Effect of Brand Loyalty on Advertising and Trade Promotions:

Effect of Brand Loyalty on Advertising and Trade Promotions: A Game Theoretic Analysiswith Empirical EvidenceAuthor(s): Deepak AgrawalSource: Marketing Science, Vol. 15, No. 1 (1996), pp. 86-108Published by: INFORMSStable URL: http://www.jstor.org/stable/184185 .Accessed: 04/04/2011 12:31

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Effect of Brand Loyalty on Advertising and

Trade Promotions: A Game Theoretic

Analysis with Empirical Evidence

Deepak Agrawal Purdue University

Abstract In this paper we examine the issue of balancing media advertising (pull strategy) and trade promotions (push strategy) for manufacturers of consumer packaged goods utilizing a three- stage game theoretic analysis and test model's implications with scanner panel data.

We develop a model of two competing manufacturers who distribute their brand to consumers through a common retailer. In the model the manufacturers directly advertise their brand to consumers and also provide trade deals to the retailer. Each manufacturer's brand has a loyal segment of consumers who buy their favorite brand unless the competing brand is offered at a much lower price by the retailer. The number of loyal consumers is different for the two brands and so is the strength of their loyalty to their favorite brand. The loyal consumers of the brand with stronger loyalty require a larger price differential in favor of the rival brand before they will switch away from their favorite brand.

The manufacturers first decide advertising spending level, and then the wholesale price of their respective brands. The two manufacturers do not observe each other's decisions while making these decisions, however they do take into account how the other firm is likely to react as a function of their own decisions. Advertising directly affects the strength of loyalty a consumer has for the favorite brand. If the favorite brand advertises, the loyalty strength increases but if the rival brand advertises, it decreases. The marginal effect of own versus competing brand advertising is different in magnitude.

The two manufacturers provide trade deals to the retailer by discounting the brand from a regular wholesale price. The trade discounts are partially passed on to the consumers by the retailer who sets the retail prices of the two brands after observing the wholesale prices. The retail shelf price discounts make the promoted brand more attractive to the consumers due to the reduced price differential between their favorite brand and the promoted brand, thus affecting their switching behavior.

The model and its analysis shed light on the role of brand loyalty in the optimal advertising and trade promotion poli-

cies for the two manufacturers. The analysis indicates that, if one brand is sufficiently stronger than the other and if advertising is cost effective, then the stronger brand loyalty requires less advertising than weaker brand loyalty, but a larger loyal segment requires more advertising than a smaller loyal segment. Moreover, stronger brand loyalty requires more trade promotion spending under these conditions. The analysis also indicates that the retailer promotes the stronger loyalty brand more often but provides a smaller price discount for it compared to the weaker loyalty brand.

These analytical results can be understood better if we view advertising as a "defensive" strategy used to build brand loyalty which helps in retaining the loyal consumers, and price promotions as an "offensive" strategy used to attract the loyal consumers away from the rival brand. For example, the result that the stronger brand invests less in advertising than the weaker brand can be explained as follows. The stronger loyalty brand does not find use of advertising attractive because it faces little threat from the weaker brand due to its sufficiently stronger loyalty. Instead it spends more on promotions (provided advertising is cost effective) to attract away the weaker brand's loyal consumers. The weaker brand, on the other hand, finds it optimal to defend its loyal franchise by spending more on advertising, as promotions do not help much due to the difficulty in attracting away the stronger brand's loyal consumers. In this sense, the stronger brand plays "offensive" by using more trade promotions, and the weaker brand plays "defensive" by emphasizing advertising.

We also conduct an empirical analysis of the model's propositions using scanner panel data on seven frequently purchased nondurable product categories. In a sample of 38 national brands from the seven categories we find that weaker loyalty brands spend more on advertising; brands with larger loyal segment spend more on advertising; and the retailer promotes stronger loyalty brands more often but provides a smaller price discount on average for them compared to weaker loyalty brands. These findings are consistent with the model. (Advertising; Brand Loyalty; Game Theory; Promotional Mix)

MARKETING SCIENCE/Vol. 15, No. 1, 1996 0732-2399/96/1501 /0086$01.25 Copyright ? 1996, Institute for Operations Research

pp. 86h108 and the Management Sciences

EFFECT OF BRAND LOYALTY ON ADVERTISING AND TRADE PROMOTIONS: A GAME THEORETIC ANALYSIS WITH EMPIRICAL EVIDENCE

1. Introduction There has been a recent revival of interest, among both practitioners and academics, in the issue of advertising versus trade promotions (see Low and Mohr 1992; Nes- lin et al. 1994a; Neslin et al. 1994b). Consumer packaged goods manufacturers are taking a hard look at their promotional mix, particularly trade promotional spending. One estimate is that 33% of the trade promotion dollars is used up in the administrative aspects of trade promotions (a major part of which goes toward the time spent by salesforce in settling retailer claims), another 33% goes directly toward retailer's revenue, and only the remaining 33% ultimately reaches the consumer in the form of a shelf price reduction (Ernst and Young Report 1993). These estimates corroborate the concerns of manufacturers that trade promotional spending is not getting the desired results, and there is a need to get out of the vicious circle of heavy trade dealing in favor of more effective activities, particularly advertising which helps build brand equity. However, it appears that some amount of trade dealing inevitably will be desirable because trade deals are used not only to induce shelf price reductions but also to secure shelf space, wider distribution, and retailer cooperation (Nar- asimhan 1990). So the real issue facing manufacturers is to achieve a balance between trade dealing and advertising.

In this paper we address this issue by developing a three-stage game theoretic model of two competing manufacturers selling their respective brands through a common retailer. Our approach is to study advertising and trade promotions simultaneously in a competitive setting. This is consistent with the Neslin et al. (1994a, p. 405) call for research addressing both advertising and promotions together and not sepa- rately. Our primary objective is to understand the role of brand loyalty in the optimal promotional mix for manufacturers. The game theoretic approach here is not intended to explain observed phenomena but is intended to understand and prescribe optimal promotional policy.

In the paper we distinguish between the strength and size of brand loyalty. Strength of brand loyalty is con- ceptualized as the intensity of customer loyalty toward the brand, whereas size of brand loyalty is conceptual- ized as the proportion of consumers in the market loyal

to the brand.1 In our model one brand enjoys strong loyalty among its loyal customers (named as stronger brand), whereas the rival brand enjoys relatively less loyalty among its loyal customers (named as weaker brand). Each manufacturer is assumed to decide advertising level and wholesale price for its brand, taking into account possible actions of the competing brand manufacturer; and the retailer sets retail prices after observing the wholesale prices of the two brands.

The analysis points to the differing roles of the strength and size of brand loyalty in the promotional mix. It indicates that stronger brand loyalty requires less advertising than weaker brand loyalty but a larger loyal segment requires more advertising than a smaller loyal segment. Thus it indicates that the weaker brand would spend more advertising dollars, and the brand with larger loyal segment size would spend more on advertising. Also, the weaker brand would promote to the trade more often than the stronger brand.

In addition we find that trade promotional spending is dependent on cost effectiveness of advertising. If advertising is cost effective, then the weaker brand would spend fewer trade promotional dollars than the stronger brand. And if advertising is costly, then the weaker brand would spend more trade promotional dollars than the stronger brand. At the retail level, however, we find that the retailer would promote the stronger brand more often but provide a smaller price discount on average for it than the weaker brand. We provide intuition for these findings and relate them to previous findings in the literature.

These analytical results can be understood better if we view advertising as a "defensive" strategy used to build brand loyalty which helps in retaining the loyal customers, and price promotions as an "offensive" strategy used to attract the customers away from the rival brand. For example, one result is that the stronger brand invests less in advertising than the weaker brand. The intuition behind this result is that the stronger brand does not find use of advertising attractive because

' In the theoretical model strength of brand loyalty is defined as the price differential needed before the consumer will switch away to the less favored brand (Pessemier 1959). It is noteworthy here that brand loyalty strength was operationalized differently in the empirical analysis.

MARKETING SCIENCE/Vol. 15, No. 1, 1996 87

AGRAWAL Brand Loyalty on Advertising and Trade Promotions

it already enjoys sufficiently stronger loyalty and therefore faces little threat from the weaker brand. Instead it finds it optimal to spend more on promotions (when advertising is cost effective) in order to attract away the weaker brand's customers. The weaker brand, on the other hand, finds it optimal to defend its loyal franchise by spending more on advertising, as the promotions do not help much because it is difficult to attract away the stronger brand's loyal customers. In this sense, the stronger brand plays "offensive" by using more trade promotions, and the weaker brand plays "defensive" by emphasizing advertising.

We also conduct an empirical analysis of the model's propositions using scanner panel data on seven frequently purchased nondurable product categories. In a sample of 38 national brands from the seven categories, we find that weaker loyalty brands spend more on advertising; brands with larger loyal segment spend more on advertising; and the retailer promotes stronger loyalty brands more often but provides a smaller price discount on average for them compared to weaker loyalty brands. These findings are consistent with the model, thereby indicating support for it. We next provide a brief review of the relevant literature and point out main contributions of this research over previous research.

2. Literature Review Advertising and trade promotions differ significantly in several respects, including their effect on consumers' purchase behavior, time frame within which effects take place, and the processes by which the effects take place. For example, in the context of frequently purchased goods, the main effects of advertising are considered to be brand positioning, category expansion, brand reinforcement (repeat purchase), and brand switching (Deighton et al. 1990), whereas the main effects of sales promotions are considered to be brand switching, purchase acceleration, stockpiling, and repeat purchase (Blattberg and Neslin 1990). Advertising is commonly believed to positively affect brand loyalty, whereas promotions may either have a negative effect or not have any effect (Neslin and Shoemaker 1989, Davis et al. 1992). Advertising is considered to have long-lasting effects with possible delayed response and slow decay (Little 1979). Promotions, on the other hand, are consid-

ered to have more immediate and short-term effects on purchase behavior (Rossiter and Percy 1987). And there is evidence that advertising effects follow a hierarchical process (AIDA model, Strong 1925), whereas sales promotion effects do not (reference price theory, Helson 1964; prospect theory, Kahneman and Tversky 1979). Given these differences and the fact that both advertising and price promotions commonly are used in the promotional mix of a brand, it becomes important to model them differently yet simultaneously in a single framework so that their opposing effects can be studied.

On the analytical side, Raju et al. (1990) examined two competing manufacturers' pricing policies as a function of brand loyalty. They define a stronger and a weaker brand in terms of strength of brand loyalty and examine how the degree of brand loyalty determines the optimal frequency and depth of price promotions. Their analysis indicates that the weaker brand promotes more often than the stronger brand (this is shown to hold empirically as well) and offers smaller price discount when it is sufficiently weaker, but offers greater discount when it is only moderately weaker, than the stronger brand. We build on this framework by incorporating manufacturer advertising and retailer pricing decisions in addition to manufacturer pricing, thereby allowing us to study advertising and trade promotion tradeoffs and retail promotion activities.

