Markus Reisinger: Two-Sided Markets with Negative Externalities

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1 Markus Resnger: Two-Sded Markets wth Negatve Externaltes Munch Dscusson Paper No Department of Economcs Unversty of Munch Volkswrtschaftlche Fakultät Ludwg-Maxmlans-Unverstät München Onlne at

2 Two-Sded Markets wth Negatve Externaltes Markus Resnger 22nd December 2004 JEL classfcaton: D43, D62, L13 Keywords: Negatve Externaltes, Prce Competton, Two-Sded Markets. I would lke to thank Smon Anderson, Tommy Gabrelsen, Sven Rady, Ray Rees, Klaus Schmdt, partcpants at the conference on "The Economcs of Two-Sded Markets" n Toulouse 2004, and at the Sprng Meetng of Young Economsts n Warsaw 2004 for very helpful comments and dscussons. Department of Economcs, Unversty of Munch, Kaulbachstr. 45, Munch, e mal: markus.resnger@lrz.un-muenchen.de

3 Two-Sded Markets wth Negatve Externaltes 1 Abstract Ths paper analyses a two-sded market n whch two platforms compete aganst each other. One sde, the advertsers, exerts a negatve externalty on the other sde, the users. It s shown that f platforms can charge advertsers only, a hgher degree of competton for users can lead to hgher profts because competton on the advertsers sde s reduced. If platforms can charge users as well, profts mght ncrease or decrease, the latter because of ncreased competton through the addtonal nstrument of the user fee. Nevertheless the equlbrum wth user fee s more effcent.

4 Two-Sded Markets wth Negatve Externaltes 2 1 Introducton There are many markets where companes produce servces for a group of agents who do not pay for t or pay only a low prce. Instead these companes get revenues from advertsers who wsh to gan access to potental consumers va the servces of these companes. Examples are prvate rado or televson statons 1 whch often nterrupt ther programme to broadcast advertsement. 2 Search engnes lke Google or Yahoo! or nternet portals lke GMX often have a multtude of advertsements on ther web stes. 3 In the case of rado t s techncally mpossble to charge lsteners for the broadcastng of programmes. In the case of search engnes t s not customary to charge users for the servces. Ths paper studes a model of platform competton n whch users dslke advertsement and therefore spend less tme to consume servces of platforms. On the other hand advertsers wsh to gan users attenton to tempt them to buy ther products. In equlbrum the level of advertsng mght be too hgh or too low compared wth the socally optmal one because platform prcng does not nternalse the externalty whch s exerted on users by more advertsng. Concernng platform profts a hgher degree of competton for users can ncrease profts because prce competton becomes less ferce. Thus a dfferent level of competton on one sde nfluences the level of competton on the other sde and may have consequences on profts whch are opposte to the one n a one-sded market. If platforms can charge users as well there mght be an ncentve to subsdse users,.e. set a negatve fee, to attract more users. But snce both platforms do so ths strategc effect lowers ther profts. A prsoner s dlemma stuaton arses. But f the user fee s postve n equlbrum the addtonal nstrument ncreases profts. 1 To get an dea of the expendtures on advertsng, n the US n 2002 approxmately $ 50 bllon were spent on TV advertsng (Knd, Nlssen & Sorgard (2003)) and a thrty second commercal on FOX had an average prce of $ 150,000 (Prme Tme Prcng Survey, The Advertsng Age (2002)). 2 In the US advertsng tme ranged from approxmately 10 to 15 mnutes per hour n 1999 (Televson Commercal Montorng Report (1999)). 3 For an nternet portal advertsng s the most mportant source of revenue snce t does not charge users. For example, the nternet portal GMX sells a banner on ts web ste for 20,000 Euros per week (

5 Two-Sded Markets wth Negatve Externaltes 3 The equlbrum wth fees for both sdes of the market s always effcent. The reason s that wth the user fee platforms do now take nto account users utlty n ther prcng behavour. More specfcally, we assume that two platforms compete for user tme and advertsers. For the advertsers platforms are completely smlar whle platforms compete for users n a standard Hotellng style. Both sdes of the market choose only one platform. 4 Profts of advertsers are ncreasng n the tme users spend on a platform. Users utlty and the tme they spend on a platform are decreasng wth advertsng. 5 Therefore an advertser causes a negatve externalty on users of that platform drectly and also on all other advertsers on that platform ndrectly. If the gans from tradng advertsers goods are hgh compared to users utlty loss all producers should advertse from a socal pont of vew. If the utlty loss s hgh some of the advertsers should be excluded. The optmal partton of advertsers among platforms s even. The ntuton s that f one platform has more than half of the advertsers the externalty on all of them s hgh and can be reduced f some advertsers shft to the other platform. In a Nash equlbrum the number of advertsers on both platforms s the same but mght be too hgh or too low compared wth effcency. Platforms only nternalse the ndrect externalty that one advertser exerts on other advertsers but not the drect utlty loss of users. Ths s the case because ths externalty s ncorporated n ther prcng behavour whle the externalty on users does not nfluence prces. So f the degree of dfferentaton between platforms s low competton for users s ferce. But platforms compete for users by reducng ther advertsement levels. Thus wth low dfferentaton there s lttle advertsng on platforms. But f the gans from tradng advertsers goods are hgh ths level of advertsng s too low compared wth the socal optmum. If nstead platforms are hghly dfferentated they wll lose only few users f they advertse more. In ths case the level of 4 The assumpton that advertsers sngle-home (use only one platform) s not crucal to the results but smplfes the modelng. See the next secton for a longer dscusson. 5 Ferrando, Gabszewcz, Laussel & Sonnac (2003) analyse a model n whch some people are advertsement-avoders whle others are advertsement-lovers. But normally commercals are consdered a nusance for users. See Bagwell (2003) or Dukes & Gal-Or (2002).

