Three Essays on Oligopoly: Product Bundling, Two-Sided Markets, and Vertical Product Differentiation

Transcription

1 Three Essays on Oligopoly: Product Bundling, Two-Sided Markets, and Vertical Product Differentiation Inaugural-Dissertation zur Erlangung des Grades Doctor oeconoiae publicae (Dr. oec. publ.) an der Ludwig-Maxiilians-Universität München 2004 vorgelegt von Markus Reisinger Referent: Prof. Sven Rady, Ph.D. Koreferent: Prof. Ray Rees, Ph.D. Prootionsabschlußberatung: 21. Juli 2004

2 Contents Acknowledgeents iii 1 Introduction 1 2 The Effects of Product Bundling in Duopoly Introduction The Model Dependence between Location and Correlation Equilibriu Price and Selling Strategies Welfare Consequences Location Choice Application Conclusion Appendix Two-Sided Markets with Negative Externalities Introduction The Model Efficiency Nash Equilibriu Pricing Behaviour of Internet Portals User Charge Conclusion

3 ii 4 Vertical Product Differentiation, Market Entry, and Welfare Introduction Related Literature The Model without Price Discriination Discussion Pricing of Pharaceuticals after Generic Entry The Market for Fragrance and Cosetics The Model with Price Discriination Epirical Exaples Airline Industry Brand-Controlled Generics in the Pharaceutical Market Conclusion Appendix Concluding Rearks 116 References i

4 Acknowledgeents First, and foreost, I would like to thank y supervisor Sven Rady for his encourageent and advise. He read all chapters of this thesis very carefully and gave e nuerous suggestions on how to iprove the. I a also very grateful to Ray Rees and Klaus Schidt, the other advisors in y thesis coittee, for any helpful coents and suggestions. I thank all participants of the internal seinar where I presented each of y papers in an early stage. I benefitted a lot fro the coents and discussions during y talks. Aong y colleagues y special thanks goes to Florian Englaier with who I wrote a joint paper and who was always available to discuss scientific and non-scientific topics. I also thank y colleagues Gregor Gehauf, Florian Herold, Ingrid Königbauer, Christian Merz, Astrid Selder and Ferdinand von Sieens who supported e in finishing the thesis, each in her or his own special way. My thanks also goes to our secretary Manuela Beckstein for helping e in handling adinistrative probles. The second chapter benefitted a lot fro coents by Mattias Polborn, Lars Stole, seinar participants at EARIE 2002 in Madrid (especially Steven Berry), the EDGE Jaboree 2002 in Copenhagen and the ESEM 2003 in Stockhol. The third chapter was presented at the conference on The Econoics of Two-Sided Markets in Toulouse, 2004, and I a grateful to Toy Gabrielsen, who served as y discussant, and all other participants. The fourth chapter was presented at the annual eeting of the Verein für Socialpolitik 2003 in Zürich, and I a indebted to y discussant Arin Schutzler for his nuerous and very helpful suggestions. Last, but certainly not least, I thank y parents for their peranent support during the tie this work was conducted.

5 Chapter 1 Introduction The study of oligopoly has a long tradition in econoic thought and has stayed up to now a ajor field which is relevant for both theoretical and practical issues. Many theories of oligopoly developed in the last century have becoe a fraework for the analysis of odels in different fields of econoics and are used in antitrust and regulatory issues. In this preface I want to give short treatise of the history of oligopoly theory and after that present a suary of the three chapters of the thesis and how they relate to and differ fro the existing literature. 1 The ter oligopoly goes back to the year 1516 where the British huanist and political scientist Sir Thoas More coined the ter in his Utopia. He noted that prices need not fall only because there is ore than one supplier. 2 But after More s work it took ore than 300 years before Cournot (1838) provided a first foral theory of oligopoly. Probably the reason why no progress could be ade in the ean tie was, as Schupeter (1954) noted, that, as we leave the case of pure onopoly, factors assert theselves that are absent in this case and vanish again as we approach pure copetition, thus the unbroken line fro onopoly to copetition is a treacherous guide. 3 In a odern terinology this is the proble of strategic interaction. 1 Nevertheless all chapters can be read independently because a otivation and suary is given in the introduction to each chapter as well. 2 A reference on More can be found in Schupeter (1954), p See Schupeter (1954), p.981.