Other research which examines pricing policies of competing manufacturers includes Narasimhan (1988), Rao (1991), and Lal (1990a, b). Narasimhan defines brand power in terms of proportion of customers loyal to the brand and predicts that the average price will be higher and the frequency of promotion lower for the stronger brand. Rao examines competition between a national brand and a private label and shows that only the national brand promotes to attract the private label customers (if they are sufficient in number). The private label does not promote because its promotions only increase the frequency of promotions by the national brand. Lal addresses the issue of why retail promotions occur and argues that national brand manufacturers al- ternate promotions in order to keep the private label brand from encroaching upon their market share.

One interesting finding in this paper is that at the manufacturer level weaker loyalty brand promotes more often than the stronger loyalty brand (consistent with Raju et al.

88 MARKETING SCIENCE/Vol. 15, No. 1, 1996


1990), and at the retail level, the retailer promotes the weaker brand less often than the stronger brand (consistent with Rao 1991). Raju et al. consider only manufacturers, whereas Rao considers retail price competition between a national brand and a private label. Thus our finding helps to reconcile the results of Raju et al. and Rao.

Neslin et al. (1994b) model a monopolist manufacturer's optimal promotional mix policy as a dynamic econometric model. They examine promotional mix policy as a function of retailer carrying costs, retail pass through, consumers' response to advertising, and consumers' response to retail price promotions. Their sim- ulations demonstrate a tradeoff effect between advertising and trade promotions consistent with our finding (when advertising is cost effective). Also, they find that as retail pass through increases (either in terms of frequency or depth), frequency of trade promotions decreases, depth of trade discounts increases, total expenditures on promotions increase, and advertising expenditures decrease for the monopolist. We also find this in our analysis for the stronger brand, which enjoys higher retail pass through in terms of frequency. Se- thuraman and Tellis (1991) also develop a monopoly model to investigate the impact of the ratio of price to advertising elasticity on the tradeoff between advertising and trade promotions. We add to this literature by incorporating competition in the analysis.

In summary, the main contributions of this research over previous research are in studying advertising and trade promotions simultaneously in a competitive setting, in developing an integrated analytic framework to examine the tradeoffs between the two, in incorporating the role of the retailer, and in empirically investigating the role of brand loyalty in promotional policies using scanner panel data from several product categories. In the next section, we describe the model in detail and present analysis of manufacturer advertising and price promotional policies and of retail pricing. Then we present details of empirical investigation, and finally summarize the discussion and conclude with directions for further research.

3. Model In our model, there are two national brands s and w offered through a common retailer to a group of consumers. Each consumer is loyal to a brand, but he/she

can be induced to switch away if there is sufficient price differential between the favorite brand and the less pre- ferred brand. In other words, both brands are in each consumer's consideration set, with one brand being the favorite. We define the extent of favoriteness by the price differential needed before the consumer will switch away to the less favored brand (Pessemier 1959). We assume that it takes a larger price differential to make a consumer who prefers brand s to switch to brand w than what it takes a consumer who prefers brand w to switch to brand s. This implies that brand s commands stronger preference among its loyal consumers compared to what brand w commands among its loyal consumers. Let the loyalty among loyal consumers to brand s be Is,, and the loyalty among loyal consumers to brand w be lw, such that Is, > Iw,.

The number of loyal consumers to each brand may differ such that a brand may have a very few but strongly loyal consumers, many but only mildly loyal, or any other combination. Without loss of generality we normalize the total number of consumers to equal one and assume that a proportion ms of consumers prefer brand s and proportion mw prefer brand w, where ms + mw = 1. We further assume that a consumer loyal to brand s has a reservation price r for brand s and a lower reservation price (r - Is) for brand w, whereas a consumer loyal to brand w has a reservation price r for brand w and a lower reservation price (r - iw) for brand s. Each consumer is assumed to buy a brand and buy one unit of the chosen brand such that surplus is maximized. Thus the demand function at the retail level for brand i (where i = s, w; i * j) can be written as (see Figure 1):

[1 if pi < pj - Ij,

Di(pi, pj) = j mi if pi - li c pj c pi + Ij,

tO if pj < pi - Ii.

The manufacturers are assumed to advertise their brands directly to the consumers. They simultaneously

Figure 1 Consumer Demand Function Consumer s Consumer w

wouldn't buy s wouldn't buy w

PS-IS PI PJ + IW _ PW

MARKETING SCIENCE/VOL 15, No. 1, 1996 89


decide advertising levels (i.e., without knowing the advertising level for the rival brand) a, and a,,, for their respective brands such that own advertising positively affects and competing brand's advertising adversely affects the strength of brand loyalty. Furthermore the effect of own advertising is assumed to differ from that of competing brand's advertising through a parameter, y. A high y means that the effect of own advertising is higher than competitor's advertising, whereas a low y

means that the effect of competitor advertising is higher than that of own advertising. In other words, a high y

means advertising works more on brand's own loyal customers than on potential brand switchers (similar to the idea that advertising affects loyals differently than switchers as in Tellis 1988 and Deighton et al. 1994).2

Finally, to incorporate diminishing returns to advertising, we assume that advertising effects have a square root formulation and that advertising costs are linear, i.e., it costs aa, and aa?., to advertise for manufacturers s and w, respectively, where a captures the cost effectiveness of advertising. A small a implies advertising is relatively cost effective, and a large a implies advertising is relatively costly. This parameter captures market- wide advertising effectiveness and is assumed to be the same for both brands. It reflects the notion that in some markets advertising may be relatively cost effective in reaching target consumers, such as when target audi- ence is geographically concentrated, or when a cam- paign has higher effectiveness because of the nature of the clientele. These assumptions translate into the following asymmetric effects formulation for the post- advertising loyalties:

Is = ISO + yFas- (1 - y) aF,

IW= lu.o + -y a5 - (1 - -y)a,

where 0 < y < 1 captures the effectiveness of own advertising.

After deciding advertising levels, the manufacturers simultaneously declare wholesale prices ws and ww

2 Many of the results in this paper are based on y > 0.5, which implies own advertising is more effective than competitor advertising in affecting brand loyalty.

for their respective brands to the retailer. As part of their promotional mix, manufacturers offer trade deals to the retailer with the intention of reducing the selling price of the brand making it more attractive to loyal and nonloyal consumers alike. The trade promotional spending is defined as the total discount given to retailers over all purchases; where discount is the difference between the regular price (i.e., the highest wholesale price) and the actual wholesale price in equilibrium. After observing the wholesale prices, the retailer is assumed to set retail prices p, and

p, for the two brands, respectively, so as to maximize expected profits. The marginal costs of production and distribution for the two manufacturers, and the marginal cost of retailing are assumed to be zero.

In this three-stage model the manufacturers are assumed to decide advertising levels first for their respective brands without knowing the advertising level for the rival brand. Next they are assumed to decide the wholesale prices for their respective brands without knowing the wholesale price of the rival brand but knowing the advertising levels of both brands. These assumptions imply that (1) in any given planning horizon advertising decision precedes pricing decision, (2) pricing is changeable more easily than advertising, and (3) once advertising is under- taken it becomes a sunk investment. Lastly, the retailer is assumed to decide the retail prices for the brands it offers to consumers after observing the wholesale prices of the two brands. There is support for this stagewise decision making in the literature (Quelch and Farris 1983, Shapiro 1987).

Now we solve this three-stage game for the equilibrium advertising and pricing strategies beginning with the third stage retail pricing strategy.

Retail Pricing Strategy The retailer's profit function is:

(P s-W)

if Ps < Pw - I,

ms(ps - ws) + mw(pzv - wW)

if Ps1 is pw c Ps + Iw,

(PW - wu,) if PZw < PS - is.

The retailer would maximize profits by charging the highest price that the consumers will pay. Intuitively,

90 MARKETING SCIENCE/VOL. 15, No. 1, 1996


there are three possibilities for the retailer as indicated by the retail demand function: (1) if the stronger brand is sufficiently cheaper than the weaker brand, promote the stronger brand and sell it to both consumer segments; (2) if the weaker brand is sufficiently cheaper than the stronger brand, promote the weaker brand and sell it to both consumer segments; and (3) if the two brands are not sufficiently different in wholesale prices then do not promote either brand, and sell each to its loyal segment. Consistent with these possibilities, we obtain the following retail pricing strategy in equilibrium:

PROPOSITION 1. The optimal pricing strategy of the retailer is to charge p, = r - 1w - E,pw = r if ww > w, + (1 / mW,)lw; charge ps = r, pu' = r if w, (1/ms)l C< ww s Ws + ( /m)1,)l1,; and charge, ps = r, pw = r - - e if w > ww + (//ms)i.

PROOF. See Appendix. To understand this equilibrium note that the retailer

can always sell a brand to its loyal segment at regular price. It promotes a brand only if the margin obtained on selling the promoted brand to all of the market is higher than selling it only to the loyal segment at regular price. The equilibrium indicates that the retailer promotes a brand if its wholesale price is sufficiently lower and that he/she promotes only one brand at a time, if at all. Moreover, when the retailer promotes a brand, he/she does not buy the nonpromoted brand from the manufacturer.

COROLLARY 1.1. The price discount offered by the retailer on the weaker brand is larger than that offered on the stronger brand.

PROOF. See Appendix. This result follows from the retail price equilibrium

above. The retailer offers a larger discount 1I on the weaker brand compared to lw on the stronger brand. Note that because the regular price is the same (=r) for both brands, this result holds for percentage discounts as well. In other words, the retailer offers a higher percentage price discount on the weaker brand than the stronger brand.

COROLLARY 1.2. The retailer promotes the stronger brand more frequently than the weaker brand.

PROOF. See Appendix. This result suggests that at the retail level, we would

expect to see more frequent promotions but lower discounts on the stronger brand. This finding is consistent with Rao (1991), whose model corresponds to a retailer setting the price of its own private label and retail price of the competing national brand. He finds that the weaker brand is promoted less often than the stronger brand. This result is interesting also because at the manufacturer level, it is reversed. We describe manufacturer results next.

Manufacturer Pricing Strategy We solve for the second-stage manufacturer pricing equilibrium treating advertising spending in the first stage of the game as a sunk investment. The post- advertising profit function for manufacturer i (i = s, w; I # j) is:

[wi if wj > w, + (1 /mj)1j,

ni = jmiwi if wi- (1/rmi)n w? c< WI. + (1/m)nJ),

to if wi > wi + (1/mi)Ii.

