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MANAGEICENT SCIENCE Vol. 18, No. 6, Februaiy, mS Prmlti in V.SJI. TOWARD A NORMATIVE MODEL OF PROMOTIONAL DECISION MAKING* DAVID A. AAKER University of California, Berkeley This paper presents a normative model of promotional decision making and re- views current literature in the model context. The model emphasizes the long-run impact of promotions and draws upon stochastic buyer-behavior model technology. In particular, a stochastic model is used to predict the level of brand acceptance ob- tained from a group of new triers attracted by a promotion—consumers with no recent use experience with the brand. This brand acceptance ia made a function of the com- position of the new-trier group. Finally, attention is focused upon the probability distribution of those attracted by the promotion, conditional on the nature of the promotion. This distribution is used to develop expressions for the expected long- term worth of a new-trier group attracted by a specific promotion. This paper presents a normative model of promotional decision making and reviews current literature in the context of this model. The objective is to help provide a more systematic basis for promotional strategy development. What kinds of promotions should be used? To what consumer types should they be directed? How long should they last? What about timing? It is to these kinds of decisions that the model construc- tion is addressed. The benefit of a normative model is usually not the machinery it makes available but, rather, the vocabulary it creates, the structure it provides, and its suggestions for future research. This model is discussed in this spirit. It was estimated that $4 billion was spent on sales promotion in 1966, about one- fourth as much as was spent on advertising [17, p. vii]. Coupon promotion alone was estimated to be $1 billion in 1960 [15]. Despite the importance of this component of the marketing mix, little attention has been paid to it by management scientists. Promotion is here defined as those short-run marketing activities other than ad- vertising and personal selling of manufacturers and retailers that are designed to stimulate consumer purchases. An important class of promotions are those that offer a direct extra value to the consumer as a purchase inducement. In this category are coupons, contests, premiums, and price-off campaigns that provide incentives for a brand purchase. They may be offered by the manufacturer directly to the consumer or indirectly through the retailer by means of a trade deal. Also in this category are special gifts and double-stamp days that encourage a consumer to visit a store and are offered by a retailer. Although this article is written from a manufacturer's viewpoint, the analysis would be identical if store choice instead of brand choice were the focus. Another class of promotions are those directed at the retailer that provide in-store stimulants to purchase. This would include inducements to use special displays. An important characteristic of promotions, as here defined, is that they are tem- porary in nature and therefore tend to stimulate immediate consumer purchases. Thus, relatively enduring purchase incentives such as trading stamps offered by re- tailers are excluded. A discussion of the various decision parameters will further serve to clarify the general problem. This will be followed by the development of the model's objective function. * Beceived Match 1971; revised November 1971, June 1972. 693

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MANAGEICENT SCIENCEVol. 18, No. 6, Februaiy, m S

Prmlti in V.SJI.

TOWARD A NORMATIVE MODEL OF PROMOTIONALDECISION MAKING*

DAVID A. AAKER

University of California, Berkeley

This paper presents a normative model of promotional decision making and re-views current literature in the model context. The model emphasizes the long-runimpact of promotions and draws upon stochastic buyer-behavior model technology.In particular, a stochastic model is used to predict the level of brand acceptance ob-tained from a group of new triers attracted by a promotion—consumers with no recentuse experience with the brand. This brand acceptance ia made a function of the com-position of the new-trier group. Finally, attention is focused upon the probabilitydistribution of those attracted by the promotion, conditional on the nature of thepromotion. This distribution is used to develop expressions for the expected long-term worth of a new-trier group attracted by a specific promotion.

This paper presents a normative model of promotional decision making and reviewscurrent literature in the context of this model. The objective is to help provide a moresystematic basis for promotional strategy development. What kinds of promotionsshould be used? To what consumer types should they be directed? How long shouldthey last? What about timing? It is to these kinds of decisions that the model construc-tion is addressed. The benefit of a normative model is usually not the machinery itmakes available but, rather, the vocabulary it creates, the structure it provides, andits suggestions for future research. This model is discussed in this spirit.

It was estimated that $4 billion was spent on sales promotion in 1966, about one-fourth as much as was spent on advertising [17, p. vii]. Coupon promotion alone wasestimated to be $1 billion in 1960 [15]. Despite the importance of this component ofthe marketing mix, little attention has been paid to it by management scientists.