6 2 Cournot (1838) presented a odel where firs copete in quantities and prices are deterined by the interplay of supply and deand. He presents a solution concept which is equivalent to a Nash equilibriu (Nash (1950)). The results of his analysis are that prices are above arginal costs and firs earn positive profits but this profits fall as the nuber of firs in the arket increase. This results are quite intuitive and realistic. But one natural objection against Cournot s odel (1838) is that in practice businesses choose prices rather than quantities. But it took 50 years before econoists get aware of Cournot s work and Bertrand (1883) brought forward the above criticis. He proposed a odel with two siilar firs copeting in prices where both firs have constant arginal costs. Bertrand (1883) pointed out that each fir has a strong incentive to undercut the other s price to capture the whole deand. In equilibriu prices equal arginal costs and firs earn zero profits. This result becae faous as the Bertrand-Paradoxon because two firs are enough to get the sae outcoe as under perfect copetition. So econoists faced the dilea that with the strange assuption of quantities as strategic variables we get a realistic result but with the reasonable assuption of prices as strategic variables the result is utterly unrealistic. But for the Bertrand result to hold any crucial assuptions have to be satisfied, aong others, that arginal costs are constant, that firs copete only in a oneshot gae, and perhaps the ost unnatural one that products are hoogeneous and therefore perfect substitutes. Addressing the first point, Edgeworth (1925) presented an analysis where firs face capacity constraints, i.e. an extree for of decreasing returns to scale, and proved the non-existence of an equilibriu in pure strategies. 4 Later Levitan & Shubik (1972) showed that an equilibriu in ixed strategies exists but pointed out that it is very hard to interpret a ixed strategy equilibri in prices. 5 For the second critique to the Bertrand odel, naely that the result only holds in a one-shot gae, it took alost one hundred years until the first foral odels of dynaic price copetition were provided. The reason is that non-cooperative gae theory ade rapid progress only in the 1970 s and 1980 s. This holds especially in the 4 This result becae known in oligopoly theory as Edgeworth cycle. 5 See also Dasgupta & Maskin (1986).

7 3 area of repeated gaes under asyetric inforation which is the appropriate tool to study dynaic price copetition. 6 The general result of this literature is that prices above arginal costs can be sustained if firs discount factors are high enough. 7 The underlying idea is that it does not pay for a fir to undercut its copetitor s price today because this triggers a punishent in the following periods. This behaviour is called tacit collusion. 8 Epirical studies, e.g. Porter (1983) or Rees (1993), also see to confir the intuition that firs in real world arkets engage heavily in tacit collusion. Let us now turn to the third and perhaps ost serious critique on Bertrand s odel, naely that products are assued to be perfect substitutes. In this case a fir can capture the entire arket by slightly undercutting the other s price. This is obviously an unrealistic assuption because there is basically always soe degree of heterogeneity between goods. The literature on heterogeneity of goods is subsued under the generic ter product differentiation and has two branches, the nonaddress branch and the address branch, 9 where the latter was the ore successful one. 10 The non-address approach started with Chaberlin s book (1933), the theory of onopolistic copetition, in which he tried to explain unexploited scale econoies. He analyses a odel where firs produce differentiated products and where the degree of copetition between each fir is the sae. This gave rise to the critique of Kaldor (1935) who argues that each fir has copetitors producing siilar products and others producing distinct products and that copetition between siilar products 6 For the theoretical foundations of the analysis of repeated gaes used in Industrial Organisation see Abreu (1988), Farrell & Maskin (1986), Fudenberg & Maskin (1986), and the references in Shapiro (1989). 7 The ost influential papers in dynaic price copetition are Green & Porter (1984), Roteberg & Saloner (1986) and the three papers by Maskin & Tirole (1987,1988,1988). 8 The idea that it is the obvious choice for oligopolists to collude was already ephasized by Bertrand (1883). 9 For a longer discussion on this classification see Eaton & Lipsey (1989). 10 The nae address approach stes fro Hotelling s (1929) idea that consuers are located on a position on the ain street of a linear city. In the non-address approach consuers are described by soe characteristics but not by a location.

8 4 should bear the ain effect of change in a fir s behaviour. So Kaldor (1935) in soe sense proposed the address approach as the ore realistic one and his arguentation was widely accepted. 11 The address approach started with the faous seinal paper of Hotelling (1929). He assues that each consuer is described by her preference which is expressed through her location on a line. Two copeting firs are located on the line as well and if a consuer s distance to fir 1 is shorter than her distance to fir 2 she prefers fir 1 s product. Hotelling shows that the higher consuers transportation costs, i.e. consuers disutility fro not consuing her ideal product, the higher profits of both firs. So by relaxing the assuption of hoogeneous goods one gets a odel with prices as strategic variables and firs earning positive profits. Hotelling s odel was developed further in any respects. 12 Since the new developents in non-cooperative gae theory the odel cae under scrutiny of any econoists. Hotelling assued that the transportation cost function is linear in the distance between the location of a consuer and a fir. But d Aspreont, Gabszewicz, & Thisse (1979) showed that if firs locations are endogenous with such a forulation an equilibriu ight not exist because profit functions are discontinuous and non concave. Instead they cae up with a quadratic transportation cost function which is now coon. They also show that firs position theselves at the opposite ends of the line to iniize price copetition. Salop (1979) considers a odel where consuers are distributed on a circle instead of a line. With this forulation he allows entry of ore than two firs. Iren & Thisse (1998) consider copetition in not only one but in any characteristics and show that firs choose axial differentiation in the ost iportant characteristic and inial differentiation in all others. The odel also serves as a building block in any papers which analyse different aspects of copetition. Exaples are Judd (1985) who used the odel to look at the case of product proliferation to deter entry and Keller & Rady (2003) who analyse a 11 For an extensive discussion of the non-address approach see Anderson, de Pala, & Thisse (1992). 12 For exale a faous new developent was ade by Lancaster (1966) who builds a odel in which consuers preferences are defined over characteristics which are ebodied in the goods.

