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Persuasive advertising and product differentiation.

1. On the Need for a Classification of Types of Persuasive Advertising

Why is there so much advertising for seemingly identical products? As discussed by, for example, Scherer and Ross (1990), there exist notable examples of industries in which products are heavily advertised and yet there is very little difference in the physical characteristics of the various brands. One example is in the soft drink industry, where the two market leaders, Coca-Cola and Pepsi-Cola, are involved in a long-lasting advertising and marketing war, although to most consumers the rival drinks are almost indistinguishable (as any simple blind test will show, even regular cola drinkers may have difficulties distinguishing between Coca-Cola and Pepsi-Cola, and many are not able to identify which is which).(1) Other examples include coffee, beer, cigarettes, and detergents.

The literature on informative advertising does not seem very helpful in explaining this phenomenon. Indeed, a robust result across a wide range of informative advertising models is that there is an inverse relationship between product substitutability and equilibrium levels of advertising. For example, Grossman and Shapiro (1984) consider a differentiated products, duopoly framework in which ex ante consumers are unaware of the existence of either product but through firms' advertising consumers are informed of their existence. In this model the equilibrium level of advertising is positively related to the degree of product differentiation; the gain from informing and attracting an additional customer equals the markup of price over marginal cost, which is higher the more differentiated are the two products (see also Butters 1977 and Wolinsky 1984).(2) In Meurer and Stahl (1994), consumers are informed about the existence of products but not about the particular characteristics of different brands. In this setup, price competition is relaxed through advertising that informs consumers of product differences. The softening effect on pricing strategies and hence the incentive to advertise depends on to what extent products actually differ. Nelson (1974) suggested that even when information is not verifiable, advertising may be used by suppliers of superior brands to signal quality. Here the incentive to advertise follows from the fact that if products are (vertically) differentiated, superior qualities command higher prices and generate more repeat purchases.(3,4)

It would appear, therefore, that the existence of a positive relationship between product differentiation and advertising is robust to alternative forms of informative advertising. On the one hand, this result provides justification for the seemingly common belief in the literature that advertising and product differentiation are closely connected; indeed, in empirical work advertising expenditures have often been used as a proxy for the degree of product differentiation within an industry.(5) On the other hand, the very generality of the result suggests that high levels of advertising in industries in which products are not much differentiated is not well explained by models in which advertising is purely informative. Consequently, it is not unreasonable to consider instead models of persuasive advertising.

Whereas the literature on informative advertising has established a clear distinction between alternative types of such advertising, it seems that a similar attempt to classify types of persuasive advertising has not been made. In fact, the literature on persuasive advertising is generally fairly vague about exactly how advertising may affect preferences, or utility.(6) Typically it has been assumed that advertising enters a general utility function as a separate argument or, more directly, that advertising "shifts demand" for the advertised goods. Notwithstanding the fact that this approach has yielded useful insights, it has, however, proved difficult to derive clear results in such a general framework. For instance, Becker and Murphy (1993) demonstrate that persuasive advertising may or may not be more profitable when demand elasticities are high, it may or may not increase equilibrium prices, and it may or may not be oversupplied at market equilibrium. To proceed further, it would be useful to attempt to classify alternative types of persuasive advertising in order to distinguish between types that generate different results.(7)

At an intuitive level, it seems that persuasive advertising may affect preferences in (at least) three genuinely different ways. First, advertising may simply enhance the value of a product in the eye of the consumer. We will term this advertising that increases willingness to pay. Second, firms' advertising efforts may be considered as a tug-of-war in which each firm attempts to attract consumers by molding their preferences to fit the characteristics of its product; that is, each firm tries to convince consumers that what they really want is its particular variety. This we will call advertising that changes ideal product variety. Third, advertising may lead consumers to attach more importance to those differences that already exist between products. In this case we will talk of advertising that increases perceived product differences.

In the rest of this paper we will undertake an analysis of persuasive advertising in a framework that allows us to distinguish between these three types of advertising. In particular, we take as our starting point the parameterization of preferences given by the Hotelling model of product differentiation. This setup is simple yet does make it possible to undertake a systematic investigation of equilibrium levels of advertising under alternative assumptions about how advertising affects preferences. The analysis suggests that a positive relationship between equilibrium levels of advertising and the degree of "inherent" product substitutability is consistent only with advertising that increases perceived product differences.

