Content Streaming As a Three Sided Market Working Version

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1 Content Streaming As a Three Sided Market Working Version Ben Casner March 15, 2017 Abstract Typical representations of media markets paint the media creators as a platform which uses media to bring consumers and advertisers together. Many online streaming platforms like YouTube or Twitch.tv do not produce their own content, but instead rely on 3rd parties to upload videos to their platform in exchange for a share of the revenue they bring in. I explore the implications of adding a third side to this market and the effects of introducing a premium subscription that allows consumers to avoid ads. I find that adding this subscription increases the provision of niche content but may reduce the welfare of consumers who enjoy content that is created without it due to a higher advertising level and concomitant high subscription price. The platform, content creators, and consumers with high nuisance costs or on newly served content markets are better off, but consumers with low nuisance costs are worse off. The impact on total welfare is ambiguous. The ability to stream media via the internet has created a number of new business models that would not be feasible using standard distribution methods. Of particular note is the decoupling of content production from ownership of the viewing platform. Websites like Youtube.com and Twitch.tv allow content creators to upload videos or live-streams to their platform. This allows the platform to have a broad variety of content without directly accruing the cost of creating it, and the creators get access to a built in audience and advertising without having to directly interact with advertisers or bear the large fixed cost associated with running the platform. There is some variation in the details, but these platforms follow a fairly set business model: Advertisers purchase a set number of ad views, paying a fixed cost per view. Any viewership that exceeds the number of ad views that a platform has sold will not have advertisement. Content creators receive a share of ad revenue (typically around 55%). Viewers can view the content for free, but must bear the nuisance of viewing ads before gaining access to it. 1

2 While this model does work well in a number of cases, the revenue is low 1 and the revenue is capped by the value of the advertisers. In the cases where the value of the impression to the advertiser is below the value of a view to the consumer, this means that the platform could significantly increase profits if it was able to induce consumers to pay directly. Additionally, the low revenue means that it is not possible for creators of niche content to make sufficient return on investment to justify continued production of videos. It should not be surprising then that these platforms have introduced services which offer benefits to consumers in exchange for a subscription fee. Programs like YouTube Red and Twitch Turbo offer a number of perks such as access to streaming music or badges to use in online chat rooms, but they are primarily marketed as advertising avoidance services. In exchange for the fee, consumers no longer have to watch any ads in order to enjoy their content. A natural question that arises upon observation of this practice is whether consumers as a group benefit from the introduction of these services. Ability to avoid advertising means that consumers who previously did not watch due to being particularly averse to advertising now have access to the content on the platform and increased revenue will allow sustainable production of more niche content. Additionally, consumers who were watching previously can now avoid advertising where they previously could not 2. On the other hand, the platform has an incentive to increase advertising levels since the consumers who choose not to use the service have revealed themselves to be less sensitive to advertising and the platform may be able to drive additional subscriptions by doing so. Thus consumers who choose to subscribe may be worse off than when no subscription was available since the choice is now between the subscription, not watching, and using the service with a higher advertising level than before. Individual consumers will be better off if they have a high nuisance cost from advertising or if the type of content they enjoy was previously not produced, but whether or not consumers as a whole benefit depends on whether the ability to avoid ads and increased variety outweighs the increase in advertising level and concomitant high subscription prices. This paper outlines a model which analyzes the welfare implication of these subscription programs. A monopoly platform brings together content creators, advertisers, and consumers. Each consumer enjoys a single type of media (e.g. cat videos or baking tutorials) and consumers are exogenously and unevenly distributed across a continuum of types. This specification is similar to Yang (2013) except that I have a continuum of product types rather than a discrete distribution. Consumers also vary in how much they suffer from advertising, with nuisance cost being a linear function of the advertising level whose slope is determined exogenously. This nuisance cost type is distributed independently of 1. The CPM (Cost per thousand impressions) can often be as low as US$2 (Green 2015). 2. while free ad blocking services do exist, these services prevent content creators from receiving revenue and excessive blocking could result in cessation of production. YouTube s advertising for the Red service emphasizes the fact that creators still receive revenue from viewers who use it, suggesting that consumers do take this effect into account when making ad avoidance decisions. 2

