Institute for Strategy and Business Economics University of Zurich

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1 Institute or Strategy and Business Economics University o Zurich Working Paer Series ISSN Working Paer No. 157 Advertising Pricing Models in Media Markets: Lum-Sum versus Per-Consumer Charges Helmut Dietl, Markus Lang, Panlang Lin May 2012

2 Advertising Pricing Models in Media Markets: Lum-Sum versus Per-Consumer Charges Helmut Dietl, Markus Lang, Panlang Lin June 19, 2012 Abstract This aer develos a model o asymmetric cometition between a ay and a ree media latorm. The ay media latorm generates revenues rom media consumers through subscrition ees, while the ree media latorm generates revenues rom charging advertisers either on a lum-sum basis (regime A) or on a er-consumer basis (regime B). We show that the ree latorm roduces a higher advertising level and attracts more consumers in regime A than B although advertisers must ay more or ads and consumers dislike ads. Moreover, the ay media latorm aces higher subscrition ees and lower consumer demand in regime A than B. Comared to regime B, the roit o the ree (ay) media latorm is higher (lower) in regime A, while aggregate roits are higher only i the consumers disutility rom ads is suiciently low. In addition, advertisers are better o in regime A than B, while the oosite is true or the media consumers. Finally, in small media markets, social welare is lower in regime A than B, while this is true in large media markets only i the media consumers disutility rom advertising is suiciently high. Keywords: Advertising, media latorm, two-sided market, lum-sum charge, er-consumer charge, asymmetric cometition JEL Classiication: D40, L10 Markus Lang is grateul or the inancial suort which was rovided by the Forschungskredit o the University o Zurich. All the authors are rom the Deartment o Business Administration, University o Zurich, Plattenstrasse 14, 8032 Zurich, Switzerland. Phone: , Fax: s: helmut.dietl@business.uzh.ch, markus.lang@business.uzh.ch, anlang.lin@business.uzh.ch. Corresonding author: Markus Lang. 1

3 1 Introduction Two generic business models coexist and comete in the various media markets: either media latorms rovide their content to the media consumers or ree and generate revenues rom advertising (ree media latorm), or media latorms do not lace ads but charge their consumers a subscrition ee or access to their contents (ay media latorm). 1 One justiication or the coexistence between ay and ree media latorms is that media consumers usually dislike the resence o ads because they decrease the entertainment value o consuming the media content. 2 As a result, some media consumers are willing to ay or media content and switching to ad-ree ay latorms to avoid ads (Tag, 2009). In general, ree media latorms ossess two basic ways to charge advertisers. Advertisers are charged a lum-sum ee or lacing an ad or they are charged on a er-consumer basis such that the advertising charges are a ositive unction o the consumer size. For examle, the online version o The New York Times can ask advertisers a certain ixed amount or lacing an ad (lum-sum charges) or it can charge advertisers via the concet o Pay-er-Click or Cost-er-Click where advertisers must ay or each click on the ad link (er-consumer charges). 3 Given these two distinct advertising ricing models, several research questions arise: What are the economic eects o both ricing models? Which ricing model generates higher roit or the ree media latorm and or the ay media latorm, resectively? What are the market reactions in both ricing models? From which ricing model can media consumers and advertisers beneit more? This aer tries to answer these and related questions by develoing a simle theoretical model o a media market that is served by one ay media and one ree media latorm. In accordance with the existing literature, media cometition is modeled in the Hotelling ashion. That is, the media consumers consume ad-ree media content on the ay latorm and ay a ositive subscrition ee or they consume the media content or ree and accet the resence o advertising. The ree media latorm can charge its advertisers either a lum-sum charge (regime A) or on a er-consumer basis (regime B). In regime A, the advertisers ay a ixed amount or lacing an ad on the ree media latorm, which does not exlicitly deend on the consumer size. In regime B, the rice that advertisers must ay or lacing an ad is an increasing unction o the consumer size. To analyze these two ricing models, we model 1 A third hybrid business model exists where media latorms lace ads and charge consumers (e.g., daily newsaers and magazines). However, in this aer we ocus on the two generic models: ay vs ree latorms. 2 See Deken II and Wilson (2004), Anderson and Coate (2005), Wilbur (2008), and Casadesus- Masanell and Zhu (2010). 3 Other examles or er-consumer advertising charges include ricing models such as CPM (cost er thousand imressions/views), CPA (cost er action, where the required action is deined by the advertisers, e.g., signing u or a service or ordering roducts etc.), and CPV (cost er view/visitor). 2

4 the advertising market exlicitly and assume that advertiser demand ositively deends on the consumer size. Our model shows that a dominant ricing strategy or the ree media latorm is to aly lum-sum charges or the advertisers because it realizes higher roit comared to a er-consumer advertising charge. Moreover, the advertising level on the ree latorm is higher and attracts more consumers under lum-sum charges although advertisers must ay more er ad and consumers dislike ads. We ind that the cometing ay media latorm s roit is lower i the ree latorm imoses a lum-sum charge on advertisers because the lower consumer demand overcomensates or the higher subscrition ee yielding a lower roit. As a result, the strength o media consumers disutility rom ads determines whether aggregate roits are higher in regime A or B. Moreover, the advertisers are always better o and the media consumers are worse o i the advertiser charge is levied on a lum-sum basis. Overall, in small media markets, alying lumsum advertiser charges always yields lower social welare; in large media markets, this inding is true only i the media consumers disutility rom ads is suiciently high. In the remainder o the aer we roceed as ollows. In the next section, we review the related literature. Section 3 introduces the basic model setu and Section 4 rovides the equilibrium analysis. In Section 5, we comare the relevant outcomes o both regimes and derive our main results. Section 6 discusses our results and concludes the aer. 2 Related Literature Our examination o asymmetric cometition between a ay media latorm and a ree media latorm that charges advertisers contributes to the literature on the economics o media markets in two dimensions. 4 First, we add to this literature by comaring lum-sum and er-consumer advertiser charges in an integrated ramework. Second, we contribute to the literature because rior research ocuses on symmetric cometition between either ree media latorms or ay media latorms and then comares the two indeendent scenarios searately. In the area o media economics, most aers that exlicitly model the advertising market exlore one o the two advertising ricing models (lum-sum or er-consumer charges). Paers that assume a lum-sum advertising charge include, e.g., Gabszewicz et al. (2001), Crames et al. (2009), Kind et al. (2009) and Reisinger (2011). Gabszewicz et al. (2001) develo a model in which two symmetric cometing newsaers lay a three-stage game and sequentially set the olitical oinion, the rices o newsaers, and the advertising rices. They show that newsaer editors oten tend to sell tasteless olitical messages to their readers in order to augment the audience size 4 For a summary o the literature, see Anderson and Gabszewicz (2006). 3