6 Two-Sded Markets wth Negatve Externaltes 4 advertsng s too hgh. Platforms profts depend on the level of dfferentaton as well. If dfferentaton s relatvely hgh profts fall wth an ncrease n dfferentaton. The ntuton s that platforms have a hgher ncentve to attract advertsers because users do not swtch easly to the other platform. Ths results n lower prces for advertsng. But snce both platforms lower ther prces the level of advertsng stays the same whle profts are decreasng. So the strategc effect hurts platforms. Ths shows that n a two-sded market a lower level of competton on one sde can ncrease the competton on the other sde and lead to lower profts. If dfferentaton s low and competton for users s ferce an ncrease n the dfferentaton leads to rsng profts. The reason s that advertsng levels are low and wth a prce decrease ths level rses, whch ncreases profts. I also analyse what happens f platforms can charge a user fee. If ths user fee s unrestrcted, e.g. can ether be postve or negatve, the effcent outcome s reached. Wth the possblty of a user fee platforms have two dfferent nstruments at hand to make profts. They therefore take users utlty nto account as well. Snce platforms compete for both sdes ths leads to the effcent outcome. In equlbrum t mght be the case that ths user fee s negatve because platforms want to attract users n order to make more profts on advertsers. In ths case the addtonal nstrument of a user fee hurts platforms and ther profts are lower. If the user fee s postve profts are hgher than wthout a user fee. If the fee s restrcted to be postve the effcent outcome cannot be reached n general but only n the case when the user charge would be postve n equlbrum. Most of the papers n the two-sded markets lterature are concerned wth partcpants exertng postve externaltes on each other lke n the market for credt cards. Examples of these papers are Rochet & Trole (2003) or Wrght (2003). In Secton 6 of ther paper Rochet & Trole (2003) brefly analyse a model n whch platforms earn revenues from users and advertsers. Platforms are able to use a two-part tarff for both groups of partcpants. Rochet & Trole (2003) show that n general both prces depend on the relatons between own- and cross-prce elastc-

7 Two-Sded Markets wth Negatve Externaltes 5 tes. 6 Recently there has been a growng lterature on platform competton for advertsers. A semnal contrbuton to ths lterature s the paper of Anderson & Coate (2003). They analyse a model of TV broadcastng and are nterested n the queston whether two channels wll offer the same or dfferent programmes and how much advertsement they wll broadcast. They fnd that dependent on parameter values there can be too lttle but also too much advertsng and also too low or too hgh a varety of programmes. In ther model vewers suffer from advertsng wth the consequence that they swtch to ther less preferred programme f ths has fewer advertsements. As a result an even dstrbuton of advertsers on platforms s effcent because otherwse some vewers would not watch ther preferred programme. My paper revsts ther frst result n a dfferent type of model. The dfference to ther paper s that n my model platforms compete drectly for advertsers whle n ther model a change n the commercal prce of channel 1 does not nfluence the commercal prce of channel 2. Ths allows me to analyse the consequences of dfferent degrees of competton on one sde for the degree of competton on the other sde and on platforms profts. Anderson & Coate (2003) also analyse the case n whch vewers can be charged for watchng the programmes. They fnd that advertsng levels are usually lower n ths case. Knd, Nlssen & Sorgard (2003) analyse the broadcastng market as well and are also concerned wth the queston f competton between channels leads to overor underprovson of commercals. Lke Anderson & Coate (2003) they do not assume drect competton for advertsers. Knd, Nlssen & Sorgard (2003) also fnd that there can be underprovson of advertsng for low degrees of dfferentaton between platforms. They show as well that a merger between the two channels can mprove welfare as t leads to more advertsements. 7 6 For a detaled overvew how to model dfferent forms of competton and externaltes n twosded markets see Armstrong (2004). For a model wth a monopoly platform see Baye & Morgan (2001). 7 A paper wth a smlar basc model s Barros, Knd & Sorgard (2003). They are nterested n the consequences of a vertcal merger between a platform and a producer. They show that such a merger can be harmful for both frms. Ths s the case f platforms are close substtutes because the ndependent platform acts as a free rder on the merger and ncreases ts advertsng prce.

8 Two-Sded Markets wth Negatve Externaltes 6 In a paper of Gal-Or & Dukes (2003) dfferentated TV or rado statons also compete for vewers/lsteners. They analyse the condtons under whch a merger of two statons can be proftable. In ther model consumers are averse to advertsng but may proft from advertsements by the fact that they are better nformed about prces. 8 If two frms merge ths results n a hgher level of advertsng whch can drve producers prces and profts down. Therefore producers can pay less for advertsng. Ths mght render a merger unproftable. In contrast to the above cted papers my paper analyse a model wth competton for both sdes, users and advertsers, and not only users. I look at the consequences on prcng behavour and profts of platforms. As s shown ths behavour can be very dfferent n a two-sded market compared wth a one-sded one and also has dfferent effects than competton for only one sde. The remander of the paper s organsed as follows. The next secton sets out the basc model. In Secton 3 the effcent outcome s presented. Secton 4 analyses the equlbrum and compares t wth effcency. Secton 5 presents the equlbrum wth the possblty of a user charge. In Secton 6 an example of prcng behavour of nternet portals s gven. A short concluson s gven n Secton 7. 2 The Model The goal s to develop a model n whch platforms compete for users (consumers) and advertsers (producers). It s assumed that f platforms are nternet portals, rado statons, or televson channels consumers have the hardware to get access to these platforms. Advertsng causes a negatve externalty on users but advertsers profts are ncreasng n the number of users. In the followng the basc model s presented. 8 A problem n ther model s that ths gan for vewers/lsteners s not ncluded n the utlty functon. The reason s that ths would complcate the model dramatcally and would change some results.

