How can firms profitably give away free products? This paper provides a novel answer and articulates

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1 MANAGEMENT SCIENCE Vol. 5, No. 0, Otober 005, pp issn eissn informs doi 0.87/mns INFORMS Two-Sided Network Effets: A Theory of Information Produt Design Geoffrey G. Parker Tulane University, New Orleans, Louisiana 708, Marshall W. Van Alstyne Boston University, and Massahusetts Institute of Tehnology, Boston, Massahusetts 05, How an firms profitably give away free produts? This paper provides a novel answer and artiulates trade-offs in a spae of information produt design. We introdue a formal model of two-sided network externalities based in textbook eonomis a mix of Katz and Shapiro network effets, prie disrimination, and produt differentiation. Externality-based omplements, however, exploit a different mehanism than either tying or lok-in even as they help to explain many reent strategies suh as those of firms selling operating systems, Internet browsers, games, musi, and video. The model presented here argues for three simple but useful results. First, even in the absene of ompetition, a firm an rationally invest in a produt it intends to give away into perpetuity. Seond, we identify distint markets for ontent providers and end onsumers and show that either an be a andidate for a free good. Third, produt oupling aross markets an inrease onsumer welfare even as it inreases firm profits. The model also generates testable hypotheses on the size and diretion of network effets while offering insights to regulators seeking to apply antitrust law to network markets. Key words: network effets; network externalities; two-sided markets; free information; business models; strategi omplements; produt design History: Aepted by Raiv D. Banker, information systems; reeived April 9, 003. This paper was with the authors 5 months for revisions.. Introdution This paper seeks to explain strategi priing behavior and produt design deisions in network markets. Given the seemingly anomalous pratie of freepriing, how is it possible that firms are willing to subsidize information and related produts, apparently expeting neither future onsumer exploitation nor tying? Why do firms give away appliations development toolkits, portable doument readers, and Internet browsers without metering tie-ins to those same onsumers? What theory explains this eonomi logi? In answer, we find that designing mathed produt pairs and disounting one relative to the independent goods ase hanges the shape of demand in markets oined by network effets. The insight is that haraterizing network markets may require not only produt standardization, essential to demand eonomies of sale (Katz and Shapiro 985, Farrell and Saloner 986), it may also require reognizing sharp distintions between onsumer types. This is essential for managing demand interdependene, implementing prie disrimination, and raising barriers to entry. Contributing to the reent two-sided network externality literature, we introdue a novel mehanism (i) that explains firms unbundled omponent sales and priing strategies, (ii) that shows whih half of a two-sided network market to disount, (iii) that is distint from tying and traditional multimarket prie disrimination, and (iv) whose formulation is robust in results to multiple speifiations of demand. Of managerial interest is the proposition that disounting an unbundled omponent an inrease profits to the point where negative pries beome optimal. This helps not only the monopolist but also the oligopoly firm seeking barriers to entry. Profits inrease onditionally, however, on promoting network effets through lever produt design. They depend also on the orret hoie of market to disount. Of legal and eonomi interest is the implied industry onentration and diffiulty applying antitrust tests of predation. Priing below marginal ost maximizes profits even in the absene of ompetition. Platform intermediaries that internalize these externalities an improve onsumer welfare as well as profit. The paper proeeds as follows. Setion provides a review of related literature in network externalities, multiprodut priing, and bundling. In 3, we first develop a model of externality-based omplements. We find the onditions for a subsidy market to exist 494

2 Management Siene 5(0), pp , 005 INFORMS 495 and identify whih market reeives the subsidy. We also demonstrate how the key insight is robust to several modeling generalizations. Setion 4 offers further appliations and extensions and 5 onludes.. Historial Context and Related Literature Several branhes of literature yield insight for this researh, inluding network externalities, multiprodut priing, and to a lesser extent bundling. In the lassi network externality story (Katz and Shapiro 985, Farrell and Saloner 986, Arthur 989), demand eonomies of sale ause growth in an existing stok of onsumer value as new onsumers oin the network. Various authors have used network effets to explain the popularity of QWERTY and VHS (Arthur 994), ad subsidies of ontent in irulation industries (Chaudhri 998), and the importane of standards and swithing osts in network eonomies (Katz and Shapiro 985; Shapiro and Varian 998, 999). In ontrast, we onsider a mathed-market, hiken-and-egg problem, supporting an alternate interpretation of onventional wisdom. We distinguish between intramarket and intermarket network externalities. Produers want onsumers and onsumers want produers before either prefers a new format. An inumbent firm produing ontent for one format probably does not welome entry by a ompeting firm produing similar ontent if there is no profitable exhange between them. This mitigates a network effet within one side of the market. Buyers in the end-onsumer market, however, welome entry beause it inreases the prospet of a viable format should the inumbent fail. It also inreases variety while possibly lowering pries. This inreases both the value to individuals and the number of individuals willing to swith formats. Thus, in the present example, the externality runs from ontent reators to end onsumers. Conversely, onsider the end onsumer s original hoie of VHS versus Beta. Initially, at least, onsumers probably are less about adding another onsumer to a new format it ould even bid up pries if supply is limited than they are about the number and diversity of firms who provide ontent for that format. Produers, however, are immensely about the size of the onsumer market. The existene of a larger onsumer base makes prodution under any given format more attrative. Again, in the present artiulation, the externality runs aross markets from onsumers to providers of ontent. Importantly, the externality benefit an run aross markets and bak again. Both ontent reators and onsumers do value growth in their own markets, but this may be mediated by the indiret effet of the internetwork externality. At issue is whether ownmarket entry expands partiipation on the other side of eah transation. Content reators may not obet to other ontent-providing firms if effetive onsumer demand rises instead of falls. Consider, finally, a third partiipant, the fous of