5 and thereore to become more attractive to advertisers. Crames et al. (2009) resent a model o media cometition with ree entry by considering the number o active media latorms as endogenous. 5 In their model o symmetric cometition, the media latorms are either inanced with advertising and subscrition revenues or they are solely unded by advertising receits. The authors ind that under constant or increasing returns to scale in the audience size, there are an excessive number o irms and underrovision o advertising in the markets. Kind et al. (2009) investigate how the number o the media latorms and the level o horizontal dierentiation between media latorms could aect the way media irms raise their revenues. They demonstrate that symmetric media latorms generate less revenue rom consumers when the horizontal dierentiation is low. Media irms also generate less revenue rom advertisers when there are more irms in the markets. Reisinger (2011) resents a two-sided market model o symmetric ree media latorms that comete or advertisers and consumers. He also extends his model to a setting in which latorms charge consumers or the consumtion o the latorm s content. He shows that media latorms roits can increase with users nuisance cost o ads. Models with a er-consumer advertising charge can be ound, or examle, in Anderson and Coate (2005) and Peitz and Valletti (2008). Anderson and Coate (2005) develo a general theory o market rovision o broadcasting and analyze the nature o market ailure in this industry. They show that symmetric commercial broadcasters rovide advertising levels and rogramming amounts that can be above or below socially otimal levels, deending on how strongly viewers dislike advertising (among other actors). Peitz and Valletti (2008) ocus on the endogenous rovision o rogram diversity by symmetric television broadcasters. They analyze how the rogram diversity and advertising level (among others) may be aected under two dierent revenue regimes adoted by the TV broadcasters, ay TV with income rom both viewers and advertisers and ree TV with only advertising receits. Broadcasters tend to vertically dierentiate their channel rograms more when they adot ay TV than ree TV. Moreover, the advertising level is higher under the ree TV regime when viewers strongly dislike advertising. The only aer that exlicitly comares lum-sum and er-consumer advertising charges is Armstrong (2006). In his ramework o a so-called cometitive bottleneck, two media latorms (newsaers) generate revenues rom two sources, readers and advertisers. There is cometition or readers, but not or advertisers. Under the assumtion that readers like (dislike) ads, the equilibrium reader rice and latorm roit is lower (higher) i latorms charge advertisers on a lum-sum rather than er-reader basis. In contrast to Armstrong (2006), who analyzes the symmetric cometition between two ay media latorms (with subscrition ees and advertising charges), we consider a scenario o asymmetric cometition between one ay media latorm (only with subscrition rev- 5 See also Choi (2006) or a model o broadcast cometition with ree entry. 4

6 enues) and one ree media latorm (only with advertising revenues). In sum, neither o the above-mentioned aers on cometition in media markets comares the two advertising ricing models in a ramework o asymmetric cometition between ay and ree media latorms. Thus, our aer can oer insights about a scenario, in which ay and ree media latorms coexist and comete or the same consumers. To the best o our knowledge, only a ew aers model the direct cometition between ay media and ree media in a integrated ramework. Casadesus-Masanell and Zhu (2010) develo a model o duooly cometition between a high-quality incumbent and a low-quality ad-sonsored entrant. They investigate what the otimal reaction regarding own business model or the incumbent could be when it aces a new ad-sonsored entrant. They consider our dierent business models or the incumbent: a subscrition-based model; an ad-sonsored model; a mixed model with both subscrition and ads; and a dual model with two roducts (one based on the adsonsored model and the other based on the mixed model). The case in which the incumbent chooses a subscrition-based model is similar to the asymmetric cometition in our setting. Lin (2011) studies the endogenous rovision o rogram quality by one ay TV broadcaster and one ree TV broadcaster cometing directly against each other. He shows that deending on the viewer s nuisance cost o ads and on the degree o horizontal dierentiation, ay TV does not always oer higher quality rogramming than ree TV. Dietl et al. (2012) also model asymmetric cometition between a ay TV broadcaster and a ree TV broadcaster to analyze the economic eects o introducing advertising on the ay TV channel. They show that under certain circumstances there is scoe or the ay TV broadcaster to lace ads on its channel. By doing so, viewers will always beneit rom it while aggregate broadcaster roits may increase i the viewer s disutility rom ads is suiciently high. However, neither o the three aorementioned aers exlicitly models the advertising market nor comares the two dierent advertising ricing models (lum-sum versus er-consumer charges). Our aer is related also to the literature on two-sided markets. 6 Media markets are canonical examles o two-sided markets in which media latorms serve two distinct grous o agents, media consumers and advertisers. It is essential or the media latorms to take into account the existence o indirect network eects between media consumers and advertisers. There are ositive network eects that oerate rom media consumers to advertisers such that the value o the media latorm or the advertisers increases with the number o media consumers. 7 In contrast, the network eects that oerate rom advertisers to consumers are considered to be mainly negative in media industries. 8 6 Classical works on two-sided markets include Caillaud and Jullien (2003), Rochet and Tirole (2003), Rysman (2004), Armstrong (2006), Hagiu (2006), Kaiser and Wright (2006), Bellelamme and Toulemonde (2009), and Weyl (2010). 7 See Gabszewicz et al. (2004) and Kind et al. (2007). 8 An excetion is Kaiser and Song (2009) who ind that in the German magazine market, readers 5

