WORKING PAPERS Col·lecció “DOCUMENTS DE TREBALL DEL DEPARTAMENT D’ECONOMIA” “Endogenous Mergers of Complements with Mixed Bundling” Ricardo Flores Fillol Rafael Moner Colonques Document de treball nº -16- 2010 DEPARTAMENT D’ECONOMIA Facultat de Ciències Econòmiques i Empresarials Edita: Departament d’Economia http://www.fcee.urv.es/departaments/economia/public_html/index.html Universitat Rovira i Virgili Facultat de Ciències Econòmiques i Empresarials Avgda. de la Universitat, 1 432004 Reus Tel. +34 977 759 811 Fax +34 977 300 661 Dirigir comentaris al Departament d’Economia. Dipòsit Legal: T – 1999 - 2010 ISSN 1988 - 0812 DEPARTAMENT D’ECONOMIA Facultat de Ciències Econòmiques i Empresarials Endogenous Mergers of Complements with Mixed Bundling Ricardo Flores-Filloly and Rafael Moner-Colonquesz November 2010 Abstract This paper studies endogenous mergers of complements with mixed bundling, by allowing both for joint and separate consumption. After merger, partner …rms decrease the price of the bundled system. Besides, when markets for individual components are suf…ciently important, partner …rms raise prices of stand-alone products, exploiting their monopoly power in local markets and making substitute ‘ mix-and-match’ composite products less attractive to consumers. Even though these e¤ects favor the pro…tability of mergers, merging is not always an equilibrium outcome. The reason is that outsiders respond by cutting their prices to retain their market share, and mergers can be unprofitable when competition is intense. From a welfare analysis, we observe that the number of mergers observed in equilibrium may be either excessive (when markets for individual components are important) or suboptimal (when markets for individual components are less important). Keywords: complements; merger; mixed bundling; separate consumption JEL classi…cation: L13; L41; D43 We thank Alan W. Beggs, Jan K. Brueckner and Jose J. Sempere-Monerris for their helpful comments and suggestions. We are also thankful to all the comments received during the congress XXXIV Simposio de la Asociación Española de Economía at Valencia (Spain). The authors acknowledge …nancial support from the Spanish Ministry of Education and Science and FEDER (SEJ2007-67891 and SEJ2007-66581), the Spanish Ministry of Science and Innovation (ECO2010-19733, ECO2010-17113 and ECO2010-20584), Generalitat de Catalunya (2009SGR900), Generalitat Valenciana (PROMETEO/2009/068) and Ramón Areces Foundation. y Departament d’ Economia, Universitat Rovira i Virgili, Avinguda de la Universitat 1, 43204 Reus, Spain. Tel.: +34977759851; fax: +34977759810; email: ricardo.‡ ores@urv.cat. z Departament d’ Anàlisi Econòmica and ERI-CES, Universitat de València, Campus del Tarongers, 46022 València, Spain. Tel.: +34963828784; fax: +34963828249; email: rafael.moner@uv.es. 1 Introduction Consumers are often interested in …nal goods that are obtained by combining complementary (compatible) products into systems or bundles, which may be substitutes for one another. A merger involving complementary products can have the bene…cial e¤ect of reducing a vertical negative externality (‘ double marginalization’ since the price of the bundle falls below the ) prices the …rms would choose if acting independently. However, in oligopoly markets, merged …rms may exercise market power through bundling, and this may be a means to foreclose rivals and/or relax price competition. Non-horizontal mergers of this type raise antitrust concerns since the net welfare e¤ect is unclear. This paper addresses the incentives for mergers and its welfare implications in markets with complementary products; the merged …rms can engage in bundling and rivalry from competing di¤erentiated systems is considered. Firms that o¤er a bundle of complementary products may practice mixed bundling: they set the price for the bundle as well as for the individual components, which may be used to form alternative ‘ mix-and-match’systems. Although separate consumption is present in this pricing policy, much of the recent literature has assumed that (complementary) components are valuable only when used together. Consumers purchase computer software and hardware components, cold and pain-relief medications, printers and ink cartridges, cellular telephones and SIM cards, ATM services and credit cards, local and connecting ‡ ights, train and bus services to get to work, contract services with telephone operators (…xed and mobile lines, Internet, etc.), transportation and hotel services, etc. Apart from bundled, these goods are also available to consumers if sold separately in the market place. Accounting both for joint and separate consumption allows us to study endogenous merger formation in a realistic setting where the issue of competition between bundles can be faithfully examined. We set up a simple four-…rm model, where there are two …rms producing a certain product (A1 and A2 ) and two other …rms producing a complementary product (B1 and B2 ). Con- sequently, four di¤erent competing systems of complementary products, which are partially substitutable, can be formed. We further assume that …rms have monopoly power in the market for individual components. A two-stage game is solved where merging decisions are made before …rms compete in prices. Three market structures are analyzed: independent ownership, single integration (one merger is formed) and parallel integration (two mergers are formed). Our main …ndings can be summarized as follows. After merger, partners decrease the price of the bundle. Besides, when markets for individual components are su¢ ciently important, partners raise prices of stand-alone products, exploiting their monopoly power in local markets and making substitute ‘ mix-and-match’ systems less attractive. Even though these e¤ects favor the pro…tability of mergers, merging is not always an equilibrium outcome. The reason is that outsiders respond by cutting their prices to retain their market share, and mergers can be unpro…table when competition is intense. This explains why independent ownership or just one merger can be observed in equilibrium, which is in contrast with the received literature. We also …nd that welfare is highest either under independent ownership (when competition is strong) or under parallel integration (when competition is weak), as in the equilibrium analysis. However, when competition intensity is moderate, social and private interests are not aligned. We may observe either too much integration (‘ overintegration’ or too little inte) gration (‘ underintegration’ depending on the relative importance of markets for individual ), components. When markets for individual components are important, price discrimination is used by merging …rms to exploit the monopoly power they have in these markets by raising prices. Naturally, this can be socially detrimental (‘ overintegration’ In contrast, when mar). kets for individual components are less important, the market-power e¤ect is mitigated and the lower system prices set by partner …rms turn mergers socially pro…table. However, in this case, the lower system price determined by partner …rms puts a downward pressure on rivals’prices and mergers become privately unpro…table when competition is intense (‘ underintegration’ ). 