Consumer Referrals. Maria Arbatskaya and Hideo Konishi. October 28, 2014

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1 Consumer Referrals Maria Arbatskaya an Hieo Konishi October 28, 2014 Abstract In many inustries, rms rewar their customers for making referrals. We analyze the optimal policy mix of price, avertising intensity, an referral fee for monopoly when buyers choose to what extent to refer other consumers to the rm. We n that the rm uses its referral fee, but not its price or avertising level, to manage referrals. When consumers hol correct expectations about the true quality of the prouct, the rm charges the stanar monopoly price. The rm always avertises less when it uses referrals. We exten the analysis to the case where consumer referrals can be targete. Keywors: consumer referral policy, wor of mouth, referral rewar program, targete avertising, prouct awareness. JEL numbers: C7, D4, D8, L1. Maria Arbatskaya, Department of Economics, Emory University, Atlanta, GA Phone: (404) Fax: (404) Hieo Konishi, Department of Economics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, MA Tel: (617) Fax: (617) Acknowlegments Thanks are ue to two anonymous referees for their helpful comments an especially to the Eitor Ben Hermalin for his amazingly insightful an etaile comments. We also woul like to thank Michael Grubb, Rick Harbaugh, Maarten Janssen, Dina Mayzlin, an participants at the International Inustrial Organization Conference, the Southern Economic Association Meetings, an the Economics of Avertising Conference for valuable comments an suggestions. 1

2 1 Introuction Firms often pay existing customers for referring potential customers to the rms proucts or services. For example, DIRECTV s Referral O er promises a $100 creit to any customer for referring a frien who signs up for the company s service. Referral policies are aopte in a variety of inustries, incluing banking, health care, web esign services, home remoeling, housing, vacation packages, home alarm systems, an high-spee Internet connection. They are use in the recruitment of nurses an technicians, as well as in selling cars, houses, an tickets to sporting events. Private schools, octors, an aycare centers give out referral bonuses as well. 1 Such referral programs are often seen as Win/Win/Win because existing customers, potential customers, an rms all bene t. This is not surprising, given consumer referrals raise consumer awareness about the prouct. They can also reuce consumer uncertainty about the prouct s quality or t. For experience goos, recommenations of other people can be more informative than irect avertising because they are more trustworthy. Potential buyers trust their friens an personal acquaintances to provie honest opinions about the prouct. 2 Oftentimes, consumers also have superior information about other consumers preferences. For example, when consumers belong to a social group or network, the members of that group ten to have similar tastes or simply know more about each other. Consumer referrals can then be better tar- 1 A casual observation of referral policies suggests that referral rewars are usually pai out to existing customers for referring new customers who buy the prouct. Referral payments are typically mae in the form of cash, eposit, gift certi cate, bonus points, free prouct or service, or entry into a lottery. 2 Accoring to Nielsen s 2012 Global Trust in Avertising Survey of 28,000 Internet responents from 56 countries, consumers aroun the worl continue to n recommenations from personal acquaintances by far the most creible: 92 percent of responents trust ("completely" or "somewhat") recommenations from people they know an 90 percent n these recommenations ("highly" or "somewhat") relevant. In comparison, as are foun trustworthy or relevant by percent of responents, epening on the meia. 2

3 gete than avertising, which explains why rms often rely on consumer referrals to sprea information about the existence of proucts an their vertical an horizontal characteristics. This paper explores the features of a rm s optimal referral policy. Designing an optimal referral policy is complicate by the interactions among a rm s pricing, avertising, an referral policies. A critical part of our analysis is that we enogenize consumers ecisions about how engage they wish to be in making referrals. To our knowlege, no other stuy has taken such a comprehensive approach to eveloping an analytical moel of consumer referrals. In our base moel, we introuce consumer referrals into an experience goo market serve by a monopoly. Some consumers can become informe about the existence of the prouct an its price irectly from the rm s avertisements. These "informe" consumers ecie whether or not to purchase the prouct base on the expecte prouct quality. Consumers who purchase the prouct recognize its true quality an ecie to what extent to refer other consumers, sharing information about the true prouct quality. The rm s referral policy provies a monetary rewar (referral fee) for each successful referral. Consumers can make multiple referrals at a constant marginal cost. Since referrals are sent inepenently an at ranom, in equilibrium, there is congestion in referral messages. The rm can manage referral incentives in our moel by changing its policy mix (price, avertising intensity, an referral fee). In this framework, our main question is whether the rm woul set a higher or lower price in the presence of consumer referrals. On the one han, the referral fee as to the marginal cost of selling the prouct, which prompts the rm to raise its price. On the other han, a higher price reuces the purchase probability, iminishing referral incentives. It is 3