9 Two-Sded Markets wth Negatve Externaltes 7 Platforms There are two platforms = 1, 2. Users cannot be excluded from usng the platforms. Therefore platforms cannot make profts from users drectly. Instead platforms make profts on advertsers. The proft functon of platform s Π = p n. p s the prce that platform s demandng from an advertser for an advert and n s the number of advertsers on platform. Each advertser can only place one advertsement and has to decde exclusvely on whch platform she wants to advertse. Thus there s rvalry for advertsers. It s assumed that platform prcng s lnear. We also assume that the costs of platforms are zero. 9 Users There s a mass of users M. Users are unformly dstrbuted on a lne wth length one where platform 1 s located at pont 0 and platform 2 located at pont 1. Each user decdes n favour of only one platform. 10 The utlty a user derves from spendng tme t on platform s v(t) where v(t) s an ncreasng and strctly concave functon. Users utlty s decreasng n the number of advertsements n on platform. The whole amount of dsposable lesure tme a user has s T. So T t s the tme a user spends on dong other thngs durng hs lesure tme. We normalze the utlty a user gets from dong ths other thngs to 1 per unt of tme. The maxmsaton problem of a user who s located at x can be wrtten as 11 max,t U = T t + v(t) γtn λ τ U x x (1) γ s a measure of the nusance costs of advertsng and s the same for all users. 9 Ths assumpton s made for smplcty. Relaxng t would change the calculatons but not the qualtatve results of the model. 10 Ths formalsaton fts the market for Internet portals or TV broadcastng well. Users or vewers decde n favour of only one portal to do e-malng or can only watch one programme at the same tme. 11 The advantage of ths formulaton s that the decson of users how much tme to spend on a platform s separated from the decson whch platform to use. See Anderson, de Palma & Thsse (1992).

10 Two-Sded Markets wth Negatve Externaltes 8 The parameter λ measures the curvature of the utlty functon n n. It s assumed that λ 1 so utlty s weakly concave n n. Ths s a realstc assumpton, e.g. one or two commercals on a homepage are not very dsturbng but f a web ste s full of adverts ths does dsturb users a lot and the tme whch s spent on these web ste decreases drastcally wth addtonal commercals. Lastly, τ U s the transportaton cost parameter and represents the degree of dfferentaton between both platforms. If a user has decded n favour of one platform dfferentatng wth respect to t yelds v (t) = 1 + γn λ. (2) t (n ) s mplctely gven by (2) and represents the demand functon for tme on platform dependent on n. From the Implct Functon Theorem we get the slope of ths demand functon t = γλnλ 1 < 0. (3) n v (t) So the amount of tme on platform s decreasng n n. The ndrect utlty functon of a user x s gven by U(x, n ) = T t(n ) + v(t ) γt(n )n λ τ U x x. In the followng we set T t(n ) + v(t ) γt(n )n λ = U B (n ) so U(x, n ) = U B (n ) τ U x x. The margnal consumer who s ndfferent between both platforms s gven by x m = τ U (U B (n 1 ) U B (n 2 )). We assume that t U s small enough so that n equlbrum all users use one platform, e.g. τ U 2U B (N/2). Thus a mass of X = Mx m chooses platform 1 and the remanng mass M(1 x m ) chooses platform 2. Wth advertsng a producer nforms users about the nature and the prce of ts products. After havng seen an advert a consumer knows hs wllngness to pay for the good. It s assumed that ths valuaton s the same for all consumers and s K wth probablty β and 0 wth probablty 1 β. For smplcty t s assumed

11 Two-Sded Markets wth Negatve Externaltes 9 that t s the same for each advertser s good. 12 Ths modelng follows Anderson & Coate (2003). Although ths formulaton s specfc t has the advantage that advertsng cannot have a postve value for users because each producer wll sell ts product at a prce K. A lower prce does not mprove the possblty of a sale. Thus the advertser s prce s equvalent to consumers valuaton and therefore a user s utlty of gettng aware of a new good s zero. The mplcaton of ths formulaton s that users do not get nformatonal benefts from usng a platform wth much advertsng. Advertsers There s a mass of advertsers N. Ex ante advertsers are ndfferent between both platforms. Advertsers choose only one platform to advertse on. Ths assumpton represents an easy way to model that platforms have to compete for advertsers. 13 If platform s chosen by an advertser her proft s P = X βkt(n ) p. If she decdes not to advertse she gets a proft of zero. The value of an advertsement on platform does postvely depend on the tme users spend on that platform. The dea s that the more tme a user spend on platform the hgher s the possblty that he gets aware of that advertsement and buys the product n the end. The gross value of an advertsement on s thus X βkt(n ). The advertser has to pay p for an advertsement on. For smplcty t s assumed that producton costs for advertsements and products are zero. Agan ths assumpton does not change the qualtatve results. 12 Ths stochastc structure s chosen to make the model more realstc and to express that not every user has a postve valuaton for each new good he gets aware of through advertsng. 13 The results of the model do not depend on the assumpton that advertsers sngle-home (choose only one platform). What s necessary s that wth a prce change of platform the number of advertsers on platform j changes. So f platform lowers p, n ncreases and n j decreases. One can get the same results wth the assumpton that advertsng frms mult-home (advertse on both platforms) but have only a certan budget for advertsng expendtures. So the last unt of ths budget can ether be spent on one or the other platform. Thus advertsers mult-home but put more commercals on the platform wth the lower prce.

12 Two-Sded Markets wth Negatve Externaltes 10 Game Structure In the frst stage the two platforms decde smultaneously about ther prces p 1 and p 2. In the second stage advertsers decde on whch platform they want to advertse f on any and users decde how much tme they spend on each platform. Then profts and utltes are realsed. Ths completes the descrpton of the model. In the analyss to follow we mantan the followng assumpton: A1 : βk > U B (n ) (2 t + 2 t n n 2 n ) n. The role of ths assumpton s to guarantee that the gan from tradng advertsers goods s hgh enough so that n = 0 s never effcent, e.g. no advertsng s never effcent. 3 Effcency In ths secton the optmal number of advertsements on each platform s derved. Ths result s later compared wth the equlbrum outcome of the prcng game. In the analyss of effcency there are two effects to consder. Frstly, a hgher number of advertsements ncreases the possblty of trade of advertsers products. Secondly, a hgher number of advertsements decreases users utlty and exerts a negatve externalty on other advertsers. Total welfare s gven by W F = MβKn 1 [ τ U (U B (n 1 ) U B (n 2 ))]t(n 1 ) +MβKn 2 [ τ U (U B (n 2 ) U B (n 1 ))]t(n 2 ) +MU B (n 1 )[ τ U (U B (n 1 ) U B (n 2 ))] +MU B (n 2 )[ τ U (U B (n 2 ) U B (n 1 ))] 1 2 τ + 1 (U 2τ B (n 1 ) U B (n 2 )) U U 0 xdx τ 11 U (U 2τ B (n 1 ) U B (n 2 ))(1 x)dx. U (4) The frst two terms are the welfare from tradng advertsers products. The thrd and the fourth term represent the utlty of users gross of transportaton costs and the ffth and the sxth term are the transportaton costs. Dfferentatng (4) wth