2 Next section relates our research with the existing literature. Section 3 introduces the model presenting the di¤erent market structures. Section 4 provides the subgame perfect equilibrium in merging decisions. The welfare analysis is undertaken in section 5. Some concluding remarks and policy implications close the paper. Proofs are in the Appendix. 2 Related Literature Our paper is related with three sets of literature, which are examined below: i) bundling, ii) network-based airline models, and iii) endogenous mergers of complements. This section provides the relevant context to understand our contribution. There exists an extensive literature on bundling. The practice of bundling is said to be either pure (i.e., technical tying) when only the bundled product is available, or mixed when separate components can also be used to form alternative ‘ mix-and-match’systems. A multiproduct monopolist that faces heterogeneous consumers will engage in (mixed) bundling because it serves as a price discrimination device (Adams and Yellen, 1976, and McAfee, McMillan, and Whinston, 1989). Strategic motivations arise in oligopoly settings and bundling can soften competition and create entry barriers. A robust conclusion is that bundling is an e¤ective tool to disadvantage rival producers (Whinston, 1990, Choi and Stefanidis, 2001, and Nalebu¤, 2004).1 The analysis of several multiproduct …rms that produce di¤erentiated systems is undertaken by Liao and Tauman (2002), who show that an equilibrium exists where …rms o¤er bundle discounts. More recently, Gans and King (2005) discuss when the economic consequences of bundling should be of concern for competition authorities. We contribute to this literature by modeling potential competition between bundles and discerning conditions under which private and social interests are in agreement. An important feature in the received literature is that the goods in the bundle are valuable 3 when consumed together. Although the idea that separate demands have always been part of the mixed bundling story, it seems to have been lost recently. Nevertheless, the research on airline competition di¤erentiates between two types of passengers on spoke-to-hub routes: i) local passengers, who just purchase a direct ‡ ight, and ii) connecting passengers, who purchase a bundle composed by two (or more) complementary ‡ ights (Hendricks et al., 1997 and 1999, Brueckner and Spiller, 1991, and Brueckner, 2001). However, none of these papers focuses on the relative market size of individual components with respect to the markets for systems. In addition, these papers make speci…c assumptions to capture important characteristics of the airline industry (e.g., economies of tra¢ c density, frequency competition, etc.). Some previous research has studied endogenous mergers. Kamien and Zang (1990) …rst formulated a two-stage game where the merger decision is endogenized prior to quantity competition. With perfect complements and price competition, Gaudet and Salant (1992) generalize their model to establish that some socially desirable mergers may fail to occur. Economides and Salop (1992) introduce competition across systems composed of compatible complementary products, and provide an extensive analysis of the e¤ects on prices of alternative (exogenously given) market structures. Beggs (1994) studies endogenous merger formation between two groups of …rms where products within a group are complementary but are substitutes across groups. However, he does not assume full compatibility among components and, the merged …rm engages in pure bundling (or technical tying), thus not making the individual components available separately. Choi (2008), assuming that the merged …rm engages in mixed bundling, builds on Economides and Salop (1992) to …nd cases where an exogenous merger, which is always privately pro…table, is socially detrimental. We further delve into the idea developed by Anderson et al. (2010), where a merger of complements turns out pro…table under some conditions (on the shape of the demand function) in the presence of competition.2 Our model complements and extends these contributions. As in these papers, we consider 4 complementarities that arise from the demand side and cost synergies are assumed away. In addition, we permit consumers to derive utility both from separate purchases of individual components, as well as from their joint purchase. As shall be seen, the results depend on the degree of substitutability among systems and the relative importance of markets for individual components. 3 A model of endogenous mergers with mixed bundling Suppose that there are two di¤erentiated brands of each of two components, A (A1 and A2 ) and B (B1 and B2 ), each o¤ered by an independent …rm, so that there are four …rms. Consumers combine A and B in …xed proportions on a one-to-one basis to form a …nal composite product (or system). Under full compatibility, there are four ways to form a system: A1 B1 , A1 B2 , A2 B1 and A2 B2 . Denote by pi the price of brand Ai and by qj the price of brand Bj , where i; j = 1; 2. The system Ai Bj is available at total price sij = pi + qj . The four systems are equally substitutable. The demand for system A1 B1 , denoted by D11 , decreases with s11 and increases with the prices of the substitute systems, s12 , s21 and s22 . Thus, brand Ai is sold as part of systems Ai B1 and Ai B2 and, similarly, Bj is sold as part of composite products A1 Bj and A2 Bj . We assume linear and symmetric demand functions as follows3 D11 (s11 ; s12 ; s21 ; s22 ) = a D12 (s12 ; s11 ; s21 ; s22 ) = a D (s21 ; s22 ; s11 ; s12 ) = a D22 (s22 ; s21 ; s12 ; s11 ) = a 21 bs11 + c (s12 + s21 + s22 ) , bs12 + c (s11 + s22 + s21 ) , bs21 + c (s22 + s11 + s12 ) , bs22 + c (s21 + s12 + s11 ) , (1) where a; b; c > 0. Further, assume that b > 3c to ensure that composite products are gross substitutes. The demand system in (1) has been employed by Economides and Salop (1992) and Choi (2008). In case the components were not compatible, we would be left with two com5 posite products, i.e., D11 (s11 ; s22 ) = a bs11 + cs22 and D22 (s22 ; s11 ) = a bs22 + cs11 , which is the demand system in Beggs (1994) who considers pure bundling (or technical tying). We follow the approach in Choi (2008) by introducing the possibility of mixed bundling. Thus if, say …rms producing A1 and B1 merge, then the merged entity can o¤er three prices: one for the bundled product A1 B1 , and one for each of the individual components A1 and B1 . Let us also assume that marginal costs of production are zero. Then, parameter a represents the basic level of demand for each composite product if prices were zero; parameter b represents the own-price e¤ect; and parameter c re‡ ects a cross-price e¤ect. The higher c is, the more substitutable the composite products are and thus the stronger competition is. As argued in the Introduction, there are consumers who derive utility from individual consumption of each of the four brands.4 The demand functions are given by5 DA1 = a where 2 (0; 1). Thus, bp1 , DA2 = a bp2 , DB1 = a bq1 , DB2 = a bq2 , (2) measures the relative importance of markets for individual compo- nents with respect to the markets for systems (i.e., the degree of demand asymmetry), and both the demands for joint and for separate consumption are more similar the closer is 1. In other words, to captures the maximum willingness to pay for the individual component can also be seen as a measure of the degree of relative to the composite product, so that complementarity between systems and individual brands.6 Since we focus on the role played by , for the sake of the exposition, we assume components A1 and A2 to be independent (and the same for components B1 and B2 ) and that the parameter re‡ ecting the own-price elasticity of demand of individual components (b) is the same as the one for systems.7 Let us normalize a = b = 1 because the level of the demand intercept (a) has no e¤ect on the relative prices, and the parameters b and c only a¤ect the results through the ratio of b=c. With the assumption of the gross substitutability of composite goods, the normalization of b = 1 implies that c 2 (0; 1=3). Hence, we are left with two parameters: c and . 6 We are interested in solving the following two-stage game. In the …rst stage, …rms A1 and A2 simultaneously and respectively propose to …rms B1 and B2 whether or not to merge. If o¤ered a merger, …rm Bi then simply accepts or rejects (if not o¤ered a merger, then no merger is formed), with i = 1; 2. Since …rms are symmetric, no merger o¤er will be declined and no …rm Ai will fail to o¤er a merger that …rm Bi would accept. Thus, we may have three di¤erent scenarios: independent ownership, single integration and parallel integration. In stage two, given the inherited outcome from the …rst stage, …rms set prices. More speci…cally, under independent ownership (the pre-merger situation), the …rms engage in pure component pricing. The other two scenarios imply that the merged …rm can practice mixed bundling since it can o¤er a price for the bundled product, as well as prices for their individual components. Independent ownership (I) The pro…t functions of the four …rms are given by A1 B1 = p1 (D11 + D12 ) + p1 DA1 , = q1 (D11 + D21 ) + q1 DB1 , A2 B2 A1 = p2 (D21 + D22 ) + p2 DA2 , = q2 (D12 + D22 ) + q2 DB2 . A2 (3) B1 Solving the system of …rst-order conditions @ @ B2 =@p1 = 0, @ =@p2 = 0, @ =@q1 = 0 and =@q2 = 0, we get the following equilibrium prices pI = pI = q I = q I = 1 2 1 2 2+ , 8 14c (4) where superscript I stands for independent ownership. Thus, the total price for each composite product is sij = 2+ , 4 7c for i; j = 1; 2. These equilibrium prices yield (Dij )I = 2+ 8 14c 2 +c(3 4 7c 1) for composite products, and (Dx )I = with x = A1 ; A2 ; B1 ; B2 , for individual brands. It to ensure positive demands for is easy to observe that we need to impose a lower bound on individual brands. This is well discussed below and in the Appendix. Finally, the equilibrium pro…ts to any of the four …rms can then be written as I = (3 2c)(2 + )2 . 4(4 7c)2 7 (5) Single integration (S) Suppose now that …rms A1 and B1 merge and jointly o¤er the bundle A1 B1 . The merged entity engages in mixed bundling so that it chooses the price for the bundled product (s11 ), as well as the prices of the individual brands (p1 and q1 ). Its pro…t is given by A1 B1 = s11 (D11 ) + p1 (D12 ) + q1 (D21 ) + p1 DA1 + q1 DB1 . (6) The pro…ts of the …rms that remain separate (A2 and B2 ) are as under independent ownership. Making the corresponding changes in (1), we can solve the system formed by @ 0, @ A1 B1 A1 B1 =@s11 = =@p1 = 0, @ A1 B1 =@q1 = 0, @ A2 =@p2 = 0 and @ B2 =@q2 = 0. The Nash equilib- rium in prices results in8 S pS = q1 = K [5 + 6 + c(5 1 4 )] , pS = q S = K 7 + 3 + c(2 + ) 2 2 c2 (1 + 4 ) , 3c2 , (7) sS = 3K 9 + 4c(1 + 3 ) 11 2 with K = 27 1 , 36c 31c2 +12c3 where superscript S stands for single integration.9 Finally, equilib- rium pro…ts of the merged …rm and outside …rms are given by h i 11 A = sS (D )S +2pS (D12 )S +(D 1 )S , ( 11 1 A A2 S B2 S 2 S ) =( B ) = (3 2c) pS 2 , (8) S since pS = q1 , pS = q S , (D12 )S = (D21 )S and (D 1 )S = (D 1 )S . 1 2 2 Parallel integration (P) We next consider a double merger scenario where both …rms A1 and B1 , and …rms A2 and B2 merge. Both merged entities engage in mixed bundling so as to maximize pro…ts given by A1 B1 A2 B2 = s11 (D11 ) + p1 (D12 ) + q1 (D21 ) + p1 DA1 + q1 DB1 , = s22 (D ) + p2 (D ) + q2 (D ) + p2 D 8 22 21 12 A2 + q2 D . B2 (9) Given the symmetry of this scenario, it follows that the equilibrium prices for bundled products and individual brands turn out to be pP = pP = q P = q P = Z [2(1 + ) + c(2 1 2 1 2 with Z = 10 1 , 11c 15c2 )] , sP = sP = Z [5 + 3c(1 + 2 )] , 11 22 (10) where superscript P indicates parallel integration.10 Finally, the equilib- rium pro…ts for any pair of merged entities P = sP (D11 )P + 2pP (D12 )P + 2pP (DA1 )P , 11 1 1 (11) with (D11 )P =(D22 )P , (D12 )P =(D21 )P and (DA1 )P =(DB1 )P =(DA2 )P =(DB2 )P . E¤ects of mergers of complements on prices Prior to analyzing the equilibrium in merger formation and the e¤ects on social welfare in the space (c; ), we must impose a lower bound on products. Lemma 1 below identi…es this condition: Lemma 1 For all c 2 (0; 1=3), there exists a function (c) < 1 such that > (c) ensures to ensure positive demands for individual positive demands for individual consumption in all the scenarios under consideration. As a consequence, the following assumption is needed to guarantee comparable results. Assumption 1 We restrict attention to values of c and region in the space (c; ) is depicted in Fig. 1. Insert here Fig. 1 The next proposition summarizes the e¤ects on prices whenever two complementary …rms merge, considering both a move