Exclusive Contracts with Complementary Inputs

Exclusive Contracts with Complementary Inputs Hiroshi Kitamura Noriaki Matsushima Misato Sato March 14, 2014 Abstract This study constructs a model of anticompetitive exclusive contracts in the presence of complementary inputs. A downstream firm transforms multiple complementary inputs into final products. When complementary input suppliers have market power, the upstream competition in a certain input market benefits not only a downstream firm by lowering the input price but also complementary input suppliers by raising complementary input prices. Thus, the downstream firm cannot earn higher profits even when socially efficient entry is allowed. Hence, the inefficient incumbent supplier can deter socially efficient entry by using exclusive contracts even in the absence of scale economies and downstream competition. JEL classifications code: L12, L41, L42. Keywords: Antitrust policy; Complementary inputs; Exclusive dealing; Multiple inputs. We thank Akifumi Ishihara, Toshihiro Matsumura, Akihiko Nakagawa, Ryoko Oki, Tetsuya Shinkai, Noriyuki Yanagawa, and seminar participants at Kwansei Gakuin University, Kyoto University, and Osaka University for helpful discussions and comments. We gratefully acknowledge financial support from JSPS Grant-in-Aid for Scientific Research (A) No. 22243022, for Scientific Research (C) No. 24530248, and for Young Scientists (B) No. 24730220. The usual disclaimer applies. Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto, Kyoto 603-8555, Japan. Email: hiroshikitamura@cc.kyoto-su.ac.jp Institute of Social and Economic Research, Osaka University 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. Email: nmatsush@ieser.osaka-u.ac.jp Department of Economics, The George Washington University, 2115 G street, NW Monroe Hall 340 Washington DC 20052, USA. Email: smisato@gwmail.gwu.edu

1 Introduction In vertical relationships, firms often engage in contracts concerned with vertical restraints. Contractual provisions of vertical restraints consist of various terms including exclusive contracts, loyalty rebates, slotting fees, resale price maintenance, quantity fixing, and tie-ins. 1 Among vertical restraints, exclusive contracts have long been controversial. 2 Once signed, exclusive contracts deter efficient entrants, and thus they seem to be anticompetitive. However, the Chicago School opposes this view by providing the model analysis that rational economic agents do not sign a contract to deter a more efficient entrant (Posner, 1976; Bork, 1978). 3 In rebuttal of the Chicago School argument, post-chicago economists indicate specific circumstances under which anticompetitive exclusive dealings occur. 4 Their studies, by extending the single-buyer model of the Chicago School argument to a multiple-buyer model, introduce scale economies wherein the entrant needs a certain number of buyers to cover its fixed costs (Rasmusen, Ramseyer, and Wiley, 1991; Segal and Whinston, 2000a) and the competition between buyers (Simpson and Wickelgren, 2007; Abito and Wright, 2008). This study provides another economic environment under which anticompetitive exclusive dealings occur by focusing on the existence of complementary inputs. In a real business situation, final good producers usually transform multiple inputs into final products. More importantly, there may exist a complementary input supplier with market power. For example, in the Intel antitrust case, there exists Microsoft which has strong market power. 5 Therefore, when we apply the analysis of anticompetitive exclusive dealings to the real-world situation, the interaction between complementary input suppliers could not be neglected. 1 See, for example, Rey and Tirole (1986), Rey and Vergé (2010), and Asker and Bar-Issac (2014). See also Rey and Tirole (2007) and Rey and Vergé (2008) for surveys of vertical restraints. 2 Exclusive dealing agreements take various forms such as exclusive territories and exclusive rights (see, for instance, Mathewson and Winter (1984), Rey and Stiglitz (1995), and Matsumura (2003)). 3 For the impact of the Chicago School argument on antitrust policies, see Motta (2004) and Whinston (2006). 4 In an early contribution, Aghion and Bolton (1987) propose a model where exclusion does not always occur. However, when it does, it is anticompetitive. See also a study by Bernheim and Whinston (1998), which explores the market circumstances under which an exclusive contract can exclude rival incumbents. 5 See Japan Fair Trade Commission (2005): http://www.jftc.go.jp/eacpf/cases/intel.pdf, the European Commission (2009): http://ec.europa.eu/competition/sectors/ict/intel.html. See also Gans (2013). 1

In this study, we develop a model of anticompetitive exclusive dealings in the presence of complementary inputs. In our model, an upstream incumbent supplier offers an exclusive contract to a single downstream firm to deter an entrant supplier that is more efficient than the incumbent supplier. Because no scale economies and no downstream competition exist, the incumbent supplier cannot deter socially efficient entry by using exclusive contracts in the framework of previous studies. The new dimension here is that the downstream firm produces a final product by using not only an input produced by the incumbent supplier but also a complementary input produced by a supplier that has market power. In the simple setting under linear demand and linear pricing, we first show that the existence of a complementary input supplier with market power allows the incumbent supplier to deter socially efficient entry by using exclusive contracts even in the case of a single downstream firm. To understand this result, consider the role of socially efficient entry. Socially efficient entry into one input market generates the input market competition, which reduces the input price and allows the downstream firm to earn higher profits. The Chicago School points out that this effect prevents the incumbent supplier from profitably compensating the downstream firm and concludes that exclusion is impossible. However, when a complementary input supplier that has market power exists, socially efficient entry into one input market increases the complementary input demand, which benefits the complementary input supplier by increasing the complementary input price. Hence, compared with the case in the absence of a complementary input supplier that has market power, socially efficient entry leads to a smaller increase in the downstream firm s profits. This allows the incumbent supplier to profitably compensate the downstream firm, and therefore exclusion is possible. We also check the robustness of the above exclusion outcome, and show that the exclusion outcome can be observed in more general setting. First, introducing non-linear demand, we show that the exclusion outcome arises as long as the demand curve for final products is not too convex; that is, exclusion is more likely to be observed in inelastic demand. Furthermore, introducing non-linear pricing and general demand function, a unique exclusion equilibrium occurs. Therefore, the exclusion outcome here can be widely applied to various vertical 2