7 In our model only the ree media latorm oerates a two-sided market strategy while the ay media latorm oerates in a traditional one-sided market. Although the ree media latorm does not rice both market sides, due to the existence o indirect network eects between advertisers and media consumers, such a latorm can also be considered two-sided. 3 Model We consider a media market with three tyes o agents: consumers (users), latorms, and advertisers. The media market is served by one ay media latorm and one ree media latorm. The ay media latorm charges its consumers a subscrition ee or access to the media content whereas the ree media latorm gives ree access to its consumers with no urther monetary charges. There are no ads on the ay media latorm while the consumers are exosed to ads on the ree media latorm. We dierentiate two ricing regimes or advertisers, lum-sum and er-consumer charges. 3.1 Consumers Suose there are θ R + media consumers uniormly distributed along the unit interval. The two media latorms are located at the extremes o the unit interval where the ay media latorm (denoted by subscrit ) is situated at 0 and the ree media latorm (denoted by subscrit ) is situated at 1. We consider the Hotelling model with linear transort cost o t R + er unit o length. Hence, the two media latorms are horizontally dierentiated rom the ersective o consumers and the arameter t can be interreted as the dierentiation arameter. A lower value o t means that the media latorms (or rather their media content) are erceived as closer substitutes by the consumers. The indirect utility unction o a consumer located at oint x [0, 1] when consuming media on the ay media latorm or on the ree media latorm is given by u = v s tx, (1) u = v γa t(1 x), (2) where s is the subscrition ee and a is the level o advertising on the ree media latorm. The arameter v R + denotes the consumers intrinsic value rom consuming media and the arameter γ R + measures the level o consumers disutility rom ads. 9 actually areciate inormative ads, such as car ads in car magazines. However, in this case, we believe advertising is rather art o media content than a searate by-roduct. 9 As mentioned in Section 2, recent works in media industries assume that consumers do not like ads and derive a disutility rom it. We ollow this aroach, which allows us to ocus on the trade-o or 6

8 We assume ull consumer market coverage, i.e., the consumers intrinsic value rom consuming media is suiciently large such that all consumers will join one media latorm. We also assume that no media latorm can corner the consumer market such that each media latorm gains a ositive market share. The marginal consumer, who is indierent between consuming ay media and ree media, is located at x = t (γa s ). All consumers to the let o x consume the content o the ay media latorm and all consumers to the right o x consume the content o the ree media latorm. As a result, the demand unction o the ay media and ree media consumers, resectively, are given by n = θ [ ] 2 t (γa s ), (3) n = θ n = θ [ ] 2 t (s γa ). (4) The consumers o the ay media and ree media derive the ollowing surluses: CS = θ x (v s tz) dz and CS = θ 1 0 x (v γa t(1 z)) dz. (5) Because the consumer market is ully covered, the aggregate consumer surlus is the sum o all consumers net beneits rom consuming media, CS = CS + CS. 3.2 Advertisers Advertisers are roducers o goods or services who want to attract otential buyers through ads on the ree media latorm. As in revious studies (see, e.g., Crames et al., 2009), we assume that each advertiser can lace only one ad on the ree media latorm such that the number o advertisers also reresents the number o ads. We assume that the advertisers incur the cost η or designing and roducing one ad. Advertisers are heterogeneous with resect to η where η is assumed to be uniormly distributed in the unit interval, η U[0; 1]. We assume that the net utility o advertisers is given by u a = βn η, where β R + measures the marginal gross beneit o an advertiser derived rom each media consumer and is the rice an advertiser has to ay er ad. An advertiser decides to lace an ad i her net utility is non-negative, u a 0. By normalizing the mass o advertisers to unity, we derive the advertiser demand as 10 a = βn. consumers between ads-ree media with a subscrition ee and ree media that includes ads. 10 For a similar derivation o advertiser demand, see e.g., Li (2009). 7

9 Figure 1: Model Illustration ay media latorm maxπ = s n s s > 0 media consumers n media cometition a la Hotelling ree media latorm advertisers a regime A: = R regime B: = r n regime A: maxπ = R a R regime B: maxπ = r n a r ree access media consumers n negative network eect ( γ < 0) ositive network eect ( β > 0) Advertiser surlus is then given by AS = a 0 (βn y ) dy. (6) Advertiser surlus is the ositive dierence between the amount that advertisers are willing and able to ay or lacing an ad and the amount that they actually ay. 3.3 Media Platorms The media latorms rovide the content or the consumers. The ay media latorm generates its revenues urely rom the media consumers through subscrition ees, while the ree media latorm generates its revenues rom advertising receits. For simlicity, all incurring costs or the media latorms are assumed to be 0. The roit unctions o the ay and ree media latorms, resectively, are then given by π = s n and π = a. We consider two advertising ricing models on the ree media latorm: In regime A, the advertising charge is levied on a lum-sum basis where R denotes the ixed rice that each advertiser has to ay er ad, i.e., = R. In regime B, advertisers are charged on a er-consumer basis where r denotes the charge that each advertiser has to ay er 8

10 consumer or lacing one ad. Hence, in regime B the rice er ad now ositively deends on the number o attracted media consumers, i.e., = r n. Figure 1 grahically illustrates our model. 4 Analysis In this section, we derive the equilibrium outcomes by assuming that both media latorms simultaneously maximize their roits. The ay media latorm sets the subscrition ee s, while the ree media latorm either sets a ixed rice or an ad or sets a er-consumer rice or an ad. First, we analyze regime A in which advertisers ay a lum-sum charge. Second, we investigate regime B where advertisers are charged on a er-consumer basis. 4.1 Regime A: lum-sum advertising charges In regime A, the advertising charge R is levied on a lum-sum basis and hence advertisers derive the net utility u a = βn R η. The advertiser demand unction is thereore given by a = βn R. By substituting this demand unction into (3) and (4), we obtain ree media and ay media consumer demand in regime A as n A = Consequently, the advertising level is given by θ 2t + θβγ (t + s + γr ) and n A = θ n A. (7) a A = βn A R = ( θβ t + s 2t ) 2t + θβγ θβ R. (8) It is intuitively clear that a higher subscrition ee s on the ay media latorm decreases consumer demand n A on this latorm and increases consumer demand n A on the ree media latorm. As a result, the advertising level a A on the ree media latorm also increases with a higher subscrition ee. On the other hand, a higher advertising charge R on the ree media latorm induces a lower advertising level a A on this latorm. Because media consumers dislike ads, this reduction in the advertising level leads to a higher ree media consumer demand n A demand n A. and consequently to a lower ay media consumer The ay and ree media latorms simultaneously solve max s>0 { π A = s n A } and max R >0{π A = R a A }, resectively. The equilibrium (sa, R A ) is then characterized 9

