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Pricing strategy of monopoly platforms

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Pricing strategy of monopoly platforms

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Content PRICING STRATEGY OF MONOPOLY PLATFORMS by Jae Hyun Gwon A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2013 Copyright 2013 Jae Hyun Gwon Dedication to my parents, Hyuk-Gang Kwon and Seung-Soon Hong ii Acknowledgments There are many people I wish to thank toward my Ph.D. degree. I am especially grateful to Harrison Cheng, my advisor, for his helpful advice and guidance. He has stood by me whenever I muddled through in the ocean of research uncertainty. Yilmaz Kocer and Simon Wilkie have provided inspiring comments regarding my research. It was lucky to have them around me. Yusun Hwang, Bo M. Kim and Heonjae Song are my old friends and excellent colleagues. They have always listened to me for better idea as well as heart-warming advice. Needless to say, I am solely responsible for all the errors that remain. iii TableofContents Dedication ii Acknowledgments iii List of Figures v Abstract vi 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Summary of Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Model 11 2.1 Single Application: Uniform Valuation . . . . . . . . . . . . . . . . . . . . 13 2.1.1 In-House Application . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.2 Third-Party Application . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2 Two Applications: Uniform Valuation . . . . . . . . . . . . . . . . . . . . 19 2.2.1 In-House Applications . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.2 Third-Party Applications . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.3 In-House and Third-Party Applications . . . . . . . . . . . . . . . 26 2.2.3.1 Components Pricing by Platform . . . . . . . . . . . . . 27 2.2.3.2 Pure Bundle by Platform . . . . . . . . . . . . . . . . . . 29 2.2.4 Comparison and Welfare Analysis . . . . . . . . . . . . . . . . . . 33 2.3 Single Application: Generalization . . . . . . . . . . . . . . . . . . . . . . 35 2.3.1 In-House Application . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3.2 Third-Party Application . . . . . . . . . . . . . . . . . . . . . . . . 38 2.4 Two In-House Applications: Generalization . . . . . . . . . . . . . . . . . 43 2.4.1 In-house Applications . . . . . . . . . . . . . . . . . . . . . . . . . 44 3 Conclusion 52 iv ListofFigures 2.1 Prices: Single Third-Party Application . . . . . . . . . . . . . . . . . . . . 17 2.2 Profits: Single Third-Party Application . . . . . . . . . . . . . . . . . . . . 18 2.3 Platform Ecosystem: In-House Applications . . . . . . . . . . . . . . . . . 19 2.4 User Demand Pattern: Uniform Distribution . . . . . . . . . . . . . . . . 21 2.5 Prices: Two Third-Party Applications . . . . . . . . . . . . . . . . . . . . 26 2.6 Profits: Two Third-Party Applications . . . . . . . . . . . . . . . . . . . . 27 2.7 Prices: Component Pricing of Access and In-House Application . . . . . 29 2.8 Profits: Component Pricing of Access and In-House Application . . . . . 30 2.9 User Demand Pattern: Platform’s Bundle Offer . . . . . . . . . . . . . . . 31 2.10 Prices: Pure Bundle of Access and In-House Application . . . . . . . . . 33 2.11 Profits: Pure Bundle of Access and In-House Application . . . . . . . . . 34 2.12 User Demand Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.13 Improvement Upon “Free Access” Strategy . . . . . . . . . . . . . . . . . 50 v Abstract From a perspective of multi-product price discrimination, this paper examines pricing strategy of a monopolistic platform. Compared to the two-sided markets literature, users are allowed to buy various assortments of applications. Considered is an example of mobile operating system through which application developers interact with end users of heterogeneous valuation. Basically two modes of application provision is taken into consideration: In-house application or outsourcing to third-party developers. With a single in-house application, what platform really concerns is total price of access charge and application fee. However, the allocation of the total price between access charge and application fee does not matter in fact, thus access to the platform can be allowed free of charge. The free access is also viable as an optimal pricing strategy even where the application is outsourced to a third-party developer. But, with two in-house applications, free access charge cannot constitute platform’s optimal pricing strategy any more. Given paid access, the users who buy both appli- cations are able to avoid duplicate access charge, which enables the platform to price discriminate the purchasers for single application from those who buy dual applica- tions. Under a revenue sharing rule with third-party applications, the platform exploits all of the profit from third-party developers while it cannot accomplish monopoly profit with in-house applications yet. Assuming uniform distribution of user’s valuation, we gain numerical results in addition more than those under general conditions. Platform with a in-house applica- tion competing with a third-party application distributes access for free. It is equivalent vi to platform’s bundling offer of the operating system with its own application, which improves consumer surplus and social welfare. vii 1 Introduction 1.1 Overview Modern technology heavily draws on digital software programs. Numerous software packages proliferate that it seems hard to imagine living a life without assistance of digital technology. Among a lot of critical achievements, the development of personal computer might be a howling success. For less than a half century, it has empowered individual users to take full advantage of high-end computing, machine control, enter- tainment apparatus, business utility, and so on. The use of personal computer is grow- ing limitless. In the wake of the personal computers, many other devices that harness microprocessors are coming out. Most of them are operated by operating system, e.g. personal digital assistant (PDA), video games, tablet PC, smart phones, and so forth. 1 At the center of this technology in common, there is a core software, called operating system (OS), that operates the electronic devices. As a kernel software programs, it uti- lizes the computing power of microprocessor. Rising complexity in modern program- ming requires program architecture to package some commonly and frequently used functions into modules for efficiency. This new architectural design approach not only avoids some replicative cost across software development divisions but also reduces possible interdependent functional conflicts when various parties communicate with each other. As a carefully designed bundle of core modular functions, operating system plays a role of platform on which many groups of agents benefit from mutual interac- tion (Evans, Hagiu, and Schmalensee, 2006). 1 Among these software platform industries, the mobile applications supported by a smart phone is one of the most recent technology. In a smart phone handset is embedded an operating system: For instances, Apple’s iOS, Google’s Android, Microsoft’s Windows, Nokia’s Symbian, RIM’s Blackberry OS, and so on. Except for open source OS, it is written in invisible or indecipherable digital codes. Surrounding this OS platform, there are application developers such as in-house manufacturing or outsourced third-party developers. They make applications compatible with the operating system. The main difference between these two types of developers is that the third-party developers cannot make compatible applications unless OS platform provides Application Programming Interfaces (APIs). 1 Paradoxically operating system as an integrated circuit of core functions has no value to interested parties by itself. It is because operating system is a general pur- pose technology that purely helps to enhance communication of different parties so a party’s ultimate value is materialized when he finds counterparts to trade with. For example of smart phone industry, neither mobile users nor application developers place any value on the operating system until users buy some applications or developers sell their products. Even though the operating system is an indispensable component to users and developers, purchase of the phone without buying application and access to the operating system without customer base rarely brings about any value. Usually there are two distinct groups of participants on platform. Despite having an OS with no value, a platform mediates the transaction between two groups in order to make profit out of gains from trade. In PC industry, Microsoft’s Windows courts pro- gram developers and PC users as well. Microsoft makes profit charging Windows and its own brand programs such as MS Office. As such an example, video game is in rich of game makers and game players as well. Platform’s profit bases are charges on video game console and game titles. Apple’s i-phone is marketing handsets equipped with i-OS to users while it develops brand applications or invites third-party application makers. When it comes to the third-party developers, they cannot make applications unless the OS platform provides the Application Programming Interfaces (APIs). Soft- ware platform often cooperates with third-party developers helping them out with a development team or subsidy, but it draws a contract of sharing the revenue. 2 On one side by the platform, outsourced developers can get the best of the core OS function to make some applications that appeal to users. On the other side, users can afford to buy the applications once they obtain access compatible with an operating system. Along with these two sides, mobile handset supported by an operating system makes 2 In Apple i-phone industry, for instance, the contract between Apple and application developers is secret. But market surveys reveal that Apple and developers share the revenue by 30/70 rule convention- ally. Thirty percent of the revenue goes to the Apple while the rest of 70% will become the developer’s share. Amazon.com runs a revenue sharing rule similar to Apple. 