! 




5 


true introduction period not known, value set equal tc 


1 



































- 27 



TABLE 5: ACTUAL LIFE CYCLE STAGE AND GROWTH RATE OF PRICE ELASTICITY 





G R 

Product 


W T H 

g 


MATURITY 
Product g 


D E C L 

Product 


. I N E 

g 


p 

H 
A 
R 
M 
A 


1.5 


-18.90 


1.3 


-11.72 


1.1 


2.90 


1.7 


-15.14 


1.4 


-5.93 


3.3 


3.50 


2.1 


-10.39 


2.2 


-9.41 


4.5 


1.14 


2.5 


-12.07 


2.3 


-4.35 


4.8 


4.71 


3.6 


-12.95 


4.6 


.66 




4.1 


-12.43 




4.2 


-19.89 


mean 


-14.53 


-6.15 


3.06 


D G 
E E 
T N 

E T 
R S 


5.4 


-14.28 


5.1 


-5.50 


5.5 


4.75 


6.4 


-3.34 


6.1 


-1.17 


6.5 


8.76 


7.2 


-6.59 


7.1 


3.77 


7.3 


3.30 


7.4 


-1.24 






7.5 


-2.03 


mean 


-5.49 




- .96 


5.60 



- 28 - 



FIGURE 1: PRODUCT LIFE CYCLES 

A 



ZOOO - 



1000 - 




Al: a =300, a ? =1.3, a ? =.05 
Al: a.=1000, a 2 =.75, a 3 =.05 



A2: a^lOO, a 2 =1.8, a 3 =.l 



A2: aj=2000, a 2 =.l, a 3 =.l 



i k i i i » i ' f i i » £ 

1 5 10 



29 - 



FIGURE 2: PRICE RESPONSE FUNCTION AND PRICE ELASTICITY 



"l.ti 


-e. 
, i 


,t 


"V 












\ • 


A Kt -l- ; 








4 

3 

2 

1 
it 


• 
• 
• 
• 
• 


• \ 




*—fr~ 








.7 .8 .9 1 


1.1 1.2 1.3 



'i,t 



30 



FIGURE 3: EXAMPLES OF PRICE ELASTICITY DEVELOPMENTS 



Product 




31 



FIGURE 4: DISTRIBUTIONS OF THE MEDIANS OF PRICE ELASTICITY 



i 

40- 


i 




i i 




30' 
20« 




•-— — i i 

i 




10- 


• 

1 n >■ ■ 1 


-4= 





.5 1 1.5 2 



«? < 



median 
.44 



median 
1.88 



pharmaceuticals 
detergents 



32 



FIGURE 5: EXAMPLES OF CLASSIFICATIONS INTO LI 



FE CYCLE STAGES 



PRODUCT 1.1 



PRODUCT 4.6 



PRODUCT 5.5 




Introduction „ . Growth ,„ = 



IV 
ty IV == Decline 



- 33 - 



FIGURE 6: AVERAGE PRICE ELASTICITIES AT DIFFERENT STAGES OF THE PLC 



= e 



l.t 1 

c 

i,t 




DETERGENTS 



INTRO- GROWTH MATURITY 
DUCT I ON 



DECLINE 



PHARMACEUTICALS 

staae of PLC 



34 



FIGURE 7: OPTIMAL AND ACTUAL PRICING STRATEGY OF PRODUCT 4.2 



p i)t .80 
.70 - 
.60 
.50 



optimal 
actual 



pricing strategy 



competitive price 



i » i * i i i i i i 

1 5 10 



t (quarters) 



35 - 



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JYOi 

SEP 27 1991 



ACME 
BOOKBINDING CO., INC. 

SEP 6 1983 

100 CAMBRIDGE STREET 
CHARLESTOWN, MASS. 



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Kalwani, Manoh/Structure of repeat buy 

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H028.M414 no.1032- 78 1979 
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HD28.M414 no.1033- 78 

Baldwin, Carli/Liquidity preference un 

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Van Breda, Mic/Bayes vs. the lens 

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Simon, Hermann/Dynamics of price elast 

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HD28.M414 no.1036- 78 

Schmalensee, R/A simple model of risk 

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Ill 



3 T060 001 EOT N 



HD28.M414 no.1038- 79 

Choffray, Jean/Methodology for segment 

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