Selling News Information to Consumers*

Transcription

1 Selling News Information to Consumers* Johannes Dittrich Heiko Karle Heiner Schumacher February 5, 07 preliminary and incomplete Abstract We develop a model of a two-sided media market, in which profit-maximizing media outlets first commit to the degree of horizontal and vertical differentiation of their news reports and then compete in prices and fees for users and advertisers. We find that media outlets maximally differentiate only in one dimension in case they are financed by advertising revenues and direct charges to consumers (Pay-tv broadcasting). In case media outlets revenues consist solely of advertising revenues (Free-to-air broadcasting), differentiation will still be only in one dimension but less than maximum. Furthermore, horizontal differentiation is more likely to arise than vertical differentiation in this case. Interpreting horizontal differentiation of news reports as ideological bias (Mullainathan and Shleifer, 005) and vertical differentiation as facts bias (Gentzkow and Shapiro, 0), we predict that the transition from Pay-tv to Free-to-air broadcasting reduces the magnitude of both sorts of media bias and renders the regime of facts (ideological) bias less (more) likely to arise. Keywords: Two-sided markets, Horizontal product differentiation, Vertical product differentiation, Price competition, Advertising, Media Bias, Ideological bias, Facts bias. *We are grateful to Vardges Levonyan, Markus Reisinger, and Martin Peitz as well as seminar audiences at the University of Mannheim and the Workshop of Intellectual Property and Competition Law at Castle Ringberg for their valuable comments and suggestions. The usual disclaimer applies. Correspondence to: J. Dittrich. University of Mannheim, CDSE, 683 Mannheim, Germany; johannes.dittrich@gess.unimannheim.de. Center for Law and Economics, ETH Zurich, 809 Zurich, Switzerland; hkarle@ethz.ch. KU Leuven, Department of Economics, Naamsestraat 69, 3000 Leuven, Belgium. heiner.schumacher@kuleuven.be.

2 Introduction A common charge against media is that they spread biased information and therefore may have a negative influence on policy outcomes. For this reason, it is important to understand what causes profit-maximizing media companies to bias their reports. A large political economy literature has dealt with this question (see Prat and Stromberg, 03 for an excellent review). A common distinction in this literature is made between models in which media companies decide to omit or manipulate information ( facts bias ) and models in which companies present or comment news in different ways ( ideological bias ). The effects of these biases on outcomes crucially depend on what consumers do with the information received through media. Information may have an instrumental value: consumers use information about the state of the world to make important decisions such as voting or investments (for example, Gentzkow and Shapiro, 0). Alternatively, information may have a consumption value: consumers enjoy reading news reports that confirm their previous views and beliefs (for example, Mullainathan and Shleifer, 005). So far, these concepts have been studied in isolation. Consumers either use information to make decisions or enjoy their consumption to get reassurance. However, what happens if both concepts are active simultaneously? What does this mean for the magnitude of the facts bias and ideological bias when media outlets are profit-maximizing firms competing for consumers and advertisers? In this paper, we develop a model of a two-sided media market, in which profit-maximizing media outlets simultaneously commit to the degree of horizontal and vertical differentiation of their news reports and then compete in prices and fees for users and advertisers. We interpret horizontal differentiation of news reports as ideological bias (as in Mullainathan and Shleifer, 005) and vertical differentiation as facts bias (in line with Gentzkow and Shapiro, 0). The latter interpretation is motivated by the observation that news reports often convey information about individual investment decisions by news consumers such as the choice of health plans. Overall, in our model, media bias is rooted in media outlets endeavour to reduce competition in prices and advertising fees. To the best of our knowledge, this is the first paper accessing this point allowing for both kinds of media biases simultaneously. Our main result is that media outlets maximally differentiate only in one dimension in case they are financed by advertising revenues and direct charges to consumers (Pay-tv broadcasting), while differentiation will still be only in one dimension but less than maximum when media outlets revenues consist solely of advertising revenues (Free-to-air broadcasting). We also find that the vertical differentiation equilibrium is less prevalent under Free-to-air broadcasting compared to Pay-tv broadcasting. The paper is structured in the following way. In the remainder of this section, we discuss the relevant literature. In Section, we present our model. Consumer demand and the ad-

3 vertising space offered by media outlets are derived in Section 3 and 4. In Section 5 and 6, we provide the analysis of our model under the regimes of Pay-tv and Free-to-air. Section 7 concludes. Unless indicated otherwise, proofs are relegated to Appendix A. Related literature. Our paper relates to the literature on two-sided markets and media economics in particular. For an excellent survey on the media economics literature see Prat and Stromberg (03). Within the media economics literature there has been extensive research on the topic of media bias. Mullainathan and Shleifer (005) consider a Hotelling model in which media outlets can slant their news to reduce price competition. A different approach to media bias is taken by Gentzkow and Shapiro (006). They consider a career concerns model in which newspapers aim to build a reputation for quality by slanting their reports towards the prior beliefs of their consumers. Whereas the type of media bias considered by Mullainathan and Shleifer (005) can be described as an ideological bias, the model by Gentzkow and Shapiro (006) instead generates a facts bias (see also Gentzkow and Shapiro, 0). Our model combines both ideas and allows media outlets to differentiate in an ideological as well as a facts dimension. This enables us, to analyze what type and magnitude of bias will endogenously arise given consumers preferences and advertising costs. There is also an extensive literature on two-sided markets in a media context. In their seminal paper Anderson and Coate (005) consider two media outlets that compete for viewers and attract advertisers. Peitz and Valletti (008) extend their model to account for endogenous location choices and the possibility to directly charge consumers. They show that media outlets are less differentiated under Free-to-air broadcasting compared to Pay-tv broadcasting but consider only the case of horizontal differentiation. Our paper also relates to Armstrong (006) who considers competition between two media outlets under Pay-tv broadcasting with exogenous content provision. In methodological terms, our model setup heavily relies on the paper with two-dimensional product differentiation by Neven and Thisse (989). In their model, firms can differentiate in a quality as well as a variety dimension of a physical good before competing in prices. They show that there exist two types of equilibria that are both characterized by maximum differentiation in only one dimension. We extend their setup by accounting for the two-sided nature of the media market. In our setting, platforms do not only compete for consumers but also advertisers or equivalently shares of the advertising budget. This is different from the competitive bottleneck model that has been used in the media markets literature (e.g. Anderson and Coate (005) or Peitz and Valletti (008)). We consider competition for advertisers both interesting and relevant: Bernhardt et al. (008) analyze a situation where media outlets suppress negative information to confirm voters prior beliefs, which leads to biased voting decisions. 3