2 the users connected to the application services and the developers to the users. Plat- form, a central mediator, acts as a catalyst for the interactions between two separate groups. This paper bears on how pricing strategy forms in two-sided platform with buyers and sellers. A major concern of this paper is placed on monopoly platform’s pricing strategy. Operating system solely belongs to platform and a monopoly platform controls access of users and developers completely. However we often observe that some applications might be produced in-house and some others might outsourced to third-party develop- ers. It is a question how the platform uses the access charge with respect to the structure of application provision: The role of access charge. In addition, application prices might change in accordance with the application provision environment. From a third-party developer’s perspective, she can gain the access making a con- tract with the platform before getting on board. How platform and developer draw a contract, especially on the revenue from application sales, is another question to ask. The contract between platform and developer is compared to the access charge on users and it is a means to control developer’s participation. Some “killer apps” in mobile application industry are in-house products and free as well. Why does a platform distributes its in-house application for free while facing other third-party applications? In this paper, I would suggest an explanation for free in-house applications. 1.2 RelatedLiterature To the best of my knowledge, Chen and Nalebuff (2006) is the most closest to my paper. In mobile application industry, operating system and applications are complements. Traditional explanation has treated both complementary goods symmetrically: If one product is complementary to the other one, then it is also true vice versa. As to the 3 mobile operating system, OS is complementary to applications in a sense that applica- tions do not run without OS. Applications, however, are not necessarily complementary to OS since operating system runs well functionally in absence of applications. Under the user’s heterogeneous valuation, Chen and Nalebuff (2006) investigate how essential product price competes with its complementary good by various ways — merger and acquisition, entering the dependent product in order to force competition, controlling compatibility, etc. Platform furnishes users with a plethora of applications. There is a strand of litera- ture dealing with multi-product feature of platforms: Bundling theory. In the example of mobile applications, a user who wants to buy a single application has to pay for the application and, if necessary, for access to the platform as well. Compared to the demand for a single application, those who are willing to purchase multiple applica- tions need to pay for the access only once, as an “entrance” fee, while they should pay for each application every time they buy it. Since the access charge does not recur even when a user buys many applications, payment for the access is saved with multi- applications purchase in actual fact. In multi-product pricing terminology, this can be construed as a “bundling discount.” Stigler (1963) suggests that bundling discount can be a profit-maximizing strategy where buyer’s valuation on multiple products are negatively correlated. Adams and Yellen (1976) classifies bundling strategy into pure bundling and mixed one: Pure bundling offers multiple products together but it does not allow standalone sales while mixed bundling offers a bundle with standalone sales. In monopoly, they illustrate that mixed bundling dominates pure bundling or compo- nents pricing 3 with stylizing examples. McAfee, McMillan, and Whinston (1989) gener- alizes Adams and Yellen (1976) in continuous valuation version. Once again, they verify that mixed bundling is the profit-maximizing strategy even though buyer’s valuation on products are not negatively correlated. 3 Components pricing is the one in which each product is priced but there is no bundle discount. 4 Platform industry also has received much attention from two-sided 4 markets (TSM) literature. The theory of traditional one-sided markets considers one group of agents fundamentally. Depending on the price, some agents are willing to be buyers and some others select to be sellers. The price tends to the equilibrium until the quantity demanded equalizes the quantity supplied. Contrary to the one-sided markets, two- sided markets consist of essentially different two groups, say, buyers and sellers, hence a dichotomy between two sides. 5 The transaction between two groups is mediated by platform. Accordingly, two-sided markets literature emphasizes the role of central plat- form, especially pricing strategy on both sides. Rochet and Tirole (2003, 2006) and Armstrong (2006) establish rudimentary frame- works which culminate in most of two-sided markets research. As to the monopoly platform, they derive an optimal pricing rule that is similar to the standard Learner’s formula for elasticity 6 but the platform skews the balance of prices on both sides reflect- ing on cross-group externality (or indirect network effect). Roughly speaking, if buyers are more valuable to sellers rather than the other way around, the platform raises the price on seller’s side and lowers the price on buyer’s side instead. 7 4 Arguably, the definition of two-sidedness is not clear. Rochet and Tirole (2003, 2006) derive the defi- nition from the equilibrium pricing strategy of their model. If the allocation of prices between two sides influences the outcome, they define that the market is structured in two-sided way. Rysman (2009) address the issue of two-sidedness beyond the matter of pricing. Platform, an organizer, chooses whether to run the market in one-sided or two-sided way. If it purchases from one side and then sell the products to the other side bilaterally, the market is defined to be one-sided. But if it allow the participants to inter- act with each other on the other side, the market is two-sided. Therefore, two-sidedness is determined by the platform’s non-pricing business strategy. The definition encompasses the platform’s openness and compatibility. Weyl (2010) remarks that the various definitions of the two-sidedness are simply modeling preference. 5 Table 1 of Rochet and Tirole (2003) lists some business models with two-sided features. Among them, the industries related to this paper are video games with content developers and gamers, operating sys- tems with application developers and clients, portals with advertisers and “eyeballs,” and internet with web sites and dial-up consumers. 6 Fori6= j2f1;2g, price on sidei is determined by[pi(fibjnj)]=pi = 1=i wherefi is the fixed access cost,bj is the agent in groupj’s per-interaction benefit,nj is the total number of participating group j agents, andi is the price elasticity of groupi demand (Armstrong, 2006). 7 Newpaper/magazine industry. Include emprical papers. 5 Regarding two-sided monopolistic platform, Rochet and Tirole (2003) integrates multi-product pricing and network theory: Multiple sides are treated by a monopoly platform and the interaction between different sides benefit all concerned in a way that the benefit gets larger as the participants gather more. The platform, as an adminis- trator, charges fee on the interaction of two involved groups. Provided that the parties get already on board, the benefit from networking cannot be achieved until they come to interact in fact. The gains of interaction are assumed to be heterogeneous across the agents, which leads to the demand for participation with respect to per-interaction fee. The optimal monopoly fee is determined by each group’s price elasticity of demand following standard Learner’s formula. 8 In this sense, Rochet and Tirole (2003) bridge the gap between network theory and multi-product pricing. Network theory neglects multi-sidedness and price allocation issue, whereas multi-product pricing literature pays scant attention to explain how the separate (multi-sided) groups are coordinated to achieve the cross-group network benefit. Compared to Rochet and Tirole (2003), Armstrong (2006) assumes that the gains from interaction are constant all across the agents in the same group, i.e. homogeneous interaction benefits. They rather study the case in which agents have different val- ues on the platform access or membership. A platform charges different fixed fees for membership on both sides instead of charging on interactions. Demand is derived as a function of membership fee. Again the optimal monopoly pricing appears similar to the standard Learner’s pricing. 9 Rochet and Tirole (2006) include the feature of Armstrong (2006) in addition to Rochet and Tirole (2003). They distinguish two kinds of charges on indirect network externalities: ex ante membership charges and ex post usage charges. In most cases, actual interaction benefit comes from usage but a platform might be able 8 There are two groups, say buyers(B) and sellers(S). Aggregate pricep is determined by(pc)=p = 1= wherec is a constant marginal interaction cost and is the price elasticity of demand. Each price is determined byp B = B =p S = S wherep=p B +p S . 9 Encompassing additional features on Armstrong (2006), Hagiu (2006, 2007, 2009) construct modified versions of demand ` a la Learner. 6 to charge prospective participants on membership even before the transaction ensues. Moreover, the platform might collect usage fees mediating transaction after the partici- pants get on board. Further away from Rochet and Tirole (2003) and Armstrong (2006), Weyl (2010) studies broader class of heterogeneity. Rochet and Tirole (2003) analyze usage fee under the assumption of heterogeneous interaction benefits while Armstrong (2006) examines membership fee under the assumption of heterogeneous membership benefits. Build- ing up the pioneering papers, Weyl (2010) accommodates both types of heterogeneity together, and he concludes that the analysis becomes simplified than expected interest- ingly. Beyond the choice between membership or usage fee schemes, the platform is able to devise a general way of charging 10 that ensures both sides to participate regard- less of the other side’s decision. In equilibrium, the platform’s optimal monopoly price departs from socially optimal one by market power and Spence distortion. 11 Two-sided markets literature simplifies that users on one side interact with all of participating users on the other side (Weyl, 2010). But, in practice, users have option to choose their transaction counterparts. It is because that they have different preferences over the applications on the other side, that is to say, heterogeneous valuation on indi- vidual applications. 12 Endogenous selection is the first departing concern of my paper from the “traditional” two-sided markets approach. Secondly, face-to-face payment transfer between two sides is taken into consideration. 13 This payment is not collected 10 He names this charge insulating tariff. See section 1.C of Weyl (2010). Of the monopoly pricing, see ibid., equation (7) in the same paper. 11 Socially benevolent dictator compares total benefit and total cost when he considers a just price. Profit- maximizing monopoly, however, compares marginal benefit and marginal cost regardless of total net ben- efit. Lack of price discrimination, the monopolist’s marginal thinking ignores infra-marginal consumers’ interests, which is called Spence distortion (Spence, 1975). 