Vertical Integration, Foreclosure, and Productive

Transcription

1 Vertical Integration, Foreclosure, and Productive Efficiency Markus Reisinger WHU - Otto Beisheim School of Management Emanuele Tarantino University of Bologna July 2014 Abstract We analyze the competitive conseuences of vertical integration in a model featuring a monopoly producer dealing with asymmetric retailers via secret two-part tariffs. When integrated with the inefficient retailer, the monopoly producer keeps the rival retailer active on the product market due to an output-shifting effect. This effect can induce the integrated firm to engage in below-cost pricing at the wholesale level, thereby rendering integration procompetitive. We study how information transmission within a vertically integrated organization affects these results, and extend the model to show that integration with an inefficient retailer emerges in a model with uncertainty over retailers costs. JEL classification: K21, L12, L13, L41, L42 Keywords: vertical relations, vertical integration, foreclosure, output shifting, antitrust policy. We are indebted to the editor (Benjamin Hermalin) and three anonymous referees for insightful comments and suggestions. The article also benefited from comments by Cédric Argenton, Heski Bar-Isaac, Felix Bierbrauer, Giacomo Calzolari, Simon Cowan, Vincenzo Denicolò, Chiara Fumagalli, Massimo Motta, Volker Nocke, Marco Pagnozzi, Emmanuel Petrakis, Salvatore Piccolo, Patrick Rey, Armin Schmutzler, Nicolas Schutz, Marius Schwartz, Greg Shaffer, Kathryn Spier, Elu von-thadden, Ali Yurukoglu, and Gijsbert Zwart. We also thank participants at the University of Bologna, Max Planck Institute for Collective Goods (Bonn), Pontificia Universidad Católica de Chile, University of Luxemburg, University of Mannheim, CSEF (Naples), University of Rochester (Simon), TILEC - Tilburg University, ETH Zurich seminars, and at the 2012 Annual Searle Center Conference on Antitrust Economics and Competition Policy (Northwestern University), the 2011 International Industrial Organization Conference (Boston), 2011 European Economic Association Annual Meeting (Oslo), the 2010 Workshop for new Researchers (Centre for Competition Policy - University of East Anglia), and XXV Jornadas de Economìa Industrial (Madrid). WHU - Otto Beisheim School of Management, Department of Economics, Burgplatz 2, Vallendar, Germany. Markus.reisinger@whu.edu. Also affiliated with CESifo. University of Bologna, Department of Economics, piazza Scaravilli 1, I-40126, Bologna, Italy; Phone: ; emanuele.tarantino@unibo.it. Also affiliated with TILEC.

2 1 Introduction How does vertical integration affect economic outcomes such as prices, uantities, and consumer surplus? Is vertical integration motivated by the desire to increase market power, or is it a device that enhances productive efficiency and welfare? On the one hand, a large theoretical literature shows that when a manufacturer deals with eually efficient retailers, vertical integration allows it to increase its market power by foreclosing rival retailers access to the input it produces (see, e.g., Rey and Tirole, 2007). On the other hand, the empirical literature presents evidence suggesting that efficiency-based mechanisms are behind vertical integration (e.g., Hortaçsu and Syverson, 2007; Lafontaine and Slade, 2007). 1 This paper theoretically analyzes the welfare conseuences of vertical integration using a model in which a dominant producer sells through retailers that have different marginal costs of production. We find that vertical integration with the less efficient retailer can raise consumer surplus and total welfare by improving productive efficiency. The mechanism we put forward features the integrated firm s upstream unit selling its input at favorable conditions to the nonintegrated efficient retailer, to induce this retailer to expand its output. This output-shifting effect gives rise to a procompetitive outcome whenever the integrated firm engages in below-cost pricing at the wholesale level. The evidence on the competitive effects of vertical integration is not fully conclusive. There is some evidence in support of foreclosure (Chipty, 2001; Hastings and Gilbert, 2005; among others). However, several empirical studies show that the efficiency gains produced by vertical integration can outweigh the welfare losses caused by foreclosure. For example, in their survey of empirical research, Lafontaine and Slade (2007) conclude that in most circumstances profit-maximizing vertical integration also raises consumer welfare. Our results suggest that vertical integration enhances productive efficiency thanks to the output-shifting strategy undertaken by an integrated company that acts as a merchant supplier (McAfee, 2002) by serving competing buyers on favorable terms. 