our attention here, who produes tools to support both ontent reators and end onsumers. These are platform intermediaries. Examples in Table inlude Sun, Apple, and Mirosoft, who support software developers as well as private and business Table Two-Sided Market Examples Produt ategory Market Intermediary Market Portable douments Doument reader Adobe Doument writer Credit ards Consumer redit Issuing bank Merhant proessing Operating systems Complementary appliations Mirosoft, Apple, Sun Systems developer toolkits Plug-ins Appliations software Mirosoft, Adobe Systems developer toolkits Ladies nights Men s admission Bars, restaurants Women s admission TV format Color UHF, VHF, HDTV Sony, Phillips, RCA Broadast equipment Broadast & publishing Content Magazine publishers, TV, Advertisements radio broadasters Computer games Game engine/player Ubisoft, ID, valve, eletroni arts Level editors Autions Buyers E-Bay, Christie s, Sotheby s Sellers Aademi ournals Artiles Management Siene Author submissions Reruiting Appliants Monster.om Employers Reservation systems Travelers Expedia, Traveloity, Orbitz Hotels, airlines, rental ars Shopping malls Shoppers Mall of Ameria Stores Streaming audio/video Content Real audio, Mirosoft, Apple Servers Paid searh Searhers Google.om Marketers Stok exhange Equity purhasers NYSE, NASDAQ Listed ompanies Home real estate Home buyers Real estate agents Home sellers Notes. This table shows how one side of a two-sided network market reeives a disounted, free, or even subsidized good (indiated with ). In general though not always, Market an be interpreted as the user/onsumer market and Market an be interpreted as the produer/developer market. We provide a test for whih side reeives the free good below.

3 496 Management Siene 5(0), pp , 005 INFORMS buyers; Sony and Phillips, who support the entertainment industry as well as households; and firms like Adobe, who produe portable doument writers as well as portable doument readers. Applied to servies, ebay oordinates buyers and sellers, while Visa oordinates merhants and ard holders. For these firms, the hiken-and-egg profit-maximization problem is how to grow mathed markets. A straightforward and widely observed solution is to disount one market in order to grow both, and to profit more from the other. This model favors an intermediary who, straddling both markets, an set pries more effiiently by internalizing these two-sided externalities. Independent firms serving either market separately lose this advantage. A key ontribution of a two-sided network model is determining whih side reeives a disount. Different firms hoose different benefiiaries. In streaming video, portable douments, and advertising, for example, the industry norm is to subsidize ontent onsumers and harge ontent developers. The opposite, however, holds true for operating systems and multiplayer games in whih ontent developers reeive subsidies and onsumers pay to oin the network. We show how this depends on ross-prie elastiities as well as the relative sizes of the two-sided network effets. This analysis adds to reent literature on two-sided network effets (Armstrong 00, Caillaud and Jullien 003, Rohet and Tirole 003) that make preise a form of indiret network effet (Katz and Shapiro 985, Liebowitz and Margolis 994). Indiret effets are onsumption externalities from purhasing ompatible produts suh as hardware and software. The key distintion for two-sidedness is that network effets must ross market populations. When they do not, the same onsumer populations hoose systems of ompatible produts only for themselves. These systems lead to peuniary externalities, effiiently handled through the priing system (Liebowitz and Margolis 994). In ontrast, two-sided networks yield true externalities in whih one population hooses a good affeting another population s hoie of a different good. In a reent working paper, Rohet and Tirole (004, p. 3) state, To use a elebrated example, the buyer of a razor internalizes in his purhase deision the net surplus that he will derive from buying razor blades. The starting point to the theory of twosided markets by ontrast is that an end-user does not internalize the welfare impat of his use of the platform on other end-users. As in Farrell and Saloner The onsequenes of mispriing internetwork markets an also be severe. In 00, the number two aution site, Yahoo, raised seller fees and listings unravelled, dropping 90% (Hansell 00). Sellers onluded that for suh fees, they preferred the larger number of buyers on ebay. (985), oordinating purhases beomes essential to avoid inertia, but in two-sided networks, oordination aross markets matters. Coordination within markets may have little effet. Rohet and Tirole (003), whih fouses on ompeting redit ard markets, parallels our work. They model two-sided network effets using multipliative demand and symmetri spillovers, and niely apture multihoming the deision to arry multiple redit ards from ompeting networks. Our framework, independently developed, differs in several important respets. () We show that key results generalize to alternative demand speifiations. () We inlude models that orret for boundary ondition problems. (3) We aount for asymmetri and even negative network effets so that we an model markets with very different properties. Caillaud and Jullien (003) onsider a mathmaking intermediary, as for dating servies. Using linear demand and a Bertrand priing model, they explain why agents register with more than one servie, as in the ase of multihoming redit ard servies. Under ompetition, two-sided network effets lead one firm to orner the market, or multiple firms to share the market with zero profits. They also show how transation osts redue total surplus. Our work fouses on information goods and produt unbundling and generalizes to nonlinear demand. Our problem is also distint from mathing distint agent pairs as in Mongell and Roth (99), instead representing an effort to inrease total mathed transations ourring on a ommon platform. A useful survey of our results and others is provided in Armstrong (00), examining whih side of a market is subsidized and whether the outome is soially effiient, and Rohet and Tirole (004), whih establishes general definitions for twosided markets... Multiprodut Priing The fat that lowering prie on one half of a mathed pair sells more of the other has preedent in multiprodut priing. This parallels Cournot s (838) observation that disounting zin sells more opper in the brass market but without the novelty that sales arue to different buyers. DeGraba (996) also presents an example of firms willing to enter a zero-profit market, relying on delining average ost urves to inreased sales. These mehanisms, however, differ in that analysis proeeds from a model of tying, like that in Whinston (990). The two papers were independently and onurrently developed and were oneived to answer related but different questions. Rohet and Tirole ite an earlier version of this paper, titled Information Complements, Substitutes, and Strategi Produt Design, whih was presented at the 999 Workshop on Information Systems & Eonomis and was posted to ssrn.om in 000.