11 by 11 π A s = n A + s A n A s = 0 and πa R = a A + R A a A R = 0. (9) The two irst-order conditions have an intuitive interretation. For the ay media latorm, a marginally higher subscrition ee s induces a direct ositive revenue eect n A and an indirect negative consumer-mediated eect s A n A s through a reduction in consumer demand. The otimal subscrition ee s A is chosen such that the revenue eect and consumer eect are balanced. For the ree media latorm, marginally increasing the lum-sum advertising charge R triggers a direct ositive revenue eect a A = βn A R and an indirect negative advertiser-mediated eect R A a A R = R A (β na R 1) through a lower advertising level. The advertiser eect aa R is comosed o two eects: the irst term, β na R, reresents the ositive eect on the advertisers through higher consumer demand and the second term, 1, is the negative eect o a higher advertising rice. The second eect dominates the irst such that aa R < 0. Again, the latorm chooses the otimal advertising rice in a way that balances both countervailing eects (i.e., revenue eect and advertiser-mediated eect). To make the notation simler, we henceorth write λ θβγ. By solving the above system o irst-order conditions, we comute the subscrition ee and the lum-sum advertiser charge in equilibrium as ( s A, R A ( ) t (4t + 3λ) = 8t + λ ) θβ (3t + λ),. 8t + λ Hence, each advertiser has to ay A = R A er ad on the ree media latorm. Substituting s A, and A into the demand unctions yields equilibrium demands o the ay media consumers and ree media consumers (n A, n A ) as well as the advertising level aa on the ree media latorm. Similarly, we obtain equilibrium latorm roits (π A, π A ), aggregate consumer surlus CS A, and advertiser surlus AS A. See the aendix or a detailed derivation o these outcomes. 4.2 Regime B: er-consumer advertising charges In regime B, the advertising charge r is levied on a er-consumer basis and the rice er ad is = r n. Advertisers thereore enjoy a net utility o u a = βn r n η and their demand unction is given by a = βn r n. With a similar aroach as in regime 11 The second-order conditions are satisied because 2 π s 2 = 2θ 2t+θβγ < 0 and 2 π r 2 = 4t 2t+θβγ < 0. 10

12 A, we obtain ree media and ay media consumer demand in regime B as n B = Advertiser demand is then given by θ 2t + θ (β r ) γ (t + s ) and n B = θ n B. (10) a B = n B (β r ) = θ 2t + θ (β r ) γ (β r ) (t + s ). (11) The same qualitative comarative statics or the demand unctions hold as in regime A. The ay and ree media latorms solve max s>0 { π B = s n B } and maxr >0{π B = r n B ab }, resectively. The equilibrium (sb, r B ) is then characterized by12 π B n B = n B + s B s π B r = n B a B + r B = 0, (12) s ( ) n B a B a B + n B = 0. (13) r r A marginal higher subscrition ee induces a direct ositive revenue eect n B and an indirect negative consumer-mediated eect s B n s. For the ree media latorm, marginally increasing the advertising charge triggers a direct ositive revenue eect n B ab and an indirect eect through changes in n B ab. This indirect eect is comosed o two eects: irst, marginally increasing r causes a ositive consumer eect nb r a B > 0 through a higher consumer demand level. Second, marginally increasing r induces a negative advertiser eect n B a B r < 0 through a lower advertiser demand level. Which o the two eects dominates deends on the level o γ. We derive nb ab r < 0 γ < γ = 2t. Hence, i (β r )θ the media consumers disutility rom ads is suiciently low, the ositive consumer eect will be dominated by the negative advertiser eect because consumer demand increases to such an extent that it cannot overcomensate or the lower advertising level. By solving the above system o irst-order conditions, we comute the subscrition ee and the er-consumer advertising charge in equilibrium as Substituting s B and r B ( s B, r B ( ) t (4t + 3λ) = 2 (4t + λ) ) β (2t + λ),. 4t + λ into the demand unctions yields equilibrium demands o the ay and ree media consumers (n B, n B ) as well as the advertising level ab on the ree ( ) 12 The second-order conditions are satisied: 2 π s = θ 1 2 2t 1 2t+λ < 0 and 2 π = r 2 θ2 (4t+λ) 2 (12t+5λ) 2 < t(2t+λ) 3 11

13 media latorm. We urther derive that each advertiser has to ay B = r B n B = βθ (12t + 5λ) 8(4t + λ) er ad. Analogous to above, we obtain equilibrium latorm roits (π B, π B ), aggregate consumer surlus CS B, and advertiser surlus AS B. See the aendix or a detailed derivation o these outcomes. 5 Comarison o Equilibrium Outcomes In this section, we comare the outcomes o the two regimes. First, we comare the subscrition ees on the ay media latorm and the rices advertisers must ay or an ad laced on the ree media latorm. Proosition 1 (i) The subscrition ee that a consumer must ay on the ay media latorm is higher in regime A than in regime B, i.e., s A > s B. (ii) The rice that an advertiser must ay er ad on the ree media latorm is higher in regime A than in regime B, i.e., A Proo. See Aendix B.1. > B. Part (i) osits that the ay media latorm charges consumers a higher subscrition ee i the ree media latorm chooses a lum-sum advertiser charge as comared to a er-consumer charge. To understand the intuition behind this result, we rearrange the irst-order conditions (9) and (12) to obtain ( ) θ ( ) t + λ γr A 2t + λ s A = s A θ, (14) 2t + λ θ 2t + θγ ( ) ( ( ) ) t + λ γθr B β r B s B = s B θ 2t + θγ ( ). (15) β r B The let-hand side (lhs) o both equations reresent the revenue eect n, while the righthand sides (rhs) characterize the consumer-mediated eects s ( n s ). Substituting the best-resonse unctions R A(sA ) = θβ(t+sa ) and r B 4t = β(2t+θβγ) into (14) and (15), we 4t+θβγ obtain the ollowing results. For a given subscrition ee s, the revenue eects (lhs) are equal in both regimes, while the consumer-mediated eects (rhs) are stronger in regime B than in regime A. Hence, increasing the subscrition ee decreases the revenue eects with equal strength in both regimes, while the consumer eect increases more strongly in regime B than in A. As a result, the equilibrium subscrition ee is larger in regime A than in B, i.e., s A ee s. > s B. Figure 2 deicts these eects as a unction o the subscrition 12