12 Rochet and Tirole (2003) assume that agents have different preferences over the other side compositely but they assume away different preference over the individual agents. 13 Extending Armstrong (2006)’s original stylized model, Hagiu (2009) addresses this unilateral charac- teristic of the payment between buyers and sellers, yet it still holds the aforementioned assumption that buyers purchase from all of participating sellers. 7 nor regulated by the platform directly. For example, in digital software platform, one group of participants consists of software vendors and the other one is comprised of users. The vendors would request for payment in exchange of supplying their prod- ucts or serving the users. Usually the payment cannot be enforced at certain price and it is not under platform’s control. 14 Lastly, I will relax the assumption that two separate groups are of equal size. 15 This paper analyzes a monopolistic two-sided platform with a few sellers but uncountably many buyers. As simple as possible, I will consider the case of two sellers. There are a few papers that study bundling issues in two-sided markets. 16 In par- ticular, Chao and Derdenger (2012) analyze mixed bundling in two-sided markets with installed base, especially video game industry. Under royalty contract, they model a platform with integrated content and third-party game developers. All of the gamers must buy third-party content similarly to the two-sided markets literature. The plat- form sells video consoles to gamers as a vehicle for access while it sells its own inte- grated game titles as well. The crucial workhorse is the assumption of two different types of gamers: Installed base and new customers. Installed base users exist equipped with video game consoles so they need not acquire access additionally. They simply buy the platform’s integrated game and also third-party content. Besides third-party content, however, new customers have option to buy either only game console or game console plus integrated content. Offering a mixed bundle of game console and inte- grated content, the platform can discriminate installed base and new customers. In addition to third-party content, users from installed base purchase only integrated con- tent, whereas new customers either buy the bundle or mix and match console and third- party content. Similarly to Chao and Derdenger (2012), my paper draws on the idea of 14 See Rochet and Tirole (2006) regarding this feature. 15 Most of two-sided markets literature assumes that agents on both sides are infinitely many so they are well approximated by a continuous distribution of standardized unit mass. 16 See Rochet and Tirole (2008), Amelio and Jullien (2012), Chao and Derdenger (2012), and Choi (2010). 8 bundling literature. In my model, all of the users are new customers and there is no installed base, thus no need for bundling. Even without physical bundling, I find that platform access can be regarded as a “bundle discount” assuming away that all of the customers buy the third-party content depicted in Chao and Derdenger (2012). 1.3 SummaryofMainResults Under a general distribution of user’s valuation on applications, I study the case of a single application which is possessed by a platform. Thus the platform has two means to make a profit from users: Access fee and application price. Similarly to “razor-blade” logic 17 of pricing, only total payment for access and application matters to users. Indi- vidual charge, however, is not of concern. Thus the platform is able to price either access or application leaving the other one free of charge. Even if the application sector should be outsourced to a third-party developer, the monopoly outcome of free access is achievable as long as the platform sets an appropriate tariff on the developer (section 2.3). With multiple applications, we can cast the same question on the free access. Con- trary to the single application case, platform is not willing to allow access for free any further. The intuition draws on bundling strategy, a particular discriminatory pricing. Given paid access as the result, users who want only one application should pay for access charge and application fee. In a similar way, those who buy multiple applica- tions should pay for each application, however, only once for the access. Users buying multiple applications would avoid recurring access cost, which is interpreted as bundle discount. In a platform’s standpoint, this kind of “bundle discount” presents a menu of prices that discern users with heterogeneous valuation on applications (section 2.4). 17 Razor and blade are perfect complements for shaving. In real world, blades are replaced as time goes by while razor is durable. By “razor-blade,” I assume both goods are durable with replacement. 9 Under the assumption of uniform user valuation, more specific results arise. Uti- lizing numerical computation, revenue sharing on third-party application developers are studied. By the assumptions as simple as possible, I conclude that platform takes all share of the revenue. In addition, equilibrium outcomes are derived and compared. For single application, the equivalence between in-house and third-party application is verified (section 2.1). Compared to the case in which all applications are supplied by third-party developers, the platform cannot achieve optimal monopoly outcome of all in-house applications. Outsourcing applications to third-parties, platform’s access charge increases and application prices do as well. In addition, it is studied an interme- diate case in which one application is in-house and the other one is third-party one. For this case, I find that in-house application is distributed for free (section 2.2). 10 2 Model Throughout the paper, we consider a monopolistic platform denoted byA 0 . The plat- form as an administrator opens a market with core technology that mediates the trans- action between users and developers. Without access to the platform’s OS, users cannot utilize application service and developers cannot make an application either. In order to purchase some applications, smart phone users ought to buy a device equipped with an operating system. Similarly, unless an operating system is open source, third-party developers require an application programming interface (API) to build compatible applications. Assumption1. Platform itself does not bring any value to users or developers. An operating system is construed as indispensable kernel, there is of no value to users and developers by itself. 1 Users need OS as means to use applications while developers want it to reach out to the users on the other side. From user’s perspective, OS is a perfect complements to the applications. 2 User’s ultimate utility comes from the use of applications. Throughout this paper, I will study the cases of a single application and two applications. Applications are denoted byA 1 andA 2 hereafter. In addition, different types of application provision are considered: In-house applications or third-party applications. The application made by the platform’s own division is called in-house application, thus its price is controlled by the platform. Some applications are outsourced to third-party developers, which 1 One of the frequently mentioned examples regarding two-sided markets is mass media industry with advertisers and viewers. Newspaper, for example, contains couple of articles that readers are endeavoring to read. But it is unlikely that most of laypeople are infatuated with operating system by itself without any applications. 2 Chen and Nalebuff (2006) remarks operating system is a one-way essential complement to application. The former is indispensable to the latter but not vice versa. They analyze the case in which users have heterogeneous valuation on the essential complement. As said, I assume away any valuation on platform itself. 11 are called third-party applications. I will investigate pricing strategies of platform and developers depending on the ownership in ensuing sections. Purchase of application is assumed to be discrete. A user decides whether to buy and what to buy and at most he is able to buy only one indivisible application each. Once he buys an application, he can enjoy the service without additional payment. Thus we can focus on the price of the application rather than service charges on the usage frequency. We assume that user’s valuation is private information that platform and developers do not know each user’s exact valuation on applications but they know the distribution of user’s valuation. For simplicity of analysis, the valuation on application A i is assumed to follow a uniform distribution on unit interval [0;1] for i2f1;2g. The valuation of individual application is identical and independent of each other. Assumption2. Letv i denote a user’s valuation on applicationA i fori2f1;2g, which follows an identical and independently distributed uniform distribution on unit interval [0;1]. More precisely, the probability density function is defined byf i (v) = 1 and the cumulative distribu- tion function byF i (v) =v on the interval. When we consider two applications, the joint distribution of (v 1 ;v 2 ) is defined on the unit rectangle, [0;1] [0;1], on which marginal and cumulative distributions are described byf(v 1 ;v 2 ) = 1 andF(v 1 ;v 2 ) =v 1 v 2 for(v 1 ;v 2 )2 [0;1][0;1]. Regardless of whether applications are provided by the platform,A 0 , as a sole pro- prietary platform, wields power to determine how much to charge on the access. Unless access to OS is free of charge, users should pay for it. Letp 0 denote the access charge on user’s side. Assumption3. The platform charges non-discriminatory fixed fee on users,p 0 , which is non- negative. Every single user faces the same access charge. With a single application, assumption 3 is not restrictive at all. However, with two applications, the platform may be able to charge a lower access fee for those who buy 12 two applications whereas it keeps relatively high access fee for single purchaser. This practice of price discrimination is assumed away. It costs to make programs for the platform and the developers. Programming requires capital expenditure such as highly trained expertise and financial investment in research and development. Even after the programs are launched, they need to be managed properly and continually to satisfy users, which incurs operational costs. One of the defining features that highlights digital technology is that the cost in R&D phase is higher than production/operation phase. In this paper, I rather focus on the platform ecosystem in which the applications are all in place. Moreover no operational costs are considered. Assumption4. No costs are assumed for the platform and application services. I would not analyze ex ante investment incentive at the stage of technological devel- opment, be that as it may, the absence of cost might not be too restrictive to describe the pricing strategy when I confine my results to digital technology with minuscule marginal cost of production. 