relationships in the real-world situation. This study is related to the literature on anticompetitive exclusive contracts. 6 Although previous studies have similar motivations to indicate specific circumstances under which firms sign exclusive contracts for an anticompetitive purpose none of these studies consider the existence of complementary inputs. Fumagalli and Motta (2006) propose an extension of the model framed by Rasmusen, Ramseyer, and Wiley (1991) and Segal and Whinston (2000a) where buyers are competing firms. 7 They show that intense downstream competition reduces the possibility of exclusion. However, Simpson and Wickelgren (2007) and Abito and Wright (2008) point out that this result depends on the assumption that buyers are undifferentiated Bertrand competitors who need to incur epsilon participation fees to stay active. They show that if buyers are differentiated Bertrand competitors, then intense downstream competition enhances exclusion even in the presence of epsilon participation fees. 8 Wright (2008) and Argenton (2010) explore extended models of exclusion with downstream competition where the incumbent and a potential entrant produce horizontally and vertically, respectively, differentiated products. 9 These studies have a common feature that exclusion results require 6 Certain studies examine procompetitive exclusive dealings. Marvel (1982), Besanko and Perry (1993), Segal and Whinston (2000b), de Meza and Selvaggi (2007), and de Fontenay, Gans, and Groves (2010) investigate the role of exclusive dealing in encouraging non-contractible investments. Chen and Sappington (2011) study the impact of exclusive contracts on industry R&D and welfare. In addition, Argenton and Willems (2012) study the trade-off between the positive effect (risk sharing) and the negative effect (exclusion) of exclusive contracts. Calzolari and Denicolò (2013) explore the procompetitive effects of exclusive contracts in an adverse selection model where differentiated firms compete in nonlinear prices. Another motivation to consider exclusive dealing is to solve the commitment problem of Hart and Tirole (1990), which arises when a single upstream firm sells to multiple retailers with two-part tariffs under unobservable contracts. See also O Brien and Shaffer (1992), McAfee and Schwartz (1994), and Rey and Vergé (2004). 7 Fumagalli and Motta (2008) also show that exclusion with scale economies arises because of coordination failure among buyers even when the incumbent does not have a first-mover advantage in making exclusive offers. Doganoglu and Wright (2010) explore exclusion in the presence of network externalities. Furthermore, economists have recently analyzed exclusion with scale economies from an experimental perspective (Landeo and Spier, 2009, 2012; Smith, 2011; Boone, Müller, and Suetens, 2014). 8 See also Wright s (2009) study, which corrects the result of Fumagalli and Motta (2006) in the case of two-part tariffs. 9 Kitamura (2010, 2011) also explores the extended model first, in the presence of multiple entrants, and next, in the presence of financial constraints. Johnson (2012) extends the models in the presence of adverse selection. DeGraba (2013) extends the models where a small rival that is more efficient at serving some portion of the market can make exclusive offers. Comanor and Rey (2000), Oki and Yanagawa (2011), and Kitamura, 3

multiple downstream buyers, while this study shows that anticompetitive exclusive contracts are signed even under a single-buyer model. In terms of a single-buyer model of anticompetitive exclusive contracts, this study is closest to Fumagalli, Motta, and Rønde (2012) who explore a model where exclusive dealing can both promote relationship-specific investment and foreclose a more efficient supplier. 10 They show that if we consider the possiblity of relationship-specific investment, inefficient market foreclosure occurs even in the single-buyer model because the investment promotion effect of exclusive dealing increases the joint surplus between the incumbent seller and the downstream buyer under exclusive dealing. By contrast, exclusion in this study arises because the existence of complementary inputs decreases the downstream firm s profits when socially efficient entry occurs. This study is also related to the literature on vertical relations with complementary inputs. Recently, Laussel (2008), Matsushima and Mizuno (2012, 2013), and Reisinger and Tarantino (2013) explore vertical integration with complementary inputs. 11 These studies point out that vertical integration is not necessarily profitable because a complementary input supplier extracts most part of profits generated by the elimination of double marginalization through vertical integration. This study shows that these ideas can be applied to the literature on the entry deterrence by using exclusive contracts. The remainder of this paper is organized as follows. Section 2 constructs the model. Section 3 introduces the analysis under linear wholesale pricing. Section 4 provides the analysis under non-linear pricing. Section 5 extends the model to multiple incumbents. Section 6 provides some concluding remarks. Appendices include some proofs. Matsushima, and Sato (2013) explore the case where exclusive contracts deter downstream entry. These studies show that the resulting exclusive dealings are anticompetitive. These studies show that the resulting exclusive dealings are anticompetitive. In contrast, Gratz and Reisinger (2013) show that exclusive contracts can possibly have procompetitive effects, if downstream firms compete imperfectly and contract breaches are possible. 10 See also Kitamura, Sato, and Arai (forthcoming), who also show that anticompetitive exclusion is possible in the case of a single buyer when the incumbent can establish a direct retailer. 11 See also Arya and Mittendorf (2007) and Laussel and Long (2012). 4