2. Three Ways in Which Advertising May Affect Preferences

We take as our starting point a variant of the Hotelling's Line model in which consumers are uniformly distributed along a line segment of unit length.(8) In particular, let x [element of] [0, 1]. Then x is the number of consumers in the interval [0, x]. Each consumer wants only one unit of the good.

There are two symmetric firms in the market, supplying differentiated products. Firm O's product is located at 0, whereas firm l's product is located at 1.(9) Consumer x's willingness to pay for products 0 and 1 are, respectively,

[Mathematical Expression Omitted],

where t(0, [Theta]) [equivalent to] 0, [t.sub.1](x, 0) [greater than] 0, [t.sub.2](x, [Theta]) [greater than] 0, [t.sub.12](x, [Theta]) [greater than] 0 and [Theta] [greater than or equal to] 0 is an index of the degree of (inherent) product differentiation.(10,11) We may interpret the location x of the consumer as indicating his "ideal product variety" and s as the willingness to pay for this variety (had it been available). Ceteris paribus the further away a consumer is located from the product he consumes that is, the more this product differs from his ideal variety - the lower is his willingness to pay. The loss in surplus is increasing in the degree of (inherent) product differentiation, [Theta].

Assuming an interior solution in which the whole market is covered, the set of consumers can be divided into those that buy from firm 0 and those that buy from firm 1. The marginal consumer, [x.sup.*], who is just indifferent between buying from firm 0 and firm 1, is found by solving the equation

s - t([x.sup.*], [Theta]) - [p.sub.0] = s - t(1 - [x.sup.*], [Theta]) - [p.sub.1].

Quantities demanded from firms 0 and 1 are, respectively, [y.sub.0] = [x.sup.*] and [y.sub.1] = 1 - [x.sup.*]. For later use we note that

[Delta][y.sub.0]/[Delta][p.sub.0] = [Delta][x.sup.*]/[Delta][p.sub.0] = [Delta][y.sub.1]/[Delta][p.sub.1] = [Delta][x.sup.*]/[Delta][p.sub.1] = -1 / [t.sub.1]([x.sup.*], [Theta]) + [t.sub.1](1 - [x.sup.*], [Theta]) [less than] 0,

and that at [x.sup.*] = 1 - [x.sup.*] = 0.5,

[Mathematical Expression Omitted]. (1)

We assume that the amount of advertising is controlled by producers and measure advertising efforts by advertising costs. A priori we do not make specific assumptions about how the marginal impact of advertising on consumer preferences depends on the level of advertising. Consequently, with respect to profits, we hold open the possibilities that the returns to scale from advertising may be either increasing, constant, or decreasing. Unit output costs are assumed constant and are normalized to zero. Profits are then given by

[[Pi].sub.i] = [p.sub.i][y.sub.i] - [a.sub.i], i = 0, 1.

In this setup, we can conceive of three different ways in which advertising may affect preferences; advertising may affect s (i.e., increase willingness to pay), x (i.e., change ideal product variety) or [Theta] (i.e., increase perceived product differences).

Advertising Increases Willingness to Pay

In this formulation, advertising increases the willingness to pay but does not affect the degree of product differentiation nor consumers' most preferred variety. In particular, we assume

[Mathematical Expression Omitted],

where

[Mathematical Expression Omitted], [Mathematical Expression Omitted] and [Mathematical Expression Omitted].

Ceteris paribus the willingness to pay for a product is increasing in the level of advertising for that product. We allow for the possibility that advertising for a product may affect the preferences of those consuming the other product also. However, we assume that, when levels of advertising are symmetric, this latter external effect, if positive, does not exceed the direct effect of advertising for the chosen product.

In Figure 1, we have illustrated the effects of advertising that increases willingness to pay for the case in which t(x, [Theta]) is linear in x and [Mathematical Expression Omitted]. The solid lines show willingness to pay for the two products when there is no advertising, whereas the dotted line shows willingness to pay for product 0 when firm 0 does some advertising. Note that the slope of the willingness-to-pay functions are unaffected by the level of advertising.