4 Management Siene 5(0), pp , 005 INFORMS 497 Two-sided network externality oupling is not traditional seond-degree prie disrimination. It differs from tying razors and blades in that one market need never onsume the omplementary good. It also differs from penetration priing in whih a good is subsidized initially on expetation of future exploitation. In both ases, a single onsumer internalizes his own value alulation suh that prie hanges affeting one mathed item are refleted in willingness to pay for the other. This property fails for two-sided network markets. Consumers of a portable doument reader may, at their disretion, forgo the ost of the portable doument reator now and forever. Similarly, two-sided network externality oupling differs from traditional third-degree prie disrimination. Firms offering nonlinear pries to mixed markets fore heterogeneous onsumers to self-selet. Business travellers hoose different options than tourists; heavy users of phones and eletriity hoose different tariffs than light users. Suh mehanisms differentially extrat onsumer surplus and transfer it to the seller (Varian 989). In ontrast, platform intermediaries operating in two-sided markets seek to profit by transfering surplus from seller to onsumer. Growth on one side of a mathed market then indues growth on the other, reating exploitable surplus. This effet an prove unusually vexing to antitrust regulators beause produer and onsumer surplus an move together, as we show in Proposition 3. Further, Rohet and Tirole (004) note that demand reation as distint from surplus division violates the Coase theorem (960). This theorem states that, regardless of externalities, transations volume will be effiient as long as property rights are learly defined and there are no information asymmetries or transation osts. Buyers and sellers will bargain their way to effiieny; pollution trading rights ome to mind as an example. The Coase theorem fails in the ase of two-sided network effets. Property rights, symmetri information, and zero-ost transations do not suffie for effiient trading volume when it is the presene of one onsumer type that itself reates value for the other type. Ladies nights, developer toolkits, ad-supported ontent, as well as ash-bak bonuses and frequent flyer points on redit ards onstitute ontinuing subsidies to one side of the market. A produt design strategy that disounts prie to zero is aided by the unique properties of information. The key, however, relies less on nonrivalry than on low marginal osts. When these are negligible, a firm an subsidize an arbitrarily large market based solely on fixed initial osts. Providing eah new sale or servie then osts the lever produt designer nearly nothing in inremental osts. Inreased onsumption of information may therefore have the potential to inrease the attrativeness of the proposed design strategy. 3. Markets This setion adapts a standard externality model to show why a firm spends resoures reating a produt it distributes for free when two-sided network externalities ross market pairs. It also shows whih market reeives the disount. Let the first market represent the general onsumer or end-user market, C, and let the seond market represent the ontent reator, developer, or oint-produer market J. Index prie p and quantity q terms by market suh that p and p desribe pries for onsumers and ontent reators, respetively. Let marginal osts for information goods be negligible with profit given by = + = p q + p q. To provide a standard onave profit funtion, let this be twie differentiable in both hoie parameters, have / p i < 0, i, and have a positive Hessian determinant. Aordingly, first-order onditions yield pries in both markets. Demand is also standard but generalizes to allow a ross-market relationship. Eah market has a ontinuum of onsumers willing to buy one disrete unit of a good. If v is arbitrary willingness to pay, then D p, with upper bound V, is simply V dd dp. v p We require the distribution of values to be bounded above and well defined over negative values to avoid orner solutions. In the linear demand ase of Katz and Shapiro (985), this is simply v V. In our model, this also has a natural interpretation of allowing prie subsidies, and we generalize to nonlinear demand. For i we assume D i is twie ontinuously differentiable and dereasing in p i.we do not require onavity or onvexity of demand but only restrit it suffiiently to ensure onavity of the profit funtion via the Hessian. Paralleling Katz and Shapiro, we also model total onsumption as the sum of a good s intrinsi demand inremented by a funtion of network size in the other market. That is, we allow onsumption q to rise with network effets as well as value v as speified next. Our main point of departure is having externalities ross markets. The internetwork externality term e measures how muh effet purhases in the developer market have on the onsumer market. More preisely, e is the partial derivative of demand in the C market with respet to demand in the J market, or q / q. Conversely, e determines how muh effet purhases in the onsumer market have on the oint-produer market. Together, these terms desribe a pair of demand equations: q = D p + e D p () q = D p + e D p ()

5 498 Management Siene 5(0), pp , 005 INFORMS Figure Markets Linked by Two-Sided Network Externalities Prie Market C Market J Market C (onsider J externality) (inrease J profit) (forgo C profit) Prie Prie V +e Q Q p V V (q, p ) Q Q + e Q p V p* p π* p π π p* q q* Quantity q q* Quantity Notes. In the linear ase, the left panel shows a network externality that shifts the demand urve out. The optimal independent pair q p inreases from the no-externality ase Q / V /. In the middle panel, a monopolist sets p > p and reaps profits. In the right panel, prie in the C market falls p < p in order to take profits in the J market. A higher prie in market J then somewhat redues the total externality impat in market C. Disounting the C market is rational when net profits rise. Several notational onventions help develop useful intuition. We refer to the marginal ross-prie ontribution to sales q / p = e D p as the two-sided network externality or simply spillover effet. The importane of network spillovers, as given by the ratio r q / p / q / p, plays an important role in subsequent analysis and will later draw attention to whih market generates relatively more surplus. For onveniene, we define p, p, and p as the optimal (oordinated aross both markets) monopoly, unoordinated (two independent firms making independent deisions), and no-externality pries, respetively. In general, p p p unless e = e = 0, and q D p unless e = 0. Where the ontext is lear, we simplify notation by suppressing parameters and write D for D p. For illustration, the linear demand urves D p = Q p /V and D p = Q p /V yield simple and elegant results in terms of onsumer surplus. Let exogenous parameters Q i and V i, i represent the maximum market size and maximum produt value in the absene of externalities, respetively. A onsumption externality from J reates an outward shift in C demand, raising value by an amount proportional to D e D ; thus, V rises from V to V + e Q /Q p /V. In the C market, interpretation in terms of surplus spae an then be found by integrating demand 3 and defining substitutions. Native surplus S Q V S Q V Two-sided network externality surplus S e Q V S e Q V Native terms are proportional to onsumer surplus in eah market individually, whereas network terms 3 V Q 0 p /V + e Q p /V dp = Q V + e Q V p /V + / Q V e QV p /V, where V = V + e Q /Q p /V. The area of the triangles in Figure gives a similar expression. are proportional to the surplus reated by onsumption externalities in the omplementary market. 