Targeted advertising and consumer information

Transcription

1 Targeted advertising and consumer information Very reliminary, do not circulate Sébastien Broos August 2016 Abstract We consider how a single roduct monoolist should target its ads if there is some correlation between consumers information about the good s existence and characteristics, and their valuation for the good. Taking this information into account, the monoolist, in contrast to most models of targeted advertising, may decrease its rice. Surrisingly, a lower rice does not necessary lead to a higher consumer surlus or welfare because some consumers sto buying. We also highlight that if one tries to estimate returns to advertising, in addition to the selection bias identified in the literature, there is an information bias due to the relation between information and valuation. 1 Introduction Over the last few years, the avalanche of available data has allowed firms to target their advertising more and more recisely. 1 So far, the literature on targeted advertising has interreted this increased recision as an ability to better segment consumers with regard to their willingness-to-ay. It is intuitively clear that it is better to sell to consumers who are ready to ay a high rice rather than a low rice. The effect of targeting is thus to increase market ower and raise rices, at least so long as there is no cometition. We argue that firms should not only segment consumers in terms of their willingnessto-ay but also in terms of their information. Indeed, most models of targeted advertising consider either that consumers who do not receive ads have absolutely no information, or We thank articiants from the IODE 2016, the ACDD 2016 and Annual Conference of the Leibniz ScienceCamus 2016 MACCI. We also thank Bertrand Koebel for helful discussions. Liege Cometition and Innovation Institute (lcii.eu), University of Liege, sbroos@ulg.ac.be 1 See for instance: The New York Times (2010) Retargeting Ads Follow Surfers to Other Sites, The New York Times (2013) What You Didn t Post, Facebook May Still Know, Mashable (2013) The Next Wave of Ads Knows Everything About You Before You Do, The Economist (2014) How online advertisers read your mind, The Economist (2014) Getting to know you. 1

2 that erhas some consumers do but that there is no relationshi between that information and their willingness-to-ay. We show that if there is some correlation, there will be imortant effects on rice, welfare and targeting strategies. Consider the following examle. We observe two consumers, Jane and Joe. Jane is a fan of best-selling author Nassim Nicholas Taleb and regularly reads blogs and forums about Taleb s work. Joe is a casual reader who does not have strong references but sometimes reads essays. Taleb is on the brink of ublishing a new book. Using the services of an intermediary, he learns the references and the information of Jane and Joe. How should he target its ads and rice the roduct, knowing that Jane has a much higher robability of being informed about this new release than Joe and that Joe has a lower willingness-to-ay for it? In other words, what is the imact of having extra knowledge about the information that Jane and Joe ossess on the strategy of the firm? The economics literature has recognized (e.g. Goldfarb, 2014) that an imortant advantage of online over offline advertising is cheaer and better targeting. We argue that the ability to recognize consumers who are likely to buy without seeing an ad is a major overlooked feature of online targeted advertising. In the main text, we assume that there is ositive or no correlation between the information that consumers osses and their valuation for the good, at least for some consumers. We examine how a monooly firm should target its ads if it takes into account this information and the imact of that tye of targeting on rice, consumer surlus and welfare. To that end, we comare three strategies. We call targeting naive if a firm does not take into account the information that consumers have, i.e. if it targets all consumers who have a match value higher than rice. On the other hand, targeting is erfect if consumer information is taken into account, e.g. Taleb does not send an ad to Jane because she will buy his new book anyway. Finally, the firm can abstain from advertising comletely. We show that, so long as (i) advertising is not too costly nor too chea and (ii) there is a sufficient discreancy between the levels of information of different consumers, then erfect targeting is more rofitable than naive targeting or no advertising. In equilibrium, some consumers will therefore not receive ads and still buy the good. Comared to naive targeting, we show that a switch to erfect targeting leads to a lower rice. Indeed, some consumers sto buying because of the lack of ads and hence, incentives to set a lower rice are increased : the higher rice will be erceived on fewer consumers. Interestingly, a lower rice does not necessarily mean a higher consumer surlus. Indeed, erfect targeting may reduce the number of transactions and, imortantly, the consumers who sto buying because they are not targeted any more are exactly those who would have obtained the most surlus from the urchase. The imact of erfect targeting on welfare is also ambiguous. 2

3 Comaring erfect targeting to no advertising, we find that erfect targeting also has ambiguous effects on rice, consumer surlus and welfare. Indeed, while targeting imroves consumer information and therefore the number of transactions, erfect targeting may also lead to a higher rice. Welfare is also affected ambiguously. That the monoolist chooses not to target some consumers leads to some non-monotonicity results. We find that there is a non-monotone relationshi between the rice under erfect targeting and the advertising cost. Imortantly, this result translates to consumer surlus and welfare: a higher advertising cost may lead to a higher consumer surlus and welfare. The reason is that, under some conditions, a higher cost may lead the monoolist to lower its rice and thus to inform more consumers. Another reason why this set-u is interesting is because the emirical literature has established that the information that consumers ossess must be taken into account to be able to estimate returns to advertising correctly(blake et al. (2015), Ackerberg (2001)). Moreover, Lewis and Rao (2015) have shown that these returns are extremely difficult to comute. We argue that the situation is even worse than these aers suggest because there is an additional information bias, i.e. a major reason behind the better rofitability of erfect targeting is not only that firms can segment in function of willingness-to-ay, but also in function of the information that consumers ossess. The next Section discusses the related literature. Section 3 sets u the basic model and the major hyotheses. Section 4 examines the conditions under which erfect targeting is otimal and its imact on rice and welfare. Section 5 covers the information bias. Section 6 consider some extensions and robustness checks. Section 7 concludes. 2 Related literature This aer is related to multile strands of the literature on advertising. 2 First and most secifically, it contributes to the literature on advertising with exogeneously informed consumers (Meurer and Stahl (1994), Xu et al. (2012) and some extensions in Iyer et al. (2005)). These aers all consider duooly models. An imortant contribution of our article is that consumers are not randomly informed, i.e. consumers with different valuations will have different robabilities to be informed about a good s existence. This is very different, for instance, from Xu et al. (2012) where one firm always obtains more exosure, or from Iyer et al. (2005) where they allow a random share of consumers, who all have the same valuation, to be informed without receiving ads. In these models, there is no scoe for the firms to discriminate based on information. More generally, our aer is art of the literature on targeted advertising (Athey and 2 See Bagwell (2007) and Renault (2016) for literature reviews. 3