14 Figure 2: Intuition or Proosition 1 2 4t 3 4(2t ) revenue eect (regime A and B) consumer eect (regime B) consumer eect (regime A) B* s A* s s According to art (ii), the er-ad rice A = R A that each advertiser must ay i it is charged on a lum-sum basis is higher than the er-ad rice B = r B nb i it is charged on a er-consumer basis. The intuition behind this result is as ollows. In both regimes, marginally increasing the advertising charge induces a ositive revenue eect and a negative advertiser eect. However, an additional eect is resent in regime B: the latorm takes into account that a higher advertising charge induces a higher consumer demand (ositive consumer eect), which enters the irst-order condition with a ositive sign. This eect is not resent in regime A because advertisers are charged on a lum-sum basis. As a result, we derive A (s A ) = θβ(t + sa ) 4t and B (s B ) = θβ(t + sb ). 4t Because we know that the subscrition ee is higher in regime A than in B, i.e., s A > s B, it must be the case that A > B. In the next roosition, we comare both regimes with resect to consumer demands and advertising level. Proosition 2 (i) The ree (ay) media latorm attracts more (ewer) consumers in regime A than in regime B, i.e., n A > n B and n A < n B. (ii) The advertising level on the ree media latorm is higher in regime A than in 13

15 regime B, i.e., a A > a B. Proo. See Aendix B.2. Even though the advertising level on the ree latorm is higher in regime A than in B, art (i) o the roosition osits that this latorm attracts more consumers in regime A than in B. To understand the intuition behind this result, recall that the subscrition ee on the ay media latorm is higher in regime A than in B and consumer demand on [ the ree media latorm is given by n = θ (s t γa ) ]. Increasing the subscrition ee on the ay latorm decreases consumers on this latorm, and in turn, increases consumer demand on the ree latorm. Hence, the higher subscrition ee on the ay latorm in regime A comared to B, overcomensates or the higher advertising level on the ree latorm such that the ree media consumer demand is higher in regime A than in B. Due to our Hotelling seciication, it ollows that the ay media consumer demand is higher in regime B than in A. Part (ii) o the roosition shows that the ree latorm attracts more advertisers in regime A than in B. This result is true desite higher rice er ad in regime A than in B. However, the ree latorm attracts more consumers in regime A than in B, which makes it more attractive or advertisers to lace ads. We conclude that the higher consumer demand overcomensates or the higher rice in regime A comared to B. Next, we comare the roits o the media latorms in both regimes and establish the ollowing roosition: Proosition 3 (i) The roits o the ree (ay) media latorm is higher (lower) in regime A than in regime B, i.e., π A > π B and π A < π B. (ii) Aggregate latorm roits are higher in regime A than in regime B i and only i the consumers disutility rom ads is suiciently low, i.e., Π A > Π B γ < γ π. Proo. See Aendix B.3. Part (i) o the roosition states that the ree media latorm generates higher roits i it rices advertisers via a lum-sum charge as comared to a er-consumer charge. Recall that roits o the ree latorm are given by π = a. Because each advertiser must ay a higher rice er ad in regime A than in B, and in addition, the advertising level a is also higher in regime A than in B, the claim ollows immediately. Regarding the ay media latorm, we ind that this latorm generates higher roits π = s n i the ree latorm charges advertisers on a er-consumer basis as oosed to a lumsum charge. Recall that the subscrition ee is lower but consumer demand on the ay latorm is higher in regime B comared to A. Hence, the higher consumer demand overcomensates or the lower subscrition ee such that roits o the ay latorms are higher in regime B than in A. Part (ii) shows that whether aggregate latorm roits is higher in regime A or B crucially deends on the consumer reerences towards ads. I the consumers suiciently 14

16 dislike ads then aggregate roits are higher in the case that the ree latorm charges advertisers on a er-consumers basis. I, however, the consumers disutility rom ads is suiciently low then aggregate roits are higher in the case that the ree latorm charges advertisers on a lum-sum basis. To understand the intuition behind this result, we analyze how the comonents o the roit unctions react to changes in the disutility arameter o ads γ. For the ay media latorm, the subscrition ee increases with γ in both regimes and the increase is stronger in regime A than in B. Hence, the sread between the subscrition ees augments in γ. The eect o γ on consumer demand n A ositive on consumer demand n B in regime A is ambiguous, while the eect is in regime B. Overall, the sread between n B and n A between increases in γ. It ollows that the dierence in ay media roits = π B π A regime B and A also augments in γ. Regarding the ree media latorm, it is intuitive that the advertising level a on the ree media latorm in both regimes decreases in γ. However, it deends on the level o γ whether the decrease is stronger in regime A or B. Furthermore, the rice that advertisers have to ay or lacing an ad increases in γ because a higher level o γ leads to a lower advertising level which, ceteris aribus, increases advertisers willingness to ay. The increase in the rice or the advertisers is more ronounced in regime A than B such that the rice sread between regime A and B augments or an increasing γ. Finally, we ind that roits π o the ree media latorm decreases with γ in both regimes but it deends on the level o γ in which regime the decrease in roits is more ronounced. Particularly, the dierence in ree media roits = π A π B between regime A and B reaches its maximum or low values o γ and then diminishes or higher values o γ. Overall, we conclude that or low values o γ the dierence in ree media roits comensates or the dierence in ay media roits such that aggregate roits are higher in regime A than in B. Because diminishes and augments or higher values o γ, a critical value o γ = γ π exist above which aggregate roits are higher in regime B than in A. The next roosition comares aggregate consumer surlus and advertiser surlus in both regimes. Proosition 4 (i) Aggregate consumer surlus is higher in regime B than in regime A, i.e., CS B > CS A. (ii) The advertiser surlus is higher in regime A than in regime B, i.e., AS A > AS B. Proo. See Aendix B.4. Part (i) states that the media consumers are better o in regime B than in regime A. This result is intuitive because the consumers beneit rom a lower subscrition ee and a lower advertising level. In contrast, advertisers enjoy a higher surlus in regime A than in regime B, as stated in art (ii) o the roosition. On one hand, advertisers beneit 15