It can be shown that a mixed strategy equilibrium in prices exists for the above game when l. c m2 r and Is 2 mj(r - lW)/(1 + msmw) (see Raju et al. 1990). We interpret the mixed strategy equilibrium as a promotional equilibrium in which the reservation price r is the regular price and a promotional price is any price below r. We obtain the following results:

PROPOSITION 2. The weaker brand manufacturer promotes more often but provides smaller discount on average than the stronger brand manufacturer.

PROOF. See Appendix. This manufacturer level finding is consistent with the

manufacturer pricing equilibrium in Raju et al. (1990); and the retail level findings (Corollaries 1.1 and 1.2) are consistent with retail pricing model of Rao (1991). A reason for this reversal of findings at the manufacturer and retail level is essentially that the retailer cares about category profit, whereas manufacturers care about their respective brand profit. The retailer realizes that the stronger brand does not have to be promoted as steeply as the weaker brand because it commands a price pre- mium with consumers. Thus promoting the stronger



brand more steeply would only erode retailer's profit margin on stronger brand and forego profits it makes on the weaker brand.

However, at the manufacturer level, the brands are in a market share game. The stronger brand increases its profits only by attracting weaker brand's customers. Therefore it keeps trying to induce the retailer to promote its brand more steeply by offering steeper trade deals. Moreover, the stronger brand, in order to be promoted at the retail level, not only has to overcome the loyalty of the weaker brand but also has to provide attractive enough margin to the retailer to entice the retailer into promoting the brand. This aggressive strategy on part of the stronger brand necessitates higher trade discounts on average compared to the weaker brand, which is only trying to keep its loyal customers from switching to the stronger brand.

But the frequency with which the stronger brand provides a trade discount is lower than the weaker brand because to induce the retailer to discount stronger brand to attract weaker brand's loyal customers, the stronger brand has to offer a lower price on all its sales to the retailer, including those that ultimately result from its own loyal customers. Therefore, it provides trade discounts relatively less often. The retailer, on the other hand, enjoys a higher margin on the stronger brand even after promotion (the stronger brand is discounted by 4, compared to a discount of 1 on the weaker brand); therefore the retailer promotes the stronger brand more often.

Thus adding a retailer to the model provides new implications and also helps in understanding the differences in the results of Raju et al. and Rao. Another interesting implication from the above results is with respect to retail pass through, stated formally next.

COROLLARY 2.1. Compared to the weaker brand, the stronger brand enjoys higher retail pass through in terms of frequency but lower pass through in terms of size of discount.

PROOF. See Appendix. Conceptually retail pass thorough (RPT, for short) is

defined as the fraction of trade deal that is passed on to the consumers in the form of a retail promotion (Che- valier and Curhan 1976). Because there are two dimensions to a retail promotion, the size and frequency of discount, there are at least three ways to look at RPT:

(1) the ratio of total retail spending over total trade promotional spending on the brand during the year; (2) the ratio of price discount in retail promotion over price discount in trade promotion for the brand in a particular promotion; and (3) the ratio of frequency of retail promotions over frequency of trade promotions in a year.

It turns out that the ratio of expected retail spending over expected trade promotional spending on the brand is higher for the stronger brand consistent with Bucklin (1988), Curhan and Kopp (1986), Blattberg and Neslin (1990), and Tellis and Zufryden (1994). More interest- ingly, however, it turns out that retail pass through is higher for the stronger brand in terms of frequency but lower in terms of size of discount.

This result is interesting because it shows that the two measures of pass through can go in different directions, and that the retailer may follow this strategy to suc- cessfully maximize its profits and yet appease both the stronger and weaker brand manufacturers with respect to compliance with the terms of the trade deals.3

COROLLARY 2.2. As the size of its loyal segment increases, the weaker brand manufacturer promotes more often and provides a larger discount on average, but the stronger brand promotes less often and provides a smaller discount on average.

PROOF. See Appendix. This result is interesting because it indicates that the

two brands follow different strategies as the size of their own loyal segment changes. Unlike the stronger brand the weaker brand manufacturer prefers to rely more on promotions as its own loyal segment size increases. The intuition behind this result is that consumers are only weakly loyal to brand w, and as more consumers become loyal to the weaker brand it uses promotions to keep them from switching to the rival brand. The stronger brand, on the other hand, does not need promotions to keep the strongly loyal consumers from switching.

PROPOSITION 3. The stronger brand manufacturer spends more trade promotional dollars than the weaker brand

3In practice, however, manufacturers may favor frequency aspect of pass through as a monitoring device because it is easier to observe and is more comparable across retailers than size of discount pass through. This issue needs to be researched further.



manufacturer, if advertising is cost effective, specifically when a* < a < a**; and spends less trade promotional dollars than the weaker brand manufacturer, if advertising is costly, specifically when a > a**.

PROOF. See Appendix. The intuition behind this result is that if advertising

is cost effective, the weaker brand is able to defend its loyal franchise by spending on advertising, and the stronger brand has to spend more trade promotion dollars to attract the rival's loyal consumers. But if advertising is costly, then the weaker brand is not able to defend its franchise very well, and the stronger brand does not have to spend more trade promotion dollars to attract the rival's loyal consumers.

COROLLARY 3.1. As the size of its loyal segment increases, the weaker brand manufacturer spends more dollars on promotions, but the stronger brand spends fewer dollars on promotions.

PROOF. See Appendix. This result is consistent with Corollary 2.2, as ex-

pected.

COROLLARY 3.2. As the relative effectiveness of own advertising, y, in affecting loyalty strength increases, both brands spend less on promotions.

PROOF. See Appendix. This result indicates that promotions become less at-

tractive for the manufacturers as advertising becomes more effective in reinforcing brand loyalty among loyal consumers.

COROLLARY 3.3. As loyalty strength of the weaker brand increases, both brands spend less on promotions.

PROOF. See Appendix. Consistent with Corollary 3.2, this result indicates

that both brands decrease promotional spending as their ability to keep loyal consumers increases.

Next we examine manufacturer advertising equilibrium.

Manufacturer Advertising Strategy The preadvertising profits for manufacturer i (i = s, w; I f j) are:

Iwi - aai if wj > wi + (1/m1)1

miw, - aa,

if wi - (1/m.)l C wj C w. + (1/m )1,

-aa, if wi > w + (1/mi)li,

where a captures the cost effectiveness of advertising such that a lower a implies more cost-effective advertising, and advertising affects initial loyalties such that (for i = s, w; i * j), li = li, + yva7 - (1 - y)Fa1. We obtain the following

Nash equilibrium:

PROPOSITION 4. 'When the stronger brand is sufficiently stronger, specifically when l, 2 1b0; l( -,- mu, r; and when own advertising has greater effect on own loyalties (y > 2), the optimal advertising levels are such that: a* = 0;

- ((m 2,r - Iwo) )/y)2 when a c a*; and a* = 0; a*U

= ((lv - lzvo)/y)2 when a > a*, where a* = mz,,r(1 + m?,

- m,)y2/(mzi,r - lu,o)2; and 1*, = l (lzLo, ISO r, a, m,L,); and

/so = msr(1 + mw)/(l + mwms) + (1 - )/(m ,r -Iz,,) if m2(1 + mZ)/(1 + mSmZV) ? m2,; and

I (1 - ) M2r(1 + mw)

?m,~ if1 mz(1mS) O

2(1 + m,,)

PROOF. See Appendix. This equilibrium suggests that if the stronger brand

is sufficiently stronger than the weaker brand, then the stronger brand would not invest in advertising for the purpose of building loyalty4 because it already enjoys sufficiently stronger loyalty. The weaker brand, on the other hand, invests in advertising to build loyalty because it pays to invest in advertising to defend its loyal franchise from switching to the stronger brand. More- over, if advertising is highly cost effective (a c a*), then the weaker brand spends more on advertising (= ((mwr - I,/ )2) compared to when advertising is not so cost effective.

4Note that advertising levels (aS, a,,) represent advertising used for building brand loyalty; these levels are over and above the minimum amount of advertising the two manufacturers may undertake to main- tain their brand in consumers' consideration set.

MARKETING SCIENCE/VOl. 15, No. 1, 1996 93


COROLLARY 4.1. As the size of own loyal segment increases, the advertising spending also increases.

PROOF. See Appendix. This result indicates that as more consumers become

loyal to a brand, the brand invests more in advertising. This is consistent with the loyalty reinforcing role of advertising in the model.

COROLLARY 4.2. As the relative effectiveness of own advertising, y, in affecting loyalty strength increases, the advertising spending decreases.

PROOF. See Appendix. Corollaries 3.2 and 4.2 provide an interesting result

on the effect of y on promotional spending (i.e., advertising and trade promotional spending) by the two brands. Note that as y increases, the advertising by a brand plays a more defensive role as it reinforces own brand loyalty. Thus both brands are better able to keep their loyal customers and hence find it less attractive to spend on promotional activities. This reasoning is also consistent with Corollary 3.3, which says that trade promotional spending would decrease for both brands as the two brands develop their own strong loyal fran- chises. One reason for these results put together may be that as both brands develop their own strong loyal fran- chises, perhaps the competitive backlash is reduced, which in turn reduces the need for promotional spending.

Finally we substitute the manufacturer pricing equilibrium into the advertising equilibrium to get the overall manufacturer equilibrium as a function of exogenous initial brand loyalties.

Overall Manufacturer Equilibrium We obtain the following results on overall manufacturer equilibrium:

RESULT 1. When the stronger brand is sufficiently stronger, specifically when lSO and lwo satisfy conditions as in Proposition 4, and when advertising is very cost effective, specifically when a c a*, the stronger brand does not advertise (a* = 0); the weaker brand advertises (a* = ((m 2r - lwo)/y)2); and both brands do not promote in equilibrium.

PROOF. See Appendix. The intuition behind this result is that if the stronger

brand is sufficiently stronger and advertising is cost ef-

fective; the stronger brand would not invest in advertising for the purpose of building loyalty because it already enjoys sufficiently higher loyalty. It also would not spend any money on promotions because the threat from weaker brand promotions is minimal. The weaker brand, on the other hand, would invest in advertising to build loyalty because advertising is cost effective and it pays to invest in advertising to defend its loyal franchise from switching to the stronger brand. Also, the two brands would not spend any money on promotions because advertising is very cost effective in keeping the loyal consumers. Thus in this situation the weaker brand would worry about defending its loyal franchise, and the stronger brand would be content with its loyal franchise.

RESULT 2. When the stronger brand is sufficiently stronger, specifically when i,o and l,o satisfy conditions as in Proposition 4, and when advertising is cost effective, specifically when a* < a < a**, the stronger brand does not advertise (a* = 0); the weaker brand advertises (a* = ((lw - lzo)/y)2); both brands promote and the weaker brand spends less trade promotional dollars than the stronger brand in equilibrium.