4 Gans (2010), Bergemann and Bonatti (2011), Brahim et al. (2011), Esteban et al. (2001), Esteves and Resende (2016) among many others). Tyically, this literature finds that in the absence of cometitive constraints, targeting is a way for firms to reach consumers with a high willingness-to-ay and therefore to increase their market ower. As a result, a monoolist that can target its ads will increase its rice (Esteban et al. (2001), Hernandez- Garcia (1997)). Our conclusion is (nearly) the oosite: even though a rice increase is ossible, in many circumstances, if the monoolist takes information into account the rice of the good will decrease. Indeed, because it stos advertising to highly informed consumers, a few of them will sto buying. The margin effect of a rice increase is therefore diminished. To the best of our knowledge, this effect of information has not been highlighted in revious literature literature. Desite higher rices, both Hernandez-Garcia (1997) and Esteban et al. (2001) find that targeting has ambiguous effects on consumer surlus, deending on whether targeting reduces the waste of ads (Esteban et al., 2001) or on whether it increases the number of informed consumers (Hernandez-Garcia, 1997). We find that even if the rice is lower, consumer surlus does not necessarily increase. The reason is that the monoolist does not internalize that the consumers who are most likely informed, and hence who should not be targeted, may have the highest valuation for the good. Therefore, even if only a few of them do not buy, they will have an imortant imact on surlus. That said, even a social lanner will always abstain from advertising to some consumers so long as they are sufficiently informed. We find the classical result of Shairo (1980) that a monoolist rices too high and under-advertises comared to a social lanner. Our aer is also linked to Johnson and Myatt (2006) and, more globally, to the literature on information rovision (Bar-Isaac et al. (2010), Lewis and Saington (1994), Ottaviani and Prat (2001), Saak (2008)). More recisely, Johnson and Myatt (2006) argue that advertising can contain two tyes of information: hye or real. Information is hye if a consumer learns the roduct s existence, rice, availability and any objective quality but not his own valuation, i.e. from this information, all consumers infer the same common willingness-to-ay. If information is real, a consumer learns his subjective reference for the roduct: his valuation. They argue that the rovision of hye information leads to an outward shift of the demand curve while the rovision of real information leads to a rotation of the demand curve because some consumers learn that the roduct is not a good fit. A major difference between the literature on targeted advertising and that on information rovision is that the former assumes that without advertising, consumers do not buy and thus that information is hye (there is a demand shift), while the latter assumes that consumers have a common ex-ante valuation and, after learning their true valuation, some may sto buying (there is a demand rotation). Information in that case is thus real. 4

5 Both cases can be accommodated in our model and, u to one difference, do not change our conclusions. The difference is that as the common ex-ante valuation increases, the outside otion of not advertising becomes more attractive. Otherwise, because advertising is erfectly targeted, the two situations do not affect our main conclusions: advertising will always induce a demand shift and not a rotation. Indeed, because targeting is erfectly recise, the monoolist will never send ads to consumers who have an ex-ante valuation that is higher than their true valuation. Hence, there will never be less buyers under advertising than under no advertising. If the monoolist chooses to advertise erfectly, he will do so in very similar ways regardless of the ex-ante valuation of consumers. Finally, this aer is related to the recent emirical literature on the measurement of advertising effectiveness. In articular, Blake et al. (2015) analyze the returns to search engine ads for ebay. They show that two categories of user queries should be distinguished. Brand queries are queries which contain the name of a brand, ebay in their aer. Nonbrand queries are those that do not. For instance, shoes ebay would be a brand query but used shoes would not. They show through a controlled exeriment that the returns for brand queries are not statistically different from zero. For non-brand queries, they find the same result if they consider all users. However, returns are ositive for users who have not recently urchased on ebay or those who do not buy frequently. As the recency and the frequency of urchase resectively increases and decreases, the effect of advertising becomes more imortant. In a nutshell, the less informed consumers are, the more effective advertising is. They argue that this suorts the informative view of advertising. In a different setting, ads for new yoghurts, Ackerberg (2001) reaches the same conclusion about informative advertising. Both Blake et al. (2015) and Ackerberg (2001) show that the information that consumers have should be taken into account and esecially, that a major distinction has to be drawn between consumers who are likely informed and those who are likely not. Our model analyses recisely this situation and shows that it is indeed imortant to consider consumer information. Also, Lewis and Rao (2015) show that even carefully-built randomized controlled trials numbering hundreds of thousands of observations are not owerful enough to correctly identify returns on advertising. They examine 25 large trials and conclude that the median confidence interval of returns of these trials is over 100% wide. The major reason behind this is the imortant sales volatility. They argue that to estimate roerly returns is very costly and would require an exeriment with millions of observations. This imlies that any additional bias our information bias (Section 5) for instance that could make these trials even more costly should be thoroughly analysed. 5