from I to S and a move from S to P . such that > (c). The relevant 9 Proposition 1 For any (c; ) in the relevant region, when two …rms merge i) the price of the post-merger bundle is lower than the sum of the pre-merger prices, ii) the price of outsiders’ system and individual components decreases for move from I to S, and for > 3 (c) > 1 (c) in the in the move from S to P , > 2 (c) iii) the price of partners’ individual components increases for to S, and for > 4 (c) in the move from I in the move from S to P . Fig. 2 below depicts the e¤ect on prices when moving from I to S, and Fig. 3 captures the move from S to P . Insert here Figs. 2 and 3 Interestingly, the same pattern is repeated for both changes in market structure. Proposition 1(i) states that a complementary merger internalizes the externality that arises when …rms set prices independently thus ignoring the e¤ects on their individual markups. This is a well-known result in the literature and explains why the price of the bundle is reduced below the pre-merger situation. For instance, Brueckner (2003) shows that the presence of codesharing and antitrust immunity on an international interline itinerary (that has similar pricing e¤ects as a merger) reduces the fare by 17%-30%. Proposition 1(ii) claims that the lower the price set by one merged entity, the lower the price the outsiders will set when is high enough, as shown in Figs. 2(a) and 3(a). Under pure bundling (as in Beggs (1994)), the decrease in outsiders’prices occurs due to strategic complementarity in prices. The incentive to reduce prices is reinforced under mixed bundling (as in Choi (2008)), and outsiders strategically respond to rivals by cutting their prices to retain their market share. We observe that the need to set lower prices is weaker the lower is the demand for individual components (i.e., the lower is ) because outsiders can take advantage of the lower prices set by partners when pricing their portion of ‘ mix-and-match’ composite products (since the demand only depends on the overall price). 10 Finally, Proposition 1(iii) asserts that the merged …rms increase the price of their standalone components for high, as shown in Figs. 2(b) and 3(b). When markets for individual components are su¢ ciently important, partners raise prices of stand-alone products, exploiting their monopoly power in local markets and making substitute ‘ mix-and-match’systems less attractive to consumers. However, when markets for individual components are less important, partners prefer to decrease prices and make ‘ mix-and-match’systems more competitive. Thus, Proposition 1 states conditions under which the results in Beggs (1994) and Choi (2008) would hold. We can conclude that their results are robust to the introduction of separate consumption as long as the market for individual components is su¢ ciently important relative to the market for systems. These …ndings constitute the cornerstone of the results that follow. 4 Equilibrium analysis In the light of the equilibrium results obtained under the three di¤erent considered scenarios, attention shifts now to the …rst stage of the game where merger decisions are made. Given the symmetry of the model, it su¢ ces to examine the best response for …rms producing A1 and B1 . Let us then de…ne the best-reply functions Hence, 1 (c; 1 (c; )= S I 2 and 2 (c; )= P 2 ( A2 S ) . ) > 0 de…nes when they will merge, given that the rivals do not; and 2 (c; )>0 de…nes when they will merge given that the rivals also merge. The joint analysis of these bestreply functions leads to the following equilibrium result. If neither pair of …rms …nds it pro…table to merge, we will have a market structure with independent ownership (I equilibrium). Parallel integration results when it is pro…table for both pairs of …rms to merge (P equilibrium), and single integration entails just one merger in equilibrium (S equilibrium). Fig. 4 below displays the equilibrium in merging decisions. Insert here Fig. 4 11 tively (see the details in the Appendix). The proposition below speci…es this result. Proposition 2 For any (c; ) in the relevant region, the equilibrium in merging decisions yields i) a unique P equilibrium for c su¢ ciently low, ii) a unique S equilibrium for c intermediate and low, intermediate, high, e Note that e(c) and e(c) are functions obtained from solving 1 = 0 and 2 = 0, respec- iii) a unique I equilibrium for c su¢ ciently large and iv) a multiple equilibrium P and I for c intermediate and in a way made clear by Fig. 4. The above proposition highlights that merging is not always an equilibrium strategy, and that mergers of complements are unpro…table when markets for individual components are su¢ ciently important and competition is intense.11 Looking at the e¤ect of competition intensity (c), there is a positive e¤ect and a negative e¤ect at work when …rms merge. The positive e¤ect comes from partner …rms jointly deciding on the price of the system; this permits to internalize the negative externality arising from the ‘ double marginalization’ existing under independent pricing of complementary components. Thus, if there were no competition from a substitute composite good, then mergers would always turn out pro…table as in Cournot (1838). However, there is a negative cross-price e¤ect coming from the presence of competing systems because a merger typically puts a downward pressure on rivals’ prices. This e¤ect is more important as competition becomes stronger. Therefore, the negative e¤ect o¤sets the positive e¤ect when competition is more intense, turning mergers unpro…table. Beggs (1994) uses the example of shops in a mall selling complementary products that may not be interested in forming a hyperstore when competition is intense. Although …rms would internalize a ‘ double marginalization’ externality allowing them to reduce prices, other competing malls would do the same making pro…ts go down. 12 The e¤ect of the size of the demand for individual components ( ) is not straightforward. However, we observe that incentives towards merger formation are typically high when markets for individual components are not important (i.e., for low values of ). Note that P is the only equilibrium that would be obtained in Choi (2008), where separate consumption is not possible.12 As independent components become more relevant and increases, outsiders be- come more competitive if a merger is formed since their prices decrease. In addition, partners’ prices increase, discouraging the demands for the ‘ mix-and-match’systems, which a¤ects the merged …rms through a lower demand for independent components (see Figs. 2 and 3). Fig. 4 also identi…es the equilibrium in integration decisions obtained