2 Model This section develops the basic environment of the model. We first explain the basic characteristics of players and the timing of the game in Section 2.1. Then, we introduce the design of anticompetitive exclusive contracts to deter socially efficient entry in Section 2.2. 2.1 Basic environment The upstream market is composed of two complementary input markets A and B (See Figure 1). The input A is exclusively produced by a supplier U A with a constant marginal cost c > 0. In contrast, the input B is produced by an incumbent supplier U B and an entrant supplier U EB. Incumbent supplier U B produces input B with a constant marginal cost c > 0. Following the previous literature, incumbent supplier U B and entrant supplier U EB produce an identical product but with differing cost efficiencies; namely, entrant supplier U EB is more efficient than incumbent supplier, with a constant marginal cost 0 c E < c. The downstream market is composed of a single firm. This modeling strategy clarifies the role of a complementary input supplier that has market power; that is, exclusion of socially efficient entry occurs even in the absence of scale economies and downstream competition, both of which require more than two downstream firms. A downstream monopolist D transforms inputs A and B into a final product. We assume that the inverse demand for the final product P(Q) is given by a simple linear function: P(Q) = a bq, (1) where Q is the output of the final product supplied by downstream monopolist D and where a > 2(2c c E ) and b > 0. 12 Downstream monopolist D uses Leontief production technology; that is, one unit of final product is made with one unit of of input A and one unit of input B: 13 Q = min{q A, q B }, (2) 12 The first inequality implies that entrant supplier U EB s monopoly price is higher than c. Exclusion will still exist, even when entrant supplier U EB is more efficient, but the analysis becomes more complicated. 13 Introducing asymmetric production technology where one unit of final product is made with m > 0 unit of of input A and k > 0 unit of input B does not change the results qualitatively. 5

where q i is the amount of input i {A, B}. Equation (2) implies that those inputs are essential to produce a final product in a downstream market, which implies that those are perfect complements. 14 The payment for q i units of input i {A, B} is given as w i q i, where w i is per unit price of input i. To simplify the analysis, we assume that downstream monopolist D does not incur any production cost except the payments for the two inputs. Thus, per unit production cost of downstream monopolist D is given as c D = w A + w B. The timing of the game is as follows (See Figure 2). Following the previous studies, the model contains 4 stages. In Stage 1, incumbent supplier U B makes the exclusive offer to downstream monopolist D with fixed compensation x 0. Downstream monopolist D decides whether to accepts the offer. 15 In Stage 2, entrant supplier U EB decides whether to enter input B market. We assume that the fixed cost of entry is sufficiently small so that entrant supplier U EB can earn positive profits. In Stage 3, active suppliers offer linear input prices to downstream monopolist D. (In Section 4, we introduce non-linear wholesale pricing.) We assume that if entrant supplier U EB enters input B market, incumbent supplier U B and entrant supplier U EB become homogeneous Bertrand competitors. The equilibrium price of input i {A, B} when downstream monopolist D accepts (rejects) the exclusive offer is denoted by w a i (w r i ) where the superscript a ( r ) indicates that the exclusive offer is accepted (rejected). In Stage 4, downstream monopolist D orders inputs and sells the final product to final consumers. Supplier U i s profit in the case where downstream monopolist D accepts (rejects) the exclusive offer is denoted by π a i (π r i ), where i {A, B, E B}. By contrast, downstream monopolist D s profit in the case when it accepts (rejects) the exclusive offer is denoted by π a D (π r D ). 14 This production technology can be widely observed in manufacturing industries. For example, to produce PC, we need CPU and operation systems and to produce car, we need body and tires. 15 Rasmusen, Ramseyer, and Wiley (1991) and Segal and Whinston (2000a) point out that price commitments are unlikely if the nature of the product is not precisely described in advance. In the naked exclusion literature, it is known that if the incumbent can commit to wholesale prices, then anticompetitive exclusive dealings are enhanced. See Yong (1999) and Appendix B in Fumagalli and Motta (2006). 6

2.2 Design of exclusive contracts For the existence of an exclusion equilibrium, the equilibrium transfer x needs to satisfy the following two conditions. First, it has to satisfy individual rationality for incumbent supplier U B ; that is, incumbent supplier U B earns higher profits under exclusive dealing, i.e.: π a B x π r B. (3) Second, the exclusive contract has to satisfy individual rationality for downstream monopolist D; that is, the amount of compensation x induces downstream monopolist D to accept the exclusive offer, i.e.: π a D + x π r D. (4) From the above conditions, it is easy to see that an exclusion equilibrium exists if and only if inequalities (3) and (4) hold simultaneously. This is equivalent to the following conditions: π a B + πa D πr B + π r D. (5) Condition (5) implies that for the existence of anticompetitive exclusive contracts, we need to examine whether exclusive contracts increase the joint profits between downstream monopolist D and incumbent supplier U B. 3 Linear wholesale pricing This section analyzes the existence of anticompetitive exclusive contracts under linear wholesale pricing. To easily understand the importance that a complementary input supplier has market power, we first discuss a benchmark case where complementary input A is competitively provided in Section 3.1. We then explore the case where complementary input A is supplied by a monopolistic supplier in Section 3.2. Finally, consider an extended model where the inverse demand function is non-linear in Section 3.3. 7