Advertising Changes Ideal Product Variety

In this case it is as if advertising by a firm shifts the distribution of consumers in the direction of this firm's product. In particular, we assume

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

where

[Mathematical Expression Omitted], [Mathematical Expression Omitted] and [Mathematical Expression Omitted].

Note that as a consequence of advertising the support of the distribution of "persuaded types," [Mathematical Expression Omitted], is not necessarily contained in the interval [0, 1]. For example, when [a.sub.0] [greater than] 0 and [a.sub.1] = 0, then [Mathematical Expression Omitted], and consequently the ideal points for those consumers with [Mathematical Expression Omitted] are negative, or "to the left of" the location of product 0. To capture the idea that advertising can at most persuade customers that their preferences are perfectly aligned with the characteristics of the advertised product, we assume [Mathematical Expression Omitted] for [Mathematical Expression Omitted].

In Figure 2 is illustrated the effects of advertising that changes ideal variety. Again, the solid lines show willingness to pay without advertising, whereas the dotted lines show the corresponding willingness to pay when firm 0 does some advertising. Note that in this case the willingness to pay for the competitor's product is always affected when a firm advertises. Although when t(x, [Theta]) is linear in x the slopes of the willingness-to-pay functions are not affected by advertising, in the more general case they may be.

Advertising Increases Perceived Product Differences

In the third case we let

[Mathematical Expression Omitted].

In this formulation, it is as if advertising increases product differentiation. In particular, we assume

[Mathematical Expression Omitted], [Mathematical Expression Omitted] and [Mathematical Expression Omitted].

Figure 3 illustrates the effects of advertising that increases perceived product differences. In this case, advertising changes the slope of the willingness-to-pay functions without affecting the intercept. Consequently, for all consumers (except the ones at 0 and 1) willingness to pay is lower when firms advertise more. Note that, since [Mathematical Expression Omitted] is a common factor in both [Mathematical Expression Omitted] and [Mathematical Expression Omitted], the [Mathematical Expression Omitted] and [Mathematical Expression Omitted] curves are symmetric irrespective of firms' advertising efforts.

It should be noted that there is an alternative way of representing the three types of advertising based on observable effects on demand. Type C advertising, by heightening the awareness that available products differ from ideal types, tends to reduce the willingness to pay not only for the competitor's product but also for the advertised product as well. This is contrary to both Type A and Type B advertising, which both tend to increase demand for the advertised product. However, Type A and Type B advertising are distinguished by their different effect on the willingness to pay for the competitor's products. Type B advertising, by molding the preferences of consumers to the characteristics of the advertised product, always has a detrimental effect on the willingness to pay for the competitor's product. Type A advertising, however, may be sufficiently generic so that it positively affects the willingness to pay for both products (this would be the case if [Mathematical Expression Omitted]).

3. Simultaneous Advertising and Pricing Decisions

In this section we assume that firms make advertising and pricing decisions simultaneously. In the next section we analyze an alternative game in which firms determine advertising efforts before making pricing decisions. With this latter formulation we have in mind cases in which firms consider the effect of advertising as long term in nature and plan their advertising strategies taking into account how advertising affects future price competition. In particular, advertising can act as a commitment to a certain pricing strategy. The game considered in this section may instead be interpreted as a setting in which advertising and pricing decisions are parallel, equally adjustable and with similar planning horizons.

When the two firms set prices and advertising levels simultaneously necessary conditions for an interior, symmetric Nash equilibrium are

[p.sub.0] [Delta][x.sup.*]/[Delta][a.sub.0] = 1

[x.sup.*] + [p.sub.0] [Delta][x.sup.*]/[Delta][p.sub.0] = 0, (2)

evaluated at ([a.sub.0], [a.sub.1], [p.sub.0], [p.sub.1]) = (a, a, p, p). The first condition states that the gain in revenue from increasing advertising efforts marginally equals advertising costs, whereas the second condition implies that the gain in revenue from increasing price equals the increase in output costs (normalized to zero).