2 This novel channel for procompetitive vertical integration arises in a framework that builds on the literature studying the anticompetitive effects of vertical restraints. In our model, a monopoly producer offers an intermediate good by means of secret twopart tariffs to two competing retailers that transform the input into a homogeneous final product. In contrast to the standard setting employed in the literature, we allow retailers to carry different marginal costs of production. Without integration, the monopoly producer s limited commitment to observable contracts prevents it from monopolizing the final product s market (e.g., Hart and Tirole, 1990; O Brien and Shaffer, 1992; McAfee and Schwartz, 1994; Rey and Tirole, 2007; White, 2007) (Lemma 1). As is well-established in the literature, integration with the more efficient retailer allows the monopoly producer to restore its market power by formulating an unfeasible 1 Specifically, the property-rights theories (e.g., Grossman and Hart, 1986), the theories highlighting the role of transaction costs (Williamson, 1971, among others) and those looking at the elimination of double marginalization (e.g., Salinger, 1988) show that vertical integration can raise efficiency. 2 Following McAfee (2002), a merchant supplier is an integrated firm that treats nonintegrated buyers on eual or favorable terms. McAfee (2002) provides a discussion and examples of merchant buyers and suppliers. Block, Bock, and Henkel (2010) document that selling to a competitor is a widespread practice in business, and report evidence from construction, tea packaging, and mining industries. 1

3 offer to the nonintegrated firm (the foreclosure effect of vertical integration) (Lemma 2). If instead the monopolist were integrated with the less efficient retailer, would the integrated firm still engage in a foreclosure strategy? We show that the newly integrated firm will reduce the unit-price offer to the nonintegrated but more efficient retailer (Proposition 1). The trade-off faced by the integrated upstream firm is as follows. With respect to a foreclosure strategy, a reduction of the unit price to the nonintegrated retailer raises the industry uantity and thus implies a reduction of industry revenue. However, a countervailing effect arises in our framework. Differently from the case with vertical separation, the reduction of the unit price to the nonintegrated retailer is observed by the integrated firm s downstream unit, which responds by reducing its uantity. A lower unit price then triggers an increase of the nonintegrated and more efficient retailer s uantity and profit. The upstream integrated firm can extract this higher profit via the fixed component of the two-part tariff. We show that the reduction of industry revenue is outweighed by the fact that the industry uantity is produced more efficiently. Indeed, we find that the nonintegrated retailer will be active on the final good s market as long as it is strictly more efficient than the integrated downstream unit (Proposition 2), thereby establishing the output-shifting effect of vertical integration. A uestion of great importance for antitrust policy is the magnitude of the output-shifting effect. Specifically, can the incentive to reduce the unit price to the nonintegrated firm be so strong as to render vertical integration procompetitive with respect to a nonintegrated industry? We show in Proposition 3 that the output-shifting effect can induce the upstream unit of the integrated firm to engage in below-cost pricing at the wholesale level. Below-cost pricing produces an expansion of industry output relative to vertical separation, and renders vertical integration procompetitive. It is optimal because it allows the integrated firm to restrict the uantity of the inefficient integrated retailer and obtain larger profits from the more efficient nonintegrated one. Indeed, we find that below-cost pricing is more likely to occur when cost differences between retailers are particularly large. In the industry structure of our main model, the upstream producer is an unconstrained monopolist. We then extend our main model to consider an industry in which a dominant producer competes with a fringe of less efficient firms. These fringe firms act as a bottleneck alternative that constrains the market power of the dominant producer. We show that the outcome mirrors that of our main model: when the dominant producer is merged with the inefficient retailer, the integrated firm will engage in output shifting that can result in below-cost pricing at the wholesale level (Proposition 4). The analysis of the model with a bottleneck alternative allows us to study the impact of information transmission within a vertically integrated firm on market prices and allocations. 3 We show that the intensity of the output-shifting effect depends on whether the upstream unit of the integrated firm can inform its downstream unit about the acceptance decision of the rival retailer. Interestingly, we find that if information transmission is possible, vertical integration results in a more competitive outcome (Proposition 5). When information transmission is possible, the downstream affiliate of the integrated firm can adjust its uantity based on the rival retailer s decision to reject the upstream affiliate s offer. 3 With the exception of Nocke and Rey (2012), studies of information sharing in models with vertical hierarchies typically analyze the implications of information exchange between organizations rather than within an organization (Bonanno and Vickers, 1988; Pagnozzi and Piccolo, 2012; Arya and Mittendorf, 2011). 2