4 Indeed, if advertisers have a limited marketing budget, they might be unable to place ads on multiple platforms. Consequently, platforms will have an incentive to attract advertisers by offering competitive fee rates. This assumption is also consistent with the empirical findings of Kaiser and Wright (006). Using data on magazines in Germany, they find that the share of multihoming advertisers is on average 6.9% and as low as around % for some categories, implying that multi-homing of advertisers is indeed limited. For our model of the advertising market, we rely on a recent paper by Reisinger (0) who considers platform competition for advertisers and consumers in a Hotelling model without endogenous location choices. In contrast, our model accounts for endogenous content provision and the possibility that media outlets can also charge consumers directly for providing news content. The Model The model features three distinct types of players: consumers, media outlets and advertisers. Consumers are interested in obtaining information in a format that matches their taste. Media outlets are firms that provide content (news) of different quality and entertainment type. Advertisers want to sell goods to consumers, but can only do so via placing ads on the media outlets. We assume that media outlets have two ways of creating revenue. They can directly charge consumers for the content they deliver and they sell advertising space to advertisers. Consumers. Consumers in our model are heterogenous in two dimensions. They differ in their taste for the quality of news, θ [0, ] and their preferred type of entertainment, x [, ]; both types are uniformly distributed. There is a unit mass of consumers and each consumer has unit demand for news produced by one of two media outlets. The utility of consumer type (x, θ) when buying news from media outlet i {, } is given by U i (p i, a i, y i, q i, x, θ) = ū p i δa i (y i x) + q i θ, () where she incurs a disutility from the price she pays and the amount of advertising a i which outlet i uses to finance its content provision. She also incurs a disutility in taste for entertainment when the location y i of the media outlet doesn t match her preferred taste x. The parameters δ and represent the corresponding utility weights. The consumer s taste for quality of news θ reflects her surplus of making a correct individual investment decision and the quality of news q i reflects the precision of the investment signal transmitted in the news reports of media outlet i. We assume that the lump-sum utility from consuming any kind of news ū is The following micro foundation applies: suppose there are two types of investments A and B and two states of nature a and b. In state a only investment A leads to a surplus of θ and investment B to zero surplus and vice versa in state b. We can then separate quality q i [q, q] R + into a utility weight ( q q) and a probability 4

5 large enough such that consumers of all types always obtain a benefit from buying from either one of the media outlets, i.e. the market is fully covered. In our baseline model, consumers only buy from one of the two media outlets, i.e. they are single-homing. Media Outlets. Media outlets (for example, newspapers or tv channels) are providers of content. We consider two competing media outlets i {, }. Each media outlet has four decision variables: it decides upon the price p i 0 it charges consumers, the fees f i 0 it charges advertisers, and its position in the two-dimensional space spanned by entertainment type y i [, ] and quality q i [q, q] R + of its new report. Without loss of generality, we assume that y y and q q. There are no production costs of news quality and media outlets can freely choose the quality level and the type of variety they want to offer. The profit function of media outlet i is then given by 3 Π i = p i D i + f i a i, where D i is the demand for media outlet i s newspaper (as shown in more detail in Section 3) and a i is the advertising space that media outlet i offers (as shown in more detail in Section 4). Advertisers. We follow Reisinger (0) in modeling the advertising market. For advertisers to sell products to consumers they must interact in the market for news. We assume that advertisers of mass A sell products of homogenous quality. 4 Each advertiser acts as a monopolist, implying that consumers have a willingness to pay of for the good sold by this advertiser. Consumer can only buy a product upon having seen the corresponding ad in the newspaper they have bought. Advertisers place an ad in either one of the two newspapers and pay a placement fee f i to the corresponding media outlet i. Advertisers revenue of placing an ad in newspaper i is determined solely by the audience they reach, i.e. the respective media outlet s demand, D i. Hence, advertiser profits are given by D i f i. Advertisers single-home and media outlets compete in fees for ads. Timing. The timing of the game can be summarized as follows:. Media outlets simultaneously choose type of entertainment y i and level of informational content q i.. Media outlets simultaneously choose price, p i, and advertising fee, f i. q i [/, ] that media outlet i s signal transmits the correct state (and therefore investment type). Hence, the consumer optimally follows the signal and q i θ = ( q q) q i θ expresses the expected surplus of her investment decision. 3 For brevity, we will omit input variables where unambiguous. 4 We normalize expected quality of a product sold by an advertiser to. The level of quality will not affect the qualitative results but only the level of profits, prices and fees. In Appendix B, we consider the case where the expected quality of an advertiser s product increases in the quality of the news report. 5