It is not obvious that such an interior pure-strategy equilibrium always exists. First, if the effectiveness of advertising is sufficiently small, there may be no advertising at equilibrium. As we will see shortly, this happens when advertising increases perceived product differences. Second, it is conceivable that firms choose to advertise to such an extent that the whole market is not covered. Third, we need to ensure that the profit functions are jointly concave in price and advertising. It turns out that these considerations are different for the three types of advertising and hence below we discuss each type separately.

When advertising increases willingness to pay, the necessary conditions for Equation 2 imply

[Mathematical Expression Omitted]

p = [t.sub.1](0.5, [Theta]). (3)

Clearly, for such an equilibrium to exist we need that advertising is sufficiently effective (i.e., [Mathematical Expression Omitted] over some range). We need also that the profit functions are concave in price and advertising efforts. Since from Equation [Mathematical Expression Omitted] at equilibrium, it is straightforward that (locally) the profit functions are always concave in price. The corresponding condition for the profit functions to be concave in advertising are [Mathematical Expression Omitted]. However, more is needed for the profit functions to be jointly concave in price and advertising; in particular, the determinant of the Hessian to [[Pi].sub.i]([p.sub.i], [a.sub.i]) is negative if and only if [Mathematical Expression Omitted].(12)

When an equilibrium exists, from Equation 3 we see that the profitability of increasing advertising efforts is, by the shift in demand, higher the higher is the product price. On the other hand, the effectiveness of advertising is decreasing in the degree of product differentiation. Now equilibrium prices are increasing in the degree of differentiation so that the effect of greater differentiation is just balanced by the corresponding higher level of equilibrium prices. Consequently, at equilibrium the marginal gain from an increase in advertising is independent of the degree of product differentiation and so are equilibrium advertising levels; that is, da/d[Theta] = 0.

Note that this last result does not depend on specific assumptions about the form of the preference function, for example, linearity of "transport costs," t([center dot]). On the contrary, we have allowed for a fairly general class of Hotelling-type consumer technologies (see the comment in footnote 10). The result follows because in this case the effects of advertising and price on demand are proportional; in particular, [Mathematical Expression Omitted]. Then, given that at equilibrium the impact on revenues from a marginal change in price is constant and independent of the degree of product differentiation (in particular, -p[Delta][x.sup.*]/[Delta][p.sub.0] = [x.sup.*] = 0.5), it follows that levels of advertising must be constant also.

When advertising changes ideal product variety, the equilibrium conditions reduce to

[Mathematical Expression Omitted],

p = [t.sub.1](0.5, [Theta]). (4)

For an equilibrium to exist in this case we again need to make assumptions about the effectiveness of advertising and about the concavity of profit functions; in particular, the condition [Mathematical Expression Omitted] ensures both concavity in advertising and joint concavity in price and advertising.(13) Given that such an equilibrium exists, we observe that the effect on demand from an increase in a firm's advertising efforts is independent of how differentiated are products. However, since prices are higher when products are more differentiated, the profitability of a given shift in demand is increasing in the degree of product differentiation. Consequently, whether or not equilibrium advertising levels are increasing in the degree of product differentiation depends on the scale economies of the advertising-demand technology. In particular, from Equation 4 it follows that

[Mathematical Expression Omitted]. (5)

The sign of the right-hand side of Equation 5 depends on how the marginal impact of advertising [TABULAR DATA FOR TABLE 1 OMITTED] changes with levels of advertising. From the second-order condition for profit maximum it follows that [Mathematical Expression Omitted]. Therefore, unless there is a strong, negative cross-effect in the advertising technology, that is, [Mathematical Expression Omitted], the marginal impact of advertising will be decreasing in the levels of advertising; in particular, [Mathematical Expression Omitted] and da/d[Theta] [greater than] 0.