9 5 dynaic gae with firs learning about the degree of product differentiation. Chapters two, three, and four of this thesis all relate in one or the other way to this odel of product differentiation. Each of the three chapters analyses a different proble of pricing behaviour in oligopoly. The second analyses coodity bundling, the third two-sided arkets with negative externalities and the fourth quality differentiation and arket entry. In what follows I suarise each chapter and point out the iportant results and the differences to the existing literature. In the second chapter, The Effects of Product Bundling in Duopoly, a duopoly odel is analysed where both firs sell two goods. These goods can be sold either only independently (independent pricing) or independently and in a package consisting of both goods at soe discount (ixed bundling). 13 In the econoics literature starting with the seinal paper by Adas & Yellen (1976) bundling for a long tie has been seen as a price discriination device for onopolists. Whether ixed bundling raises a onopolist s profit depends on the correlation of consuers reservation values for the two goods. If this correlation is negative, i.e. there exists any consuers with high valuation for good A but low valuation for good B and vice versa (extree preferences), ixed bundling is ore profitable than independent pricing. This result was shown by Adas & Yellen (1976) in soe exaples and was generalised by Schalensee (1984) to a joint noral distribution and by McAfee, McMillan, & Whinston (1989) to general distribution functions. The intuition behind this result is the following. If correlation is negative there are any consuers with extree preferences. The onopolist charges high independent prices and these consuers buy only the good for which they have a high valuation. Yet, there are soe consuers with iddle range valuations for both goods and they buy the bundle. Thus with the instruent of the bundle the onopolist can sort its consuers into three categories instead of only two and can extract ore consuer rent. This is especially profitable 13 There are any exaples of this practice. Electronic copanies sell stereo systes consisting of CD-player and receiver at a low price. In the USA long distance telephone copanies sell internet access together with long distance service. This package is cheaper than if both services are bought independently.

10 6 with negative correlation because of the consuers with different valuations for both goods. Those do not exist under positive correlation. Now let us look at the duopoly situation. Firs copete for consuers with the help of the bundle. So in addition to the sorting effect there is a business-stealing effect which lowers profits. Whether ixed bundling is profitable depends on which effect is doinant. In y odel both firs products are axially differentiated on two circles a la Salop (1979). The correlation of consuers valuations can be expressed through their location on both circles. If any consuers are located near the sae fir on both circles they have higher valuations for both goods of that fir than for the goods of the other fir and correlation is positive. If there are any consuers who are located on circle A near fir 1 but on circle B near fir 2 and vice versa, correlation is negative. First let us look at the case of positive correlation. In this case firs can act in soe sense as local onopolists because only few consuers are undecided between both firs. So it does not pay to lower prices uch in order to get these consuers at the argin. The sorting effect of bundling doinates the business stealing effect and profits are higher than without the ability to bundle. Thus the consequences are siilar to the ones in the onopoly case. If correlation is negative the situation is copletely different and bundling lowers profits. The intuition is the following. If we look only at the bundle any consuers are indifferent between the bundle of fir 1 and fir 2. Thus by undercutting the copetitor s bundle price a fir can capture any new consuers. This results in harsh copetition and low bundle prices. But this affects the independent prices as well and profits are lower than without the ability to bundle. Firs are in a prisoner s dilea. The business-stealing effect doinates the sorting effect. The results are exactly opposite to the onopoly case where negative correlation renders ixed bundling profitable. Concerning welfare I can show that bundling reduces welfare. The reason is that the bundle price is cheaper than the su of the independent prices. This induces consuers to buy the bundle although they ay prefer the goods of different firs. I also analyse

11 7 the consequences of endogenous fir location. In choosing their locations on the circles firs influence consuers reservation price correlation. Thus firs try to avoid strong negative correlation. They achieve this by choosing axial differentiation in the good with the higher transportation costs and inial differentiation in the good with the lower transportation costs. Thus they forego profits with the second product to avoid the negative consequences arising fro additional copetition in the bundle. 14 The literature on coodity bundling in a duopolistic fraework is up to now ainly concerned with bundling as strategic foreclosure and entry deterrence. The ain question is if a onopolist in one arket can onopolise a second arket with the help of bundling. This is odelled in different ways by Choi (1996), Nalebuff (2004), and Whinston (1990). Exceptions are the papers by Anderson & Leruth (1992) and Matutes & Regibeau (1993) who analyse duopolistic copetition in both goods as in y odel. They get the result that a prisoners dilea will always arise. But they are not concerned with the consequences of different correlations of reservation prices. I show that this correlation is the driving force for the results in duopoly as well as in onopoly but has copletely different effects in duopoly as copared to onopoly. The third chapter analyses Two-Sided Markets with Negative Externalities. The ter two-sided arket is a relatively new one in econoics and is, to y best knowledge, coined by Rochet & Tirole in an early draft of their 2003 paper Platfor Copetition in Two-Sided Markets. It refers to a arket where two distinct sides are present interacting with each other on a coon platfor. The platfor s proble now is to get both sides on board. The real world exaples inspiring these literature usually are arkets where both sides exert positive externalities on each other. 15 These arkets have been studied extensively by Rochet & Tirole (2003) and Wright (2003,2004). 14 Such fir behaviour can be observed by US telephone copanies where the long distance offer in each package is very siilar while firs try to differentiate theselves a lot in the offer of internet access. 15 An exaple is the arket for credit cards. Card holders value their cards only to the extent that the cards are accepted by erchants and erchants benefit fro widespread diffusion of cards they accept.