Promotion is here defined as those short-run marketing activities other than ad-vertising and personal selling of manufacturers and retailers that are designed tostimulate consumer purchases. An important class of promotions are those that offera direct extra value to the consumer as a purchase inducement. In this category arecoupons, contests, premiums, and price-off campaigns that provide incentives for abrand purchase. They may be offered by the manufacturer directly to the consumeror indirectly through the retailer by means of a trade deal. Also in this category arespecial gifts and double-stamp days that encourage a consumer to visit a store and areoffered by a retailer. Although this article is written from a manufacturer's viewpoint,the analysis would be identical if store choice instead of brand choice were the focus.Another class of promotions are those directed at the retailer that provide in-storestimulants to purchase. This would include inducements to use special displays.

An important characteristic of promotions, as here defined, is that they are tem-porary in nature and therefore tend to stimulate immediate consumer purchases.Thus, relatively enduring purchase incentives such as trading stamps offered by re-tailers are excluded. A discussion of the various decision parameters will further serveto clarify the general problem. This will be followed by the development of the model'sobjective function.

* Beceived Match 1971; revised November 1971, June 1972.693

594 DAVID A. AAEER

Decision ParametersLet 6 represent a decision vector with respect to a particular promotion. Ultimately,

we want to determine an admissible 6 that will maximize an objective function. Thenumber and nature of the components of 6 will depend upon the specific context of thedecision. We shall specify here only a few of the more important and most representa-tive components.

One promotion decision involves the selection of the promotion type. Several ex-amples, such as couponing, have already been mentioned, but the number of differentkinds is actually limited only by the inventiveness of creative staffs. Let p denote thepromotion vehicle or type. After the type is selected, its unit value still must be de-termined. Should the unit value (to the consumer) of the premium or cents-off couponbe ten cents or twenty cents? Let s denote the unit value or size of the promotion.

The determination of the target audiences for the promotion is a third decision.Clearly, the effectiveness of the promotion will depend upon the segnientation strategyaccompanying it. Let x denote a vector of relevant descriptors of those upon which thepromotion is to be focused. For example, x could specify target levels in terms of age,income, and product-class usage of those to whom the promotion is addressed.

A fourth decision is the timing of the promotion. When is the optimal time to under-take such an event? Let t be the number of months since the firm's last promotion.Such a variable will certainly represent a relevant timing consideration. Promotionsthat are too frequent will jeopardize the temporary image that is usually important totheir success. There are many other ways to specify the timing, of course. It may beworthwhile, for example, to consider the history of competitive promotions. The degreeof detail included in this dimension will depend upon the information available to thedecision maker and on the nature of certain functions to be introduced.

There are many other decision dimensions that could be considered. One of these isthe duration of the promotion. Another is the selection of the method used to distri-bute the promotion if this is needed (direct mail versus magazine advertising). How-ever, we shall not formally introduce any additional decision dimensions. Once themodel is formulated, the 6 vector can easily be expanded or modified as required. Thedecision vector 6 can now be written in terms of the decision parameters introduced ase = (p, s, X, <, • • •).

The Objective Function

The objective function, to be denoted by F(e), represents the value to the firm thatthe promotion is expected to generate. Value is interpreted to mean the net presentvalue of the incremental sales stream generated by the promotion. It is really a predic-tion of the promotion's value, conditioned upon 6, the decision parameter vector. Theproblem can be formally stated as:

,.. select 0 to max y(6),^ ' subject to: 7(6) ^ 0, Budget Constraints,where:

0 = (p, s, X, t, • • •), the decision parameter vector,F(9) = the net present value to a firm expected from a promotion described by 6.In the balance of the paper the objective function wiU be expanded by considering

why promotions are used and the nature of the buying process involved. As additionalterms are introduced, the estimation problem will be addressed, drawing upon existingresearch.