4 therefore not clear in which irection the optimal price woul move. We also answer the following questions: when woul a rm use consumer referrals, woul it engage in more or less avertising uner referrals, an what are the overall welfare e ects of referral policies? We rst characterize the consumer referral equilibrium for any nite number of referring consumers an any policy mix chosen by the rm (Proposition 1). By consiering a large population of consumers, we then analyze the rm s optimal policy an, in particular, its pricing strategy. We n that the pro t-maximizing price is the monopoly price for the mixture of consumers it faces, as long as the referral fee is optimally chosen (Proposition 2). In particular, when consumers hol correct expectations about the true quality of the prouct, the rm charges the stanar monopoly price (Corollary 1). The rm uses its referral fee to manage the referral activity an its price to maximize the pro tability of sales to consumers aware of its prouct. We show that when the referral fee is set below the optimal level or the marginal referral cost is increasing, the rm sets its price below the monopoly level. We also show that the rm always avertises less when it uses consumer referrals. We provie comparative static results for the optimal policy mix (Proposition 3) an show that the rm chooses to use referrals as long as the referral cost is not too high (Proposition 4). We also explore if a referral policy woul be pre-announce by the rm as a part of its avertising message an n that it woul not o so because some consumers elay their purchases waiting for recommenations to resolve the uncertainty about the prouct quality (Proposition 5). Naturally, consumers may have better information than the rm about other consumers valuations for the prouct. This informational avantage allows them to target their re- 4

5 ferrals. To stuy targete referrals, we assume that there are two groups of consumers: high-type an low-type. High-type consumers ten to have higher valuations than low-type consumers. Although the rm cannot tell which group consumers belong to, consumers can. If willingness-to-pay istributions are signi cantly i erent across groups, then only high-type consumers receive referrals, the price is higher, the ratio of referral fee to pro t margin is lower, an the avertising level is lower uner targete referrals than in the case of consumers unable to tell which group others belong to (Proposition 6). Quite intuitively, if consumers have better information, the monopoly relies less on avertising an more on referrals. The proofs not foun in the text are in the appenix. 2 Brief Literature Review A few streams of literature are relevant to our moel. First, there is the literature strictly on consumer referrals: Jun an Kim (2008), Byalogorsky et al. (2005), an Galeotti an Goyal (2009). Jun an Kim (2008) assume a nite chain of consumers with i.i.. ranom valuations. Consumers are rational an forwar-looking - they consier the expecte bene t from giving a referral when making their purchase ecisions. The authors show that even though the rm sets a common price an referral fee, it e ectively price-iscriminates between the consumers locate early in the chain (who are more valuable to the monopoly) an those later in the chain. 3 Byalogorsky et al. (2005) take the same setup as Jun an Kim (2008), but aopt a behavioral assumption that consumers make referrals whenever the expecte utility from making a referral excees a critical level of "consumer elight." When consumers are easy to 3 Arbatskaya an Konishi (2014) justify the tie-breaking rule use in the paper, showing that e ective price iscrimination is inee a common feature of the moel in the secon-best environment (with a common referral fee an same price for all consumers) an the rst-best environment (with a su cient number of policy tools). 5

6 elight, a referral program woul not be use because referrals woul be mae even without it. But when consumers are not so easy to elight, the rm woul use both a positive referral fee an a lower price. These papers rule out referral congestion. 4 In contrast, Galeotti an Goyal (2009) consier a more complex network moel in which consumers make multiple referrals with no cost. They analyze the optimal avertising policy an show that using consumer referrals woul unambiguously increase pro ts. At the same time, an increase in the level of social interaction can increase or ecrease the level of avertising an pro ts. While they concentrate on the relationship between network structure an optimal avertising strategy, we assume a simple complete network an analyze the optimal policy mix for the rm when consumer referral ecisions are etermine enogenously. The secon stream of literature focuses on avertising an congestion. In his pioneering paper, Butters (1977) formulate a competitive moel of avertising in which rms sen a number of as to consumers ranomly, informing them about the existence of the prouct an its price. Butters shows that price ispersion occurs in equilibrium. In his moel, some portion of as are waste ue to congestion, but the level of congestion (the number of as) is socially optimal. Van Zant (2004), Anerson an e Palma (2009), an Johnson (2013) present alternative information congestion moels in which consumers ignore some avertisements they receive. 5 They all show that, as the number of as ecreases, both rms an consumers are better o ue to a reuction in congestion, though the reasons for 4 The papers o not consier avertising as an alternative communication channel. In contrast, Mayzlin (2006) looks at the case where avertising an wor of mouth are both use to in uence consumer choices between vertically i erentiate proucts. While in her moel consumers cannot istinguish between promotional chat an consumer recommenations, in our moel, avertising an referrals are two istinct information channels. 5 Van Zant (2004) assumes that all consumers can process up to a certain number of as, while Anerson an e Palma (2009) assume that a consumer s cost of processing as epens on the number of as she receives. Johnson (2013) allows consumers to ecie what fraction of as to block. 6

7 this result i er. In contrast, in our moel, referrals are subject to congestion because we enogenize the referral intensity. Despite the presence of referral congestion, referrals are unerprovie in our monopoly moel. There is also literature on targete avertising. Van Zant (2004) an Johnson (2013) assume that rms sell heterogeneous proucts an have some information about consumer preferences. They analyze targete avertising policies in oligopolistic markets (Van Zant, 2004) an competitive markets (Johnson, 2013). Although the mechanisms are i erent, both papers show that improve targeting increases rms pro ts an makes consumers better o. Esteban et al. (2001) consier a monopoly choosing between mass an targete avertising. With targete avertising, the number of waste as is reuce, but the monopoly power increases. The authors show that the latter welfare loss tens to excee the former bene t. Galeotti an Moraga-Gonzalez (2008) analyze a simple oligopolistic moel of targete avertising an show that market segmentation generates higher profits in equilibrium. These papers assume that rms possess information on consumer types an therefore can conuct targete avertising. In contrast, we assume that consumers have superior information an the rm uses them as sales agents. 3 The Moel of Consumer Referrals Each of N consumers purchases at most one unit of a prouct. A consumer s utility from the prouct is the sum of a common match (quality) parameter an an iiosyncratic value v, net of the price p of the prouct: u + v p. Consumers iiosyncratic values v follow a known istribution function G (), with a log-concave survival function 1 G () an a continuously i erentiable ensity g, e ne on [v; v] with v 0. Prouct quality is ex 7