12 8 In chapter three I analyse a odel where one side causes a negative externality on the other. A proinent exaple for such an industry are the edia. Platfors are e.g. radio stations or internet portals, one side are listeners or users and the other side are advertisers. Users dislike advertising and spend less tie to consue platfor s services if there are any coercials. 16 By contrast, advertisers wish to gain users attention to tept the to buy their products. So users exert a positive externality on advertisers while advertisers cause a negative externality on users. I study a odel in which two platfors copete for advertisers and users. In the basic odel platfors can only charge advertisers because it is either ipossible to set a user fee (like in case of radio stations) or it is not custoary to do so (like in the case of internet portals). Fro the users point of view platfors are differentiated a la Hotelling while advertisers have no special preference for one of the platfors. Both sides decide for only one platfor. 17 First take a look at the efficient outcoe. If the gains fro trading advertisers goods are high copared to users utility loss fro advertising all advertisers should advertise while soe should be excluded if users utility loss is coparatively high. The optial allocation of advertisers aong platfors is even. The reason is that if one platfor has ore advertisers the externality on its users is high and the overall externality can be reduced if soe advertisers switch to the other platfor. Coparing the efficient outcoe with the Nash equilibriu of the gae I find that there can be too uch or too little advertising. The intuition behind this is the following. An additional coercial on a platfor causes a negative externality directly on 16 The assuption that users are disturbed by advertising is strongly confired in the literature. See Bagwell (2003) for an overview. 17 This is a realistic assuption with regard to users who usually use only one platfor to do e-ailing or listen to only one radio station at a tie. Advertisers instead can advertise on both platfors which is not possible in y odel. But this is not crucial to the results because the only thing which atters is that a change in the price of platfor 1 changes the nuber of advertisers on platfor 2. So one gets the sae result with the assuption that advertisers are ulti-hoing (can advertise on both platfors) but have only a certain budget for advertising expenditures where the last unit can either be spend on one or the other platfor.

13 9 the users but indirectly on all other advertisers as well because users spend less tie on a platfor and soe switch to the other platfor. In their pricing behaviour platfors consider only the indirect externality on advertisers because they cannot charge users. If differentiation between platfors is sall any users switch to platfor 1 if platfor 2 broadcasts any advertiseents. This results in high prices for advertising and too little advertising. If differentiation is high advertising prices are low and there is too uch advertising. Platfors profits depend on the level of differentiation as well. But contrary to standard results in y odel a higher level of differentiation can lead to lower profits. This is the case if differentiation is relatively high. The reason is that in this case platfors want to attract any advertisers and set low prices. But since both platfors do so advertising levels stay the sae and profits fall. This shows that in a twosided arket a lower level of copetition on one side can increase copetition on the other side and lead to lower profits. If differentiation is relatively sall an increase in differentiation raises profits because ore firs advertise. 18 I also analyse the case if platfors can set a user charge. I show that if this user charge is positive in equilibriu profits always increase. But dependent on paraeters it is well possible that the user charge is negative in equilibriu. Platfors subsidise users to ake higher profits on advertisers. If this is the case profits are lower and the additional instruent of a user charge hurts platfors. Nevertheless the equilibriu with two instruents is efficient. The intuition is that platfors have two instruents for two groups and copetition induces the to use the instruents efficiently. Recently several papers dealt with edia copetition and advertising. 19 The ones closest to y odel are Anderson & Coate (2003) and Kind, Nilssen & Sorgard (2003). I replicate the result of their papers that there can be too uch or too little advertising. The big difference to y odel is that they only consider copetition for users but not 18 In Section 3.5 I present an exaple of a such pricing behaviour by the internet portals AOL and GMX. 19 See Section 3.1 for an overview of this papers.

14 10 for advertisers while in y odel platfors copete for both sides of the arket. Thus the result that profits can fall with an increase in differentiation cannot be generated in their odel. Kind, Nilssen & Sorgard (2003) do also not analyse the case where a platfor can set a user charge. Anderson & Coate (2003) briefly analyse this possibility but obtain different results to y odel because in their odel platfors decide in addition whether they want to provide the sae or different contents. In contrast to the first two chapters which analyse odels of horizontal product differentiation the fourth chapter deals with Vertical Product Differentiation, Market Entry, and Welfare. In odels of horizontal product differentiation consuers have different preferences for the goods. By contrast, in a odel of vertical product differentiation everyone agrees on the ost preferred good, e.g. because it is of superior quality. The pioneering papers in this field are Gabszewicz & Thisse (1979) and Shaked & Sutton (1982). In both odels consuers differ in their incoe levels and in equilibriu consuers with higher incoe buy the high quality good at a high price while consuers with a lower incoe buy the low quality good at a lower price. Shaked & Sutton (1982) show that ex-ante siilar firs choose different qualities to relax price copetition. In chapter four I copare two duopoly odels with respect to welfare. In one odel firs can produce only one quality level while in the other odel they can produce a whole quality range and engage in second-degree price discriination. Both odels have a leader-follower gae structure. The leading fir (incubent) chooses a quality or a quality range in the first stage to which it is coitted for the rest of the gae. After observing this choice the follower (entrant) decides whether it wants to enter the arket at soe fixed entry costs. If it enters it chooses its quality or quality range. 20 In the third stage firs set their prices depending on the chosen quality levels. First consider the case where each fir produces only one quality. The incubent has an incentive to deter entry if its onopoly profit (given entry deterring quality) is higher than the duopoly profit. The way entry can be deterred depends on the 20 It is assued that it is profitable for the leader to be the high quality fir. So in equilibriu the entrant always produces a lower quality or quality range than the incubent.