TOWARD A NORMATIVE MODEL OF PROMOTIONAL DECISION MAKING 595

A promotion can increase sales by enticing present users to increase their purchasesand by obtaining sales from highly price-sensitive buyers. However, the dominantpurpose of most promotions involves a longer time horizon. The hope is to entice newcustomers to the brand, who will ultimately develop some level of loyalty toward it,and to increase the loyalty of existing customers. Thus, the promotion is largely aninvestment expected to return future sales that would not materialize without it.To formalize these remarks, let

(2) y(e) = .s(e) - A - C(e) + L(e) -\where:

5(6) = total gross margin contributed by the brand during and just after the promo-tion,

A = total gross margin that would have been generated in the absence of the promo-tion during a comparable time period,

C(6) = direct promotion cost, excluding the unit cost,L(6) = the value of any increase in loyalty among existing customers as a result of

the promotion,W(6) = the long-run value of a group of new triers of a brand attracted during

promotion.

The Short-Term Value of the PromotionThe first three terms in equation (2) reflect the immediate financial impact of the

promotion on the firm. The sales pattern of the product and unit cost data will de-termine the total gross margin, *S(0), obtained during and just after the promotion.The relevant time period must extend beyond the promotion when sales are oftendepressed because of loyal buyers and others who use the promotion to "stock up"on the brand. The tendency for a temporary sales decline after a promotion has beenfrequently observed [16, p. 86], but, in at least one case [8], it did not materialize. Thegross margin that would be generated in the absence of the promotion. A, and thepromotion cost, C(6), must be subtracted to obtain the net short-run contribution ofthe promotion. The promotion cost will include the costs of distributing the promotion,administrative costs, an appropriate allocation of the supporting advertising program,and costs of misredemption. The latter term can be quite significant—as high as 80percent [16, p. 47]. The determination of C(6) is usually fairly tractable; the predictionof the (>S(6) — A) term is normally more difficult.

There have been several approaches proposed that provide a start toward determin-ing (iS(6) — A). The dependent variable in a study by Hinkle [13] was the increase inmarket share enjoyed by a brand during a quarter in which a promotion was operating.The base from which the increase was measured was either the previous quarter'smarket share or a projection based upon a flow-type Markov model. The study, in-volving coffee, tissues, and frozen dinners, generated the following findings. A promo-tion was more effective if it represented a large value (s), was unique (p), and includedacceptable packaging innovations (p). The impact of a promotion was reduced if thebrand engaged in dealing activities too frequently (t). Ehrenberg and Goodhardt [8]also used a stochastic model projection as a reference for determining the immediatesales induced by a deal.

Massy and Frank [20] explored short-term price and promotion effects using weeklymarket share as the dependent variable. Current and lagged indexes of relative promo-tion magnitude were among the independent variables. They applied their regression

596 DAVID A. AAKER

model to different segments, showing that those with high promotion elasticitiestended to be nonbrand loyal, users of small packages, and patronizers of chain grocerystores (x). Webster [28] found that deal-proneness was positively related to housewifeage and negatively related to brand loyalty and the size of the individual purchase (x).Montgomery [22] found dealing activity to be related to venturesomeness, mediaexposure, and gregariousness as well as to nonbrand loyalty (x).

Kuehn and Rohloff [16, p. 119] made an effort to relate promotion-stimulated salesto promotion size, s. Sales data were used on a liquid household cleaner that had price-off deals of 8ff, lOff, 12^, 13{i, and 15f(. The dependent variable was a measure of therate at which the promotion is sold through at the retail level. From the results, theypostulated an s-shaped response curve which indicated that there exists a thresholddeal size. Sales seem much more sensitive to changes in s above the threshold thanbelow it.

Determining L(6)We now turn to the inherently less tractable concept of the long-term value of a

promotion. Central to these discussions is the distinction between two types of buyersattracted during the promotion period. The first are those who have previously pur-chased and used the brand and are thus familiar with it. The second are those who areunfamiliar with the brand—"new triers." They have never used it or the use experi-ence occurred sufficiently long ago that it has been effectively forgotten. One researcher[3] found that when fifteen months had elapsed since the previous purchase of a brandin one product class, the buyer's subsequent purchasing patterns were similar to thoseof a new trier who had never before purchased the brand.