3 content type. Consumer decisions include whether or not to watch the content, and if they watch, whether or not to purchase the premium subscription. Creators are assigned exogenously to content type, with each type having a single creator, thus the content creator s only choice is whether or not to produce. Creators face a cost of production, and receive revenue per view at a rate assigned by the platform. Advertisers have a fixed probability per impression of converting an ad view into a sale, which gives the consumer no surplus and a fixed surplus to the advertiser. The platform decides what price to charge for ads, what advertising level to set, how much to charge for the subscription, and how much revenue to share with the content creators. I impose the restriction that the platform cannot differentiate by content type, and so must charge the same price to advertisers and consumers, and must give the same fee per view to each creator. Compared to a baseline equilibrium with no advertising the equilibrium with the subscription has a higher advertising level, more viewership, and broader content provision. Individual consumers are better off if they have a high nuisance cost from advertising, but the change in total consumer welfare has ambiguous sign. The intensive change in welfare (the change in markets that are served under both equlibria) depends on the distribution of nuisance costs. If too much mass is at the low end of the distribution, few consumers switch to the premium service and the increase in nuisance cost outweighs the gains from advertising avoidance. If too much is at the high end of the distribution, then the platform can charge a high price for the subscription and the gains are diverted to the platform and content creators. The consumers in markets that only have content produced with the subscription are all weakly better off than they were without it, so the extensive change in welfare is always non-negative. 1 Previous Literature As far as I am aware, this paper is the first to separate content production from the platform in this species of model, but there is an extensive literature exploring the welfare effects of advertising avoidance in multi-sided markets. The paper that is most similar to this model is Tåg (2009). He studies the implications of allowing a standard 2-sided platform to introduce a fee to avoid advertising. Introducing the subscription induces the platform to increase the advertising level in order to drive more adoption of the subscription, but market clearing requires a reduction in the price paid by advertisers. While individual consumers may be better off, the effect on consumer welfare is unambiguously negative since consumers either face a high nuisance cost of ads or they must pay a high subscription fee. Total welfare can increase or decrease, platform profits increase and advertisers are better of since they pay a lower price for ads, but the effect on consumers outweighs these effects unless advertisers receive high value from trade. Tåg s result that consumer welfare is unambiguously reduced comes partly from an assumption that consumers have no outside option. Allowing consumers the option of not watching means that the subscription can increase 3

4 total consumer welfare, as this paper demonstrates. Anderson and Coate (2005) analyze competition in market provision of content via platforms. They find that competition can reduce social welfare due to increased incentives to provide mass market content. Equilibrium advertising levels can be below or above optimal levels depending on consumer s nuisance costs. Allowing the platform to charge a subscription price can raise or lower total welfare depending on whether consumers value for programming is sufficient to cause the platform to increase content variety. Anderson and Gans (2011) consider the effects of ad avoidance technologies (AATs) on media provision platforms when the avoidance technology is external. They find that the introduction of AATs increases the advertising level since consumers who do not use the technology are precisely those who are least sensitive to advertising, consistent with the findings of this paper. However they also find that AATs eliminate the platform s ability to extract value from viewers of niche content through higher advertising levels, causing the platform to shift to greater provision of mass market content. This contrasts with the findings of this model where the subscription fee allows the platform to capture viewer surplus more effectively and the increase in revenue per viewer as well as the increase in viewership allow production of niche content to become more worthwhile. Johnson (2013) models the value of advertising to advertisers as a function of the total advertising audience rather than specific ad-consumer interactions. Thus his model is better suited to a TV or radio context rather than an online platform. One of the consequences of this difference in representation is that the advertiser incentives have a much greater effect on advertising levels than in the previously discussed papers. Johnson finds that AATs reduce the appeal of advertising by reducing the size of the audience, meaning that consumers who avoid ads create a positive externality for other consumers. Thus advertising avoidance may actually be below socially optimal levels in Johnson s model. Wilbur (2008) conducts an empirical analysis of television as a two-sided market. He finds that consumers are averse to ads, but networks tend to favor advertiser preferences more than consumer preferences when making programming decisions. Viewers tend to prefer Action and News, whereas advertisers prefer Reality and Comedy programming. The former two categories account for 16% of broadcasting schedules in his data whereas the latter two comprise 47%. In a counterfactual estimate he finds that introducing AATs would reduce platform profits and increase advertising levels. 2 Baseline Model This section describes a baseline model without a subscription to avoid advertising. The platform is a monopoly on which content creators can host videos and to which consumers come to watch content. Advertisers purchase ads on a per-view basis. 4

