Bundling and Complementarity

Transcription

1 undling and Complementarity Thierno iallo January 005 bstrat We analyze bundling inentives in markets where produts are omposed of two omplementary omponents eg hardware and software One of the omponents is monopolized and the other is sold by a duopoly We assume quality differentiation between omponents, and we develop a model of quality ompetition à la Mussa and Rosen 978 We demonstrate that the monopolist s bundling deision depends on the quality of the omponent where he faes ompetition We show that: i if the monopolist s omponent has a higher quality than the ompetitor s, then the monopolist prefers not to bundle separate selling; and ii if the quality of monopolist s omponent is lower than the ompetitor s, then the monopolist prefers bundling Thus, the monopolist s inentive not to bundle is related to narrowing of market for its monopolized omponent with bundling We also onsider a dynami game where firms ompete in two-stages quality and prie and determine the subgame perfet Nash equilibrium Finally, we disuss antitrust impliations of these findings Keywords: bundling, omplementarity, quality, soial welfare, antitrust JE Classifiation: 4, 5, 40, 4, 4 I am indebted to braham ollander and ars Ehlers for ontinued guidane and enouragements ll errors are of ourse my own Correspondene : Thierno iallo, département de sienes éonomiques, Université de Montréal, C 68, suursale Centre-ville, Montréal QC 3C 3J7, Canada, thiernodiallo@umontreala

2 I Introdution I Overview Many produts are onsumed in ombination with other produts to form a omplete system of produts that annot be onsumed separately Eg, a omputer system an be deomposed into a basi unit and a monitor, a stereo system is an amplifier and a speaker, a omputer is omposed of hardware and software ut produts an be sold and purhased either separately or as pakages elling as pakages an be ahieved either by tehnial bundling, ie by making one omponent ompatible only with omponents sold by the same firm or by engaging in tied selling omponent is inompatible with omponents sold by other firms, if it annot be assembled with them to form a usable system The eonomi onsequene of ompatibility versus inompatibility have been examined by Chou and hy 989, Matutes and Regibeau 989 for the ase where eah omponent is sold by an independent firm Matutes and Regibeau 988, Eonomides 989, 99, and Einhorn 99 have looked at the ase where eah firm supplied all the omponents neessary to form the omplete system Eonomides 99 proved that for firms supplying all omponents neessary to form a usable system, ompatibility is profitable if the relative inrease in the demand for the systems when making omponents ompatible exeeds the number of omplementary omponents supplied by other firms standard result of this literature is that ompatibility inreases industry demand and profits Tied selling or tying restritions are of two types: requirement tie-ins and bundling Under requirement tie-ins the seller of produt requires all purhasers of also to purhase all their requirements of produt from him Under a bundling arrangement or pakage tie-ins the seller offers two or more produts in fixed ombination as a single Formally, Eonomides 99 onsiders a model where the market for one omponent say market is a duopoly, and the other say market is monopolistially ompetitive e shows that when the addition of a new variety of leads to little or no inrease in the demand for the system, the profits of a firm of type- are higher under inompatibility and they will hoose this regime y ontrast, when the addition of a new variety of inreases the demand for the system, the profits of a firm of type- are higher under ompatibility The profitability of ompatibility depends on its apaity to inrease the demand for

3 pakage The differene between these two types of tying is that, in the ase of bundling the prie of is not separately stated but is bundled into the prie of produer who makes its omponents inompatible with omponents produed by others or engages in tehnial bundling imposes a de fato 3 tie In this paper, we are interested in bundling To rule out tehnial bundling, we assume a ompatible world Thus, selling as pakages is ahieved only by bundling We analyze bundling inentives in markets where produts are omposed of two omplementary omponents eg hardware and software in the ontext of vertial produt differentiation One of the omponents is monopolized and the other is sold by a duopoly We ask what is the monopolist s best selling strategy between separate selling and bundling? What are the onsequenes for welfare? To answer these questions, we review first the literature on bundling and then we solve a model of quality ompetition for systems omposed of two omplementary omponents I The undling iterature Three reasons are given in the literature to explain bundling The traditional explanation for bundling is that it ahieves better prie disrimination by a monopolist tigler 968, dams and Yellen 976, hmalensee 984, and Mfee, MMillan and Whinston 989] Usually, a firm has to harge one prie to all onsumers In these ases heterogeneity in onsumers valuations frustrates the seller s ability to apture onsumer surplus undling redues onsumers heterogeneities in reservation pries and aptures the maximum of their surplus tigler s analysis and dams and Yellen 976 are based on stylized examples with a disrete number of ustomers In these examples, the reservation values of the omponents of the bundle are negatively orrelated undling serves muh the same purpose as prie disrimination hmalensee 984 onsiders the entire lass of aussian demands and shows that bundling also helps to redue the effetive dispersion of reservation values and thereby makes it possible for the seller to 3 ee Tirole 988 3