6 3. Advertisers decide where to place ads. 4. Consumers choose a product from one of the media outlets. We will analyze the cases of a market that is fully financed by prices, the case of mixed financing through advertising and paid access as well as the case of fully advertisement-based financing.. Free-to-air: Media outlets make profits solely through advertising, i.e. p i = 0 for all i {, }.. Pay-tv: Media outlets make profits through advertising and directly charging consumers. 3. Content-on-demand: Media outlets make profits solely through charging viewers directly. The third case is a variant of the game analyzed by Neven and Thisse (989) and is relegated to Appendix B. Note that, in contrast to the results of Peitz and Valletti (008), we do not have profit neutrality w.r.t. advertising under advertiser competition. Thus, the third case is not nested in the second case, but separate. Note also that it could be the case that media outlets in our model do not intend to offer advertising space because users just dislike it too much. Similarly, advertisers could have no incentive to advertise if profits from advertising are negative. The solution concept is subgame perfection. We solve the game by backward induction. 3 Consumer Demand We proceed by deriving the demand function D i for both media outlets on the last stage of the game. Consumers base their purchase decision on media outlets location in the twodimensional space, price and advertising level but not on the advertising fee which is relevant only for advertisers in the advertising stage. To simplify notation, define a = a a, q = q q, y = y y and p = p p. Given her utility function described in (), a consumer of type (x, θ) is indifferent between buying from either one of the media outlets if θ(x) = min{max{ y (y + y x) + p + δ a, 0}, }. () q Since consumer types (x, θ) are uniformly distributed over the unit square and the market is fully covered, demand of both media outlets will always add up to one. For media outlet, 6

7 demand D is obtained by integrating θ(x) over [, ]. Figure shows the partitioning of the set of consumer types into the market shares of media outlets. Depending on the slope of θ(x) we have to distinguish between two different scenarios: vertical and horizontal dominance. Since we assume that x x and θ θ, media outlet always offers weakly higher quality and chooses a location weakly to the right of its opponent. Thus, holding location preferences x fixed, a consumer with a high preference for quality θ tends to buy from media outlet, while a consumer with low preference for quality tends to buy from media outlet. Similarly, holding taste for quality fixed, a consumer that prefers varieties at the right end of the spectrum tends to buy from media outlet. Hence, if θ(x) is relatively flat, the taste for quality will be similar for all indifferent consumer types along the horizontal dimension. In such a scenario, quality differences will be more important than differences in varieties offered. In line with Neven and Thisse (989), we will refer to that situation as vertical dominance. If θ(x) is relatively steep, differences in terms of variety offered will be more impactful than differences in quality. We will refer to such a situation as horizontal dominance. More precisely, vertical dominance occurs if θ θ x <, whereas horizontal dominance occurs if x >. Vertical dominance Horizontal dominance θ(x) media outlet s market share θ(x) media outlet s r market share θ media outlet s market share θ media outlet s market share 0 x 0 x x x Figure : Market shares under vertical dominance and horizontal dominance Demand will consist of three segments. Holding locations and advertising levels fixed, changing prices will shift θ(x) in Figure up and down. For very low prices of media outlet, the line separating the two market segments will cross the top and right sides of the unit square. Similarly, for very high prices of media outlet, the same line will cross the bottom and left side of the unit square. In both cases, changes in prices will affect market shares in a non-linear fashion. For intermediate prices, the same line will either connect the left and right or the top and bottom side, depending on whether vertical or horizontal dominance prevails. In this case, changes in prices will cause linear changes in market shares. Let D I be the non- 7

8 linear segment of demand for high prices of media outlet, D II h (DII v ) be the linear segment of demand for intermediate prices and horizontal (vertical) dominance and D III be the non-linear segment of demand for low prices. The demand of media outlet is illustrated in Figure. p I We proceed by deriving all three demand segments for media outlet. All else given, let be the lowest price such that firm has no demand. I.e. even the left-most consumer type with the lowest taste for quality will consume media outlet s product. Thus, θ(x = ) = 0 together with () yields the following expression for price p I : p I = p + δ a + y (y + y + ). (3) p p I D I p II Dh II or DII v p III D III p IV 0 D Figure : Demand function for media outlet For every price below p I, media outlet will have positive demand. Let x be the right-most consumer type that would be willing to buy from media outlet. By construction, this will be the type with the lowest taste for quality that is just indifferent between buying from media outlet and. Its location is implicitly defined by setting θ(x) = 0 and solving for x, which yields x = ( p + δ a y Hence, the first segment of demand is given by D I = x + y + y ). θ(x)dx = ( y ( + y + y ) + p + δ a). 4 q y This demand function is valid as long as the function θ(x) is steep enough and does not cross 8