2.1 SingleApplication: UniformValuation Before we study pricing strategy of a monopoly platform dispensing multiple appli- cations, we investigate the basic case in which there is only one application on board. The application is denoted byA 1 . According to assumption 2, heterogeneous consumer valuation is uniformly distributed on unit interval[0;1]. Two different ownership structures between platform A 0 and application A 1 are taken into consideration: The platform supplies the application in-house or it out- sources to a third-party developer. I will start with the case of in-house application and then proceed to that of third-party application. 13 2.1.1 In-HouseApplication The platform is to maximize profit by setting two prices – access charge to the platform, p 0 , and application price, p 1 . Given prices, a user is willing to buy the application as long asvp 0 +p 1 . The platform faces demand D(p 0 ;p 1 ) = 1F(p 0 +p 1 ) = 1(p 0 +p 1 ): Platform’s profit 0 (p 0 ;p 1 ) := (p 0 +p 1 )(1p 0 p 1 ) which is quadratic polynomial in total price,p 0 +p 1 . Thus we can verify that there is a unique total price that maximizes the profit. Denoting total price byP =p 0 +p 1 , we solve the optimal total price and profit, P I = 1 2 and I 0 = 1 4 : (2.1) Note that individual prices are not determined so there are uncountably many prices,p 0 andp 1 , which satisfyp 0 +p 1 =P I = 1=2. It is commonly observed where two products are perfect complements 3 . 2.1.2 Third-PartyApplication We examine a platform environment in which applicationA 1 is outsourced to a third- party developer. The application price, p 1 , is not under platform’s direct control any longer. It may incur huge costs to invent a new application out of nowhere or it may be hard to use the well-known technology without infringing intellectual property rights. 3 OS is an essential complement to the application. 14 Whatever the reason is, the only way for the platform is to yield application provision to a desired developer outside as long as it is also beneficial to the platform. Here I assume that a third-party developer can supply the application only with the monopoly platform,A 0 . There is no alternative platform to which the developer is able to provide its application so that it is to no avail if the developer is not allowed to join the platform. Assumption5. Third-party application developer has zero reservation utility. In place of possessing the application section in-house, the platform allows the third-party developer to run business if the prospective developer agrees to contract with the platform about revenue or profit. A specific form of contract is considered throughout this paper: Revenue sharing on the final profits of the application sales. The platform takes share of developer’s profit and the developer takes the residue, (1) share of its own profit. 4 The platform offers a contract and then the developer takes it or leave it. Provided that both parties agree on the term of the contract between the platform and the developer, the platform and the third-party developer call out the prices simul- taneously. Observing the prices, users determine whether to get on board or stay out of the market at the same time. The following time-line displays the sequence of pricing: 1. Contracting stage: Platform offers a revenue sharing contract, , to third-party developer. If the developer accepts the condition of revenue split, she is autho- rized to price the application, A 1 in the following stage. Otherwise, she cannot take part in the market. 2. Pricing stage: Once the developer gets on board, platform and application devel- oper set access fee, p 0 , and application price, p 1 , simultaneously. Depending on how much the application has a value to a user, she decides whether to buy it as well as access or not. 4 There are various kinds of contract we can take into consideration: Fixed fee, two-part tariff, and non-linear pricing. Revenue split is a special type of two-part tariff. 15 I start to study pricing stage behavior firstly. Given a revenue split,, platform and provider set out to charge the prices simultaneously. Profits of the platform and the developer are denoted by 0 (p 0 ;p 1 ;) =p 0 (1p 0 p 1 )+(p 1 (1p 0 p 1 )) = (p 0 +p 1 )(1p 0 p 1 ); 1 (p 0 ;p 1 ;) =p 1 (1p 0 p 1 )(p 1 (1p 0 p 1 )) = (1)p 1 (1p 0 p 1 ); respectively. Solving the first-order conditions of profit maximization, we derive equi- librium prices such that p T 0 ();p T 1 () = 1 3 ; 1 3 : There is a trade-off between revenue sharing and access charge. As the platform takes more (less) share of the developer’s profit, it lowers (raises) the access fee sinceA 0 gets bigger (smaller) portion of profit from A 1 ’s revenue. The revenue sharing, however, does not directly affect the developer’s pricing since it simply reduces the profit from application proportionately. Anticipating that platform lowers access fee as its share rises, the developer increases the application price to maximize the profit. Figure 2.1 shows this pattern of the prices graphically. The maximum profits conditional on the contract,, are T 0 (); T 1 () = 1 (3) 2 ; 1 (3) 2 respectively. Part of the developer’s profit transfers to the platform by share so that the platform gathers additional profit from the developer while it loses a profit from the access. Figure 2.2 displays the conditional profits on revenue sharing. 16 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Revenue Sharing (β) Prices application access Figure 2.1: Prices: Single Third-Party Application Back in the contracting phase, the platform draws a sharing rule,2 [0;1], as a take- it-or-leave-it offer to the developer. The platform will offer = 1 in order to maximize the monopoly profit. In exchange, the access fee will set at zero,p 0 = 0. Total profit of the developer is fully extracted by the platform in equilibrium such that T 0 ; T 1 = 1 4 ;0 (2.2) where = 1 and(p T 0 ;p T 1 ) = (0;1=2). Equilibrium outcome with third-party developer (2.2) belongs to one of the equi- libria with in-house application (2.1). The former is equivalent to the latter with free distribution of access. Now proposition 1 follows. 17 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 Revenue Sharing (β) Profits total developer platform Figure 2.2: Profits: Single Third-Party Application Proposition1. Suppose that user’s valuation on a single application follows a uniform distri- bution on interval[0;1]. i. Where the application is provided in-house, the platform sets access fee,p I 0 , and application price,p I 1 , such that (p I 0 ;p I 1 )2 (p 0 ;p 1 )2R 2 + p 0 +p 1 = 1 2 and the equilibrium profit I 0 = 1 4 : ii. Where the application is provided by a third-party developer, the platform offers a revenue sharing that asks all of the developer’s profit (i.e. I = 1). The equilibrium access charge and application price are p T 0 = 0 and p T 1 = 1 2 18 and the profits are T 0 = 1 4 and T 1 = 0: iii. The ownership of the application does not change platform’s equilibrium profit. 2.2 TwoApplications: UniformValuation In practice, there are multiple applications on the mobile platform. Improving upon section 2.1 of single application, I consider a platform ecosystem in which there are two applications. Let A 1 and A 2 denote two applications. Customer’s valuation on two applications is denoted by a vectorv := (v 1 ;v 2 )2 [0;1] 2 . In distribution, the valuation follows a uniform distribution,U[0;1] 2 and the distribution function isF(v) =v 1 v 2 for anyv2 [0;1] 2 due to assumption 2. Figure 2.3 presents an illustration of how the platform and application sectors are structured. Similarly to the notations as before, p 0 denotes for access fee and p i for Figure 2.3: Platform Ecosystem: In-House Applications 19 application price indexed byi2f1;2g. Given access charge and application fees, users with different valuation decide to buy none, one, or both of the applications. Turning the point to user’s demand for the applications, we can arrange purchase or demand pattern by four classes which are characterized such that Users buy onlyA 1 if 8 > > > > > > < > > > > > > : v 1 (p 0 +p 1 ) 0 v 1 (p 0 +p 1 )v 2 (p 0 +p 2 ) v 1 (p 0 +p 1 ) (v 1 +v 2 )(p 0 +p 1 +p 2 ) , 8 > > < > > : v 1 p 0 +p 1 v 2 p 2 Users buy onlyA 2 if 8 > > > > > > < > > > > > > : v 2 (p 0 +p 2 ) 0 v 2 (p 0 +p 2 )v 1 (p 0 +p 1 ) v 2 (p 0 +p 2 ) (v 1 +v 2 )(p 0 +p 1 +p 2 ) , 8 > > < > > : v 2 p 0 +p 2 v 1 p 1 Users buy bothA 1 andA 2 if 8 > > > > > > < > > > > > > : (v 1 +v 2 )(p 0 +p 1 +p 2 ) 0 (v 1 +v 2 )(p 0 +p 1 +p 2 )v 1 (p 0 +p 1 ) (v 1 +v 2 )(p 0 +p 1 +p 2 )v 2 (p 0 +p 2 ) , 8 > > > > > > < > > > > > > : v 1 +v 2 p 0 +p 1 +p 2 v 1 p 1 v 2 p 2 Users buy none of them if 8 > > > > > > < > > > > > > : v 1 (p 0 +p 1 )< 0 v 2 (p 0 +p 2 )< 0 (v 1 +v 2 )(p 0 +p 1 +p 2 )< 0 , 8 > > > > > > < > > > > > > : v 1 <p 0 +p 1 v 2 <p 0 +p 2 v 1 +v 2 <p 0 +p 1 +p 2 20 The users who demand for onlyA 1 , onlyA 2 , and bothA 1 andA 2 are defined by D 1 (p) := Pr (v 1 ;v 2 )2 [0;1] 2 v 1 p 0 +p 1 ;v 2 p 2 =p 2 (1p 0 p 1 ); D 2 (p) := Pr (v 1 ;v 2 )2 [0;1] 2 v 2 p 0 +p 2 ;v 1 p 1 =p 1 (1p 0 p 2 ); D 12 (p) := Pr (v 1 ;v 2 )2 [0;1] 2 v 1 +v 2 p 0 +p 1 +p 2 ;v 1 p 1 ;v 2 p 2 = (1p 1 )(1p 2 ) 1 2 p 2 0 : Figure 2.4 displays the user’s demand pattern graphically. Given prices p := (p 0 ;p 1 ;p 2 ), there are three types of purchase. Figure 2.4: User Demand Pattern: Uniform Distribution 21 Access charge, p 0 , affects every type of demand for applications. The lower the access charge is, the more users are willing to buy. Likewise, for eachi2f1;2g, appli- cation price,p i , affects demand for the other application beyond its own demand. For example, other prices being equal, an increase inp 1 raisesD 2 but it lowersD 1 andD 12 . The above demands are the ones classified by the consumer’s purchase pattern. Instead we can rearrange the demands by the developer’s profit sources, that is, D 0 (p) :=D 1 (p)+D 2 (p)+D 12 (p) = 1 p 2 0 2 p 1 p 2 p 0 (p 1 +p 2 ); D 1 (p) :=D 1 (p)+D 12 (p) = 1 p 2 0 2 p 1 p 0 p 2 ; D 2 (p) :=D 2 (p)+D 12 (p) = 1 p 2 0 2 p 2 p 0 p 1 : 2.2.1 In-HouseApplications The platform is assumed to have both applications in-house and it completely controls the prices. As a sole platform organizer,A 0 is able to design various types of product packages: Separate sales of OS and each application, bundle of OS and one application, tying