4 extrat a greater fration of the potential surplus even if demands are unorrelated and possibly positively orrelated The seond reason for bundling is the leveraging of market power that exists in one market into another market, ie the use of monopoly power position in one market to exlude rivals, deter entry or forelose ompetition in others markets urstein 960, lair 978, hmalensee 98] s noted by urstein 960, firms an raise profits by bundling goods that are omplementary urstein has argued that a firm with a monopoly over one good ould monopolize another by selling them in onjuntion with eah other If it did so, a firm seeking to ompete in the market for the bundled good would be forelosed from selling to all those who reeived the bundled good in onjuntion with their purhase of the bundling good This theory has ome under heavy attak from the Chiago hool iretor and evi 956, osner 976, ork 978] They argued that if a monopolist does employ tying or bundling, his motivation annot be leverage The reason is that there is only one monopoly profit that an be extrated lso, they defended the fat that bundling ould provide onveniene for ustomer and lower transation ost Whinston 990 and Nalebuff 004 re-examined the role of bundling as an entry deterrent Whinston 990 presents a series of models in whih he first makes the assumption in whih bundling does not inrease profits and then alters the assumption slightly so that it does e shows that the Chiago hool's ritiism of leveraging monopoly power from one market say market to another say market applies only if market is perfetly ompetitive With this latter assumption he proves that the use of leverage to affet the market is atually impossible owever, when the monopolized produt is no longer essential for all uses of produt, he shows that in the presene of sale eonomies, bundling an be an effetive and profitable strategy to alter market struture by making ontinued operation unprofitable for bundled good rivals and eventually indue them to exit ue to the sale eonomies, an entrant would need to attain suffiiently sale to survive in the market of undling an forelose the entrant from sales to be the differene between making entry profitable an unprofitable In these ases, bundling an inrease the profits of the monopolist of and harm onsumers 4

5 The third reason is that bundling leads to redue osts by enabling eonomies of sope in prodution and distribution to be ahieved alinger 995 reognizes that ost synergies from bundling are most valuable when onsumer valuations are positively orrelated Fousing on the ase of pure bundling, alinger introdues the role of ost savings to interat with demand effets and proposes a graphial analysis of the eonomi properties of bundling Thus, if most onsumers would buy both or neither and when sold separately, then any ost savings from selling them together will reate an inentive for a monopolist to sell bundled produts when valuations are positively orrelated Finally, we onlude this review of literature with the speifi ases of omplementary and systems goods Whinston 990, Matutes and Regibeau 99 and Eonomides 993] ere, prie disrimination plays a minor role beause the goods are highly positively orrelated in value and now there is more than one seller in the market oligopoly markets For these speifi ases, a standard result is that bundling is dominated by separate selling There is also no lear ut about welfare impliations of bundling in these studies Whinston 990 demonstrates that separate selling is more profitable than pure bundling for a firm whih is monopolist in and faes a ompetitor in when onsumers demands are for the system made by and e shows that if a ommitment to bundling auses the ompetitor in of the monopolist of to be inative, the latter an do no worse and possibly better by ommitting to separate selling roposition 3 This is beause if the ompetitor is inative, this redues the sales of Matutes and Regibeau 99 and Eonomides 993 extend the basi framework of monopoly bundling to a duopoly setting, with horizontally differentiated omponents ere ompetition is between fully integrated firms, where eah firm produes all omponents neessary to form a system Matutes and Regibeau 99, show that if two firms sell ompatible omponents, then bundling is dominated by separate selling This result omes from two effets For example, if we onsider that two omponents and are available, the first effet is that under ompatibility separate selling inreases the number of systems that an be assembled from two and to four,,, This enables some onsumers to obtain a system that is loser to their ideal speifiation, and then industry demand is larger without bundling The seond 5