in Beggs (1994) and Choi (2008) in the (c, ) space. By Assumption 1 above and looking at the degree of substitutability across systems, we …nd that forming a merger is a dominant strategy when systems are su¢ ciently poor substitutes (i.e., competition is weak), whereas independent ownership arises when system competition is strong. We observe that the equilibrium con…guration obtained in Beggs (1994) can be recovered when 2 ( 3; 4 ). On the other hand, Fig. 4 also displays the equilibrium that would follow in the setting considered by Choi (2008) for 2 ( 1; 2 ), where both mergers take place in equilibrium. Furthermore, in contrast with these previous papers, the possibility of a single merger arises in equilibrium, a result that seems to be sensible in the light of the observed behavior in certain industries. For instance, looking at the airline industry after its deregulation, among the major European carriers, only Air France and KLM merged on 2004. Such asymmetric equilibrium has been obtained without alluding to …rms’asymmetries or demand shocks and without considering internal ‘ governance’costs associated with merger, and it occurs for intermediate values of . Therefore, our setting o¤ers a more parsimonious transition between the two extreme market structures. 13 5 Welfare analysis Choi (2008) constitutes the …rst attempt to provide a welfare analysis of complementary mergers, studying the move from independent ownership to single integration. This section complements his analysis in a setting with separate consumption and extends it to the case with parallel integration. In addition, the comparison between the socially-optimal results and the equilibrium results allows us to identify potential market failures. Choi (2008) concludes that, as c approaches 0, competition across systems vanishes and the ‘ vertical’ positive externality (between complements) stemming from the elimination of the ‘ double marginalization’problem turns mergers welfare enhancing. However, as c increases, a merger becomes socially harmful due to the ‘ horizontal’negative externality coming from the increase of partners’ individual component prices, which yields an increase in the price of the ‘ mix-and-match’systems. Our analysis with individual consumption complements this analysis, con…rming that mergers of complements may be socially detrimental. We denote by W I , W S and W P the social welfare under each market structure, which is computed as the sum of …rm pro…ts and utilities from system and individual components consumption. Let us de…ne solving 1 1 3 = WS W I, 2 = WP W S and 3 = WP W I . From = 0, 2 = 0 and = 0, we can …nd the functions (c), (c) and (c), respectively, which determine the di¤erent regions plotted in Fig. 5 below (details in the Appendix). Insert here Fig. 5 The function (c) delimits the two di¤erent regions appearing in Fig. 5. Proposition 3 below summarizes the e¤ect of complementary mergers on social welfare. Proposition 3 For any (c; ) in the relevant region, mergers are welfare reducing for high values of c together with high values of . Mergers are welfare enhancing for low values of c. 14 On the one hand, we observe that the ‘ vertical’positive externality prevails when in weak competition environments (i.e., c low), regardless of the relative importance of markets for individual components. On the other hand, the ‘ horizontal’ negative externality is more marked and overcomes the previous positive e¤ect when competition is su¢ ciently intense and the markets for systems and for components are rather symmetric (i.e., is high). This result is related to the price behavior commented before since, as shown in Figs. 2 and 3, when two …rms merge, the price of their individual components increases only for high values of , thus making the ‘ horizontal’negative externality more important. Although a priori the result in the proposition above seems to be similar to the one obtained in equilibrium, setting the welfare results against …rms’ equilibrium choices (by comparing Figs. 4 and 5) uncovers a market failure. This is shown in Fig. 6 below Insert here Fig. 6 In the …gure above, we can distinguish three regions where the best outcome from the social viewpoint di¤ers from …rms’equilibrium.13 A con‡ between public and private interict ests may arise when competition intensity is moderate (intermediate values of c). We observe that the number of mergers observed in equilibrium may be either excessive (‘ overintegration’ ) or suboptimal (‘ underintegration’ depending on the relative importance of markets for indi), vidual components. In the upper con‡ region, there is ‘ ict overintegration’since the socially preferred structure is I but the equilibrium leads to P . However, in the other two con‡ ict regions, we observe ‘ underintegration’because P is socially preferred and the equilibrium may be either I or S. This result is summarized in the corollary below. Corollary 1 There is ‘ overintegration’ when the demand for individual components is high. There is ‘ underintegration’when the demand for individual components is low. There are two opposing forces driving this result. On the one hand, market power in15 creases with mergers (‘ horizontal’ negative externality) and partners can price-discriminate and set di¤erent prices to systems and individual components. On the other hand, complementary mergers lead to lower bundle prices because they internalize the externality that arises when …rms set prices independently (‘ vertical’positive externality), as shown in Proposition 1(i). When markets for individual components are important, price discrimination is used by partner …rms to exploit the monopoly power they have in these markets by raising prices. Naturally, this can be socially detrimental. In contrast, when markets for individual components are less important, the market-power e¤ect is mitigated and the lower bundle prices set by partner …rms turn mergers socially pro…table. However, in this case, the lower system price determined by partner …rms puts a downward pressure on rivals’ prices and, when competition is intense, mergers become privately unpro…table. The aforementioned e¤ects are clearly observed in the airline industry. When airlines pricecooperate, either by means of alliances (with antitrust immunity) or mergers,14 they separate passengers into connecting and local. Fares charged to connecting passengers are determined by the competitive characteristics of the interline markets. However, fares charged to local passengers often increase and the overall e¤ect could yield a worse social outcome, depending on the relative size of local and connecting markets (as well as on demand elasticities). 