Advertising as Noisy Information about Product Quality Hendrik Hakenes Leibniz University of Hannover Martin Peitz University of Mannheim June 6, 2010 preliminary and incomplete Abstract A firm has to make consumers aware of a new product introduction. It also has to convince them that the product is of high quality. In this paper, we consider the interplay between directly and indirectly informative advertising in a monopoly model with repeat purchase. When consumers observe the advertising expenditure, the firm may excessively advertise high quality. However, when consumers only learn from seeing the product advertised, a high-quality firm cannot perfectly distinguish itself from low quality and advertises less than absent quality uncertainty. Keywords: Informative advertising, advertising signal, product quality Department of Economics, Königsworther Platz 1, 30167 Hannover, Germany, hakenes@fmt.uni-hannover.de. Also affiliated with Max Planck Institute, Bonn. Department of Economics, University of Mannheim, 68131 Mannheim, Germany, Martin.Peitz@googlemail.com. Also affiliated with CEPR, CESifo, ENCORE, and ZEW.
1 Introduction A firm introducing an experience goods faces two hurdles it has to overcome: It has to make consumers aware of the product, and it has to convince consumers that the product is likely to be of high quality. Both hurdles can possibly be overcome, the first by informing consumers that a new product is available, the second by using advertising to convince consumers of high product quality. As we analyze in this paper, the equilibrium advertising strategy depends on whether the advertising expenditure is public or private information of the firm. One of the celebrated results in industrial organization is that consumers can infer the quality of a product from the amount of advertising that is spent (see Nelson, 1970, 1974, Milgrom and Roberts, 1986, and the survey by Bagwell, 2005). Here, advertising is equivalent to public money burning. Arguably, advertising in the super bowl constitutes such public money burning because viewers know that such advertising is very expensive. While consumers may have some imprecise knowledge of the advertising expenditure in the typical advertising campaign, we consider the perfect observability assumption to be in many cases a bad approximation of reality and may rather postulate the opposite: Consumers may be exposed to advertising, but they do not know the total advertising expenditure. This applies in particular to advertising campaigns that involve a number of competing media (e.g., different newspapers or different channels). What happens if consumers cannot observe the amount of advertising but only realize that a particular product was advertised to them? We present a simple stylized model to answer this question: Receiving the ad provides noisy information about product quality. We show this result in a simple repeatpurchase monopoly model in which a larger advertising expenditure increases the probability that a consumer is exposed to an ad. The assumption that consumers are homogeneous, allows us to abstract from price signaling issues. Due to the repeat-purchase effect, a consumer who becomes informed about the existence of a product is more valuable to a high-quality than a lowquality producer. Consequently, a high-quality producer spends more on advertising than a low quality producer. However, since informing the first consumer is assumed to be costless, the low-quality producer will necessarily 1
spend a strictly positive amount on advertising and is able to free-ride on the advertising effort of the high-quality firm. Hence, a high-quality firm cannot fully separate from a low-quality firm. Consumers are Bayesian rational. They use the fact that a high-quality firm advertises more than a low-quality firm to update their belief about the quality of the firm from which they have seen the ad. Hence, directly informative advertising also contains some noisy information about unobservable product quality. Our theory predicts a positive but not perfect correlation between product quality and advertising expenditure. To our knowledge, the idea that informative advertising about the existence of a product provides noisy information about product quality has not been previously studied. As a starting point of our analysis, we observe that advertising serves two functions, a directly informative (about a product s existence) and an indirectly informative (about a product s quality). Previous work on indirectly informative advertising, starting with Nelson (1970,1974), Kihlstrom and Riordan (1984), and Milgrom and Roberts (1986), postulated that consumers observe the advertising expenditure. Hertzendorf (1993) considers noisy advertising in a signaling model in which all consumers are aware of the product. From the point of view of the consumer, advertising is stochastic, because the consumer observes only a (random) fraction of the advertising. In his setting with downward sloping demand, the firm may use