3.1 Benchmark: When complementary input is competitively supplied Assume that complementary input A is competitively provided. Then, the price of complementary input A does not depend on whether the exclusive offer is accepted in Stage 1; i.e., w a A = wr A = c. In this setting, the model of the Chicago School argument can be interpreted as the special case where downstream monopolist D can purchase complementary input A for free; i.e., w a A = wr A = 0.16 Therefore, as the Chicago School argues, incumbent supplier U B cannot deter socially efficient entry. Proposition 1. Suppose that the inverse demand is a linear function and upstream suppliers adapt linear wholesale pricing. When complementary input A is competitively provided, incumbent supplier U B cannot deter socially efficient entry by using exclusive contracts. The result here can be explained by a similar logic as in the Chicago School argument. When downstream monopolist D accepts the exclusive offer in Stage 1, it purchases input B from incumbent supplier U B at higher input price, which allows incumbent supplier U B to earn monopoly profits. However, under linear wholesale pricing, incumbent supplier U B and downstream monopolist D cannot maximize the joint profits because of double marginalization problem. Thus, the left-hand side of inequality (5) is considerably small. In contrast, when downstream monopolist D rejects the exclusive offer in Stage 1, entrant supplier U EB enters input B market in Stage 2. In Stage 3, suppliers U B and U EB compete to deal with downstream monopolist D. Compared with the case of exclusive dealing, upstream competition in input B market reduces input B s price, which solves the double marginalization problem. Thus, downstream monopolist D earns considerably large rejection profits; that is, the right-hand side of inequality (5) becomes large. In the absence of scale economies and downstream competition, incumbent supplier U B cannot compensate downstream monopolist D profitably, which implies that there is no x which satisfies participation constraints (3) and (4) simultaneously. Therefore, when downstream market consists of a monopolist, 16 Although in the model of the Chicago School, a buyer is a final consumer, the results does not qualitatively change even when we assume that the buyer is a downstream monopolist. See Lemma 1 of Kitamura, Sato, and Arai (forthcoming). 8

anticompetitive exclusive dealing cannot occur if complementary input A is competitively supplied. 3.2 When complementary input is provided by a monopolist We now assume that complementary input A is exclusively provided by complementary input supplier U A. Input A s price now depends on whether entry into input B market occurs although it does not in the previous subsection. Like the case where complementary input A is provided competitively, entry into input B market generates the competition in input B market, which reduces input B s price. To understand the pricing behavior of complementary input supplier U A when input B price decreases, we first examine the relation between entry into input B market and input A s price. The following lemma summarizes the relation: Lemma 1. When complementary input supplier U A has market power, socially efficient entry into input B market raises the equilibrium price of input A; that is, w r A > wa A. To understand this result, consider the reaction function of supplier U i given input j s price w j ; w i (w j ) = a + c w j, 2b where i, j {A, B} and i j. It is easy to see that the strategic interaction between two of the upstream firms is strategic substitute; that is, raising input A s price is the best response for complementary input supplier U A when the price of input B decreases. 17 Therefore, entry into input B market induces complementary input supplier U A to raise input A s price and to enjoy higher profits. The following proposition shows that this relation between entry into input B market and input A s price allows incumbent supplier U B to deter efficient entry by using exclusive contracts: 17 If inputs A and B were substitute, the reduction of input B s price would decrease the demand of input A, and thus supplier U A would be required to reduce input A s price. In contrast, if inputs A and B are complement, the reduction of input B s price increases the demand of input A. 9

Proposition 2. Suppose that the inverse demand is a linear function and upstream suppliers adapt linear wholesale pricing. If complementary input supplier U A is the monopolist for input A, incumbent supplier U B can deter socially efficient entry by using exclusive contracts. Note that the crucial difference from the benchmark case exists in the subgame where downstream monopolist D rejects the exclusive offer. Like the case where complementary input A is competitively supplied, entry into the input B market generates the upstream competition in this market, which benefits downstream monopolist D. However, Lemma 1 implies that entry into this market also benefits complementary input supplier U A by increasing the price of input A, which prevents downstream monopolist D from earning considerably large profits when it rejects the exclusive offer; that is, the right-hand side of inequality (5) does not becomes large enough. This allows incumbent supplier U B to profitably compensate downstream monopolist D by using its profit under exclusive dealing. Therefore, the existence of complementary supplier that has market power leads to anticompetitive exclusive dealing even in the absence of scale economies and downstream competition. 3.3 Non-linear demand We have assumed that the inverse demand function is linear. We now extend the analysis in Section 3.2 to the case where the inverse demand function is non-linear: P(Q) = a bq α. (6) We assume that α > 0 so that the second-order conditions of firms are satisfied. By comparing equations (1) and (6), it is easy to see that the linear demand in the previous subsections is the special case where α = 1. The price elasticity of demand is given by dq/q dp/p = p α(a p). (7) Equations (6) and (7) imply that as α increases (decreases), the demand curve becomes concave (convex) or inelastic (elastic). The following proposition shows that the likelihood of exclusion depends on the shape of demand curve. 10