5 2.1 Structure There are a continuum of content types indexed by t. Each content type holds only one content creator and has a market size g(t). Each consumer is exogenously assigned precisely one type of content and they only enjoy that type. 2.2 Consumers Consumers in the baseline model choose to either watch or not watch and face no other decisions. Consumer utility is 0 if they choose not to watch and utility if they do watch is given by u t aη (1) Consumer utility from watching (u t ) is u if the content creator for that type decides to produce and 0 otherwise. Consumers are also differentiated by the nuisance cost η from advertising. η is exogenously assigned and distributed across consumers independently from content type according the the density function 3 f(η). Note that not every video will have an ad (see 2.4) but consumers do not know whether or not they will receive an ad before watching, so the expected nuisance cost is the advertising level a multiplied by η. Consumers will choose to watch iff they receive positive utility from doing so. This means that only consumers with relatively low nuisance costs will watch. If eq. (1) is equal to 0 it is easy to see that the critical η is u a and so the proportion ν of consumers who watch will be ν = 1 F ( u a ) W here F (η) = η η f(n)dn (2) 2.3 Content Creators Content creators receive a payment from the platform per ad view. Their profit will then be based on the total number of views they receive and the fee set by the platform. The creators face only one decision: produce or not. If they choose not to produce they receive a payoff of 0, if they do produce they face a cost c, and receive a payment s A p from the platform per ad view. Given a market size g(t), viewership proportion ν, and advertising level a, total ad views will be aνg(t), so the profit on production is 3. note that the total measure of consumers can be greater than 1 when summed across content markets, so f( ) should be thought of as a population distribution 5

6 s A p a ν g(t) c (3) The content creators will produce if they earn positive profit from doing so. This means that there will be a critical market size above which the content creator will produce. Without loss of generality one can reorder the content types so that the market size is monotonically decreasing. Assuming that g( ) is a continuous bijection, it is then simple to solve for the critical content type who is indifferent between producing and not: ( ) c t = g 1 s A p aν (4) 2.4 Advertisers In the baseline model, the advertising sector is intentionally simple. For each ad view, there is a probability z that the consumer will like the advertised product and engage in trade. All consumers have the same value for trade, so the advertisers can extract full value from the consumers 4. Trade will net the advertiser v A in surplus and the consumer 0. The platform will charge a price p a per ad view. The advertiser value per ad will then be π ad = zv a p a (5) Since advertisers are homogeneous, the platform can set p a = zv A and extract all of the surplus from the advertisers. The advertisers will then be indifferent between purchasing any number of ads, meaning that the platform is free to set the advertising level at any point in [0, 1]. 2.5 The Platform The platform earns profit on the margin between the fee it receives per ad view and the creator payment per ad view. The platform s total profits will be the sum of these margins across all ad views. In other words π plat = (p a s A p )aνg(t ) W here G(t ) = t 0 g(t)dt p a was determined in section 2.4, so all that remains is to evaluate the platform s choice of a and s A p. The solutions are given in the following proposition (proofs for all propositions appear in the appendix): 4. This is similar to specification for trade used in Anderson and Coate s (2005) model 6