price and advertising signals. He shows that a low-quality firm partly mimics a high-quality firm. In equilibrium, high and low-quality firms post ads, while the price is independent of quality. Previous work on directly informative advertising focused on search good (see, in particular, Grossman and Shapiro, 1984, who analyze competitive effects of informative advertising). An exception is Moraga (2000), who analyzes informative advertising in a single-period monopoly market in which consumers are initially uncertain about product quality but receive a noisy signal about quality. However, his setting is markedly different from ours: Consumers who become exposed to advertising become perfectly informed about product quality (i.e., advertising provides truthful information on product characteristics, as in Anderson and Renault, 2006). Thus, a lowquality firm does not have an incentive to advertise. Probably closest to our work, Zhao (2000) considers a market in which a high-quality firm can signal its quality and at the same time generate aware- 2
ness of its product. In a standard single-period price-advertising signaling context he shows that the high-quality firm advertises less than the lowquality firm. This contrasts with our repeat-purchase environment, in which the low-quality firm advertises strictly less than the high-quality firm. 2 The Model We consider a market with a single-product monopolist who sells an experience good over two periods. In the first period, the product is introduced in the market. The product is either of high or low quality, q {q H,q L }. Nature draws high quality with probability λ. The quality is then observed by the firm but not by consumers. At the beginning of the game, consumers neither know the existence nor the quality of the product. In the firstperiod,themonopolistcaninformconsumersabouttheexistenceofits product through advertising. However, the firm cannot make credible informative statements about product quality. The probability that a consumer sees an ad is φ(a) [0, 1], wherea is the expenditure for advertising. The advertising technology is assumed to have decreasing returns. More precisely, we asumme that 0 <φ(a) < 1 for A>0, φ 0 (A) > 0, φ 00 (A) < 0, lim A φ(a) =1, φ(0) = 0, andlim A 0 φ 0 (A) =. 1 These ensure that an interior solution to the firm s maximization problem exists. Since φ is monotonic, we can invert this function to obtain the advertising expenditure A(φ) that is needed to reach a share φ of consumers. Consumers have a willingness to pay v H for high quality and v L <v H for low quality. Since consumers are homogeneous, we abstract from the issue of price signaling by restricting the analysis to those equilibria in which the firm s price is equal to the full expected surplus. 2 In the first period, consumers form expectations about the quality of a product they see advertised as 1 These assumptions are borrowed from the literature on directly informative advertising, see e. g. Grossman and Shapiro (1984). Note that most of the work on directly informative advertising only concerns the existence of a product. For a recent contribution on content advertising, see Anderson and Renault (2006). 2 Here, we follow Tadelis (1999) and Cabral (2000), who made the same assumption in a different context. In our model, full surplus extraction follows from standard equilibrium selection arguments such as the dominance criterion (see Mas-Colell, Whinston, and Green, 1995). 3
we will show, the expected probability of high quality is different from the unconditional probability λ. Consumers who have purchased the product in period 1 observe the quality of the product which is then sold in the second period to consumers who know about its existence. To keep the analysis as simple as possible we abstract from the possibility of advertising after the firstperiod. Theaggregatesizeofthemarketisδ in the first period, and 1 δ in the second period. Because information about product quality is released between periods 1 and 2, δ can be interpreted as the (inverse) speed of information revelation. A product with δ =0is a pure credence good. If δ =1, consumers are perfectly informed about product quality before their purchase. The marginal cost of producing one unit of the good is c with v L <c<v H. Hence, the introduction of high quality is socially efficient and the introduction of low quality is not. We abstract from fixed costs of production. Thefollowingtablesummarizesthetimingofthegame. 0 Nature draws the quality of the product, q {H, L}, which is private information of the firm. 1a After observing its type, the firm sets first-period price p 1, spends A on advertising, where A is private information of the firm. A consumer becomes informed about the existence of the product with probability φ(a). 1b Consumers who learn about the product s existence, update their beliefs about product quality, and decide whether to buy. 2a The firm sets the second-period price p 2. 2b Consumers who have bought in period 1 learn the product quality and decide whether to buy again. 3 We solve for perfect Bayesian Nash equilibria. 3 The assumption that only period-1 consumers can buy the product in period 2 has also been made e.g. in Milgrom and Roberts (1986) 4