6 3 Model We build a model to determine the imact of consumer information on rice, rofit and welfare. 3.1 Consumers There is a unit mass of consumers, each of whom has use for maximum one unit of a roduct. Consumers are endowed with references for the roduct and have match values v distributed on [0, 1] according to log-concave density function f(v) and the corresonding cumulative distribution function F (v). 3 receiving ads. Consumers do not incur any nuisance cost from Consumers are imerfectly informed about the good. More recisely, there is an information function g(v) which links the match values of consumers and the robability they have of being informed about the goods without receiving ads. That is, a consumer with valuation v has a robability g(v) of being informed about the good and to learn his (true) valuation for it. We assume that g(v) is log-concave and invertible. The log-concavity of the information function renders the relationshi between information and the match value fairly flexible. 4 There are two imortant questions that must be considered regarding consumer information. First, how uninformed are uninformed consumers? The bulk of the aer assumes that uninformed consumers have absolutely no information about the roduct: they do not know its existence nor its characteristics. Therefore, uninformed consumers do not buy. Equivalently, we could say that they have a match value of 0. An informed consumer therefore always has a higher match value than an uninformed one. As discussed in Section 2, this is a common assumtion in most (targeted) advertising models. In Section 6.2, we consider what haens if uninformed consumers have a common valuation ṽ (0, 1]. In contrast to the revious case, it imlies that information may decrease the valuation of a consumer: a consumer with v < ṽ who becomes informed, through an ad for instance, will only be ready to be ay v instead of ṽ. This way to model the absence of information is closer to the literatures on information rovision. It does not change the nature of our conclusions although it may affect under which circumstances they hold. Second, what is the structure of information and in articular, what is the link between the information function and the match values of consumers? We assume that the valuation 3 Many standard distributions such as the uniform or the normal distribution resect log-concavity. For more on log-concavity, see Bagnoli and Bergstrom (2005). 4 Log-concavity is a sufficient condition but not a necessary one, see Section 3.2 for an examle of an information function that is not log-concave. 6

7 of a consumer and its robability to be informed are uncorrelated or ositively correlated, i.e. g (v) 0. What this means exactly is the subject of Section 4. Because it does not add much insight and comlicates the notation, the case of a negative correlation is examined in Aendix B. 3.2 The firm There is a monoolist selling one good. It is roduced at a constant marginal cost which is normalized, without loss of generality, to 0. The firm sets a uniform rice for the good (see Section 6.1 for the case of ersonalized ricing). Advertising costs a er consumer 5 and is erfectly informative: after receiving an ad, consumers know their valuation v with certainty. Equivaletnly, we could that a consumer v who receives an ad has g(v) = 1). Advertising is also erfectly recise: an ad intended for consumer v will reach consumer v. 6 The monoolist has three advertising strategies. First, if it has no access to consumer information or ignores it, the monoolist can target naively, i.e. it will target consumers based on their willingness-to-ay only. Consumers with v will receive ads. Second, the firm can advertise erfectly by using both willingness-to-ay and information to target. Formally, it can set a targeting bound v h [, 1] such that consumers between with v [v h, 1] do not receive advertising. 7 For instance, suose that the information function has the following form: 8 g(v) = 0 if v < 0.9, (1) g(v) = 1 otherwise. (2) Clearly, the monoolist should not send ads to consumers with v [0.9, 1]: they are already informed. Finally, the monoolist can choose to abstain from advertising. Because of the information function, some consumers will still be informed and it will make some rofit. Formally, 5 The linearity of the cost function is similar to that in Iyer et al. (2005). 6 The more usual convexity assumtion of the cost function (as in Grossman and Shairo (1984) or Esteves and Resende (2016) for instance) imlies decreasing returns to scale to advertising. There is no reason for this here since (i) consumers can t be reached twice inadvertently and (ii) ads do not miss their targets. 7 Note that it is easy to show that additional targeting bounds, for instance v l (, v h ) will always collase to a single bound due to the shae of the information function, which is either increasing or constant in v. See Section Note that strictly seaking, g(v) is not log-concave on [0, 1] in this examle. It is however log-concave on [0, 0.9) and in [0.9, 1]. This shows that discontinuities can easily be accommodated. This examle was chosen for its simlicity. 7

8 if nt, t and no stand resectively for naive targeting, erfect targeting and no advertising, we have the following 9 rofit functions: vh E(Π t ) = ( a) E(Π nt ) = ( a) E(Π no ) = f(v)dv + f(v)g(v)dv, v h (3) f(v)dv, (4) f(v)g(v)dv. (5) The second and the third equations (Equations 4 and 5) are limit cases of Equation 3. The former arises when = v h and the latter when < v h = 1. Therefore, we dro the subscrits and refer to these three scenarios using the same equation. We also dro the exectation oerator for clarity. We therefore have: vh Π = ( a) f(v)dv + f(v)g(v)dv, v h (6) 4 The imact of erfect targeting 4.1 When is erfect targeting otimal? The first question we want to tackle is that of the conditions under which erfect targeting is otimal, i.e. the conditions under which a monoolist maximizes its rofit by choosing (i) v h < 1 and (ii) < v h, where denotes otimal rices and bound. The first requirement states that the firm refers erfect over naive targeting and the second that it refers to advertise rather than not to advertise. The otimal v h satisfies the following first-order condition: 10 Π = ( a)f(v h ) f(v h )g(v h ) = 0 vh (1 v = g 1 a ). (7) h To satisfy requirement (i), assuming that < v h, we need that: 11 9 If there was a negative correlation between valuation and information, these rofit functions would be different. See Aendix B. 10 We assume that second-order conditions are resected. See Aendix?? for more details. 11 Note that the case where f(1) = 0 is uninteresting. Indeed, in that case, because there are no consumers at v = 1, the naive targeting scenario imlies that the targeted consumers are those with v [, ṽ] where ṽ is the highest v with ositive density. Therefore, the corner solution is not defined as v h = 1 but as v h = ṽ. This does not change any of the conclusions. 8