of two applications, and so on. Here I focus on the component sales in which access fee and each application price are offered without any type of bundled packages. The objective of the platform is to maximize the monopoly platform by changing prices, that is, max p 0 ;p 1 ;p 2 (p 0 ;p 1 ;p 2 ) := max p 0 ;p 1 ;p 2 [ 0 (p 0 ;p 1 ;p 2 )+ 1 (p 0 ;p 1 ;p 2 )+ 2 (p 0 ;p 1 ;p 2 )] := max p 0 ;p 1 ;p 2 p 0 D 0 (p 0 ;p 1 ;p 2 )+p 1 D 1 (p 0 ;p 1 ;p 2 )+p 2 D 2 (p 0 ;p 1 ;p 2 ) : 22 The first-order conditions are 2 6 6 6 6 4 1 3p 2 0 2 3p 1 p 2 3p 0 (p 1 +p 2 ) 1 3p 2 0 2 2p 1 3p 0 p 2 1 3p 2 0 2 2p 2 3p 0 p 1 3 7 7 7 7 5 = 2 6 6 6 6 4 0 0 0 3 7 7 7 7 5 ; which leads to a set of solutions (p 0 ;p 1 ;p 2 )2 ( 2 3 ;0; 1 6 ; 2 3 ; 1 6 ;0 ; r 2 3 ;0;0 ! ; p 2 3 ; 1 3 (2 p 2); 1 3 (2 p 2) !) that solves for this system of first-order necessary conditions. The first two solutions are asymmetric application pricing in which one of the application price is set at zero. The third one stands for the free distribution of application with paid access. The last one is the symmetric application prices with paid access. The second-order sufficient condition is described by Hessian matrix H = 2 6 6 6 6 4 3p 0 3p 1 3p 0 3p 2 3p 0 3p 1 3p 0 3p 2 2 3p 0 3p 0 3p 1 3p 0 2 3 7 7 7 7 5 whereH is a negative definite matrix if the prices maximizes the total profit locally. The only set of prices that satisfies the second-order condition is the symmetric application prices with paid access,( p 2=3;(2 p 2)=3;(2 p 2)=3) (0:4714;0:1953;0:1953). We remark that platform’s access charge is no longer free. In single application case, “free access” constitutes an equilibrium for both in-house and third-party application cases (proposition 1). It is because access fee plays a role of price discrimination for single purchasers and multiple purchasers. Intuitively, a user buying both applications paysp 0 +p 1 +p 2 whereas a user buying onlyA 1 paysp 0 +p 1 . It means that multiple purchaser gets bundle discount by p 0 . We will explain this reason more carefully in section 2.4. 23 Therefore we obtain equilibrium profits I 0 = 2 p 2 9 0:3143 I 1 = I 2 = 2 27 (3 p 2) 0:1175 I = 2 27 (6+ p 2) 0:5492 at unique equilibrium prices,p I = p 2=3;(2 p 2)=3;(2 p 2)=3 . 2.2.2 Third-PartyApplications There are two applications that are provided by separate third-party developers. In the beginning, the platform offers a revenue split contract for each developer bilater- ally. Here I focus on the symmetric revenue sharing rule placed on each application developer;' i = i for eachi2f1;2g. Provided that both application developers get on board, the platform maximizes a profit max p 0 0 (p 0 ;p 1 ;p 2 ;) =max p 0 " p 0 D 0 (p)+ 2 X i=1 p i D i (p) # ; which leads to the first-order condition 1 3p 2 0 2 p 1 p 2 2p 0 (p 1 +p 2 ) [2p 1 p 2 +p 0 (p 1 +p 2 )] , 1 3p 2 0 2 (2 +1)p 1 p 2 ( +2)p 0 (p 1 +p 2 ) = 0: (2.3) 24 Given revenue sharing, developeri is to max p i i (p 0 ;p 1 ;p 2 ;) :=max p i (1)p i D i (p) fori2f1;2g. The first-order conditions for developer 1 and developer 2 are 1 2 (1) 2p 2 0 4p 1 2p 0 p 2 = 0 (2.4) 1 2 (1) 2p 2 0 4p 2 2p 0 p 1 = 0 (2.5) respectively. Plugging the developer’s first-order condition (2.4) and (2.5) into the plat- form’s first-order condition (2.3), we derive a third-order polynomial in p 0 . Going around complicated algebraic analysis, we now turn to numerical analysis. Equilib- rium prices and profits will be depicted by graphs, thus all of the following graphs show the pattern apparently 5 . The equilibrium prices are graphed by figure 2.5. As platform’s share goes up, the platform charges access fee lower while the developers price applications higher. Similarly to section 2.1, revenue sharing does not affect developers’ application price directly. The reason of high application prices is that the platform gets to lower the access charge owing to profit sharing. Figure 2.6 shows the equilibrium profits conditional on sharing. The platform’s profit is maximized where the revenue sharing is contracted at T = 1, which means 5 It follows convention of Schmalensee (1984): Numerical results supported by “computer analysis and not by general proofs are often indicated by the italicized adverb apparently.” 25 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 Revenue Sharing (β) Prices application access Figure 2.5: Prices: Two Third-Party Applications that the platform extracts the revenue from application sales completely. The corre- sponding prices and profits are p T 0 = 0:4826; p T 1 =p T 2 = 0:3559; T 0 = 0:4528; T 1 = T 2 = 0: Developers gain no profits. This result is similar to the case of a single third-party appli- cation. Compared to the case of two in-house applications, both access and application prices become higher. Therefore total profit becomes lower and the platform cannot recover optimal monopoly outcome. 2.2.3 In-HouseandThird-PartyApplications One of the applications are owned by the platform and the other one is outsourced to a third-party developer. LetA 1 denote the in-house application andA 2 the third-party application and price p 1 and p 2 respectively. Similarly to section 2.1.2, the platform 26 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Revenue Sharing (β) Profits total developer platform Figure 2.6: Profits: Two Third-Party Applications is supposed to offer a linear revenue sharing, , to the third-party developer in the beginning. 2.2.3.1 ComponentsPricingbyPlatform Firstly, we consider the case in which the platform charges access fee,p 0 and in-house application price,p 1 . Given sharing, the platform is to max p 0 ;p 1 01 (p 0 ;p 1 ;p 2 ;) :=max p 0 D 0 (p)+p 1 D 1 (p)+p 2 D 2 (p) ; which leads to the first-order condition 2 4 1 3p 2 0 2 (2+)p 1 p 2 p 0 (3p 1 +(2+)p 2 ) 1 3p 2 0 2 2p 1 (2+)p 0 p 2 3 5 = 2 4 0 0 3 5 : (2.6) 27 The second-order condition is summarized by a Hessian matrix 2 4 3p 0 3p 1 (2+)p 2 3p 0 (2+)p 2 3p 0 (2+)p 2 2 3 5 which is a negative definite matrix. Reducing two first-order conditions in (2.6), we derive an equation p 1 [2(2+)p 2 3p 0 ] = 0 ) )p 1 = 0: In words, the in-house application should be distributed for free no matter what the revenue split is. The developer is to max p 2 2 (p 0 ;p 1 ;p 2 ;) :=max p 2 (1)p 2 D 2 (p) : The first-order condition for developer’s maximization problem is 1 2 (1)(2p 2 0 2p 0 p 1 4p 2 ) = 0 (2.7) and the second-order condition is immediately verified. Solving first-order condition (2.6) and (2.7), we derive equilibrium prices and figure 2.7 graphs the changes in prices depending on revenue sharing. Apparently access charge is decreasing and third-party application price increases as the platform asks bigger share. It is interesting that in-house application price is zero constantly no matter what the sharing ratio is. In other words, in-house application is distributed for free once a user pays for the access. However, third-party application should be paid. 28 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Revenue Sharing (β) Prices access in−house app third−party app Figure 2.7: Prices: Component Pricing of Access and In-House Application Figure 2.8 graphs the profits of the platform and the third-party developer. The platform’s profit is maximized at revenue sharing IT comp = 1 apparently. Thus the equi- librium prices are such that p IT 0 = 0:4871; p IT 1 = 0; and p IT 2 = 0:4407 and equilibrium profits are IT 01 = 0:5190 and IT 2 = 0: 2.2.3.2 PureBundlebyPlatform Since the in-house application is not priced, OS and in-house application can be treated as a bundle. Now we consider a strategy of tying OS and in-house application. Letp B denote the bundle price andp 2 third-party application price. Given bundle price and third-party application price, users with different valua- tion decide to buy none, only the bundle, or the bundle and the application. Turning 29 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Revenue Sharing (β) Profits total platform third−party Figure 2.8: Profits: Component Pricing of Access and In-House Application the point to user’s demand for the applications, we can arrange purchase or demand pattern by three classes which are characterized as the followings: Users buy both the bundle by platform and third-party application if 8 > > < > > : v 1 +v 2 (p B +p 2 ) 0 v 1 +v 2 (p B +p 2 )v 1 p B , 8 > > < > > : v 2 v 1 +p B +p 2 v 2 p 2 Users buy only the bundle by platform if 8 > > < > > : v 1 p B 0 v 1 p B v 1 +v 2 (p B +p 2 ) , 8 > > < > > : v 1 p B v 2 p 2 Users buy none of them if 8 > > < > > : v 1 +v 2 (p B +p 2 )< 0 v 1 p B < 0 , 8 > > < > > : v 2 <v 2 +p B +p 2 v 1 <p B 30 The users who demand for only the bundle and both of the bundle and the third- party application are denoted by D B (p B ;p 2 ) :=p 2 (1p B ); D B2 (p B ;p 2 ) := (1p 2 ) 1 2 p 2 B ; respectively. Figure 2.9 displays the user’s demand pattern graphically. Given pricesp B andp 2 , there are two types of purchase. Figure 2.9: User Demand Pattern: Platform’s Bundle Offer Now we can rearrange the demands by the participant’s profit sources D 0 (p B ;p 2 ) :=D B (p B ;p 2 )+D B2 (p B ;p 2 ) =p 2 (1p B )+(1p 2 ) 1 2 p 2 B ; D 2 (p B ;p 2 ) :=D B2 (p B ;p 2 ) = (1p 2 ) 1 2 p 2 B : 31 Given revenue sharing, the platform is to max p B B (p B ;p 2 ;) :=max p B p B D 0 (p B ;p 2 )+p 2 D 2 (p B ;p 2 ) : The first-order condition for platform’s profit maximization is 1 3p 2 B 2 p B (2+)p 2 = 0 (2.8) and the second-order condition is immediately verified. The third-party developer maximizes the profit such as max p 2 2 (p B ;p 2 ;) :=max p 2 (1)p 2 D 2 (p B ;p 2 ;): The first-order condition for the developer’s profit maximization is (1p 2 ) 1 2 p 2 B p 2 = 0: (2.9) Solving first-order condition (2.8) and (2.9), we obtain a third-order polynomial in p B . Again, we draw on the numerical analysis to show the equilibrium apparently. Figure 2.10 depicts the equilibrium bundle price and the third-party application price 6 . As expected, figure 2.10 is equivalent to figure 2.7 of component pricing. As the platform’s share on the third-party’s revenue get bigger, the bundle price declines, whereas third-party application price rises. Figure 2.11 graphs the profits of the platform and the third-party developer. Again, we can verify that figure 2.11 is equivalent to figure 2.8. 6 Without linear sharing, lemma 1 of Chen and Nalebuff (2006) proves that optimalpB = 2 p 2 0:5858 andp2 = p 210:4142. 