Exclusive contracts with complementary inputs

International Journal of Industrial Organization 56 (2018) 145–167

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International Journal of Industrial Organization www.elsevier.com/locate/ijio

Exclusive contracts with complementary inputsR Hiroshi Kitamura a, Noriaki Matsushima b,∗, Misato Sato c a

Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto 603-8555, Japan b Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan c Research Fellow of the Japan Society for the Promotion of Science (JSPS), Faculty of Economics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto 603-8555, Japan

a r t i c l e

i n f o

Article history: Received 20 October 2016 Revised 5 November 2017 Accepted 27 November 2017 Available online 8 December 2017 JEL classification: L12 L41 L42 C72

a b s t r a c t 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, upstream competition within a given input market benefits not only the downstream firm, but also the

R We thank the Co-Editor—Giacomo Calzolari—and two anonymous referees for their constructive comments and suggestions. We also thank Yuki Amemiya, Eric Avenel, Chiara Fumagalli, Toshihiro Matsumura, Patrick Rey, Dan Sasaki, and Tetsuya Shinkai for their insightful comments, which greatly assisted the research. For the helpful discussions and expertise, we appreciate the help of Zhijun Chen, Akifumi Ishihara, Akira Ishii, Bruno Jullien, Akihiko Nakagawa, Tatsuhiko Nariu, Ryoko Oki, Noriyuki Yanagawa, and the conference participants at APIOC 2016 (University of Melbourne), EARIE 2014 (Bocconi University), the Japanese Economic Association (Seinan Gakuin University), and Japan Association for Applied Economics (Hiroshima University), as well as the seminar participants at Kwansei Gakuin University, Kyoto University, Kyoto Sangyo University, Nagoya University, Osaka University, Université Catholique de Louvain, The University of Rennes 1, and Yokohama National University. Finally, we thank Shohei Yoshida for his research assistance. The second author is grateful for the warm hospitality at MOVE, Universitat Autònoma de Barcelona, where part of this paper was written, and acknowledges the financial support from the “Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation” of JSPS. We gratefully acknowledge the financial support from JSPS KAKENHI Grant Numbers JP22243022, JP24530248, JP24730220, JP15H03349, JP15H05728, JP15K17060, JP17H00984, JP17J03400, and JP17K13729, and the program of the Joint Usage/Research Center for Behavioral Economics at ISER, Osaka University. The usual disclaimer applies. ∗ Corresponding author. E-mail addresses: [email protected] (H. Kitamura), [email protected] (N. Matsushima), [email protected] (M. Sato).

https://doi.org/10.1016/j.ijindorg.2017.11.005 0167-7187/© 2017 Elsevier B.V. All rights reserved.

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Keywords: Antitrust policy Complementary inputs Exclusive dealing Multiple inputs

complementary input suppliers, by raising complementary input prices. Thus, the downstream firm is unable to 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, downstream competition, and relationship-specific investment. © 2017 Elsevier B.V. All rights reserved.

1. Introduction In vertical supply chain relationships, firms often engage in contracts including vertical restraints, such as 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; thus, they may appear to be anticompetitive. However, scholars from the Chicago School oppose this view. Based on analytic models, they argue that rational economic agents do not sign contracts to deter more efficient entrants (Posner, 1976; Bork, 1978).3 In rebuttals of this argument, following Aghion and Bolton (1987), several researchers present market environments in which anticompetitive exclusive dealing occurs (e.g., Rasmusen et al., 1991; Segal and Whinston, 2000a; Simpson and Wickelgren, 2007; Abito and Wright, 2008). The present study considers complementary inputs, and provides an economic environment within which anticompetitive exclusive dealing occurs. In a real-world business situation, final-goo d producers often transform multiple inputs into final products. More importantly, there exist complementary input suppliers with market power. In the Intel antitrust case, for example, Microsoft is a supplier with strong market power.4 Moreover, in the antitrust case of Ticketmaster, popular artists, who provide complementary inputs for ticketing services, can have strong bargaining power over concert venues that sign exclusive contracts with Ticketmaster.5 Therefore, when analyzing anticompetitive exclusive dealing in real-world situations, the interaction between complementary input suppliers cannot be neglected. 1 The pioneering work of Rey and Tirole (1986) comprehensively considers these topics. More recently, Asker and Bar-Isaac (2014) use a repeated game to consider the matter. Excellent surveys of vertical restraints are provided by Rey and Tirole (2007) and Rey and Vergé (2008). 2 Setting exclusive territories is a typical example of exclusive-dealing agreements. For instance, see Mathewson and Winter (1984), Rey and Stiglitz (1995), and Matsumura (2003). 3 For analyses of the impact of this argument on antitrust policies, see Motta (2004) and Whinston (2006). 4 Intel was accused of awarding rebates and various other payments to major original equipment manufacturers (e.g., Dell and HP). In a single quarter in 2007, conditional rebates and payments from Intel amounted to 76% of Dell’s operating profit (Gans, 2013). See also Japan Fair Trade Commission (2005), and the European Commission (2009). 5 See Finkelstein and Lagan (1995) for a discussion of the Ticketmaster case.