9 Π v h = ( a)f(1) f(1)g(1) < 0 1 a < g(1). (8) vh =1 In words, consumers with the extreme valuation of 1 should have a sufficiently high robability to be informed without advertising, such that sending them ads would be a waste of resources. More generally, this can be extended to v h smaller than any threshold valuation. This also rules out the case of a = 0. Obviously, if it is costless, there is no reason to abstain from advertising. Requirement (ii) has two different imlications. First, a should not be too high : Π = =v h v h f(v)g(v)dv (vh a)f(v h ) < 0 a < v h v f(v)g(v)dv h f(vh ) = a. (9) This is intuitive: if the cost of advertising is high, it reinforces incentives not to advertise and the firm might abstain from advertising comletely. Second, we must also have that consumers are not too informed. To take an extreme case, if all consumers are erfectly informed, there is obviously no reason to advertise. Formally: Π v h = ( a)f( ) f( )g( ) > 0 g( ) < 1 a vh =. (10) If we combine this condition with that of requirement (i) (Equation 8), we have that: g( ) < 1 a < g(1). (11) A necessary (but not sufficient) condition for this to hold is that there is some difference in the levels of information of consumers. Therefore, information functions such as g(v) = k with k [0, 1] will not lead to erfect targeting. Intuitively, in that case, it would not make sense to have a targeting strategy based on information because all consumers have the same information. To use an analogy, there would be no reason to set different rices for different consumers if they all have the same willingness-to-ay. This condition can also be reinterreted in terms of the advertising cost: it should neither be too high nor too low: 9

10 (1 g(1)) < a < (1 g( )). (12) If the advertising cost is too low, it is better to target naively. If it is too high, it is better not to advertise. The easiest case to see this is if g(v) = v. Then, it is never otimal to have naive targeting excet if a = 0. The following Proosition summarizes these conditions. Proosition 1. If: 1. g( ) < 1 a < g(1) < a < a. Then, we have that < vh < 1. There are many sets of sufficient conditions that would satisfy this Proosition. One instance is if g (v) > 0, g(0) = 0 and g(1) = 1. Let us take two examles to clarify this Proosition. Examle 1. Suose that v U[0, 1] and that g(v) = v. Then, it can be shown that so long as 0 < a < 0.244, we have < vh < 1 and erfect targeting is otimal. If a = 0, = 1 and naive targeting is otimal. Finally, if a, it is more rofitable not to v h advertise. This case is illustrated on Figure 1a Examle 2. Suose that v U[0, 1] and that g(v) = kv with 0 < k < 1. The interesting feature of this examle is that g(1) = k. Therefore, we can establish how g( ) and g(1) should vary relatively to a to obtain erfect targeting. It can be shown that 1 a/ = g(1) = k 1 leads to k 1 = (1 a)/(1 + a). We must also have that 1 a/ = k To have erfect targeting, we must therefore have k 1 < k < k This is deicted on Figure 1b. Note that both thresholds are decreasing in a: as a increases, no advertising becomes more rofitable than advertising. Also, if a < , we will never have no advertising (k 2 > 1). As shown by the examles, Proosition 1 alies to numerous situations. All we need is that advertising is not too chea nor too costly and that some consumers are more informed than others if they have a higher valuation for the good. 12 This leads to k 2 = 1 a 2a a (1+2a) We can ignore ignore the threshold resulting from the second condition above because it is weaker. 10

11 (a) Examle 1: rices and targeting bound if v U[0, 1] and g(v) = v. (b) Examle 2: how k 1 and k 2 evolve with a. Figure 1: Examles. Notes: in the left anel, the dashed curve is v h, the dot-dashed curve is, the gray line is no and the full black line is nt. In the right anel, the full black curve is k 1 and the dashed curve is k 2. Of course, the imact of consumer information is not limited to this set-u. For instance, if g(v) = k with k [0, 1], information affects rofit and targeting strategies but in a simler way: the outside otion of not advertising becomes more rofitable. We now turn to the effects of having < vh < 1 on rices and welfare. 4.2 Prices and welfare if erfect targeting is otimal For the remainder of this aer, we assume that the conditions of Proosition 1 are fulfilled. Let us start by analysing rices, for which we highlight three conclusions. For clarity, we slit rofit in three cases again: Π if < vh < 1 (targeting is erfect), Π nt if vh = 1 (targeting is naive) and Π no if = vh (there is no advertising). The first-order conditions, with regard to rice, are the following: 14 Π Π nt Π no = = = vh v h f(v)g(v)dv + f(v)dv ( a)f( ) = 0, (13) f(v)dv ( a)f() = 0, (14) f(v)g(v)dv f()g() = 0. (15) Denote by nt and no, resectively the otimal rice under naive targeting and under 14 In the case of naive targeting and no advertising, the second-order conditions with regard to rices can safely be ignored because (i) the roduct of two log-concave functions is a log-concave function and (ii) log-concavity imlies an increasing hazard rate. Hence, the second-order conditions are satisfied, see Tirole (1988). For the second-order conditions related to the erfect advertising case, see Aendix??. 11