Finally, in this section we turn to the case in which advertising increases perceived product differences. Unlike in the two previous cases, here advertising tends to reduce consumers' willingness to pay. As seen from Figure 3, if advertising is sufficiently inexpensive, it is therefore conceivable that firms would want to advertise so as to move them into a separating market situation, that is, so that they become local monopolists. Such an outcome cannot be an equilibrium, however, since as a monopolist a firm would always want to reduce advertising expenditures in order to increase demand. Hence (assuming that the market is covered when there is no advertising), the only equilibrium candidates are cases in which firms compete effectively for the marginal consumer. But even in such cases costly advertising will not be undertaken since then advertising does not affect demand (i.e., the location of the marginal consumer). We conclude that (whether or not the market is assumed to be covered) there is no advertising at equilibrium.(14)

The results of this section are summarized in Table 1. Note that in all three cases equilibrium prices are the same as they would be in the corresponding model in which firms do not have the option to advertise. This is obvious in the case when advertising increases perceived product differences since then firms do not advertise at equilibrium. However, also in the two other cases prices are unaffected by advertising; as seen from Equations 3 and 4, equilibrium prices depend on the degree of product differentiation only and are consequently independent of advertising levels.

4. Advertising as Commitment Strategies

In the previous section we considered a model in which firms' advertising and pricing decisions are made simultaneously. In some cases it may be more reasonable to think of advertising strategies as longer term than pricing strategies. Whereas prices can often be adjusted rapidly at relatively low cost and the impact on demand will be quickly felt, it may be much more costly to alter advertising strategies, and it can take considerable time until the effect on demand is noticeable. Since informative advertising often contains information about prices, in informative advertising models, it may seem reasonable to assume that advertising and pricing decisions are taken simultaneously. Persuasive advertising however, by its nature, may perhaps more often be thought of as having long-lasting effects given that, if successful, it affects consumer preferences. In that case it is reasonable to model advertising decisions as long term and pricing decisions as short term.

In this section we consider a two-stage game in which firms first determine advertising efforts and then compete in prices. We consider the symmetric subgame-perfect equilibria of this game, implicitly assuming that firms, when choosing advertising strategies, take into account the effects of advertising decisions on second-stage price competition.

For given advertising levels the necessary conditions for an interior Nash equilibrium in the second, price-competition stage are

[x.sup.*] + [p.sub.0] [Delta][x.sup.*]/[Delta][p.sub.0] = 0,

1 - [x.sup.*] - [p.sub.1] [Delta][x.sup.*]/[Delta][p.sub.1] = 0. (6)

Assuming that such an equilibrium exists, solutions are [p.sub.i] = [p.sub.i]([a.sub.0], [a.sub.1], [Theta]), i = 0, 1. At the symmetric equilibrium, firm 0's stage 1 first-order condition for profit-maximizing advertising efforts, taking into account how second-stage equilibrium prices depend on advertising, reduces to

[p.sub.0] [Delta][x.sup.*]/[Delta][a.sub.0] + [p.sub.0] [Delta][x.sup.*]/[Delta][p.sub.1] [Delta][p.sub.1]/[Delta][a.sub.0] = 1, (7)

evaluated at ([a.sub.0], [a.sub.1], [p.sub.0], [p.sub.1]) = (a, a, p, p).

We note that in this model advertising has an effect that is not present when advertising and pricing decisions are made simultaneously. Here advertising not only affects demand but may also have an impact on pricing strategies. In particular, a firm's advertising decision may influence the pricing strategy of its competitor. Whereas the first term on the left-hand side of Equation 7 represents the direct effect of advertising on demand, the second term captures the indirect, strategic effect. From Equation 6 it follows that the strategic effect may be decomposed into two parts; advertising may both shift the demand curve and change its slope:

[Mathematical Expression Omitted] (8)

where we have used the facts that at equilibrium [Delta][x.sup.*][Delta][a.sub.1] = -[Delta][x.sup.*]/[Delta][a.sub.0], [Delta][x.sup.*]/[Delta][p.sub.1] = -[Delta][x.sup.*]/[Delta][p.sub.0] [[Delta].sup.2][x.sup.*]/[Delta][a.sub.1][Delta][p.sub.0] = -[[Delta].sup.2][x.sup.*]/[Delta][a.sub.0][Delta][p.sup.0], and [[Delta].sup.2][x.sup.*]/[Delta][a.sub.0][p.sub.1] = -[[Delta].sup.2][x.sup.*]/[Delta][a.sub.0][Delta][p.sub.0]. Since -[Delta][x.sup.*]/[Delta][a.sub.0] [less than or equal to] 0 and [Delta][x.sup.*]/[Delta][p.sub.1] [greater than] 0, the shift in demand tends to reduce the competitor's price. Ceteris paribus this strategic shift-in-demand effect therefore reduces the profitability of advertising. Furthermore, the demand-shifting, strategic effect on profits is similar to, albeit smaller and of the opposite sign of, the direct effect. Therefore, by inserting Equation 8, Equation 7 reduces to

[Mathematical Expression Omitted].