17 rom higher consumer demand in A comared to B, but on the other hand, they ace higher rices. As we know rom Proosition 2, the higher consumer demand outweighs the higher rice such that the advertising level in A is higher than in B. Overall, the higher advertising level together with the higher consumer demand comensate or the higher rice such that the advertiser surlus is higher in A comared to B. In a inal ste, we comare social welare in both regimes. We deine social welare W, as the sum o aggregate latorm roits, aggregate consumers surlus and advertiser surlus We establish the ollowing roosition: W = Π + CS + AS. Proosition 5 In large media markets (i.e., θ > θ ), social welare is higher in regime B than in regime A i and only i the consumers disutility rom ads is suiciently high, i.e., W B > W A γ > γ W. However, in small media markets (i.e., θ θ ), social welare is always higher in regime B than in regime A regardless o the consumers disutility rom ads. Proo. See Aendix B.5. The roosition shows that the welare eect o charging advertisers on a lum-sum basis or a er-consumer basis deends on the market size o consumers and the consumers disutility rom ads. In large media markets (i.e., θ > θ = 8t ) the disutility must be 9β 2 suiciently low to ensure that social welare is higher in regime A than in B. I, however, consumers suiciently dislike ads then the oosite holds true. In small media markets, in contrast, social welare is always higher i advertisers are charged on a er-consumer basis than i they are charged on a lum-sum basis. Figure 3 illustrates the result or large media markets by deicting social welare in regime A and B as a unction o the disutility γ. For the igure, we set the arameters as ollows: N = 50, t = 30, v = 50 and β = 3.5. The igure shows that in both regimes social welare is a concave unction in γ and that or γ = 0, social welare would be equal in both regimes. For low values o γ, social welare is higher in regime A than in B because welare decreases with γ stronger in regime B than in A. However, or intermediate values o γ, social welare decreases less strong in regime B than in A such that there exists a critical value γ = γ W which welare is equal in both regimes. Above this critical value γ W, welare is higher in regime B than in A. To understand the intuition behind this result, recall that the aggregate consumer surlus is always lower in A than in B, while the oosite is true or the advertiser surlus. In addition, aggregate latorm roits are higher in regime B than in A i the consumers disutility rom ads is suiciently high. Hence, i γ is low, then the higher advertiser surlus together with the higher aggregate latorm roits or 16

18 Figure 3: Social Welare W A W B Γ W outweigh the higher aggregate consumer surlus in regime A comared to B such that W A > W B, which is is true as long as γ < γ W. I γ increases above this critical value γ W, the dierence in the aggregate consumer surluses between regime B and A is so large that it comensates or the lower advertiser surlus and eventually lower latorm roits, yielding a higher level o social welare in regime B comared to A. In the case o small media markets, this overcomensation o aggregate consumer surluses between regime B and A is true regardless o the consumers disutility rom ads such that social welare is always higher in regime B comared to A Conclusion This aer is motivated by the observation that in reality ay and ree media latorms oten coexist and directly comete with each other. The existing literature, however, widely neglects to model asymmetric cometition in media markets. To begin illing this research ga in this aer, we develo a simle model o asymmetric cometition between a ay media latorm and a ree media latorm. Seciically, we question how dierent advertising ricing models (lum-sum versus er-consumer charges) aect relevant equilibrium outcomes. Our aer shows that roit-maximizing ree media latorms should charge their 13 Formally, the dierences o aggregate latorm roits as well as advertiser surluses between regimes B and A decrease more strongly than the resective dierence o consumer surlus between regimes A and B or low arameters o θ. 17

19 advertisers on a lum-sum basis rather than a er-consumer basis because in doing so they can realize higher roits. However, rom the ersective o a social lanner this is not always desirable because, at the same time, the roit o the ay media latorm will be lower such that the eect on aggregate latorm roits deends on the media consumers disutility rom ads. Particularly, i the disutility is suiciently low, aggregate latorm roits are higher under lum-sum charges. Furthermore, the advertisers are always better o i they are charged on a lum-sum basis, while the media consumers are better o i advertisers are charged on a er-consumer basis. Hence, choosing one o the two advertising ricing models beneits either the consumers or the advertisers. Finally, our model shows that social welare is higher i the advertisers are charged on a er-consumer basis when the media market is small, while this is true in large media markets only i the media consumers disutility rom ads is suiciently high. Our analysis has imlications or olicy makers and regulators in the media industries. One common orm o advertising regulation is to directly limit the number or length o ads on media latorms through so-called advertising cas. Our results suggest another indirect instrument could achieve the aim o low advertising levels. According to our model, the rohibition o lum-sum advertising charges and the enorcement o erconsumer charges lead to a lower advertising level on ree media latorms. Such an enorced er-consumer advertising charge could be articularly relevant or the television broadcasting industry where lum-sum advertising charges are redominant due to the diiculty o measuring the exact number o ree TV viewers. However, olicy makers and regulators should be aware o the resulting welare eects o such a regulation because in large media markets social welare could decrease through er-consumer charges, esecially i the consumers disutility rom ads is low. Our model could be extended in several directions. For examle, a romising avenue or urther research would be the integration o endogenous quality rovision by the media latorms. In our model, we ocused on the role o consumers disutility rom ads as a reason or the existence o ay media. However, this is obviously not the only reason. In addition to ad-ree content, ay media latorms oten rovide high-quality content such as Hollywood Blockbusters or exclusive remium sorts rights. Another ossible extension o our model is to consider a situation in which the ay media latorm also generates advertising revenues. An examle or such latorms can be ound in the newsaer industry where traditional aid newsaers (revenue rom readers and advertisers) comete against ree newsaers (revenue rom advertisers). In such a setting, it could be interesting to investigate whether an asymmetric equilibrium arises in which the ay latorm chooses lum-sum advertising charges and the ree latorm decides or er-consumer charges, or vice versa. 18

