V\

Tot, U, Ko. t, Jniiurr,PHiiMinUJ3.A..

A NEW PRODUCT GROWTH FOR MODEL CONSUMERDURABLES* '

FRANK M. BASS

Purdue University

A growth model for the timing of initial purohaae of new produets is developedand tested empirically against data for eleven consumer durables. The bsaic asaump-tion of the model is that the timing of a consumer's initial purchase is related to thenumber of previous buyers. A behavioral rationale for the model is oSered in terms ofinnovatire and imitative behavior. The model yields good predictions of the salespeak and the timing of the peak when applied to historical data. A long-range fore-cast is developed for the sales of color television sets.

^The concern of this paper is the development of a theory of timing of initial purchaseof new consumer products. The empirical aspects of the work presented here de^ exclu-sively with consumer durables. The theory, however, is intended to apply to thegrowth of initial purchases of a broad range, of distinctive "new" generic classes ofproducts. Thus, we draw a distinction between new classes of products as opposed tonew brands or new models of older products. While further research concerning growthrate behavior is currently in process for a wider group of products, attention focuseshere exclusively upon^infrequently purchased products.

Haines [6], Fourt and Woodlock [6], and others have stiggested growth models fornew brands or new products which suggests exponential growth to some a^^ymptote.The growth model postulated here, however, is best reflected by growth patterns simi-lar to (hat shown in Figure 1. Sales grow to a peak and then level off at some magnitudelower than the peak. The stabilizing effect is accounted for by the irelative growth ofthe replacement purchasii^ component of sales and the decline of the initial purchasecomponent. We shall be concerned here only with the timing of initial purchase.

Long-range forecasting of new product sales is a guessing game, at best. Some things,however, may be easier to guess than others. The theoretical framework presentedhete provides a rationale for long-range forecasting. The theory stems mathematicallyfrom the contagion models which have found such widespread application in ^idemol-ogy [2]. Behaviorally, the assumptions are similar in certain rejects to the theoreticalconcepts emerging in the literature on new product adoption and diffusion, [7, 8, 9,13] as well as to some learning models [3, 12]. The model differs from models based onthe lc^-Bormal distribution [1,4,10] and other growth models [11] in that the behavioralassumptions are explicit.

The Theory of Adoption and Diffusion

The theoty of the adoption and diffusion of new ideas or new product by a social^stem haa been discussed at length by Rc^rs [13]. This discussion is largely literary.It is, therefore, not always easy to separate the premises of the theory from the conclu-sions, la the discussion which follows an attempt wiU be made to outline the majorideas of the theoiy as they apply to the timing of adoption.

* Receired March 1967 and revised August 1967.' Some of the basic ideas in this paper were originally suggested to the author by Peter Frevert,

now of the University of Kansas. Tbpmas H. Bruhn, Gordon Constable, and Miu-ray Silvermanprovided programming and computational a«istaace.

215

2 1 6 FIULNK M. B&BS

SALES

TIME

FIG. 1. Growth of a new product

Some individuals decide to a.dopt an innovation independently o{ the decisions ofother individuals in a social syatem. We shall refer to these individuals as innovators.We might ordinarily expect the first adopters to be innovators. In the literattire, thefollowing classes of adopters are specified: (1) Innovators; (2) Early Adopters; (3)Early Majority; (4) Late Majority; and (5) Laggards. This classification is basedupon the timing of adoption by the various groups.^ Apart from innovators, adopters are influenced in the timing of adoption by the

pressures of the social i yrstem, the pressure increasing for later adopters mth the num-ber of previous adopters. In the mathematical formulation of the theory presentedhete vre shall aggregate groups (2) through (5) above and define them^as imitators.Imitators, unlike innovators, are Influenced in the timing of adoption by the decimonsof otlier members of the social system. Eogers defines innovators, rather arbitrarily,as the first two and one-half percent of the adopters. Innovators are described as being

and daring. They also interact with other jimovators. When we say thatare not infltienced in the taming of purchase by other members of the social sys-

tem, we mean that the pressure for adoption, for this group, does not increase with thegrowth of the adoption process. In fact, quite the opposite may be true.