3 Advertising Strategy Before turning to asymmetric information environments, we characterize the solution to monopolist s advertising decision when consumers do not face uncertainty with respect to product quality. We then characterize equilibria in the game in which advertising expenditure is perfectly observable. This will allow us to contrast our results in a market in which advertising expenditure and advertising intensity are unobservable. 3.1 Advertising under Symmetric Information As a benchmark, consider the case that the quality of a product is observable. That is, even though consumers are initially unaware of the existence of a product, they observe its quality before they buy it. Consequently, firms use advertising as a means to inform consumers about a product s existence. A high-quality firm s expected profit is π H =(v H c) φ H A(φ H ). The full information advertising expenditure is uniquely determined by the first-order condition A 0 (φ H)=v H c. (1) Low-quality firms will have negative margins v L c, hence they will not advertise at all. Some properties are immediate: Advertising increases with product value v H but decreases with marginal cost c; it does not depend on δ. Examples. An example is φ =1 e χa. Consequently, the fraction of uninformed consumers after two campaigns is the square of the fraction of uninformed consumers after one campaign. This requires consumer targeting to be impossible. Another example (which however does not satisfy all the regularity assumptions) is A(φ) =φ 2 /2. Thus,φ H = v H c. Wewillreturn to this latter example below. 5
3.2 Advertising as a Signal As in the previous subsection, we assume that consumers need to be made aware of a product before purchasing. In contrast to the symmetric-information benchmark, consumers do not observe product quality. In line with most of the signaling literature on advertising, let us for the moment assume that the consumers who see an ad (fraction φ) alsoobservethesizeofthecampaignφ (or A). Consumers who do not happen to see an ad (fraction 1 φ) remain uninformed and do not observe φ; they do not even know about the existence of the product. Informed consumers condition their beliefs on φ. Hence, firms use their advertising effort A not only to make potential consumers aware of their product but possibly also to signal their product quality. For now, let us concentrate on fully separating equilibria. A high-quality firm chooses a critical φ H such that the low-quality firm is indifferent between imitating the strategy of the high-quality firm and not advertising at all. Thus, we are in a fully separating equilibrium in which informative advertising about the existence of the product allows consumers to infer the quality of the firm. If consumers infer the actual quality of a low-quality firm, then they will pay at most v L for the product right from the beginning, and the firm will not produce in the first place. As a consequence, a high-quality firm must choose φ H sufficiently high such that the profits for a low-quality firm that chose the same φ would be non-positive, δφ H (v H c) A(φ H ) 0. Denote the minimal φ H that satisfies the inequality by φ s H. In addition, the incentive constraint of the high-quality firm must be satisfied. In other words, the high-quality firm may want to advertise more than the above φ H if its profits increase from reaching more consumers. If φ H >φ s H (with φ H as in (1)) then the high-quality firm chooses the advertising expenditure A(φ H) instead. In this case, there is no signal distortion (over-advertising), whereas in the case φ H <φ s H, the high-quality firm would have to over-invest in advertising only to deter the low-quality firm from mimicking. Thus, the high-quality firm chooses max{a(φ H),A(φ s H)}. 6
Remark 1 When φ is observed by informed consumers, in a separating equilibrium the low-quality firm does not sell and does not advertise. The highquality firm either advertises the same as in the symmetric information case, or it distorts advertising upward to signal that it is of high quality.. Hence, inefficient production of the low-quality product is avoided. However, the high-quality firm advertises above the efficient level. As is well-known in signaling games, typically also pooling equilibria exist in which inefficient production of the low-quality product takes place. In a pooling equilibrium, high and low-quality firm choose the same advertising expenditure A(φ p ). Observing A(φ p ) consumers believe that the product they see advertised is of high quality with probability λ. Thus, they are willing to pay λv H +(1 λ)v L.Ifλv H +(1 λ)v L >cit is profitable for low and high-quality firm to sell the product and pooling equilibria exist. We proceed under this assumption. Applying the dominance criterium as the