8 ante unknown to consumers. We assume that consumer beliefs about prouct quality follow a known istribution function F, e ne on [; ] with 0. We enote by e the expecte quality of the prouct, e R F (). After purchasing the prouct, a consumer realizes the value of. The rm is choosing its (non-iscriminatory) price p 0, its level of avertisement a 2 [0; 1] (a fraction of consumers reache by avertisements), an a referral policy characterize by a referral fee r 0. The marginal cost of prouction is c 0. 6 Avertisements inform consumers about the existence of the rm s prouct an its price, while referrals also inform them about the true quality of the prouct. 7 Only consumers who are informe of the prouct through an avertisement ("the informe") or a referral ("the fully informe") can purchase the prouct. In the base moel, we assume that the rm informs consumers about its referral program only after they purchase the prouct. 8 Then, the informe consumers purchase the prouct whenever their values v satisfy v + e p, which happens with probability (p; e ) = 1 G (p e ). Consumers can attempt to collect referral fees by referring other people. The number of referrers is enote by n. The expecte value of n is a (p; e ) N because a consumer nees to receive an a an purchase the prouct to be able to refer. Each referral attempt costs 6 To avoi issues with signaling a prouct s quality, we assume that the marginal cost of prouction c is the rm s private information an that consumers o not upate their belief about upon receiving an avertisement. In Section 7.5, we consier the case where the rm itself is not aware of the true quality. 7 We assume that referrers honestly inform others about the true prouct quality. In our moel, consumers inee o not have an incentive to oversell the prouct to others because, in the referral equilibrium, they obtain a zero expecte net referral bene t. 8 For example, a aycare woul sen the following message to its current families: "You may or may not be aware that you can earn a free week of chilcare by referring a family to our program." This assumption implies that consumers who become informe through as o not anticipate participating in a referral program. The assumption prevents consumers who receive as from elaying the purchase until the uncertainty in is resolve by a referral. In an extension to our moel, we show that the rm may inee prefer not to announce its referral policy as a part of its avertising message. 8

9 > 0, which captures the cost of informing a contact about the prouct an its quality. On the bene t sie, referral attempts can be successful or unsuccessful. If a referrer s contact has a low willingness-to-pay an/or is alreay informe, the referral attempt will not be successful. Furthermore, potential referrals may have been contacte by others an may assign creit for the referral to another person. Referrers simultaneously an inepenently choose the probability q 2 [0; 1] of sening a referral to other consumers at ranom, but without contacting the same person more than once. 9 As more referrals are sent out, an increasingly smaller fraction of referrals are successful. The referral reach R is the fraction of all consumers reache by referrals. When each of n consumers refers a given consumer (who is not a referrer) with probability q, the reach is escribe by R = 1 (1 q) n. The per-consumer number of referrals sent by n referrers is calle the referral intensity S = nq. We e ne referral congestion as the expecte ratio of the number of referral messages sent by all referrers to the uninforme to the expecte number of referrals registere by them: (q; n) S(q; n) R(q; n) = nq 1 (1 q) n > 1: (1) For any q > 0, there is congestion in referral messages an (q; n) > 1. In the symmetric consumer referral equilibrium, each of n referrers suggests the prouct to another consumer with probability q E. To n the equilibrium q E, we nee to look at the incentives of consumers to refer. Denote by R the probability that a consumer who receives a referral buys the goo: R = R (p; a; ; e ) = a max f (p; ) (p; e ) ; 0g + (1 a) (p; ) : (2) 9 In the base moel, we assume that a referrer oes not know the willingness-to-pay of other people. We stuy targete referrals in Section 6 an Section

10 The rst term in (2) correspons to consumers having receive an a, who i not initially purchase the prouct base on the expecte quality e, but purchase it upon receiving a referral that reveale a higher than expecte quality, > e. The secon term captures consumers who have not receive an a. Proposition 1. Suppose the rm chooses a policy mix of price p, avertising intensity a, an referral fee r. Then, for any number of referrers n, the equilibrium probability of consumer referral q E is uniquely etermine by r R (p; a; ; e ) = (q E ; n) (3) for all r above the critical level r 0 = R ; no referrals are sustaine for lower levels of the referral fee. For r > r 0, the equilibrium referral probability q E an referral congestion increase when the referral fee r an prouct quality increase an when price p, avertising intensity a, an referral cost ecrease. In the equilibrium, each referring consumer is ini erent between sening an not sening an aitional referral. An interesting observation from this fact is that, even if there was another perio for referrals to be mae after the initial referral market clears, no consumer woul make an aitional referral. Moreover, ue to constant referral cost, the expecte net bene t from making each referral is zero for any referrer an at the aggregate level. We explore the referral equilibrium in the case of increasing marginal cost of referral as one of the extensions in Section 7.1. The comparative statics results of Proposition 1 are intuitive. The factors that increase the bene t of making referrals (a higher referral fee r, higher prouct quality, lower price p, or lower avertising intensity a) or reuce referral cost (lower referral cost ) must 10