The long-term value of the first type of consumer is denoted by L(0) in equation (2).It reflects the HuUian learning theory concept that a brand purchase and use experi-ence will increase habit strength and therefore brand loyalty. An approach to deter-mine 1/(0) has been developed by Kuehn and Rohloff [16]. They start by suggestingthat the state of a family with respect to a brand can be represented by the family'sbrand purchase probability. The measure of a promotion's long-term impact is thechange in this "state" (conversion) caused by the promotion. The pre-promotion stateis obtained by applying the linear learning model (the parameters of which are previ-ously estimated from aggregate data) to an individual family's purchase sequence. Thefamily's initial probability is estimated separately from prior data. The post-promotion"state" is determined either by applying the model to subsequent purchases or fromsubsequent family purchasing statistics. A measure of the long-term impact of a spe-cific promotion type is then an average of these "conversions" weighted appropriatelyby the family purchase volume. Using this measure, they compare a wide variety ofpromotion types.

This creative approach of Kuehn and Rohloff, though appropriate for the measure-ment of L{(t), cannot be applied to W{(i) for two reasons. First, for new triers, the pre-deal state should clearly be zero. Yet the linear learning model constrains the proba-bilities away from zero. This constraint can be significant (e.g. above 0.3), particularlyfor light users. Second, the linear learning model has been demonstrated [2 (for oneproduct class)] to be an inadequate model of the purchasing process following the"first" purchase of a new trier.

The determination of all functions becomes particularly difficult when competitorsfrequently run promotions and where there is substantial competitive interaction.Thus, a promotion may be retaliatory and defensive in nature. An attempt to intro-

TOWARD A NORMATIVE MODEL OF PROMOTIONAL DECISION MAKING 597

duce competitive factors would involve, as a minimum, focusing market models uponmore than just one brand. In one such effort, MacLachlan [18] developed a nonsta-tionary Markov model in which the state space included the brand of interest, all othernational brands, and all private label brands. He then explored the influence thatvariables such as the relative dealing activities of the major competitive aggregateshad upon the transition probabilities. He found, for example, that loyalty to the brandof interest had some tendency to increase as it increased its dealing activities relativeto other national brands, but had a definite tendency to decrease when it did moredealing than the private label brands. Dealing activity had little effect on the brand'sability to increase transition rates from the competitive aggregates. Loyalty to privatelabel brands was much more sensitive to dealing than was loyalty to national brands.

It is possible to argue that L(e) is often zero or insignificantly positive. The act ofpurchasing familiar brands is usually habitual in nature. The purchases merely reflectprevious decisions made with respect to the product class. Therefore, the buyer's"cognitive map" tends to be unaffected by the purchase and subsequent use experi-ence. The process is similar to that denoted by Howard and Sheth [14, p. 258] as rou-tinized response behavior, where the buyer exercises his predisposition toward anevoked set of a few brands. What positive effect the purchase might have would proba-bly be offset by the image-tarnishing effects of the promotion.

Empirical support for this position has been provided for one nondurable consumerproduct class [1]. The following specific hypothesis was tested:

With respect to a given brand, aggregate long-run purchase patterns of families familiarwith this brand (non-new triers) are not affected by interim promotion purchases of thesame brand.

A Bernoulli model was assumed to be operative for this type of consumer. The spe-cific hypothesis inquired as to whether the Bernoulli parameter changed as a result ofa promotion purchase of that brand. For each sample member, an estimate of hisBernoulli parameter was obtained, both before and after the promotion purchase. Theinterest was in the difference between these estimates. The estimates were made fromthe two five-purchase sequences preceding and following the promotion purchase. Onlythose who had purchased the brand in question during the past fifteen months priorto the promotion purchase were included in the sample. Since the average interpur-chase time was about six weeks, there were many in the sample whose previous pur-chase of the brand was separated from the promotion purchase by more than five pur-chases. A total effective sample size of more than 4,000 was used. The data source wasthe MRCA National Consumer Panel. Overall, there was no observed tendency for a(non-new trier) buyer to alter his brand loyalty on the basis of an interim promotionpurchase. In fact, for four of the seven brands considered, there was an average de-crease in the Bernoulli parameter estimate.