standard equilibrium refinement (see Mas-Colell, Whinston, and Green, 1995) we focus on the least-cost pooling equilibrium. The share φ p in this equilibrium is uniquely determined as the solution to A 0 (φ) =δ (λv H +(1 λ) v L )+(1 δ) v H c. The associated equilibrium profits are denoted by π p H and πp L, respectively. For this equilibrium to exist, the low-quality firm must make positive profit i.e., φ p δ (λv H +(1 λ) v L c) A(φ p ) 0. We show that the least-cost pooling equilibrium does not survive the intuitive criterion by Cho and Kreps (1987). According to this criterion, we have to show that there exists a deviation φ e that is profitable for the high-quality firm but not for the low-quality firm with the out-of-equilibrium belief that eφ is associated with high quality with probability 1. Taking the smallest value, the incentive constraint for the low-quality firm binds. Hence, φ e has to satisfy φ p δ (λv H +(1 λ) v L c) A(φ p )= e φδ(v H c) A( e φ). 7
For given φ p, there exists a unique solution φ e > φ p. To destabilize the pooling equilibrium, it remains to be shown that the deviating high-quality firm obtains a strictly higher profit than in the pooling equilibrium i.e., φ p δ ((λv H +(1 λ) v L c)+(1 δ)(v H c)) A(φ p ) < e φ(v H c) A( e φ). Using the incentive compatibility constraint of the low-quality firm, this inequality reduces to φ p (1 δ)(v H c) < e φ(1 δ)(v H c). It holds for φ p < e φ. Hence, the pooling equilibrium is unstable, in the sense that is does not survive the intuitive criterion. 4 3.3 Advertising as a Noisy Signal In this subsection, we assume that consumers do not observe φ (nor do they observe A). However, rational consumers will make inferences about product quality from all available information, especially from the fact that they have seen an ad. Assume that, in period 1, consumers expect the average quality ofaproducttobeρ, hence they pay the price ρv H +(1 ρ) v L. Assume furthermore that this price exceeds the marginal cost c, so both high- and low-quality firms produce in the first period (we will discuss the necessary condition later on). In the second period, if the consumer has learned that the value of the product is v L, he is not willing to pay more than that. Because the marginal cost exceeds his valuation, c>v L,thefirm will choose to stop production. The expected profit of a low-quality firm that spends A(φ L ) on advertising is π L = φ L (δ (ρv H +(1 ρ) v L c)+(1 δ)0) A(φ L ). Thus, the first-order condition that defines the level of advertising is A 0 (φ L )=δ (ρv H +(1 ρ) v L c) (2) 4 Note that there is also a continuum of fully separating equilibria. Here, we selected the equlibrium that satisfies the dominance criterion. 8
The expected profit of a high-quality firm that spends A(φ H ) on advertising is π H = φ H (δ (ρv H +(1 ρ) v L c)+(1 δ)(v H c)) A(φ H ). A high-quality firm s level of advertising is defined by A 0 (φ H )=δ (ρv H +(1 ρ) v L c)+(1 δ)(v H c). (3) Since A 0 (φ H ) A 0 (φ L )=(1 δ)(v H v L ) > 0 and A 00 > 0, thelevelof advertising by a high-quality firm φ H exceeds that of a low-quality firm φ L. This result is not surprising. From each consumer who is reached by advertising both, high and low-quality firms, earn the same in the first period, but the high-quality firm obtains a positive margin from any period-1 consumer in the second period. Hence, a consumer is relatively more likely to be reached by a high-quality firm; advertising (about the existence of a product) mitigates the asymmetric information problem of the high-quality firm. A consumer with self-fulfilling beliefs who becomes aware of a product through advertising expects that the product is of high quality with probability ρ with λφ ρ = H. (4) λφ H +(1 λ) φ L Clearly ρ>λ; advertising is indirectly informative as it conveys noisy information on product quality. Proposition 1 When φ is not observable, the unique equilibrium is characterized by equations (2), (3), and (4). What determines a firm s advertising expenditure? If high quality is rather valuable (high v H ), the price (at least in the first period) is higher, highquality and low-quality firms want to sell more; their advertising expenditure rises. Hence, dφ H /dv H > 0 and dφ L /dv H > 0. The argument is similar for a product with a high λ. Because the consumers ex ante expectations about product quality increases, they are willing to pay a higher price, and, hence, both firm types advertise more. The following proposition gives a complete picture of the comparative statics results. 9