4 In this case, the outside option of the rival retailer, i.e., the profits it obtains when buying from the bottleneck alternative, does not depend on the terms of the upstream unit firm s offer. Instead, when information transmission is not possible, the downstream unit believes that the rival retailer buys at the euilibrium per-unit price. The upstream unit can then reduce the outside option of the nonintegrated retailer by setting a higher unit price. The imposition of behavioral remedies such as information firewalls is one of the most common forms of conduct relief in merger decisions. 4 Our analysis of information transmission within a vertical organization allows us to assess the conseuences of such firewalls on economic outcomes and welfare. We show that, within our model, this type of remedy can be detrimental to consumer surplus. To check the robustness of our results, we solve the model under a number of alternative assumptions. Motivated by the empirical evidence on manufacturer-retailer relationships in vertically related industries (e.g., Villas-Boas, 2007; Bonnet and Dubois, 2010), we employ two-part tariff contracts in our main set-up. We first extend the model by letting the upstream monopoly use uantity-forcing contracts, and find that the euilibrium allocations with uantity-forcing arrangements coincide with those obtained using two-part tariffs. Second, although in our main model we assume that retailers hold passive beliefs, our conclusions are robust to the adoption of wary beliefs. Third, in the main model, we assume that retailers offer a homogeneous good. We extend the model to consider retailers offering differentiated products and again find that when the monopoly producer is integrated with the inefficient retailer, it engages in output shifting, which can result in a procompetitive outcome. Finally, we argue that the asymmetry in retailers marginal costs that we exogenously impose can be endogenized in a setup with providers of complementary intermediate goods (consistently with the results in Reisinger and Tarantino, 2013). 5 When the monopoly producer is integrated with the inefficient retailer, it would like to shutter its downstream unit and let the efficient retailer produce the monopoly uantity. However, it lacks the commitment to internally transfer the input good at any price above marginal cost. This commitment problem prevents the integrated firm from monopolizing the final good market. To show that this result survives even when the upstream unit of the integrated organization can commit to shutting its downstream subsidiary down, we introduce a variant of the main model in which we assume that the integrated firm deals with the nonintegrated retailer via Nash bargaining (Horn and Wolinsky, 1988; O Brien and Shaffer, 2005; Milliou and Petrakis, 2007). We show that the integrated firm wants to keep 4 For example, firewall provisions have been recently adopted by the FTC in vertical merger cases like Lockheed Martin (Lockheed Martin Corp., FTC File No ), Raytheon (Raytheon Co., FTC File No ) and PepsiCo (PepsiCo Inc., FTC Docket No ). See the 2008 UK Competition Commission guidelines or the 2011 US Department of Justice guidelines to merger remedies for further references. 5 Other papers focusing on settings that feature complementarity in the provision of inputs or services are Laussel (2008), Laussel and Van Long (2012), Matsushima and Mizuno (2012), and Hermalin and Katz (2013). The analysis in Reisinger and Tarantino (2013) departs from these papers by analyzing vertical integration rather than exclusivity arrangements of service providers, which is the main focus of Hermalin and Katz (2013). In addition, the results in Reisinger and Tarantino (2013) do not rely on the efficiency incentives for vertical integration such as the elimination of double marginalization, a common feature of Laussel (2008), Laussel and Long (2012) and Matsushima and Mizuno (2012). 3