20 A Aendix: Equilibrium Outcomes A.1 Regime A Plugging (s A media consumers as, R A ) into the demand unction yields equilibrium demands o the ay n A = θt (4t + 3λ) (2t + λ) (8t + λ). On the ree media latorm, consumer and advertiser demands, resectively, are ( n A, a A ) (2t + λ) (8t + λ), 2θtβ (3t + λ). (2t + λ) (8t + λ) ) = ( θ (3t + λ) (4t + λ) By noting that the marginal consumer in equilibrium is given by x = consumer surlus is given by CS A = and advertiser surlus is Equilibrium roits are then given by π A t(4t+3λ) (2t+λ)(8t+λ), ( v 5t t3 + 8λt 2 27 (2t + λ) ) (326t3 + 37λt 2 ) 27 (8t + λ) 2 θ > 0, (16) = s A n A = θt2 (4t + 3λ) 2 2 and πa (2t + λ) (8t + λ) A.2 Regime B AS A = 2θ2 t 2 β 2 (3t + λ) 2 (2t + λ) 2 (8t + λ) 2. (17) = A a A = 2tθ2 β 2 (3t + λ) 2 (2t + λ) (8t + λ) 2. (18) Plugging (s B, r B ) into the demand unction yields equilibrium demands o the ay media consumers as n B θ (4t + 3λ) = 8 (2t + λ). On the ree media latorm, consumer and advertiser demands, resectively, are ( n B, a B ( ) ) θ (12t + 5λ) = 8 (2t + λ), θtβ (12t + 5λ). 4 (2t + λ) (4t + λ) By noting that the marginal consumer in equilibrium is given by x = 4t+3λ 8(2t+λ), consumer surlus and advertiser surlus are resectively given by CS B = AS B = ( v 103t ) t3 + 5λt 2 16 (2t + λ) 2 + 4t2 θ > 0, (19) 4t + λ θ 2 t 2 β 2 (12t + 5λ) 2 32 (2t + λ) 2 (4t + λ) 2. (20) 19

21 Equilibrium roits can be derived as π B = s B n B = θt (4t + 3λ) 2 16 (2t + λ) (4t + λ) and πb = B a B = tθ2 β 2 (12t + 5λ) 2 32 (2t + λ) (4t + λ) 2. (21) B Aendix: Proos B.1 Proo o Proosition 1 Part (i). This art osits that the subscrition ee is higher in regime A than in regime B (s A > s B ). This roo is straightorward and thus omitted. Part (ii). This art claims that the advertiser s rice er ad is higher in regime A than in regime B, i.e., A > B = r B nb. We derive A > B θβ (3t + λ) 8t + λ > β (2t + λ) θ (12t + 5λ) 4t + λ 8 (2t + λ) = θβ (12t + 5λ) 32t + 8λ. We rearrange the inequality in the ollowing way and obtain θβ (3t + λ) (32t + 8λ) θβ (12t + 5λ) (8t + λ) > 0. Ater simliying, we have 4θ 2 β 2 tγ + 3θ 3 β 3 γ 2 > 0, which roves art (ii) o roosition 1. This comletes the roo o roosition 1. B.2 Proo o Proosition 2 Part (i). This art o the roosition 2 claims that the consumer demand or the ay (ree) media latorm is lower (higher) in regime A than in regime B, i.e., n A > n B. First, we rove the claim or the ay media latorm. Hence, n A n A < n B θt (4t + 3λ) (2t + λ) (8t + λ) < θ (4t + 3λ) 8 (2t + λ). We rearrange the inequality in the ollowing way and obtain < n B and θt (4t + 3λ) 8 (2t + λ) (2t + λ) (8t + λ) θ (4t + 3λ) < 0. Ater simliying we get λθ (4t + 3λ) (2t + λ) < 0 and conclude n A < n B. By noting that n k = θ n k, k {A, B}, it immediately ollows that the consumer demand or the ree media latorm is higher in regime A than 20

22 in regime B, i.e., n A > n B. Part (ii). This art o roosition 2 claims that the advertising level in regime A exceeds that in regime B, i.e., a A a A > a B > a B. Hence, 2θtβ (3t + λ) (2t + λ) (8t + λ) > θtβ (12t + 5λ) 4 (2t + λ) (4t + λ). We rearrange the inequality in the ollowing way and obtain 2θtβ (3t + λ) 4 (2t + λ) (4t + λ) (2t + λ) (8t + λ) θtβ (12t + 5λ) > 0. Ater simliying we get 3t (2t + λ) θ 3 β 3 γ 2 > 0. and it ollows that art (ii) o roosition 2 holds. This comletes the roo o roosition 2. B.3 Proo o Proosition 3 Part (i). To rove art (i) o roosition 3, that is, the ree media latorm realizes a higher roit in regime A than in regime B (π A > π B ), we have to show that 2tθ 2 β 2 (3t + λ) 2 (2t + λ) (8t + λ) 2 > tθ2 β 2 (12t + 5λ) 2 32 (2t + λ) (4t + λ) 2. We rearrange the inequality in the ollowing way and obtain 2tθ 2 β 2 (3t + λ) 2 32 (2t + λ) (4t + λ) 2 (2t + λ) (8t + λ) 2 tθ 2 β 2 (12t + 5λ) 2 > 0. Ater simliying we get tθ 2 β 2 (2t + λ) ( 768t 3 λ t 2 λ tλ λ 4) > 0. Equivalently, or the roo o the other claim in art (i), i.e., the roit o the ay media latorm is higher in regime B than in regime A (π A θt 2 (4t + 3λ) 2 (2t + λ) (8t + λ) 2 < θt (4t + 3λ) 2 16 (2t + λ) (4t + λ). We rearrange the inequality in the ollowing way and obtain < π B ), one has to show θt 2 (4t + 3λ) 2 16 (2t + λ) (4t + λ) (2t + λ) (8t + λ) 2 θt (4t + 3λ) 2 < 0. 21