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In this study, we develop a model of anticompetitive exclusive dealing in the presence of complementary inputs. Our model is based on the framework of the Chicago School argument. Here, 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—and, thus, would constitute a socially efficient entry. The new dimension in our model is that the downstream firm needs two perfectly complementary inputs to produce a final product. In this case, the final product is produced by an input from the incumbent supplier, as well as a complementary input from a supplier with market power. In a simple setting with linear demand and linear wholesale pricing, we first show that the existence of a complementary input supplier with market power allows the incumbent supplier to deter socially efficient entry via exclusive contracts. To understand this result intuitively, consider the effects of socially efficient entry. Socially efficient entry into an input market generates competition, which reduces the price of the input and, thus, allows the downstream firm to earn higher profits. Under the Chicago School argument, this effect prevents the incumbent supplier from profitably compensating the downstream firm. As a result, Chicago School scholars conclude that exclusion is impossible. However, when there is a complementary input supplier with market p ower, so cially efficient entry into one input market increases the demand for the complementary input, which benefits the complementary input supplier by increasing the complementary input price. Hence, compared with the case in which there is no complementary input supplier with 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 it can be observed in a broad range of settings. First, introducing non-linear demand, we show that the exclusion results remain valid, as long as the demand curve for the final products is not overly convex; that is, exclusion is more likely to be observed under inelastic demand. Second, the exclusion mechanism works in the case of Cobb–Douglas production technology. Third, we can derive exclusion outcomes in a context of non-linear wholesale pricing and a general demand function. Therefore, the exclusion outcome identified in this study can be applied to diverse real-world vertical relationships. This study is related to the literature on exclusive contracts that deter socially efficient entry.6 Mainstream studies derive exclusion results by adding another downstream 6 Several studies examine pro-competitive exclusive dealings, for example, non-contractible investments (Marvel, 1982; Besanko and Perry, 1993; Segal and Whinston, 2000b; de Meza and Selvaggi, 2007; de Fontenay et al., 2010), industry R&D and welfare (Chen and Sappington, 2011), and risk sharing (Argenton and Willems, 2012). Exclusive dealing is also considered a way to solve the opportunism problem posited by 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). Finally, several studies focus on the fact that active firms may compete for exclusivity and explore the welfare effect (Mathewson and Winter, 1987; O’Brien and Shaffer, 1997; Bernheim and Whinston, 1998). Recently, Calzolari and Denicoló (2013; 2015) and Calzolari et al. (2016) introduced asymmetric information in this literature.

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buyer into the framework of the Chicago School argument. There are two types of exclusion mechanisms, both of which generate negative externalities. First, Rasmusen et al. (1991) and Segal and Whinston (2000a) introduce scale economies, in the sense that an entrant needs to trade with a certain number of downstream buyers. In the presence of scale economies, exclusive contracts generate a negative externality among downstream buyers; that is, signing exclusive contracts reduces the possibility of entry and, thus, prevents other downstream buyers from obtaining benefits of entry. The incumbent supplier can profitably exclude socially efficient entry by exploiting this externality. Second, Simpson and Wickelgren (2007) and Abito and Wright (2008) introduce downstream competition that generates a negative externality, such that entry induces downstream buyers to earn considerably smaller profits. This is because most of the benefit from entry is extracted by final consumers, who are third parties.7 ,8 Because exclusive contracts solve this rent extraction problem, the incumbent supplier can obtain exclusion outcomes profitably. This study shares several common features with these prior studies. For example, we introduce a complementary input supplier as another economic agent, and there exists a negative externality, such that entry allows the complementary input supplier to extract the downstream firm’s rent. More importantly, from the viewpoint of the third party’s rent extraction, those studies on exclusion with downstream competition are more closely related to this study. In contrast to the above studies, several economists derive exclusion results even in the single-buyer model, which is a feature of the Chicago School argument. Focusing on the nature of upstream competition, these studies show that the exclusion result is obtained in cases where the incumbent supplier sets liquidated damages for the case of entry (Aghion and Bolton, 1987), where the entrant is capacity constrained (Yong, 1996), suppliers compete à la Cournot (Farrell, 2005), suppliers can merge (Fumagalli et al., 2009), or the incumbent supplier makes relationship-specific investments (Fumagalli et al., 2012).9 This study has a shared feature with these studies in terms of a single-buyer model; thus, this study provides an alternative route that leads to exclusion outcomes in the case of a single buyer. This study is also related to the literature on vertical relationships involving complementary inputs, such as the works of Laussel (2008) and Matsushima and Mizuno (2012; 2013).10 These studies demonstrate that vertical integration is not necessarily profitable, 7 In the literature on exclusion with downstream competition, Fumagalli and Motta (2006) show that the requirement of participation fees to remain active in the downstream market plays a crucial role in exclusion if buyers are undifferentiated Bertrand competitors. See also Wright (2009) study, which corrects the result of Fumagalli and Motta (2006) in the case of two-part tariffs. 8 For extended models of exclusion with downstream competition, see Wright (2008), Argenton (2010), and Kitamura (2010; 2011). Whereas these studies all show that the resulting exclusive contracts are anticompetitive, Gratz and Reisinger (2013) show potentially pro-competitive effects if downstream firms compete imperfectly and contract breaches are possible. See also DeGraba (2013), who constructs a model for the situation in which a small rival that is more efficient at serving a portion of the market can make exclusive offers. 9 See also Kitamura et al. (2017), who show that anticompetitive exclusive dealing can occur if the downstream buyer bargains with suppliers sequentially for the case of entry. 10 See also Arya and Mittendorf (2007) and Laussel and Long (2012).