6 Conclusions and policy implications We have developed a model of complementary mergers with mixed bundling, allowing for separate consumption, to identify conditions under which mergers are pro…table for their members, and we have studied the possible discrepancies between private and social interests. Since the foregoing analysis has assumed away the presence of any e¢ ciency gains, one could expect a negative e¤ect of mergers on consumers and society at large, since partners can 16 price-discriminate and market power increases with mergers (‘ horizontal’negative externality). Yet a merger can rationalize production when there are complementary products involved (‘ vertical’positive externality). In this framework, we have analyzed when socially detrimental mergers may occur in equilibrium and when some socially bene…cial mergers may fail to occur. For antitrust authorities, non-horizontal mergers are less likely to signi…cantly impede competition than horizontal mergers.15 However, they may raise antitrust concerns if creating or strengthening a dominant position. In a controversial decision, the European Commission blocked the proposed GE/Honeywell merger (Nalebu¤, 2002) and the primary concern was on ‘ conglomerate e¤ects’of bringing complements together.16 The authorities feared that mixed bundling would restrict competition in the markets for jet aircraft engines and avionics; that rivals could not match the bundle o¤er could lead to foreclosure in the component markets. All in all, a more faithful assessment of the e¤ects on competition requires the consideration of the markets for individual products and rivals’counter-strategies. These are indeed incorporated in the EU non-horizontal merger guidelines (2008, section V on conglomerate mergers).17 Our setting may prove useful as it precisely combines endogenous integration of complements (rivals’response), along with the markets for the bundle and for separate components. We have found that, in line with most of the received literature, a non-horizontal merger pushes rivals’pro…ts down. However, this is not in itself deemed a problem. Rather, the Commission’ s main focus is on the likely harm to consumers. Clearly, consumers that purchase the bundle will face a lower price than before the merger; but those who ‘ mix-and-match’ could be worse , o¤. Consumer surplus indeed diminishes when the cross-price e¤ects are important. Given the symmetry assumptions of our model, compatibility is preferred by …rms and foreclosure issues do not arise. Still, mixed bundling by integrated producers of complementary products can adversely a¤ect consumer and social welfare. The divergence between private and social interests might be resolved by imposing some constraints on …rms’ bundling behavior, e.g., 17 that the bundle discount be …xed to a maximum (behavioral remedies). In June 2007, the Commission prohibited the hostile takeover by Ryanair of Aer Lingus. As is known (and as advanced in the literature review), complementarities play an important role when airlines that join an alliance (or merge) are granted antitrust immunity. At the time of the decision, Ryanair and Aer Lingus competed directly on 35 routes to and from Ireland. On 22 of these routes, customers would have faced a monopoly after the merger (i.e., routes where networks of the two airlines overlap). This aspect gave the merger a horizontal nature and a price regression analysis helped to con…rm these e¤ects. Only recently, the US Department of Justice has cleared the merger between United and Continental Airlines arguing that complementarities prevail. Our analysis emphasizes the role played by the crossprice elasticity of demand across systems (c) and the relative importance of the markets for individual components ( ). Thus, regulators might use econometric demand speci…cations to elicit values for own-price and cross-price elasticities. These values, coupled with relative measures of the market for composite and stand-alone products, can be employed to calibrate the model and obtain an assessment of the (expected) variations in prices. For example, when composite products are su¢ ciently good substitutes (high values of estimated c) and both the composite and individual markets are similar ( rather high), the price of the bundle is close to the sum of the pre-merger prices; mixed bundling is not marked and …rms have no incentive to merge, yet remark that independent ownership is the socially-preferred setting. Interests are also aligned when c is rather low ending up with parallel integration. It is for intermediate values of the estimated c that the authorities need to discourage (high ) or to encourage (low ) integration processes, to have private interests conform to social ones. Future work should introduce more complex network structures and cost considerations in the analysis that would allow for more precise assessments by looking into e¢ ciency justi…cations for mergers of the type herein analyzed. The consideration of asymmetries would make 18 the model suitable to investigate any likely exclusionary behavior, the main theory of harm speci…ed in the legislation regarding non-horizontal mergers. References [1] Adams, W.J. & Yellen, J. (1976). Commodity bundling and the burden of monopoly. Quarterly Journal of Economics, 90, 475-498. [2] Anderson, S.P., Loertscher, S. & Schneider, Y. (2010). The ABC of complementary products mergers. Economics Letters, 106, 212-215. [3] Beggs, A.W. (1994). Mergers and malls. Journal of Industrial Economics, 42, 419-428. [4] Boyer, K.D. (1992). Mergers that harm competitors. Review of Industrial Organization, 7, 191-202. [5] Brueckner, J.K. (2001). The economics of international codesharing: an analysis of airline alliances. International Journal of Industrial Organization, 19, 1475-1498. [6] Brueckner, J.K. (2003). International airfares in the age of alliances: the e¤ects of codesharing and antitrust immunity. The Review of Economics and Statistics, 85, 105-118. [7] Brueckner, J.K. & Spiller, P.T. (1991). Competition and mergers in airline networks. International Journal of Industrial Organization, 9, 323-342. [8] Brueckner, J.K. & Whalen, W.T. (2000). The price e¤ects of international airline alliances. Journal of Law and Economics, 53, 503-545. [9] Choi, J.P. (2008). Mergers with bundling in complementary markets. Journal of Industrial Economics, 56, 553-577. 