32 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.45 0.5 0.55 0.6 0.65 Revenue Sharing (β) Prices bundle third−party app Figure 2.10: Prices: Pure Bundle of Access and In-House Application 2.2.4 ComparisonandWelfareAnalysis Throughout section 2.2, I have shown how equilibrium prices and profits vary with respect to different modes of application ownership. This section briefly summarizes the changes in prices and profits and then compares social welfare and consumer sur- plus accordingly. By the results in section 2.2.1, 2.2.2, 2.2.3.1, and 2.2.3.2, access charges are ordered by p I 0 0:4714<p T 0 0:4826<p IT 0 =p IT B 0:4871: Access charge with all third-party applications is greater than that with all in-house ones. It gets even larger where one application is in-house and the other one is provided by a third-party developer. Application prices are compared as follows: p IT 1 = 0<p I 1 0:1593<p T 1 =p T 2 0:3559<p IT 2 0:4407: 33 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Revenue Sharing (β) Profits total platform third−party Figure 2.11: Profits: Pure Bundle of Access and In-House Application Once the platform has an in-house application competing with a third-party developer, the in-house application is priced at zero, that is, free distribution. The price with all third-party applications is larger than that with all in-house applications. Third-party application price is at the highest level where in-house and third-party applications coexist. Definitely platform makes a maximum profit having all applications in-house (sec- tion 2.2.1). The profit decreases where the platform outsources one application to a third-party and it even more decreases where all application production is outsourced to third-party developers. Precise order of platform’s profits is described by I 0 0:5492> IT 0 = IT B 0:5190> T 0 0:4528: Since no cost is considered throughout this paper, social welfare (SW) is the aggre- gate reservation utility of the users who participate in the platform. Of social wel- fare, some portion ends up with the profit of platform and developers and the residue 34 belongs to consumer surplus (CS). Various types of application ownership leads to social welfare as the following order: SW T 0:6428<SW I 0:6885<SW IT 01 =SW IT B 0:8095: Social welfare with all in-house applications is greater than that with all third-party applications. User base declines as access fee and application prices with all third-party applications get higher than that with all in-house applications. Interestingly, social welfare is improved where one application is in-house and the other one is a third-party product. Consumer surpluses are ordered as follows: CS I 0:1393<CS T 0:1900<CS IT 01 =CS IT B 0:2905: Users gain the least of consumer surplus when the platform provides all of the appli- cations monopolistically. Consumers are better off with all third-party applications. Coexistence of in-house and third-party application leads to the maximum consumer surplus. 2.3 SingleApplication: Generalization Letv denote a user’s valuation. It is distributed with no atom on non-negative support, R + = [0;1). Total population size of users is standardized into the unit mass. In short, cumulative distribution functionF(v) depicts the composition of user valuation on the application completely. Naturally followed notation is the probability density function f(v). Often it is of concern to the platform and the developer how many users are willing to buy the application given some charges. A portion of users with reservation utility greater thanv is denoted by demandD(v) := 1F(v). 35 Assumption6. Letv denote a user’s valuation on applicationA 1 . Non-negative valuation is assumed, that is,v2 R + . The cumulative distributionF(v) is a twice continuously differen- tiable function fromR to unit interval[0;1]. User’s demandD(v) is assumed to satisfy d 2 logD(v) dv 2 < 0, f(v) 1F(v) 0 > 0, 1F(v) f(v) 0 < 0: Assumption 6 is called log-concavity of the demand function and it guarantees the existence of the solution. 7 Two different ownership structures between platform A 0 and application A 1 are taken into consideration: The platform supplies the application in-house or it out- sources to a third-party developer. I will start with the case of in-house application and then proceed to that of the third-party application. 2.3.1 In-HouseApplication To begin with, I suppose a platform ecosystem in which the application is developed or owned by the platform. The platform runs application A 1 in-house so it exerts its authority to set application price, p 1 , on users at its own discretion. Complete sub- scription to the application requires a user to payp 1 as well as access charge, p 0 . The platform quotes both prices ofp 0 andp 1 simultaneously. Withp 0 andp 1 , the platform’s objective is to maximize the profit, that is, max p 0 ;p 1 0 (p 0 ;p 1 ) = max p 0 ;p 1 [(p 0 +p 1 )D(p 0 ;p 1 )] 7 We can impose the log-concavity either on probability density function,f, or cumulative density func- tion,F . It is worth to remark that log-concavity off implies that ofD. But log-concavity ofF does not imply that ofD in general. One can refer to Bagnoli and Bergstrom (2005). For instances, Gaussian den- sity function satisfies the strict log-concavity so the demand satisfies log-concavity, however, the uniform density does not satisfy the strict log-concavity even though its demand does. Focusing on pure bundling of multi-products, Fang and Norman (2006) draw on the log-concavity and derive the condition for the choice of pure bundle or separate sales. 36 where user’s demand for the application is determined by D(p 0 ;p 1 ) = 1F(p 0 +p 1 ): The first-order condition of the profit maximization leads to (p 0 +p 1 )f(p 0 +p 1 )+(1F(p 0 +p 1 )) = 0 , p 0 +p 1 = 1F(p 0 +p 1 ) f(p 0 +p 1 ) (2.10) , 1 = 1 (p 0 +p 1 ) where(p) = pD 0 D . Here we can verify the simplest version of Learner’s formula, that is, the mark-up ratio is inversely proportional to the price elasticity of demand. Condition (2.10) is sufficient for a unique solution by assumption 6. Denoting the effective total price a user faces by P =p 0 +p 1 , we can ensure that optimal aggregate monopoly priceP solves condition (2.10), that is, P = 1F(P) f(P) : It is immediately noticed that there are infinite number of price pairs (p 0 ;p 1 ) that sat- isfies p 0 +p 1 = P I so the set of solution is (p I 0 ;p I 1 )2R 2 + p 0 +p 1 =P I . Among the equilibrium pairs of monopoly prices, two extreme solutions deserve to be noticed: (p I 0 ;p I 1 ) = (0;P I ) and(p I 0 ;p I 1 ) = (P I ;0). The former pricing strategy is free access charge with paid application while the latter is free application with paid access. Thus we can recapitulate the classical logic of “razor-blade” in perfect complementary product, that is, the monopoly distributes one product for free and charges a consumer on the other perfect complementary goods. In this mobile application example, the platform per- mits access for free but it charges a monopoly price on the application instead. To the 37 opposite extreme, the platform is able to distribute the application for free while it asks users to pay for the access. 2.3.2 Third-PartyApplication Similarly to the uniform valuation case, the platform offers a take-it-or-leave-it type of contract in the beginning, which is denoted by'. Once a third-party developer agrees on the offer, both parties charges the prices simultaneously. Even if a linear revenue sharing is still the major concern, we will consider somewhat broader set of contract: Two-part tariff, that is, '(p 0 ;p 1 ) = +p 1 D(p 0 ;p 1 ) for 2 R and 2 [0;1]. Fixed amount of can be interpreted as a non-refundable deposit and as the platform’s share on the developer’s profit. Provided that the developer gets on board, she is to maximize the profit, max p 1 0 1 (p 0 ;p 1 ;') := max p 1 0 [p 1 D(p 0 ;p 1 )'(p 0 ;p 1 )] and the first-order condition for the developer’s profit maximization is p 1 f(p 0 +p 1 ) = [1F(p 0 +p 1 )] @'(p 0 ;p 1 ) @p 1 ,p 1 = 1F(p 0 +p 1 ) f(p 0 +p 1 ) @'(p 0 ;p 1 ) @p 1 1 f(p 0 +p 1 ) : (2.11) By raising application price, p 1 , the developer loses a customer base marginally by f(p 0 +p 1 ), hence lower profit. However the increase in p 1 , given the existing users, earns more profit. Ignoring contract' that might affect the choice ofp 1 , the third-party developer maximizes the profit weighing the loss (benefit) from marginal users and the gain (loss) from infra-marginal users by changingp 1 . The third-party developer’s optimal pricing condition (2.11) contrasts with that of the platform having the application in-house, condition (2.10). First of all, change in user’s demand with respect top 1 has an external effect on the profit from access. When 38 the application is owned by the platform,A 0 would have taken this external effect into consideration and setp 0 optimally beforehand. Contrasting with in-house application, the third-party developer needs not take care of the external effect on platform’s profit from access. The left-hand side of condition (2.10) and (2.11) highlights this difference. Second, the contingent contract between the platform and the developer influences the developer to change application price, p 1 , correspondingly. If the money transfer to the platform were designed to increase as the application fee rises, then the third-party developer steers the price downwards. At the same time, the platform expects that the third-party developer will set the application price following (2.11), the developer’s best response function. Given the promised contract, ', the platform is to maximize the profit by setting an access fee, that is to say max p 0 0 0 (p 0 ;p 1 ;'(p 0 ;p 1 )) :=max p 0 0 [p 0 D(p 0 ;p 1 )+'(p 0 ;p 1 )] =max p 0 0 [p 0 (1F(p 0 +p 1 ))+'(p 0 ;p 1 )]: With respect to access fee, p 0 , the first-order condition for the platform’s profit maxi- mization program is (1F(p 0 +p 1 ))p 0 f(p 0 +p 1 )+ @' @p 0 = 0 , p 0 = 1F(p 0 +p 1 ) f(p 0 +p 1 ) + @' @p 0 1 f(p 0 +p 1 ) (2.12) Were it not for the contract, the platform cannot achieve the monopolistic outcome since it does not take account of the effect of access fee on the developer’s profit analogously to the problem that the developer faces. Now I turn to the platform’s contract design problem at the beginning. To illustrated the problem of externality, fixed and two-part tariffs are considered in brief. 39 Fixed tariff [2 R and = 0]. Since a fixed tariff does not depend on the prices, it is obvious that that @'=@p 0 = @'=@p 1 = 0. From the optimal pricing strategies described by first-order condition (2.11) and (2.12), we can derive that the equilibrium prices should satisfy the following first-order conditions as follows: p 0 =p 1 = 1F(p 0 +p 1 ) f(p 0 +p 1 ) =:h(p 0 +p 1 ); which leads to the best responses ofp 0 (p 1 ) andp 1 (p 0 ). Sinceh 0 ()< 0 due to assumption 6, they are one-to-one functions. In order for the stability of Nash equilibrium, we need to check the slopes of the best response functions: dp 0 dp 1 = h 0 (p 0 +p 1 ) 1h 0 (p 0 +p 1 ) < 1; dp 1 dp 0 = h 0 (p 0 +p 1 ) 1h 0 (p 0 +p 1 ) < 1: Hence, a stable unique Nash equilibrium pair of access fee and application price. From a user’s perspective, what matters is the total price,P =p 0 +p 1 , whereas the allocation between individual prices is not important. Thus, in equilibrium with a fixed tariff, the access charge and the application fee should be equalized (i.e. ^ p 0 = ^ p 1 = ^ P=2). The optimal aggregate price, ^ P , solves P 2 = 1F(P) f(P) : (2.13) Comparing equilibrium condition (2.10) and (2.13), we conclude that the total price with third-party application is higher than that with in-house application, that is, ^ P >P I by assumption 6. Therefore, users should pay more when the application is supplied by a third-party rather than they do when the application is in-house. Since the platform and the developer fail to coordinate on the optimal monopoly prices, the monopoly outcome is not achievable under fixed tariff. 