13 Two-Sded Markets wth Negatve Externaltes 11 respect to n, = 1, 2 yelds the frst order condtons 1 2τ U U B(n )M[βKn t(n ) + U B (n )] M[βKt(n ) + βkn t (n ) + U B(n )] 1 2τ U U B(n )M[βKn j t(n j ) + U B (n j )] = 0,, j = 1, 2. (5) So the frst order condton s the same for both n 1 and n 2. Thus t s effcent f n 1 = n 2. The second order condton s globally satsfed because of A1. Smplfyng (5) yelds the followng proposton. Proposton 1 If βkt(n/2) + βk(n/2)t (N/2) + U B(N/2) > 0, (6) n eff = N 2 s effcent. Otherwse, the effcent number of advertsers n eff, = 1, 2 s mplctly gven by βkt(n ) + βkn t (n ) + U B(n ) = 0. (7) It s therefore effcent f advertsers allocate equally among platforms. The ntuton behnd ths s smple. If we look only at the gans from trade the externalty whch one advertser causes on another one s ncreasng convexly. So f one platform has many advertsers users spend lttle tme on ths platform and thus many advertsers gan lttle attenton. To reduce ths externalty as well as possble t s optmal that each platform has the same number of advertsers. Transportaton costs can be reduced wth an even partton as well. If βk s hgh whch means that the probablty and the welfare gans from trade are hgh all producers should advertse and n = N/2. If these gans are lower compared to the utlty loss of users, n 1 + n 2 < N.

14 Two-Sded Markets wth Negatve Externaltes 12 4 Nash Equlbrum In ths secton we solve for the Nash equlbrum of the prcng game. Snce platforms can only quote prces to advertsers and are not dfferentated from ther pont of vew we are n a standard Bertrand game. The dfference s that wth a negatve externalty one platform cannot wn all advertsers by undercuttng ts compettor s prce. The platform wth the lower prce gets more advertsers but ths results n a hgher externalty on all of them and reduces ther profts. It s thus optmal for some advertsers to stay on the other platform. Thus platforms earn postve profts n equlbrum. 14 It turns out that the model s solvable n a smlar way as the product dfferentaton model of Hotellng. To see ths let us assume frst that all N producers advertse. Snce all advertsers are the same n equlbrum each advertser must be ndfferent between platform 1 and 2. If ths would not be the case one platform can ncrease ts prce wthout losng any advertsers whch cannot be an equlbrum. Thus we can determne the margnal advertser who s ndfferent between both platforms. She descrbed by MβKt(n 1 )[ τ U (U B (n 1 ) U B (N n 1 ))] p 1 = (8) MβKt(N n 1 )[ τ U (U B (N n 1 ) U B (n 1 ))] p 2 The left hand sde s the proft of an advertser on platform 1 and the rght hand sde the proft of an advertser on platform 2 f the number of advertsers are n 1 and n 2 = N n 1. Contrary to standard analyss t s not possble to solve (8) for n 1 because users utlty s concave n n 1. To get a soluton (8) s solved for p 1 whch yelds a max- 14 It should be mentoned that ths result s completely dfferent n a model wth postve externaltes. If n such models buyers (n our model advertsers) can coordnate on the platform that gves them the hghest surplus prces would be drven down to zero because of the standard Bertrand argument. For an overvew of ths lterature see Farrell & Klemperer (2001) or Katz & Shapro (1994).

15 Two-Sded Markets wth Negatve Externaltes 13 msaton problem of platform 1 of max n1 Π = {p 2 + MβKt(n 1 )[ τ U (U B (n 1 ) U B (N n 1 ))] MβKt(N n 1 )[ τ U (U B (N n 1 ) U B (n 1 ))]}n 1. (9) Maxmsng profts for both frms yelds two frst order condtons. These frst order condtons n combnaton wth equaton (8) and equaton (8) wth 1 and 2 reversed yelds the equlbrum values of n and p. After applyng the Envelope Theorem, U B(n ) = γλn λ 1 t(n ), we get n = N 2 (whch s obvous because of symmetry) and p = βkmnγλ(n/2) λ 1 [ t(n/2)2 t U 1 2v (t(n/2)) ]. It remans to calculate the equlbrum f n 1 + n 2 < N. 15 The equlbrum of the game s descrbed n the followng proposton. Proposton 2 If τ U τ 1 U = (N/2)λ γλt(n/2) 2 n the unque Nash equlbrum n s mplctly gven by t(n/2)+ γλ(n/2)λ v (t(n/2)) t(n ) + t(n ) n t(n ) 2 γλn λ = 0, (10) n τ U where a unque soluton n (0, N/2) exsts, and Profts of the platforms are p = MβKt(n ). (11) 2 Π = MβKt(n ) n. (12) 2 15 The method of soluton s smlar to a standard product dfferentaton game where consumers gross surplus from buyng s so low that frms are local monopolsts. See e.g. Gabszewcz & Thsse (1986).

16 Two-Sded Markets wth Negatve Externaltes 14 If τ 1 U < τ U τ 2 U = 4(N/2)λ γλt(n/2) 2 t(n/2)+ 2γλ(N/2)λ v (t(n/2)) N 2 and p Profts of the platforms are n the unque Nash equlbrum n = = MβKt(N/2). (13) 2 Π = MβKt(N/2) N/2. (14) 2 If τ U > τ 2 U n the unque Nash equlbrum n = N 2 (15) and p = βkmnγλ(n/2) λ 1 [ t(n/2)2 τ U 1 2v (t(n/2)) ] (16) Profts of the platforms are Π = βkmnγλ(n/2) λ [ t(n/2)2 τ U 1 ]. (17) 2v (t(n/2)) Proof When calculatng the margnal advertser n equaton (8) t was assumed that all producers advertse. But ths s only the case f t pays the Nth producer to advertse on a platform nstead of not advertsng and gettng profts of zero. Thus wth a prce p = βkmnγλ(n/2) λ 1 [ t(n/2)2 1 τ U ] ths s only the case 2v (t(n/2)) f or M 2 βkt(n/2) > βkmnγλ(n/2)λ 1 [ t(n/2)2 1 τ U 2v (t(n/2)) ] τ U > τu 2 = 4 (N/2)λ γλt(n/2) 2. t(n/2) + 2γλ(N/2)λ v (t(n/2)) The next queston s what the optmal prce of a platform s f t does not have to compete for advertsers because n 1 +n 2 < N. In ths case the number of advertsers on a platform depends on p and s gven by MβKt(n )[ τ U (U B (n ) U B (n j ))]