9 the left and right sides of the unit square in Figure at the same time and prices are not too low. In particular, for D I θ to be the correct segment of demand we require x > and p [p II, pi ]. If p decreases further, we will transition to the linear segment of demand. Depending on the slope of θ(x), we are either in the case of vertical ( θ x < ) or horizontal dominance > ). We will consider both cases in turn. If vertical dominance prevails, θ(x) will cross ( θ x the left and right sides of the unit square at the same time. In this case, demand is given by D II v = θ(x)dx = y (y + y ) + p + δ a. q If horizontal dominance prevails, θ(x) will cross the top and bottom sides of the unit square and demand is instead given by where D II h = x + + x x θ(x)dx = ( y ( + y + y ) + p + δ a) q, 4 y x = δ a + y (y + y ) + p q y represents the left-most indifferent consumer type. It remains to derive the demand function for very low prices, when θ(x) crosses the top and right sides of the unit square. In this case, demand is given by D III = x + + x θ(x)dx = + δ a + y (y + y ) + p q y (δ a y ( (y + y )) + p) q. 4 q y Finally, we need to derive the cut-off prices for the different demand segments. As outlined above, for every price below p I given in (3), media outlet will have positive demand. If media outlet s price decreases further, θ(x) will shift upwards. Under vertical dominance, θ(x) will cross the lower right corner of the unit square before the upper left corner while shifting up. Let pv II be the price for which θ(x) passes through x = and θ = 0. Using () we obtain p II v = p + δ a y ( (y + y )). (4) If horizontal dominance prevails, θ(x) will cross the upper left corner of the unit square first. 9

10 Let ph II be the price for which θ(x) passes through x = and θ =. Using () we obtain p II h = p + δ a + y (y + y + ) q. (5) Thus, p II and p III will differ depending on whether vertical or horizontal dominance prevails in the linear demand segment. Under vertical dominance, demand is given by D I for any p [pv II, pi ]. Under horizontal dominance, demand is given by DI for any p [ph II, pi ]. For any price p < pv II or p < ph II, DII v or DII h is the correct demand segment as long as θ(x) does not cross the upper and right sides of the unit square at the same time. It remains to determine the cutoff prices below which demand is given by D III. Under vertical dominance, θ(x) will reach the upper left corner of the unit square after the lower right corner when shifting up. Let p III v p III v be the price for which θ(x) passes through x = and θ =. Hence, piii v = pii h and is given by (5). Similarly, piii is given by (4). Therefore, under vertical dominance, for any p [p III v, pii v h ] demand is given by DII, whereas under horizontal dominance, DII is the v correct segment of demand for any p [p III h, pii h ]. Finally, let p IV be the price such that media outlet covers the whole market. For any price below p IV will not increase further. Media outlets will cover the whole market if even the right-most consumer type with the highest taste for quality will consume media outlet s product, i.e. whenever θ(x) just passes through x = and θ =. Using (), we obtain that p IV = p + δ a y ( (y + y )) q is the highest price such that media outlet has full market coverage. Thus, under vertical dominance, for any p [p III v, piv any p [ph III, piv ] demand is given by DIII. The following lemma summarizes. ] demand is given by DIII. Under horizontal dominance, for For given advertising fees and location choices of media outlets, the demand for media outlet s newspaper as a function of prices equals: Lemma. The demand of media outlet consists of two non-linear and one linear segment. Depending on what location dimension is relatively more valuable to consumers, the linear demand segment either heavily depends on the magnitude of horizontal differentiation (horizontal dominance) or vertical differentiation (vertical dominance). The functional forms can h 0

11 be found in the text above. D (p, p ) = D I (p, p ), D II D II v (p, p ), h (p, p ), D III (p, p ), if θ x < and p [p IV D (p, p ) = D (p, p ). if θ x < and p [pv II, pi θ ] or x > and p [ph II, pi ] if θ x < and p [p III v, pii v ] if θ x > and p [p III h, pii h ], piii v ] or θ x > and p [p IV, piii h ] Proof of Lemma. In the text. 4 Advertising Space We proceed by deriving media outlets supply of advertising space as a function of advertising fees given the pricing and location choice of media outlets. Assume that all advertisers are active, i.e. every advertiser is able to place an ad. In equilibrium an advertiser needs to be indifferent between placing an ad on either media outlet or. Therefore, the profit of placing an ad in either one of the newspapers needs to be equal, i.e. D (a, a,.) f = D (a, a,.) f. (6) Note that demands are functions of the advertising amount. Thus, (6) implicitly defines a and a. If all advertisers are active in equilibrium, we have A = a + a and (6) can be solved for a or a using the functional form appropriate for the corresponding segment of demand. Assume that the advertising market is fully covered, i.e. a + a = A. If horizontal dominance prevails, media outlets supply of advertising space is given by a h = A + p + ((y + y ) + f ) y q 4δ a h = A p + ((y + y ) + f ) y q. (8) 4δ (7)

12 If vertical dominance prevails, media outlet s supply of advertising space is given by a v = A + p + (y + y ) y q ( f ) 4δ (9) a v = A p + (y + y ) y q ( f ). 4δ (0) However, if enough advertisers are active in the market, it might not be optimal for media outlets to offer enough advertising space such that every advertiser is able to place an ad. In this case, media outlets act as monopolists on the market for ads and the optimal advertising fee is given by the zero profit condition for advertisers, i.e. media outlets will set f i = D i (a, a,.). In this case media outlets will offer the amount of advertising space that maximizes their profits. 5 Equilibria Under Pay-TV We first consider the regime of Pay-tv, where media outlets make profits through both, advertising and directly charging consumers. 5. Equilibrium Prices and Advertising Fees Before solving for the location stage of the game, we derive the optimal prices and advertising fees given the location choice of media outlets. Thus, for every segment of demand, we need to determine equilibrium prices as a function of location parameters q and y. Solving the game backwards, for given choices of (y, y, q, q ), the solution to the pricing and advertising stage is the solution to the FOCs in () if the advertising market is competitive. As outlined above, if the advertising market is non-competitive, media outlets will set f i = D i (a, a,.) and choose optimal prices and advertising space. In this case, we can show that Π i a > Π i i p, implying i that we obtain a corner solution in which media outlets will always offer as much advertising space as possible. This directly contradicts the initial claim that the advertising market is non-competitive. Thus, in any Pay-TV equilibrium the advertising market will be competitive independent of the type of dominance. Π i D i a i = D i + p i + f i = 0 () p i p i p i Π i D i = p i + a i + a i f i = 0, f i f i f i Here, we use that in this regime, a i is a function of p i and f i. The following Lemma presents the equilibrium prices and advertising fees given the location choice of media outlets. As