19 [10] Choi, J.P. & Stefanadis, C. (2001). Tying, investment, and the dynamic leverage theory. RAND Journal of Economics, 32, 52-71. [11] Church, J. & Gandal, N. (2000). Systems competition, vertical merger, and foreclosure. Journal of Economics and Management Strategy, 9, 25-51. [12] Cournot, A. (1838). Recherches sur les principes mathematiques de la theorie des richesses. Paris: Hachette. English translation (N. Bacon, trans.): Research into the mathematical principles of the theory of wealth, Mountain Center, CA. [13] Denicolo, V. (2000). Compatibility and bundling with generalist and specialist …rms. Journal of Industrial Economics, 48, 177-188. [14] Economides, N. & Salop, S. (1992). Competition and integration among complements, and network market structure. Journal of Industrial Economics, 40, 105-123. [15] Gabszewicz, J.J., Sonnac, N. & Wauthy, X. (2001). On price competition with complementary goods. Economics Letters, 70, 431-437. [16] Gans, J. & King S. (2005). Potential anticompetitive e¤ects of bundling. Australian Business Law Review, 33, 29-35. [17] Gaudet, G. & Salant, S. (1992). Mergers of producers of perfect complements competing in price. Economics Letters, 39, 359-364. [18] Hendricks, K., Piccione, M. & Tan, G. (1997). Entry and exit in hub-spoke networks. RAND Journal of Economics, 28, 291-303. [19] Hendricks, K., Piccione, M. & Tan, G. (1999). Equilibria in networks. Econometrica, 67, 1407-1434. 20 [20] Kamien, M. & Zang, I. (1990). The limits of monopolization through acquisition. Quarterly Journal of Economics, 105, 465-500. [21] Liao, C-H. & Tauman, Y. (2002). The role of bundling in price competition. International Journal of Industrial Organization, 20, 365-389. [22] Matutes, C. & Regibeau, P. (1992). Compatibility and bundling of complementary goods in a duopoly. Journal of Industrial Economics, 40, 37-54. [23] McAfee, P., McMillan, J. & Whinston, M.D. (1989). Multiproduct monopoly, commodity bundling, and correlation of value. Quarterly Journal of Economics, 104, 371-384. [24] Nalebu¤, B. (2002). Bundling and the GE-Honeywell merger. Yale School of Management Working Paper #22. [25] Nalebu¤, B. (2004). Bundling as an entry barrier. Quarterly Journal of Economics, 111, 159-187. [26] Neven, D.J. & de la Mano M. (2009). Economics at DG Competition 2008-2009. Review of Industrial Organization, 35, 317-347. [27] Pardo-Garcia, C. (2010). Equilibrium mergers in a composite good industry, ERI-CES Discussion Papers in Economic Behavior 04/10. [28] Whalen, W.T. (2007). A panel data analysis of code-sharing, antitrust immunity, and open skies treaties in international aviation markets. Review of Industrial Organization, 30, 39-61. [29] Whinston, M.D. (1990). Tying, foreclosure and exclusion. American Economic Review, 80, 837-859. 21 Notes 1 The case of bundling with complements has been studied by Matutes and Regibeau (1992), Economides and Salop (1992), Denicolo (2000), and Church and Gandal (2000), among others. 2 A merger with complements typically results in lower pro…ts for …rms outside the merger. Boyer (1992) shows that this can be so even in a horizontal merger between producers of substitute products. 3 This demand structure for di¤erentiated products follows from solving the optimization problem of a representative consumer with a quasi-linear utility function. See Choi (2008) for the details. 4 The consideration of both separate and joint consumption with complementary products in a duopolistic vertical di¤erentiation model is taken up in Gabszewicz et al. (2001). They follow from the optimization problem of a representative consumer with a quadratic quasi-linear P 2 1 utility function of the type U (DA1 ; DA2 ; DB1 ; DB2 ) = x ba Dx 2b Dx + m, where x = A1 ; A2 ; B1 ; B2 and m is the amount of numeraire good. 6 5 An alternative demand speci…cation would be DA1 = (a bp1 ), so that changes in would a¤ect both the intercept and the slope of the demand curve. However, under this modeling speci…cation, we would lose the interpretation of as the relative market size of individual components with respect to the markets for systems, which is useful from an antitrust perspective. 7 8 The case of substitutability between components is discussed in Footnote 11. Non-arbitrage conditions need to hold: i) the price of the bundle has to be greater than the price of the individual components (s11 > p1 ; q1 ), and ii) the price of the bundle has to be smaller than the sum of prices of individual components (s11 < p1 + q1 ). The equilibrium prices in (7) and (10) ful…ll these conditions. h i 2 11 S 9 2) c (23 4 ) , The equilibrium quantities are (D ) = K 27 + 4c(3 2 h i 2 3 12 S 21 S (D ) =(D ) = K 6(5 3 ) + c(36 7) + 2c (17 11) + 3c (1 4 ) , 2 h i 22 S K 2 3 (D ) = 2 2(13 6 ) + c(32 5) + 2c (12 5) + 3c (3 4 ) , (D A1 S ) =(D B1 S ) = K [(5 + 6 ) + c(5 4 )], (D A2 S ) =(D B2 S ) = K[(7 + 3 ) + c(2 + ) 3c ]. As in 2 the I scenario, a lower bound on (D12 )P = (D21 )P = Z 6 is needed to ensure positive demands (details in the Appendix). h i P 2 10 The equilibrium quantities are (D11 ) = (D22 )P = Z 5 c(1 2 ) 2c (2 ) , 4 + 5c2 (2 1) + c(6 1) , (D ) = x P Z [2(1 + ) + c(2 )] with x = A1 ; A2 ; B 1 ; B 2 . As in the previous scenarios, a lower bound on 11 is needed to ensure positive demands (details in the Appendix). The analysis can be extended to consider substitutability between individual components. This setting would sit well with some examples in the airline industry. For instance, passengers may travel from an 22 airport, say Orange County (SNA), to another, say London-Heathrow (LHR), while stopping at a hub, say Chicago O’ Hare (ORD); suppose that each segment of the interline trip is served by two di¤erentiated carriers (e.g., American and United on the route SNA-ORD, and British Airways and British Midland on the route ORD-LHR). We assume that demand functions for individual components A1 and A2 are given by DA1 = a bp1 + cp2 , DA2 = a bp2 + cp1 , and the corresponding functions for B1 and B2 . Thus, local markets are duopolies characterized by the same competition intensity as the market for systems (c). The results remain qualitatively unchanged under this speci…cation (computations available from the authors on request). Furthermore, this modeling would allow us to examine a horizontal merger A1 -A2 . It has been proven that a merger between …rms producing components of the same type is always pro…table to partners and that it leads to higher pro…ts than a merger between complementary components when systems are not too di¤erentiated (Pardo-Garcia, 2010). Nevertheless it must be noted that a horizontal merger of this type would be challenged by antitrust authorities (see the last section of the paper for policy implications). 12 13 Although merger formation is not studied in Choi (2008), the equilibrium can be computed in his setup. e In addition, other con‡ icts could arise in the multiple-equilibria region (i.e., between e(c) and e(c)), but Brueckner (2001), Brueckner and Whalen (2000) and Whalen (2007) analyze the e¤ects of alliances on these cases are not analyzed since there is not a clear equilibrium prediction. 