17 Two-Sded Markets wth Negatve Externaltes 15 p = 0. So the advertser n s the last one whose proft s not negatve gven a prce of p. Thus the proft of platform s Π = MβKt(n )n [ τ U (U B (n ) U B (n j ))]. (18) Maxmsng ths wth respect to n for both platforms yelds that n s gven by whch s equaton (10). t(n ) + t(n ) n t(n ) 2 γλn λ = 0. n τ U If n = 0 the left hand sde of (10) s postve because t(0) > 0. If n = N/2 the left hand sde s negatve because proft functon (18) s only relevant f τ U < τ 1 U. Thus a soluton wth n (0, N/2) exsts. Snce all terms of (10) are contnuous functons of n ths soluton s unque. Ths n equals N 2 f t(n/2) + t(n/2) N/2 t(n/2)2 γλ(n/2) λ = 0 n τ U or τ U = (N/2)λ γλt(n/2) 2 t(n/2) + γλ(n/2)λ v (t(n/2)) = τ 1 U. So for τ U τ 1 U = (N/2)λ γλt(n/2) 2 p = MβKt(n ) 2. t(n/2)+ γλ(n/2)λ v (t(n/2)) n s gven by t(n ) + t(n ) n n t(n ) 2 γλn λ τ U = 0 and It remans to calculate what happens f If τu 1 < τ U τu 2 = 4(N/2)λ γλt(n/2) 2. In ths t(n/2)+ 2γλ(N/2)λ v (t(n/2)) case n 1 = n 2 = N/2 and both platforms set ther prces such that the advertsers have zero utlty, e.g. p = MβKt(N/2) 2

18 Two-Sded Markets wth Negatve Externaltes 16 whch s equaton (13). q.e.d. The proft functon s contnuous but has two knks. In the followng we provde some comparatve statc analyses. Frst let us look at a change n the transportaton cost parameter τ U. Proposton 3 Platform profts are ncreasng n τ U as long as τ U τu. 1 Profts are ndependent of τ U f τu 1 < τ U τu 2 and profts are decreasng n τ U f τ U > τu. 2 Proof If τ U τ 1 U proft s gven by (12) and the optmal number of advertsers s gven by (10). As was shown n the proof of Proposton 2 (10) s the frst order condton for the maxmsaton problem of platform wth respect to n. Applyng the Implct Functon Theorem to (10) yelds that sgn( n τ U ) = sgn( (10) τ U ) = 1 2(τ U ) 2 βkmn t(n)u B(n ), whch greater than zero. Dfferentatng equaton (12) wth respect to τ U gves Π τ U t(n ) = MβK 2 (t(n ) + t(n ) n n ) n τ U. So sgn( Π τ U ) = sgn(t(n ) + n n ). By equaton (10), t(n ) + t(n ) n n t(n ) 2 γλn λ τ U = 0. Snce the last term of the left hand sde s negatve t(n ) + t(n ) n n > 0 whch yelds Π τ U > 0. If τ 1 U < τ U τ 2 U proft s gven by (14). Here n = N 2 and therefore (14) s ndependent of τ U. If τ U > τ 2 U proft s gven by (17). In ths case Π t U = βkmnγλ(n/2) λ [ t(n/2)2 (τ U ) 2 ] < 0. q.e.d. The ntuton behnd ths result s the followng. τ U represents the level of dfferentaton between the two platforms from the perspectve of the users. If τ U s small platforms have to compete fercely for users. They do ths by reducng ther

19 Two-Sded Markets wth Negatve Externaltes 17 amount of advertsng. Thus prces are hgh and only few producers advertse. If τ U ncreases prces decrease. But proft s rsng because more advertser choose to advertse on the platforms. 16 In ths regon platforms do not compete for advertsers snce n 1 + n 2 < N. But when τ U reaches τ 1 U all producers are advertsng and competton for advertsers starts. In the regon between τ 1 U and τ 2 U profts stay the same snce t does not pay for one platform to lower prces. But f τ U rses further competton for advertsers lowers prces. The reason s that t pays platforms to attract more advertsers because fewer consumers wll swtch to the other platform. Ths strategc effect drves prces down. But also profts are lower because both frms lower ther prces and n stays the same. Ths shows that n a two-sded market wth negatve externaltes a lower degree of competton on one sde can ncrease the competton on the other sde and lead to lower profts. Ths s never possble n a standard market wth only one sde. It s also possble to derve a comparatve statc result wth respect to γ, the nusance cost of advertsng. Proof Proposton 4 If τ U τ 2 U platform profts are decreasng n γ but f τ U > τ 2 U the effect of a change n γ on profts s ambguous. Frst look at the case τ U τ 1 U. Equaton (10) s the frst order condton of the maxmsaton problem of platform. By applyng the Implct Functon Theorem we have Multplyng (10) wth τ U t(n ) yelds sgn( n γ ) = sgn( t(n ) γ + n 2 t(n ) n γ + n U B(n ) 1 τ U t(n ) γ ) t(n )γλ v (t(n ) )) = sgn( nλ (1+λ)τ U n 2λ = sgn( (1 + λ)τ U + n λ γλt(n )). τ U + t(n ) n n τ U t(n ) t(n )γλn λ = A smlar result s obtaned by Barros, Knd & Sorgard (2003) n a dfferent model.