7 Proposition 1. If F (x) f(x)x satisfies single crossing and g(x) is concave, then there is a unique baseline equilibrium which solves the following equation: [s A p ] 1 c 2 g (t ) s A p (s A p aν) 2 (p a s A p ) = G(t ) (6) The platform either solves the following equation or the advertising level is at the corner solution of 1: [a] F ( u a ) = f(u a )u a (7) ν and t will be determined by the above and the price of advertising will be p a = z v A. eq. (6) represents the platform s tradeoff between attracting additional creators and increasing the payment to existing creators. A solution to this FOC always exists since no creators will produce when the payment is 0 and marginal benefit of additional markets is 0 when the payment is equal to the price of advertisements. The requirement that g(x) be concave ensures that platform profit is concave in creator payment and gives uniqueness of the solution to the FOC. When the platform increases the advertising level, it will increase the number of videos with ads, but drive away some consumers due to the increased nuisance cost. Equation (7) captures this tradeoff, and the single crossing requirement ensures a unique solution which will maximize total ad views. 3 Simple Premium The simplest version of the model with the premium is the same as the baseline model, but now allows the platform to offer the subscription. 3.1 Consumers u is the same across consumers, so if p c > u no consumer will purchase the subscription. If p c u then the minimum possible utility from watching is u p c > 0 so all consumers will watch and their only decision will be whether to purchase the subscription. They purchase if u p c u ηa = η p c a Define η = pc a. Then ν = 1 and the proportion of consumers who watch ads will be 1 F (η ) 7

8 3.2 Content Creators From the above, creator revenue is now ( s A p af (η ) + s P p (1 F (η )) ) g(t) c and so ( ) t = g 1 c s A p af (η ) + s P p (1 F (η )) (8) Note that if we let s = (Average per-view creator revenue) ν, then in both of the models so far ( t = g 1 c ) s (9) 3.3 The Platform With the new income stream, the platform s revenue is now π plat = [ (p a s A p )af (η ) + (p c s P p )(1 F (η )) ] G(t ) Since the advertising sector is unaffected, the platform now has 4 undetermined decision variables: s P p, s A p, p c, a. To understand the platform s decision making, it is helpful to define r as the average per-view revenue of the platform. Then in both versions of the model we can write the profit as Then we have the following lemma: π plat = (r s) G(t ) Lemma 1. There exists a continuum of optimal pairs (s P p, p p A ), but in the representation above they are all equivalent to a single optimal value of s. This s solves c 2 r s g (t ) s 3 = G(t ) (10) If g( ) is concave, this solution exists and is unique for a given value of p a, p c, a. The same representation and solution can be used in the advertising only-model with equivalent definitions of r and s for that model. 8

9 The reason for this is fairly straightforward, if the platform increases s A p by ɛ and decreases s P af (η p by ) (1 F (η )) ɛ, then both producer and platform profits are unchanged. This means that there is no point prediction for the revenue shares, but rather a prediction that equates the marginal benefit of adding an additional market to the cost of giving producers a greater revenue share. The equilibrium in this market will then be given by the following proposition: Proposition 2. In the simple premium model, advertising levels will go to 1 if p a a < p c in equilibrium 5. t will increase and creators will receive more total revenue than when the subscription is not available. Platform profits will increase the and the price of the premium subscription will be the solution to the following equation or the corner solution at p c = u 1 F (η ) f(η ) = p c p a (11) s will solve the problem from lemma 1 and the price of advertising will remain at z V A. Advertising levels go to the corner solution when a subscription view is more valuable than an advertising view. The solution to the subscription fee will always be weakly below u, so increasing the advertising level drives additional subscriptions rather than losing viewership. The FOC for the subscription fee balances additional revenue from subscribers with the lost revenue as the marginal consumer moves from the subscription to the free version. Creator profits increase for two reasons: i.) The option to subscribe increases viewership which means that the creators get additional revenue even if s remains constant, and ii.) The marginal value of an additional content market to the platform has increased, meaning that the the platform will be willing to increase s in order to capture more markets even though this means increasing payments to creators who already produce. 4 Welfare Comparison Platform and creator profits unambiguously increase with the introduction of the subscription fee. Consumers with a low nuisance cost in previously served markets are worse off with the subscription due to increased advertising levels, but all other consumers are weakly better off. When comparing the total welfare change it is helpful to separate the intensive change on the content markets which were previously served from the extensive change on the markets which are only served when the subscription is available. Since the platform captures all of the advertiser surplus and content creator revenue is a fraction of platform revenue, we can represent the total nonconsumer welfare as 5. Given the numbers on CPM referenced earlier, this seems likely to occur in practice 9