5 its downstream affiliate alive to improve its bargaining position vis-à-vis the independent retailer. The discussion thus far begs the uestion why would the upstream monopolist merge with the inefficient retailer. This might happen because the antitrust authority forbids a merger with the efficient retailer because it leads to market monopolization (as shown in Lemma 2). In this respect, the model provides a motivation why the upstream monopolist can only merge with the less efficient retailer. There are also several alternative explanations. For example, the efficient retailer might be part of a large conglomerate, which prevents the upstream monopolist from acuiring it. Also, due to historical reasons the upstream firm might be integrated with a retailer when the industry is liberalized, and a more efficient retailer enters the market. In addition, we demonstrate that a market structure in which the monopoly producer is integrated with the inefficient retailer can arise in a model where the upstream monopolist s integration decision is taken under uncertainty over retailers marginal cost of production. Specifically, we provide the conditions such that the monopoly producer merges with a retailer that is less efficient in expectation and this merger leads to a procompetitive outcome (Proposition 6). The Chicago School has challenged the view that an upstream monopolist needs to integrate in order to monopolize a competitive downstream market (e.g., Bork, 1978; Posner, 1976; among others). It has also disputed that an integrated monopoly producer has an incentive to exclude competing firms that can be the source of extra rents thanks to, say, cost efficiency. The post-chicago School literature has noted that, when wholesale contracts are secret, the upstream monopolist s market power is eroded by a commitment problem that prevents it from monopolizing the final good market. 6 In this literature, vertical integration allows a dominant supplier to restore its market power by foreclosing the competing retailer s access to the intermediate good. We build on the post-chicago School literature by embracing its approach. At the same time, we borrow from the Chicago School the idea that the dominant producer might deal with retailers with different marginal costs of production. We show that in line with the Chicago School argument, these differences in marginal costs give rise to an output-shifting effect that can render vertical integration procompetitive with respect to nonintegration. This result suggests that, for example, policies of divestiture imposed by regulatory agencies to prevent foreclosure can have unintended conseuences and may well be misguided. Rey and Tirole (2007) list some of the major decisions of divestitures taken by antitrust authorities, from the 1984 breakup of AT&T to the separation of electricity generation systems from high voltage electricity transmission systems in most countries. Consistent with our conclusions, Lafontaine and Slade (2007) document that studies assessing the implications of these forced vertical separations generally find that such legal decisions lead to price increases. Other papers have analyzed vertical integration in different, but related, contexts. For example, Ordover, Saloner, and Salop (1990) and Chen (2001) consider the case of public offers in linear prices. Choi and Yi (2000) develop a model in which upstream firms can 6 This commitment problem was first noticed by Hart and Tirole (1990), and then further analyzed by O Brien and Shaffer (1992), McAfee and Schwartz (1994), Rey and Vergé (2004), and Marx and Shaffer (2004), among others. Recently, Nocke and Rey (2012) have proposed a model featuring upstream manufacturers that produce differentiated goods. 4

6 choose to customize their inputs to fit the needs of downstream firms, and Riordan (1998) considers a model in which a dominant firm has market power in the final and intermediate goods market. Finally, Nocke and White (2007) analyze the effects of vertical integration on the sustainability of upstream collusion. These papers find that integrated firms have an incentive to foreclose their downstream rivals. Instead, we show that an integrated firm wants to keep a more efficient rival retailer alive, and serve it at favorable conditions when particularly efficient. Our paper is also related to the literature on vertical relationships that emphasizes the role of differences among retailers. Inderst and Shaffer (2009) and Inderst and Valletti (2009) study the implications of price discrimination in input markets when buyers are asymmetric. 7 Relatedly, Chen and Schwartz (2013) analyze the welfare effects of monopoly price discrimination when costs of service differ across consumer groups. Finally, Spiegel and Yehezkel (2003) analyze the case in which retailers are vertically differentiated. However, this literature does not study vertical integration and therefore does not examine the forces at work in our model. The article is structured as follows: Section 2 presents the main model, and Section 3 provides the euilibrium analysis. In Section 4, we extend the model to include a less efficient fringe of alternative producers of the intermediate good, and in Section 5, we test the robustness of our main results to alternative assumptions. Section 6 presents a model with euilibrium vertical integration when retail costs are uncertain, and Section 7 concludes. The formal proofs of the results are relegated to the Appendix. 