23 Ater simliying we get θλ 2 t (4t + 3λ) 2 (2t + λ) < 0. and it ollows that art (i) o roosition 3 holds. Part (ii). To rove art (ii) o roosition 3 (Π A > Π B γ < γ π ), irst let Π A Π B H with Π A = π A H = κ 1 κ 2 I, where + π A and Π B = π B + π B. One can calculate that κ 1 = θ 3 β 2 γt (4t + 3λ) and κ 2 = 32 (2t + λ) (4t + λ) 2 (8t + λ) 2, I = 32t 2 (6β γ) + 4t (27β 8γ) λ + (13β 6γ) λ 2. We now derive the ollowing roerties: (1). κ 1 κ 2 > 0 γ (0, ). (2). lim γ H = lim γ I =. (3). I(γ = 0) = 192t 2 β > 0. (4). I(γ) has two critical oints with γ 1 = 32θtβ+13θ2 β 3 448θ 2 t 2 β tθ 3 β θ 4 β 6 18θ 2 β 2 and γ 2 = 32θtβ+13θ2 β 3 +. Moreover, γ 1 is a global minimum and 448θ 2 t 2 β θ 3 tβ θ 4 β 6 18θ 2 β 2 γ 2 is a global maximum because 2 I 2 γ=γ1 = 2 θ 2 β 2 (448t θtβ θ 2 β 4 ) > 0 and 2 I = 2 θ γ=γ2 2 β 2 (448t θtβ θ 2 β 4 ) < 0. 2 I (5). = 4t (27θβ 2 8t), γ=0 we thus distinguish three dierent cases: (5.1). I I < 0, then γ 1 < 0 and γ 2 < 0 with γ 1 < γ 2. γ=0 (5.2). I I > 0, then γ 1 < 0 and γ 2 > 0 with γ 1 < γ 2. γ=0 (5.3). I I = 0, then γ 1 < 0 and γ 2 = 0 with γ 1 < γ 2. γ=0 From (1)-(5) it ollows that Π A < Π B i and only i γ exceeds a critical level γ crit. For all values o γ smaller than γ crit it is the case that Π A > Π B. This comletes the roo o roosition 3. B.4 Proo o Proosition 4 Part (i). This art o roosition 4 states that media consumers enjoy higher surluses in regime B than in regime A (CS A < CS B ). To rove it, we need to derive ( v 5t ) ( 2 + µ 1 θ < v 103t ) 64 + µ 2 θ. We rearrange the inequality in the ollowing way and obtain 5t 2 + µ t 64 µ 2 < 0, 22

24 with µ 1 = 19t3 + 8λt 2 27 (2t + λ) (326t3 + 37λt 2 ) 27 (8t + λ) 2 and µ 2 = 11t3 + 5λt 2 16 (2t + λ) 2 + 4t2 4t + λ. Ater simliying, we get tλ (4t + 3λ) (256t λt tλ λ 3 ) 64 (2t + λ) 2 (4t + λ) (8t + λ) 2 < 0. It ollows that art (i) o roosition 4 is true. Part (ii). This art o roosition 4 indicates a higher advertisers surlus in regime A than in regime B, i.e., AS A > AS B. Hence, we have to show that 2θ 2 t 2 β 2 (3t + λ) 2 (2t + λ) 2 (8t + λ) 2 > θ2 t 2 β 2 (12t + 5λ) 2 32 (2t + λ) 2 (4t + λ) 2. We rearrange the inequality in the ollowing way and obtain 2θ 2 t 2 β 2 (3t + λ) 2 32 (2t + λ) 2 (4t + λ) 2 (2t + λ) 2 (8t + λ) 2 θ 2 t 2 β 2 (12t + 5λ) 2 > 0. Ater simliying, we get θ 3 β 3 t 2 γ (2t + λ) 2 (4t + 3λ) ( 192t tλ + 13λ 2) > 0. It ollows that art (ii) o roosition 4 is true. This comletes the roo o roosition 4. B.5 Proo o Proosition 5 We derive social welare in regimes A and B as with W A = θ 54 (54v 135t + Ψ 1 + Ψ 2 ) and W B = θ 64 (64v 67t + Ψ 3 + Ψ 4 ) Ψ 1 = 3t2 (2t + θβ 2 ) (2t + λ) 2 + 2t (11t + 4θβ2 ), Ψ 2 = 20t (61t + 5θβ2 ) (2t + λ) (8t + λ) Ψ 3 = 2t2 (2t + θβ 2 ) (2t + λ) 2 + 2t (14t + 5θβ2 ), Ψ 4 = 8t (16t + 5θβ2 ) (2t + λ) (4t + λ) 375t2 (8t + θβ 2 ) (8t + λ) 2, 32t2 θβ 2 (4t + λ) 2. I γ = 0, then W A = W B = θ 128 (128v + 27θβ2 40t). Moreover, we derive W A = θ2 tβ 27 (Ψ 5 Ψ 6 ) < 0 and W B = θ2 tβ 64 (Ψ 7 Ψ 8 ) < 0 23

25 with Ψ 5 = 375t (8t + θβ2 ) (8t + λ) 3 10 (61t + 5θβ2 ) (8t + λ) 2, Ψ 6 = 3t (2t + θβ2 ) 11t + 4θβ2 (2t + λ) 3 + (2t + λ) 2, Ψ 7 = 64tθβ2 (4t + λ) 3 8 (16t + 5θβ2 ) (4t + λ) 2, Ψ 8 = 4t (2t + θβ2 ) (2t + λ) 3 + In addition, with 2 W A 2 = θ3 tβ 2 27 (Ψ 9 + Ψ 10 ) > 0 and 2 W B 2 = θ3 tβ 2 28t + 10θβ2 (2t + λ) (Ψ 11 + Ψ 12 ) > 0, Ψ 9 = 20 (61t + 5θβ2 ) (8t + λ) t (8t + θβ2 ) (8t + λ) 4, Ψ 10 = 9t (2t + θβ2 ) 22t + 8θβ2 (2t + λ) 4 + (2t + λ) 3, Ψ 11 = 6t (2t + θβ2 ) (2t + λ) t + 10θβ2 (2t + λ) 3, Ψ 12 = 8 (16t + 5θβ2 ) (4t + λ) 3 96tθβ2 (4t + λ) 4. Hence, welare is a strictly concave unction in γ. Moreover, W A = θ2 β (136t + 27θβ 2 ) < 0 and γ=0 512t For θ > θ = 8t 9β 2, we derive W A > γ=0 W B W B = θ2 (32tβ + 9θβ 3 ) < 0. γ=0 128t. Hence, at γ = 0, welare in regime γ=0 A decreases less strongly in γ than welare in regime B. It ollows that W A > W B or low values o γ. Increasing the arameter γ, numerical simulations show that there exists a critical value γ such that W B > W A γ > γ. It ollows that there must exist another critical value γ W such that W B > W A γ > γ W. For θ θ = 8t, we derive 9β 2 <. Hence, at γ = 0, welare in regime B decreases less strongly in γ γ=0 γ=0 W A W B than welare in regime A. Furthermore, numerical simulations show that this is true or all γ > 0. It ollows that W B > W A γ > 0. This comletes the roo o roosition 5. 24