In appl}dng the theoiy to the liming of initial purchase of a new consumer product,we formulate the following precise and basic assumption which, hopefully, charafi-terizes t l ^ literary theory: Ti» •probcbUity (hat an initial purchase will be made at Tgiven that no purchase hae y^ been made is a linear fimdiUm of the number of premmbuyers. Thus, P ( r ) = p -f- (j/»n)F(T), where p and q/m are constaats amd Y(T) isthe number of previous buyeta. Since F(0) - 0, the constant p is the probability ofan initial purchase at T » 0 and its miagnitude refiec1» the importance of innovatoniin the social system. Since the parajneters of the model depend upon the scale used tomiMsuie time, it is posmble to select a unit of measure for tioie such that p z^eote ijwfraoiion of all adopters who are itmovatois in the sense in which Eq^is ds&am them.The product q/m iimes Y{T) lefiects the pressures opemting on imitators as <khe num-ber of previous buyers increases.

In the section which follows, the baac assumption of the theory will be foimulatedin tenns of a coniinuous model and a density function of tiii» to initial purchase. Weshall therefore refer to the linear probability eleimnt as a likelihood.

Aaaumptionfl and the Model

The following assumptions ohaxacterixe the model:a) Over the period of interest ("life of the product") theie will be m initial pvaohBaes

d the product. Since we are dealing with infrequentiiy purchased products, tlie unitsales of ihs product, will coincide with the number of imtial purchases during that part

A NEW PBOSUCT OBOWTH UODBL FOB CONStmSR DtTBABLBS

sm

217

Fia. 2. Growth rate (5 > p)

of the time interval for which replacement sales are excluded. After replacementpurchasing begins, sales wUl be composed of both initial purchases and replacementpurchases. We shall restrict our interest in sales to that time interval for which replace-ment sales are excluded, although our interest in initial purchase will extend beyondthis interval,

b) Tke likelihood of purchase at time T given that no purchase has yet been made is

- F(T)] = P(T) ==p+q/

where/(IT) is the likelihood of purckaae at T and

Y(T) qF{T),

F(0) == 0.

Since J(T) is the likelihood of purchase at T and m is the total number purchasingduringjthe'period for which the denaty function was constructed,

Y(T) - j S(t)dt == m j f{t)dt== mF{T)

is the total number pufchasing in the (0, T) interval. Therefore, sales at T =

8{T) = mj{T) = Pihlm - Y(T)] = [p + g f S(t) dt/m\lm - f S(t) eul.

Expanding this product-%e have

S(T) = pm + (4 - p)Y{T) - q/m[Y{T)f.

• The behavioral rationale for these assumptions are summarized: .a) Initial purchases of the product are made by both "innovators" and "imitators,"

the important distinction between axi innovator and an imitator being the buyinginfluence. Innovators are not influenced in the timing of their initial purchase by^thenumber of people who have already bought the product, while imitators are influencedby the number of previous buyers. Imitators "learn," in some sense, from those whohave already bought.

b) The importance of innovators will be greater at first but will diminish monotoni-cally with time.

c) We shall refer to p as the coefficient of iimovation and g as the co^cieni of imi-tation.

Since/(T) =»

[p + qF(T)]ll - FiT)\ = p -f (g - p)F{T) - q[F{T)\\

218 M. BASS

S«T)

FiQ. 3. Growth rate {q i& p)

TABLE 1Growth Model Regression Eetmlts For Eleven Conawner Durei^le Prodvcls

PRwhict

Etetrksnfric-• 1 , i , . , 1 1 ,

ccmoraBomebcontsBlank and -white

MlvririonWatataoitaiHnBoom«lrooo-

ditioomQothai (bironijpoirtr bnm-

momnEtwtriebcd

Aotomatio nrf-feeiokksn

9t«amiron«

covaicd

1920-1940

lH»-t9611»4«-1961

1M9-I9611949-1961

1948-19611948-1961

194H961

1948-1961

1949-1960196»-1961

. ( 1 0 .

104.67

308.122,696.2

.10266176.69

269,67410,98

460.04

1,008.3

1,694.7643.94

b

.2130S

.16298

.22317

.27925

.40820

.33968.32871

.23800

.28436

.29928

.62931

f (10-')

-.053913

-.077868-.026967

—612.69-.24777

-.23647-.076606

-.031842

-.061242

-.068876-.29817

IP

.903

.742

.676

.919

.911

.896

.982

.976

.883

.828

.899

a/<r.

1.164

4.1963.312

3.6931.916

2.9411.936

3.622

3.109

3.6491.911

Vn

(,143

4,75«S,734

(,0898.817

T,427r.4O8

«.82O

8.186

6.2886.1«4

t/r.