6 effet relates to the fat that separate selling softens prie ompetition The intuition is that in a ompatible world with separate selling a derease in the prie of one firm s omponent inreases the demand for its own system, as well as for the mixed system system omposed by different firms' omponents owever, the greater demand for the mixed system redues the demand for the firm s seond omponent While with bundling, if a firm lowers the prie of one omponent, it attrats additional onsumers for its two omponents; utting the prie of one omponent inreases equally the demand for both omponents in the system It follows that a firms prie-utting inentives are lower with separate selling than with bundling I3 pproah in this paper This paper extends the literature on bundling in a number of ways First, it onsiders quality differenes in system omponents with onsumers taste à la Mussa and Rosen 978 peifially, we study a market for systems omposed of two omplementary omponents where we assume the unit ost inreasing in quality and variable in prodution 4 One of the omponents is sold by a firm that has a monopoly in that omponent; the other is sold by the same firm as well as by one other firm Consumers derive utility only from using one unit of the monopolized omponent in ombination with one unit of the other omponent eond, it answers the question how the introdution of quality affets the bundling deision of a firm that is a monopolist for produt and faes a single ompetitor in market for produt We prove that the monopolist s bundling deision depends on the quality level of the omponent produed by two firms We demonstrate that the monopolist of earns higher profits by selling and separately than selling the system as bundle when its produt is of higher quality than that of its rival On the 4 Quality differenes in system omponents and onsumers taste has been onsidered also by Einhorn 99 and Eonomides and ehr 994 The former uses the model of quality differentiation of abszewiz and Thisse 979 to analyze ompatibility of systems omponents and find that profits are higher when omponents are fully ompatible The latter use the framework of Mussa and Rosen 978 to study the quality hoie of omplete systems under many types of market strutures with quadrati fixed ost of quality improvement They do not find any equilibrium in quality in a similar market situation In this paper by ontrast, the unit ost is inreasing in quality and variable in prodution We find results that are qualitatively different and more general s noted by Crampes and ollander 995, this speifiation of variable ost inreasing in quality appears as the empirially more relevant ase 6

7 other hand if the monopolist s produt has the lower quality, then the bundling strategy yields more profits than separated selling The intuitions for these results are quite simple and similar to those of Eonomides 99 The profitability of separate selling depends on the relative inrease in the demand for ompared to the losses inurred due to ompetition faed in eparate selling leads to a onsiderable inrease in the demand for through sales with when the monopolist produes the higher quality of Conversely, separate selling brings no inrease in the demand for when the monopolist produes the lower quality of These results extend Whinston 990 and Matutes and Regibeau 99, when firms omponents are vertially differentiated lso, in ontrast to these studies, we demonstrate that bundling redues soial welfare Third, it onsiders the question how the deision to sell omponents separately or to bundle affets quality hoie We model a two stages game In the first stage, firms hoose qualities and determine whether they sell separately or bundle In the seond stage they set pries We find the set of equilibrium quality and priing deisions for eah firm that are outomes of the subgame perfet Nash equilibria We show that a firm who is monopolist in produt produes always the highest quality of produt and makes more profits by selling and separately The plan of the paper is as follows In setion II, we present the model In setion III, we determine the possible relevant selling strategies In setion IV, we study and ompare the separated selling strategy to the bundling strategy under different assumptions about qualities of firms produts lso in this setion, we perform a welfare analysis and we investigate the endogenous ase of quality hoies with a quadrati ost funtion Finally, we give antirust impliations of findings and onlude in setion V II The Model There are two firms, denoted and and two produts denoted and Firm sells the produts and, whereas firm sells only produt The produt omes in two distint levels of quality, high and low Quality means reliability It is the 7

8 probability of not breaking down et denote the probability that produt does not breakdown imilarly, let denote the probability that produt of quality i not i breakdown, where i {, } y assumption > We simplify by assuming that is produed at zero marginal ost with no fixed ost While is produed at onstant unit ost that depends on the probability of breakdown We assume the ost funtion to be of the form: C q, q, where q and denote respetively the quantity of output and the probability that a omponent does not breakdown 5 lso, we assume that 0, 0, 0 for all Convexity of the unit ost funtion implies for >, that: > 0 Consumers derive utility only from using one unit of in ombination with one unit of They an, however, ombine with any quality of Consumers are indexed by, where is uniformly distributed on 0,] When none of the omponent breakdown, onsumer obtains utility ; if one or both omponents breakdown his utility is zero s shown in figure, under separate selling, onsumers an potentially hoose between two systems: and and the lower quality of inludes and the higher quality of and inludes uy: nothing U0,] Figure 5 We have this form of ost struture when the main part of quality improvement omes from more expensive material and input 8