20 Two-Sded Markets wth Negatve Externaltes 18 Thus τ U > t(n )γλn λ and therefore τ U (1 + λ) > t(n )γλn λ. Ths shows that n γ < 0. If τ U τ 1 U proft s gven by (12). Dfferentatng (12) wth respect to γ yelds Π γ = MβK 2 [t(n ) n Dfferentatng t(n ) γ + t(n ) γ γ yelds n ]. n λ v (t(n ) < 0 and thus Π γ < 0. If τ 1 U < τ U τ 2 U proft s gven by (14). Dfferentatng yelds Π γ If τ U = MβKN 4 t(n ) γ < 0. > τ 2 U proft s gven by (17). Dfferentatng proft wth respect to γ yelds sgn( Π γ ) = sgn(2t(n ) 2 (v (t(n ))) 2 t(n )v (t(n ))+4t(n )γv (t(n )) 2 t(n ) γ +γτ U t(n ) γ v (t(n ))). The frst two terms are postve the thrd term s negatve and the fourth term s unclear. So proft may ncrease or decrease n γ. q.e.d. γ represents the nusance costs of advertsng. So one would guess that proft should decrease n γ because consumers spend less tme on the platforms. Proposton 4 states that ths s only true f platforms do not compete for advertsers,.e. f τ U s low. In ths case each user spends less tme on platforms whch results n a lower possblty of trade of advertsers goods and thus n lower prces. But f τ U s hgh and platforms compete for advertsers, proft mght ncrease n γ. The ntuton s that wth a hgh τ U platforms have an ncentve to lower ther prces to attract new advertsers. Ths reduces profts. Wth a hgher nusance cost ths effect s dampened because each platform makes lower profts on new advertsers and thus prces mght be hgher compared wth a lower γ. Thus a hgher γ causes two effects on prces. The frst s that users are more dsturbed by commercals whch reduces prces. The second s that competton s reduced whch ncreases prces. The consequences on profts are therefore not clear. Now let us turn to the comparson of the Nash equlbrum wth the effcent outcome. Proposton 5 If βkt(n/2) + βkn/2t (N/2) + U B(N/2) > 0 advertsng s effcent f τ U τu 1 and there s too lttle advertsng f τ U < τu. 1 If there exsts n s.t.βkt(n ) + βkn t (n ) + U B(n ) = 0, there can be too much or too lttle advertsng n equlbrum.

21 Two-Sded Markets wth Negatve Externaltes 19 Proof There s too lttle advertsng f τ U much f τ U > mn[τu, 1 βkn eff t(n eff )]. Only f τ U = βkn eff < mn[τ 1 U, βkn eff t(n eff ) τu 1 the equlbrum s effcent. t(n eff )] and too From Proposton 1 the optmal number of advertsers on each platform s gven by (6) or (7). Frst look at the case where there exsts an n < N/2 such that (7) holds. In the Nash equlbrum of the game n eq = N/2 f τ U > τ 1 U. Thus t follows that n eq > n eff f τ U > τ 1 U. If τ U < τ 1 U, n eq s gven by the frst order condton (10). If we nsert n eff order condton we get from (7) n ths frst γλt(n eff )(n eff ) λ 1 βk γλt(neff τ U ) 2 n eff > = < 0 or τ U > = < βkn eff t(n eff ). So f τ U > βkn eff t(n eff ) the left hand sde of equaton (10) s than zero at n eq but t s greater zero at n eff. Thus n eq > n eff. If τ U < βkn eff Thus n eq < n eff. It therefore follows that n eq τ U < mn[τ 1 U, βkn eff equlbrum s effcent. t(n eff ) equaton (10) s zero at n eq but t s lower than zero at n eff. t(n eff > n eff Now look at the case where n eff τ U τ 1 U and n eq < N/2 f τ U < τ 1 U. The proposton follows. f τ U > mn[τ 1 U, βkn eff )]. Only n the case when τ U = βkn eff t(n eff )] and n eq < n eff f = N/2. We know that n equlbrum n eq t(n eff ) τu 1 the = N/2 f q.e.d.

22 Two-Sded Markets wth Negatve Externaltes 20 Ths shows that t depends on the level of τ U whether the equlbrum s effcent or not. 17 If τ U s low competton for users s ferce and therefore advertsng levels are low. Platforms do not take nto account the users utlty loss from an addtonal commercal but only the ndrect externalty on all advertsers. The reason s that only ths ndrect externalty can be reflected n ther prcng behavour. If competton for users s harsh many users swtch to the compettor f one platform has an addtonal advertser. Thus the advertsng level s lower than the effcent level. From (6) and (7) we know that τ U does not play a role n determnng the effcent advertsng level. But t s the mportant varable for platform competton. In the case when not all producers should advertse there can be too much advertsng f τ U s hgh because competton for users s low. If all producers should advertse there can only be too lttle advertsng. Ths s the case f competton s ferce wth the same lne of reasonng as before. 5 Prcng Behavour of Internet Portals In ths secton we dscuss the prcng behavour of two nternet portals, namely AOL and GMX. We argue that the structure of ther commercal prces fts the results of the precedng secton qute well. Both AOL and GMX are portals where members have access to free e-mal, get nformed about cheap offers of products and can nform themselves about specfc topcs n so called affnty groups. It s costless to become a member of theses portals. The portals get revenues from members only f these buy some servces from the portals, lke sendng SMS or prntng pctures. Usually these servces are sold at low prces. The most mportant source for profts of the portals s advertsng. There are dfferent forms of advertsng on both portals but the most common ones are banners on ther web ste. AOL sells a full-sze banner on ts homepage for 15 Euros per thousand eye-balls, a half-sze banner s sold for 10 Euros. A full-sze banner on 17 In a model of TV-advertsng a smlar result s obtaned by Knd, Nlssen & Sorgard (2003).