10 (r s)νg(t ) + sνg(t ) t c = rg(t ) t c The first term represents total revenue, the second the cost of the creators who are producing. Let t a denote equilibrium t in the advertising-only model. Then total welfare in the advertising-only model is [p a af ( ua ) + u a η u aηf (dη) ] G(t a) t ac Let t p denote equilibrium t in the simple premium model. Then total welfare is [ η p a af (η ) + p c (1 F (η )) + u = [ p a F (η ) + u η η ηf (dη) and so the change in total welfare is ] η G(t p) t pc ] ηf (dη) p c (1 F (η ) G(t p) t pc ω = [p a (F (p c ) af ( ua ) ) + (1 F ( u a ))u + ae(η η u ] a ) E(η η p c) G(t a) + [p a F (η ) + u E(η η p c )] (G(t p) G(t a)) (t p t a)c (12) Note that there is no uncertainty in the consumer types who choose to watch. The expectation operator here should be interpreted as a weighted average. The first term in ω is the change in welfare on the intensive markets, which can be either positive or negative. 4.1 Platform and Creator Profits We can separate the change into the change in platform/producer welfare and the change in consumer welfare. Since a = 1 with the subscription, a in the following equations refers to the advertising level in the advertising-only model. [ π = p a (F (p c ) a F ( u ] a )) + p c(1 F (p c )) G(t a) }{{} Content covered in both models + [p a F (p c ) + p c (1 F (p c ))] (G(t p) G(t a)) +(t a t p)c }{{} Content produced with addition of subscription 10

11 Profit is unambiguously higher in the subscription model. This is sensible since, as was mentioned before, the advertising only structure remains available with the addition of the subscription. 4.2 Consumer Welfare [ U = (1 F ( u ( a ))u (1 F (p c))p c (E(η η < p c ) ae(η η < u ) ] a ) G(t a) }{{} Content covered in both models + [u (1 F (p c ))p c E(η η < p c )] (G(t p) G(t a)) }{{} Content produced with addition of subscription (13) Again, the expectation should be interpreted as a weighted average of the nuisance costs. The intensive change in welfare has ambiguous sign: some consumers are worse off since they have to bear more advertising or pay a subscription cost. But consumers with η > pc a are better off since they either did not watch due to a high nuisance cost or bore more nuisance than the subscription costs. The extensive change is purely positive since those content types were previously not produced. The change in intensive welfare depends on the distribution of η. The consumers who are better off with the subscription are those with a high nuisance cost. If there is a relatively high mass of consumers with high nuisance cost, then the intensive consumer welfare may increase, although if the proportion is too high then this effect is counteracted by an increase in the subscription price. If the proportion of consumers who are using the free version of the service is high under the the subscription model, then the intensive consumers are worse off. The change in extensive welfare depends on the curvature of g(t). If the market size function is very concave, then t will not react much to an increase in creator revenue and the increase in content production will be small. If it decreases slowly, then a small increase in revenue will create a much greater increase in the types of content provided. Total welfare change under the two models then depends on the shape of the distributions. As the mass of consumers with high nuisance cost increases, total surplus will increase and the intensive surplus will increase. As the size of the content markets becomes more even, the extensive increase in surplus becomes greater and the total welfare will improve. While an increase in welfare from the discrimination seems more likely, it is possible that the subscription model will reduce welfare if consumers are highly insensitive to ads and the distribution of consumers across content markets is extremely concentrated. 11

12 5 Conclusion This paper analyzes the implications of separating content production from the platform in content streaming markets. This separation means that the platform cannot directly choose what content it hosts and so which consumers it attracts. I also show that unless consumers are highly concentrated in a few markets and consumers are extremely unresponsive to ads, the advertising-only model is inferior to one with a subscription from the perspective of efficiency and social welfare, although the benefits of the subscription may be captured by the platform and content producers. There are a number of other potential implications from separation of content from the platform (e.g. creators competing for viewers or advertising dollars) that are not explored in this paper, but would be fruitful avenues for further research. References Anderson, Simon P., and Stephen Coate Market provision of broadcasting: a welfare analysis. The Review of Economic Studies 72 (4): issn: , X. Anderson, Simon P., and Joshua S. Gans Platform siphoning: ad-avoidance and media content. American Economic Journal: Microeconomics 3, no. 4 (): doi: /mic id= /mic Green, Hank The $1,000 cpm. Accessed January 16, medium.com/@hankgreen/the cpm-f a4b#.3lxhobg3q. Johnson, Justin P Targeted advertising and advertising avoidance. The RAND Journal of Economics 44 (1): issn: doi: / Tåg, Joacim Paying to remove advertisements. Information Economics and Policy 21 (4): issn: doi: 1016/j.infoecopol science/article/pii/s Wilbur, Kenneth C How the digital video recorder (dvr) changes traditional television advertising. Journal of Advertising 37 (1): doi: /JOA eprint: Yang, Huanxing Targeted search and the long tail effect. RAND Journal of Economics 44 (4): bla:randje:v:44:y:2013:i:4:p:

13 A Proofs Proof of Proposition 1 Begin by noting the following identities: t s A p = 1 g (t ) s A p c 2 aν > 0 (14) t a = c s A p ν + as A p ν a g (t ) 2 > 0 aν) 2 (s A p and Substituting in gives ν a = f(u a ) u a 2 t a = csa p g (t ) F ( u a ) f( u a ) u a 2 > 0 (15) aν) 2 (s A p The first term in the product is positive since g (t) < 0. Thus the sign of the derivative is positive iff the increased revenue from having more ad views (F ( u a )) outweighs the loss in viewership caused by the increase in nuisance (f( u a ) u a ). Now take the derivative of platform profit with regard to creator payment, substituting appropriately using the identities above: s A p ( g(t ) = aν g (t ) s A p ) c 2 aν (p a s A p ) G(t ) Using the definition of t s A p ( 1 = aν G (t ) c 2 ) s A p (s A p aν) 2 (p a s A p ) G(t ) (16) The derivative will be positive when G(t ) = 0 and negative at s A p = p a, it is also continuous, so a solution always exists. Checking for concavity: Take the second derivative 13

14 2 ( π plat 1 2 s A = aν p g (t ) 3 g (t ) t s A p c 2 s A p (s A p aν) 2 (p a s A p ) c 2 s A4 p (aν) (p 2 a s A p ) 1 c 2 ) g (t ) s A p (s A p aν) 2 g(t ) t So long as the first term is negative and/or sufficiently small, the platform s profit is concave in prices. Thus g (t) 0 is sufficient, but not necessary to ensure that there is a unique profit maximizing creator payment for every advertising level so long as there are a positive number of views. This establishes the first FOC in the proposition. Take the FOC with regard to advertising level: s A p a =(p a s A p ) [G(t )ν + g(t ) t =(p a s A p ) [ ( G(t ) F ( u a ) f(u a )u a a aν + ag(t ) ν ] a ) + g(t ) t a af (u a ) ] Using the identities established above and the definition of t, then pulling out common factors: a ( = (p a s A p ) F ( u ) [ a ) f(u a )u G(t ) af ( u a ) c 2 ] a g (t ) (s A p aν) 3 (17) Since g( ) is decreasing all terms in this product are positive with the exception of ( F ( u a ) f( u a ) u a ), so this is the only relevant part of the platform s decision. So long as it satisfies single crossing, there will be a unique solution. A.1 Proof of Lemma 1 The following identities are useful: t s P p = c 1 F (η ) g (t [ ) s A p af (η ) + s P p (1 F (η )) ] 2 > 0 (18) t s A p = c af (η ) g (t [ ) s A p af (η ) + s P p (1 F (η )) ] 2 > 0 (19) 14