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because the complementary input supplier extracts the majority of the profits generated from eliminating double marginalization through vertical integration.11 The present study extends this work, showing that these ideas can be applied to the literature on entry deterrence via exclusive contracts. Finally, this study is related to the literature on the hold-up problem in vertical relationships. In studies on organizational economics, the hold-up problem arises when an ex-ante enforceable contract cannot be written, and part of the investment return is extracted by the trading partner in the ex-post bargaining. In such a case, the level of investment by one agent does not maximize the joint profit in a vertical relationship, because the agent anticipates the ex-post rent extraction by the trading partner with market power (Williamson, 1975; Hart and Moore, 1988). In contrast, this study provides another type of hold-up problem in vertical relationships. Here, the downstream firm accepts exclusive offers, for fear of the ex-post rent extraction by the complementary input supplier with market power, which reduces the joint profit between the downstream firm and the complementary input supplier. The remainder of this paper is organized as follows. Section 2 constructs the basic model. Section 3 presents the main results under linear wholesale pricing, and extends the basic model in several dimensions. Section 4 reports the results under non-linear wholesale pricing. Lastly, Section 5 concludes the paper. Appendix A presents the proofs of the results. 2. Model This section develops the basic model environment. We first explain players’ characteristics and the game’s timing in Section 2.1. Section 2.2 then introduces the design of the anticompetitive exclusive contracts. 2.1. Basic environment The upstream market is composed of two complementary input markets: A and B (Fig. 1). Input A is exclusively produced by supplier UA with a constant marginal cost c > 0. In contrast, input B is produced by an incumbent supplier UIB and an entrant supplier UEB . Following the Chicago School model, UIB and UEB produce an identical product, but with differing cost efficiencies; that is, UEB is more efficient than UIB , with a constant marginal cost cE ∈ [0, c), as opposed to UIB ’s constant marginal cost c.12 ,13 11 Reisinger and Tarantino (2013) also consider a market in which downstream firms need complementary inputs sold on two-part tariffs. The key factor of their result is shared with this study, that is, the rent extraction of complementary product suppliers. 12 We assume that UA and UIB have the same marginal costs, for simplicity. The results presented here also hold under different marginal costs. 13 As in Argenton (2010), we extend the setting to a case in which the inputs are vertically differentiated. The results are which is available upon request.

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Input A Market

wA

Input B Market

wB

Fig. 1. Market structures.

The downstream market is composed of a single firm. This modeling strategy clarifies the role of UA as having market power; that is, the prevention of socially efficient entry occurs even in the absence of scale economies and downstream comp etition, b oth of which require more than one downstream firm. A downstream monopolist D transforms inputs A and B into a final product. Then, D uses Leontief production technology: one unit of the final product is made with one unit of input A and one unit of input B:14 Q = min{qA , qB },

(1)

where qi is the amount of input i ∈ {A, B}. Eq. (1) implies that the two inputs are essential to produce a final product in a downstream market; that is, they are perfect complements.15 The payment for qi units of input i ∈ {A, B} is given as wi qi , where wi is the price of input i. To simplify the analysis, we assume that D incurs no production costs, aside from paying for the two inputs. Thus, the per unit production cost of D is given by cD = wA + wB . We assume that the inverse demand for the final product P(Q) is given by a simple linear function: P (Q) = a − bQ, (2) where Q is the output of the final product supplied by D, c < (a + 2cE )/4, and b > 0 (in Section 4, we consider a general demand case). The first inequality implies that UEB ’s monopoly price is higher than c; that is, the existence of UIB always acts as a constraint on the pricing of UEB when UEB enters the market for input B.16 We assume that D cannot merge with UA because vertical integration is costly.17 In addition, we can regard UA as an industry-wide labor union of downstream firms, 14 Intro ducing asymmetric pro duction technology, where one unit of the final product is made with h > 0 units of input A and m > 0 units of input B, does not qualitatively change the results. 15 Such production technology is widely observed in real-world manufacturing. For example, producing a PC requires, among other things, a CPU and an operating system. Producing a car requires a body and tires. 16 Exclusion will still exist, even when UEB is more efficient, but the analysis becomes more complicated. 17 Moreover, although our study does not explicitly consider multiple downstream firms in the main model, a vertical merger with common suppliers is sometimes prohibited by antitrust authorities because such a

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Fig. 2. Timeline.

which cannot merge with D. In the literature on oligopoly mo dels incorporating labor unions, the labor union is usually assumed to maximize the wage level and the number of employees, which can be interpreted as wA and qA in this study.18 The model contains four stages (Fig. 2). In Stage 1, UIB makes an exclusive offer to D, with fixed compensation x ≥ 0. Then, D decides whether to accept the offer.19 Here, D immediately receives x if it accepts the offer. In Stage 2, UEB decides whether to enter the market for input B. We assume that the fixed entry cost is sufficiently small that UEB can earn positive profits. In Stage 3, active suppliers offer linear input prices to D (in Section 4, we introduce non-linear pricing). We assume that if UEB enters the market for input B, then UIB and UEB become homogeneous Bertrand competitors. We assume that if they charge the same input price, the efficient supplier, UEB , supplies its input to D. That is, we impose the so-called tie-breaking rule. The equilibrium input price offered by Uk when D accepts (rejects) the exclusive offer is denoted by wka (wkr ) , where k ∈ {A, IB} (k ∈ {A, IB, EB}), and the superscript “a” (“r”) indicates that the exclusive offer is accepted (rejected). In Stage 4, D orders inputs and sells the final product to consumers. Then, Uk ’s profit in the case where D accepts (rejects) the exclusive offer is denoted by πka (πkr ), and D’s profit in the case when it accepts (rejects) the exclusive offer is denoted a r by πD ( πD ). 2.2. Design of exclusive contracts For an exclusion equilibrium to exist, the equilibrium transfer x∗ must satisfy the following two conditions: First, it must satisfy individual rationality for UIB ; that is, UIB earns higher profits under exclusive dealing: a r a r πIB − x∗ ≥ πIB or x∗ ≤ πIB − πIB .

(3)

vertical merger can generate a foreclosure problem. An example is mentioned in Matsushima and Mizuno (2012, footnote 12). Furthermore, we can extend the downstream monopoly to a downstream oligopoly, in which vertical integration between UA and one of downstream firms is not socially desirable; that is, the first interpretation is reasonable. The extension is available upon request. 18 See, for example, Horn and Wolinsky (1988a; 1988b), Davidson (1988), Dowrick (1989), Mumford and Dowrick (1994), Naylor (2002), Lommerud et al. (2003) and Lommerud et al. (2009). 19 Rasmusen et al. (1991) and Segal and Whinston (2000a) point out that price commitments are unlikely if the product’s nature 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 of Fumagalli and Motta (2006).

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Second, the exclusive contract must satisfy individual rationality for D; that is, the amount of compensation x∗ induces D to accept the exclusive offer: a r r a πD + x∗ ≥ πD or x∗ ≥ πD − πD .