23 Two-Sded Markets wth Negatve Externaltes 21 the logout-page of AOL costs only 7 Euros, a half-sze banner 5 Euros. 18 A smlar prcng structure can be observed at GMX. 19 At GMX a logout banner costs 15 Euros whle a comparable banner on the homepage costs 24 Euros. 20 Where does ths dfference come from? Snce these prces are per thousand eyeballs one cannot argue that homepage prces are hgher because more people are watchng the homepage. Instead a reason can be found from the arguments of the precedng secton. To attract advertsers portals have to attract users at frst. But before a user decdes whch portal to use he wll compare the homepages of the portals. If one ste s plan whle the other one s full of commercals whle both portals can be used for free he wll most lkely decde n favour of the plan one. Thus competton for users takes manly place on the homepages. Ths can explan the hgh prces for the homepage banners. Thus homepages of portals do usually have few advertsements on t. By contrast, only f a user has already decded to use a portal he wll see the logout page. So there s no more competton for users and prces for logout-banners are cheap. For example, on the portal GMX usually four advert banners are on the logout page but at most one the start page. Ths provdes some evdence that the degree of competton for users has a hgh nfluence on commercal prces. 6 User Charge In some markets t s not only possble for platforms to make money on advertsers but to charge users for the consumpton of platforms servces as well. Examples are pay-tv channels and newspapers. For example n Europe drect broadcast satellte channels lke Canal Plus or Premere are partally fnanced by user charges. Ths s also of polcy nterest snce n the TV case t s becomng techncally easer to exclude vewers. 18 See 19 See 20 Prces are hgher at GMX than at AOL because banners are bgger and the form of advertsng s fancer.

24 Two-Sded Markets wth Negatve Externaltes 22 In our model the possblty of a user charge can be ncorporated n an easy way. In the followng we assume that each platform can charge users a fee c for ts servces. Then platform proft s gven by Π = p n + X c. The ndrect utlty of a user who s located at x and uses platform s gven by U(x, n ) = T t(n ) + v(t ) γt(n )n λ c τ U x x. Agan, as n Secton 2 we set T t(n ) + v(t ) γt(n )n λ = U B (n ) so U(x, n ) = U B (n ) c τ U x x. The assumpton that all users choose one platform s mantaned so τ U 2(U B (N/2) c ). The margnal user s then gven by x m = τ U (U B (n 1 ) U B (n 2 ) + c 2 c 1 ). Conductng the same analyss as before gves a maxmsaton problem of platform 1 of max n1,c 1 Π 1 = {p 2 + βkmt(n 1 )[ τ U (U B (n 1 ) U B (N n 1 )) + c 2 c 1 ] MβKt(N n 1 )[ τ U (U B (N n 1 ) U B (n 1 ))]}n 1 +c 1 M( τ U (U B (n 1 ) U B (n 2 ) + c 2 c 1 )) f all producers advertse. Formulatng the frst order condton and solvng for p and c yelds p = Mγλ(N/2) λ 1 [t(n/2) NβK 2v (t(n/2)) ] and c = τ U βknt(n/2) For the moment we assume that c can be postve or negatve.

25 Two-Sded Markets wth Negatve Externaltes 23 The proft of the platform s gven by Π = Mγλ(N/2) λ [t(n/2) NβK 2v (t(n/2)) ] + M 2 [τ U t(n/2)nβk]. Comparng ths proft wth the proft wthout a user charge we get Π wth charge = Π wthout charge + [1 t(n/2) NβK ][Mλγt(N/2)(N/2) λ M + τ U τ U 2 ]. Thus the proft wth user charge s hgher f 1 t(n/2) NβK τ U the formula for the user charge to be postve. > 0. But ths s exactly The profts n the case that not all producers advertse are computed n the same way as n Secton 3. Ths leads to the followng equlbrum. Proposton 6 If βk (N/2)λ 1 γλt(n/2) t(n/2)+ γλ(n/2)λ v (t(n/2)) then n s mplctly gven by t(n ) + n t t(n ) nλ 1 γλ n βk = 0, (19) where a unque soluton n (0, N/2) exsts, and p = M 2 βkt(n ) (20) and c = τ U βkn t(n ). (21) Profts of the platforms are Π = 1 2 Mτ U (22) If (N/2)λ 1 γλt(n/2) t(n/2)+ γλ(n/2)λ v (t(n/2)) then n = N 2, < βk 2(N/2)λ 1 γλt(n/2) t(n/2)+ γλ(n/2)λ 2v (t(n/2)) p = M 2 βkt(n/2) (23)

26 Two-Sded Markets wth Negatve Externaltes 24 and c = τ U βknt(n/2). (24) Profts of the platforms are Π = 1 2 Mτ U. (25) If βk > 2(N/2)λ 1 γλt(n/2) t(n/2)+ γλ(n/2)λ 2v (t(n/2)) then n = N 2, p = Mγλ(N/2) λ 1 [t(n/2) NβK 2v (t(n/2)) ] (26) and c = τ U βknt(n/2). (27) Profts of the platforms are Π = Mγλ(N/2) λ [t(n/2) NβK 2v (t(n/2)) ] + M 2 [τ U t(n/2)nβk]. (28) Proof If platforms set prces p = Mγλ(N/2) λ 1 [t(n/2) t(n/2) under whch N producers advertse s gven by or NβK 2v (t(n/2)) M 2 βkt(n/2) p = Mγλ(N/2) λ 1 NβK [t(n/2) 2v (t(n/2)) ] > 0 βk > 2(N/2)λ 1 γλt(n/2). t(n/2) + γλ(n/2)λ 2v (t(n/2)) In ths case p = and c are gven by (26) and (27). ] the condton If not all N producers advertse there s no competton for advertsers. Thus each platform set the prce p = M 2 βkt(n ). The maxmsaton problem of platform s