9 We note by, the prie of the omplete system i i, i {, } If the omponents of the omplete system are purhased individually, then the prie of the omplete system is the sum of the individual omponents prie Else the prie of the omplete system is the bundle prie, where i i i represents the bundle, i {, } i Consumers are assumed to be risk neutral They maximize expeted surplus This means that they hoose the ombination of reliabilities of and that maximizes:, i i { } i,, where, is the expeted utility derived by onsumers indexed from the quality i i of produt onsumed with produt We assume that the reliability of and, i {, } i is ommon knowledge We indiate by the preferene parameter of a onsumer who is indifferent between purhasing the higher quality system and the lower quality system The onsumer indexed is indifferent between purhasing the lower quality system and not purhasing at all The demand funtion for eah omplete system depends on pries and breakdown probabilities To obtain the demands, we use the individual-rationality IR onstraints and the inentive onstraints IC of eah demand onsumer For the onsumer who purhases the higher quality system the following onstraints are used: 0, IR IC 9

10 For the one who purhases the lower quality system the individual rationality onstraint is: 0 IR This implies that From the IR onstraint we derive: If we denote by, and the respetive demands for selling, we an write that:, and and under separate We onsider in turn two ases Case is where firm produes and and firm produes ; Case is where firm produes and and firm produes Without any further loss of generality, we set, ie we assume that is produed with perfet reliability III Relevant ossible elling trategies We assume that bundling is ahieved ostlessly ine firm produes the two omplementary omponents that form the omplete system, it has five marketing strategies In ase firm produes and and firm produes these are: i sell and separately; ii sell the bundle only; iii sell and separately and sell the bundle at a prie lower than the sum of individual pries mixed bundling; 6 6 ording to dam and Yellen 976 the first three marketing strategies refer respetively to pure omponents strategy or separate selling strategy, pure bundling strategy and mixed bundling strategy M 0

11 iv sell and the bundle ; v sell and the bundle The strategies iv and v are not relevant Indeed, strategy iv is equivalent to strategy ii The reason is that without, demand for alone has no value Thus iv and ii yield only a This analysis applies equally to strategy v, whih is equivalent to strategy iii oth strategies yield demands for and The remaining strategies to onsider are: i, ii, and iii We show that strategy iii is equivalent to strategy i roposition : Mixed bundling yields the same profits as separate selling roof Case firm produes and and firm produes : the profits of firm under separate selling are: ] et M and M respetively denote the demand and the prie for the bundle Under mixed bundling profits are: M M M M M ] ] M M M 3 M M If, learly 0 Therefore: M and M M M M ] M M If, also 0 Therefore: M M M M M M M ] 3*

12 This shows that separate selling yields the same profits as mixed bundling 3*, when is defined as the sum of individual omponents pries Therefore, M This proves that mixed bundling strategy an t do better than separate selling M Case firm produes and separate selling are: and firm produes : firm s profits under ] Whereas with mixed bundling they are: M M M M M ] ] M M M M M M M if, learly 0 Therefore: ] M M M M M M M if, also 0, Therefore: M M M M ] M M M M It is obvious that pries when M M is the sum of pries of individual omponents From proposition, it follows that a omplete disussion of strategies only requires a disussion of the hoie between separate selling and pure bundling To gain some intuitions for this result, note that mixed bundling indues a onsumer who prefers to purhase only one omponent of the system, to purhase the whole system of omponents ere produts are omposed of different omponents that annot be used individually Therefore, the inentive to buy the whole system is related to the funtional dependene of omponents Thus, all forms of mixed bundling are irrelevant in this model

13 3 IV Choosing a elling trategy We now haraterize, for ase and ase, the model s equilibrium with separate selling, and develop the omparison with that arising with bundling IV Case : the produer of also produes eparate selling When firm sells and separately, there are two available systems in the market, and ine the demands for and are, and respetively, the profits under separate priing are given for firm by: ], nd for firm by: ] 4 Firms hoose pries to maximize their profits and 4 We have the following first- order onditions for firm : 0 ], 0 ] nd for firm : 0 ] From these onditions, we obtain: 6 3, 5