(4)

From the above conditions, it is evident that a unique exclusion equilibrium exists if and only if inequalities (3) and (4) hold simultaneously. This is equivalent to the following condition: a a r r πIB + πD ≥ πIB + πD . (5) Condition (5) implies that to determine whether anticompetitive exclusive contracts exist, we must examine whether exclusive contracts increase the joint profits of UIB and D. 3. Linear wholesale pricing This section analyzes the existence of anticompetitive exclusive contracts under linear wholesale pricing. To intuitively understand the importance of a complementary input supplier having market power, we first discuss a benchmark case in which complementary input A is provided competitively (Section 3.1). We then explore the case in which complementary input A is supplied by a monopolistic supplier, and examine how the curvature of the inverse demand function and the production technology influence the result (Section 3.2). 3.1. Benchmark: when a complementary input is supplied competitively Assume that complementary input A is provided competitively. Then, input A’s price a r does not depend on whether the exclusive offer is accepted in Stage 1 (i.e., wA = wA = c). In this setting, the Chicago School mo del can be interpreted as a special case in a r which D can purchase complementary input A for free (i.e., wA = wA = 0).20 Therefore, as the Chicago School argues, UIB cannot deter socially efficient entry. Proposition 1. Suppose that inverse demand is given by a linear function, and that upstream suppliers adopt linear wholesale pricing. When complementary input A is provided competitively, UIB cannot deter socially efficient entry using exclusive contracts. This result can be explained using similar logic to that underlying the Chicago School argument.21 When D accepts the exclusive offer in Stage 1, it purchases input B from UIB at a higher input price, which allows UIB to earn monopoly profits. However, under linear wholesale pricing, UIB and D cannot maximize their joint profits because of the double-marginalization problem. Thus, the left-hand side of inequality (5) is quite small. 20 Although a buyer is the final consumer in the Chicago School model, the result does not change qualitatively if we assume that the buyer is a downstream monopolist. See Lemma 1 of Kitamura et al. (2014). 21 Note that the result in Proposition 1 holds under a general demand function.

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In contrast, when D rejects the exclusive offer in Stage 1, UEB enters the market for input B in Stage 2. In Stage 3, UIB and UEB compete to manage D. Compared with the case of exclusive dealing, upstream competition in the market for input B reduces the price of input B, which solves the double-marginalization problem. Thus, D earns considerably higher rejection profits; that is, the right-hand side of inequality (5) becomes large. UIB cannot compensate D for such profits profitably, implying that there is no x that simultaneously satisfies participation constraints (3) and (4). Therefore, when the downstream market consists of a monopolist, anticompetitive exclusive dealing cannot occur if complementary input A is supplied competitively. 3.2. When a complementary input is provided by a monopolist We now assume that complementary input A is provided exclusively by UA . Input A’s price now depends on whether entry into the market for input B occurs, unlike in the previous subsection. As in the case in which complementary input A is provided competitively, entry into the market for input B generates competition within the market, reducing input B’s price. To understand the pricing behavior of UA when input B’s price decreases, we first examine the relationship between entry into the market for input B and input A’s price. The following lemma summarizes the relationship. Lemma 1. When UA has market power, socially efficient entry into the market for input r a B raises the equilibrium price of input A—that is, a/2 = wA > wA = (a + c)/3 . To understand this result, consider the reaction function of the monopolistic supplier of input i, given input j’s price wj : wi (wj ) =

a + c − wj , 2

(6)

where i, j ∈ {A, B} and i = j. It is easy to see that wi is a strategic substitute of wj ; that is, raising input A’s price is the best response for UA when input B’s price decreases.22 Therefore, entry into the market for input B induces UA to raise input A’s price and enjoy higher profits. The following proposition shows that this relationship between entry into the market for input B and input A’s price allows UIB to deter efficient entry using exclusive contracts. Proposition 2. Suppose that inverse demand is given by a linear function, and that upstream suppliers adopt linear wholesale pricing. If UA is the monopolist for input A, UIB can deter socially efficient entry as a unique exclusionary equilibrium outcome. 22 If inputs A and B were substitutes, a reduction in input B’s price would decrease demand for input A and, thus, UA would be required to lower A’s price. In contrast, if inputs A and B are complements, a reduction in input B’s price increases demand for input A.

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As in the case in which input A is supplied competitively, entry into the market for input B generates upstream competition in this market, which benefits D. However, Lemma 1 implies that entry into this market also benefits UA by increasing input A’s price, which prevents D from earning considerably higher profits upon rejecting the exclusive offer; that is, the right-hand side of inequality (5) does not become sufficiently large. This allows UIB to compensate D profitably using its profits under exclusive dealing. Therefore, the existence of a complementary supplier with market power leads to anticompetitive exclusive dealing. Note that this result crucially depends on the hold-up problem between UA and D, which is generated by the bargaining externality such that entry allows UA to extract D’s rent. To understand this, consider the case where UA is able to make a commitment not to change input A’s price in the case of entry. For the sake of comparison with r a a a r Proposition 2, if UA set wA = wA = (a + c)/3, we would have πIB = 2 πD , πIB = 0, r a a a r r a 23 and πD = 4πD , which would lead to πIB + πD − (πIB + πD ) = −πD < 0. Hence, UIB could not deter socially efficient entry using exclusive contracts. More importantly, we r a would have πA = 2 πA ; in other words, UA could enjoy higher profits from the increased demand for input A through its lower wholesale price. From the viewpoint of UA , such a price commitment is a serious concern. However, the long-term price commitment through complete contracts is unrealistic in industries in which the environment changes rapidly, because of the exchange-rate fluctuation risk or rapid technological progress. Therefore, anticompetitive exclusive dealing is more likely to be observed in these industries. Remark 1 (Non-linear demand). The previous results rest on the assumption of a linear inverse demand function. We now relax this assumption to extend the analysis in Section 3.2 using a non-linear inverse demand function: P (Q) = a − bQα .