PROOF. See Appendix. RESULT 3. When the stronger brand is sufficiently

stronger, specifically when Is, and lwo satisfy conditions as in Proposition 4, and when advertising is costly, specifically when a > a**, the stronger brand does not advertise (a* = 0); the weaker brand advertises (a* = - Iwo)/ y)2); both brands promote and the weaker brand spends more trade promotional dollars than the stronger brand in equilibrium.

PROOF. See Appendix. We first note that these results apply to a situation

where the two brands sufficiently differ with respect to strength of brand loyalty. In other situations, such as when both brands command strong loyalties, both brands do not advertise or promote in equilibrium (re- fer to Lemma 2 in the appendix). Still other cases, such as when both brands have weak loyalties or when loyalties are not sufficiently different, we leave for future research.

The results indicate that given sufficient difference in loyalty strength, the weaker brand would spend relatively more on advertising than the stronger brand. Intuitively, the stronger brand does not invest in

94 MARKETING SCIENCE/VOl. 15, No. 1, 1996


Figure 2A Advertising Expenditures

Size of loyal segment Ad spending a w

.~~~~~~~~~~ Large Small Adsenig 'ge a I

Strong a > aS w Sm aS

Strength of Loyalty l A A __ oy lty

Weak aS > ~~~~~~~~~~~~~~~~~Strength Weak a as Weaker Stronger w w

Ad spending al

as

> Loyalty Weaker Stronger Strength

advertising to build loyalty because it already enjoys sufficiently stronger loyalty to begin with. The weaker brand, on the other hand, invests in advertising to build loyalty so that it is better able to defend its loyal franchise. In contrast to relative advertising spending, the relative trade promotional spending is affected by the cost effectiveness of advertising. The results suggest that manufacturers would price promote only if advertising is not very cost effective, i.e., if they believe that consumer pull is sufficient for their category, they will

not price promote for the push effect. If advertising is only moderately cost effective (a* < a < a**), the weaker brand is moderately able to defend its loyal franchise by spending on advertising and the stronger brand needs to outspend the rival on trade promotions to attract the rival's loyal consumers. And if advertising is costly (a > a**), then the weaker brand is not able to defend its franchise very well, and therefore, the stronger brand does not need to outspend the rival on trade promotions to attract the rival's loyal consumers.

Figure 2B Trade Promotional Expenditures When Advertising Is Cost Effective

Size of loyal segment Promotional Large Small Spending

s MEP~~~~~~~~~~~~~~~~~~~~~~S

Strong MEPs MEP MEPX 1

v v Lav%o ~~~~~~~MEPS Strength of | VL Loyalty 1

Weak MEP > MEP PW

~ Loyalty Weaker Stronger Stength



Figure 2C Trade Promotional Expenditures When Advertising Is Costly

Size of loyal segment Promotional Large Small Spending

MEP < MEP 5 MIEPW Strong s s

srn~~~~~~~~~ Strength of A X Loyalty EWeakP MEPW

Weak MEPw >w MEPS

I I > Loyalty Weaker Stronger Strength

These results are summarized graphically in Figures 2 (a), (b), and (c).

The results can be further illustrated with the help of an example. Consider two real but disguised brands X and Y in a food category. Brand X is a strong national brand (loyalty estimate = 0.66) competing with a weaker national brand Y (loyalty estimate = 0.52). The model suggests that since the loyalty to X is already very strong, it only needs to do minimal advertising to main- tain its brand in consumers' consideration set. Brand Y, on the other hand, needs to invest in advertising to build brand loyalty; otherwise, it may lose its loyal consumers to X. Indeed, the market share adjusted advertising spending for brand X is almost half that of brand Y. In addition if advertising is costly (such as when there are no significant economies of scale of advertising; perhaps because consumers are spread all over the market), X needs to spend fewer dollars on promotions also, because given costly advertising Y is not able to increase its loyalty strength much, and with fewer trade promotional dollars X is able to attract Y's loyal customers. Indeed, the trade promotional spending of X is less than 30% of spending of Y. If advertising is cost effective (such as when customers are geographically concentrated and easy to reach), the model suggests that X would need to spend relatively more trade promotional dollars to make the rival's loyal customers switch.

The main results from the theoretical analysis relating strength of brand loyalty and size of loyal segment to advertising and pricing policies are summarized in Fig- ure 3. Note that the retailer provides a discount of ls on the weaker brand and a discount of l,7, on the stronger

brand, thus the average retail price discount is independent of the segment size. Given this we do not derive the comparative statics results of retail promotions as a function of segment size. We empirically examine four of these results. The empirical analysis is presented next.

4. Empirical Analysis In this section we attempt an empirical analysis of the model by examining data, to see if the patterns in data are consistent with the model's implications. To the extent the data patterns are consistent, it increases our confidence in the underlying assumptions and structure of the model.

Hypotheses Development An ideal method for examining model's propositions

would be to identify pairs of strong and weak loyalty brands which compete with each other and compare their promotional activities. In reality, however, several brands compete with one another, making it difficult to unambiguously identify two brands which compete with only each other. Therefore we develop an across category framework in which we obtain brand loyalty estimates for brands in several product categories and relate these estimates to measures of their promotional activities using regression analysis.5 Furthermore, since

'We use the terms manufacturer advertising/ promotions and brand advertising / promotions interchangeably in this section even though the same manufacturer may offer multiple brands in a category.



Figure 3 Main Theoretical Results

Manufacturer Trade Promotion Average Price Discount Frequency of Promotions

Advertising Expenditures

Expenditures

Manufacturer Retailer Manufacturer Retailer

Strength of Brand as < aw MEPs>MEPw if x*<anx** ADS > ADw RADS < RADw MPS < MPw RPS > RPw

Loyalty (Proposition 4) MEPs<MEPw if >(Xa** (Proposition 2) (Corollary 1.1) (Proposition 2) (Corollary 1.2)

(main effects) (Proposition 3)

Size of Loyal (,aI/n,)> ? (dMEPI/dm,)< 0 (dAD /dd)< 0 (dMP / dm)< 0

Segment (da&/Idm.)> | (dMEPI/d w,)>0 (ADA./d o )> - (dMFP/ dm)>O -

(comparative statics) (Corollary 4.1) (Corollary 3.1) (Corollary 2.2)_ (Corollary 2.2)

Notation:

aj : Manufacturer advertising expenditures for brand i (i=s,w)

MEPi : Trade promotion expenditures for brand i (i=s,w)

ADi : Average price discount offered by manufacturer of brand i (i=s,w)

RADi : Average price discount offered by retailer for brand i (i=s,w)

MPi : Frequency of trade promotions for brand i (i=s,w)

RPj : Frequency of retail promotions for brand i (i=s,w)

mi : Size of loyal segment of brand i (i=s,w)

a : Cost effectiveness parameter of advertising (a higher a implies costlier advertising)

not all data are accessible to us (for example, wholesale prices and corresponding retail prices), we focus on only those propositions for which we are either able to obtain data or construct proxy measures. Thus we do not test hypotheses concerning trade promotion expenditures.

Manufacturer Advertising Results 1-3 imply that the weaker brand manufacturer spends more advertising dollars than the stronger brand, and Corollary 4.1 implies that advertising spending is higher for the larger loyal segment size, thus indicating following expected patterns in the data:

H1. The manufacturer advertising spending is negatively related to the strength of brand loyalty.

H2. The manufacturer advertising spending is positively related to the size of loyal segment.

Retail Promotions Corollaries 1.1 and 1.2 imply the following patterns

in the data:

H3. The average price discount at the retail level is negatively related to the strength of brand loyalty.

H4. The frequency of price promotions at the retail level is positively related to the strength of brand loyalty.

Construct Measurement

Brand Loyalty (LOYALTYi, SIZEi). In the theoretical model, the strength of brand loyalty is defined as the relative price differential needed to switch given that the two competing brands have same regular price. In reality, however, it is difficult to estimate such a price differential because, first, unambiguously identifying a competing pair of brands in a category with several competing brands is not possible, and second, brands have different regular prices. Even if such price differentials were available, how to relate them to measures of brand advertising and promotional activities is not clear. Therefore we focus our efforts on developing an interval scaled estimate of brand loyalty which reflects relative strength of loyalty among consumers in the market and which could be related to the interval scaled



estimates of brand advertising and promotional activities.

In the literature brand loyalty has been measured in several different ways. Raj (1982) defines highly loyal customers as those who devote more than 50% of their product class purchases to the brand. Krishnamurthi and Raj (1991) use the proportion of times each brand is bought on all preceding purchase occasions, updating it as each purchase occurs, as a measure of brand loyalty. These share of purchase driven measures do not capture the effect of marketing mix. For example, a brand may have high share of purchases just because it is heavily price promoted. Guadagni and Little (1983) use an exponential smoothing formulation for brand loyalty which incorporates the effect of past purchases (including past marketing mix activity) on the current purchases. Fader and Lattin (1993) develop an alternative measure assuming choice probabilities are distrib- uted according to a Dirichlet distribution which also incorporates the effect of past purchases. Allenby and Rossi (1991), on the other hand, define brand loyalty as the residual of the predicted probability of choice from the choice indicator averaged over all occasions. This measure filters out the effect of past marketing mix activities in computing brand loyalty. All these measures capture the heterogeneity across households in propensity to purchase different brands quite well, and treat this heterogeneity as a direct measure of brand loyalty.

Chintagunta et al. (1991) and Gonul and Srinivasan (1993) conceptually distinguish between household heterogeneity and intrinsic brand preference. These au- thors use the intercept term in the brand utility model as a measure of intrinsic brand preference and use semiparametric methods for estimation.

It can easily be shown that the intercept term in the utility model is perfectly able to capture the rank order information in the relative price differentials needed to make a consumer switch away from one brand to the other. In other words, the relative price differentials (the definition of brand loyalty used in this paper) and the intercept values have a perfect rank order correlation. Therefore we develop a measure of brand loyalty here along the lines of Chintagunta et al. (1991) and Gonul and Srinivasan (1993) which is based on the intercept term in the brand utility model and which also incorporates heterogeneity across households. We discuss

the similarities of our brand loyalty measure with these approaches later in this section (after Equation 5).

We next describe the method for estimating strength of brand loyalty (LOYALTYi) and size of brand loyal segment (SIZEi) using scanner panel data which contain purchase histories of several households over several weeks.

We estimate the following logit model:

h-exp(uZ)i it

exp ( uhj)(1)

uh= ai + y propen, + , fkXk,I where (2) k

Pith the probability that household h purchases brand i at purchase occasion t,

i= the utility to household h of purchasing brand i at purchase occasion t,

propeni = a measure of household h's propensity toward brand i based on purchase behavior before time t,

t = the level of marketing mix variable k for brand i at purchase occasion t, and

a i, y, fk = model parameters.