How the change of slope influences the competitor's pricing strategy depends on the sign of [[Delta].sup.2][x.sup.*]/[Delta][a.sub.0][Delta][p.sub.o]. When advertising either increases willingness to pay or changes ideal product variety, [TABULAR DATA FOR TABLE 2 OMITTED] [[Delta].sup.2][x.sup.*]/[Delta][a.sub.0][Delta][p.sub.0] = 0 at equilibrium; that is, since these types of advertising leave the slope of the demand curve unchanged, the overall effect of advertising on revenues is proportional, albeit smaller in magnitude, to the effect when advertising has no indirect, strategic effect on pricing strategies. Consequently, up to a multiplicative constant, the first-order conditions for profit maximum are the same as in section 4. This has two implications. First, the incentives to advertise and hence equilibrium advertising levels are smaller when advertising and prices are determined sequentially than when they are set simultaneously. Second, the relationship between equilibrium advertising levels and the degree of (inherent) product differentiation are the same in both models (compare Tables 1 and 2).

When advertising increases perceived product differences, matters are different, however. In particular, since [Mathematical Expression Omitted] and at equilibrium [Delta][x.sub.*]/[Delta][a.sub.i] = 0, i = 0, 1, the first-stage equilibrium condition (Eq. 7) reduces to

[Mathematical Expression Omitted],

evaluated at ([a.sub.0], [a.sub.1], [p.sub.0], [p.sub.1]) -- (a, a, p, p). From this we find

[Mathematical Expression Omitted], (9)

where we have used the facts that at equilibrium [Mathematical Expression Omitted] and [Mathematical Expression Omitted]. If the advertising technology has constant returns to scale, in particular, [Mathematical Expression Omitted], Equation 9 reduces to [Mathematical Expression Omitted]. If we assume that equilibrium is "stable,"(15) the denominator in the above expression is negative and consequently sign (da/d[Theta]) = sign([[Delta].sup.2][p.sub.1]/[Delta][[Theta].sup.2]). At equilibrium, the second-order condition for profit maximum is

[Mathematical Expression Omitted],

so that if [Mathematical Expression Omitted], and consequently da/d[Theta] [less than] 0. Only if [Mathematical Expression Omitted] and [Mathematical Expression Omitted] can we have da/d[Theta] [greater than] 0.

In the previous section we saw that if firms make pricing and advertising decisions simultaneously and advertising is of either of the three "pure" types, equilibrium prices were the same as they would have been had firms not had the option to advertise. This continues to be the case also when advertising decisions precede pricing decisions if advertising either increases willingness to pay or changes ideal variety. However, whenever advertising increases perceived product differences, equilibrium prices will be affected by firms' opportunity to advertise; indeed, since equilibrium prices are increasing in the degree of product differentiation, prices will be higher in this model than in the corresponding model in which firms do not have the option to advertise.

This latter result points to an interesting similarity with the informative advertising model of Meurer and Stahl (1994). In their model consumers have imperfect information about the particular characteristics of available brands. They therefore tend to consider products as more similar than what is actually the case. By informative advertising consumers are made aware of the actual differences between products; that is, product differentiation, as perceived by consumers, is increased. Consequently, informative advertising relaxes price competition and leads to higher equilibrium prices. Note that the incentive to advertise is greater the less prior information consumers have about product differences; that is, equilibrium advertising levels will be higher the more substitutable products are perceived to be ex ante. However, ceteris paribus (specifically, for given levels of ex ante information) the incentive to advertise is less when actual product differences are small. In particular, if products are, in their physical composition, perfect substitutes there will be no advertising at equilibrium in the Meurer-Stahl model.