15 11 strategic relation between the two qualities, e.g. if they are strategic copleents or strategic substitutes. If qualities are strategic copleents welfare in the case of entry deterrence is lower than in the case of pure onopoly. The intuition is that the incubent produces a lower quality than in onopoly to induce the entrant to produce a lower quality as well which reduces the entrant s profit. If fixed costs are high the entrant stays out of the arket. But since quality is lower welfare is reduced. If qualities are strategic substitutes the reverse is true. Even in the case where entry is accoodated the incubent ight lower its quality as copared to onopoly. This is the case if production costs of quality are high. The reason is that due to copetition it is harder for the incubent to extract consuer rent, inducing it to produce lower quality. If costs are low it produces higher quality to reach a higher level of differentiation in order to reduce price copetition. In this case welfare increases. 21 If firs can produce a quality range and engage in second-degree price discriination results are different. I show that the lowest quality of the incubent and the highest quality of the entrant are strategic copleents. Thus if the incubent wants to deter entry he has to expand its quality range which leads to an increase in welfare. So the result is quite different to the one-quality odel where welfare in case of entry deterrence can be lower than in onopoly. If entry is accoodated I find that consuer rent unabiguously increases. The reason is that copetition leads to lower prices. By contrast, the consequences for welfare are not clear. The intuition is that the incubent ight contract its quality range to avoid fierce price copetition. There is a gap between the two quality ranges of the firs. More consuers are served but soe consuers buy lower quality than in onopoly. The welfare effects are therefore abiguous. 22 Concerning the related literature on product differentiation and entry Donnenfeld 21 I provide two exaples of such fir behaviour fro different industries, naely the pharaceutical industry and the cosetic industry. 22 Again, I give two exaples for such fir behaviour, one fro the airline industry and the other, again, fro the pharaceutical industry.

16 12 & Weber (1992,1995) in two papers analyse a situation with two incubents and one potential entrant, but neither do they provide a welfare analysis nor are they interested in price discriination. A paper which is very close to y quality range odel is the one by Chapsaur & Rochet (1989). They analyse a odel of siultaneous quality choice. My analysis in soe respects draws heavily on theirs. The difference is that in y odel firs choose their quality ranges sequentially which gives rise to the question of entry deterrence and that I a ainly interested in the welfare consequences of potential copetition while they only look at a pure duopoly situation and do not give a welfare analysis. I conclude the work with soe rearks on the liitations of the odels and give an outlook on how they can be interrelated.

17 Chapter 2 The Effects of Product Bundling in Duopoly 2.1 Introduction Product bundling refers to the practice of selling two or ore goods together in a package at a price which is below the su of the independent prices. This practice can be observed very often in the real world. For exaple in the USA internet access is sold by long distance telephone copanies. If a consuer buys internet access and long distance service together fro the sae copany this is cheaper than if he buys both services independently. Another well known exaple is the selling of stereo systes. Big electronic copanies always supply a package consisting of CD-player, stereo deck and receiver which is sold at a low price. There are any other exaples of bundling in big departent stores or cultural organisations, e.g. theaters and concert halls always offer season tickets. In the industrial organisation literature bundling has been extensively studied for onopolists and it is shown that ixed bundling, that is selling the goods individually and bundled together in a package, will in general increase the onopolist s profit. 23 However, the industry structure in the exaples above is clearly not onopolistic. 23 See Varian (1989) for an overview.