11 increase referral probability an congestion in orer for consumers to remain ini erent between referring an not referring. In the proof of Proposition 1, we show that, quite intuitively, congestion increases in q an n; therefore, the equilibrium referral intensity q E is also negatively a ecte by the number of referring consumers n. 4 Monopoly Choice of Price, Avertising, an Referral Policy In this section, we characterize the optimal (pro t-maximizing) monopoly policy mix an erive conitions uner which a rm woul choose to support consumer referrals. The cost of avertising per consumer is escribe by function C(a), which increases at an increasing rate in the fraction a of consumers reache, C 0 (a) > 0 an C 00 (a) > 0. To guarantee the interior solution for avertising intensity in the presence of referrals, we aitionally assume that C 0 (0) < an C(a) is su ciently convex: C 00 (a) > = (1 a) 2. From this section on, we assume that N is a large number, which allows us to obtain a very useful approximation argument (Ju, 1985). By the law of large numbers, there are n = a (p; e ) N consumers who purchase the prouct an make referrals. As N grows large, n grows large as well, an q E goes own to zero. 10 Thus, with a large N, we can use an approximation R E = 1 1 q E n ' 1 e nq E = 1 e SE because ln(1 q) n = n ln(1 q) ' nq for large N an S E = nq E. This approximation argument is use in the presentation of the avertisement moel by Butters (1977) in Tirole (1988). Inverting this relationship, we can then write referral intensity an congestion as functions of R only: 10 To see that q E! 0 as n! 1, note that from Proposition 1, the equilibrium congestion E = (q E ; n) = nq E (n)= 1 (1 q E (n)) n remains constant as n changes. From E nq E (n), it follows that q E (n) E =n. Since E =n converges to zero as n goes to in nity, so oes q E (n). The (expecte) number of referrals each consumer sens is k E ' Nq E, which oes not approach zero as q E approaches zero. 11

12 S = S (R) = ln (1 R) an ' = '(R) = S = (ln (1 R)) =R. R Summarizing the above, we have the following useful lemma. Lemma 1. Suppose that N is large. The referral congestion can then be written as a function of referral reach only: '(R) = (ln (1 R)) =R, where ' 0 (R) > 0. Throughout the rest of the paper we will assume that N is a large number an, therefore, the equilibrium referral congestion is inepenent of the number of referrers n. In particular, for any rm s policy mix (p, a, r), the equilibrium referral congestion (q E ; n) can be written as a function of only the equilibrium referral reach R E : '(R E ). We can then use Proposition 1 to escribe the equilibrium referral reach R E as a function of policy variables p, a, an r: R E = R E (p; a; r). The rm can achieve a higher equilibrium referral reach when it sets a lower price, avertises less, o ers a higher referral fee, an has a higher prouct quality. > > 0. The referral reach is also higher when the referral cost < 0. The rm s per-consumer pro t is: (p; a; r; ; e ) = a(p c) (p; e ) + R E (p c r) R (p; a; ; e ) C(a); (4) where R is e ne in (2) an R E = R E (p; a; r). The rst term captures pro ts from consumers who purchase after receiving an a an the secon one from consumers who purchase the prouct by referrals. Let (p; e ) = (p c) (p; e ) be the pro tability of a sale to a consumer who expects prouct quality e. We can prove the following useful properties of this function uner the assumption of log-concave survival function 1 G (). 12

13 Lemma 2. Function (p; ) has a unique pro t-maximizing price p m () that is increasing R 0 for p Q p m () hols for all. Let p m ( e ) an p m () enote the monopoly prices that maximize the per-consumer pro ts (p; e ) an (p; ) from the informe an the fully informe consumers. The equilibrium referral conition (3) of Proposition 1 implies that r R R E = S R E : (5) This permits us to rewrite the rm s pro t as: (p; a; r; ; e ) = a(p; e ) + R E R (p; a; ; e ) S R E C(a); (6) where R = R (p; a; ; e ) = (p c) R (p; a; ; e ) = (1 a) (p; )+a max f (p; ) (p; e ); 0g is the pro tability of a referral consumer. Absent referrals, the rm s pro t is 0 (p; a; e ) = (7) a (p; e ) C(a). The rm sets its price p m ( e ) an avertising level a 0, where a 0 is the solution to the rst-orer conition: 0 a = (p; e ) C 0 (a) = 0. We next investigate the optimal policy mix for the rm that uses referrals. Note that the rm s pro t in (6) is a ecte by referral r only through referral reach R E = R E (p; a; r). The rst orer conition with respect to r is, therefore, @r = 0; = R (p; a; ; e ) S 0 (R) : (9) 13

14 Since > 0 for r > r 0, the referral reach R is optimize uner the optimal = 0. Then, the inirect e ects of p an a on pro ts through their e ects on R E are zero. This ramatically simpli es our analysis: as long as the referral fee is optimally set, the rst orer conitions for p an a set partial erivatives with respect to p an a to zero: p an = = 0 The pro tability of a referre consumer epens on whether consumers are optimistic about prouct quality ( e ) or pessimistic about it ( > e ). Using (6) an (7), we can write the rm s pro t as: (p; a; r; ; e ) = We arrive at the following Proposition. a(p; e ) + (1 a) R E (p; ) if e a 1 R E (p; e ) + R E (p; ) if > e : (10) Proposition 2. Provie that the rm chooses its referral fee optimally, it sets its price p between the monopoly price for the informe consumer p m ( e ) an the fully informe consumer p m (). The rm avertises less when it uses referrals. This proposition says that the optimal price p is pulle away from the monopoly price for the informe consumers p m ( e ) towars the monopoly price for the fully informe consumers p m (). The key observation here is that the optimal price is essentially the monopoly price for the mix of consumers the rm faces. It is signi cant that we can separate the pricing ecision from the consumer referral consierations when the referral fee is optimally set. In such a case, the rm can ignore the e ect of its price on referral reach an simply use the price to maximize the pro tability of sales to consumers who are informe by as an/or referrals. If we assume no uncertainty in prouct quality ( e = ), then we have the following statement. 14