14 4 h , 6 l 3 7 y substituting these equilibrium pries bak into profits funtions, we obtain for eah firm the following level of profits: ] 6, 8 9 These results differ from the standard model of vertially differentiated duopoly In our model, firm sells to all onsumers and sells to those with high reservation pries for While firm sells to onsumers with low reservation pries for These onsumers also purhase Therefore the willingness of firm to apture its rival s onsumers is limited sine it loses omponent s onsumers Firm pries its omponents suh that rival in market annot apture enough surplus of omponent s onsumers, then it extrats all remaining surplus in the market, where it is monopoly lso, in ontrast to a single integrated firm providing both omponents, firm raises the prie of and lowers the prie of to indue firm to lower the prie of Firm does not engage in suh pratie to sell more of, but instead to inrease the demand of ure bundling Now assume that firm bundles and Under this strategy no one purhases Therefore, this is a way to exlude firm from the market Only the system is available at prie Thus firm s profits are:

15 ] ˆ, 0 where ˆ ˆ, with ˆ ˆ represents the preferene parameter of a onsumer who is indifferent between purhasing the bundle and not purhasing The first- order ondition is: ˆ ˆ ] 0 The equilibrium prie and profit are:, ] 4 Observe that the prie of the bundle is the sum of 5 and 6, whih are the pries of the individual omponents of the bundle when firm sells its omponents separately In fat, the deision to bundle does not affet the systems pries given the qualities The intuition is that, there is no need to offer a disount to the onsumers who purhase the whole system from firm The reasons are: i omponents are perfetly positively orrelated in value; and ii omponents are differentiated in quality eparate selling vs pure bundling To see whether separate selling or bundling is more profitable for firm, we must ompare 8 to roposition : If the monopolist produes the higher quality version of, then he earns higher profits from separate selling than from bundling 5

16 6 roof Under separate selling firm s profits are: ] ] While under bundling its profits are: ˆ ] ˆ ] 0 We an rewrite this latter funtion as: ˆ ] ] ˆ ] 0* ine, the first terms of and 0* are equal Then to ompare to, we have just to ompare the last term of, to the one of 0*, ˆ ] When we ompute these two terms, we find that the former an be written as: ] 3 While the latter is: ] 3 ] ˆ ] Therefore separate selling is better than bundling if and only if: > ˆ ] ] > s, we have: > ˆ ] 0 3 > ine 0 >, we have >

17 undling uy: nothing ˆ eparate elling uy: nothing U0,] Figure The intuition behind the result of proposition is the following see figure : when firm sells its produts separately, it sells and to onsumers and to onsumers When it deides to bundle, then it sells the bundle to onsumers ˆ and does not sell any more to onsumers Then to see whih strategy is better, we must ompare the additional benefits from bundling that result from selling to additional onsumers ˆ, to losses from bundling that result from not selling to former onsumers The additional benefits from bundling are: ] ˆ, the benefits oming from new onsumers demanding While the losses from bundling are:, the resulting losses from onsumers who do not buy any more Therefore separate selling is better than bundling if and only if: > ] ˆ 7

18 This is the ase when the prodution ost is onvex: > 0 ere the result of bundling is a narrowing of market sine onsumers ˆ who bought the system of lower quality dot not buy under bundling IV Case : the produer of also produes eparate selling When firm sells and separately, the profits of firm and firm are respetively given by: ], 3 ] 4 nd equilibrium pries are:, 5 6, We observe that the prie of is higher and the pries of and are lower ompared to the ase where the monopolist produes This omes to the fat that firm inreases the prie of to apture more surplus of onsumers with high reservation pries for system Therefore the pries of strategi substitute, and, derease ere there is muh more surplus to apture in the market of y substituting 5, 6 and 7 into the profit funtions 3 and 4, we obtain: 8

19 ] ], 8 6 ] 9 In omparison to ase, we find that firm s profits are lower while firm s profits are higher This is beause now firm serves the high reservation prie onsumers of, whih is the most profitable segment of the market ure bundling If firm bundles, its profits are: ] ˆ, 0 where ˆ ˆ with ˆ, where ˆ is the preferene parameter of a onsumer indifferent between purhasing bundle and not purhasing ine there is ompatibility, the onsumers who desire to purhase the higher quality system, must purhase in addition to bundle They will do so if: If we denote by *, the preferene parameter of an indifferent onsumer between purhasing the lower bundle * in addition to the bundle alone, we obtain from : to form the higher quality bundle Consequently the demand for the higher quality bundle * * This gives firm s profits as: * is: ] 3 and 9