Proposition 3. Suppose that upstream suppliers adapt linear wholesale pricing. If complementary input supplier U A is the monopolist for input A, exclusion is a unique equilibrium outcome as long as the final product demand is not too convex, α α 0.40692. The result here provides an important implication that exclusion is more likely to be observed for inelastic demand. The curvature of inverse demand influences the degree of demand-expansion when socially efficient entry occurs. When the inverse demand is concave (α > 1), the demand-expansion effect of a new upstream entry is weak and thus socially efficient entry does not lead to a large increase in downstream monopolist D s profits, which allows incumbent supplier U B to profitably compensate downstream monopolist D. However, as the inverse demand becomes convex, the demand-expansion effect becomes significant; in other words, the double marginalization problem is more serious for the convex inverse demand. This leads to a large increase in downstream monopolist D s profits and prevents incumbent supplier U B from profitably compensating downstream monopolist D. 3.4 When complementary input market consists of multiple firms Thus far, we have assumed that complementary input supplier U A is a monopolist. We now extend the analysis in Section 3.2 to the general case where complementary input A is produced by multiple firms. In this subsection, we assume that input A is produced by not only complementary input supplier U A but also an inefficient supplier U EA that is less efficient than complementary input supplier U A ; that is, U EA s marginal cost is d A > c. The timing of game in this subsection is as follows. In contrast to 3.2, in Stage 1, not only incumbent supplier U B but also complementary input supplier U A make the exclusive offers to downstream monopolist D with fixed compensation x i 0, where i {A, B}. Downstream monopolist D decides whether to accept the offers and its decision is denoted by jk {aa, ar, ra, rr}. For instance, the superscript ar indicates that downstream monopolist D accepts the offer by complementary input supplier U A but rejects the offer by incumbent supplier U B. In Stage 2, entrant supplier U Ei decides whether to enter input i market. We assume that the fixed cost of entry is zero so that entrant supplier U Ei can enter input i mar- 11

ket whenever the exclusive offer by U i is rejected. 18 In Stage 3, active suppliers offer linear input prices to downstream monopolist D. We assume that if entrant supplier U Ei enters input i market, incumbent supplier U i and entrant supplier U Ei become homogeneous Bertrand competitors. In Stage 4, downstream monopolist D orders inputs and sells the final product to final consumers. Supplier U i s profit in Case jk is denoted by π jk i downstream monopolist D s profit in Case jk is denoted by π jk D (π jk D ). (π jk i ). By contrast, There are three possibilities that at least one exclusive contract is achieved: (i) Case aa occurs; (ii) Case ar occurs; (iii) Case ra occurs. For the existence of each exclusion equilibrium, the equilibrium transfer x i needs to satisfy the following conditions: (i) Case aa occurs if and only if π aa D + x A + x B π ar D + x A, π aa D + x A + x B π ra D + x B, π aa D + x A + x B π rr D, π aa A x A π ra A, π aa B x B π ar B. (8) (ii) Case ar occurs if and only if π ar D + x A π aa D + x A + x B, π ar D + x A π ra D + x B, π ar D + x A π rr D, π ar A x A π rr A, π ar B πaa B x B. (9) 18 If the fixed cost of entry is positive, inefficient entrant supplier U EA does not enter input A market because it anticipates zero operating profits and cannot cover the fixed cost. It may be harder to justify this assumption. However, even when inefficient entrant supplier U EA needs to incur the fixed cost, it would enter. For example, there is some upstream differentiation in input A market. Alternatively, inefficient entrant supplier U EA is an established firm that is already operating in other industries and can make input price offers before they incur fixed cost. 12

(iii) Case ra occurs if and only if π ra D + x B π aa D + x A + x B, π ra D + x B π ar D + x A, π ra D + x B π rr D, π ra A πaa A x A, π ra B x B π rr B. (10) The following proposition shows that the likelihood of exclusion in input B market depends on inefficient entrant supplier U EA s efficiency level. Proposition 4. Suppose that complementary input A is produced by complementary input supplier U A and inefficient entrant supplier U EA. Incumbent supplier U B can deter socially efficient entry by using exclusive contracts if the efficiency difference between suppliers of input A is sufficiently large, that is, d A d A where d A = a c a 2c 3 > c. Furthermore, there are two types of exclusion equilibria; (i) downstream monopolist D accepts both exclusive offers; Case aa occurs, or (ii) it only accepts the exclusive offer from supplier U B ; Case ra occurs. Complementary input supplier U A is indifferent between both equilibria; that is, it always offers x A = 0 in both types of exclusion equilibria. The results here fill the gap between Propositions 1 and 2 and conform the significance of complementary input supplier U A s ability to control its input price. When inefficient supplier U EA s efficiency is high (that is, d A is close to c), the existences of both inefficient entrant supplier U EA and incumbent supplier U B work as constraints on the pricing of complementary input supplier U A and inefficient entrant supplier U EB if entries occur in both markets. In this environment, downstream monopolist D prefers entries into both input markets because it becomes the sole firm to obtain benefits from the competitions in both input markets. By contrast, when inefficient input supplier U EA becomes sufficiently inefficient (that is, d A > 13