14 airfares and their pro and anticompetitive e¤ects. 15 16 Neven and de la Mano (2009) study some economic analyses used for merger control in recent EU cases. A strand of antitrust law in the EU and the US …nds that mixed bundling can be anticompetitive, absent any merger. See, e.g., i) Bristish Airways v Commission, where discounts to travel agents who used a particular airline were provided, ii) the LePage’ Inc v 3M case on bundling rebates in the Scotch-brand tape, and iii) s the renowned US v Microsoft on bundling Internet Explorer with Windows OS. 17 Concentrations in the EU are evaluated on the basis of Regulation 4064/89, amended by Council Regulation 139/2004. In the US, the ruling is under the 1992 Horizontal Merger Guidelines, later amended in 1997. Price discrimination in the EU is ruled under Art. 82 of the Treaty, while in the US it is judged according to Section 2 of the Clayton Act amended by the Robinson-Patman Act (1936). 23 Figures Figure 1: The relevant region a) E¤ect on outsiders b) E¤ect on partners Figure 2: E¤ect on prices of the move from I to S 24 a) E¤ect on outsiders b) E¤ect on partners Figure 3: E¤ect on prices of the move from S to P Figure 4: Equilibrium analysis 25 Figure 5: Welfare analysis Figure 6: Con‡ between private and public interests ict 26 A Appendix: Proofs Proof of Lemma 1. In our simple model, prices and demand for systems are always positive. Only the demands for individual components (that are given by (2)) could be negative. To ensure that these demands remain positive, under each scenario (i.e., I, S and P ), we require a certain lower bound (c). De…ning i (c) to be higher than < 1 that depends on the degree of substitutability across systems as the upper envelope of all the previous conditions, i.e., (c) = maxf i (c)g < 1 > (c) to remain within the relevant region. > 2 ; 7(1 2c) for i = 1; 2; 3; 4, we just have to require From (Dx )I > 0 with x = A1 ; A2 ; B1 ; B2 we get we get > 5(1+c) ; 21 c[32 c(12c 31)] from (DA1 )S = (DB1 )S > 0 > 7+c(2 3c) ; 24 c[37 c(12c 31)] from (DA2 )S = (DB2 )S > 0 we get > 2(1+c) . 8 5c(2+3c) and from (Dx )P > 0 with x = A1 ; A2 ; B1 ; B2 , we get It is easy to observe that the latter condition is dominated by the previous ones and thus (c) = max which is depicted in Fig. 1. n 2 7(1 ; 2c) 21 5(1+c) 7+c(2 3c) ; c[32 c(12c 31)] 24 c[37 c(12c 31)] o , (A1) The proofs that follow compare prices, pro…ts and welfare under the di¤erent scenarios. Proof of Proposition 1. In the move from I to S, partner …rms A1 and B1 merge, and thus A2 and B2 are the outsiders. Let us de…ne 1 1 = sS 11 I (pI + q1 ), 1 2 = pS 2 pI and 2 3 = pS 1 pI . 1 a < 0 requires > a (c) 3c+c(28 . It can be checked that c 2c[c(119 30c) 27c) 108]+54 < (c) for any (c; ) in the relevant region. Therefore 2 > a I is always observed and thus sS < pI + q1 . 11 1 < 0 requires > 1 (c) 5] 2 31+c[c(5+9c)12c)] . Both c[2+c(17 > 1 (c) and < 1 (c) are possible, and thus both pS < pI and pS > pI can be observed, as shown in Fig. 2(a). 2 2 2 2 3 < 0 requires > 2 (c) 7 2 21 c(3+2c)(7 6c) . c[80 3c(29 4c)] Both > 2 (c) and < 2 (c) are possible, and thus both pS > pI and pS < pI can be observed, as shown in Fig. 2(b). 1 1 1 1 27 In the move from S to P , partner …rms A2 and B2 merge, and thus A1 and B1 are the outsiders. Let us de…ne 4 4 = sP 22 S (pS + q2 ), 2 5 = sP 11 sS , 11 6 = pP 1 pS and 1 b 7 = pP 2 pS . 2 < 0 requires > b (c) 5 3cf5+c[17 c(13+18c)]g . 4fc[52 c(26+3c(13 6c))] 15g It can be checked that < (c) for any (c; ) in the relevant region. Therefore 5 > b S is always observed and thus sP < pS + q2 . 22 2 < 0 requires > c (c) c[41+27c(3+c)] 21 . 12f3 c[7+3c(1 c)]g It can be checked that c < (c) for any (c; ) in the relevant region. Therefore 6 > c is always observed and thus sP < sS . 11 11 Both > 3 (c) < 0 requires > 3 (c) 4 c[17 c(13+24c)] . (1+c)[6 c(19 12c)] and < 3 (c) are possible, and thus both pP < pS and pP > pS can be observed, as shown in Fig. 3(a). 1 1 1 1 7 < 0 requires > 4 (c) 16 c(1 c)[39+c(62+21c)] . 24 2cf38 c[15+c(35 6c)]g Both > 4 (c) and < 4 (c) are possible, and thus both pP > pS and pP < pS can be observed, as shown in Fig. 3(b). 2 2 2 2 Proof of Proposition 2. From 1 = S I 2 , we get H , (7c 4)2 (27 36c 31c2 +12c3 )2 with H = 568 2216c 1367c2 +11320c3 +3886c4 18784c5 9039c6 +2304c7 30096c2 +36104c3 +480c4 36312c5 +6984c6 +2304c7 ) 2 + ( 2136 + 12368c + 2 (4842 From = 34572c + 85180c P 70408c3 23926c4 +54356c5 15600c6 +576c7 ). K , (15c2 +11c 10)2 (27 36c 31c2 +12c3 )2 2 2 ( A2 S ) , we get with K = 489 2018c 2343c2 +11548c3 +16925c4 16590c5 41596c6 18272c7 +4818c8 +3492c9 18868c2 +13280c3 +45864c4 52884c5 54796c6 +17504c7 +9672c8 2 + ( 1872 + 9012c + 2 (6264 The sign of 4032c ) 9 36720c + 52074c and 49810c3 126588c4 17324c5 +88890c6 422c7 16368c8 +3618c9 ). 1 2 depends on the sign of H and K, respectively. Solving H = 0 and K = 0 for , we obtain two roots in each case (the precise values of these roots are available from the authors upon request). Restricting attention to the relevant region, only the positive root is e¤ective in each case (since the negative root is below (c) for any (c; ) in the relevant e region). We denote these positive roots by e(c) and e(c) respectively (see Fig. 4). 28 Proof of Proposition 3. From 1 = WS W I , we get L , 8(4 7c)2 f27+c[c(12c 31)] 36g2 with L = 9984 + ( 144 + 2 (3996 From M= 58104c + 81401c2 +69680c3 134762c4 45440c5 +21297c6 7848c7 19200c + 59568c2 +9112c3 80616c4 31672c5 +3048c6 +9792c7 ) 38592c + 109272c W S , we get 2 86520c3 43348c4 +51112c5 +2064c6 4608c7 ). with 2 = WP M , 8[c(11+15c) 10]2 f27+c[c(12c 31) 36]g2 409404 + 990132c + 1492507c2 3303610c3 2901651c4 +3168368c5 +2700453c6 10867776c + 5964720c2 +32106152c3 352434c7 271953c8 +100008c9 + (2354112 27919912c4 41211920c5 +28154752c6 +26353896c7 7102152c8 4131648c9 +1036800c10 ) + 2 ( 1862784 + 9279072c 6757536c2 26915112c3 +28997808c4 +35155152c5 30400032c6 24845832c7 +7465104c8 +3946752c9 1036800c10 ). From N= = WP W I , we get N , 2(4 7c)2 [c(11+15c) 10]2 3 with 1904 + 5472c + 2462c2 12282c3 918c4 +5442c5 71056c + 101708c2 +59344c3 188852c4 +7248c5 +88200c6 ) 90269c2 41090c3 +171867c4 20952c5 88200c6 ). depends on the sign of L, M and N , respectively. Solving L = 0, + (12912 + 2 ( 10084 + 58172c The sign of 1, 2 and 3 M = 0 and N = 0 for , we obtain two roots in each case (the precise values of these roots are available from the authors upon request). Restricting attention to the roots that are e¤ective in the relevant region, we are left with (c), (c) and (c), which are depicted in Fig. 5. Proof of Corollary 1. Straightforward. 29