3.. Monopoly Choie A simple linear example then illustrates how the model funtions, although linearity is not required. Consider first a monopolist s profit-maximizing deision in the absene of network externalities, e = e = 0. A straightforward maximization on = p Q p /V yields p = V /, q = Q /, with profits of = V Q /4 = S /4 and similarly for as in the left-most panel of Figure. Optimal pries and quantities are simply half the onsumer value and half the onsumer market, respetively. Allowing for positive spillover, the J market externality shifts the demand urve in the C market up and to the right relative to the no-externality ase. Inreasing p, however, redues the total outward shift in the C market as shown in the rightmost panel. Taking externality effets into aount, the deision of how muh to harge in eah market is analyzed below. This graphi aptures the idea that ontent providers stimulate demand among onsumers, ust as onsumers stimulate interest from ontent providers. The number of ontent providers who atually enter the market, however, governs the degree of shift. The externality or oupling between these two markets implies that the more a monopolist an oax onsumers into adopting one of his produts, the more it an harge for and sell of the other. If the inrement to profit on one omplementary good exeeds the lost profit on the other good, then a disount or even subsidy beomes profit maximizing. Free-goods markets an therefore exist whenever the profit-maximizing prie of zero or less generates ross-market network externality benefits greater than intramarket losses. Firms do, in fat, offer subsidized goods when they offer free servie and tehnial expertise. Historially, for example, Mirosoft offered tehnial help on appliations program interfaes (API) in addition to free systems development

6 Management Siene 5(0), pp , 005 INFORMS 499 Figure Interseting Prie Reation Curves Show Consumer Prie p Rising and Developer Prie p Falling as the Developer-to-Consumer Externality e Rises from 0 to 3 to in the Linear Case with Parameters { } Q 4 0 = Q = V = V = ] and e = 3 II p I II p I II p p p p III IV III IV III IV I toolkits, and this may have inreased the number of user appliations developed for its operating system. Apple did not and has sine hanged its strategy. This form of subsidy also addresses an interesting problem of adverse seletion arising from a subsidy to a general audiene. Only developers request API support, so the subsidy is not wasted on nondevelopers. In general, the optimal prie pair for markets linked by network externalities is not obvious. Figure illustrates that a priing deision falls into one of four quadrants. Regions II and IV represent a free-goods market beause a firm harges nothing or spends money to plae produt in the hands of onsumers or developers, respetively. In region I, both markets are harged positive pries while region III represents a subsidy to both markets and is never profit maximizing. In priniple, the markets are symmetri; in pratie, omputer games manufaturers harge onsumers but give developers free toolkits, while streaming media ompanies give onsumers free software players but harge developers to reate ontent. Interestingly, banks selling redit ard servies harge both merhant and onsumer fees, illustrating region I. The deision about whih market to subsidize, if any, and whih to harge, then rests on Corollary below. Before analyzing this ase, we first develop onditions for optimality in terms of elastiities. Definitions for own- and ross-prie elastiities yield = p D / D + e D and = e p D / D + e D. Reall also that = + = p q + p q. Proposition. Network effets on one side of the market render the mathed side more inelasti. Optimal pries, however, also depend on ross-prie elastiities and the ratio of surplus reated on both sides. That is, p depends on ross-market elastiity of C sales with respet to J prie times the spillover ratio. Equivalently, p depends on rossmarket elastiity of J sales with respet to C prie times the profit ratio: = + r (3) = + (4) The ondition for a free-goods market to exist is optimal subsidy prie p 0, whih ours at the point r. Proof. To see that e makes = p D / D + e D more inelasti, note that inreases push toward zero, dereasing sensitivity to hanges in p. To establish the unit elastiity ondition, use the first-order ondition on total profit with respet to prie in the C market to find = D p + e D + p D + e p D = 0 (5) whih rearranges to = + e p D / D + e D. Reall that r = q / p / q / p = e D / e D. Multiplying the final term by = e D / e D and substituting for provides Equation (3). Then, when prie dereases through zero p 0, we have 0, proving the ondition on existene of a free-goods market. Note that although r is undefined when e D 0, r is still defined beause the multipliative term, e D anels out. To produe the final expression, insert definitions for elastiities and simplify to onfirm that / / / = r. Substituting this equality in Equation (3) produes Equation (4). Note that symmetry implies a parallel set of expressions in the J market where the optimality ondition is = + /r. Intuitively, rising network effets from J to C allow prie to rise in C. If this were the only effet, we might expet network effets to inrease pries on both sides of the market in small neighborhoods around the no-externality pries p and p. A firm, however, must manage ross-prie effets and the ratio of spillovers. These effets are so strong that at the point a subsidy beomes optimal, a firm is hoosing pries opposite those implied by own-prie elastiities onsidered separately. To see this, let p < 0, and thus neessarily p > 0 with < 0 and > 0. Then signing terms in the definition of implies > 0. At the same time, Proposition establishes the relation = r = e p D / D + e D e D / e D <. In short, p < 0 implies that one-sided elastiities by themselves are < < 0 <. When subsidies are optimal in the C market, prie hikes rather than subsidies would (loally) inrease sales in the C market and prie drops in the J market would (loally) inrease sales in the J market.