-2 ,648

-3.619-3,187

-6.461-6,034

-6.701-4 .740

-1 .826

-4 .363

-4 .318-3 .718

m

40,001

21,97396,717

6,7W16,8M

16,0924<4,761

76,689

68.838

66,69421,937

*

.0026167

,018119,027877

,017703.010899

,017206,0091837

,00C876

.017136

.028632

.024796

f

.21M6

.17110

.26106

. M 9 (

.41861

.86688

.33790

.24317

.301M

.32791

.66410

Date Btmtem: Sattmtie jUmanae, Stati$Keal Mutnett tiftli* UM., mtdriai tlwnlianiitint, Ukd KiMtnea] MprelUniMngfr«t.

in order to find F(T) we must solve this non-linear differential equation:

(3 - p)FThe solution is:

(g -

Since

- C

Then,

and

0, the int^:ration constant may be evaluated:

Ln(g/p) and F(T) =» (1 •— e

+ l)%

1)

((p + qf

To find the time at which the sales rate reaches its peak, we differentiate 8,

5' « (m/p(p + q)*e-"^'\q/pr'^'' - DVCg/p*-**^' + 1)*

Thus, r* =« ~l / (p + g) Ln (p/g) »» l/{p + g) l a (g/p) and tf an inteiior iaaxi>mum exusts, g > p- The solution is depicted graphically in Figuzes 2 mid 3. We Qote

that S(T*) « {mlv + g)V4g and F(5r*) - J SO) <8 - i«(g ~ p)/2q. Since for

A trnVf PROSTTCiT aSOWlH MODEL rOB CONBXTIODB DtTBA.BUn

1800

1600

1400

1200-

213

IilOOO

800

600

400

soq

ACTUALPREDICTED

1947 1949 I9SI I9S3 I95S i957 I9S9 1961

YEARFia. 4. AwOtual sales and sales predicted by regression equation

successful new produots the coefficient of imitation will ordinarily be much latferthan the coefficient of innovation, sales will attun its maximum value at about thetime that cumitlaiive sales is {^proximately one-half m. We note also that the ex-pected time to purchase, E(T), is 1/g Ln ((p + q)/p).

The Discrete Analogue

The basic model is: 5 ( r ) » pm + (g - p)Y(T) - q/mY*{T). In ^rtdmating theparameters, p, q, and m from discrete time series data we use the following analogue:Sr = a + bYr-i + CYT-I . T = 2, 3 • • • where: *Sr = sales at T, and Yr-i ==Xri-i St » cumtilative sales through period 7 — 1 . Since a estimates pm, b estimates<j — p, and c estinutes —q/m: —me =» q, a/m = p.

Theng — p = —me— a/m »• 6, and c m ' + b»» + a == O,orm«= (—6±\/6* — 4<»/2c, ffiad the panunetetB p, q, tuid m are identified. If we write SiYr-t) and differ-entiate with respect to Yr-i, dSr/drr-^ =^ b + 2CYT-I . Setting this equal to 0I ^ ^ - -5/2c » m(j - p)/2g = F(r*) , and -Sr(r?^) = o - b*/^. + fe'/^c »'''(p + ff)*/^? « S(T*). Therefore, the maximum value of 5 as a function of timecoinddes with the maarimum v£due of S as a function of cumulative

R^presaion AnalyBis

order to test the mo(tel, regresmon estimates of the parameters wereannual time seriea data for eleven different consumer durables. The period of

analysis was restricted in every^ case to include only those intervals in which repeat

220 M. BABB

12001-

1947 1949 1951 1953 1955 1957 1959 1961YEAR

Fio. 6. Actual sales and sales predicted by regression equation (home freezers)

purchasing was not a factor of importance. These hitervaJs were^ determined on thebasis of a subjective appraisal of the durability of the product as well as from limitedpublMied data concerning "scrappage rates" and repurchase cycles.

Table 1 displays the regression results. The data appear to be in good agreement withthe model. The 22* values indicate that the^model (describes the growth rate behaviorrather well. Furthermore, the parameter estimates aeem reasonable for the model. Ther^ression estimates for the parameter c are negative in every case, as required in orderfor the model to make sense, and the estimates of m are quite plausible. One of themore in^portant contributions derived from the regression analysis is the impliedestimate of the total number of initial purchases to be made over the life of the prodiwt.Inures 4, 5, and 6 show the actual values of sales and the values predicted by the re-gre^on equation for three of the products analyzed. For every product studied theregression equation describes the general trend of the time path of growth vety wdU.In addition, the regression equation provides a veiy good fit with respect to both themagnitude and the timing of the peaks for all of the products. Deviations from trendare largely explainable in terms of short-term income variations. This is especiallyapparent in Figure 5, where it is easy to identify recessions and booms in the yeara ofsharp deviations from trend.