15 The following inequalities hold if s P p > as A p (a marginal subscriber view is more valuable to creators than a marginal free view). t p c = c 1 a f(η ) ( ) as A p s P p g (t [ ) s A p af (η ) + s P p (1 F (η )) ] 2 < 0 (20) t a = c s A p F (η ) + pc a f(η ) ( ) s P 2 p as A p g (t [ ) s A p af (η ) + s P p (1 F (η )) ] 2 > 0 (21) Using the above identities, take the derivative of platform profit with regard to: The share of subscription fees (s P p ) s P p = [ (p a s A p )af (η ) + (p c s P p )(1 F (η )) ] g(t ) t s P p (1 F (η ))G(t ) and advertising revenue (s A p ) s A p = [ (p a s A p )af (η ) + (p c s P p )(1 F (η )) ] g(t ) t s A p af (η )G(t ) Define m [ (p a s A p )af (η ) + (p c s P p )(1 F (η )) ], and note that both of these derivatives give the same FOC. m c2 1 g (t [ ) s A p af (η ) + s P p (1 F (η )) ] 3 = G(t ) (22) For any pair (s A p, s P p ) that solves this FOC, we get that (s A p + ɛ, s P p af (η ) (1 F (η )) ɛ) will also be a solution, with ɛ arbitrarily small, thus there are a continuum of solutions. Now define: r = (p a s A p )af (η ) + (p c s P p )(1 F (η )) s = s A p af (η ) + s P p (1 F (η )) and note that m = r s. For any (s A p, s P p ) on our continuum, m, r, and s will all be constant, so we can restate the platform s problem as setting s to solve. 15

16 c 2 r s g (t ) s 3 = G(t ) (23) If g( ) is concave, then the left hand side is decreasing in s and is above 0 at the s where G(t ) = 0. The right hand side is increasing in s, thus there is precisely one solution for any set of p a, p c, a. To show that the same representation is possible for the advertising-only model, set r = aνp a and s = aνs A p and substitute into eq. (16). The result follows. A.2 Proof of Proposition 2 The increase in platform profits comes from the fact that the baseline business model is still available after introducing the subscription. The platform can set the subscription fee at any number above u, receive no subscribers and make the same profit as before. Therefore profits at the optimal subscription fee and advertising level must be greater than before. The value of p a arises from the fact that the advertising sector is unchanged. The value of s comes from lemma 1. To see the increase in advertising level, take the derivative of platform profit with regard to advertising level a = Using eq. (9) and eq. (21) [ ( (p a s A p ) F (η ) af(η ) p ) c a 2 + (p c s P p )f(η ) p c a 2 + Mg(t ) t a ] G(t ) a = [ ( (p a s A p ) F (η ) af(η ) p ) c a 2 + (p c s P p )f(η ) p c a 2 ] G(t ) + M c2 s A p F (η ) + pc a (s P 2 p as A p ) g (t [ ) s A p af (η ) + s P p (1 F (η )) ] 3 Setting s A p = s P p in accordance with lemma 1 and using eq. (22) a a [ = (p a s A p )F (η ) + (p c ap a ) p ] c a 2 f(η ) + s A p F (η ) G(t ) [ = p a F (η ) + (p c ap a ) p ] c a 2 f(η ) G(t ) 16

17 This is unambiguously positive if p c > ap a. Advertisement will then go to a corner solution at 1. To find the subscription fee, take the derivative of profit w.r.t. the subscription fee [ = (p a s A p )af(η ) 1 p c a +(1 F (η )) Use eq. (9) and eq. (20) to get (p c s P p )f(η ) 1 a + mg(t ) t p c ] G(t ) =(1 F (η ))G(t ) p c [ + (p a s A p )a (p c s P p ) ( ) + m c2 as A p s P ] p g (t [ ) s A p af (η ) + s P p (1 F (η )) ] 3 G(t )f(η ) 1 a Equating the creator payments [ =G(t ) (1 F (η )) + (p a a p c )f(η ) 1 ] p c a which gives a relatively straightforward FOC 1 F (η ) f(η ) = p c p a a a (24) Since a = 1 1 F (η ) f(η ) = p c p a (25) To show that the payment to creators will increase, consider eq. (23) from lemma 1. The platform solves this problem in terms of s and r for both the advertising-only and the simple premium problem. If we let a denote the advertising level in the baseline model, then note that aνp a < (p a s A p )af (η ) + (p c s P p )(1 F (η )) 17

18 So r will increase with the introduction of the subscription. Since ( t = g 1 c ) s in both problems then the solution to eq. (23) can be thought of as an implicit function of r, and we can see that the left hand side increases with r, meaning that the right hand side must as well. Thus G(t ) must increase with the subscription, meaning that both creator payments and variety of content will increase. 18