15 Corollary 1. Suppose that the rm sets the referral fee optimally. If e =, then the optimal price p is exactly the same as the monopoly price p m (). What if for some reason r cannot be optimally set? Suppose that there is a cap on r, but the cap is higher than r 0 so that referrals still occur. Then, the resulting referral reach is less than the optimal > < 0 hols, the optimal price p is set below the monopoly price in this case. Similarly, the optimal avertising level a is lower than the one when there is no cap on r. In Section 7.1, we analyze the case where the marginal cost of making referrals increases with an increase in the number of referrals mae. In this case, the optimal price woul also be less than the monopoly price as a lower price implies more referrers an lower total referral costs. Proposition 3 escribes the comparative static responses of the optimal monopoly policy mix (p ; a ; r ), assuming > 0 hols at (p ; ) an (p ; e ). 11 Proposition 3. Suppose 2 > 0 hols at (p ; ) an (p ; e ). Assuming the regular optimum, the comparative statics results on the optimal policy (p ; a ; r ) are summarize in Table 1: Table 1. Comparative statics results for the optimal policy mix. p a R ( r p c) p a R ( r p c) p e a e R e ( r p c) e e + +???? + + > e ???? It is natural that when referral cost goes up, the resulting equilibrium referral reach R ecreases. It is also natural that the optimal avertising intensity a increases since referrals 11 Note that the log concavity of 1 G () (p;) > 0 only at (p; ), satisfying p = p m () (see the proof of Lemma 2). We nee more than that to obtain the comparative statics results of Table 1. 15

16 an as are alternative information channels, even though the content of avertisements an referrals is not the same. The response of the optimal price p to an increase in nees more explanation. From (10), the marginal is a weighte sum of the marginal pro t from an informe an a fully informe If < e, then by Lemma 2 Proposition 2, p m () < p < p m ( e < 0, ) > 0. Since a higher results in a lower R an higher a, the rm faces relatively more informe consumers than fully informe consumers (10), an the optimal price must increase. By similar arguments, the price ecreases in case > e. Notice also that if price were xe, then a higher or lower e woul have comparative statics results that o not epen on the relationship between an e. Intuitively, the higher the prouct quality is relative to the expecte quality, the more the rm relies on referrals rather than avertising. Ajustments of price, which epens on whether is higher than e an on the signs of cross-partial erivatives of pro t function with respect to p an, complicate matters through the interactions of price p with a an R. The ambiguity in the e ects of changes in makes it harer for consumers to guess the quality of goo base on the observe rm s choices. The sign of the comparative statics results with respect to the marginal cost of prouction c also cannot be etermine in general. Proposition 4 provies a necessary an su cient conition for the rm to use consumer referrals. Proposition 4. For any given p an a > 0, the rm supports consumer referrals if an only if <, where = R (p; a; ; e ) : 16

17 The pro tability of the referral consumer, R = R (p; a; ; e ) is etermine in (7). Note that the threshol level for referral cost is higher when avertising a is low, prouct quality is high an the expecte quality e is low provie > e. That is, referral policy aoption is more likely when the prouct is of higher quality, the rm avertises less, an consumers are pessimistic about prouct quality. Corollary 2. The rm supports consumer referrals if the referral cost is su ciently small, < 0, where 0 = R (p m ( e ) ; a 0 ; ; e ) : The result is intuitive. A rm that has no referral policy can improve its pro ts by introucing a referral policy with a referral fee r 2 (r 0 ; p m ( e ) c), while keeping its price p m ( e ) an avertising a 0 at the same level. Such a referral fee exists when is su ciently low: < 0. The rm then earns aitional pro ts from consumers purchasing by referral. 5 Avertising Referral Program: Dynamic Consierations So far we have assume that consumers are not aware of the rm s referral program until they purchase the prouct. However, some rms openly avertise their referral programs. This generates an entirely new type of consumer behavior: consumers may elay purchases while waiting for a referral that woul resolve uncertainty about prouct quality. To analyze the consumers strategic incentives to wait for recommenations, we assume that there are two perios, an consumers an the rm iscount future bene ts an costs using a common iscount factor 2 (0; 1). In the beginning of perio 1, a subset of consumers receive as containing information about the rm s price an its referral policy. Out of these consumers, some purchase the prouct an then make referrals to other consumers. In the 17