(7)

We assume that α > 0 so that the firms’ second-order conditions are satisfied. We also assume that a > ((1 + α)(c − cE ) + 2αc)/α, so that UEB ’s monopoly price is higher than c. Comparing Eqs. (2) and (7) reveals clearly that the linear demand case considered in the previous subsections is a special case, where α = 1. The price elasticity of demand is given by p dQ/Q − = . (8) dp/p α(a − p) Eqs. (7) and (8) imply that as α increases (decreases), the demand curve becomes concave (convex) or inelastic (elastic). The following proposition shows that the likelihoo d of exclusion depends on the curve’s shape. 23 a r The optimal prices of input A are actually wA = wA = a/2, which yields qualitatively the same results as the example provided in the main text.

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Proposition 3. Suppose that upstream suppliers adopt linear wholesale pricing. If UA is the monopolistic supplier of input A, UIB can deter socially efficient entry as a unique equilibrium outcome as long as the demand curve for the final product is not overly convex, α ≥ α  0.40692. This result has an important implication: exclusion is more likely to be observed when demand is inelastic. The curvature of the inverse demand curve influences the degree of demand expansion following socially efficient entry. When the inverse demand curve is concave (α > 1), the demand-expansion effect of a new upstream entrant is weak; as a result, socially efficient entry does not lead to a large increase in D’s profits, allowing UIB to compensate D profitably. However, as the inverse demand curve becomes convex, the demand-expansion effect becomes significant; in other words, the double marginalization problem is more serious in the case of convex inverse demand. This leads to a large increase in D’s profits, preventing UIB from compensating D profitably. Note that we can characterize Proposition 3 as the pass-through rate, ρ ≡ dp/dt, where p is the price of the final product and t is the input price. Following a simple calculation, we find that UIB can deter socially efficient entry as a unique equilibrium outcome, as long as the pass-through rate is lower than ρ = 1/(1 + α ¯ ) (i.e., ρ ≤ ρ = 1/(1 + α ¯ )  0.7108). Remark 2 (Cobb–Douglas production technology). The results in Proposition 2 are obtained under the Leontief production technology. Although such a production technology is appropriate for analyzing certain real-world situations, such as the Intel antitrust case, we extend the model to the case where D needs two imperfectly complementary inputs in order to produce a final product. We now assume that D has the following Cobb–Douglas production technology: √ Q = qA qB . (9) In order to obtain the results analytically, we assume that a = b = 1. We further assume that c ∈ (0, 1/2), so that all firms decide to be active. The following proposition shows that UIB can deter socially efficient entry, even under the Cobb–Douglas production technology. Proposition 4. Suppose that upstream suppliers adopt linear wholesale pricing. When D has the Cobb–Douglas production technology, UIB can deter socially efficient entry as a unique equilibrium outcome if UA is the monopolistic supplier of input A. This result implies that the exclusion mechanism in this study does not depend on the Leontief production technology. The Cobb–Douglas production technology is used in relatively many cases where the final product is produced by b oth capital input and labor. Therefore, this result may confirm the exclusion scenario with a strong labor union of D.

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4. Non-linear wholesale pricing In this section, we extend the analysis of the model in Section 3 to the case in which upstream suppliers use two-part tariffs in Stage 3. Two-part tariffs consist of a linear wholesale price and an upfront fixed fee. The two-part tariff offered by input supplier Ui when D accepts (rejects) the exclusive offer is denoted by (wia , Fia ) ((wir , Fir )), where i ∈ {A, IB, EB}. Under non-linear pricing, the double-marginalization problem is avoidable, and the joint profit is maximized within the technological endowments available to firms. For notational convenience, we define Π∗ (z) as follows: Π∗ (z) ≡ max(p − z − c)Q(p), p

where z ≥ 0, and Q(p) is a well-behaved general demand function, under which Π∗ (c) > 0 holds. Here, Π∗ (z) can be interpreted as the maximum joint profit among all firms when input B is produced with marginal cost z. If entry occurs, z = cE ; otherwise z = c . Hence, the difference between Π∗ (cE ) and Π∗ (c) depends on the difference between the efficiencies of UEB and UIB . To simplify the analysis, we assume that Π∗ (z) is continuous and strictly decreasing in z. We explore the existence of an exclusion equilibrium when the industry profit is allocated by bargaining with random proposers, as introduced by Fumagalli et al. (2012). In their study, the relationship-specific investment by the incumbent is a key factor to derive the exclusion results. In contrast, we do not consider the incumbent’s investment in order to clarify that the complementary input supplier with market power plays an essential role in anticompetitive exclusive dealing. Under bargaining with random proposers, the industry profit allocation in Stage 3 is determined as follows. There are two negotiations, composed of Negotiation A between D and UA , and Negotiation B between D and the supplier(s) of input B. In each negotiation, the proposer is determined randomly and independently. In each negotiation, D becomes the proposer of two-part tariffs with probability β ∈ (0, 1), while the supplier(s) of each input becomes the proposer with probability 1 − β. We interpret β as the degree of D’s bargaining power over the supplier(s) of each input. The rest of this section is organized as follows. To clarify the role of a complementary input supplier with market power, we explore a benchmark case in which complementary input A is provided competitively, in Section 4.1. We then explore the case in which complementary input A is supplied by a monopolistic supplier, in Section 4.2. 4.1. Benchmark: when a complementary input is competitively supplied Assume that complementary input A is provided competitively by the suppliers that have a marginal cost of c; namely, in Negotiation A the equilibrium tariff of input A is (c, 0) regardless of whether the exclusive offer is accepted. Therefore, in this subsection, we only focus on Negotiation B between D and the supplier(s) of input B.

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When the exclusive offer is accepted, D offers (c, 0) to UIB with probability β, and UIB offers (c, Π∗ (c)) with probability 1 − β. The resulting expected profits, excluding the fixed compensation x, are a a a πA = 0, πIB = (1 − β)Π∗ (c), πD = βΠ∗ (c).