Measuring Tr(6)

We now turn to the problem of measuring W^d), the worth of a group of new triersattracted to a brand during a promotion. The worth of a new-trier group will certainlydepend upon their buying potential, the brand's profitability, their acceptance of thebrand, and some discount factor. More specifically, the group's value can be repre-sented by the following expression:

(3) W{B) = £ iNim)g-P - TFo = {Nvm){P - W,)/{1 - g) = Wy-Wa,

598 DAVID A. AAKEB

where:= the long-run value of a group of new triers attracted during a promotion,

n = index of a time period of analysis (i.e. one year),N = the number of new triers in the group,V = average per capita product-class purchasing volume per time period of the

new-trier group,m = gross margin of the brand,g = discount factor representing the cost of capital and the risks of the market,P = factor representing the brand's long-run share of the group's purchasing volume

—operationally, the asymptotic market-share prediction of a brand choice stochasticmodel.

Wo = long-run worth of new triers who would have been attracted in the absenceof the deal,

TFi = iNvm){l/l - g)P.The first term, N, indicates the number of new triers attracted during a promotion.

The expression, W(fi), must directly refiect the promotion's success in gaining newtriers. The second term, v, represents the buying potential of the new-trier group—theproduct class purchasing volume expected in the future. It reflects the fact that heavyusers are potentially more worthwhile than light users. The third term, m, representsthe profit contribution of the brand. Clearly, the brand's profitability should be ex-plicitly considered in an evaluation of promotions aimed at attracting new customers.

An implicit assumption in equation (3) is that both v and m are constant over time.If information in a brand's long-range plan would support an alternative assumption,it could easily be introduced with a simple modification of equation (3). Perhaps, forexample, the product class is expected to decline and face price pressure because ofexternal technical developments.

The discount factor, g, should normally be fairly large—perhaps 25 percent per year—since it is absorbing the uncertainties of the market. It might be reasonable to re-quire it to increase over time, though this complication is not considered.

The term, P, is a summary measure of the brand's ability to gain acceptance andits "staying power." It is the asymptotic market-share prediction of a brand-choicestochastic model that is applied to the group of new triers attracted during the deal-ing period. There are many future market forces that will influence market share, ofcourse, possibly causing it to move away from P, its predicted level. This risk will in-crease as one moves out in time measured in years. Still, P is, in a Bayesian sense, abest expectation of the future. In the absence of other information, it should be anappropriate indicator of the brand's ability to gain future sales among the new-trier group.

The transient market-share prediction is omitted in equation (3) to avoid compli-cating the discussion. It can be added easily when the circumstances warrant. Thetransient in one nondurable product class was found to span three or four purchasesfor new triers of existing brands and six or seven purchases for new triers of a newbrand [3].

There are several brand choice models that seem capable of representing the deci-sion process following a first purchsae of a brand. Two [3], [24] were designed spe-cifically for this task. Another [21] has demonstrated success in a similar situation.Purchase-incidence models, designed to model interpurchase times and predict saleslevels, may also be considered, especially where the product class is not well defined[9], [19]. These models would provide NvP instead of just P. An assumption is that

TOWARD A NORMATIVE MODEL OF PROMOTIONAL DECISION MAKING 599

these models can be applied to new triers of existing brands as well as new triers ofnew brands. The buyer who has not bought a brand for an extended time period isthus assumed to have a capacity for learning about the brand purchased that iscomparable to that of a new trier of a new brand. There is empirical support for thisassumption [3], [24].

It should be noted that the group of new triers obtained during a promotion willcontain members whose first purchase was not associated with the promotion, since apromotion rarely achieves 100 percent coverage due to distribution complications.Including these new triers in the data base used for the stochastic model parameterestimation will, of course, provide a welcome increase in sample size. There is someevidence that it will not severely inhibit model performance [3].

The term Wa is the corresponding value of those new triers who would be attractedin the absence of a deal. It would be a distortion to credit a deal \\'ith those newtriers who would have appeared in its absence. Ehrenberg and Goodhardt present arare eflort to measure Wo using the Negative Binomial Distribution Model [8].

It should be noted that two problems have been by-passed in our analysis. First,we have corrected for those who would have been new triers during the dealing periodeven if the deal had not existed. We have not, however, considered those who wouldhave tried soon after this time period. Obviously, it is of little value to alter a date ofpurchase by only a few months. Second, there are going to be users who are attractedto the brand by the recommendation or more indirect influence of the new triers at-tracted by the deal. This secondary effect will be particularly relevant when the brandis new. It will be less so for existing brands in relatively low-risk, established productclasses in which word-of-mouth activity would tend to be minimal. Parfitt and Collins[24] handle both problems rather elegantly by fitting a penetration curve for a brandand observing the change in its asymptote that can be associated with a promotion.