Modtel Performance

The performance of the tegresdon equation relative to actual sales is a relativelyweak test of the model's performance since it amounts to fm ex post conq>arison

A NBW FBODVCt GBOWTH UOHM. FOB CONSTrsOBB STTBABLBS

regression equation estiiuates with the data. A much stronger test is the performanceof the basic model with time as the variable and controlling parameter values as deter-imned from the iegieaaon estimates. Table 2 provides a comparison of the model'sprediction of time of peak and magnitude of peaJc for the eleven products studied.

Since, according to the model S(0) » pm, we identify time period 1 as that period

8000

7000

6000

•§5000oM

24000

UI3000<V)

2000

1000

ACTUALPREDICTED

1947 1949 1951 1953 1955 1957 1959 1961YEAR

Fia. 6. Actual sales and salea predioted by regression equation (black & white teteviaion)

TABLE 2Comparison o/ Predicted Time and Magnitude of Peak wilk Actual Value*

f«r Ekven Consumer Durable Prodvcts

Product tipPndicted time ofpeak r* - (!/(# Actual time

of peek*

Predicted muni-tndcof p n lscr*) - «(* tndeof peak

(10«)

Electric refrigeratorsHome freezersBlack h white televisionWater softenersEoom air conditionersClothes dryersPower lawnmowersElectric bed coveringsAutomatic coffee makersSteam ironsRecover players

82.49.49.0

16.740.220.735.741.618.1U.426.3

20.111,67,88,98,68,1

10,314,99,06.84,8

t137977

11141076

2.201.27.6

.51.81.54.04.84.85.S3.8

t1.27.8

.S1.71.54.24.54.95.93.7

* Time period one is defined la that period for which sales equal or exceed p m for the fitst time.t Interrupted by war. Prewar peak in yeur 16 (1940) at 2.6 X 10* units.

rSANK H. BASS

TABLE 3Forteaating Accuracy of the Model for Eleven Consumer Durable Product*

Ptoduct

Electric refrigeratorsHome freezersBlack & white televisionWater softenersRoom air conditionersClothes dryersPower lawnmowersElectric bed coveringsAutomatic coffee makers3team ironsRecover players

ferlod of foreeut

192&-19401947-1961194^-19611950-19611950-196119S0-1961194»-19611950-19611951-19611950-19611953-1968

ri

.762

.473

.077*

.920

.900

.858

.898

.934

.690

.730

.953

• The low "explained" variance for this product is accounted for by extreme deviation from 'trend in two periods. Actually, the model provides a fairly good description of the growth rate, ^aa indicated in Figure 9.

in which sales equal or exceed pm for the first time. It is clear from the comparison;shown in Table 2 that the model provides good predictions of the timing and magni- jtude of the peaks for all eleven products studied. :

In order to determine the accuracy with which it would have been possible to "fore-cast" period sales over a long-range interval with prior knowledge of the pt^rameter ivalues, the regiesrion estimates of the parameters were substituted in the basic model, '<S(T) = {m{p + g)Vp)[e~""^'7(«/pe"''"^"' + 1)'], and sales estimates generated!for each of the products for each year indicatod in the intervals shown in Table 3. In;most cases the model provides a good fit to the data. Even in the few instances of low lr* values, the model provides a good description of the general trend of the sales curve, ithe deviations from trend being sharp, but ephemeral. Figures 7, 8, and 9 illustrate |the predicted and actual sales curves for three of the products. :

It would appear fair to conclude that the data are in generally good agreement withthe model. The model has, then, in some sense, been "tested" and verified. We maynow claim to know something ^ou t the phenomenon we set out to explore. The ques-tion is, however, will this knowledge be useful for purposes of long-range forecasting?

Long •Range Forecasting

There aie two cases worth conackring in long-range forecasting: the no-data caseand the limited-data case. For either of these possibilities one may well ask: is it eaderto guess the stJes curve for the new product or easier to guess the parameters of themodel? No attempt willjse made here to answer this qu^tion, in general, but it doesseem likely that for some products it would be possible to make plauMble guesses ofthe parameters. Analysis of the potential market and t l^ bujdng motives should mak»ii possible to guess at m, the mm of the^market, and of the relative values of p and q,the latter guess being determined by a consideration of buying motives. If the aalmcurve is to be determined by means other than the model suggested in this paper, theimplications of this forecast in terms of the parameters of the model might be usefulas a test of the credibility of the forecast.