Households are heterogeneous in their propensity to purchase different brands. To capture this heterogeneity in preferences across households we use the measure propenh (Srinivasan and Kibarian 1989). To compute this measure, we first estimate (using maximum likelihood estimation procedure) the above logit model without the propenh term on first half of the data, which we call calibration period data. Next we use the estimated parameters to compute predicted probability of choice,

qt over the calibration period. The heterogeneity measure is then computed as:

propenh = 6 propen h

+ (1i- tq)(y i_-q_i) where (3)

I 1 if i chosen at t -1,

=0 otherwise.

Here Yi propenh =0, and 0 < 6 < 1 is a smoothing parameter, usually in the range of 0.70 to 0.85. The propenh measure was initialized as 0.0 for all brands. Note that propenhincreases if the brand is chosen on



previous occasion and decreases if it is not. If the brand is not chosen on previous occasion then yh _I = 0, which will have a negative effect on propen h. And if the brand is chosen on previous occasion then y- = 1, which will have a positive effect on propenZh, as desired. The propen h estimates were found not to be significantly sensitive to different values of 6, therefore we use a value of 0.75 in all our estimations. Finally, the propenh vector for household h on the last purchase occasion T in the calibration period is used as a measure of household heterogeneity as it represents the most stable vector in the calibration period of household pro- pensities towards different brands.

Next, we estimate the logit model in Equation (1) with the marketing mix variables X"'s and the propenh term on the second half of data, which we call estimation period data, using maximum likelihood estimation procedure. This provides us with the estimates of model parameters a's, ', and, 's. Next we estimate the household level predicted probability of choice of each brand on each occasion at equal marketing mix activity on the estimation period data using the following model:

mht - IPP h where (4)

=j exp(&, + 5y propen )

i= predicted probability of choice of brand i for household h at purchase occasion t keeping the marketing mix activity constant across brands.

This step (Equation 4) in effect gives the brand specific preference (relative to other brands in the category) for each household when all brands have equal marketing mix support, akin to a measure of intercept term (incorporating household heterogeneity) in the utility function.

Next, we classify each household into a loyal segment based on the predicted probability vector on the last purchase occasion T in the estimation period, Mh, for that household. We assume that the household is loyal to that brand which has the highest predicted probability of choice (i.e., h E segment1 s.t. mih > mh- Vi * j). We use the last purchase occasion here because it represents the most stable probability vector given the purchase history of the household. Lastly, we compute the interval scaled loyalty measure for each brand by av- eraging the predicted probabilities of choice of the

brand over the households in its loyal segment reflect- ing the strength of loyalty among its loyal consumers:

>h m LOYALTYi = , where (5)

Nh

LOYALTYi = estimated brand loyalty6 for brand i, Nh = number of households in the segment loyal to

brand i. The size of loyal segment, SIZE,, is computed as the

percentage of households that belong to the loyal segment of brand i.

We note that our brand loyalty measure is similar to the two approaches available in the literature. One approach is to use a measure of household heterogeneity similar to propenh measure to capture brand loyalty (Allenby and Rossi 1991, Fader and Lattin 1993, and Guadagni and Little 1983), and the other approach is to use the intercept term in the utility model in Equation (2) to capture the intrinsic brand preference (Chinta- gunta et al. 1991, Gonul and Srinivasan 1993). The difference in our method is that instead of using only the intercept term or the household heterogeneity, we com- bine the effects of both to capture brand loyalty and use a computationally easier estimation procedure compared to the semiparametric procedures. Also, our method guarantees a loyalty and segment size estimate for each brand in the category unlike semi-parametric methods. We need these estimates for each brand to test the hypotheses.

Manufacturer Advertising Expenditures (EXPENADV.). We note that our interest is in examining the effect of exogenously specified initial brand loyalties on manufacturer advertising and retail price promotion policies. Accordingly, we use advertising data from a period subsequent to the time period of scanner panel data to account for this direction of causality.7 The data on

6 A simple share of purchases measure has a correlation of 0.51 (p = 0.0003) with LOYALTY,, indicating that as intended LOYALTYi is not simply capturing share of purchases.

7Note that as with advertising, the causality in the empirical data may work in reverse with price promotions also, i.e., price promotions may affect brand loyalty rather than brand loyalty affecting price promotions. Thus to test the model it would also be desirable to ensure loyalty estimates precede price promotion estimates in time. The inability to do this is a limitation of our empirical analysis.



brand advertising were obtained from Arbitron's advertising dollar summary published yearly. This pub- lication reports dollar advertising expenditures in nine media for most national brands. The measure of advertising expenditures is computed as the brand advertising expenditure expressed as a percentage of the total advertising expenditures for all brands analyzed in the category.

Average Price Discount Offered by the Retailer (PRICED- ISi). We operationalize this construct by the percentage reduction in the average price when the brand goes on promotion (i.e., feature and/or display), where price reduction is the difference between the estimated regular price and the posted price. The regular price is estimated by the average price when the brand was not featured or displayed.

Frequency of Retail Promotions (FREQPROMi). We operationalize the frequency of retailer promotions by the frequency of price cuts observed in the scanner panel, defined as the number of occasions on which the estimated regular price exceeds the actual price posted in the store, expressed as a percentage of the total number of occasions on which the brand could have been available. This proxy measure captures the relative frequency of retailer promotions across brands.

Data Description We estimated brand loyalties, loyal segment sizes, retail promotion frequencies, retail average price discounts, and brand advertising expenditures for seven product categories: orange juice, crackers, coffee, laundry detergent, catsup, peanut butter, and dishwashing liquid. A brief description of the datasets is provided in Table 1.

There are 46 brands in these seven categories, of which eight are private labels. We include the private labels in the estimation of brand loyalties and segment sizes, but exclude them in further analysis because theoretical analysis concerns brands which may promote to the trade. Private labels do not promote to the trade as they are owned by the trade itself. This implies a sample size of 38 national brands for examining the data patterns. We present the estimates of the various measures in Table 2 for all the brands in the seven categories. Note that all measures within a category are defined in relative terms rather than absolute terms thus making across category comparisons possible.

Table 1 Description of Data

Category # Purchases # Brands # Households #Stores #Weeks

Orange Juice* 2958 6 115 Crackers* 3159 6 252 15 104 Coffee* 4946 4 398 6 108 Laundry Detergent* 2275 7 300 13 52 Catsup* 4502 4 333 5 161 Peanut Butter* 8465 6 404 5 161 Dishwashing Liquid* 5356 13 256 5 161

From I.R.I., Inc. ** From A.C. Nielsen, Inc.

To examine the data patterns implied by H1 - H4, we begin by noting that the theoretical analysis assumes a sequential decision making process in which retail promotion frequency and average price discount decisions are dependent on manufacturer advertising expenditures decided earlier on in the first stage. To incorporate this dependence among decisions in the model, we include EXPENADVi as an explanatory variable in retail promotion equations. We estimated the following three linear statistical models to derive the data patterns:

EXPENADVi = a0 + ajLOYALTYj

+ a2SIZEj + E ajDj+ (, (6)

PRICEDISi = jo + j3LOYALTYi

+ j32EXPENADVi + ,lfjDj + 2, (7)

FREQPROMi = yo + yjLOYALTYj

+ y2EXPENADV- + E 71D1 + i, (8)

where subscript i (i = 1 to 38) refers to a national brand and D1s (j = 1 to 7) are the 0-1 category specific dummy variables included to capture any category specific differences on variables not included in the above equations.

It is hypothesized that a1 < 0 (H1), a2 > 0 (H2), 81 < 0 (H3), and yi > 0 (H4).

We estimated the above three equations using Joint Generalized Least Squares (SUR) estimator which



Table 2 Measurement Estimates on Seven Product Categories

Category Brand Loyalty Size EXPENADV PRICEDIS FREQPROM

Orange Juice 1 0.6077 0.1910 0.1544 0.1379 0.1105 2 0.4373 0.4494 0.4859 0.1254 0.1579 3 0.4828 0.2584 0.2917 0.1705 0.1870 4* 0.4897 0.0112 0.0852 0.0352 5* 0.3424 0.0377 0.1700 0.3110 6 0.4774 0.0562 0.0436 0.1381 0.1024

Crackers 7* 0.5039 0.1382 0.0244 0.0603 8* 0.5693 0.4431 0.0396 0.0615 9 0.5698 0.0203 0.1685 0.2403 0.3237

10 0.5763 0.0610 0.1774 0.0702 0.3212 11 0.7204 0.0285 0.2957 0.1682 0.3051 12 0.6012 0.3089 0.3548 0.1345 0.3103

Coffee 13 0.4439 0.0244 0.0251 0.1753 0.6929 14 0.6071 0.2774 0.4948 0.1587 0.6821 15 0.5712 0.5488 0.4730 0.0164 0.6543 16 0.6140 0.1494 0.0070 0.0991 0.6435

Laundry 17 0.5668 0.3808 0.4188 0.1222 0.6561 Detergent 18 0.5263 0.1967 0.1204 0.0875 0.6617

19 0.5544 0.1715 0.0868 0.1190 0.5683 20 0.4633 0.1130 0.1195 0.1022 0.6496 21 0.5482 0.0502 0.0455 0.0656 0.5389 22 0.5633 0.0586 0.1517 0.0938 0.4399 23 0.5566 0.0293 0.0572 0.0649 0.3360

Catsup 24 0.0000 0.0000 0.3561 0.4320 0.2820 25 0.8022 0.9153 0.4307 0.0189 0.5019 26 0.5633 0.0780 0.1983 0.0577 0.4870 27* 0.7046 0.0068 0.0126 0.4919

Peanut Butter 28 0.6594 0.3137 0.3742 0.0214 0.5764 29 0.6097 0.3217 0.2111 0.0405 0.5602 30 0.4072 0.0054 0.1571 0.0197 0.5180 31 0.5246 0.0563 0.2212 0.0872 0.5180 32 0.2979 0.0027 0.0299 0.0545 0.5764 33* 0.6631 0.2949 0.0943 0.6286

Dishwashing 34 0.5303 0.0241 0.0413 0.0785 0.5640 Liquid 35 0.4635 0.1124 0.1107 0.0602 0.4634

36 0.4182 0.0120 0.0250 0.0011 0.4410 37 0.5160 0.0161 0.1306 0.0677 0.4484 38 0.0000 0.0000 0.0670 0.0894 0.0882 39 0.3935 0.0723 0.0900 0.1532 0.5093 40 0.0000 0.0000 0.0167 0.0102 0.0882 41 0.3091 0.0040 0.0255 0.0106 0.3056 42 0.5573 0.2731 0.1498 0.0398 0.5851 43 0.4989 0.2289 0.2595 0.0279 0.5528 44 0.5293 0.2169 0.0720 0.0591 0.5540 45* 0.5722 0.0361 0.2456 0.3540 46* 0.7041 0.0040 0.0013 0.1441

Private label brand. ***** Data not available.