(a+c)/3), the existence of inefficient entrant supplier U EA does not always work as a constraint on the pricing of complementary input supplier U A even if entry into input A market occurs. In this case, input A s price depends on how entry into input B market decreases input B s price. As we have pointed in Section 3.2, the monopoly power of complementary input supplier U A weakens downstream monopolist D s profitability in which entry into input B market occurs, inducing downstream monopolist D and incumbent supplier U B to sign an exclusionary contract. By interpreting results here, we can obtain an important policy implication for antitrust agencies; an increase in the cost efficiency of a dominant input supplier may facilitate anticompetitive exclusive contracts in complementary input markets. As the dominant input supplier becomes efficient, industry output usually increase, which is socially efficient. However, if we consider the possibility of exclusive contracts in complementary input markets, the dominant input supplier s efficiency increase may trigger exclusion outcomes in complementary input markets, which is socially inefficient. Therefore, for the discussion of real-world exclusive contracts, antitrust agencies should pay attention to not only the market structure where exclusive contracts are signed but also the change of complementary input market structures. 4 Non-linear wholesale pricing In this section, we extend the model analysis in Section 3.2 to the case where upstream suppliers use non-linear contracts. Under non-linear pricing, the double marginalization problem is avoidable, and the joint profit is maximized within the available technology of firms. For notational convenience, we define Π (z) as follows: Π (z) max(p z c)q(p), p where z 0, and where Q(p) is a general demand function. Π (z) can be interpreted as the maximum value of the joint profits when input B is supplied with marginal cost z. When entry does not occur (occurs), we have z = c (z = c E ). Hence, the difference between Π (c E ) 14

and Π (c) depends on the efficiency level of entrant supplier U EB. To simplify the analysis, we assume that Π (z) is continuous and strictly decreasing in z. The rest of this section is organized as follows. In Section 4.1, we explore the case where upstream firms adapt simple two-part tariffs and make take-it-or-leave-it offers. In Section 4.2, we explore the existence of anticompetitive exclusive contracts by introducing the Shapley value bargaining, one of general allocation rules. 4.1 Two-part tariffs with take-it-or-leave-it offers Assume that upstream suppliers adapt two-part tariffs (w i, F i ), where F i is fixed fee offered by supplier U i, where i {A, B, E B }. We also assume that upstream suppliers have all bargaining power toward downstream monopolist D and make take-it-or-leave-it offers. We first consider the case where the exclusive offer is accepted in Stage 1. In the equilibrium, there are multiple equilibria where complementary input supplier U A and incumbent supplier U B respectively offer (c, FA a) and (c, Fa B ) such that Fa A + Fa B = Π (c). The equilibrium profits of firms before compensation are 0 π a A Π (c), 0 π a B Π (c), π a D = 0, where π a A + πa B = Π (c). Multiple equilibria consist of any F a B 0 and Fa A 0 such that FA a + Fa B = Π (c). We next consider the case where the exclusive offer is rejected in Stage 1. In Stage 2, entrant supplier U EB enters input B market. In Stage 3, incumbent supplier U B offers its best term (c, 0), and entrant supplier U EB matches this to attract downstream monopolist D. Therefore, downstream monopolist D and complementary input supplier U A earn exactly same profits as if downstream monopolist D dealt with incumbent supplier U B. Complementary input supplier U A offers (c, Π (c)). The equilibrium profits of firms are π r A = Π (c), π r B = π r D = 0, π r E B = Π (c E ) Π (c). Finally, we check the existence of exclusion. Because we have π a B + πa D (πr B + πr D ) 0 with equality for π a B = 0, inequality (5) always holds. Therefore, exclusion always becomes 15

an equilibrium outcome. Proposition 5. Suppose that upstream suppliers adapt two-part tariffs and make take-it-orleave-it offers. If complementary input supplier U A has market power, there exists a unique exclusion equilibrium. The analysis here has several problems. First, there exist multiple equilibria in Stage 3 as pointed out above. Second, there is another problem that the profit allocation is not consistent with the case of linear pricing. When complementary input suppliers adapt two-part tariffs, downstream monopolist D earns zero operating profits regardless of its decision in Stage 1. Hence, the main intuition of the Chicago School argument, the downstream buyer can enjoy a considerably large surplus, cannot be applied. In the next subsection, we provide the profit allocation rule which leads to a unique Stage 3 equilibrium outcome and downstream monopolist D can enjoy a larger surplus when entry occurs. 4.2 Shapley value bargaining In this subsection, we consider the existence of anticompetitive exclusive dealing by introducing the Shapley value bargaining, which is one of the reasonable allocation rules. 19 The set of independently negotiating groups, denoted by Ψ, depends on downstream monopolist D s decision in Stage 1. If downstream monopolist D accepts the exclusive offer in Stage 1, we have Ψ a = {U A, U B, D}. By contrast, if downstream monopolist D rejects the exclusive offer in Stage 1, we have Ψ r = {U A, U B, U EB, D}. According to the Sharply value, the payoff of firm ψ Ψ is given by ψ Ψ, Ψ Ψ ( Ψ 1)!( Ψ Ψ )! Ψ! [ W Ψ W Ψ\{ψ} ], (11) where Ψ and Ψ denote the number of elements in these sets and where W Ψ W Ψ\{ψ} is the degree of decrease in joint profits when firm ψ exits from group Ψ which is a subset of Ψ. 19 For the application to the industrial organization literature where industry profits are distributed according to the Shapley value, see Inderst and Wey (2003) and de Fontenay and Gans (forthcoming). 16