12 no advertising. Our first result is that < nt. In other words, when the monoolist targets in function of both willingness-to-ay and information, it sets a lower rice than when it only takes willingness-to-ay into account. The reason is simly that vh < 1. To see why, suose that the two rices are equal and that they are lowered by a small amount. We have the two traditional effects of a change in rice in a monooly setting: (i) the firm loses the rice differential on consumers to whom it sells but (ii) it gains some additional consumers. That second effect is the same whether the firm targets erfectly or naively because these consumers receive ads. However, the first effect is different. Indeed, the lost rofit is comuted on consumers who actually buy. For consumers between and vh, it does not make a difference: they all buy regardless of the targeting strategy. But for those between, vh and 1, the effect is smaller under erfect targeting: all consumers buy under naive targeting but only those who are informed make a urchase under erfect targeting. Formally, this can be seen by rewriting the first-order condition in the naive case as follows: Π nt = v h v h f(v)dv + f(v)dv ( a)f() = 0. (16) This conclusion contrasts strongly with the literature on targeted advertising. In general, targeting is seen as a device that enables firms to reach consumers with a high willingness-to-ay so that rices can be raised. Here, better targeting lowers the rice. Second, we find that is not necessarily monotone increasing in a, i.e. as a increases, can either increase or increase. The reason is again that vh < 1. The imact of a change in a on can be decomosed in two terms: d da = a + vh vh a. (17) It can be shown that the first term is always ositive, 15 but the sign of the second term is undetermined. In many cases, their sum is ositive for all a, for instance if v U[0, 1] and g(v) = v, but in others it can become negative, e.g. if v Kumaraswamy(2, 5) and g(v) = v. Rather than use the cumbersome exressions that result from the alication of the imlicit function theorem, let us try to rovide some intuition using grahical examles 15 Using the imlicit function theorem, we have that: a = f( ) 2f( ) ( a)f ( ) = f( ) > 0. (18) 2 Π 2 12

13 Figure 2: Equilibrium rices and targeting bound if v Kumaraswamy(2, 5) and g(v) = v. Notes: the dashed curve is v h, the dot-dashed curve is, the gray line is no and the full black line is nt. Note also that for the Figure to be as clear as ossible, we only show the range where a [0.09, ] with the uer bound equal to a. (Figures 2 and 3) reresenting the case where v Kumaraswamy(2, 5), and g(v) = v. 16 Figure 2 shows that indeed, for some values of a, is increasing but, for others, it is increasing. Figure 3 is most helful to understand this result. The solid line reresents the distribution of willingness-to-ay f(v), i.e. the demand the monoolist would face if all consumers were informed, while the dotted line is f(v)g(v), i.e. the demand the monoolist would face if no ads were sent. From Figure 2, we see that there is a clear asymmetry between v h and : as a increases, v h decreases much faster than increases This is intuitive: increasing leads to less demand with certainty while lowering v h leads to less demand with some robability only. robability of not buying for a consumer with willingness-to-ay v is reresented grahically on Figure 3 by the difference between f(v) and f(v)g(v). Suose first that a = 0.1 and that it increases slightly. The At a = 0.1, we have that = and vh = The situation is reresented on Figure 3a. The first term in the first-order condition (Equation 13) is Area A, the second term is Area A +B+C and the third term is Area D. Now suose that a increases slightly. This imacts the first-order condition in the following ways. First, the first and the second term are affected by the subsequent decrease in v h. The first term of the first-order condition becomes Area A+A. The second term becomes B. Overall, the sum of the two term decreases by C, which is 16 The use of this relatively obscure distribution is due to the simlicity of its closed-form exression. Given enough comuting ower, there is no limitation on using other, more common, distributions. For more details on the Kumaraswamy distribution, see Aendix C. 13

14 (a) A change in a if a = 0.1. (b) A change in a if a = 0.2. Figure 3: Changes in a if v Kumaraswamy(2, 5) and g(v) = v. Notes: the full black curve if f(v). The dashed curve is f(v)g(v). quite small. Second, the rise in a leads to a decrease (in absolute value) in the third term (D becomes smaller). Because C is small, the sum of the effects becomes ositive and the rice rises. The same exercise at a = 0.2 ( = 0.37 and vh = 0.46) leads to a different conclusion. Now we see that Area C is much bigger, i.e. when the uer targeting bound is lowered, many consumers sto urchasing because they are uninformed. However, the third term of the first-order condition (Area D) is imacted aroximatively in the same way as in the revious scenario because has not changed much. Here, the loss of C is more imortant than the loss in D and the rice must decrease. The intuitive reason behind this is that there are two effects to a rise in rice: a negative demand effect and a ositive margin effect. As a increases, the negative demand effect remains quite constant but the ositive margin effect becomes smaller because of the lower v h. If a is sufficiently high and the effect of a lower v h on demand sufficiently strong, it can be that the demand effect overcomes the margin effect and that it is better to decrease the rice to benefit from more demand. This is similar to the reason why < nt. Naturally, the existence and scoe of this effect will deend very much on the shaes of the willingness-to-ay distribution and of the information function. A corollary of this result is that if the rice can decrease in a, then there is no a riori ordering of and no. This is quite surrising and due to the ossible non-monotonicity of the erfect targeting rice. We summarize these results in the following Proosition. Proosition 2. We have the following rice effects: 1. < nt. 14