2 The Model We study a vertically related industry along the lines of McAfee and Schwartz (1994) and Rey and Tirole (2007). An upstream firm, U, is a monopoly producer of an intermediate good with marginal production cost c. It supplies two retailers, D 1 and D 2, that are Cournot rivals in a downstream market (see Figure 1). The retailers transform the intermediate good into a homogeneous final product on a one-to-one basis. In contrast to previous literature, we allow retailers to carry different marginal costs of production. Specifically, retailer D 1 s constant marginal cost of production is µ 1, and retailer D 2 s marginal cost is µ 2, with µ 2 µ 1. We assume that the difference between µ 2 and µ 1 is small enough that both retailers are active when they obtain the intermediate good at marginal cost c. Each retailer produces a uantity of i, i = 1, 2, resulting in an aggregate retail output of Q = The (inverse) demand function for the final good is p = P (Q). It is strictly decreasing and thrice continuously differentiable whenever P (Q) > 0. Moreover, we employ the standard assumption that P (Q) + QP (Q) < 0, which guarantees that the profit functions are (strictly) uasi-concave and that the Cournot game exhibits strategic substitutability (e.g., Vives, 1999). We also assume that P (Q) is not too negative. As we show below, this ensures concavity of the monopoly producer s profit function. 7 Hansen and Motta (2013) consider a model in which retailers differ in their production costs due to cost shocks, but neither the manufacturer nor rival retailers observe the cost realization. They show that if retailers are sufficiently risk averse, the manufacturer optimally sells through a single retailer. 5

7 D 1 U Consumers D 2 Figure 1: Framework with Vertical Separation. When contracting with retailer D i, i = 1, 2, the upstream monopolist offers a take-itor-leave-it two-part tariff contract consisting of a fixed component, F i, and a unit price, w i. Upon accepting the monopolist s offer, retailer D i s total marginal costs are µ i + w i. We consider two scenarios. In the first, firms are not integrated (vertical separation), whereas in the second, the monopoly producer U is integrated with either retailer D 1 or retailer D 2 (vertical integration). In the scenario with vertical separation, the game proceeds as follows: 1. U secretly offers to each retailer D i a two-part tariff contract denoted by T i = {w i, F i }. 2. Retailers simultaneously and secretly accept or reject the contract offer. 3. Retailers order a uantity of the intermediate good, i, and pay the tariff. Then, they transform the intermediate good into the final good and simultaneously choose uantities. Afterwards, retail purchases are made, and profits are realized. We assume that the offers formulated by the monopoly producer U are secret: retailer D i observes the contract it is offered by U but not the contract that U offers to retailer D i, and vice versa. Moreover, the upstream monopolist U produces on order because retailers accept their offers and pay the respective tariff before competing in the final good market. We solve for the perfect Bayesian Nash euilibrium that satisfies the standard passive beliefs refinement (e.g., Hart and Tirole, 1990; O Brien and Shaffer, 1992; McAfee and Schwartz, 1994; Rey and Tirole, 2007; Arya and Mittendorf, 2011). With passive beliefs, a retailer s conjecture about the contract offered to the rival is not influenced by an offeuilibrium contract offer to itself. This is a natural restriction on the potential euilibria of a game with secret offers and production on order because, from the perspective of the upstream monopolist, under these two assumptions retailers D 1 and D 2 form two separate 6

8 markets (Rey and Tirole, 2007). In Section 5, we discuss the impact of alternative belief assumptions on our results. In stage 2, we assume that retailers secretly decide on the contract offer made by U. Note, though, that the analysis would not change if these decisions were public. This is because each retailer D i correctly anticipates the euilibrium action of the rival retailer (which is to accept U s offer) and because the out-of-euilibrium action to reject U s offer leads to zero profits and is therefore independent of the unit price w i. In the scenario with vertical integration, the monopoly producer U and its downstream affiliate maximize joint profits. The game proceeds as laid out above, with the exception that, as is natural and in line with Hart and Tirole (1990) and Rey and Tirole (2007), the downstream affiliate of the integrated firm is informed about the terms of U s offer to the rival retailer. We also assume that the downstream affiliate is informed about the acceptance decision of its rival. However, for the same reasons as above, the outcome would be identical if the downstream affiliate was not informed about this decision. 