18 beginning of perio 2, consumers who receive referrals become fully informe. Then, all consumers who are aware of the prouct an have not yet purchase it have a chance to purchase the prouct. Suppose that a consumer with value v p e receives an a. If she purchases the prouct right away, her expecte utility is: U p (v) = v + e p = E (u) ; (11) where e = E (). If she elays purchasing until perio 2, she can make a more informe ecision if she obtains a referral. Her expecte utility is then: U (v) = (1 R) E (u) + R Pr (u 0) E (uju 0) : (12) The i erence in the expecte utility from purchasing an waiting is: U p (v) U (v) = (1 ) (v + e p) R Pr ( p v) [E (j p v) e ] ; (13) where the rst term is ue to the iscounting of future purchases an the secon term is ue to the information gaine from obtaining a referral. As we show in Lemma 3, there exists a unique v = v (p; ; R), such that consumers with values v > v buy immeiately because U p (v) > U (v), an consumers with values v < v elay their purchase ecisions because U p (v) < U (v). The value of the person who is ini erent between purchasing an waiting v is implicitly etermine by U p (v ) U (v ) = 0. Lemma 3. Suppose that e + v p e + v. Then, there exists a unique consumer value v 2 (p e ; p), such that consumers whose value v < v elay their = 1, 18

19 @v > > e < 0: Quite intuitively, as the iscount factor increases, more consumers choose to wait for referrals. As referral reach R increases, consumers have a higher chance of receiving a referral, which encourages them to wait. A price increase lowers the expecte utility of buying the prouct an iscourages purchases. An as e increases, fewer consumers wait to receive referral information. We will now show that it is not pro table for the rm to announce its referral program to consumers. We enote by = (p; a; r) the pro t of the rm when it avertises its referral program an by (p ; a ; r ) the associate pro t-maximizing policy mix. The rm s pro t comes from four consumer segments: i) consumers who receive an a an purchase in perio 1; ii) consumers who receive an a, elay their purchase, receive no referral, but buy anyway in perio 2; iii) consumers who receive an a, elay their purchase, receive a referral, an buy by referral in perio 2; an iv) consumers who o not receive an a, receive a referral, an buy by referral in perio 2. We rst prove the following lemma. Suppose that the rm chooses an arbitrary policy combination an announces its referral program as a part of its avertising message. We show that the rm can earn more pro t by not avertising the referral policy. If e, then not avertising is simply better for the rm without a change in the policy combination. However, if > e, then consumers purchase elays make the referral market more vital, thus increasing the referral reach R E, an it may increase the rm s sales in comparison with not avertising the referral program. Therefore, if the policy mix is kept the same, the rm may earn more pro t by avertising the referral program. However, even in this case, the 19

20 rm can achieve the same e ect by merely reucing a an it can earn more pro t by not avertising the referral program. Lemma 4. Suppose that the rm chooses a policy combination an avertises its referral policy. There is another policy combination for which the rm can earn a higher pro t while not avertising its referral policy. The arbitrary policy combination can be (p ; a ; r ). Thus, we have the following statement. Proposition 5. Announcement of a referral program as part of an avertising message reuces the rm s pro t: (p ; a ; r ) > (p ; a ; r ): (14) Intuitively, a pre-announcement of a referral program by the rm generates elays in consumer purchases. This is not in the rm s best interest since the rm nees to pay referral fees an iscounts future payments The Two-group Moel: Targete Referrals In the base moel, we assume that, unlike the rm, consumers can creibly transmit information about prouct quality to other consumers. In this section, we assume that consumers have another type of avantage over the rm. Consumers can tell what group other con- 12 In our framework, some consumers have an incentive to wait for referrals to reveal true prouct quality. However, in reality, these consumers may actively search for such information from the users of the prouct, provie their search costs are not too high. Therefore, the rm may have less to lose from announcing its referral program. 20

21 sumers belong to, while the rm cannot istinguish between consumer groups. 13 For simplicity, in this section we assume that there is no prouct quality uncertainty an = e = 0. There are two groups of consumers: H an L with fractions H an L, respectively ( H + L = 1). Group H consumers ten to have a higher willingness-to-pay in the sense of the hazar-rate ominance than group L, i.e., for all p, g H (p) < gl (p) 1 G H (p) 1 G L (p) hols, where G H (v) an G L (v) are the cumulative istribution functions of values for groups H an L. The supports of the istribution functions overlap, so that some consumers who belong to group L have a higher willingness-to-pay than some consumers in group H. The general istribution G (v) is a weighte average of G H (v) an G L (v): G(v) = H G H (v) + L G L (v) for all v. Let (p) = (p c) (1 G (p)) for 2 fh; Lg an (p) = (p c) (1 G(p)). We assume the log concavity of 1 G () for 2 fh; Lg. This assures the uniqueness of pro t-maximizing prices: p arg max p (p) an p m arg max p (p). The hazar-rate ominance conition an Lemma 2 imply p H > p m > p L. Consumer i who receives the rm s avertisement can choose qi H an qi L as referral intensities for two i erent groups because she can istinguish which of her friens belong to H an L groups. We have the same referral equilibrium as before, but the conition applies for each group = H; L. The equilibrium referral reach for group consumers R = R (p; a; r) is e ne implicitly by (1 a)(1 G (p))rr = S(R ) (15) for all r > r 0, an the equilibrium referral intensity is higher when referral (1 a)(1 G (p)) fee r is higher an price p, avertising intensity a, an referral cost are lower. Note that 13 The moel can also be interprete as a social circles moel. Consumers in a group know each other an referrals are mae only within that group. 21