When the exclusive offer is rejected, D offers (cE , 0) to extract all the surplus with probability β, and UIB and UEB are assigned proposer roles with probability 1 − β. In the latter event, they compete and offer (c, 0) and (cE , Π∗ (cE ) − Π∗ (c)) to D, respectively. The resulting expected profits are r r r r πA = πIB = 0 , πD = (1 − β)Π∗ (c) + βΠ∗ (cE ), πEB = (1 − β)(Π∗ (cE ) − Π∗ (c)).

Finally, we consider the existence of exclusion. From the above results, we have a a r r πIB + πD − (πIB + πD ) = −β(Π∗ (cE ) − Π∗ (c)) < 0,

which implies that condition (5) never holds. Proposition 5. Suppose that upstream suppliers adopt two-part tariffs and that industry profits are allocated by bargaining with random proposers. If complementary input A is provided competitively, UIB cannot deter efficient entry using exclusive contracts. This result implies that if complementary input A is provided competitively, the Chicago School argument can be applied, even for the case in which the industry profit is allocated by bargaining with random proposers in Stage 3. As in Section 3.1, this result can be explained by D’s higher rejection profits. 4.2. When a complementary input is provided by a monopolist Assume now that complementary input A is provided exclusively by UA ; namely, in Negotiation A the equilibrium tariff of input A depends on whether the exclusive offer is accepted. There are four patterns of proposer assignments in Negotiations A and B: (i) D is the proposer in both Negotiations A and B (denoted by Case DD); (ii) D is the proposer in Negotiation A and the supplier(s) of input B is the proposer in Negotiation B (Case DB); (iii) UA is the proposer in Negotiation A and D is the proposer in Negotiation B (Case AD); and (iv) UA is the proposer in Negotiation A and the supplier(s) of input B is the proposer in Negotiation B (Case AB). Table 1 summarizes the probability with which each case occurs and the equilibrium two-part tariffs in each pattern of proposer assignment when the exclusive offer is accepted. The notable feature here is that multiple equilibria exist in Case AB; UA and

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Table 1 Equilibrium tariffs when the exclusive offer is accepted in Section 4.2 (α ∈ [0, 1]). Probability 2

Negotiation A

Negotiation B

D offers (c, 0) to UA

D offers (c, 0) to UIB

Case DD

β

Case DB

β(1 − β)

D offers (c, 0) to UA

UIB offers (c, Π∗ (c)) to D

Case AD

β(1 − β)

UA offers (c, Π∗ (c)) to D

D offers (c, 0) to UIB

Case AB

(1 − β)2

UA offers (c, (1 − α)Π∗ (c)) to D

UIB offers (c, αΠ∗ (c)) to D

Table 2 Equilibrium tariffs when the exclusive offer is rejected in Section 4.2 (γ ∈ [0, 1]). Probability 2

Case DD

β

Case DB

β(1 − β)

Negotiation A

Negotiation B

D offers (c, 0) to UA

D offers (cE , 0) to UIB and UEB

D offers (c, 0) to UA

UIB offers (c, 0) to D UEB offers (cE , Π∗ (cE ) − Π∗ (c)) to D

Case AD

β(1 − β)

UA offers (c, Π∗ (cE )) to D

Case AB

(1 − β)2

UA offers (c, Π∗ (cE ) − γ(Π∗ (cE )

UIB offers (c, 0) to D

−Π∗ (c))) to D

UEB offers (cE , γ(Π∗ (cE ) − Π∗ (c)))

D offers (cE , 0) to UIB and UEB

to D

UIB share all of industry profit Π∗ (c) in the proportion of 1 − α to α, where α ∈ [0, 1].24 Because both firms’ outside options are zero, α could be interpreted as UIB ’s bargaining power over UA , while we do not explicitly introduce bargaining between UA and UIB . The resulting expected profits, excluding the fixed compensation x, are a a a πA = (1 − β)(1 − α(1 − β))Π∗ (c), πIB = (1 − β)(β + α(1 − β))Π∗ (c), πD = β 2 Π∗ (c).

Table 2 summarizes the probability with which each case occurs and the equilibrium two-part tariffs in each pattern of proposer assignment when the exclusive offer is rejected. Here also, multiple equilibria exist in Case AB; UA and UEB earn (1 − γ)(Π∗ (cE ) − Π∗ (c)) + Π∗ (c) and γ(Π∗ (cE ) − Π∗ (c)) respectively, where γ ∈ [0, 1]. Given UIB ’s offer (c, 0), UA can earn Π∗ (c) in the absence of UEB ; thus, the additional contribution from the participation of UEB is Π∗ (cE ) − Π∗ (c). Because UA and UEB share this additional contribution in the proportion of 1 − γ to γ, γ could be interpreted as UEB ’s bargaining power over UA . The resulting expected profits are r r πA = (1 − β){βΠ∗ (cE ) + (1 − β)(Π(cE ) − γ(Π∗ (cE ) − Π∗ (c)))}, πIB = 0, r r πD = β((1 − β)Π∗ (c) + βΠ∗ (cE )), πEB = (1 − β)(β + γ(1 − β))(Π∗ (cE ) − Π∗ (c)).

Finally, we consider the existence of exclusion. Condition (5) holds if and only if a a r r πIB + πD − (πIB + πD ) = −β 2 (Π∗ (cE ) − Π∗ (c)) + α(1 − β)2 Π∗ (c) ≥ 0. 24 See also the online Appendix, which is available on the author’s website. In Appendix A, we introduce another type of bargaining model based on Kitamura et al. (2017). In such a setting, we obtain a unique Stage 3 equilibrium outcome, as well as exclusion results.

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Fig. 3. Results of Proposition 6 (α = 1/2).