In order to illugtrato the forecasting possibilities in the limited data case, we shidlcfevelop a forecast for color television set sales. In principle, since tl^re are thiee

A NEW PBODXrcT OiBOVfTB UODBL rOB C0NST7HER DtJBABLEiS 2 2 3

45CX>-

4000 •

1000

500

ACTUAL• PREDICTED

1949 I9SI I9S3 1995 1957 1959 1961YEAR

Fia. 7. Actual sales and sales predicted by model (power lavnmoweis)

parameters to be eetimated, some kind of estimate is possible with only three observa-tiona of the jEirst of these observations occurs at T = 0. Any such estimate should beviewed with some skepticism, however, since the parameter estimates are veiy sensi-tive to small variations in the three observations. Before applying estimates obtainedfrom a limited number of observations, the plausibility of these estimates should beclosely scrutLoized.

In substituting 23«-« St in the discrete analogue for f S{t)dt in the continuous

model, a certain bias was introduced. This bias is mitigated when there are severalobservations, but can be crucial when there are only a few. Thus, the proper formula-tion of the discrete model, 'd Sr " 8(T) ia: 8T = a + bk{T)Yr.-.i + ck*(T)Yl.-i,where k(T) == Y{T)/Yr-i - We note that for any probability distribution for which:a)/(a:) == l/k[F(x + 1)- F(x)], and b) F(0) = 0, Z J - J / ( O = l/kF(x). In par-ticular, these two properties hold for the exponential distribution. Therefore, for thisdistribution S?3/ ' (*) / / (<) = k. The density function f{T) in the growth modeldeveloped in this paper is approximately exponential in character when p and T aremaU. Thve,Up,(T) « l/h[F^{T + 1) - F.^(r)] and l/k - (p H- q)/[e^-^^ - 1].For sinall values of T we therefore write: Sr = a + b'Yr-i + c'Y*r-t, where 6' = *6,and c = fc*c. Tben m== km,q'= 1/kq', and p « I/ftp'- The value of l/k for each ofseveral different values of p -f g has been calculated and appears in Table 4.

On the basis of the relationship between k and (p -|- q) indicated in Table 4: l/k -.97 - .4(p + q), ip/q')q - «r = 1/kq' - .97g7(l + .4(1 -f 4e)q'), where 0 -q/p - g/p,andp = (p'/s')? = .97p7(i -|- .4(1 + fl)p').

We turn now to the forecast of color television set asiles. The following data are

224 FRANK M. BASS

1600

1950 1952 1954 1956 1956 I960

YEARFio. 8. Actual sales and sal^ predicted by model (clothes dryers)

available:Sales

{Millions of Units)

.71.362.50

Solving the foUowiag system of equations:

Year

196319641965

5o = .7 = o I

S, = 1.35 = o -f .7b' + .49c' '

St = 2.50 = o + 2.056' + 4.20c', we find:

a ' = .7,6' = .964, c' == -.0374,

m = 26.2, q = .96, p = ,0267,

q = .67, p = .018, m = 37.4.

Since these parameter values appear plauMble, they have been used in the bamc modeito generate the series of estimates of sales shown in Table 5 and Figure 10. The pro-jected peak occurs in 1968 at around 7 million units. This forecast differs somewhatfrom some industry forecasts. At this writing, one company's research department hasestimated that sales will "top out" in 1967 at between 7 and 8 million units. The fore-cast speaks for itself and the ultimate reality of actual sales and one's personal critericaof "goodn^s" will determine whether or not the forecast was a good one.

The preceding forecast was made in late 1966. The following report was publishedin the May 19, 1967 issue of the WaU Sired Journal:

. . . Industry sourees say most color set producers are contintiing to trim production. "OnlyR.C.A., Zemth Aadio Corp. and Philco-Ford Corp. aren't cutting baflk now, and they'retaking a big gamble by banking on a big sdes pickup this fall," asserts one industry analyst.