Proposition 2 (Comparative Statics) In equilibrium, φ H > 0, v H φ L > 0, v H φ H > 0, v L φ L 0, v L φ H λ > 0, φ L λ > 0, φ H δ < 0, φ L δ > 0, φ H c < 0, φ L c < 0, ρ > 0, v H ρ < 0, v L ρ λ > 0, ρ δ < 0, ρ c > 0. Most comparative statics properties are straightforward. Concerning dφ H /dδ, we use the implicit function theorem, dφ H dδ = (v H c) φ H (v H c) δ A 0 (φ H ). Here, the numerator is positive. The denominator is negative because A(φ H )= (v H c) δφ H, and due to the assumptions with respect to A( ), A 0 (φ H ) > A(φ H )/φ H. Hencethederivativeispositive. Ifthemarketshareforgoods in period 1 is relatively high (high δ), then a high-quality firm must spend more on advertising in order to deter a low-quality firm from mimicking. Example To obtain a closed-form solution, we impose a functional form on A(φ). Let A(φ) =(α/2) φ 2, c =0, v L =0,andv H = v. 5 Then, for α 5 This example has the property that under symmetric information it does not matter in terms of efficience whether or not low quality is produced. However, selling the low-quality product is necessarily inefficient under asymmetric information (due to costly advertising). In addition, the example does not satisfy lim A φ(a) = 1, but is algebraically tractable. Note that this assumption on φ(a) is only needed to guarantee, in general, a unique, interior solution to various first-order conditions and has no further purpose. An algebraically less tractable example that meets all assumptions on φ(a) is A(φ) =αφ/(1 φ) this has been used in Zhao (2000). 10
1 H.5 L 0.2 0.4 0.6 0.8 1 Figure 1: Equilibrium advertising as a function of the degree of asymmetric information δ. sufficiently large such that φ H 1, the equilibrium is characterized by φ H = v (1 + (1 2δ)(1 λ)+ψ), 2 α φ L = v ( (1 2δ) λ + Ψ), 2 α λ(1 + (1 2δ)(1 λ)) + λψ ρ = with q λ + Ψ Ψ = 4 δ(1 δ)λ(1 λ)+λ 2 In Figure 1, we set α =1and λ =1/2 and plot φ H and φ L as a function of δ. In particular, this illustrates that the advertising expenditure of the high-quality firm is decreasing in δ. The extent to which consumers update their belief depends on the degree of asymmetric information δ and the level of the prior belief λ, asfigure2 illustrates (we use the same parameter constellation as in the previous figure, except that we allow for different values λ). 11
1.8.6.4.2 0.2 0.4 0.6 0.8 1 0.5 0. 25 0.1 0. 05 Figure 2: Posterior belief ρ as a function of prior belief λ and the degree of asymmetric information δ 12
4 The Role of Consumer Information In this section we point out qualitative differences between the case of observable and unobservable advertising expenditure. Our first finding is immediate: Remark 2 When the advertising expense A(φ) is unobservable, both highand the low-quality firms advertise. By contrast, when A(φ) is observable, only the high-quality firm advertises, and φ L =0. One condition is necessary for this statement. We must have that v L <c. For the opposite case v L >c, a low-quality firm would advertise in the case of observable φ. If the advertising expenditure is observable, a high-quality firm can use the advertising expense as a signal and distort the advertising upward, which is tantamount to raising φ H. If it is unobservable, the low-quality firm can hide behind the advertising effort of the low-quality firm and reduce the willingness to pay for period-1 consumption. Proposition 3 Relative to the symmetric information setting, the high-quality firm weakly overinvests if φ is observable. It strictly underinvests if φ is unobservable. As discussed in the previous section, the fact that max{φ H,φ s H} φ H establishes the first part of the proposition. Concerning the second part of the proposition, compare (3) with the equation that defines φ H, namely A 0 (φ H)=v H c. Because v H c exceeds the right-hand side of (3), φ H exceeds the solution to (3). Since a low-quality product is not advertised in separating equilibrium when the level of advertising is observable, while it is strictly positive when it is unobservable, the previous remark implies the following: Remark 3 In separating equilibrium, the difference φ H φ L is larger when the level of advertising is observable compared to when it is unobservable. 13
[missing: results on industry advertising expenditure] The following remark shows that comparative statics with respect to the degree of asymmetric information δ differ depending on whether φ is observable or not. Remark 4 If φ is observable and there is signal distortion (over-advertising), then dφ H /dδ > 0. Ifφ is unobservable, however, then dφ H /dδ < 0. The argument goes as follows. If φ is unobservable, high and low-quality firms have to pool. A higher δ then means that the information asymmetry problem becomes more severe, and the experience good character of the product becomes more pronounced. Hence, φ H and φ L converge against one another. φ H decreases, whereas φ L increases. In a separating equilibrium where φ is observable, a higher δ again implies that the information asymmetry problem is more severe. The incentives of low-quality firms to mimic the high-quality firms behavior is larger. Hence, the high-quality firms must choose a higher φ s H to make their strategy credible. There are a number of additional comparative statics that differ depending on whether φ is observable. In particular, a separating equilibrium does not depend on v L or λ. If φ is unobservable, both φ H and φ L depend on v L and λ, and so does the expected quality in the first period; dρ/dλ > 0 and dρ/dv L < 0. With observable φ, alow-qualityfirm does not produce; hence, ρ =1.With unobservable φ, a higher value of high quality v H makes advertising more valuable, especially for high-quality firms. Consequently, these firms expand their advertising volume, and the expected quality of goods increases, dρ/dv H > 0. These comparative statics properties are in principal testable. Empirical work may therefore be able to provide evidence whether the hypothesis of non-observability of the advertising expenditure is supported by the data. 14