7 500 Management Siene 5(0), pp , 005 INFORMS Relative ross-prie effets are dramati. Further rearranging Equation (3) shows that it is not onesided pries alone that must be unit elasti,, but rather the one-sided pries adusted for an externality adusted prie ratio + e p /p =. Graphially, the intuition is again that of Figure. These results are surprisingly robust and are true more generally for eah of the following. Corollary. The demand elastiity properties of Proposition hold for any of the followingalternative demand speifiations (equations are symmetri for q ): Additive Additive reursive Multipliative Shifted multipliative Multipliative reursive q = D + e D q = D + e q q = D D e q = D + D e q = D q e Proof. Define M / e e as a market multiplier, noting that e e < must hold to render the definition meaningful. Resolving the simultaneous pairs q q for the two reursive ases results in q = M D + e D and q = D D e M. These differ only by the onstant term M from nonreursive ases and the differenes disappear in the optimality alulations. Applying the sequene of steps from Proposition yields equations idential to Equations (3) and (4). Moreover, elastiities have the struture e e =. A minor exeption ours for the shifted ase whih also shifts, beoming e e D D / + D + D =. The reursive formulations allow reiproal externalities on both sides of the market. An additive formulation has a natural interpretation in allowing demand shifts as in Figure whereas a multipliative formulation pivots around the point of maximum value V. The latter is used in Rohet and Tirole (003), whih makes the speialized assumption that e = e =. The multipliative formulation has an advantage in foring high prie, zero demand in the native market to anel externalitydriven demand from the ross-market. Introduing the shifted multipliative ase orrets for the exoti ondition where 0 <D < auses q to fall in a rising externality. Equivalene of these five funtional forms shows that the main insight is robust to nonlinear demand as well as several alternative ombinations of demand. For ompleteness, we will oasionally ompare results using the notations p + and p for the additive and shifted multipliative formulations, respetively. Proposition implies that ross-prie elastiities matter in both diretions. The proposition onstrains (6) prie through times the spillover ratio. The bidiretional nature of spillovers demonstrated in Proposition implies that priing deisions depend heavily on their relative sizes and, in fat, no differene in size an imply no differene in prie. In the ase of additive demand, this leads to the unusual result that pries will be optimal, even if set under the myopi assumption of no network effets, when spillovers between markets are equal. Proposition. For additive demands, a monopolist sellingto omplementary markets with symmetri spillovers sets optimal prie independent of the level of two-sided network effets. Mathematially, r = if and only if p+ = p + and p+ = p +. In the (shifted) multipliative ase, a monopolist always sets p less than or equal to the independent and no-externality pries. That is, p p = p. Proof. Reall that M = / e e. First-order onditions (Equation (5)) indiate p = D + e D + e p D / D. For referene, we also alulate independent firm and no-externality pries p and p.in the ase of independent firms the final term in the numerator of p is zero, so that p = D + e D / D, and in the ase of no externalities of either sort, p = D / D. For optimal profits, simultaneous solution of p and p yields impliit prie ) (7) p = M ( D + e D D e D + e D D with a symmetri expression for p. More intuitively, this an be interpreted as the market multiplier times the differene in independent pries M p e p, showing that own-prie generally delines in own externality. To omplete the proof, note that r = requires e D = e D. Combining frations and twie substituting e D for e D ollapses the equation to p = D / D = p. Symmetry fores p = p, whih is the required forward result. If both no-externality pries are optimal, then reversing eah step of the equality requires e D = e D. For the (shifted) multipliative ase, FOCs give: = D p + D e + p D + D e + e p D + D e D = 0 (8) It is then straightforward to establish that p = p = D / D and that p = D / D e p D + D e / + D e + D = p e / + D e + D. Beause all terms in the rightmost expression are positve, p must fall relative to p. The proposition states that if the demand externality is additive and network effets aross markets are approximately equal in size the presene of developers is as attrative to onsumers as the presene

8 Management Siene 5(0), pp , 005 INFORMS 50 of onsumers is to developers then a monopolist an safely ignore these effets in all priing deisions. A firm an set pries as if the network terms e and e were both zero. This does not imply that network externalities have no effet on quantity sales. In general, output exhibits substantial inreases due to the market multiplier M = / e e. This result is unusual in that one might have expeted pries to rise with inreased demand, but the monopolist takes the gain exlusively in terms of inreased sales rather than higher pries. The point is that firms need to onsider a oint priing deision that aounts for network externalities only when the differene between the spillover effets on sales, e D e D, is substantial. Proposition shows that for additive demand externalities, optimal prie equals no-externality prie p = p whenever r =, while for the multipliative ase, independent prie equals no-externality prie ˆp = p always. Building on this analysis, we an now answer the more general question of whih market a profitmaximizing firm disounts when spillover levels are unequal. Corollary. A monopolist sellingto omplementary additive demand externality markets disounts the produt with the greater spillover effet. That is, r< p < p. The optimal C market prie falls relative to the no-externality prie if and only if market C ontributes more network externality surplus to market J,orp < p S >S. Proof. We have that r< implies e D = e D for >0. An idential sequene of substitutions as those above yields p = D ( M D D )( D + e D D ) (9) Only