40 Two-part tariff on revenue [2 [0;1] and2R]. I would like to investigate whether two-part tariff is able to achieve monopoly outcome. The platform asks lump-sum amount of fixed fee and charges additional transfer depending on the developer’s profit (revenue). Given the two-part tariff, the developer is to max p 1 [p 1 D(p 0 ;p 1 )f+p 1 D(p 0 ;p 1 )g] =max p 1 [(1)p 1 D(p 0 ;p 1 )]; which satisfies the first-order condition p 1 = 1F(p 0 +p 1 ) f(p 0 +p 1 ) : Similarly, given two-part tariff, the platform is to max p 0 [p 0 D(p 0 ;p 1 )+(+p 1 D(p 0 ;p 1 ))] =max p 0 [(p 0 +p 1 )D(p 0 ;p 1 )+] which requires platform access fee,p 0 , satisfies p 0 = 1F(p 0 +p 1 ) f(p 0 +p 1 ) p 1 : For stability of the equilibrium prices, we can check dp 0 dp 1 = h 0 (p 0 +p 1 ) 1h 0 (p 0 +p 1 ) < 1; dp 1 dp 0 = h 0 (p 0 +p 1 ) 1h 0 (p 0 +p 1 ) < 1: 41 Solving two first-order conditions, we can find a Nash equilibrium prices such as ~ p 0 (;) = 1 2 ~ P ~ p 1 (;) = 1 2 ~ P where total price ~ P(;) satisfies 1 2 P = 1F(P) f(P) : There are a few things to note: a) Access charge is lower than application price; ~ p 0 (;)< ~ p 1 (;) for any and. By the revenue transfer from developer to platform,A 0 earns extra profit from the application users. Lowering the access fee though, the platform can garner profits through the tariff. b) As sharing ratio tends to 0, in other words, two-part tariff converges to a fixed transfer scheme, optimal prices get to equilibrium (2.13) ~ p 0 = ~ p 1 = ^ P 2 : c) As sharing ratio tends to1 in the limit, the equilibrium prices converge to opti- mal monopoly ones (2.10) such as ~ p 0 = 0; ~ p 1 =P I : Now I would focus on case c). In the beginning, the platform needs to set opti- mally. Due to assumption 5, the platform ensures non-negative profit for developer while maximizing its profit. Thus, must be zero and the two-part tariff is a trivial 42 revenue sharing scheme such as ' = p 1 D(p 0 +p 1 ). The platform extracts all of the developer’s profit. Proposition2. Suppose that user’s demand satisfies the log-concavity (assumption 6). i. Where the application is provided in-house, the platform sets access fee,p I 0 , and application price,p I 1 , such as (p I 0 ;p I 1 )2 (p 0 ;p 1 )2R 2 + p 0 +p 1 =P I ;P I = 1F(P I ) f(P I ) and the equilibrium profit I 0 =P I 1F(P I ) : ii. Where the application is provided by a third-party developer, the platform offers a rev- enue sharing that asks all of the developer’s profit. The equilibrium access charge and application price are p T 0 = 0 and p T 1 =P I and the profits are T 0 = I 0 and T 1 = 0: iii. The ownership of the application does not change platform’s equilibrium profit. 2.4 TwoIn-HouseApplications: Generalization This section generalizes the case of two in-house applications. With uniform valuation, we have shown that the access fee cannot be free of charge. This property extends to comprehensive class of distribution. 43 LetA 1 andA 2 denote two applications. A user values the applications byv 1 andv 2 , respectively, and the valuation is private information. In similar fashion of assumption 6, I place distributional restriction on v 1 and v 2 , that is, each valuation satisfies log- concavity 8 . Once a user gets access to the platform, he intends to buy either one or two applica- tions. If he buys an application and then purchases the other one sequentially, the plat- form or a developer might differentiate his willingness to buy from those who demand only one application. In this case of sequential purchase, discriminatory pricing strat- egy could be employed depending on the different purchasing pattern. The following condition assumes away the possibility of that kind of discrimination. Assumption7. The platform or application developers cannot monitor how many applications a user purchases. Neither platform nor developers can exercise price discrimination based on this type of user’s purchase pattern. Assumption 7 implies assumption 3 that access charge is the same all across the users. Since the model draws on discrete choice, assumption 7 implies naturally that the developers cannot utilize discriminatory pricing either. 9 2.4.1 In-houseApplications Now we consider a case in which the platform controls the provision of both appli- cations in-house. The platform charges access fee, p 0 , on user’s side and it also sets application prices,p 1 andp 2 , of in-house applicationA 1 andA 2 , respectively. 8 An (1998) points out that a linear combination of log-concave densities does not satisfy log-concavity necessarily. Without joint log-concavity, we derive some meaningful results in this section. 9 Chao and Derdenger (2012) construct a model in which the platform proposes a bundle discount for the purchase of access and application together while each individual price is quoted. Mixed bundling strategy, as a discriminatory pricing, is possible since their model assumes that installed base with obtained access does not garner access anew. New users who need both access and application naturally differ from those who are in the installed base, which opens a room for an additional price discrimination. My model, however, need not account for such a discriminatory price: Standalone prices court no users since the access is indispensable one-way complement and the access is of no value by itself. 44 Given access charge and application subscription fees, users with different valuation decide to buy none, one, or both of the applications. Turning the point to user’s demand for the applications, we can arrange purchase or demand pattern by the following four classes which are characterized such that Users buy onlyA 1 if 8 > > > > > > < > > > > > > : v 1 (p 0 +p 1 ) 0 v 1 (p 0 +p 1 )v 2 (p 0 +p 2 ) v 1 (p 0 +p 1 ) (v 1 +v 2 )(p 0 +p 1 +p 2 ) , 8 > > < > > : v 1 p 0 +p 1 v 2 p 2 Users buy onlyA 2 if 8 > > > > > > < > > > > > > : v 2 (p 0 +p 2 ) 0 v 2 (p 0 +p 2 )v 1 (p 0 +p 1 ) v 2 (p 0 +p 2 ) (v 1 +v 2 )(p 0 +p 1 +p 2 ) , 8 > > < > > : v 2 p 0 +p 2 v 1 p 1 Users buy bothA 1 andA 2 if 8 > > > > > > < > > > > > > : (v 1 +v 2 )(p 0 +p 1 +p 2 ) 0 (v 1 +v 2 )(p 0 +p 1 +p 2 )v 1 (p 0 +p 1 ) (v 1 +v 2 )(p 0 +p 1 +p 2 )v 2 (p 0 +p 2 ) , 8 > > > > > > < > > > > > > : v 1 +v 2 p 0 +p 1 +p 2 0 v 1 p 1 v 2 p 2 Users buy none of them if 8 > > > > > > < > > > > > > : v 1 (p 0 +p 1 )< 0 v 2 (p 0 +p 2 )< 0 (v 1 +v 2 )(p 0 +p 1 +p 2 )< 0 , 8 > > > > > > < > > > > > > : v 1 <p 0 +p 1 v 2 <p 0 +p 2 v 1 +v 2 <p 0 +p 1 +p 2 45 Figure 2.12 displays the user’s demand pattern graphically. Given prices p (p 0 ;p 1 ;p 2 ), there are three types of purchase. The users who demand for onlyA 1 , only A 2 , and bothA 1 andA 2 . These types are defined by D 1 (p) := Pr (v 1 ;v 2 )2R 2 + v 1 p 0 +p 1 ;v 2 p 2 = Z 1 p 0 +p 1 f 1 (v 1 )dv 1 Z p 2 0 f 2 (v 2 )dv 2 = (1F 1 (p 0 +p 1 ))F 2 (p 2 ); D 2 (p) := Pr (v 1 ;v 2 )2R 2 + v 2 p 0 +p 2 ;v 1 p 1 = Z 1 p 0 +p 2 f 2 (v 2 )dv 2 Z p 1 0 f 1 (v 1 )dv 1 = (1F 2 (p 0 +p 2 ))F 1 (p 1 ); D 12 (p) := Pr (v 1 ;v 2 )2R 2 + v 1 +v 2 p 0 +p 1 +p 2 ;v 1 p 1 ;v 2 p 2 = Z p 0 +p 1 p 1 Z 1 p 0 +p 1 +p 2 v 1 f 1 (v 1 )f 2 (v 2 )dv 2 dv 1 + Z 1 p 2 f 2 (v 2 )dv 2 Z 1 p 0 +p 1 f 1 (v 1 )dv 1 ; = Z p 0 +p 1 p 1 f 1 (v 1 ) Z 1 p 0 +p 1 +p 2 v 1 f 2 (v 2 )dv 2 dv 1 + Z 1 p 2 f 2 (v 2 )dv 2 Z 1 p 0 +p 1 f 1 (v 1 )dv 1 = Z p 0 +p 1 p 1 f 1 (v 1 )(1F 2 (p 0 +p 1 +p 2 v 1 ))dv 1 +(1F 2 (p 2 ))(1F 1 (p 0 +p 1 )): Access charge,p 0 , affects every type of demand for applications. The lower the access charge is, the more users are willing to buy. Likewise, for eachi2f1;2g, application price,p i , affects demand for the other application beyond its own demand. For exam- ple, other prices being equal, increase inp 1 definitely lowersD 1 . Furthermore, someone who bought both applications discontinue to buyA 1 and turns to buyingA 2 only while some others even exit out of the market. 46 Figure 2.12: User Demand Pattern From the platform’s point of view, profit comes from the different sources of sale. One is the access permission on the user’s side and the other source is the application sales either fromA 1 orA 2 . Therefore user’s demand can be rearranged by profit sources, i.e. D 0 (p) :=D 12 (p)+D 1 (p)+D 2 (p); D 1 (p) :=D 12 (p)+D 1 (p); D 2 (p) :=D 12 (p)+D 2 (p): No user who wants to buy at least one application can afford without access to the platform so the profit from access permission covers all users who participate in the platform. Users buying both applications are triple-counted for profit sources: A 1 sale, A 2 sale, and access permission. 