MARKETING SCIENCE/VOl. 15, NO. 1, 1996 101


resulted in more efficient (but qualitatively identical) estimates compared to OLS and 2SLS estimators, as this estimator takes into account the correlations in error terms across the equations. We checked for multicolli- nearity and model misspecification problems by estimating various specifications including SIZE, and the LOYALTYi* SIZEi interaction terms in all three equations but found no difference in qualitative results.

5. Empirical Results The results of the SUR estimation presented in Table 3 indicate that the equations fit the data reasonably well, with the system weighted R2 being 0.743.

With respect to advertising expenditures, the data support the patterns hypothesized in H1 and H2. The stronger brands spend less on advertising (p < 0.10), and brands with larger loyal segments spend more on advertising (p < 0.0001).

With respect to retail promotions, the data support the patterns postulated in H3 and H4. The retailer provides higher price discount on average for the weaker loyalty brands (p < 0.01) and promotes the weaker loyalty brands less often as compared to stronger brands (p < 0.0001). We note that this particular empirical result supports the analytical finding of the retail pricing model in Rao (1991).

We also estimated the three equation system with the advertising expenditure variable adjusted for market share points. In other words, we divided the EXPEN- ADV by the market share (in %) to take into account the possibility that a large share brand may spend more just because of its greater size. The market share measure was computed as a share of purchases in the panel. The results with respect to H1 (p < 0.01), H3(p < 0.05), and H4(p < 0.05) did not change. But because the correlation between SIZE and market share is high (=0.91, p < 0.01), the pattern hypothesized in H2(p > 0.35) was significant only at the 0.35 level.

Overall the data seem to be consistent with the patterns implied by the model. This is by no means a con- clusive test of model's validity; however, we believe that good regression fits combined with strong signifi- cance of the results is encouraging. We also believe that the testing methodology presented here is useful and that efforts should continue to further test the theory.

Table 3 Estimation Results

Dependent variable Independent variables EXPENADV PRICEDIS FREOPROM

0.107C2 0.1 35a2 0.231 a2

CONSTANT* (1.963) (4.112) (4.957) -0.1 83' - 0.1 98a 0.477al

LOYALTY (1.422) (2.82) (4.768) 0.607a1

SIZE (5.364) -0.05 0.049

EXPENADV (0.591) (0.397) 0.084 0.1 20a2 _0.343a2

Dl** (1.348) (2.973) (5.969) 0.191 a2 0.1 53a2 -0.222a2

D2 (2.869) (3.627) (3.696) 0.093 0.101 b2 0.158b2

D3 (1.4575) (2.451) (2.702) 0.048 0.073b2 0.055

D4 (0.907) (2.198) (1.157) 0.104 0.141a2 -0.04

D5 (1.456) (3.037) (0.609) 0.098c2 0.109 0.071

D6 (1.712) (0.514) (1.358) SYSTEM WTD R2 0.743 n 38

tvalues in parentheses with each estimate. * The Di variables capture category specific effects.

al significant at 0.01 level using one-tailed test. a2 significant at 0.01 level using two-tailed test. bl significant at 0.05 level using one-tailed test. b2 significant at 0.05 level using two-tailed test. cl significant at 0.10 level using one-tailed test. c2 significant at 0.10 level using two-tailed test. Note: All directional hypotheses are tested using a one-tailed test.

6. Conclusions and Future Research The theoretical analysis presented here provides implications for the optimal advertising and price promotion policies for competing manufacturers selling through a common retailer. For example, the analysis indicates that if the stronger loyalty brand is sufficiently stronger than the weaker loyalty brand and if advertising is cost effective, then stronger brand loyalty requires less advertising than weaker brand loyalty, but a larger loyal segment requires more advertising than a smaller loyal segment. Moreover, stronger brand loyalty requires more trade promotion spending under these conditions. In addition, the retailer should promote the stronger loyalty brand more



often but provide a smaller price discount for it compared to the weaker loyalty brand. The empirical analysis, based on scanner panel data on seven product categories, provides encouraging evidence for the model. However, there are several caveats associated with these analyses in addition to their strengths.

The results with respect to brand loyalty strength may at first seem counter-intuitive. For example, recently the consumer packaged goods company, Proctor and Gam- ble, announced a strategy to move away from trade dealing in favor of advertising. P&G is widely regarded as a strong national brand manufacturer. One way to interpret P&G's actions in the model's context would be that P&G is trying to build brand loyalty so that it becomes unquestionably a stronger brand. Once the brands are sufficiently stronger, P&G wouldn't need to invest further in advertising. In a way, the model implies that P&G's brands are not "sufficiently" stronger in loyalty strength yet.

The model and its analysis in this paper has the ad- vantage of parsimony. It integrates the advertising and pricing decisions in a very parsimonious way through the construct of brand loyalty in a three-stage formulation. It incorporates main effects of advertising- namely, brand reinforcement-and of promotions- namely, brand switching and repeat purchase in a competitive setting in the context of established product categories. The model also considers the role of the retailer, thus capable of providing implications for retail pass through. The analyses highlight the distinction between the strength and size of brand loyalty, which is appeal- ing theoretically and also useful practically. For example, marketers may benefit directly from knowing the composition of their category franchise; specifically, how many loyal customers there are for each brand, and how loyal they are to each brand.

The main caveats associated with the model relate to the absence of (1) dynamic effects of advertising and promotions; (2) of repeated interactions among the manufacturers, retailers, and consumers; and (3) retail competition. Retail competition, for example, plays a significant role in the retailer pricing strategy as the retailers continuously monitor competitors' pricing and promotional activities for designing their own strategies. Moreover, retailer's primary objectives, to maximize store traffic and shelf turnover, do not necessarily

coincide with the objectives of the manufacturers. In future, extensions of the model to incorporate these features would be desirable. Another limitation is the linear additive form used for the effect of advertising on brand loyalty. Although it helps to keep the model tractable, this functional form does not capture the possible advertising threshold effects. Lastly the assumption that the size of loyal segment remains un- changed after advertising takes place is a limitation. In reality, advertising may induce changes in the size of loyal franchise.

In addition to advertising and trade dealing, manufacturers also use consumer promotions in the promotional mix to attract customers such as cents- off coupons, sampling, and contests. It will be desirable to consider consumer promotions also in the model.

In the empirical investigation, the most limiting fac- tor is the unavailability of trade promotions data, which precluded us from investigating propositions regarding trade promotion spending. Also the definition of strength of brand loyalty does not exactly match in the theoretical and empirical analysis. More- over, in the theoretical model we analyze a sufficiently stronger brand competing with a weaker brand; however, it is difficult to identify empirically if the stronger brand is indeed sufficiently stronger than the weaker brand. This is a limitation of our empirical analysis. Another limitation is the assumption that each consumer is loyal to some brand as each household is classified as a loyal household (to some brand). In reality a consumer may not be loyal to any one brand but may regularly switch among a subset of brands. Inclusion of a switching segment in the analysis will enrich the framework.

In summary we develop a parsimonious analytic framework to examine the tradeoffs between advertising and trade promotion strategies. Extensions of this framework to incorporate dynamic and repeated interaction effects and retail competition should prove fruitful in enhancing our understanding of the promotional mix. In addition we develop a methodology for estimating the size and intensity dimensions of brand loyalty using readily available scanner panel data. Further work on refining this methodology should also prove fruitful because these estimates (of size and intensity of



brand loyalty) are of direct and significant relevance in optimal brand strategy.8

Appendix

PROOF OF PROPOSITION 1. The retailer's profit function is:

PS mi(ps-ws)+ ( if p < p-1,

rlr ms(ps - Ws) + mW(pU1, - W70) if p5

- Is C:- p7V CpS + IlV,/

(Pw -ww) if p7,, < pS-Is

Given the reservation prices, (r, r - IS) for the customer loyal to brand s, and (r - I,. r) for the customer loyal to brand w, for brands s and w, respectively, the retailer does not charge a price above r.

There are three possible actions for the retailer: Action 1: Sell only brand s to the whole market. Action 2: Sell each brand to their own loyal segments. Action 3: Sell only brand w to the whole market. Retailer's optimization problem under Action 1 is:

max = (ps - Ws)

s.t. Ps < pw -w, (Al)

O -p-7V - r, O c ps C r. (A2)

Since lO1H1r /lips > 0, retailer will choose the maximum p. that satisfies constraints (Al) and (A2). Also, since flr is independent of Pw, retailer can pick any Pw that satisfies (Al) and (A2). Therefore, the retailer will pick pw = r and ps = pw - l7 - e r- -l0v - , where eis an infinitesimal number. The profits will be flr = [r - 17- e - wS.

Retailer's optimization problem under Action 2 is:

max flr = mS(ps - Ws) + mw(pw - ww)

s.t. PS -IS pw PS+1w, WA)

0 ' pw c r, 0 p5 C r. (A4)

Condition (A3) represents all possible pairs of prices (ps, pw) for which each brand retains its loyal customer. The retailer can maximize profits by charging the highest price for each brand, because 19H/2

ps > 0 and OHr/Opw > 0. The optimal prices, therefore, are ps = r and

pw = r. Retailer will earn profits of H-2 = r - msws - MWwU Retailer's optimization problem under Action 3 is:

8 author thanks Rajiv Lal, V. Srinivasan, James Lattin, Scott Neslin (area editor), and two anonymous reviewers for several useful sug- gestions and Faruk Gul, Richard Staelin, Allen Weiss, Brian Gibbs, Daniel Putler, and Peter Reiss for helping to improve this paper. The author also wishes to acknowledge James Lattin, Randolph Bucklin, Peter Fader, A. C. Neilsen Inc., and Information Resources Inc. for making the scanner datasets available, and the Marketing Science In- stitute for financial support.

s.t. p", < p -1I, (A5)

? C p7V C r, O c p5 C-- r. (A6)

Since this is symmetric in lv, 1, to Action 1, the retailer will pick pS

=rand pUI = r - 15 - E, and earn profits of I = [r - 15 - E - w].

Now, the retailer will follow Action 1 only if fl > fl, fl1. Now, rl > [lr if

(r - - e - w5) > r - mvwv - mSwS,

1 or if, w7, > ws +-IW, (A7)

and, flr > rlr if (r - lw- e - w5)

> (r - 1, - E - w5), or if, ww > w5 + (lw - Is).

Since mwlu, > (17?. - IS), therefore condition (A7) is sufficient. Thus, when W7., > Ws + m7V17V, retailer follows action 1. By symmetry, when

wI > w7, + m5sl, retailer follows Action 3. And for all intermediate prices, wI - mI" c W7V c wI + mWl17V retailer follows Action 2.