15 2. is not necessarily monotone increasing in a. 3. < no or no. Proof. See Aendix A for details. The imact of erfect targeting on rice therefore deends highly on the counter-factual situation. Moreover, this Proosition contrasts strongly with the literature on targeted advertising. In general, targeting is seen as a device that enables firms, esecially in a monoolistic context (Esteban et al. (2001), Hernandez-Garcia (1997)) to reach consumers with a high willingness-to-ay so that rices can be raised. The reason for that difference is the correlation between willingness-to-ay and information. The effect of erfect targeting on consumer surlus also deends on the counter-factual. Formally, consumer surlus is: CS = CS nt = CS no = v h f(v)(v )dv + nt no f(v)(v nt)dv = vh v h nt f(v)g(v)(v )dv, (19) f(v)(v nt)dv + v h f(v)(v nt)dv, (20) f(v)g(v)(v no)dv. (21) Let us first comare erfect and naive targeting. A move to erfect targeting imacts consumers in two ways. There is a rice effect which is unambiguously ositive: consumers ay a lower rice. But there is also a demand effect which is ambiguous: more consumers buy because of the lower rice but other consumers sto urchasing because vh < 1. Imortantly, consumers that do not buy and have v [vh, 1] have a strong negative imact on consumer surlus because these are exactly the consumers who would benefit the most from a urchase. The monoolist does not internalize this at all since it can only set a single rice. 17 The global imact of erfect targeting on consumer surlus is therefore ambiguous. A lower rice is not necessarily synonymous with a higher consumer surlus. The ambiguity remains if we comare erfect targeting with no advertising but for oosite reasons. There will always be a ositive demand effect from erfect targeting because at least some consumers will receive ads and be better informed than under no advertising. The ambiguity therefore hinges on the non-monotonicity of the rice under erfect targeting. If < no then, unambiguously, CS > CS no. On the other hand, if > no, it is ossible, but not always the case, that CS < CS no. 17 See Section 6.1 for the case of erfect rice discrimination. 15

16 (a) v U[0, 1] and g(v) = v. (b) v Kumaraswamy(2, 5) and g(v) = v. Figure 4: Consumer surlus. Note: the dashed curve is CS, the gray line is CS no and the full black line is CS nt. Because of the non-monotonicity of, consumer surlus is also non-motonone in a: if decreases in a, it is ossible that consumer surlus increases in the advertising cost. These effects are illustrated on Figure 4. The ambiguous effects of erfect targeting on consumer surlus also affect welfare (defined as the sum of rofit and consumer surlus). It is therefore unclear a riori whether the switch to erfect targeting increases or decreases total surlus desite a ossible lower rice. The non-monotonicity result also carries on to welfare. Generally, welfare will decrease in a, but it is ossible that it rises (see Figure 5) if consumer surlus increases sufficiently so that the loss in rofit is more than comensated. These results are summarized in the following Proosition. Proosition 3. The imact of erfect targeting on consumer surlus and welfare is ambiguous. A lower rice guarantees neither a higher consumer surlus nor a higher welfare. Under erfect targeting, consumer surlus and welfare are not necessarily monotone decreasing in a. Proof. See the examles in Figures 4 and First-best Finally, we would like to comare the erfect targeting outcome with what a social lanner would choose. The social lanner maximizes the following function: 16

17 Figure 5: Welfare if v Kumaraswamy(2, 5) and g(v) = v. Note: the dashed curve is W, the gray line is W no and the full black line is W nt. Note also that a [0.16, ] so that the different effects are dislayed clearly. W = CS + Π = ( a) vh vh f(v)dv + f(v)g(v)dv + f(v)(v )dv + f(v)g(v)(v )dv (22) v h v h The first-order conditions, after some algebra, are: W = ( a)f() = 0, (23) W v h = v h (1 g(v h )) a = 0. (24) Let us call w and vh w the rice and targeting bound that maximize welfare. From the first-order conditions, it is easy to verify that w = a, i.e. we get the usual result that rice should be equal to marginal cost. Unsurrisingly, we find that so long as erfect targeting is otimal, vh w > v h. The social lanner takes into account that consumers with a high v have a high imact on consumer surlus and, accordingly, targets more of them. That said, even a social lanner does not target naively: v w h < 1. We summarize these findings in the following Proosition. Proosition 4. w = a < and vh < vw h high and targets too narrowly. < 1. A monoolist targeting erfectly rices too Proof. The rice result is obtained directly from the first-order condition. For the second 17

18 result, we have that: W v h = vh vh =vh Given that < vh, this exression is strictly negative. (1 a ) ( v ) a = a h 1 < 0 (25) This is reminiscent of the classical result of Shairo (1980): a monoolist advertises too little because it can not extract the surlus of high valuation consumers (who, here, are most likely informed anyway). Interestingly, because vh w < 1, a is not incurred for all consumers and the welfaremaximizer allows the monoolist to make a ositive rofit on consumers to which ads are not sent. 5 Returns to advertising We have highlighted in the introduction that (i) returns to advertising are extremely difficult to comute (Lewis and Rao (2015) and (ii) they seem to be very low and deending on the way consumer information is taken into account (Blake et al. (2015)). Lewis and Rao (2015) exlain that the difficulty to comute returns stems from two issues. First, individual-level sales are very volatile. Second, there is a selection bias because of the targeted nature of the advertising, i.e. ads are not targeted to consumers through luck but because these consumers are selected as those to whom sending ads is the most rofitable. Therefore, comuting returns by comaring, within the same market, consumers who have seen ads and have urchased and those who have not seen ads and have urchased is misleading. The selection bias can be illustrated easily using our model. We argue that there is an additional bias, which we call the information bias. Suose that a firm, which advertises otimally, wants to know the returns to its ads and turns to a marketer. That marketer will comute returns to advertising using his usual methods which seem to be the industry standard, see 18 e.g. Abraham (2008) that is, he will comare consumers who see ads and those who do not. Therefore, returns will be comuted in the following way: Biased Returns = vh f(v)dv 1 v f(v)g(v)dv h a 1. (26) vh f(v)dv 0 The numerator is the difference between revenues on consumers with v [, v h ] those 18 This is also argued by Lewis and Rao (2015) and Blake et al. (2015) 18