From this condition, we obtain the following proposition. Proposition 6. Suppose that upstream suppliers adopt two-part tariffs and that industry profits are allocated by bargaining with random proposers. If UA has market power, UIB can deter socially efficient entry using exclusive contracts if there is a sufficiently small difference in efficiency between UIB and UEB , and if D has weak bargaining power; that is, Π∗ (cE )/Π∗ (c) ≤ ψ(β|α), where ψ(β|α) ≡ 1 +

α(1 − β)2 . β2

Note that for all (α, β) ∈ (0, 1)2 , we have ψ(β|α) > 1, ψ  (β|α) < 0, and ψ   (β|α) > 0, and that ψ(β|α) → ∞ as β → 0, ψ(β|α) → 1 as β → 1, and ψ(β|α) → 1 as α → 0. Fig. 3 summarizes the result of Proposition 6. Using non-linear wholesale pricing, we confirm the robustness of the exclusion mechanism in this study. The new dimension here is that the possibility of exclusion depends on D’s bargaining power. When D has weak bargaining power, UA extracts most of the increase in the firms’ joint profits from UEB ’s entry, whereas D enjoys a smaller increase in profits, which increases the possibility of exclusion. Proposition 6 also implies that exclusion is less likely for a small value of α, which is UIB ’s share of the total profit Π∗ (c) between UIB and UA when D does not have any proposer role in the case of exclusion. As the value of α becomes smaller, UA earns higher profits, while UIB earns lower profits, which leads to smaller joint profits for a a the contracting parties under exclusive dealing πIB + πD . Therefore, the possibility of exclusion becomes lower, and for α = 0, which is the extreme case, the exclusion result never holds. By interpreting α as UIB ’s bargaining power over UA when D does not have any proposer role in the case of exclusion, we can claim that anticompetitive exclusive

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dealing is more likely to be observed when the incumbent supplier has a strong position relative to that of the complementary input supplier.

5. Concluding remarks This study has explored the existence of anticompetitive exclusive dealing, extending the work of previous studies to consider the role of complementary inputs in the upstream market. It is essential that this interaction between complementary input suppliers not be neglected, because it is common for real-world downstream firms to transform multiple inputs into final products. Our analysis showed that seemingly small differences in the model’s setting can have crucial ramifications for the results. If the complementary input supplier has market power, then the inefficient incumbent supplier can deter socially efficient entry using exclusive contracts, even under the Chicago School’s framework. On checking the robustness of our exclusion outcome, we showed that it does not depend on the assumption of linear demand, Leontief production technology, or linear wholesale pricing. That is, our results remain valid when the final product demand curve is not too convex, when the downstream firm uses the Cobb–Douglas production technology, or when non-linear wholesale pricing is introduced. Thus, this study’s analysis can be applied widely to real-world vertical relationships. Our results also have novel and important implications for antitrust agencies: it is necessary to consider the existence of complementary inputs when considering the possibility of anticompetitive exclusive dealing. If we discuss the anticompetitiveness of exclusive contracts, while ignoring the existence of complementary input suppliers with market power, we might over-emphasize the results of the Chicago School argument. This study’s results suggest that rational economic agents can easily engage in anticompetitive exclusive dealing in a market requiring multiple inputs to produce a downstream product, for which demand is inelastic. Moreover, if the complementary input supplier considered here is interpreted as an industry-wide labor union, our results imply that the existence of labor unions with strong bargaining power plays a role in facilitating anticompetitive exclusive dealing. Despite these contributions, there remain several outstanding issues requiring further research, in particular, with regard to the generality of our results. First, the present study’s analysis assumed Leontief production technology. While we show that the exclusion mechanism works in the case of Cobb–Douglas production technology, the result might also remain valid under more general production technologies, such as CES production technology. Second, we assumed that the complementary input supplier is a monopolist in this study. Even if we assumed that differentiated input suppliers compete in the complementary input market, the exclusion result would remain valid. A real-world example of this is the case of Eastman Kodak vs. Fuji, in which Kodak complained of exclusive contracts between Fuji and Japanese wholesalers that prevented Kodak from

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successfully entering Japan’s photographic film market.25 The Japanese camera market, which complements the film market, is characterized by dominant manufacturers such as Canon and Nikon. These manufacturers are somewhat differentiated and have market power, because consumers face switching costs when considering changing cameras. Thus, extensions and applications of our model can help researchers and policymakers address similar real-world issues. Appendix A. Pro ofs of results Pro of of Prop osition 1. Before proceeding to the proof, we explain D’s maximization problem. Given input prices wA and wB , the problem is given as max (a − bQ − wA − wB )Q. Q

(10)

The output of the final product supplied by D and the demand for each input are given by a − wA − wB q A = q B = Q(wA , wB ) ≡ . (11) 2b a r When input A is provided competitively, we have wA = wA = c . We first explore the case in which the exclusive contract is accepted in Stage 1. The outcome in Stage 4 is given in (11). In Stage 3, UIB sets the input price: a wIB = arg max(wIB − c)Q(c, wIB ). wIB

a a The equilibrium input prices are wIB = a/2 and wA = c . From (11), the equilibrium a a a production levels are Q (c, a/2) = qA = qIB = (a − 2c)/6b . The firms’ equilibrium profits, excluding the fixed compensation x, are a a πA = 0, πIB =

(a − 2c)2 (a − 2c)2 a , πD = . 8b 16b

(12)

We next explore the case in which the exclusive offer is rejected in Stage 1. Then, UEB enters the market for input B in Stage 2. In Stage 3, D purchases input B from UEB at r r UIB ’s marginal cost (i.e., wIB = wEB = c). From (11), the equilibrium production levels r r r r are Q (c, c) = qA = qEB = (a − 2c)/2b and qIB = 0. The equilibrium profits are r r r πA = πIB = 0 , πD =

(a − 2c)2 . 4b

(13)

Finally, we check for the existence of an exclusion equilibrium. From (12) and (13), we have (a − 2c)2 a a r r πIB + πD − (πIB + πD )=− < 0, 16b which implies that condition (5) never holds. 