27 Two-Sded Markets wth Negatve Externaltes 25 thus max n,c Π = n M 2 βkt(n ) whch yelds that n s mplctly gven by (19) and c = τ U βknt(n ). For the same reason s n the proof of Proposton 2 a unque soluton n (0, N/2) exsts. Insertng n = N/2 n (19) gves t(n/2) + N/2 t n t(n/2) (N/2)λ 1 γλ βk = 0 or βk = (N/2) λ 1 γλt(n/2). t(n/2)+ γλ(n/2)λ v (t(n/2)) Thus f βk (N/2)λ 1 γλt(n/2) then n t(n/2)+ γλ(n/2)λ s gven by (19). If βk > (N/2)λ 1 γλt(n/2) v t(n/2)+ γλ(n/2)λ (t(n/2)) v (t(n/2)) n = N/2 and p = and c are gven by (23) and (24). then q.e.d. The proft can now be compared wth the proft f a user charge s not possble. Proposton 7 Suppose that platforms can set an unrestrcted user charge. If ths user charge s postve n equlbrum profts are hgher than wthout the user charge. Proof To prove the proposton we have to compare the hghest proft wthout a user charge wth the lowest proft wth user charge. Because of Proposton 2 the hghest proft wthout a user charge s gven by Π wthout charge = MβKt(N/2) 2 N/2. NβK The lowest proft wth user charge s Π wth charge = 1 2 Mτ U. Ths s the case because Mγλ(N/2) λ [t(n/2) ]+ M [τ 2v (t(n/2)) 2 U t(n/2)nβk], whch s the proft wth user charge f βk > 2(N/2)λ 1 γλt(n/2) t(n/2)+ γλ(n/2)λ 2v (t(n/2)), s hgher than 1Mτ 2 U f βk > 2(N/2)λ 1 γλt(n/2). t(n/2)+ γλ(n/2)λ 2v (t(n/2)) Now comparng Π wth charge = 1 2 Mτ U wth Π wthout charge = MβKt(N/2) 2 N/2 yelds that Π wth charge > Π wthout charge f and only f τ U But ths exactly the condton for the user fee to be postve. > N/2βKt(N/2). q.e.d.

28 Two-Sded Markets wth Negatve Externaltes 26 We have shown that profts always ncrease f the user charge s postve. But f t s negatve profts mght be lower than wthout ths possblty. The ntuton behnd ths result s the followng. If platforms have the possblty to set a user charge there are two dfferent ways to do that. The frst s to set a hgher commercal prce to get rd of some advertsers and then make profts on users wth a postve user charge. Ths s the case f τ U > βknt(n/2). Both platforms set a hgher p so none of them loses many advertsers. But they set c > 0 as well whch results n hgher profts. The second possblty s to subsdse users wth a negatve fee n order to attract more advertsers. 22 But snce both platforms do so n equlbrum they reduce ther advertser prce as well and profts are lower than wthout a user charge. Thus a prsoner s dlemma stuaton arses. 23 the addtonal nstrument of the user charge were not avalable. Dfferentatng wth respect to τ U yelds that Π τ U = M 2 Profts would be hgher f > 0. So n contrast to the case wthout user charge profts are always ncreasng n τ U. The reason s that p s ndependent of τ U whle c s ncreasng n τ U. Thus f platforms can charge both sdes of the market the degree of competton on one sde s only reflected n the prce of that sde. Let us turn now to the welfare analyss. Proposton 8 If platforms can set an unrestrcted user charge the equlbrum s effcent. Proof If βk (N/2)λ 1 γλt(n/2) t(n/2)+ γλ(n/2)λ v (t(n/2)) γλn λ 1 then n equlbrum n s gven by (19). But snce U B(n ) = t(n ) equaton (19) s the same as βkt(n ) + βkn t (n ) + U B(n ) = 0 whch s equaton (7), the condton for effcency f n eff < N/2. 22 A smlar way of reasonng s gven by Rochet & Trole (2003). In two-sded markets the platforms charge prces such that the sde wth the hgher demand elastcty s subsdsed by the sde wth the lower demand elastcty. 23 Smlar effects are at work n Anderson & Leruth (1993) and Thsse & Vves (1988) where an addtonal prcng nstrument hurt frms.

29 Two-Sded Markets wth Negatve Externaltes 27 If βk > (N/2)λ 1 γλt(n/2) then n t(n/2)+ γλ(n/2)λ = N/2. Routne manpulatons of the nequalty v (t(n/2)) yelds that ths nequalty s the same as βkt(n/2)+βkn/2t (N/2)+U B(N/2) > 0. But ths s nequalty (6), the condton for effcency f n eff = N/2. q.e.d. Why does the addtonal nstrument of a user charge lead to the effcent outcome? The ntuton s that platforms now take users utlty drectly nto account and not only ndrectly n the commercal prces. Snce there s competton for users both platforms set the fees n such a way that users allocate effcently. On the sde of the advertsers there s Bertrand competton (although profts are postve). Advertsers are allocated effcently as well. The reason s that the effcent allocaton helps both frms to get hgher revenue. Thus wth a second nstrument at hands competton for users and advertsers leads to the effcent outcome. Up to now we assumed that the user charge s unrestrcted so t can be negatve. But n many stuatons ths s not practcable. TV watchers are not pad by statons or nternet users are not subsdsed by portals. If the user fee s restrcted to be postve ths means n our analyss that c = max{0, τ U βknt(n )}. If τ U < βknt(n ) ths constrant s bndng. In ths case t would be optmal for platforms n a symmetrc equlbrum to set c = 0. But ths exactly what we observe n many markets. Take agan the case of an nternet portal. For them t would be techncally no problem to charge users f they want to get access to ther ste. Instead they do not requre users to pay a fee n order to attract many users and make profts on advertsers. In terms of welfare f a user charge has to be postve the equlbrum s no longer generally effcent but only f τ U > βknt(n ). So f the constrant on c s bndng the result s the same as n the case wthout a user charge. To reach effcency both prcng nstruments have to be unrestrcted For a dscusson of polcy mplcatons for two-sded markets see Evans (2004).

30 Two-Sded Markets wth Negatve Externaltes 28 7 Concluson Ths paper analysed a model of platform competton n whch each advertser exerts a drect negatve externalty on users and ndrect one on all other advertsers on the same platform. It was shown that the number of advertsements n equlbrum can be too hgh or too low compared wth the effcent one. Profts of platforms can ncrease f they become less dfferentated because ths leads to lower competton on the advertsers sde. If platforms can set a user charge as well profts ncrease only f ths charge s postve n equlbrum. A prsoner s dlemma result s possble. But welfare s always hgher wth a user charge. We have also gven anecdotal evdence that supports our results n an example of prcng behavour of nternet portals. An nterestng suggeston for further research mght be to analyse the dynamcs of such a two-sded market. Usually f people are used to one nternet portal or read a newspaper for several years they would not swtch easly f another one has fewer advertsements. People form habts. It would be nterestng to analyse how such habt formaton mght change the results. A new platform whch enters the market after the others (such as Google n the search engne case) needs a very low level of advertsng to nduce consumers to swtch. Ths s what was actually observed for Google. So the queston arses f ths low level of advertsng wll persst or vansh over tme.

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