19 who see ads and revenues on consumers with v [vh, 1] those who do not see ads. The denominator is the difference between the advertising exenditures on these same grous of consumers. The obvious mistake is that the choice of consumers who see ads is not random. Both and vh, the targeting bounds, are endogenous. In other words, the assumed counter-factual is wrong: if it was not advertising, the monoolist would not set = and v h = vh. Suose now that our marketer has read Blake et al. (2015) and Lewis and Rao (2015) and wants to correct for the selection bias by using the right counter-factual. He knows that what he should comare is one market where ads are sent and one where they aren t (in other words, he should erform an exeriment). He comutes returns in the following way: Less Biased Returns = v h f(v)dv no f(v)g(v)dv no a 1. (27) vh f(v)dv 0 This corrects for the selection bias: the second member of the numerator is now the right revenue under no advertising. Still, there remains a bias, which we call the information bias : the monoolist consciously chooses v h < 1. Therefore, returns should also take into account that revenues on consumers with v > vh are exactly the reason why erfect targeting is so much more rofitable than naive targeting or no advertising. The correct returns should be: Unbiased Returns = v f(v)g(v)dv + v h h f(v)dv no f(v)g(v)dv no a 1. (28) vh f(v)dv 0 These three returns are illustrated on Figure 6 for the case where v U[0, 1] and g(v) = v. We see that in this case, correcting for the selection bias only will lead to an underestimation of the true returns to advertising. This difference grows with a and this is intuitive: it is recisely when advertising is exensive that abstaining to advertise to consumers who are already informed is the most rofitable. Taking into account the information bias by correcting for the endogeneity of vh is therefore imortant because it can lead to very different estimates of the returns to advertising. Blake et al. (2015) exlain that advertising returns are very low excet if they break down users between those who have urchased recently on ebay and those who haven t. The effect of advertising on those who haven t seems to be ositive. That is intuitive: it can be argued that they are exactly those consumers who would not have urchased if they had 19

20 Figure 6: Different ways to comute returns if v U[0, 1] and g(v) = v. Note: the dashed curve denotes the biased returns, the gray curve the less biased returns and the black line the unbiased returns. not seen ads. However, they state that Attributed sales are total sales of all urchases by users within 24 hours of that user clicking on a Google aid search link. This is equivalent to our vh f(v)dv. That is, they only take into account the sales made by users who have clicked on the ad. If there is indeed an information bias, this may be a roblematic way to comute returns because it does not take into account that some of the users who bought without seeing an ad did not see it exactly because the firm knew they would buy. The rofitability of targeted advertising may therefore be underestimated. Could it be a reason for their finding of the low returns of ads? Perhas, but this would require emirical verification and is beyond the scoe of this aer. 6 Extensions 6.1 Personalized ricing If a firm knows the valuation of consumers for its good, a natural extension of our framework is ersonalized ricing or erfect rice discrimination. Since the firm can not control the way consumers become informed if they do not receive ads, we make the following assumtions: 1. Consumers who receives ads face ersonalized rices (first-degree rice discrimination). 2. Consumers who do not receive ads face a uniform rice. The firm thus decides who faces which rice. 19 For instance, if it is a third-arty that 19 Note that some consumers will be informed and will nevertheless receive ads. This can be ignored so long as the uniform rice is higher than the ersonalized rice, which is the case. 20

21 sells ads, it may be the only one with access to the information about consumers. Consumers who become informed without advertising may therefore not be identifiable by the selling firm and hence, it can not offer them a ersonalized rice. The rofit in that case is Π d = a (v a)f(v)dv + f(v)g(v)dv (29) The first term reresents rofit made on consumers who face erfect rice discrimination while the second term is rofit on consumers who do not receive ads and face a uniform rice. Intuitively, it is clear that not advertising to a consumer is more costly than in the model with a uniform rice, instead of losing, the monoolist loses the entire valuation (minus a) of the consumer. Therefore, the conditions under which erfect targeting arises are more stringent than in the uniform rice scenario. Formally, denoting the otimal rice in this case by, the first-order condition is: Π d = ( a)f( ) + f(v)g(v)dv f( )g( ) = 0 (30) And the requirement to have < 1 is therefore: Π d 0 g(1) > 1 a. (31) =1 So long as a > 0, 20 this requirement is strictly suerior to the requirement to have v h < 1 in Section 4, which is g(1) > 1 a/. If this condition is satisfied, the firm will increase its rofit by targeting erfectly. We define naive targeting as = Consumers also benefit unambiguously from erfect targeting. Nothing changes for consumers who face erfect rice discrimination: their surlus is zero. However, consumers with v [, 1] are bound to gain. Under naive targeting, they face erfect rice discrimination and their surlus is zero. Under erfect targeting on the other hand, they face a uniform rice and consumer surlus has to be ositive. The fact that some consumers face instead of v is the analogue of the < nt 20 See Footnote 11 for a discussion of the (uninteresting) the case where f(1) = We do not examine the case of no advertising as it would only arise under extremely high advertising costs. It can be shown that in this case, erfect targeting will increase the rice and have ambiguous effects on consumer surlus (a higher rice but less informed consumers) and welfare. 21