18 14 This shows that there is a need to exaine bundling in oligopolistic or copetitive arkets. The objective of this paper is to analyse, how the ability to bundle affects profits and consuer rents in a duopolistic arket structure. It is shown that duopolists generically have an incentive to use ixed bundling, but the consequences on profits are abiguous. If consuers are hoogeneous, i.e. correlation of their reservation prices is positive, firs are better off with bundling. If instead consuers are heterogeneous, i.e. their reservation values are negatively correlated, profits are lower than without bundling. This is in sharp contrast to the onopoly case, where bundling raises the onopolist s profit, especially if consuers are heterogeneous. The intuition behind this result is the following. First look at the onopoly case. If correlation of reservation values is negative there exist any consuers with extree preferences, that eans with a high valuation for good A but a low valuation for good B and vice versa. The optial pricing strategy for a onopolist is to charge a high individual price for each good and the consuers with these extree preferences buy only the good for which they have a high valuation. But still there are soe consuers with iddle range valuations for both goods and they buy the bundle at soe discount. Thus bundling has a sorting effect. It allows the onopolist to sort its consuers into three categories instead of two and it can therefore extract ore consuer rent. Now let us look at a situation with two firs. Each fir ust copete for deand and will do this with the help of the bundle. So beside the sorting effect, bundling now causes a second effect, which is called business-stealing effect. This effect goes in the opposite direction than the sorting effect, because it results in a higher degree of copetition and thus in lower profits. Whether bundling is profitable for the firs depends on which effect is doinating the other one. The first result is that there is always an incentive for the duopolists to engage in ixed bundling as long as the correlation of valuations is not perfectly positive. This result is in line with the onopoly case. Since the firs have an additional instruent to sort their consuers they will use it. Now assue consuers are hoogeneous. This eans that any of the have a

19 15 strong preference for both goods of one fir. Therefore firs can act in soe sense as local onopolists and can extract ore consuer rent with bundling. There are only few consuers who are undecided between both firs. So it does not pay for a fir to undercut its copetitor s prices to get these consuers at the argin. Thus prices and profits are relatively high. The sorting effect doinates the business-stealing effect. The consequences of bundling are very siilar to the onopoly case. If instead consuer preferences are heterogeneous the situation is copletely different. In this case any consuers prefer good A fro fir 1 and good B fro fir 2 and vice versa. For siplicity assue first that both firs can sell their goods only in a bundle. These bundles are now alost perfect substitutes to each other. Each fir can gain any new custoers by lowering the price of its own bundle. Thus harsh price copetition arises. If the firs can sell their products independently as well, this business-stealing effect endures. The price of the bundle is driven down to nearly arginal costs and this influences the unbundled prices which are now very low. Thus profits are low and consuer rent is high. The initial idea of the bundle, naely to price discriinate in a ore skilful anner, is doinated by the business-stealing effect. So the result is copletely opposite to the onopoly case. In this second case firs are in a prisoner s dilea situation. It would be better for both of the not to bundle. There is also an interesting welfare effect. Since the bundle is cheaper than the su of the two independent prices, consuers are encouraged to buy the bundle. If heterogeneity increases firs react in equilibriu with an increase of their independent prices. Thus ore consuers buy the bundle. This results in distributive inefficiency because soe consuers prefer the products fro different firs. So if arkets are covered bundling reduces social welfare as it can only cause consuers to purchase the wrong good. It is also analysed what will happen if firs can influence the correlation of valuations. This can be done with the introduction of an additional stage in which firs choose their location in the product range. It is shown that firs ay choose inial differentiation in one product and thus forego profits with that product. They do this

20 16 to avoid copetition on the bundle which is very fierce if correlation is negative. Such fir behavior can be observed in the US by telephone copanies which sell long distance service and internet access in one package. The long distance service offer is very siilar in each package while firs try to differentiate theselves a lot in the offer of internet access with each fir offering different rates and aounts of installation gifts. In the literature econoists attention on bundling was first drawn by the seinal paper of Adas and Yellen (1976). They show in a series of exaples with an atoistic distribution of consuers that selling goods through bundling will raise the profit of a onopolist. This result was generalized by Schalensee (1984) to a joint noral distribution and by McAfee, McMillan and Whinston (1989) to general distribution functions. They all show that bundling will raise the onopolist s profit, because it is an additional instruent to sort its custoers. This is especially the case if reservation values for different goods are negatively correlated. There are soe papers which study bundling in a ore copetitive environent. The focus of these papers is if and how a ultiproduct fir, which has onopoly power in one arket, can increase its profit through bundling. Such a strategy is called tying. Whinston (1990) analyses whether a fir which has onopoly power in the first arket can onopolize a second arket with duopolistic arket structure by coitting to engage in pure bundling. He shows that this is possible. The reason is that the onopolist prices the bundle aggressively with the consequence that any consuers will now buy the bundle and therefore the profit of the rival is very low, which induces hi to exit. Carbajo, demeza and Seidann (1990) study a odel with the sae arket structure as in Whinston (1990). They present another idea why a tying coitent can be profitable for a onopolist. This is that with pure bundling products in the second arket are differentiated and thus prices are higher. Profits of both firs are increased. 24 Nalebuff (2004) shows that pure bundling is ore profitable for an incubent even if coitent is not possible. This is the case if the entrant 24 Chen (1997) presents a odel with the sae intuition only the arket structure is different. He assues duopoly in one arket and perfect copetition in the second. The duopolists can differentiate theselves by one fir selling the bundle and the other fir selling the goods only independently.