The pricing strategy of the retailer is therefore:

charge p, = r - 17V - C; p7V = r if W7v > wI + (1 /mW)lW

charge p, = r; pw = r if w5 - (1 /m5)1 C W7V C wI + (1 /mW)lW

charge p5 = r; p7V = r - 1- e if wS > wW + (1 /m5)lI. L

PROOF OF COROLLARY 1.1. This result directly follows from the retail price equilibrium above. The weaker brand has to offer a larger discount Is in order to attract the stronger brand loyal consumers, whereas the stronger brand has to offer 17V to attract weaker brand loyal consumers, where 1I > lw in equilibrium (shown later in Proposition 4). 0

PROOF OF COROLLARY 1.2. Retailer promotes the stronger brand with a probability, Prob.[ww > ws + (1/mW)17V], and promotes the weaker brand with probability, Prob.[ws > ww + (1 /ms)Isj. As shown in Raju et al. (1990), the asymmetry in loyalties (lw c m2%r and 15 2 ms(r - lIj)/(1 + msmj)) ensures that the probability with which the weaker brand is able to attract stronger brand's loyal consumers is zero, i.e.,

Prob.[ws > W71, + (1 /mS)1J] = 0. Thus at the retail level, weaker brand's promotion frequency is lower than that of the stronger brand. As shown later the asymmetry in post-advertising loyalties is preserved in equilibrium. O

PROOF OF PROPOSITION 2. The mixed strategy pricing equilibrium for 0 c lw c m%2 r and 15 2 ms(r - lW)/(1 + mSmW) available from Raju

et al. (1990) is:

0 if 0 _ w5 < msr,

mW(msmwr + l1V) . mw

(mwWs + Iw)2 if mr ? w, r--

f *(Ws) = O if r - f c-ws < r,

mSm7vr + l17 if w, =

10 if w>r.



p0 if O c W7,, < m,r + - '7V

if m,r + - cw7,_ <r, g*(w7,,)

- MSZV

1- w) w =,2

m7J,m7,,r 17 IZV

O if W7V>irf

where f*, g* represent probability distribution functions of wholesale prices for brands s and w, respectively.

Probability of a promotion by manufacturer i, (MP), is the cumu- lative probability of charging a price below r. The equilibrium pricing strategy implies:

MP,= ZV 7V

MP7,, =

m7vr m7,(m7,,r - Izv)

If 17 c m7,r, then mW,r - lw < r, therefore, MP,, > MPs. As shown later (proof of Proposition 4), the post-advertising loyalties satisfy 17V

c5 m 2 r.

The average trade discount offered by manufacturer i, (AD), is regular price minus average price when on promotion, i.e., AD, = r - fti<r wif(wl/w; < r)dw,, implying

(m3U,r2 - .12 - 1,,m5m7,,r + (mIm7vr

+ l,,)m7r log s 7 U)

ADS = m70(m72r -4IW)

- lr ) (m r - W. +mSmwr log( ' 1))

AD.,, = mW(mWr - lw)

Using numerical enumeration, it can be shown that ADs > AD7,, when 17V c Wr. 0

PROOF OF COROLLARY 2.1. In equilibrium, the weaker brand promotes to the trade more often but the retailer promotes the stronger brand to consumers more often, implying that retail pass through in terms of frequency is lower for the weaker brand. Similarly, the stronger brand provides a larger price discount on average to the trade but the retailer offers a larger price discount on the weaker brand, implying that retail pass through in terms of depth of discount is lower for the stronger brand.

PROOF OF COROLLARY 2.2. The first-order derivatives,

aMP, 17V ad MPW, mwlwr(2 -

aMW,. m7vr DmiV mv(mw,r -

are both positive when 17, c mZ2 r. Similarly, it can be shown that

OAD, < 0 and >ADw - 0. D am,i aMDV

PROOF OF PROPOSITION 3. The expected promotional expenditure MEP, for brand i is Li (r - wj)f(wj)dw,:

(mwr + lw)(m2,r - 17,) MEPV- zin

(M7,,r - M2 r + lW) 1 m(imnwr + 1)7

MW, M7vr

MEPW = m% r-l, + - mlog). m, 7V , MV M7,,,r- 17,,

We plot the trade promotion expenditures as a function of 17., for various values of M7n0 in Figure 4.

The plot shows that at 17V = mVr, MEP. = MEP,, = 0; for 17 < 17.

< Wm,r, MEP, > MEP,,; at 17. = 171MEI. = MEP,; and for 0 l,7

< w, MEP, < MEP7.

For 0 ? l7. - m 2r and Isv 2 ll, the equilibrium advertising levels (derived in the proof of Proposition 4) suggest that 4,. will be > lu provided advertising is cost effective; specifically, when a* < a < a** where a* solves OEHU'[l, = mWr]/017 = 0, and a** solves OEFw[l.,

= l]w/Ol,, = 0; and, 1,, will be < Iu, when a > a**. Therefore, MEP, > MEPW when a* < a < a** (advertising is cost effective); and MEP, < MEPl,, when a > a** (advertising is costly). O

PROOF OF COROLLARY 3.1. The two derivatives,

OMEPs 212 _ w +7V W__ _ log m, +

9mw m7Vr \m7V U

and

OMEP7v 21w 21lVm7vr- 1,lr- mr2vr2 r m 7,,rl- lu, 3- + 2+ -log OmW mw m%(m,,r - Ij) mz, \ msmz,.r

are both 2 0 for lw m 2r. O PROOF OF COROLLARIES 3.2 AND 3.3. The two derivatives

MEP, 1 - 2u, +1 logM + 17V

mw mi, MV

and

aMEPw (m%2r - lW)

'91w m 2,(mwr -1,,)

Figure 4 Trade Promotional Expenditures

0.9

0.8U

0.7

0.6

0. 5

0.4 <

0.3

0.2 -

0.1 -.P s

0o 0 I - cc OL c

o 6 6 6 6 6 6 6 6

mw

MARKETING SCIENCE /Vol. 15, No. 1, 1996 105


are both c 0 for lV, c m' r. Since I,V = 1,, + ya1,, - (1 - y)a,, therefore,

OMEP, / &y < 0; OMEP,O / &y < 0; OMEPI / Ml,T,, < 0; and OMEP,V/ aOl710

<0. EL

PROOF OF PROPOSITION 4. We first show that given a* = 0 and a < a*, it is optimal for firm w to have a* = ((m%,r - 17,,0)/Y)2. Next we show that given a* = ((m%2r - l700)/y)2 and a - a*, it is optimal for firm s to have a = 0.

Let a* = 0. The initial loyalties are asymmetric (i.e., la,. c mz2r and

is, 2 Is,); the stronger brand enjoys sufficiently stronger loyalty such that the retailer promotes only the stronger brand). If post advertising loyalties are also asymmetric then firm w solves the following problem to choose a,v:

max EHl'1(a* = 0, a71,)

s.t. Il7, = 17?O0 + Ya7 m Wr, (A9)

IS = I,, - (1- y) A;2 m(r - MM7

(A10) 1 + mSm1,,

From Lemma 1 (proved below), OEH?7/O1l1. > 0. Therefore firm w chooses aw such that 17v is at its maximum and constraints (A9) and (A10) are satisfied. a* = ((m2r - lw")/Y)2 is the optimal level at which constraint (A9) is binding and constraint (A10) is satisfied because

m 2r(l + mJU (l - Y) M2

IS 2: + (m,r - 17t(1)

0 i 7(1+rM:S) y ( l

The expected profits to firm w are:

EHlw= =0O, a7t= =m1,r-aa1*.

If a7V is chosen at a level beyond a*, the post advertising loyalties now fall in the pure strategy regime wherem2r < 17,, < 1. From Lemma 2 (also proved below), under pure strategy, expected profits to firm w are:

EHw(a* = 0, a,v

>a) = m7vr-aa7V,

which are lower than what the firm earns at a*l,.

If aw is increased further, 15 continues to decrease and 14, continues to increase. At aZV = ((IS( - mwr)/( 1 - ))2, the competition moves

from pure strategy to asymmetric regime where the weaker brand is now asymmetrically stronger. The loyalties now are:

l = Is, + Y7a - (1 - y)f a= 1s0 + 0 - (1 - y) (h. - m M%Vr) r

'IV = 17Wo + Ya7 -(1-) = IV + '

- m7,r) ly

Asymmetry conditions 15 < m 2r and 174 ms(r -1s)(1 + m,mw,) are

satisfied for ISO 150 where

Ms r(l + mw) (l - y) (m2 . fMs2( + M71)

M m2 mS( (1 + m'M') (1y Umr-l1V,)if m M(1+mm70,)

and

(l- m) fmr(1+ mV) + 2 Ms___ < <i2 01.-X = 1 (1 + M,m) -1ITOV W 7,r if (,S

+ ,

M <7 m70'

Expected profits to firm w now are:

Er7"(a=V , V

= (a'l=' )) = m,,r - aa,

which are lower than what the firm earns at au,. If a7, is increased even further, the regime continues to remain asym-

metric and expected profits to firm w continue to decrease. Therefore, given a* = 0, it is optimal for firm w to have a* = ((m%2 r - 1",O)/Y)2

provided a ? a*. Now let a* = ((m%2r _l,,")/y)2 and a - a*. The loyalties are asym-

metric. If firm s advertises, the loyalties continue to remain asymmetric. Firm s solves:

max Efls(as, a*) a,

st. I 17VI + Y(m,r- lvt) - (1 - Y)v ?a m2r, (A1)

/S = ?St1 +~ 4-(1 - )(m7wr 17) 2 m*(r-IW I't,+ y a

Y) 1 + msmzv

A 2

From Lemma 1, OEHs/Olu, > 0. Therefore firm s will choose as such that 1,, is at its maximum and constraints (All) and (A12) are satisfied. a = 0 is the optimal level at which constraint (All) is binding and constraint (A12) is satisfied because Is, to. The expected profits to firm s are:

EHs(aa = 0, a*, = (m,r l)2) =mSr-aa, = mr.

If a, is increased beyond a*, i.e., if as > 0, the post advertising loyalties continue to remain asymmetric and the expected profits

EflW(as, a*) = mr - aa, are lower than what the firm earns at a*.

Therefore, given aT* = ((mT2r- 1ot) /Y)2 and a _ a*, it is optimal for firm s to have a* = 0. Hence, a* = 0; a*, = ((m2,r - Ir)/y)2 is a Nash

equilibrium when l (- mzvrt l'; i1S0/ and a 2 a*.

Now, we show that for a > a*; a* = 0 and a* = ((I* - 17.,.>)/Y)2.