22 has no e ect in etermining the consumer referral intensity an reach in each group. The rm s per-consumer pro t in this environment is: (p; a; r) = X 2fH;Lg a + (1 a)r (p) X where R = R (p; a; r) > 0 for r > r 0 an R = 0 otherwise. 2fH;Lg S C(a); (16) Equation (16) is clearly a natural extension of (6), but there is an important i erence. The rm can no longer control R H an R L inepenently by using a single referral fee r. We cannot use the technique we use in the base moel to simplify p an a because (1 a) (p) S 0 (R ) = 0 is not assure for either. 14 For this reason, calculating the optimal monopoly price uner active referrals for both groups is no longer simple. There is no ichotomy in the rm s ecision problem, where p is use to maximize pro t per consumer an r is use to control R E. However, we can show that the rm chooses to increase its price after the introuction of consumer referrals when only group H gets consumer referrals (i.e., when r H 0 < r r L 0 ). In this case, r nees to control only R H, an we can apply the same technique as before. We compare the optimal policies uner ranom referrals (p ; r ; a ) an targete referrals (p T ; a T ; r T ). We will assume the following su cient conition for no referrals to be extene to type-l consumers uner targete referrals: L (p m ). Proposition 6. Suppose that L (p m ) hols. Uner targete referrals, the rm s optimal policy (p T ; a T ; r T ) is such that group-l consumers receive no referrals, an the rm avertises less uner targete referrals than uner ranom referrals, a T < a. Moreover, 14 Of course, if the rm coul use i erentiate referral fees (r H an r L ), the optimal referral reach R H an R L can be set for each group separately: (1 a) (p) S 0 (R ) = 0. However, it is unreasonable to assume that the rm can set type-epenent referral fees because the whole point of this extension is to examine how the rm may use consumer referrals to utilize superior consumer information. 22

23 the optimal price p T is higher than the stanar monopoly price p m an p H > p T > p m > p L hols. The equilibrium referral reach is higher, while the ratio of referral fee to pro t margin is lower uner targete referrals than uner ranom referrals: R T > R an r T = p T c < r = (p m c). Proposition 6 shows that if consumers possess superior information about who woul be likely to purchase the prouct, then the rm woul reuce its reliance on mass avertising an shift to using more consumer referrals. Interestingly, consumers can be better o or worse o by the rm s use of referrals when consumers have an information avantage. Uner no referrals, every consumer has an equal probability of receiving information about the prouct. However, with targete referrals, consumers who belong to a low willingnessto-pay type are less likely to receive the information, although some of them may have high valuations for the prouct. Thus, the impact of targete referrals on consumers may epen on consumer type. 7 Extensions We can exten our base moel in various ways. 7.1 Increasing Marginal Referral Cost The constant marginal referral cost assumption is important for establishing the monopoly pricing result of Corollary If the marginal referral cost (k) is increasing in the number 15 We owe this insight to the Eitor, Ben Hermalin. 23

24 of referrals k each consumer makes ( 0 (k) > 0), the referral equilibrium formula becomes: 16 r R (p; a; ; e ) = (k E )(q E ; n (p; a)): (17) The proof is available upon request. The number of referrals each referring consumer makes k E is now a ecte by the number of referring consumers n = a (p; e ) N. The optimal referral fee r still eliminates the impacts of p an a on pro t ue to changes in R E, but changes in p an a have a irect impact on k E. An increase in p reuces n, an this results in an increase in the marginal referral cost. Thus, the optimal price in this case is lower. Similarly, the optimal avertisement level uner increasing (k) is higher than the one with constant. This is an intuitive result: if (k) is increasing in k, the rm has an incentive to reuce the equilibrium k. Price cuts an higher avertising intensity increase the number of referrers. Therefore, in orer to achieve the same level of referral reach R, fewer referrals per referrer are mae an referral costs are lower. 7.2 Private Referral Bene ts We can allow for consumer referrals to be motivate by reasons other than monetary payo s. For example, suppose that each time a successful referral is mae, a referrer receives not only a referral fee r but also a non-monetary private bene t B > 0. Then, the consumer referral equilibrium is (r + B) R = '(R E (p; a; r)) an the rm s pro t can be written as: (p; a; r; ; e ) = a(p c) (p; e ) + (p c + B)R E R (p; a; ; e ) S R E C(a): (18) 16 For the analysis of this subsection, we assume that the referrers choose the number of referrals k instea of referral probability q, treating k as a real number. When N is large, these two formulations of our referral moel are essentially the same. 24

25 The private referral bene t B e ectively reuces the marginal cost of selling by referrals. Not surprisingly, we n that the rm supports more referrals an avertises less. Its price is lower if consumers are optimistic ( e ) an higher when they are pessimistic ( > e ) about the prouct quality. 7.3 Consumers Know Valuations of Others Suppose consumers know other consumers valuations for a prouct (or know that the valuations are high enough for consumers to buy the prouct). Then, consumers target referrals to iniviuals whose valuations are su ciently high. In this case, the rm chooses a higher price than in the base moel. A price increase has an aitional bene t of a more precisely targete referrals. Although referral messages are not waste on unlikely prospects, the savings are not fully capture by either consumers or the rm because of a higher congestion level. To reuce congestion, the monopoly sets a lower referral fee relative to its pro t margin when referrals are targete than when they are ranom. Less avertising is sustaine in this case than in the base moel because referrals are more targete an are therefore cheaper to use. An aitional reason for less avertising is that ue to the price istortion, the pro tability of each sale is lower. 7.4 Price Discrimination Consier the possibility of a monopoly o ering i erent prices to consumers who come by avertising p a an referral p R. If e, then the rm woul choose to iscriminate in favor of referral consumers: p R = pm () p m ( e ) = p a. If > e, then p R > p a, an in this case, the referrals woul not be use because referre consumers woul not acknowlege referrals an woul purchase using the avertise price. Similarly, we coul also allow the 25