22 result in Section 4. Formally, we have that: CS d nt = 0, (32) CS d = (v )f(v)g(v) > 0. (33) Since both rofit and consumer surlus increase, erfect targeting also increases welfare. By taking into account information, the monoolist wastes less resources on advertising for consumers who are likely to be informed. Consumers benefit because some face a uniform rice and obtain ositive surlus. The conclusions are therefore slightly stronger than those in the main model. That said, the assumtion of erfect rice discrimination is also much stronger. In slightly different settings, more ambiguous results may reaear. One examle would be to have only two different rices ( and ), one targeting bound (v h such that < < v h ) and that informed consumers who do not receive ads ay the higher rice ( ). Then, consumer surlus (and hence also welfare) may suffer from erfect targeting because it may be that more consumers face the high rice. 6.2 The valuation of uninformed consumers A major assumtion of the model of Section 4 is that uninformed consumers have absolutely no information about the good, i.e. they have v = 0. What haens if instead they have a common rior valuation and that advertising/information reveals their true valuation? As highlighted in Section 2, this setting is closer to the literature on information rovision. Formally, suose that uninformed consumers have valuation ṽ [0, 1]. If ṽ = 0, we are back to the main case. The monoolist has two strategies to maximize rofit. First, it can set ṽ and nearly all consumers buy: only those with v < and who are informed will not urchase the good. The downside is that is constrained to be low. Here, advertising has no role lay. Sending ads to consumers with v < ṽ would decrease demand and increase costs while sending ads to consumers with v ṽ is useless: they are already buying and nothing more can be extracted out of them. In equilibrium, it is likely that the constraint is binding ( = ṽ). Indeed, setting a lower rice would mean a lost margin on all buyers while only attracting some of those with v < ṽ and who are uninformed. Second, the firm can set ṽ and in that case, we are back to the general framework, with the additional rice constraint. Indeed, without being informed or receiving ads, all consumers will abstain from buying. The fact that ṽ > 0 does not change anything to rices and surlus so long as the rice constraint is not binding If the rice constraint is binding but the monoolist still chooses to advertise, rofit is reduced but 22

23 Formally, rofit is resectively: Π = 0 Π = ( a) f(v)(1 g(v))dv + vh f(v)dv if ṽ, (34) f(v)dv + f(v)g(v)dv v h if > ṽ. (35) The interesting imact of having ṽ > 0 is thus that it increases the rofitability of not advertising. So long as the monoolist chooses to advertise, the nature of the conclusions of Section 4 does not change. 6.3 Other targeting bounds We show in this section that having an additional bound v l (, v h ) is never a rofitmaximizing strategy. To see this, write the rofit as: vl vh Π = f(v)g(v)dv + ( a) f(v)dv + f(v)g(v)dv (36) v l v h The first-order condition of this equation with regards to v l and v h are Π v l = f(v l )g(v l ) f(v l )( a) = 0, (37) Π v h = f(v h )( a) f(v h )g(v h ) = 0. (38) If both first-order conditions are satisfied, then we have: v l = v h = g 1 ( 1 a ). (39) In that case, there is no advertising. Therefore, for advertising to be ossible, we need a corner solution for at least one of the variables. If v l =, we are back to our mainstream case and the oint is roven. We show that the other corner solution, vh = 1 can not arise. If vh is a corner solution, then, from Equation (38): consumer surlus (and welfare) is affected ambiguously. Indeed, while consumers suffer from the higher rice, the constraint on also has an imact on v h and it is a riori unclear how these two effects will interact. 23

24 g(1) < 1 a. (40) But from Equation (37), we also have that: g(v l ) = 1 a. (41) This imlies that g(1) < g(v l ). Given g (v) 0, this is a contradiction and the oint is roven. 7 Conclusion We have tried to show how the relationshi between information and valuation can influence market outcomes. We have highlighted that this relationshi can have many consequences for rices and welfare. To the best of our knowledge, these effects had not been described in revious literature. This work is also imortant for emiricists who try to determine what the returns to advertising are. That said, we have worked with a very stylized model which has been useful to make our major oints and there are many issues that we have ignored. First, there is the obvious issue of cometition. How would advertisers behave if they knew that there is another firm that could steal consumers to which they do not send ads? Although that tye of set-u has been artially analysed by the literature, as highlighted in Section 2, it may be interesting to consider the interlay of cometition and the fact that eole may be informed without ads. We have also assumed that the information contained in the ads is comlete and truthful. One way to extend the model would be to consider artial information. For instance, an ad may contain only the mean valuation of consumers and may lead some of them to buy even though their true valuation would be lower than the rice. This would be esecially interesting in a cometitive setting. One could also imagine that the content of an ad may deend on the match value of the targeted consumers. Another way to extend the model would be to include false information that is, the advertiser may lie about the match value of consumers. This would be difficult to include in our current set-u as there would be reutation issues. Finally, it may be interesting to model more recisely the way ads are sold and bought. Indeed, it may be that erfect advertising leads to a decrease in the number of ads. Hence, an ad seller might have incentives not to imlement the best advertising technology because 24