When the cost effectiveness of advertising is such that a > a*, firm w wishes to increase its loyalty only upto l/*, because beyond l* the expected profits decrease. The level l* can be computed by solving

aEnI[17,, = *Ia,I/Ol, = O. Therefore, for a > a*, the optimal advertising levels are: a* = 0 and

a*, = ((MZ1 - 17,, /y)2; where

M,,,r(l + M7,-ml,,)y 9E l17[V = Wrl2, a* = 2 solves [ =0;

and l* = I*(1l,,o, 1,,,, r, a) solves &En1vilw = l*vllV = 0. ?I

PROOF OF LEMMA 1. To show: aEUsI/Dali > 0 and aETw/Oalw > 0.

The expected profits of manufacturer i are given by:

106 MARKETING SCIENCE/VOL 15, No. 1, 1996


EHl = jI (wi - aaj)g(wj)f(wj)dwjdw,

+ f (mw - aaj)g(wj)f(wj)dwjdwj

+ f f (-aaj)g(wj)f(wj)dwjdw.

For loyalties satisfying 15 2 m,(mz,r - 21,,,/m?,,) and 1, < m2 r, the expected profits are:

(m%r2 + 172, + m,,7vr(l - 3m7,))(m,r - aa) Ens 2

mIVr(mvr - 1w)

EL =m(mmwr + I,, +m% Wr(m7,r

- 214,,) m.V mVr(mVr - 1V,)

+ m m log ( m rmwr

w + m7,,1,vr(m - - )+mv

- aa4lv mzlt,r(12 - 3m,,) + m

The derivatives with respect to 1t, are:

EH'_ (m,r - aa,)(m%r2 - 3m73r2 + m72r2 + 2m,v1,vr - 12,)

m 2r(m,Vr - 17V)2

The second term in the numerator is always positive (for mw, < 1); therefore the derivative is positive if m,r > aa,, i.e., when the expected profits net of advertising are positive, a condition required to hold in equilibrium.

9EIIv (m,m.,,r + j )(m 2 r2 + m2%4j,,r + m2,,,l,r - 2m,r2 - 12)

0l1W m 2,mr(m,vr -JU)2

m 3 r2 - 2m2l Ir + 12

mr(m,r -

(1 - m)\ l( mm,vrA V mV m m,r - I J

m 2r(mU,r

- 17V)2 1

The first, second, and third terms are positive, whereas the fourth term is negative. The numerator of the difference between first and fourth term is positive when m,,,r > aau,, i.e., when the expected profits net of advertising are positive, a condition required to hold in equilibrium. Thus, for all lw c M2 r, 9EHs/oil,, > 0, and oEI-UI/417,V > 0. C]

PROOF OF LEMMA 2. To show, under pure strategy, where 1, > lw > mU,r, the expected profits are:

EFIS = mr - aa,; EnT" = m,,r - aa7,.

This proof proceeds as in Appendix A in Raju et al. (1990). If there is an equilibrium in pure strategies, it must be that both firms charge r and that (w, = r; w,, = r) is a Nash equilibrium. At these prices (w, = r, w7, = r), the two firms sell to the retailer at r (who in turn sells

the two brands to respective loyal segments at price r), and earn expected profits, net of advertising, equal to:

EHll = m,r - aa,; Ell" = m,0r - aa,,. O

PROOF OF COROLLARIES 4.1 AND 4.2. In equilibrium, the optimal advertising levels are a* = 0; a* = ((mX2r - 10W)/ ))2. The first derivatives Oaa/&mzv > 0 and Na */&Yy < 0 for brand w. Since the optimal advertising is a direct function of own segment size and y, the derivatives will have the same signs for brand s. O

PROOF OF RESULT 1. The condition a ? a* implies that the equilibrium advertising levels area* = 0 anda*, = ((mX2r - l0,)/y)2. At these levels l, = m%2r which implies that the equilibrium promotional frequencies (MP*, MPI*) are both zero. Similarly, the promotional spending levels (MEP*, MEP*) are also both zero. El

PROOF OF RESULT 2. The condition a > a* ensures that the optimal post-advertising loyalty 1X*,, is below m72r. Similarly, the condition a <a** ensures that loyalty 1* is above i:. Thus when a* < a < a**, the equilibrium advertising levels areas = 0 anda* = ((I* - l",,)/ y)2. At these levels, the equilibrium promotional frequencies are both nonzero, and trade promotional expenditures are such that MEP* > MEP*t (see Figure 4). El

PROOF OF RESULT 3. The condition a > a** ensures that the optimal post-advertising loyalty I* is below i: and equilibrium advertising levels are a* = 0 and a* - ((jxt _ ) / y)2. At these levels, the equilibrium promotional frequencies are both nonzero, and trade promotional expenditures are such that MEP* < MEP* (see Figure 4). El

References Allenby, G. M. and P. E. Rossi (1991), "Quality Perceptions and Asym-

metric Switching Between Brands," Marketing Science, 10, 185- 204.

Blattberg, R. C. and S. A. Neslin (1990), Sales Promotion: Concepts, Meth- ods, and Strategies, Englewood Cliffs, NJ: Prentice Hall, Inc.

Bucklin, R. (1988), "Pass Through of Manufacturer Trade Promotions by Grocery Retailers," Unpublished Ph.D. Dissertation, Grad- uate School of Business, Stanford University, CA.

Chevalier, R. and R. C. Curhan (1976), "Retail Promotions as a Func- tion of Trade Promotions: A Descriptive Analysis," Sloan Man- agement Review, 18, 19-32.

Chintagunta, P. K., D. C. Jain, and N. J. Vilcassim (1991), "Investigat- ing Heterogeneity in Brand Preferences in Logit Models for Panel Data," Journal of Marketing Research, 28, 417-428.

Curhan, R. C. and R. J. Kopp (1986), "Factors Influencing Grocery Retailers' Support of Trade Promotions," Report No. 86-104 (July), Marketing Science Institute, Cambridge, MA.

Davis, S., J. J. Inman, and L. McAlister (1992), "Promotion has a Neg- ative Effect on Brand Evaluations-or Does It? Additional Dis- confirming Evidence," Journal of Marketing Research, 29, 143- 148.

Deighton, J., C. M. Henderson, and S. A. Neslin (1994), "The Effects of Advertising on Brand Switching and Repeat Purchasing," Journal of Marketing Research, 31, 28-43.

Ernst and Young Report (1993), "Do Trade Promotions Really Work?," a talk presented by Steve Laughlin at Krannert School of Management, Purdue University.



Fader, P. S. and J. M. Lattin (1993), "Accounting for Heterogeneity and Nonstationarity in a Cross Sectional Model of Consumer Behavior," Marketing Science, 12, 304-317.

Gonul, F. and K. Srinivasan (1993), "Modeling Multiple Sources of Heterogeneity in Multinomial Logit Models: Methodological and Managerial Issues," Marketing Science, 12, 213-229.

Guadagni, P. M. and J. D. C. Little (1983), "A Logit Model of Brand Choice Calibrated on Scanner Data," Marketing Science, 2, 202- 238.

Helson, H. (1964), Adaptation Level Theory, New York: Harper and Row, Inc.

Kahneman, D. and A. Tversky (1979), "Prospect Theory: An Analysis of Decision Making Under Risk," Econometrica, 47, 263-291.

Krishnamurthi, L. and S. P. Raj (1985), "The Effect of Advertising on Consumer Price Sensitivity," Journal of Marketing Research, 22, 119-129.

(1991), "An Empirical Analysis of the Relationship Between Brand Loyalty and Consumer Price Elasticity," Marketing Sci- ence, 10, 172-183.

Lal, R. (1990a), "Manufacturer Trade Deals and Retail Price Promo- tions," Journal of Marketing Research, 27, 428 444.

(1990b), "Price Promotions: Limiting Competitive Encroach- ment," Marketing Science, 9, 247-262.

Little, J. D. C. (1979), "Aggregate Advertising Models: The State of the Art," Operations Research, 27, 629-667.

Low, G. S. and J. J. Mohr (1992), "The Advertising-Sales Promotion Trade-Off: Theory and Practice," Report No. 92-127, Marketing Science Institute, Cambridge, MA.

Narasimhan, C. (1988), "Competitive Promotional Strategies," Journal of Business, 61, 427-449.

(1990), "Managerial Perspectives on Trade and Consumer Pro- motions," Marketing Letters, 1, 239-251.

Neslin, S. A. and R. Shoemaker (1989), "An Alternative Explanation for Lower Repeat Rates After Promotional Purchases," Journal of Marketing Research, 26, 205-213.

et al. (1994a), "A Research Agenda for Making Scanner Data More Useful to Managers," Marketing Letters, 5(4), 395-412.

S. G. Powell, and L. G. Schneider (1994b), "The Effects of Re- tailer and Consumer Response on Optimal Manufacturer Ad- vertising and Trade Promotion Strategies," Working Paper, Amos Tuck School of Business, Dartmouth College.

Pessemier, E. A. (1959), "A New Way to Determine Buying Deci- sions," Journal of Marketing, 24, 41-46.

Quelch, J. A. and P. W. Farris (1983), Cases in Advertising and Promotion Management, Plano, Texas: Business Publications, Inc.

Raj, S. P. (1982), "The Effects of Advertising on High and Low Loyalty Consumer Segments," Journal of Consumer Research, 9, 77-89.

Raju, J. S., V. Srinivasan, and R. Lal (1990), "The Effects of Brand Loyalty on Competitive Price Promotional Strategies," Manage- ment Science, 36, 276-304.

Rao, R. C. (1991), "Pricing and Promotions in Asymmetric Duopo- lies," Marketing Science, 10, 131-144.

Rossiter, J. R. and L. Percy (1987), Advertising and Promotion Manage- ment, New York: McGraw Hill, Inc.

Sethuraman, R. and G. J. Tellis (1991), "An Analysis of the Trade Off Between Advertising and Price Discounting," Journal of Mar- keting Research, 28, 160-174.

Shapiro, C. (1987), "Theories of Oligopoly Behavior," Discussion Pa- per No. 126, Woodrow Wilson School, Princeton University, Princeton, New Jersey.

Srinivasan, V. and T. Kibarian (1989), "Purchase Event Feedback: Fact or Fiction," Unpublished paper, Graduate School of Business, Stanford University (February).

Strong, E. K. (1925), The Psychology of Selling, New York: McGraw-Hill, Inc.

Tellis Gerard J. (1988), "Advertising Exposure, Loyalty, and Brand Purchase: A Two-Stage Model of Choice," Journal of Marketing Research, 25, 134-144.

and F. S. Zufryden (1995), Tackling The Retailer Decision Maze: Which Brands to Discount, How Much, When, and Why?," Marketing Science, 14, 271-299.

Walters, R. G. (1989), "An Empirical Investigation into Retailer Re- sponse to Manufacturer Trade Promotions," Journal of Retailing, 65, 253-272.

Tlhis paper was received September 14, 1993, and has been with the author 223 days for 4 revisions; processed by Scott Neslin, Area Editor.


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