20 y maximizing 0 and 3 with respet to pries, one obtains:, 4 5 * From 5, we an rewrite as: * 6 We have 0 *, ie: 7 Condition 7 is the onstraint for firm to remain in the market Firm sells only if the differene of reliability between and if and is greater than the unit prodution ost of Otherwise all onsumers prefer to purhase the bundle of lower quality ie nobody will purhase in addition Equilibrium profits for firm and firm are respetively: ], ] if else eparate selling vs pure bundling The ranking of profits for the monopolist firm is summarized in the following proposition 0

21 roposition 3: If the monopolist produes the lower quality version of, then he earns lower profits from separate selling than from bundling roof ine the prie of the bundle is the same under both strategies and sine we have ˆ ; ie the onsumer who is indifferent between purhasing and not purhasing at all, is the same under both strategies, we have: ˆ Therefore the demand for under separate selling equals the demand for under pure bundling, ie ˆ On the other hand the demand for under separate selling is smaller than the demand for under pure bundling eause: Consequently the demand for the bundle is weakly higher under pure bundling for the same bundle pries Thus, firm s profits are higher under pure bundling than those under separate selling undling uy: nothing ˆ eparate elling uy: nothing U0,] Figure 3

22 For proposition 3, the intuition is simple see figure 3 The prie of the bundle is the same under both regimes and demands under pure bundling are greater than demands under separate selling Therefore for firm, bundling is better than separate selling We found a ase where bundling is a profitable strategy and an lead to forelosure and exlusion of the rival from the market To sum up, firm who is monopolist on never finds it worthwhile to bundle in order to redue the level of ompetition in market for when the result of bundling is a narrowing of market for its monopolized omponent The reason lies in the fat that sine the monopolized produt is essential for all uses of produts and, the monopolist an benefit from ompetition in through sales of its monopolized produt with separate selling This is the ase when the monopolist of produes Therefore he prefers separate selling over bundling On the other hand when the monopolist of produes, separate selling brings no inrease in the demand for its monopolized produt and even redues the demand for its produt through ompetition with Therefore, separate selling is dominated by bundling Corollary : The monopolist will sell its produts separately if and only if its produt has the higher quality Whinston 990 and Matutes and Regibeau 99 stated that if firms sell ompatible omponents, then bundling is dominated by separate selling The set up of Whinston 990 is same as here exept that: i he onsiders the ase of tehnial bundling; and ii he does not onsider produts differentiated in quality In the model of Matutes and Regibeau 99, no firm has a monopoly over either omponent and produts are horizontally differentiated Therefore our results annot be diretly ompared to their results owever, our results extend theirs to the ase where omponents are vertially differentiated Our results are also in ontrast to Choi 003 who demonstrated in asymmetri information setting that a monopolist will hoose to bundle a produt of established quality to one of unknown quality by onsumers only if for the latter the monopolist produes a quality higher than rivals

23 IV3 Welfare nalysis Now let us see how onsumers surplus and soial welfare are affeted by bundling deision When firm sells its omponents separately, onsumers surplus denoted by C is: C d d While the soial welfare denote by W is: W C When bundling is allowed onsumers surplus C is: C i ˆ nd the soial welfare W is: i ˆ i d i ˆ i i i i i, i {, }, i {, } W C i roposition 4: Consumers surplus and soial welfare are always higher under separate selling than under pure bundling roof Intuitively for ase firm produes and, whereas firm produes, pure bundling inreases the number of onsumers of from to ˆ and eliminates of onsumers of see figure Therefore, onsumers surplus under pure bundling is greater than under separate selling if and only if the additional surplus obtained by new onsumers of, ˆ when onsuming the higher quality under bundling rather than the lower quality under separate selling is lower than the 8 Remark that when osts of quality improvement are fixed, the result is easily dedutible The monopolist hooses bundling suh to forelose its ompetitor in Indeed, as proved by iallo 004, for symmetrial distribution of onsumers taste for quality, the monopolist prefers to produe only one variety of a system when osts of quality improvement are fixed o he would like to eliminate the others varieties from the market 3