5 Discussion A key variable in our analysis is the degree of asymmetric information. In particular, in Remark 4, we obtained qualitatively different comparative statics properties depending on whether φ is observable. Depending on the application, there are particular interpretations of δ. For instance, in the market for restaurants, in places with a small numberoftouristsrepeatpurchaseisimportantandδ takes a low value, while in places with a large number of tourists repeat purchase is less important. In other markets δ can be interpreted as the speed of changing tastes. Markets with fast changing tastes i.e., where fashions and fads are prominent are characterized by a high δ. In age-segmented markets tastes of younger people may change more frequently so that for these consumers repeat purchase is less often an option which is reflected by a high δ. In markets such as those for mobile calling plans, the duration of the contract is an important variable. The shorter the length of the contract, the higher the repurchase frequency and, thus, the higher δ. When advertising expenditures are unobservable, we should observe a negative correlation between contract length and advertising levels of high-quality firms. By contrast, when advertising expenditures are observable we should observe a positive correlation. 6 We have assumed that the net value of a low-quality product is negative, v L <c. As a consequence, if advertising was observable, a lowquality firm did not advertise at all. If we instead assume that v L >c, then a low-quality firm will produce and advertise even in a separating equilibrium. However, it will advertise more when φ is unobservable. Hence, the qualitative result that, when φ is observable, a low-quality advertises less, whereas a high-quality firm advertises more remains valid. We have assumed that firms advertise only in period 1. In period 2, the advertisements are still effective, and it is not possible to advertise anew. In a more general model, one could allow for advertising in the second period. Whether firms choose to advertise at all at date 2 depends on the structure of the cost function A(φ 1,φ 2 ) if φ 1 and φ 2 are 6 As a health warning, our insights obtain in a monopoly setting. A non-trivial extension is to include competitive effects in the analysis. 15
the levels of advertising in the two periods. For example, if A depends only on the sum φ 1 + φ 2, firms would advertise only at date 1. Now, if the structure of A is such that some firm chooses to advertise at date 2, we may postulate that low-quality firms will by then have revealed themselves to be of low quality to everybody who is informed of the existence of the product in period 2. Thus they will gone out of business in period 2, and only high-quality firms will advertise. Consequently, the possibility to advertise at date 2 can be interpreted as a bonus for high-quality firms. The level of the advertising effort at date 1 can be influenced, but the structure of the information problem of the consumer will be qualitatively unaffected. [downward sloping demand curve. To be written.] 6 Conclusion This paper has developed a simple repeat-purchase advertising model in which consumers initially neither know about the existence of a product nor the quality of an experience good. We compare a market in which the total advertising expenditure is observable to a market in which this is not the case. In the former market,the high-quality firm can fully separate itself from low quality and signal its quality through advertising. Such advertising is not fully wasteful since it makes more consumers aware of the product. By contrast, in the latter market, the high-quality firm cannot fully separate itself from low quality. However, due to the repeat-purchase effect, the highquality firm has a stronger incentive to advertise. This allows consumers to draw inferences from the fact that they see an ad i.e., the belief of consumers who become informed about the existence of the product are more optimistic than the prior belief. From a social perspective, when advertising expenditures are observable, possibly excessive advertising by the high-quality firm give rise to a welfare loss compared to symmetric information. By contrast, when advertising is not observable, insufficient advertising by the high-quality firm and excessive advertising by the low-quality firm give rise to a welfare loss compared to symmetric information. 16
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