13 outlined below, it will suffice to derive equilibrium prices and advertising fees for the linear demand segments. Lemma. First suppose that q y. () Then, demand is linear and horizontal dominance prevails, i.e. demand is given by Dh II and Dh II = DII h. Equilibrium prices are p h = ( (y + y ) y q) ( δ) p h = ( q (y + y ) y) ( δ) A + y A + y. Second suppose that () is not satisfied. Then, demand is linear and vertical dominance prevails, i.e. demand is given by Dv II and DII v = DII v. Equilibrium prices are p v = q ( δ) + (y + y ) y ( δ) p v = q (3 δ) (y + y ) y ( δ) This lemma implies that for any given location choice (y, y, q, q ), we are either in the region of horizontal or vertical dominance. Changing location choices, we will either remain in the respective demand segment or directly transition to the other linear demand segment without passing through the non-linear demand segments Di I or Di III. Thus, every location equilibrium that satisfies the conditions such that prices in Lemma are indeed equilibrium prices, will be on a linear demand segment. With respect to advertising fees on the linear demand segments we obtain the following result. Lemma 3. If demand is linear, i.e. demand is given by either Dv II and DII v = DII v or DII h and Dh II = DII h, equilibrium advertising fees are f = f = δ independent of the type of dominance. Media outlets will offer the following amount of advertising space, independent of the type of dominance: A A. a = Aδ 4A q + (y + y ) y 4δ 8 a = Aδ 4A + q (y + y ) y 4δ 8 Advertiser profits are ( δ) in every equilibrium with linear demand. 3

14 The striking result from Lemma 3 is that advertising fees, no matter if the correct demand segment is vertical or horizontal dominance, will only depend on consumers disutility of advertising. Whereas prices will be affected by location choices and exogenous parameters, advertising fees will be the same for both media outlets and won t be affected by location choices. Instead of changing fees, media outlets will adjust the amount of advertising space they offer in response to changes in parameters other than the disutility of advertising. If the disutility of advertising is high, media outlets opportunity cost of offering advertising space increase. As a result, competition on the market for ads will be less intense and advertiser profits will decrease when the disutility of advertising increases. One further implication of Lemma 3 is that media outlets will split the market equally in any price equilibrium on the linear demand segments. This follows directly from the condition on advertiser indifference, D f = D f, and the result that f = f = δ. Thus, both media outlets have a strong incentive to reach a large audience, as their consumer demand is directly tied to the revenue of advertisers. Reaching a smaller audience would require media outlets to lower their advertising fees to prevent advertisers from switching to the competitor. Hence, in our model, lowering demand has two negative effects. Not only will there be less consumers that can be charged directly, but also advertising revenues will decrease. Lemma 3 also directly imposes a condition on the participation of advertisers. Corollary. For advertisers to participate in the market, their profits must be weakly positive. This is satisfied whenever ( δ) 0 or δ. Proof of Corollary. The proof follows directly from Lemma 3. From Lemma 3 we know that Corollary imposes a condition on the disutility of advertising. If advertising fees are too high, advertisers will stay out of the market entirely as their profits become negative. This, however, implies that the assumption a + a = A, under which prices and advertising fees were derived, will not hold. Indeed, the correct advertising fee for δ > will always set advertiser profits equal to zero and thus solve fiv = D i, implying that both media outlets will act as if they were monopolists on the market for ads and offer the amount of advertising space that maximizes their profits. Since we require that a [0, A] and a [0, A], Lemma 3 also imposes an additional restriction on location parameters. Both statements are true whenever q [max{0, (y + y ) y A( δ)}, (y + y ) y + A( δ)]. (3) Thus equation (3) imposes an upper bound on (exogenous) quality difference for equilibrium prices and advertising fees derived in the previous Lemmata to be valid. If quality difference 4

15 was higher, media outlet would abandon the advertising market, thereby creating an advertising monopoly for media outlet. This resembles a market situation where one media outlet is financed by direct charges to consumers, whereas the other one s financing is mixed. Further note that the restriction on quality differences in (3) together with the results on prices in Lemma imply that prices could indeed be negative in equilibrium. We will verify in Section 5. that media outlets charge the same prices under horizontal dominance. Hence, if negative prices occur under horizontal dominance, both media outlets will charge negative prices. Therefore, if we restrict media outlets to only charge non-negative prices, we would have to consider the case p h = p h = 0, which resembles the Free-to-air market situation discussed in section 6. The same argument can be applied if it turns out that both media outlets prices would be negative under vertical dominance. 5. Product Equilibria Under Pay-TV We next consider stage, where media outlets simultaneously choose both, their type of entertainment and their level of informational content. There arise two types of equilibria, that have the common property that firms choose maximum differentiation in one dimension while duplicating content in the other dimension. We will discuss both types of equilibria in turn. The derivations are relegated to the appendix. Proposition describes the Pay-tv equilibrium that exhibits vertical differentiation. Both media outlets duplicate content in the horizontal dimension while choosing vastly different levels of informational content. The high quality outlet is able to charge a higher price and offer more advertising space as consumers are compensated with higher levels of quality, while the low quality outlet needs to cut prices and use less advertising to preserve demand. While both media outlets share the market equally, the high quality outlet always earns higher profits due to higher prices and advertising revenues. Proposition. Suppose that δ 3 q. Then, media outlets differentiate maximally vertically, i.e. q = q, q = q, y = y = 0 and prices are given by (p v, p v ). Proposition describes the Pay-tv equilibrium that exhibits horizontal differentiation. While both media outlets provide the maximum level of content quality, they maximally differentiate themselves in terms of the type of entertainment they offer. Both outlets always share the market equally, earn the same profits and offer the same amount of advertising space. Proposition. Suppose that δ q 3 (7 ). Then, media outlets differentiate maximally horizontally, i.e. q = q = q, y =, y = and prices are given by (p h, p h ). 5