D D < 0 so that p falls. Alternatively, this an be interpreted as p = p / D M p, and we note that onlusions are similar for e D = e D +. To establish the ondition on linear surplus, observe that when D p = Q p /V then q / p is simply e Q /V, with a similar expression for q / p. Arrange both terms as an inequality. The result, e Q /V < e Q /V, then simplifies to e Q V > e Q V, whih ompletes the proof. Disounting the C market must reate more J market surplus than vie versa for C s prie to fall. A few additional points follow from this analysis. First, for additive demand externalities, a firm an rationally disount only one market at a time. This means that a disount in one market implies a prie premium in the other, or p < p if and only if p > p. The reason is the fat that p < p implies e D <e D and the markets are symmetri. An immediate orollary shows that in the linear ase, optimal pries fall in the market that ontributes more externality surplus to the other market. While the preeding analysis ompares no-externality and optimal pries, it is straightforward to ompare independent and optimal pries. In an example of a lassi result on the unoordinated priing of omplements, we show below that fatoring network externalities into the priing deision, but failing to oordinate the pries aross markets, leads to ineffiient prie setting. Where p is again optimal, let p represent independent firm prie as distint from the no-externality prie p. Corollary 3. In the ase of symmetri spillovers, if independent firms set pries in additive demand externality markets without oordination, then pries vary with the level of spillover and are ineffiiently high, p p. Proof. Proposition established that for r =, pries are independent of network effets, but for independent pries, we have p = D + e D / D. The differene p p is then e D / D. For independent firms, pries are always positive and inreasing in the size of ross-market network effet. Without externalities, pries p and p are idential and the ineffiieny disappears. With externalities, however, independent firms err in diret proportion to their own level of network effet on their market omplement. One onsequene of Corollary 3 is that independent firm pries are strategi substitutes and a prie inrease by one firm auses a prie derease by the other. 3.. Consumer Surplus A firm s ability to manipulate two-sided network externalities to inrease profits raises a onern about whether its gains represent onsumer losses. Does the ability to link markets, partiularly when two produts are ombined under monopoly ownership, hurt onsumers? In the ase of symmetri spillovers, Proposition and Corollary 3 imply that the answer is learly no. Consumer surplus improves under monopoly ownership. Beause two independent firms both prie too high, integrated ownership redues pries even as it inreases profits. Asymmetri spillovers may leave onsumer welfare ambiguous beause p = / e e p e p and a areful hoie of e, e an fore p > p. For linear demand, however, welfare analysis of asymmetri spillovers provides a partiularly strong result. Welfare exhibits a strit Pareto improvement in the sense that even the market paying the inreased premiumgoods prie prefers monopoly ontrol. This result is stronger still in the ase of multipliative demand externalities. Let supersripts on onsumer surplus CSˆ and CS represent the independent and oint optimization values from the firm s perspetive.

9 50 Management Siene 5(0), pp , 005 INFORMS Proposition 3. Consumers and produers benefit when firms merge or oordinate pries in markets with linear demand and two-sided network externalities. That is, CS CS ĉ and CS CS ĵ and thus neessarily CS + CS CS ĉ +CS ĵ., so total welfare improves. This is always true for multipliative demands. Proof. The upper bound on V p q r dr is hosen to avoid negative quantities and is given by V = D q e D. For q = 0, this beomes V + e Q /Q p /V. Integrating Equation () and substituting for V gives onsumer surplus in the C market as CS = e Q V p V + Q p V V (0) Q V V In omputing optimal p p and independent p p pries, we ondense several steps. We also simplify these expressions by onverting to surplus notation. This ollapses six apparent degrees of freedom to four true degrees. Substituting for p p in (0) yields onsumer surplus at optimal pries. CS = S + S + S S S S S S S + S 4S S () A similar substitution for p p yields onsumer surplus at independent pries. CS ĉ = S S S S S + S S S 4S S () Note that squares imply these are always positive. Imposing the Hessian ondition 4S S S +S > 0 and simplifying the differene in total surplus CS CS ĉ always proves nonnegative. Equality is ahieved only when the markets are independent (e = e = 0 implying S = S = 0), in whih ase, CS = CS ĉ = S 8. The ase for CS is symmetri. In the ase of multipliative demand, Proposition proves p p = p always, thus CS improves. Finally, from the produer s perspetive, a monopolist an always hoose to set pries independently, thus and total welfare Pareto improves. The underlying intuition is that linking the markets allows a firm to manipulate the markets total size via the ross-market network externality. Consumers then benefit to the extent that a self-interested firm sets pries more effiiently but annot apture all onsumer surplus from the effiieny gains. A firm internalizes the market externality but wins only a fration of this effet. 