21 17 can enter only in one arket. The intuition is that the entrant ust copete for consuers in the first arket as well since the incubent only offers the bundle. This greatly reduces the profit of the entrant. Choi (1996) analyses the effects of bundling on research & developent. In his odel there is originally duopoly in both arkets but both firs can invest in R&D to lower their production costs before reaching the price copetition stage. If the difference in production costs for one good is large after the R&D gae the arket for this good is onopolised by the low cost fir. Choi (1996) shows that in this case bundling serves as a channel to onopolise the second arket. Finally, Mathewson and Winter (1997) study a odel with onopoly in one arket and perfect copetition in the other. They show that requireents tying is profitable for the onopolist provided that deands are stochastically dependent. For a great paraeter range the optial prices are Rasey prices. 25 There are two papers which have the sae arket structure as in y odel (duopoly in both arkets), naely Matutes and Regibeau (1992) and Anderson and Leruth (1993). The result in both papers is that if firs cannot coit not to bundle in equilibriu they choose ixed bundling. But this results in increased copetition and lowers profits. A prisoner s dilea dilea arises because profits would be higher without bundling. However, in these papers the driving force of the onopoly case, the correlation of consuers reservation values, is not odelled. In y odel it is shown that this is also the crucial variable for the oligopoly case, but can create opposite effects. Also these papers are not concerned with welfare and location choice. This chapter is also in the spirit of a relatively new literature which studies the effects of price discriinating ethods in a copetitive environent. An extensive overview of the different branches of these literature is given in a paper by Stole (2003) which is prepared for the forthcoing volue of the Handbook of Industrial Organization. In the section about bundling Stole (2003) suarizes any of the recent papers which are concerned with the question how bundling affects profits and arket structure when coitent is possible or not. 25 Seidann (1991) and Denicolo (2000) analyse the consequences of bundling in other arket structures.

22 18 The structure of the chapter is as follows. Section 2.2 sets out the odel. The particular structure of consuer heterogeneity and the correlation of reservation values is presented in Section 2.3. Equilibriu selling and price policy is deterined in Section 2.4. Section 2.5 studies the welfare consequences of bundling. Section 2.6 analyses the effects if firs have the possibility to choose their location and influence the reservation price correlation. An application of the odel to the US telephone industry is considered in Section 2.7. Section 2.8 concludes the chapter. The proofs of all results are given in the Appendix of this chapter. 2.2 The Model The odel is a variant of Salop s (1979) odel of spatial copetition on the circle but with two goods. There are two firs i = 1, 2. Both firs produce two differentiated goods j = A, B at the sae constant arginal costs c A and c B. 26 The product space for each good is taken to be the unit-circuference of a circle. The product variants are then the locations of the firs on each circle. It is assued that fir 1 is located at point 0 on both circles and fir 2 is located at point 1 on both circles. So there is axiu 2 product differentiation in both goods. The firs have the choice to sell their products not only independently but also together as a bundle. So each fir i can choose between two possible selling strategies. It can sell its goods separately at prices p i A and p i B (independent pricing) or it can sell the goods independently and as a bundle at prices p i A, p i B and p i AB (ixed bundling). 27 Firs have to decide siultaneously about their selling and price strategies. It is assued that they cannot onitor the purchases of consuers. So the strategy space for each fir i is to quote three prices p i A, p i B and 26 The assuption of the sae cost function for both firs is ade for siplicity and is not crucial to the results. 27 There can also be a third strategy, naely to sell the goods only as a bundle at price p i AB. Adas & Yellen (p. 483) and McAfee, McMillan & Whinston (p. 334) have shown that this cannot be the unique optial strategy because ixed bundling with prices p i A = pi AB c B and p i B = pi AB c A always does weakly better. This also holds in y odel.

23 19 p i AB. If p i AB < p i A + p i B fir i engages in ixed bundling while if p i AB p i A + p i B fir i practice independent pricing as no consuer would buy the bundle fro fir i. Last, resale by consuers is ipossible. There is a continuu of consuers and without loss of generality we noralize its total ass to 1. Each consuer is described by her location on both circles, x = (x A, x B ) T. Every consuer has a unit deand for both goods and purchases each good independently of the other. So there is no copleentarity between the products. This allows e to focus on the pure strategic effect of bundling. The consuers are uniforly distributed on each circle j. This is ainly for tractability reasons and to copare the results with previous papers. 28 In the next section we give soe structure to the joint distribution and present the odelling of the correlation of reservation values. A consuer who is located at 0 x A, x B 1 2 good B fro fir 2 enjoys an indirect utility of and buys good A fro fir 1 and V (x A, x B ) = K A p 1 A t A (x A ) 2 + K B p 2 B t B ( 1 2 x B) 2. (2.1) A siilar expression holds for consuers who are located soewhere else or buy different products. K A and K B are the surpluses fro consuption (gross of price and transportation cost) of good A and B. p i j is the price of variant i of product j. The transportation cost function is the weighted squared distance between the location of the consuer and the variant produced by the fir where she buys. The weight is the salience coefficient for each product, t j, and without loss of generality we assue that t A > t B > The reservation price of a consuer for variant i of good j, Rj, i is thus K j t j (d i ) 2, where d i is the shortest arc length between the consuer s location and fir i on circle j. It is also assued that K j is sufficiently large such that both arkets are covered. This eans that the reservation values are high enough such that in each price equilibriu all consuers buy both goods. When dealing with welfare considerations this eans that there is no welfare loss due to exclusion of consuers who should 28 For analyses without unifor distributions see Neven (1986), Tabuchi & Thisse (1995) and Anderson, Goeree & Raer (1997). 29 The cases t B t A and t B 0 are analysed in Section 2.4.