5. Summary and Concluding Remarks

We argued in the introduction for the need to classify types of persuasive advertising and to systematically investigate the robustness of relationships between advertising and other economic variables across different types of advertising. In this paper we have attempted to do so by exploring Hotelling-type, differentiated-products duopoly games under alternative assumptions about how advertising affects consumer tastes. In particular, we have investigated the relationship between the degree of (inherent) product differentiation and equilibrium levels of persuasive advertising under different assumptions on the advertising technology.

What motivated our initial interest in this topic were the seemingly very high levels of advertising in some industries in which the degree of (inherent) product differentiation appears to be low. From this perspective, cases in which equilibrium levels of advertising are decreasing in the degree of product differentiation are of particular interest. There is only one such case: If advertising increases perceived product differences and acts as a commitment for firms' pricing strategies, equilibrium advertising levels are decreasing in the degree of (inherent) product differentiation for a wide range of parameter values. On the other hand, if advertising changes ideal product variety, advertising levels are increasing in the degree of product differentiation,(16) whereas the incentives for undertaking advertising that increases willingness to pay are independent of the extent to which products are differentiated.

Our results are derived in a framework that in certain respects is fairly restrictive. In particular, it has been assumed throughout that aggregate demand is exogenously given. Clearly, an important role of advertising (especially persuasive advertising) is to increase aggregate demand. Needless to say, incorporating endogenous demand into our framework would have complicated the analysis considerably. However, for the classification and comparison of alternative types of persuasive advertising that has concerned us here, such a generalization may not affect results significantly.

We conclude that whereas informative advertising is generally more effective in differentiated products industries, there are circumstances in which certain forms of persuasive advertising are particularly effective when products are not much differentiated. Clearly, in practice most actual advertising and marketing efforts will contain a mix of the three pure types considered here. However, firms will design advertising and marketing campaigns so as to maximize their effectiveness. Our results suggest that in industries in which products are fairly similar, firms will aim their marketing and advertising efforts at heightening "perceived" product differences. Casual observation suggests that there may be some validity in this point; confer the efforts in, say, the soft drinks and beverages industries to differentiate the packaging of products and to focus on these differences in advertising campaigns. Indeed, if the product does not lend itself to true differentiation, advertising becomes the necessary medium for influencing demand. That would suggest that advertising and differentiation are substitutes in some larger marketing decision. We leave the exploration of this last issue for future research.

We are grateful to the editor Jonathan H. Hamilton, two anonymous referees, as well as Dag Morten Dalen, Kai-Uwe Kuhn, Tore Nilssen, Atle Seierstad, Lars Sorgard, Knut Sydsaeter, and seminar participants at the Universitat Autonoma de Barcelona, the University of Oslo and the 1996 EARIE meeting for useful comments on earlier versions of the paper.

1 Some years ago, Pepsi-Cola ran a series of television commercials in which the main characters were blind tested on two brands of cola. The focus of the commercials was on the surprise of those tested when they discovered that their favored brand was Pepsi. Apparently, the view of the creators of those commercials was that most people do not know which cola they like best.

2 The result that the incentive to advertise rises as the elasticity of demand for the advertised good falls is often attributed to Dorfman and Steiner (1954).

3 Milgrom and Roberts (1986), in a model based on the ideas of Nelson, demonstrate that the extent to which advertising is used as a signal of superior quality depends in a rather complicated way on model parameters, such as the difference in costs across qualities. Schmalensee (1978), in an advertising-signaling model in which consumers follow a rule-of-thumb, shows that low-quality producers may do most of the advertising because markups are negatively correlated with quality and consumers do not recognize the negative advertising-quality relationship. However, in both models the incentive to advertise disappears if it is known that products do not differ (see also Kihlstrom and Riordan 1984 and Bagwell and Ramey 1993).

4 When advertising conveys price information (a case that appears to be of somewhat limited interest for the examples alluded to previously), matters are more complicated. For example, Bester and Petrakis (1995), in a model in which sellers are differentiated by traveling costs, demonstrate that for high levels of differentiation equilibrium advertising levels may increase as goods become more substitutable (i.e., traveling costs are reduced). However, also in this model incentives to advertise disappear as goods become perfect substitutes (see also Robert and Stahl 1993).