PredictingEquation (3) provides an expression for the net present value of an income stream

generated by a new-trier group enticed during a promotion. To shift the focus frommeasurement to prediction it is useful to consider N and P as random variables andto introduce two additional expressions. The first is the joint probability distribution:f{N, y I e), where y, also a random variable, is a vector of descriptors (age, usagelevel, etc.) of the new-trier group. In a probabilistic sense, f{N, y \ 6) indicates the sizeand composition of the new-trier group that -will be attracted by a promotion de-scribed by e. It might be useful also to condition fiN, y | 6) on the market share andmaturity of the brand. It is reasonable to assume that the quantity of potential newtriers might be negatively related to each of these dimensions. A dominant brand hasprobably received more trials than a small brand. Similarly, as the brand matures, thenumber of potential new triers will decline. However, the temptation to add variablesat this point will be resisted. Appropriate generalizations should be evident.

There has been some effort to relate the intensity and nature of promotions to N,the number of new triers the promotion attracts. Parfitt and Collins [24] providedseveral examples involving new and existing brands where a promotion dramaticallyincreased the number of new triers the brand was projected to receive. One was arare example of a trade promotion designed to temporarily reduce the price. In thatinstance, the projected penetration level went from 25 to 36 percent.

Claycamp and Liddy [6] developed a regression model to predict early trial of newconsumer packaged goods. The model explained more than 70 percent of the variance

600 DAVID A. AAKER

when it was applied to thirty-five new product introductions. The independent vari-able with the highest beta weight was the coverage of consumer promotions adjustedfor type and value of offer. Among the other variables included were product aware-ness, whether a family brand was used, and packaging distinctiveness. Hamm et al.[11] showed that a free sample increased purchase intentions. Chien [5], using experi-mentation, determined the effect of various promotions on obtaining new physicianprescriptions. He found that the quantity of new prescriptions was significantly af-fected by samples, and also by literature mailings. Pessemier et al. [25] cross-tabulatednew triers (early and late) and non-new triers of new heavy-duty detergent againstfifty-seven descriptive variables. Among the more significant descriptor variables werewillingness to try new brands, certainty about current brands, information transmis-sion habits, and whether the housewife received a free sample.

There has been little effort to relate promotion characteristics, 6, to the type of newtrier attracted, y. There is, of course, a rich and relevant literature concerned withdescribing those who tend to try new products—the early adopters [26], [27]. Thestudy by Pessemier et al. was in this tradition. Another was the Montgomery andArmstrong study [23], although they focused on new triers of an existing product,Crest, just after the American Medical Association's endorsement. They found thatthose trying Crest tended to have children and to be nonbrand loyal, gregarious,venturesome, exposed to mass communication, and somewhat deal-prone.

The second expression used to shift the focus of equation (3) to prediction is thefollowing:

(4) P = P{y, e).

This equation states that P is likely to depend upon promotion descriptors and uponthe type of new trier attracted during the promotion. Let us illustrate equation (4)with an example taken from a recent study [4]. In that example, equation (4) tookthe form of a linear regression model with four independent variables:

(5) P* = a -\- a^v -\- aJ, + a^d -f a^s,

where :V = index of purchasing volume,I = index of brand loyalty,d = dummy variable—coded as 1 if the first purchase was associated with a promo-

tion; otherwise as 0,s = size of the promotion,P* = the asymptotic market-share of a brand choice stochastic model conditional

upon a given purchase sequence.Thus, in this case:

y = {v, I) and 6 = (d, s).

In equation (3), P was defined as the asymptotic market share prediction of a brandchoice stochastic model applied to a new-trier group. In this example, the definitionof P was modified (yielding the P* of equation (4)) to expand the number of datapoints and to exploit the available information. The modification consisted of condi-tioning P upon the purchase sequence. Since a binary choice was postulated and sincefive purchase sequences were considered, thirty-two different subgroups of new trierswere created, with potentially thirty-two distinct values of the dependent variable.The exact form of P* in general will depend upon the model specified. In most models.