4. Appliations and Extensions Two-sided markets oupled by network externalities are distinguished from other market types by heterogeneous mathed onsumers with interdependent demands. This has a number of impliations beyond those of the present model. One impliation is that firms an deploy network effets to stimulate new surplus in ontrast to prie disrimination strategies that extrat stati surplus (Parker and Van Alstyne 00). This provides ounterpoint to key theories of bundling (Adams and Yellen 976, Salinger 995, Bakos and Brynolfsson 999), the advantage of whih is redued demand heterogeneity. As long as buyer values are not perfetly orrelated, bundled demands onverge to a point mass based on the entral limit theorem. With zero marginal ost goods, firms an ostlessly smooth idiosynrati demands simply by ombining items in a bundle. This allows a firm to predit and therefore extrat onsumer surplus. Rather than seeking to redue market heterogeneity, two-sided produt design seeks to leverage it. Unbundling together with a one-sided subsidy sarifies the ability to predit transations value in favor of growing transations volume. Introduing ompetition, analysis of two-sided network effets an also answer the question of why a duopolist might voluntarily enter into Bertrand prie ompetition, foring profits to zero in one market segment (Parker and Van Alstyne 999). Even with an undifferentiated produt, an entering firm an use a two-sided produt omplement to generate profits on the far side of a market. A firm an soften an inumbent s first-mover advantage and survive a market that beomes ompletely ompetitive post-entry. The produt omplement makes an entry threat redible. As in the ase of the Internet browser wars, onsumer surplus rises from the arrival of a zero prie substitute and entrants an be unusually fiere ompetitors (Jakson 999). Empirially, a two-sided model has the advantage of suggesting new approahes for estimating network effets. Models of intramarket externalities suffer from endogeneity of demand estimation in that instruments an barely distinguish demand shoks from the network externality ripple effets they reate. If, on the other hand, network effets ross markets, then instrumenting demand shoks in one market an proeed while holding demand onstant in the oupled market, thus traing a demand relationship. The proposed framework might therefore simplify estimation of network effets relative to earlier models. Testable propositions inlude whih internetworked market to disount in markets with priing power, whih of several produts firms will favor disounting in markets without priing power, and whether disounting lasts longer than predited by models of

10 Management Siene 5(0), pp , 005 INFORMS 503 penetration priing with lok-in. An empirial test of Parker and Van Alstyne (999) and Rohet and Tirole (000, 003) appears in Gallaugher and Wang (00). They find signifiant positive externalities between the Web browser and Web server markets. Failing to aount for externality-based omplements might therefore lead to priing and produt design errors. Using a produt tying model, for example, firms might meter sales to both onsumer types, missing the opportunity to manage network effets between them. Using a lok-in model, they might inudiiously disontinue disounts for the market stimulating ross-market sales, hoking network effets. Using unoupled multimarket prie disrimination, they might fail to offer disounts at all. Eah model suggests subtle differenes in the lous and timing of priing deisions. Suitable market divisions fall along several different lines based on demand attributes, produt features, or time. Some pratial appliations of these divisions are given below. () Tangible goods and servies with externalities between tangible and intangible goods, e it > 0 and e ti > 0. Example: Historially, the first olor TV broadast ourred in 95 but no firm realized a profit on olor TV sets for almost a deade. Consumers delayed buying olor TVs until the arrival of substantial ontent. RCA solved the hiken-and-egg problem in 96 by subsidizing Disney s Wonderful World of Color (Shapiro and Varian 998). In 00, the Federal Communiations Commission resolved an idential problem for HDTV by mandating the provision of HDTV sets by eletronis firms. () Temporal omplements with externalities between time and time. Example: Vendors of preedent and ase law databases ommonly subsidize student lawyers in time while harging premium pries to these same people one they beome professional lawyers in time. The time version is fully funtional, so there is no need to upgrade, nor is aess ephemeral beause it runs the full three years of law shool. The spillover benefit is to save law firms the (re)training osts of having new lawyers learn the ommand struture and apabilities of a prinipal researh tool. The benefit in the other diretion is that, eteris paribus, law students prefer to adopt the pakage adopted by more law firms. (3) Upgrades with externalities between novie and pro users, e np > 0. Example: Many firms give away novie versions of simulation or CAD software but harge for a professional version. The less funtional or time-limited version enourages experimentation and purhase of the full-featured version. In ontrast, onventional prie disrimination uses a menu of different pries to fore onsumers with intrinsially different demand profiles to self-selet on the basis of willingness to pay. The standard prie disrimination model, however, leaves open the question of why a firm should inur development osts on a good for whih it never antiipates revenues. (4) Advertising market with externalities between onsumers and advertisers, e a > 0 and e a < 0 or e a > 0 and e a > 0. Example: Magazine publishers, TV and radio stations, software vendors, and Web portals offer free or disounted onsumer ontent in sponsored mode in whih onsumer market C enoys low pries while advertiser market A buys ad plaement from the vendor in order to reah the C market. This has also long been an eonomi model supporting the free information ontent found in irulation industries (Chaudhri 998). A larger onsumer market inreases the attrativeness of buying ads suh that e a > 0, but the presene of ads may or may not inrease the attrativeness of onsuming ontent. For fashion magazines, the network externality term may be positive, e a > 0. But for many forms of advertising, onsumers may experiene lutter osts suh that e a < 0. In effet, these points illustrate different dimensions along whih to leave the halves of a two-sided market. These dimensions inlude tangibility, time, skill level, and ontent. As noted in Table, the fore of two-sided network effets an also extend to near zero marginal ost servies suh as redit ards and autions. Future researh will likely enumerate various platforms aross whih providers meet onsumers, and transations volume is governed by tipping the platform to favor one or the other. 