26 rm to o er a referral bene t to both the referrer an the person they refer or for the referral partners to split the referral bene t. 7.5 Pro t Maximization when is Unknown to the Firm We next consier the case where the rm ex ante oes not know the true quality of the prouct. In the base moel, the rm has more information than consumers, an so the rm s policy (p; a; r) may serve as a signal of true quality. This issue isappears when is unknown to the rm. 17 Assume that the rm is also uncertain about the quality of the prouct until the rm receives feeback from buyers. In this case, we can minimally moify our analysis by assuming that the rm ecies on its referral fee r after the value of is realize. That is, the rm chooses (a; p) before the value of is realize an then picks r to optimize the referral reach for the realize value of using equations (8) an (9). This secon stage optimization gives us an explicit formula for R (), an the rm s expecte pro t can be written explicitly. We can show that the rst orer conition for pro t maximization is similar to the one in the base moel, but with relatively lower weights on the eman from referral consumers. (The erivations are available from the authors upon request.) 7.6 Cap on the Number of Referrals We explore the implications of a cap on the number of referrals each referrer can make. Let us assume that consumers (marginal) referral cost is constant at up to K referrals, but they cannot make more referrals than K. This moi cation requires the moel to have multiple perios in which consumer referrals are mae. For simplicity, we assume that 17 This comment especially applies if the marginal cost of prouction c is known to consumers. Consumers know that the rm charges the monopoly price, an they can ientify the true quality from the price p in the base moel. If consumers o not know c, it is harer for them to infer the value of. 26

27 avertising is one only initially (at perio 0); in subsequent perios, consumer referrals sprea the information about the prouct. In orer to get ri of the elay incentive iscusse in Section 5, we assume that the consumer referral program is not announce in avertising perio Therefore, from perio 1 on, referrals are the only meium use to transmit prouct information to other consumers. This moel briges our moel with the moels of referral chains in inustrial organization an marketing, in which consumers are locate on a line an each consumer can make at most one referral without congestion (Jun an Kim, 2008, Byalogorsky et al., 2008, an Arbatskaya an Konishi, forthcoming). Notice that with the cap on the number of referrals, the initial success probability of a referral is high an the net bene t of the referral is positive because many consumers are not aware of the prouct. As time goes by, more an more consumers become aware of the prouct, an the net referral bene t goes own. Depening on the size of K, two things can happen. If K is small, then the referral chain may fall short of achieving the referral reach for which the net referral bene t is zero. If K is large enough, then the referral chain terminates in nite number of perios, thus achieving the level of awareness for which aitional referrals are no longer bene cial. In either case, consumer referrals an avertising are no longer substitutes. A larger number of referring consumers spees up the process of consumer referrals. The rm may have an incentive to increase avertising intensity (an lower its price), especially if the rm is not very patient. This extension seems worthwhile to pursue. 18 This assumption oes not mean that consumers will not know about the consumer referral program from perio 1 on because, from perio 1, prouct information spreas only through referrals an a consumer who sens referrals alreay knows both an the existence of the referral program. She tells her contacts about the quality of the prouct an a consumer referral program. 27

28 8 Conclusion Several information channels are available to sellers who market their proucts to consumers. These inclue traitional mass avertising on TV an in newspapers an consumer referral policies. In the base moel, we assume that, unlike mass avertising, consumer referrals can provie accurate information on the quality of the prouct for an experience goo. We look at the optimal avertising, referral, an price policies for the monopoly. Uner correct consumer expectations ( = e ), we n that the pro t-maximizing price is the stanar monopoly price, provie that the referral fee is optimally chosen. Intuitively, a monopoly oes not use its price to manage consumer referrals, but instea irectly uses a referral fee. We also argue that the rm woul not inform consumers about its referral program as a part of its avertising message. A consumer referral program can improve the rm s pro t when referral cost is relatively low. The rm relies more heavily on referrals when consumers have superior information about other consumers preferences an when they erive non-monetary private bene ts from making helpful recommenations. The welfare e ects of referrals ten to be positive. Referrals increase consumer awareness about the prouct an help solve the averse selection problem of uncertain prouct quality. For any given level of avertising an price, referrals are unerprovie because of the nonappropriability of consumer surplus. Consumers who are informe through referrals are not worse o. Whether consumers informe through avertisements bene t as well epens on the price ajustment. For optimistic or rational consumers ( e ), the rm s price is lower (or the same) when referrals are use. We also show that increasing marginal referral costs an caps on referral rewars incentivize the rm to reuce its price in an attempt to stimulate 28

29 referrals. Hence, in all the cases where referral cost is su ciently small for the rm to use referrals an where the price oes not increase, referrals result in a Pareto improvement. No consumer is worse o an some are better o because they are better informe. It follows that in such a case, if the rm supports consumer referrals, it is socially optimal to o so. However, in the case of pessimistic consumers ( > e ) or with targete referrals, the price is higher than in the absence of referrals, an the ex ante welfare change woul epen on the relative magnitues of the price change, which epens on the istribution of consumer valuations. 29

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