5 See Geroski (1991, p. 171 ff) for references and a critical discussion of this practice.

6 Despite some well-articulated opposition (see e.g., Stigler and Becker 1977 and Ekelund and Saurman 1988), it seems that the phenomenon of "persuasive advertising" is generally acknowledged also among economists. The theoretical literature on persuasive advertising has tended to concentrate on whether unregulated markets produce too much of such advertising, with notable contributions from, among others, Dixit and Norman (1978, 1979, 1980), Fisher and McGowan (1979), Shapiro (1980), Schmalensee (1986), Kotowitz and Mathewson (1979), Nichols (1985), and Becker and Murphy (1993).

7 An alternative route is to put more restrictions on taste formation. This could be done by drawing on psychological theory, as in Akerlof and Dickens (1982), which contains a discussion of how the theory of cognitive dissonance may help explain "how advertising works." Nagler (1993), referring to Akerlof and Dickens, also appeals to the theory of cognitive dissonance in his discussion of "deceptive advertising." If one is willing to treat advertising as an ordinary good, some restrictions follow from consumer theory (Becker and Murphy 1993). Stigler and Becker (1977) impose certain restrictions by assuming a Lancasterian framework in which advertising is considered an input along with market goods and other inputs to produce those commodities that are the ultimate objects of consumer choice (see also Nichols 1985).

8 For a textbook presentation of the Hotelling model, see Tirole (1988, chap. 7).

9 Consequently, here we take (inherent) product characteristics as given. A possible extension of our analysis would be to allow for endogenous product locations.

10 This formulation of the consumer technology is fairly general and includes as special cases the original formulation of Hotelling (1929) as well as those of d'Aspremont, Gabszewicz, and Thisse (1979) and Economides (1986). For an overview of the literature on "location" models, see Gabszewicz and Thisse (1992).

11 Here [t.sub.1](x, [Theta]) [equivalent to] [Delta]t(x, [Theta])/[Delta]x, [t.sub.2](x, [Theta]) [equivalent to] [Delta]t(x, [Theta])[Delta][Theta] and [t.sub.12](x, [Theta]) [equivalent to] [[Delta].sup.2]t(x, [Theta])/[Delta]x[Delta][Theta]. A corresponding notation is used for other functions below.

12 Concavity conditions would be the satisfied if, for example, t([Theta], x) = [Theta]x, [Theta] [greater than or equal to] 1, and [Mathematical Expression Omitted].

13 Concavity conditions would be satisfied if, for example, t([Theta], x) = [Theta]x, [Theta] [greater than or equal to] 1, and [Mathematical Expression Omitted].

14 To elaborate on the issue of existence of equilibrium, let ([a.sub.0], [a.sub.1], [p.sub.0], [p.sub.1]) = (0, 0, p, p) be a strategy combination that satisfies d[[Pi].sub.i]/d[p.sub.i] = 0, i = 0, 1 (such a strategy combination exists given that the standard, no-advertising model has got an equilibrium). Assume that there exists a profitable deviation, that is, a strategy combination (a[prime], p[prime]), a[prime] [greater than] 0, such that [[Pi].sub.i](a[prime], p[prime], 0, p) [greater than] [[Pi].sub.i](0,p; 0, p). By the argument just given, we have [[Pi].sub.i](0, p[prime]; 0, p) [greater than] [[Pi].sub.i](a[prime], p[prime]; 0, p), which implies [[Pi].sub.i](0, p[prime]; 0, p) [greater than] [[Pi].sub.i](0, p; 0, p), contradicting the assumption that (0, p) is a best response to (0, p).

15 Stability of the equilibrium in the sense of Dixit (1986) requires that the second-order conditions hold and that [Mathematical Expression Omitted] at equilibrium. Because of the symmetry of the model, the stability conditions imply [Mathematical Expression Omitted].

16 An inverse relationship between the degree of product differentiation and equilibrium levels of advertising may exist also in the case of advertising that changes ideal product variety. However, as we discuss in section 4, the conditions under which this occurs seem unlikely.

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