5. Conlusions The model presented here argues for several simple and intuitive results. First, a firm an rationally invest in a produt it intends to give away into perpetuity even in the absene of ompetition. The reason is that inreased demand in a omplementary premiumgoods market more than overs the ost of investment in the free-goods market. In this ase, market omplementarity arises from an internetwork externality. This strategy also takes advantage of information s near zero marginal ost property as it allows a firm to subsidize an arbitrarily large market at a modest fixed ost. Seond, we identified distint markets for ontent providers and end onsumers and showed that either market an be a andidate for disounting or free distribution. Deiding whih market to subsidize depends on the relative network externality benefits. At a high level of externality benefit, the market that ontributes more to demand for its omplement is the market to provide with a free good. At lower levels, firms may harge positive pries in both markets but keep one prie artifiially low. Third, we show that, in general, onsumer welfare is not harmed when firms set pries aross markets

11 504 Management Siene 5(0), pp , 005 INFORMS with positive omplementarities. Firms an manipulate total market size through hoie of prie in eah market. Consumers then benefit to the extent that a self-interested firm sets pries more effiiently but annot apture all onsumer surplus from the effiieny gains. A firm internalizes the market externality but wins only a fration of this effet. The modeling ontribution is distint from tying or seond-degree prie disrimination in the sense that onsumers need never purhase both goods. Unlike razors and blades, the produts are standalone goods. It also differs from multimarket or thirddegree prie disrimination in the sense that the firm may extrat no onsumer surplus from one of the two market segments, implying that this market would have traditionally gone unserved. Aknowledgments The authors are grateful to partiipants of the 999 Workshop on Information Systems and Eonomis, the 000 Assoiation for Computing Mahinery SIG E-Commere, the 000 International Conferene on Information Systems, the 00 Stanford Institute for Theoretial Eonomis (SITE) workshop on Internet Eonomis, the 003 Insitut D Eonomie Industrielle seond onferene on The Eonomis of the Software and Internet Industries, as well as numerous partiipants at university seminars. They thank Tom Noe for helpful observations on oligopoly markets; Lones Smith, Kai-Uwe Kuhn, and Jovan Grahova for orretions and model generalizations; Jeff MaKie-Mason for valuable feedbak on model design and bundling; and Hal Varian for helpful omments on firm strategy and model impliations. Frank Fisher provided helpful advie on, and knowledge of, the Mirosoft trial. Jean Tirole provided useful suggestions and examples, partiularly in regard to redit ard markets. Paul Resnik proposed the desriptive term Internetwork externality to desribe two-sided network externalities. Tom Eisenmann provided useful feedbak and examples. They also thank Robert Gazzale, Moti Levi, and Craig Newmark for their many helpful observations. This researh has been supported by NSF Career Award IIS Referenes Adams, W. J., J. L. Yellen Commodity bundling and the burden of monopoly. Quart. J. Eonom. 90(August) Armstrong, M. 00. Competition in two-sided markets. Mimeo, Nuffield College, Oxford University, Oxford, UK. Arthur, W. B Competing tehnologies, inreasing returns, and lok-in by historial events. Eonom. J Arthur, W. B Inreasing Returns and Path-Dependene in the Eonomy. University of Mihigan Press, Ann Arbor, MI. Bakos, Y., E. Brynolfsson Bundling information goods: Priing, profits, and effiieny. Management Si. 45() Caillaud, B., B. Jullien Chiken & egg: Competing mathmakers. RAND J. Eonom. 34() Chaudhri, V Priing and effiieny of a irulation industry: The ase of newspapers. Inform. Eonom. Poliy Coase, R. H The problem of soial ustie. J. Law Eonom Cournot, A. A Reherhes sur les prinipes mathematiques de la theorie des rihesses. Libraririe des sienes politiques et soiales M. Rivere & ie., Paris, Frane. DeGraba, P Why lever into a zero profit industry: Tying, forelosure, and exlusion. J. Eonom. Management Strategy 5(3) Farrell, J., G. Saloner Standardization, ompatibility and innovation. RAND J. Eonom. 6() Farrell, J., G. Saloner Installed base and ompatibility: Predation, produt preannounements and innovation. Amer. Eonom. Rev. 76(5) Gallaugher, J. M., Y. M. Wang. 00. Understanding network effets in software markets: Evidene from Web server priing. MIS Quart. 6(4) Hansell, S. 00. Red fae for the Internet s blue hip. New York Times (Marh ). Jakson, T. P U.S. v. Mirosoft: Findings of Fat. United States Distrit Court for the Distrit of Columbia, Washington, D.C. Katz, M. L., C. Shapiro Network externalities, ompetition, and ompatibility. Amer. Eonom. Rev. 75(3) Liebowitz, S. J., S. E. Margolis Network externality: An unommon tragedy. J. Eonom. Perspet. 8() Mongell, S., A. E. Roth. 99. Sorority rush as a two-sided mathing mehanism. Amer. Eonom. Rev. 8(3) Nalebuff, B Bundling. Yale ICF working paper series 99-4, Parker, G., M. Van Alstyne Information omplements, substitutes, and strategi produt design. Workshop on Information Systems and Eonomis, Charlotte, NC, abstrat= Parker, G., M. Van Alstyne. 00. Unbundling in the presene of internetwork externalities. Mimeo, University of Mihigan, Ann Arbor, MI. Rohet, J. C., J. Tirole Platform ompetition in two-sided markets. Working paper, Institut d Eonomie Industrielle, Frane. Rohet, J. C., J. Tirole Platform ompetition in two-sided markets. J. Eur. Eonom. Asso. (4) Rohet, J. C., J. Tirole Two-sided markets: An overview. Working paper, Institut d Eonomie Industrielle, Frane. Salinger, M A graphial analysis of bundling. J. Bus. 68() Shapiro, C., H. Varian Information Rules. Harvard Business Shool Press, Boston, MA. Shapiro, C., H. Varian The art of standards wars. California Management Rev. 4() 8 3. Varian, H Sequential provision of publi goods. J. Publi Eonom Whinston, M Tying, forelosure, and exlusion. Amer. Eonom. Rev. 80(4)

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