8 Before solving the model, it is useful to introduce some notation. First, we denote by i m the monopoly uantity produced by retailer D i when it obtains the intermediate good at marginal cost (w i = c), m i arg max {(P () c µ i )}, whereas π m i denotes retailer D i s monopoly profit when producing m i : π m i max {(P () c µ i )}. Analogously, we use c i and π c i to denote the Cournot uantity and profit of D i when both retailers obtain the intermediate good at marginal cost i c arg max {(P ( + i) c c µ i )}, πi c max {(P ( + i) c c µ i )}. Finally, we denote by i (w i, w i ) the Cournot uantity produced by retailer D i when it pays a unit price of w i for the intermediate good, and the unit price paid by retailer D i is w i, i (w i, w i ) arg max {(P ( + i ) µ i w i ) }. (1) 3 Euilibrium Analysis We now examine the euilibrium allocations with vertical separation and integration. 8 As we will show in Section 4, considering the case in which the transmission of this information is not possible becomes relevant in the analysis of the model with a bottleneck alternative. 7

9 3.1 Vertical Separation We start with the case in which no firm is vertically integrated. Because retailer D 1 is (weakly) more efficient than retailer D 2, U will seek to monopolize the product market by inducing D 1 to sell the monopoly output (1 m ). It can attain this outcome by making an unfeasible offer to D 2 and an offer such as T1 m = {c, π1 m } to D 1. However, D 1 anticipates that when offers are secret, U s unfeasible offer to D 2 is not robust to secret renegotiation. The reason is that the monopoly producer has the incentive to sell an additional amount to D 2, thus causing D 1 to incur a loss. 9 Retailer D 1 will then turn T1 m down, implying that the euilibrium of the game without integration features the same commitment problem as in Hart and Tirole (1990). In Lemma 1 we show that with passive beliefs, the monopoly producer offers contracts such that the unit price of the intermediate good is eual to its marginal cost of production (c) and these contracts are accepted by both retailers in euilibrium. LEMMA 1. The monopoly producer (U) offers a contract T i = {c, π c i } to retailer D i with i = 1, 2. Thus, the euilibrium uantities with vertical separation are given by c 1 and c 2. The result in Lemma 1 is well-known in the literature, and its intuition is as follows. A retailer s decisions (contract acceptance and intermediate good purchases) are unaffected by an unobserved change in the input price to the rival retailer. Therefore, when the monopoly producer contracts with each retailer D i, i = 1, 2, it acts as if the two are integrated, given the contract to retailer D i. This pairwise maximization problem reuires that the contractual arrangements between U and D i maximize bilateral profits. Bilateral profit maximization yields a unit price eual to the monopoly producer s marginal cost (c). Conseuently, each retailer produces its Cournot uantity, and the upstream monopolist reaps the sum of Cournot profits π c 1 + π c 2 via the fixed components of the two-part tariff. 3.2 Vertical Integration With vertical separation, the euilibrium production profile features retailer D 1 producing c 1 and retailer D 2 producing c 2. From the monopoly producer s perspective, it would be better if the profile were instead given by c and c 2 1. This alternative production profile would allow the upstream monopolist U to reap greater profits from the final good market. The aggregate retail output and, therefore, the retail price are the same, so industry revenues are the same, but costs have fallen, because D 1 is (weakly) more efficient than D 2. Integration is an obvious way for U to implement a more profitable production profile. Thus, we proceed by analyzing a framework in which the monopoly producer U is integrated with one of the retailers. We consider two distinct cases: first, U is integrated with the efficient retailer (D 1 ), and second, U is integrated with the inefficient retailer (D 2 ). 9 This result follows from the observation that given 1 = m 1, 2 = arg max {(P ( + m 1 ) c µ 2 )} = R C ( m 1 ) > 0, where R C denotes the standard Cournot reaction function. Given T1 m, when secretly renegotiating with D 2, the upstream monopolist maximizes the value of the contractual relationship with this retailer, and the profits that U can extract from D 2 are positive. 8