TOWARD A NORMATIVE MODEL OF PROMOTIONAL DECISION MAKING 601

however, those new triers with a purchase sequence following a trial purchase of(1,1,1,1,1) would have a higher P* than those with (1,0,0,0,0).

Equation (5) was explored empirically with four brands with some interesting re-sults. As equation (3) indicates, the value of a new trier will increase with his usage.However, these results suggest that the higher-volume user is more difficult to "winover," once he is brought to trial, than the more average user. Evidence relevant tothe f{N, y \ 6) distribution indicated that a person who has exhibited a high level ofbrand loyalty may be difficult to attract. In our example, however, there was a clearindication that those buyers with a tendency toward brand loyalty are more likelythan others to accept a brand once they are brought to trial. The effect of d and s onbrand acceptance was negative, as expected, reflecting the image-tarnishing effects ofa promotion, but not as markedly as other research had found [24], [8].

Haines [10] also attempted to relate brand acceptance among new triers to promo-tions. He applied a learning model to the introduction of a new product in thirty-three different geographic areas. The projected brand share and the rate at which themarket moved toward this projection were obtained for each area. This rate was af-fected by prior product availability and advertising expenditures. The steady statebrand share level was primarily infiuenced by per capita promotional expenditures.

With f{N, y I 6) and P{y, 6) introduced, it is now possible to develop an expressionfor E[W{B)]. In equation (3), Wi is presented as a function of five terms:

(6) W, = W,{N, V, m, g, P).

Substituting equation (4) into equation (6), we have:

(7) Wr = WriN, V, VI, g, y, 6).

In equation (7), the term, v, is now redundant. As equation (5) showed, the term, y,logically can contain v as one descriptor of the new-trier group. Dropping v leaves:

(8) TTi = W,{N, m, g, y, 6).

The terms m and g are determined internally by the firm. The term 6 is a vector offirm decision parameters. The remaining two terms, A and y, are random variablesdetermined by the market in accordance with the probability distribution/(A?^, y | 6).

Taking the expectation of Wi, with respect to f{N, y | 6), yields Ef(Wi | 6). It pro-vides a precise expression for the long-term value of a group of new triers that may beattracted during a promotion. It recognizes that the size and composition of the new-trier group will depend upon the characteristics of the promotion. Further, thr ac-ceptance of the brand by the new-trier group will depend upon the nature of that groupand also upon the type of promotion that attracted them to try the brand.

It can now be observed that the expectation of the second term. Wo, in equation(3) is simply Ef[Wi | s = 0]. It is the expected long-term value of the new-trier groupthat would be obtained, on the average, in the absence of a promotion. The expression,s = 0, here symbolizes that no promotion is offered.

Some Implications

As noted at the outset, the benefit of a normative model is usually not the machineryit makes available but, rather, the vocabulary it creates, the structure it provides, andits suggestions for future research. The model reported in this paper is no exception.It suggests that research on promotions should be directed toward the long-run impactof promotion instead of toward short-run measures such as change in market share.

602 DAVID A. AAKER

In particular, research on the f(N, y, 6) and P(y, e) functions is needed. How will thesize and composition of the new-trier group be affected by promotion characteristicsand competitive interactions? And, how will the promotion and new-trier characteris-tics affect brand acceptance? Data bases and stochastic model technology now permitmanagement scientists to make real progress toward the development of an opera-tional model of promotional decision making.

Hardin and Johnson recently surveyed users of consumer panels and concluded:

National consumer panel data appear to be underutilized, , , , The dynamics of brandswitching, new trial and repeat buying, items likely to be purchased in combination, andthe extent to which new business is created by promotional activities rank relativelyfar down the list of purposes to which national panel data are put. The full utilizationof these data may depend to a large extent on the development of better marketingdecision models [12, p, 367],

Hopefully, the model suggested in this article will, in some measure, contribute to thisdevelopment.

References

1, AAKEH, DAVID A,, "The Long-Term Value of Temporary Price Reductions," UnpublishedPh.D. dissertation. Graduate School of Business, Stanford University, 1969,

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