We first consider the case where the exclusive offer is accepted in Stage 1. The equilibrium profits of firms before compensation are 20 π a A = πa B = πa D = Π (c) 3. (12) We next consider the case where the exclusive offer is rejected in Stage 1. The equilibrium profits of firms are π r A = π r D = 4Π (c E ) + Π (c), π r B = Π (c) 12 12, πr E B = 4Π (c E ) 3Π (c). 12 Note that π r D πa D = (4Π (c E ) 3Π (c))/12 > 0, which implies that unlike the case where upstream firms make take-it-or-leave-it offers in terms of two-part tariffs, socially efficient entry increases the profit of downstream monopolist D. Thus, the Shapley value leads to a similar profit allocation to linear wholesale pricing. 21 We finally consider the existence of exclusive contracts. When the exclusive offer is accepted in Stage 1, the joint profit of contracting party becomes π a B + πa D = 2Π (c)/3. By contrast, when the exclusive offer is rejected in Stage 1, the joint profits between the contracting party becomes π r B + πr D = (2Π (c E ) + Π (c))/6. Inequality (5) holds if and only if 3Π (c) 2Π (c E ). Therefore, entrant supplier U EB is not too efficient, socially efficient entry is deterred by using exclusive contracts: Proposition 6. Suppose that upstream suppliers adapt non-linear wholesale pricing and industry profits are allocated according to the Sharply value (11). Then, exclusion is a unique equilibrium if the efficiency difference between incumbent supplier U B and entrant supplier U EB is sufficiently small; that is, Π (c E )/Π (c) 3/2. The result here implies that the exclusion result under linear wholesale pricing is valid even when we apply the general demand function and profit allocation rule. From the view 20 For calculations, see Appendix B. 21 There is a major difference from linear pricing arises when the exclusive offer is rejected in Stage 1; the Shapley value allocates positive profits to incumbent supplier U B, which may not be reasonable because suppliers U B and U EB are homogeneous Bertrand competitors. Nonetheless, the Shapley value leads to a similar allocation to linear wholesale pricing because entry of entrant supplier U EB reduces incumbent supplier U B s profits; that is, π r B < πa B. 17

point of profit allocation, socially efficient entry into input B market decreases the contribution level of input B suppliers, which increases allocation profits for other negotiating group members. In the framework of Chicago School argument where no complementary input suppler exists, downstream monopolist D is the only member to obtain these benefits, which makes exclusion impossible. However, when we consider the existence of complementary input supplier, downstream monopolist D cannot be the unique member to obtain all of these benefits. This makes anticompetitive exclusive dealing possible. 5 Multiple incumbents We now extend the model analysis in Section 3.2 to the case where multiple incumbents exist. In this section, there are three upstream firms, U A, U B, and U C that produce complementary inputs A, B, and C with a constant marginal cost c > 0. In the markets of inputs B and C, potential entrants U EB and U EC respectively exist. For simplicity, we assume that each entrant supplier has same marginal cost 0 c E < c. If entrant supplier U Ei enters the input market i {B, C}, a homogeneous Bertrand competition between incumbent supplier U i and entrant U Ei occurs. The production technology of downstream monopolist D is given by the following Leontief type: Q = min {q A, q B, q C }, where Q is the amount of the final product and q A, q B, and q C are the amount of three inputs. By assuming that downstream monopolist D does not incur any production cost except the payments for the three inputs, per unit production cost of downstream monopolist D is given as c D = (w A + w B + w C ), where w A, w B, and w C are the prices of three inputs, respectively. The inverse demand for the final product is given as P(Q) = a bq. We now assume that a > 3(2c c E ) so that the competition between incumbent supplier U i and U Ei decreases the equilibrium price of input i {B, C} to c. In contrast to previous sections, in this section, we consider two scenarios. In the first scenario, the incumbent suppliers U B and U C make exclusive offers in Stage 1. Given the 18

offers, downstream monopolist D decides whether to accept in Stage 2. In the second scenario, downstream monopolist D makes exclusive offers in Stage 1. Given the offers, each incumbent supplier decides whether to accept the offer in Stage 2. When there are multiple incumbents, we have following two types of exclusion equilibrium candidates: (i) socially efficient entry is deterred in both input markets, or (ii) socially efficient entry is deterred in one of input markets. The following proposition shows that the types of exclusion outcomes depend on who makes exclusive offers: Proposition 7. Suppose that there are multiple incumbents U B and U C in upstream markets and that complementary input supplier U A has market power. If multiple incumbents make exclusive offers in Stage 1, there exists a unique exclusion equilibrium where socially efficient entry are deterred in both input markets. By contrast, if downstream monopolist D makes exclusive offers in Stage 1, there exists a unique exclusion equilibrium where one of socially efficiency entries is deterred. Note that from the welfare view point, entry deterrence in one of input markets leads to higher welfare than the one in both input markets. In addition, entry deterrence in one of input markets leads to higher joint profits among contracting parties. When downstream monopolist D makes exclusive offers, it can choose one input supplier to engage in exclusive dealing and can extract all profits. By contrast, when incumbent suppliers U B and U C make exclusive offers, they independently make exclusive offers by not taking into account the joint profits among contracting parties. Thus, in the absence of side payments between incumbent suppliers, they cannot coordinate. This leads to the difference in the pattern of exclusion outcomes. 6 Concluding remarks This study explored the existence of anticompetitive exclusive dealing by focusing on complementary inputs. Previous studies do not consider the role of complementary inputs for anticompetitive exclusive dealing in the upstream market. However, downstream firms usually 19