25

See, for example, Nagaoka and Goto (1997).

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Proof of Lemma 1. Suppose first that the exclusive offer is accepted in Stage 1. The maximization problem faced by D in Stage 4 is given by (10). The output of the final product supplied by D and the demand for each input are given by (11). The maximization problem of Ui in Stage 3 is given as max(wi − c)Q(wi , wj ),

(14)

wi ≥c

where i, j ∈ {A, IB} and i = j. The first-order conditions in (6) lead to the equilibrium input prices: a+c a a wA = wIB = . (15) 3 a a From (11), the equilibrium production levels are Qa = qA = qIB = Q((a + c)/3, (a + c)/3) = (a − 2c)/6b. The firms’ equilibrium profits, excluding the fixed compensation x, are (a − 2c)2 (a − 2c)2 a a a πA = πIB = , πD = . (16) 18b 36b Next, suppose that the exclusive offer is rejected in Stage 1. In this case, UEB enters the market for input B in Stage 2. The maximization problem faced by D in Stage 4 is given by (10). The output of the final product supplied by D and the demand for each input are given by (11). The competition in the market for input B in Stage 3 leads to r r wIB = wEB = c. In contrast, the maximization problem of UA in Stage 3 is given by (14), with wj = c. From (6), the equilibrium price of input A is r wA =

a . 2

(17)

r r From (11), the equilibrium production levels are Qr = qA = qEB = (a − 2c)/4b r qIB = 0. Then, the equilibrium profits of the firms are

r πA =

(a − 2c)2 (a − 2c)2 r r , πIB = 0 , πD = . 8b 16b

(18)

From (15) and (17), we have the following relation: a r wA − wA =−

a − 2c < 0. 6

Therefore, entry into the market for input B increases input A’s price. Proof of Proposition 2. From (16) and (18), we have a a r r πIB + πD − (πIB + πD )=

which implies that condition (5) always holds.



(a − 2c)2 > 0, 48b

and



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163

Pro of of Prop osition 3. We first consider the case in which the exclusive offer is accepted in Stage 1. The firms’ equilibrium profits, excluding the fixed compensation x, are a πA

=

a πIB

α = 1 ((1 + α)b) α



a − 2c 1 + 2α

 1+αα ,

a πD

α = 1 bα



α(a − 2c) (1 + α)(1 + 2α)

 1+αα .

We next consider the case in which the exclusive offer is rejected in Stage 1. The equilibrium profits of the firms are given by r πA =

α 1 ((1 + α)b) α



a − 2c 1+α

 1+αα

r r , πIB = 0 , πD =

α 1 bα



a − 2c (1 + α)2

 1+αα .

Finally, we consider the existence of exclusion. From the above results, we have a πIB

+

a πD

−

r (πIB

+

r πD )

α(a − 2c) = 1 bα ≥ 0,

1+α α

(1 + α)

2(1+α) α

(2 + α) − ((1 + α)(1 + 2α))

(1 + α)

3(1+α) α

(1 + 2α)

if and only if α ≥ α . Therefore, condition (5) holds if and only if α < α.

1+α α

1+α α



Proof of Proposition 4. Before proceeding to the proof, we solve the game using backward induction, starting from Stage 4. The cost minimization problem of D under the Cobb– Douglas production technology (9) leads to the following input demands, given Q, wA , and wB :   wB wA qA (Q, wA , wB ) = Q, qB (Q, wA , wB ) = Q. (19) wA wB Then, D’s cost function given wA and wB is given by √ C(Q, wA , wB ) = 2 wA wB Q. Given input prices wA and wB , D’s profit maximization problem in Stage 4 is given as √ max (1 − Q − 2 wA wB )Q. Q

The output of the final product supplied by D becomes Q(wA , wB ) ≡

√ 1 − 2 wA wB . 2

By substituting (20) into (19), the input demands, given wA and wB , become  q A (wA , wB ) =

 √ √ wB 1 − 2 wA wB wA 1 − 2 wA wB , q B (wA , wB ) = . wA 2 wB 2

(20)

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0.07 0.06 0.05

+

−(

+

)

0.04 0.03 0.02 0.01 0.00

0.0

0.1

0.2

0.3

0.4

0.5

a a r r Fig. 4. Properties of πIB + πD − (πIB + πD ) under Cobb–Douglas Production Technology.

The game in Stage 3 depends on D’s decision in Stage 1. We first consider the profit maximization problem of Ui in Stage 3 when the exclusive offer is accepted in Stage 1. The profit maximization problem of Ui in Stage 3 is given as  max(wi − c) wi ≥c

√ wj 1 − 2 wi wj , wi 2

(21)

where i, j ∈ {A, IB} and i = j. The first-order condition leads to √ wi + c = 4wi wi wj .

(22)

By assuming symmetric equilibrium, the solution of (22) becomes a wA

=

a wIB

=

1+

√ 1 + 16c . 8

The firms’ equilibrium profits, excluding the fixed compensation x, are a πA

=

a πIB

=

(3 −

√ √ √ 1 + 16c)(1 − 8c + 1 + 16c) (3 − 1 + 16c)2 a , πD = . 64 64

We next consider the case where the exclusive offer is rejected in Stage 1. Because r r entry occurs in market for input B in Stage 2, we have wIB = wEB = c in Stage 3. In contrast, the maximization problem of UA in Stage 3 is given by (21), with wj = c. The equilibrium price of input A becomes r wA =

1 + λ(1 + λ) + 96c2 , 48λ

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where

165

 13   λ ≡ 1 + 144c2 (1 + 24c2 ) + 192 3c6 (1 + 108c2 ) .

The equilibrium profits of the firms are  r r πA = (wA − c)



c 1−2 r wA 2b

rc wA

√ r r , πIB = 0 , πD =

48λ − 2



1 + λ(1 + λ) + 96c2 192λ

2 .

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