16 The common theme in both types of equilibria is that media outlets will differentiate in one dimension only and duplicate content in the other dimension. Moreover, differentiation under Pay-tv will always be such that media outlets position as far away from each other as possible. Both types of equilibria can be separated by the nuisance parameter δ. For a given level of advertising disutility, the lower q relative to, the more likely is the horizontal-differentiation equilibrium to occur. Similarly, if the maximum quality difference is high and consumers care more about facts, the vertical differentiation equilibrium becomes more likely. However, as long as 7 q > 0 there is always a range of values for δ in which both types of equilibria exist. Figure 3 illustrates which equilibria exist under different parameter constellations. horizontal differentiation equilibrium (ideological bias) both equilibria vertical differentiation equilibrium (facts bias) 0 3 q q 3 (7 ) δ Figure 3: Equilibria under Pay-tv 6 Free-to-air Equilibria Now consider the regime of Free-to-air broadcasting, where media outlets are solely financed by advertising, i.e. p = 0. Under Free-to-air, the demand of the last stage of the game can be derived as a function of advertising levels given location choices similar to Section Equilibrium Advertising Fees In case the advertising market is competitive, i.e. a + a = A, media outlets will maximize profits subject to the indifference condition on advertisers given by (6). Their profits are given by Π i = f i a i for i =,. Hence, fih and f iv will be the solution to Π i f i = a i + a i f i f i = 0 (4) 6

17 with demand being either Div II or DII ih. If the advertising market is non-competitive, i.e. a +a < A, media outlets will set f i = D i (a, a,.) and choose the optimal amount of advertising space offered. In this case aih N and an iv will be the solution to Π i a i = D i + D i a i a i = 0. (5) The following lemmata summarizes our results with respect to advertising fees and advertiser profits under horizontal and vertical dominance for the competitive and non-competitive advertising market. Lemma 4. The following advertising fees solve the FOCs if a + a = A, i.e. media outlets are actively competing for advertisers. If demand is in the region of vertical dominance, we obtain and advertiser profits are given by f v = 6Aδ + (y + y ) y q 3 q f v = 6Aδ (y + y ) y + q 3 q Aδ q. If demand is in the region of horizontal dominance we obtain and advertiser profits are given by f h = 6Aδ + (y + y ) y q 6 y f h = 6Aδ (y + y ) y + q 6 y Aδ y. In contrast to the results derived in section 5, advertising fees now depend on location choices as well as parameters and are different for both media outlets and under both types of dominance if the advertising market is competitive. Whereas media outlets are mainly relying on prices as instruments under Pay-tv, advertising fees are the only available instrument under Free-to-air. Moreover, the result that the market will always be equally split between both media outlets, which was the case under Pay-TV, does not hold in general under Free-to-air. 7

18 Corollary. For advertisers to participate in the market, their profits must be weakly positive. From Lemma 4 we know that this is satisfied whenever q 4Aδ in the region of vertical dominance and y Aδ in the region of horizontal dominance. Corollary imposes additional restrictions on location choices and parameters as advertiser profits are required to be positive. If those conditions are not be satisfied, advertisers will not participate in the market and the results derived in Lemma 4 under the assumption that a + a = A will not be valid. As we have discussed above, media outlets may also decide to offer less than the maximum amount of advertising space. Lemma 5. The following amounts of advertising space solve the FOCs if a + a < A, i.e. media outlets are not actively competing for advertisers. If demand is in the region of vertical dominance, we obtain av N = q + (y + y ) y 3δ av N = q (y + y ) y. 3δ If demand is in the region of horizontal dominance we obtain ah N = (3 + y + y ) y q 6δ ah N = q (y + y 3) y. 6δ If the advertising market is non-competitive, media outlets will behave as if they were monopolists on the advertising market and set fees such that advertisers make zero profits. We still need to find conditions such that the equilibrium advertising spaces indeed satisfy a + a < A. Corollary 3. For the advertising market to be non-competitive, we require a + a < A. Using the equilibrium amounts of advertising space offered from Lemma 5, this is satisfied whenever q < Aδ in the region of vertical dominance and y < Aδ in the region of horizontal dominance. Corollary 3 implies that media outlets must not differentiate too much when choosing locations if they want to keep the advertising market non-competitive. Indeed, platforms might commit themselves to not offer too much advertising space in the second stage, which would intensify advertising competition, by setting closer locations in the first stage. We can show that there exists no location equilibrium in which the advertising market will be noncompetitive. The corresponding proof can be found in Appendix B. 8