24 losses of surplus of onsumers who do not onsume under pure bundling Formally we havec C if: ˆ ] d d 9 fter omputation we obtain the following ondition for 9 to be true: 0 Thus, onsumers surplus is higher under separate selling than under pure bundling ine this is also true for firms profits, this is true for soial welfare For ase firm produes and, whereas firm produes, the result is straightforward Indeed by bundling, onsumers purhase instead of This redues the surplus of these onsumers who had higher surplus with t the same time, the surplus of onsumers does not hange sine pries and qualities are idential see figure 3 Consequently onsumer surplus dereases under bundling lso, under bundling firm s losses not to sell exeed firm s additional benefits sell more ine firms profits also derease under bundling, immediately soial welfare also derease under bundling IV4 Numerial ppliation with Endogenous Quality Choie We onsider now a game where firms ompete in two-stages In the first stage, the monopolist hooses its marketing strategy bundling or not and the two firms simultaneously hoose their quality levels In the seond they onurrently determine pries- given the qualities and strategy already hosen- and produe the output whih 4

25 satisfies onsumers demands solution of this game onsists of a set of equilibrium quality and priing deisions for eah firm We fous on subgame perfet Nash equilibria We also assume that the marginal ost of prodution is quadrati, ie: ine quality is endogenous both firms may hoose the same quality for If firm does not bundle then ertrand ompetition leads to a unique equilibrium where pries equal unit ost ene, both firms make zero profits Therefore, firm produes a omponent differentiated in quality from firm s under separate selling and bundling From the previous results we know that the only ertain equilibrium with two ative firms is where firm produes the higher quality of In that situation it sells its omponents separately otherwise it bundles its omponents and this an exlude firm Then the profits are given by for firm and by 4 for firm With a quadrati ost funtion, we rewrite these profits as: ], 30 ] 3 For any given pair of reliability, maximizing 30 and 3 with respet to pries, gives the following equilibrium pries: 6, , y the first derivatives in quality, we observe that is dereasing in and inreasing in, h is inreasing in and dereasing in and is inreasing in 5

26 and These variations suggest that for firm to indue firm to lower the prie of, it must hoose as lose as possible to lso, we know that is inreasing in ; this implies that the quality dispersion differene of qualities will be lower under this market struture ompared to the traditional model of duopoly in a Mussa and Rosen 978 framework We look now for the solution of the quality game Firms hoose their quality speifiation to maximize their profits 30 and 3 y substituting the equilibrium pries 3, 33, and 34 bak into profit funtions, and maximizing these latter funtions with respet to qualities, we get a nonlinear system of equations of, whih is solved numerially to obtain the following s: 0700, Equilibrium pries and profits for separated selling are therefore: 0355 ; ; ; Expressions 35 and 36 give the pair of andidate equilibrium qualities The seond derivatives with respet to qualities given the equilibrium qualities are negative: and owever, that shows only that 35 and 36 represent a loal maximum This is not enough to ensure we have found a Nash equilibrium To be sure that our andidate maximum is indeed an equilibrium we also have to hek first that firm has no inentive to leapfrog firm and itself produe the highest quality and seond that firm makes more profits as a monopolist in and a duopolist produing than as a monopolist in both markets and 6

27 If firm produes its omponent at a quality level above the one of firm, we know that the best strategy of firm would be bundling We show that in this ase firm makes zero or less profits than before leapfrogging fter leapfrogging firm profits are given by: ] ˆ 37 fter optimization of 37, we obtain easily the following results for equilibrium quality, prie and profits: ; ; ine is onave in quality, by showing that < 0, is a suffiient ondition for being a global maximum That is the ase sine h h For firm, its profits are: 0 4 ] if else Under the onstraints: and , there is no solution whih satisfies 38 for the maximization of 38 with respet to qualities Therefore, we have 0 Now we must hek whether firm makes more profits as a duopolist produing than as a monopolist in It is straightforward that firm s profits under separate selling are higher than those under bundling sine: >