24 20 buy the product fro a social point of view. The for of utility in (2.1) looks special but it is the standard for in odels with spatial copetition if consuers can buy any products. 30 The consuers thus have the choice between four alternative consuption cobinations. They can buy the bundle fro fir 1 (AB1), the bundle fro fir 2 (AB2), good A fro fir 1, good B fro fir 2 (A1B2), and good B fro fir 1, good A fro fir 2 (B1A2). 2.3 Dependence between Location and Correlation In the onopoly case the correlation of reservation values is crucial for the incentive to bundle. It is a known result that especially in case of independence or negative correlation bundling doinates unbundled sales. In our case it is possible to infer the joint distribution function of reservation values G(R i A, R i B) for fir i and therefore the correlation between the reservation values fro the joint distribution function of consuer location F (x A, x B ). If for exaple every consuer has the sae location on both circles then the conditional density function of x A given x B is 0 if x A x B f(x A x B ) = 1 if x A = x B. The conditional density function g(ra i RB) i of reservation values for fir i is then 0 if R g(ra i RB) i A i RB i K A K B (t A t B )(d i ) 2 = 1 if RA i RB i = K A K B (t A t B )(d i ) 2. This would iply a reservation price correlation of ρ[r i A, R i B] = 1. This is a siple exaple and there are possibly infinitely any ways how the consuers can be 30 In the literature the assuption of a quadratic transportation cost function is usually ade to guarantee existence of an equilibriu if firs can choose their locations before setting prices (see e.g. D Aspreont et al (1979) and Iren & Thisse (1998)). In y basic odel this assuption is not necessary since firs are axially differentiated and one could also work with a linear transportation cost function. However, in Section 2.6 the odel is extended to allow for location choice of firs. To keep the analysis consistent quadratic transportation costs are assued right fro the beginning.

25 21 distributed on one circle given the location on the other circle. To keep the odel tractable, we have to give soe structure to this conditional distribution, which still captures the ain point of expressing different correlations. This is done in a very siple way. It is assued that if a consuer is located at x A on circle A then she is located at x A + δ if x A + δ 1 x B = x A + δ 1 if x A + δ > 1 on circle B, where 0 δ This eans a δ-shift of all consuers on circle B. So a δ of 0 corresponds to the forer exaple. The advantage of doing this is that with this siple structure correlations of values can be obtained easily by altering δ. Reark 2.1 The function ρ[r A, R B ](δ) = Cov[R A,R B ](δ) σ(r A )σ(r B ) 30δ is given by 1 30δ δ 3 Thus correlation is strictly decreasing in δ. 33 If δ = 0, ρ(δ) = 1, i.e. perfect positive correlation while if δ = 0.5, ρ(δ) = Correlation here relates to the products of one fir. So negative correlation eans that a consuer who values product A fro fir i highly has a low valuation for product B of fir i. Obviously this siple structure has iportant characteristics. First, there is a oneto-one apping between positions on circles. This iplies that there is no stochastic in the odel. Second given the location on circle A the location on circle B is exactly ordered by δ and can not be crisscross. 31 It suffices to consider δ between 0 and 1 2. A δ greater than 1 2 expresses the sae correlation as one between 0 and 1 2. For exaple a δ of 0.8 expresses the sae correlation as a δ of The proof of this and all other results can be found in the appendix of this chapter. 33 The ter correlation does not ean a stochastical correlation in this odel, because there is no stochastic eleent. It describes the relation between known reservation values. So it is a ter fro descriptive statistics. 34 We do not get the whole range of correlation coefficients because distance enters quadratically in the utility function. With a linear transportation cost function the whole range of coefficients could be reached but the results of the analysis would stay the sae.

26 22 However, this structure captures the ain point of correlation. With a low δ, there are any consuers having high reservation values for both goods of fir i. For a high δ, any people have extreely different reservation values for both goods of fir i. So this structure represents exactly what is eant with correlation. Its ain advantage is that it keeps the odel tractable and gives clear cut results. 2.4 Equilibriu Price and Selling Strategies In this section the equilibriu price and selling strategies of a fir conditional on the correlation of values is analysed. Before doing this the equilibriu of the gae without the bundling option is deterined. The result will later be used as a benchark. If bundling is not possible there is no connection between the two products. Each arket is independent and we are in a standard situation of product differentiation on the circle. The Nash equilibriu can be deterined in the usual way. In this equilibriu firs set prices p 1 A = p 2 A = p A = c A t A, p 1 B = p 2 B = p B = c B t B and earn profits Π 1 = Π 2 = 1 8 (t A + t B ). Now assue that bundling is possible. In the following the profit functions of the firs for different correlations are deterined. First, the question arises if firs have an incentive to bundle. Proposition 2.1 If δ > 0, i.e. ρ < 1, then in equilibriu both firs choose ixed bundling. This is in line with the onopoly case. The firs have an additional instruent to sort their custoers and so they will use it. The exception is, if δ = 0, i.e perfect