19 6. Product Equilibria Under Free-to-air Similarly to Pay-tv there arise two types of equlibria under Free-to-air broadcasting. Differentiation in only one dimension and content duplication in the other dimension remain the common theme of both equilibria. However, the lack of price competition weakens the incentive for media outlets to differentiate in the dominant dimension. In fact, the incentive for outlets to duplicate content in both dimensions is only limited by the need to compete for advertisers and the requirement that advertiser profits must be weakly positive. In every Freeto-air equilibrium with a competitive advertising market, there is differentiation up tp the point where advertiser profits are just zero. Propositions 3 and 4 describe both types of equilibria in detail. As in the case of Pay-TV, both equilibria can be separated by the nuisance parameter. For a given level of advertising disutility, the vertical differentiation equilibrium is less prevalent and only occurs for medium levels of A and δ. Moreover, there is no set of parameters such that vertical differentiation is the unique equilibrium, while horizontal differentiation is the unique equilibrium for low levels of A and δ or high levels of A or δ. The intuition behind this result is that the lack of price competition makes vertical differentiation less attractive for the low quality firm as it is no longer able to attract consumers via low prices and will therefore deviate to horizontal differentiation and high facts quality. Proposition 3. Suppose that A < δ < A. Then, media outlets differentiate vertically, i.e. q = q 4Aδ, q = q, y = y = 0 and prices are given by (p v, p v ). horizontal differentiation equilibrium (ideological bias) both equilibria horizontal differentiation equilibrium (ideological bias) 0 A A A δ Figure 4: Equilibria under Free-to-air Proposition 4. Suppose that δ < A. Then, media outlets differentiate horizontally, i.e. q = q = q, y = Aδ, y = Aδ and prices are given by (p h, p h ). 9

20 7 Conclusion In this paper, we present a media market model that accounts for both, the two-sided nature of the media market and the possibility that media outlets can differentiate their reports in two different ways. In our model, media outlets are either financed through advertising and direct charges to consumers (Pay-tv broadcasting) or solely through advertising fees (Free-toair broadcasting) and can differentiate their news reporting in a horizontal as well as a vertical dimension (generating ideological bias and facts bias, respectively). We find that media outlets will always differentiate in only one dimension and duplicate content in the other dimension. Our results show that there will always be maximum differentiation under Pay-tv broadcasting, while differentiation under Free-to-air broadcasting will always be less than maximum. Our conjecture is that the magnitude of differentiation will be reduced when moving from a Pay-tv regime to a Free-to-air regime. We also find that the vertical differentiation equilibrium is less prevalent under Free-to-air broadcasting compared to Pay-tv broadcasting. Under Pay-tv broadcasting, facts bias will be more likely to occur if consumers value entertainment less relative to facts quality and the range of reportable quality is sufficiently large. In the Free-to-air regime, facts bias will only occur in a very narrow set of parameters and will never be the unique location equilibrium. 0

21 Bibliography Anderson, Simon P. and Stephen Coate, Market Provision of Broadcasting: A Welfare Analysis, Review of Economic Studies, 005, 7 (4), Armstrong, Mark, Competition in two-sided markets, RAND Journal of Economics, 006, 37 (3), Bernhardt, Dan, Stefan Krasa, and Mattias Polborn, Political polarization and the electoral effects of media bias, Journal of Public Economics, 6 008, 9 (5 6), Gentzkow, Matthew and Jesse M. Shapiro, Media Bias and Reputation, Journal of Political Economy, 006, 4 (), and Jesse Shapiro, Ideological Segregation Online and Offline, Quarterly Journal of Economics, 0, 6 (4), Kaiser, Ulrich and Julian Wright, Price structure in two-sided markets: Evidence from the magazine industry, International Journal of Industrial Organization, 006, 4, 8. Mullainathan, Sendhil and Andrei Shleifer, The Market for News, American Economic Review, 005, 95 (4), Neven, Damien and Jacques-Francois Thisse, On quality and variety competition, Technical Report, Universit{é} catholique de Louvain, Center for Operations Research and Econometrics (CORE) 989. Peitz, Martin and Tommaso M. Valletti, Content and advertising in the media: Pay-tv versus free-to-air, International Journal of Industrial Organization, 008, 6 (4), Prat, Andrea and David Stromberg, The Political Economy of Mass Media, Vol. 50, Reisinger, Markus, International Journal of Industrial Organization Platform competition for advertisers and users in media markets, International Journal of Industrial Organization, 0, 30 (), 43 5.

22 Appendix A: Relegated Proofs Proof of Proposition Proof. Suppose that q = q, y = 0 and show that q = q, y = 0 is a best reply. Media outlet s profit function evaluated at prices (p v, p v ) is given by Π v = δ (y y ) + ( (y y ) + q q ) 4(δ ) + A(δ ). (6) Note that unlike in Peitz and Valletti (008) profits are not independent of the value of δ, i.e. advertising affects not only prices, but also profits. Taking the FOC w.r.t. y, we obtain y v = 0. As y v = 0 by assumption, (6) reduces to Π v = (q q ) 4( δ) A( δ) which is maximized for q = q. Hence, in the region of vertical dominance the best reply to q = q and y = 0 will be q = q and y = 0. It is left to show under which conditions there will be no profitable deviation for media outlet in the region of horizontal dominance. Consider media outlet s profit function evaluated at prices (p h, p h ). Π h = ( (y y ) q + q ) ( δ) 4( δ) + (y y ) A( δ) (7) Media outlet s profit is maximized by setting q = q = q v and thus (7) reduces to Π h = ( (y y ) ) ( δ) + 4( δ) (y y ) A( δ) (8) The FOC of this expression w.r.t. y yields y ( δ) h = ( δ) which is smaller than. If we restrict locations to be within [, ], we have y h =.