47 Setting three prices, p = (p 0 ;p 1 ;p 2 ), the monopoly platform is to maximize profit, 0 , i.e. max p 0 (p) := max p 0 ;p 1 ;p 2 p 0 D 0 (p 0 ;p 1 ;p 2 )+p 1 D 1 (p 0 ;p 1 ;p 2 )+p 2 D 2 (p 0 ;p 1 ;p 2 ) : In section 2.3 with single application, free access can be as an equilibrium pricing strategy (proposition 2). From now on, I will prove that we cannot maintain that free access constitutes an equilibrium pricing strategy any further. In regard to the access charge, we can divide pricing strategies into the following categories: Free access: The platform allows access for free (p 0 = 0) while making profit from applications. Paid access: The platform sells off the access at some positive amount, p 0 > 0. Applications might be either paid or even free of charge. I proceed to show that “paid access” strictly dominates “free access” pricing strat- egy. Proposition3. Suppose the platform with two in-house applications dictates access fee,p 0 , and application fees,p 1 andp 2 . Given the assumptions, “free access” cannot be a profit maximizing strategy. Therefore the optimal prices,(p I 0 ;p I 1 ;p I 2 ), should be a “paid access” (i.e.p I 0 > 0). Proof. Essentially the following proof draws on Proposition 1 and Corollary 1 of McAfee, McMillan, and Whinston (1989). It is enough to show that the best “free access” pricing is dominated by a “paid access” strategy. Suppose the platform would like to maximize the profit constrained to “free access.” ThenA 0 is to max p 1 ;p 2 ;p 0 =0 p 0 D 0 (p)+p 1 D 1 (p)+p 2 D 2 (p) =max p 1 ;p 2 [p 1 (1F 1 (p 1 ))+p 2 (1F 2 (p 2 ))] =max p 1 [p 1 (1F 1 (p 1 ))]+max p 2 [p 2 (1F 2 (p 2 ))]: 48 Suppose that the platform exercises a “free access” pricing,p = (0;p 1 ;p 2 ). Then the optimal application prices ^ p i = argmax p i p i Z 1 p i f i (v i )dv i = argmax p i [p i (1F i (p i ))] for eachi2f1;2g. Thus ^ p i solves p i = 1F i (p i ) f i (p i ) fori2f1;2g. Now we consider a particular “paid access and application” strategy. Suppose the platform sets a sufficiently small positive access fee,p 0 => 0, and adjustsA 1 ’s price top 1 = ^ p 1 . Given this price change, a user who bought onlyA 1 pays the same, i.e. ^ p 1 =p 0 +p 1 = (^ p 1 )+ so that the payment for onlyA 1 is not affected at all. Similarly, the users who bought bothA 1 andA 2 still purchase both products at the same effective price since they now have to pay ^ p 1 + ^ p 2 =p 0 +p 1 +p 2 =+(^ p 1 )+ ^ p 2 . Figure 2.13 shows how user’s demand changes due to this incremental access fee. The only change in purchase pattern happens among those who boughtA 2 only. Some users do not buy at all due to the increased effective price,p 2 +p 0 = ^ p 2 +. Some others will rather buy both applications because additional purchase ofA 1 now costs ^ p 1 rather than ^ p 1 . It is because the user withA 2 does not need to pay extra access fee so access fee is saved by. The cost of getting an additional application is discounted by. 49 Figure 2.13: Improvement Upon “Free Access” Strategy Given this particular “paid access and application” pricing, the new profit () (^ p 2 +) Z 1 ^ p 2 + Z ^ p 1 0 f(v 1 ;v 2 )dv 1 dv 2 +(^ p 1 + ^ p 2 ) Z ^ p 1 ^ p 1 Z 1 ^ p 1 +^ p 2 v 1 f(v 1 ;v 2 )dv 2 dv 1 = (^ p 2 +)F 1 (^ p 1 )(1F 2 (^ p 2 +)) +(^ p 1 + ^ p 2 ) Z ^ p 1 ^ p 1 f 1 (v 1 )(1F 2 (^ p 1 + ^ p 2 v 1 )) dv 1 : The derivative of() with respect to is 0 () = (^ p 1 )f 1 (^ p 1 )[1F 2 (^ p 2 +)] +F 1 (^ p 1 )[1F(^ p 2 +)(^ p 2 +)f 2 (^ p 2 +)]: 50 Evaluating the profit change at the optimal application prices with free access,(^ p 1 ;^ p 2 ), that is to say lim !0 () = 0 (0) = ^ p 1 f 1 (^ p 1 )[1F 2 (^ p 2 )]> 0; platform is beguiled by charging for access. Therefore all of the “free access” pricing strategy is strictly dominated by a “paid access” strategy. 51 3 Conclusion Platform as an essential operating system is complementary to application programs. Yet at the same time it could be a competitor when it runs an in-house application. High price quotation for third-party application reduces the demand for OS, which diminishes the demand for platform’s in-house application. Assuming uniform distribution of user’s valuation on the applications, I started with a single application example as a benchmark case. If the application is provided by platform, standard “razor-blade” logic applies: Platform charges either application or access since application is a perfect complementary good to the platform technol- ogy. Pricing structure does not matter. Even outsourcing application provision to a third-party developer, the platform is able to achieve the same monopoly profit by dis- tributing access for free while taking all of the developer’s profit. Whether the appli- cation is provided by platform or by third-party developer does not change monopoly price and profit. All of the results extend in broader set of distributional assumption – log-concave demand for application. Under the same assumption of uniform demand, this paper investigates the pricing strategy with multiple applications as well. I compute the optimal pricing strategy of monopoly platforms, which depends on the ownership type of third-party applications. In regard to the revenue sharing rule, the platform always demands 100% share of the third party’s profit, thus the developer ends up with no profits. It is mainly due to two reasons: 1) Third-party developer has no outside option, and 2) the platform has the complete bargaining power over the contract with the developer. Monopoly platform’s profit with all in-house applications is larger than that without in-house applications nevertheless, that is, revenue sharing does not lead to optimal monopoly outcome. In terms of profit, platform can do better with its own in-house application than no in- house application. Facing one third-party application developer with in-house appli- cation, the platform makes a more profit than it does without in-house applications. It 52 is achieved by distributing the in-house application for free while charging access or bundling OS and in-house application in package. The reason is that OS is a one-way essential complement to the application so tying platform’s application into OS appeals to those who want only third-party application as well. Some, not all, of the results extend to the case of log-concave demand. So far the only result that extends generally is the case of all in-house applications. Contrary to a single application case, free access strategy cannot constitute an equilibrium strategy. It is mainly because the user’s access fee plays a role of “bundling discount” in a sense that the purchase of multiple applica- tions saves the non-recurrent access fee. Drawing on monopoly bundling literature, we deduce that access should be charged since “mixed bundling” effect dominates other strategies. It is worth to note which results under uniform distribution do not extend to general ones. Above all, we cannot assure that equilibrium prices exist uniquely under log- concavity of demand. Lack of unique equilibrium, it is hard to compare the prices and the profits between different environment of application ownership. Therefore we need to investigate the conditions under which unique equilibrium prices occur. Another line of research is to study multiple applications more than two. In this paper, three possibilities of application provision are compared: Two in-house, two third-party, and one in-house coupled with one third-party application. With multi- ple applications, it is hoped that we can investigate how monopoly platform’s pricing strategy changes in the composition of in-house and third-party applications compara- tively. 53 Bibliography Adams, William J. and Janet L. Yellen. 1976. “Commodity Bundling and the Burden of Monopoly.” Quarterly Journal of Economics 90 (3):475–498. An, Mark Yuying. 1998. “Logconcavity versus Logconvexity: A Complete Characteri- zation.” Journal of Economic Theory 80 (2):350–369. Armstrong, Mark. 2006. “Competition in Two-Sided Markets.” RAND Journal of Eco- nomics 37 (3):668–691. Bagnoli, Mark and Ted Bergstrom. 2005. “Log-Concave Probability and Its Applica- tions.” Economic Theory 26 (2):445–469. Chao, Yong and Timothy Derdenger. 2012. “Mixed Bundling in Two-Sided Markets in the Presence of Installed Base Effects.” Working paper, Social Science Research Network. Chen, M. Keith and Barry Nalebuff. 2006. “One-Way Essential Complements.” Yale Economic Applications and Policy Discussion Paper #22. Evans, David S., Andrei Hagiu, and Richard Schmalensee. 2006. Invisible Engines: How Software Platforms Drive Innovation and Transform Industries. Cambridge, Mas- sachusetts: The MIT Press. Fang, Hanmin and Peter Norman. 2006. “To bundle or not to bundle.” RAND Journal of Economics 37 (4):946–963. Hagiu, Andrei. 2006. “Pricing and Commitment by Two-Sided Platforms.” RAND Journal of Economics 37 (3):720–737. ———. 2007. “Proprietary vs. Open Two-Sided Platforms and Social Efficiency.” Har- vard Business School Strategy Unit Working Paper #09-113, Harvard Business School Strategy Unit. ———. 2009. “Two-Sided Platforms: Product Variety and Pricing Structures.” Journal of Economics & Management Strategy 18 (4):1011–1043. McAfee, R. Preston, John McMillan, and Michael D. Whinston. 1989. “Multiproduct Monopoly, Commodity Bundling, and Correlation of Values.” Quarterly Journal of Economics 104 (2):371–383. 54 Rochet, Jean-Charles and Jean Tirole. 2003. “Platform Competition in Two-Sided Mar- kets.” Journal of the European Economic Association 1 (4):990–1029. ———. 2006. “Two-sided Markets: A Progress Report.” RAND Journal of Economics 37 (3):645–667. Rysman, Marc. 2009. “The Economics of Two-Sided Markets.” Journal of Economic Per- spectives 23 (3):125–143. 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Abstract (if available)

Abstract From a perspective of multi-product price discrimination, this paper examines pricing strategy of a monopolistic platform. Compared to the two-sided markets literature, users are allowed to buy various assortments of applications. Considered is an example of mobile operating system through which application developers interact with end users of heterogeneous valuation. Basically two modes of application provision is taken into consideration: In-house application or outsourcing to third-party developers. ❧ With a single in-house application, what platform really concerns is total price of access charge and application fee. However, the allocation of the total price between access charge and application fee does not matter in fact, thus access to the platform can be allowed free of charge. The free access is also viable as an optimal pricing strategy even where the application is outsourced to a third-party developer. ❧ But, with two in-house applications, free access charge cannot constitute platform's optimal pricing strategy any more. Given paid access, the users who buy both applications are able to avoid duplicate access charge, which enables the platform to price discriminate the purchasers for single application from those who buy dual applications. Under a revenue sharing rule with third-party applications, the platform exploits all of the profit from third-party developers while it cannot accomplish monopoly profit with in-house applications yet. ❧ Assuming uniform distribution of user's valuation, we gain numerical results in addition more than those under general conditions. Platform with a in-house application competing with a third-party application distributes access for free. It is equivalent to platform's bundling offer of the operating system with its own application, which improves consumer surplus and social welfare.

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Creator Gwon, Jae Hyun (author)

Core Title Pricing strategy of monopoly platforms

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 07/18/2013

Defense Date 06/14/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag bundling,mobile application,OAI-PMH Harvest,operating system,platform pricing,price discrimination

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Cheng, Harrison (committee chair), Kocer, Yilmaz (committee member), Lin, Thomas (committee member)

Creator Email gwon@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-292126

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