A NBW PBODUCT GBOWTH MODEI* BOB C0N8UMBB

8000

^7000

II 6000

(O 5 0 0 0UJ

W 4000

50001949 1951 1955 1955 1957 1959 1961

YEARFiQ. 9. Actual salea and sales predicted by model (black Sc white television)

TABLE 4Calculated Valueg of 1/k and (p + q)

225

ACTUAL• PREDICTED

(P + t)

,3.4.5.6.7.8.9

.85

.81

.77

.73

.69,65,61

TABLE 5Forecast of Color Television Sales 1968-1970

Yeu

1964196519661967196819691970

Sales (miUioas)

1.352.54.15.86.76.34.7

| s

UJ

1964 1966 . t96B

YEARFia. 10, Projected sdes color television

1970

FRANK M. BABS

Executives at E.C.A., tbe biggest producer of color sets, have turned reticent about pub-licly forecasting industry sales for 1967. Their silence contrasts markedly with last fall, wheaR.C.A. and other companies were exuberantly predicting industry sales of 7 milUoB colorsets in 1967.

Admiral recently pared it's 1967 foreoaat to 6.1 million color-set sales for the indus t ry . . . .

If the model developed in this paper does nothing else, it does demonstrate vividly theslowing down of growth rates as sales neu the peak. In focusing upon the vital theoreti-cal issues the model may serve to d management in avoiding some of the more obvi-ously absurd forecasts as have been m&de m the past.

While our forecast of color televieion sales was objectively determined in the sensethat it was derived, from data, it is also based upon a subjective judgment of the plausi-bility of the parsbtueters. Since the parameter estimates are very sensitive to smallvariations in the observations when there are only a few observations, the importanceof the plausibility test cannot be overamphadzed. The parameter for which one hasthe strongest intuitive feeling is m.. The plausibility test for this parameter is thereforeperhaps the most easily derived. An examination of the parameter vsdues implied byearly sales of the other products analyzed in this paper indicates that in some instancesthese are remarkably close to the regression estimates, while in others they differ mark-edly. In every instance in wbich the early year estimates differ substantially from theregression ^im^tes, these estimates are easily rejected on the basis of the implaud-bility of the implied value of m.

Conclusion

^ The growth model developed in this paper for the timing of initial purchase of newproducts is based upon an assumption that the probability of purchase at any time isrelated linearly to the number of previous buyers. There is a behavioral rationale forthis assumption. The model implies exponential^growth of initial purchases to a peakand then exponential decay. In this respect it differs from other new product growthmodels. '.

Data for consuiner durables ai« in good agreement with the model. Parameterestimates derived from regression analysis when used in conjunction with the model •provide good descriptions of the^growth of sales. From a planning viewpoint, probably :the central interest in long-range forecasting lies in predictions of the timing Bad mag- .nitude of the sdles p«ak. The model provides good predictions of both of these variables 1for the products to which it has been applied. Insofar as the model contributes to an •understanding of the process of new product adoption, the mx)del may be useful in ;providing a ratiooiJe for long-range forecasting. i

B«f«r«nc«« :

1. BAIN, A. D., The Growth of Television Ownership in Oie United Kingdom, A LognormcH Model, ICambridge. The University Press, 1964. ,

2. BABTUBTT, M . S., Slochaette PopuiMion Modeh in Ecology and Epidemiology, London, Me- Ithuen, 1960. *

3. Buss, E.E.A.m> MoeT«i.ijiB,F., iSiocAcwtu; ilfode^/or L«amin{t, New York, Wiley, 1965. :4. DBBMBVBG, T . F . , "Consumer Response to Innovation: Television," in Studies in Soueehotd I

Economic Bdtm/ior, Yale Studies in Economics, Vol. 9, New Haven, Connecticut: Yale, 1968. i6. FotjBT, L. A. AND WOODLOCK, J. W., "Early Prediction of Market Success for New Qrocery !

Products," J0umal of Marketing, No. 2, Vol. 26, October, 1960. »6. EUiKxs, G. H., JB. , "A Theory of Market Behavior After Innovation," Management Science, >

No. 4, Vol. 10, July, 1964.7. EATSS, E . ANb LAJE«.B8rKU>, F., P»t(malTnflwnee, New York: The Free Press, 1956.

A KSSW PBODTTCT OBOWTH XODBL FOB CONBUHBB DUH&BIiEB 2 2 7

8. Kitta, C. W., "Adoption and Diffusion Research ia Marketing: An Orenriew," in Science,Teahtuftogtf and Marketing, 1966 Fall Cionferenee of the American Marketing Asaociation,Chicago, 1966.

0. MAcrsFiBtiO, E., "Technological Change and the Rate of Imitation," Economebrica, No. 4,Vol. 29, October, 1961.

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