transform multiple inputs into final products. Therefore, the interaction between complementary input suppliers could not be neglected. We show that the seemingly small difference in model setting turns out to be crucial; if the complementary input supplier has market power, then the inefficient incumbent supplier can deter socially efficient entry by using exclusive contracts even in the framework of the Chicago School argument where a single downstream buyer exists. We then check the robustness of the exclusion outcome here, and show that the exclusion outcome here does not depend on the model setting with linear demand and linear pricing; that is, the results here are valid when the final product demand is not too convex or when we introduce non-linear pricing. Therefore, the analysis here can be widely applied to the real-world vertical relationships. The results here provide new implications for antitrust agencies; it is necessary to take into account the existence of complementary inputs when we discuss the possibility of anticompetitive exclusive dealings. If we discuss the anticompetitiveness of exclusive contracts by ignoring the existence of complementary input suppliers that have market power, we might overemphasize the results in the Chicago School argument. The results here predict that anticompetitive exclusive dealings are more likely to arise in the market where multiple inputs are required to produce a downstream product and the demand for it is inelastic. There are several outstanding concerns requiring further research. The first concern is about this study s relationship with other studies on anticompetitive exclusive dealing. For example, we assume that a downstream firm is a monopolist. We predict that as Simpson and Wickelgren (2007) and Abito and Wright (2008) discussed, if we add downstream competition to our model, the likelihood of an exclusion equilibrium increases. In addition, we have assumed that a single entrant in each input market. As Kitamura (2010) discussed, if we add multiple entrants to our model, the likelihood of an exclusion equilibrium increases. The second is about the generality of our results. For example, the analysis here is presented in the Leontief production technology, which could be suitable to analyze the Intel antitrust case. The result might be valid in more general production technologies. We hope this study 20

facilitates researchers in addressing these issues. A Proofs of All Results Proof of Proposition 1 When input A is competitively provided, we have w a A = wr A = c. We first explore the case where the exclusive contract is accepted in Stage 1. Then, U EB does not enter input B market in Stage 2. In Stage 3, U B sets the input price to D to maximize its profit by taking into account D s pricing in Stage 4 given its input price; i.e.: subject to w a B = arg max w B c (w B c)q(c, w B ) Q(c, w B ) = arg max Q 0 (a bq c w B)Q. The equilibrium input price is w a B = a/2 and wa A = c. The equilibrium production levels are Q a = q a A = qa B = (a 2c)/6b. The equilibrium profits (before compensation) are π a A = 0, πa B (a 2c)2 =, Π a D 8b (a 2c)2 =. (13) 16b We next explore the case where the exclusive offer is rejected in Stage 1. Then, U EB enters input B market in Stage 2. In Stage 3, the competition in input B market reduces the price of input B to the marginal cost of U B ; i.e., w r B = c. Given this input price and wr A = c, D determines price of final products; i.e., Q(c, c) = arg max Q 0 (a bq c c)q. The equilibrium production levels are Q r = q r A = qr B = (a 2c)/2b. The equilibrium profits are π r A = π r B = 0, π r D = (a 2c)2. (14) 4b Finally, we check the existence of exclusion dealing. From (13) and (14), we have π a B + πa D (πr B + π r (a 2c)2 D) = 16b inequality (5) never holds. Therefore, exclusion is impossible. < 0, 21

Proof of Lemma 1 Suppose first that the exclusive offer is accepted in Stage 1. In this case, U EB does not enter the market of input B in Stage 2 and D deals with U A and U B. In Stage 3, each U i set the input price to D to maximize its profit by taking into account D s pricing in Stage 4 given its input price; i.e.: subject to w i = arg max w i c (w i c)q(w i, w j ), Q(w i, w j ) = arg max Q 0 (a bq w i w j )Q, where i, j {A, B}, i j. The equilibrium input prices are The amounts of equilibrium production are Q a = q a A = qa B profits of firms (before compensation) are π a A = πa B w a A = wa B = a + c 3. (15) (a 2c)2 =, π a D 18b = (a 2c)/6b. The equilibrium (a 2c)2 =. (16) 36b Suppose next that D rejects the exclusive offer in Stage 1. In this case, U EB enters the input B s market in Stage 2 and the competition in input B market leads to w r B = c in Stage 3. The profit maximization problems of U A and D do not change. The equilibrium price of input A is w r A = a 2. (17) The amounts of equilibrium production are Q r = q r A = qr B = (a 2c)/4b. The equilibrium profits of firms are π r (a 2c)2 A =, π r B = 0 π r (a 2c)2 D =. (18) 8b 16b By comparing equation (15) with equation (17), we have the following relation: w a A wr A = a 2c 6 < 0. Therefore, entry into input B market increases the input price of input A. 22 Q.E.D.

Proof of Proposition 2 From (16) and (18), we have π a B + πa D (πr B + π r D) = (a 2c)2 48b > 0, which implies that inequality (5) always holds. Therefore, exclusion becomes a unique equilibrium outcome. Proof of Proposition 3 Q.E.D. We first consider the case where the exclusive offer is accepted in Stage 1. The equilibrium profits of firms (before compensation) are given as π a B = α ((1 + α)b) 1 α ( ) 1+α a 2c α, π a 1 + 2α D = α b α 1 ( ) 1+α α(a 2c) α. (1 + α)(1 + 2α) We next consider the case where the exclusive offer is rejected in Stage 1. The equilibrium profits of firms are given as π r B = 0, π r D = α b 1 α ( a 2c (1 + α) 2 ) 1+α α. Finally, we consider the existence of anticompetitive exclusive contracts. By using above results, we have the following equation. π a B + πa D (πr B + π r D) = 1+α α(a 2c) α b 1 α (1 + α) 2(1+α) α (2 + α) ((1 + α)(1 + 2α)) 1+α α (1 + α) 3(1+α) α (1 + 2α) 1+α α. (19) Equation (19) becomes positive if and only if α < α. Therefore, exclusion is possible if and only if α < α. Q.E.D. 23