28 Corollary : The monopolist will always produe the higher quality of in a dynami game Thus, the outome of the subgame perfet Nash equilibrium is suh that firm selets equals to 0 700, and firm selets equals to is half of and their differene equals to When we determine quality hoie in a standard model of duopoly in a Mussa and Rosen 978 framework, we obtain that equals to and equals to ; their differene equals to0 408 ine is greater than , immediately we dedue that the spread of omponent quality in our market struture outome is too low relative to the standard profit maximization duopoly outome The reason is that the monopolist want to extrat more surplus in market from intensifying prie ompetition in market e ahieves that by not differentiate its omponent from rival s Consequently, quality differentiation in market between the firms is tighter and prie ompetition is intensified V ntitrust Impliations and Conlusion We analyzed bundling inentives in markets where produts are omposed of two omplementary omponents One of the omponents is monopolized and the other is sold by a duopoly We assumed quality differentiation between omponents We developed a model of quality ompetition and we demonstrated the monopolist s bundling deision depends on the quality level of the omponent where he faes ompetition We proved that if the monopolist s omponent has a quality higher than the ompetitor s then the monopolist prefers not to bundle On the other hand if the quality of this omponent is 9 When we ompute onsumers surplus and soial welfare under both marketing strategies, we find that: C ; C ; W 0 7 ; W 0 s proved in the preeding setion, onsumers surplus and soial welfare are higher under separate selling than pure bundling 8

29 lower than the ompetitor s then the monopolist prefers bundling For the monopolist the inentive not to bundle is related to market extensions for its monopolized omponent e hooses the marketing strategy whih helps to ahieve this goal Consequently it may appear a possible exlusion or forelosure of ompetitor Thus, we showed that this is an exlusionary bundling owever, when we look for the subgame perfet Nash equilibrium, we found that the monopolist hooses to produe the higher quality of the omplementary produt and separate selling is its best strategy The results of this paper, whih show that bundling ould be antiompetitive an be used to asses a proper legal rule regarding bundling in market for omplementary omponents when quality matters For example in the Mirosoft litigation ourts have had to determine whether it was lawful for Mirosoft to bundle its Internet Explorer browser with Windows operating system ine Mirosoft is almost a monopoly in the personal omputer operating system, faes ompetition in the browser market essentially from Netsape and both produts are omplementary, this ase fits appropriately our model if we onsider the two web browsers to be quality differentiated bsent the possibility that the omplementary omponent, Netsape Navigator might later in the future beome a substitute to Windows, the presene of network externality, and predatory priing, our results suggest that the bundling strategy adopted by Mirosoft implies that Internet Explorer is of lower quality than Netsape Navigator and that Mirosoft leverage its market power from the operating system market to the web browser market In most of the studies on bundling there is no lear ut about welfare effets of bundling We found that the welfare effets of bundling are learly negative This establishes that an effiieny presumption of bundling in markets where produts are omposed of two stritly omplementary omponents, with market power in one omponent is unwarranted This suggests a prohibition per se of bundling in these types of markets In an imperfet and asymmetri information world, bundling may also be a signal for bad quality of the monopolist s omplementary produt It is worthwhile to note that the results of this paper must be interpreted under the following simplifiations: we ignored 9

30 positive demand externalities or network externalities and we assumed no ost savings result from bundling Network externalities will inrease the profitability of separate selling, while ost savings that result from eonomy of sope in distribution will inrease the profitability of bundling Finally, for future researh, it will be interesting to look at the ase where eah firm supplied all the omponents neessary to form the omplete system Referenes dams, W James and Yellen, Janet, 976, Commodity undling and the urden of Monopoly, Quarterly Journal of Eonomis, 90, iretor, and evi, Edward, 956, aw and the Future: Trade Regulation, Northwestern University aw Review, 5, 8 96 ork, Robert, 978, The ntitrust aradox, New York: asi ooks urstein, Meyer, 960, The eonomis of Tie-in ales, Review of Eonomis and tatistis, February, 4, Carbajo, J, e Meza, and eidman, J, 990, strategi motivation for ommodity bundling, Journal of Industrial Eonomis, 38, Chou, C, and Oz hy, 990, Network Effets Without Network Externalities, International Journal of Industrial Organization, 8, Choi, J, il, 003, undling new produts with old to signal quality, with appliation to The sequening of new produts, International Journal of Industrial Organization,, Crampes, Claude and braham ollander, 995, uopoly and quality standards, European Eonomi Review, 39, 7-8 iallo, Thierno, 004, orizontal Mergers, Quality Choie, and Welfare, mimeo, Université de Montréal Eonomides, Niholas, 989, esirability of Compatibility in the bsene of Network Externalities, merian Eonomi Review, 79, Eonomides, Niholas, 99, Compatibility and Market truture, isussion aper tern hool of usiness, NYU 30

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