23 Therefore, y = is a best reply in the region of horizontal dominance and Π h simplifies to Π h = (3 δ) 8( δ) A( δ). Finally, we consider the location choices of media outlet and show under which circumstances y = 0 and q = q is indeed as best response to y = 0 and q = q. Assume that q v = q and y v = 0. Similar reasoning yields Π v = (3 δ) (q q ) 4( δ) A( δ) for the profit of media outlet given prices p v, p v under vertical dominance. Given prices p h, p h under horizontal dominance, media outlet s profit can be expressed as Π h = ( (y y ) + q q ) ( δ) 4( δ) + (y y ) A( δ). (9) Again, the best response in terms of q is q = q, as long as we remain in the demand segment of horizontal dominance. In fact, the best response of media outlet regarding the quality choice will be such that q is chosen as high as possible under the condition that we remain in the region of horizontal dominance. I.e. the condition on equilibrium prices derived in Lemma must be just binding. We obtain q = q + (y y ), where q = q by assumption. Furthermore, it can be shown that y h = ( δ) ( δ) and hence y h = is the unique best response by media outlet. Together with y h = 0 by assumption, we obtain Π h = (5 3δ) 8( δ) A( δ). Finally, media outlets best responses will be in the region of vertical dominance whenever Π v Π h and Π v Π h. The former is true whenever q q (3 δ) (0) 3

24 and the latter is true whenever q q 5 3δ. () (3 δ) From Corollary we know that δ (3 δ). Thus, we can show that > 5 3δ (3 δ) conditions hold if and only if q (3 δ). and both Proof of Proposition Proof. Assume that q v = q, y v = and show that q v = q, y v = is a best reply by media outlet. As shown in the analysis above when media outlet s profits are evaluated at prices (p h, p h ) it is optimal for media outlet to set q = q and profits are given by (8). As media outlet s best response is y = and y v = by assumption we get Π h = ( A( δ)). Next, consider media outlet s profit under vertical dominance when prices are (p v, p v ) which is given by (6). The first derivative w.r.t. q is negative for all values of y and hence q v = q. Define q = ( q q) and plug in to get: Π v = ( 4 y ) ( δ) + q A( δ) 4( δ) which is obviously maximized at y v = 0. Therefore and Π v = ( δ) + q A( δ) 4( δ) Π h Π v whenever q (7 3δ). Finally, consider q v = q, y v = and show that q v = q and y v = is a best reply. Media outlet s profit is then given by (9) if prices are (p h, p h ). Furthermore, we have shown above that 4

25 y h = independent of y, q and q and hence, Π h = ( A( δ)). If prices are (p v, p v ), Π v is given by Π v = (q q ) (3 δ) (y y ) ( δ) A( δ). () 4( δ) First note that in this region of demand media outlet will never set q = q, as then (p v, p v ) would not be equilibrium prices anymore, given y v =. However, we used the assumption q q in the construction of demands. For q < q the expression for media outlet s profits will be identical to media outlet s profits with the variables of choice relabeled as m i = y i for i, j =,. Hence, the analysis is similar to the one for Π v above. We get and Π v = ( δ) + q + A(δ ) 4( δ) Π h Π v whenever q (7 3δ). Proof of Proposition 3 Proof. Suppose that y = 0 and q = q and show that y = 0 and q = q 4Aδ is a best response. Media outlet s profit function evaluated at optimal advertising levels (a v, a v ) is given by: Π v = (6Aδ + (y y ) (q q )) 36 (q q ) δ (3) Taking the derivative with respect to y yields Π v = y (6Aδ + (y y ) (q q )) y 9 (q q ) δ = 8y a 3 (q q ) 5

26 which can only be zero if either y = 0 or a = 0. Since offering no advertising space at all leads to zero profits and media outlet can ensure itself a positive profit by just offering a little bit of advertising space, we obtain y v = 0 and (3) becomes Π v = (6Aδ (q q )). 36 (q q ) δ Since q = q and Π v only depends on the difference in quality, choosing q is equivalent to choosing q. Taking the first order derivative with respect to q yields Π v q = ( 36δ A δ q ). (4) Note that the second-order derivative is always positive and hence Π v is convex in q. Thus, the optimal q v should be a corner solution. We know that (4) is positive, whenever q > 6Aδ, which is required for media outlets to offer advertising space. Further, advertisers are required to make weakly positive profits. From Corollary we know that this is true under vertical dominance whenever q 4Aδ. Thus, there will be differentiation in the quality dimension down to the point where advertisers are indifferent between placing and not placing ads. It is left to show that there is no best response for media outlet in the region of horizontal dominance. Under Free-to-air, media outlet s profit in the horizontal dominance region is given by Π h = (6Aδ + (y y ) + q q ). 7δ (y y ) The first order derivative with respect to q is given by Π (6Aδ + (y h = y ) + q q ) = q 36δ (y y ) a 3 (y y ). (5) which is positive whenever a > 0, i.e. media outlet provides any advertising space. Since providing no advertising space yields zero profits, any a > 0 is a profitable deviation as long δq as f > 0. However, since f i = (y y ) a i, advertising fees will be positive whenever advertising space is positive and thus a = 0 can never be a best response. Hence, q v = q under horizontal 6