10 Vertical Integration between U and D 1 The monopoly producer U can acuire the efficient retailer (D 1 ) and foreclose the inefficient retailer s (D 2 ) access to the intermediate good. Hart and Tirole (1990) and Rey and Tirole (2007) establish this result in a framework with symmetric retailers; the intuition is that with vertical integration, U internalizes the effect of selling to the rival retailer via the reduced downstream profits made by its own affiliate. Therefore, the temptation of opportunism vanishes and the monopolist can credibly commit itself to reducing supplies to the rival retailer. This is the foreclosure effect of vertical integration. In our framework with asymmetric retailers, the same result occurs. The argument is standard. Suppose that the monopoly producer supplies the monopoly uantity 1 m to its downstream affiliate (D 1 ) and denies access to the intermediate good to the nonintegrated retailer D 2. The integrated firm U D 1 then receives the monopoly profit π1 m, so that any deviation to supply the nonintegrated retailer D 2, which is less efficient than D 1, will result in a lower profit for the integrated firm. 10 LEMMA 2. Suppose the upstream monopolist U is integrated with retailer D 1. In euilibrium, the integrated firm U D 1 forecloses retailer D 2 s access to the intermediate good. Hence, retailer D 1 produces 1 = m 1, retailer D 2 remains inactive ( 2 = 0), and U D 1 obtains the monopoly profit π m. Clearly, for the upstream producer (U), integration with retailer D 1 is more profitable than remaining separated, because it allows the integrated firm to monopolize the final good s market. Vertical Integration between U and D 2 Let the monopoly producer be integrated with the inefficient retailer (D 2 ). As explained in the introduction, a reason for this could be that regulation prohibits U from merging with D 1 on the grounds that such a merger is anticompetitive. In Section 6, we show that a market structure in which U is integrated with the inefficient retailer can arise when retailers costs are uncertain. Here we analyze U s pricing decisions when integrated with retailer D 2. We solve for U s optimal offer to its downstream unit D 2 and the competing retailer D 1, leading us to Proposition 1. PROPOSITION 1. Suppose the upstream monopolist U is integrated with retailer D 2. The uniue euilibrium features firm U D 2 trading the intermediate good internally at marginal cost (w 2 = c) and setting and w 1 = P (Q) 2µ 2 + µ 1 + P (Q) (µ 2 µ 1 ) (P (Q) c µ 2 ) (P (Q)) 2 (2) with 1 = 1 (w 1, c), 2 = 2 (c, w 1) and Q = F 1 = 1 (P (Q) µ 1 w 1), (3) 10 The proof of Lemma 2 follows the same lines as in Hart and Tirole (1990) and is therefore omitted. 9

11 Proposition 1 shows that, if U and D 2 are vertically integrated, they internally trade the intermediate good at a price eual to marginal cost. The two firms maximize joint profits; thus, any alternative internal pricing policy is not robust to secret renegotiation (Ordover, Saloner, and Salop, 1990, Chen, 2001, Choi and Yi, 2001). It follows that the downstream unit of the integrated firm (D 2 ), although inefficient, will be active in the final good s market. As the following discussion suggests, the upstream unit of the integrated firm is better off seeing its inefficient downstream unit shuttered. However, in our setting, U cannot credibly commit to such a policy. Note, though, that U would not shut D 2 down in more elaborate models that dispense of the commitment assumption. As we show in Section 5.4, if D 1 has some bargaining power vis-á-vis U D 2, then U D 2 keeps the downstream unit alive to reduce D 1 s outside option. Another reason why U might not want to end D 2 s business could be because D 2 allows U to capture valuable information about demand conditions. Alternatively, D 2 might retail multiple products; thus, shuttering D 2 would reduce the profits of the integrated firm across its full range of products. More importantly, Proposition 1 shows that the integrated firm U D 2 does not necessarily foreclose the competing retailer s access to the intermediate good. To grasp the incentives of U D 2 when setting w 1, note that the integrated firm fixes w 1 to maximize bilateral profits with D 1, subject to the constraint that the internal trading price is at marginal cost. The trade-off it faces is as follows. By raising the unit-price offer to the competing retailer D 1, U forecloses D 1 s access to the intermediate good and monopolizes the market for the final good via D 2 (the foreclosure effect). However, a countervailing effect emerges in our framework. U benefits if the uantity produced by the efficient retailer D 1 increases, at the expenses of D 2. How can the upstream firm achieve this, given that it cannot commit to restricting its downstream affiliate s uantity? Since with vertical integration D 2 observes U s offer to D 1, U needs to lower the unit price w 1 : in this way, D 1 s uantity increases and D 2 responds by reducing its output. U then extracts the profit of D 1 via the fixed component of the two-part tariff. This establishes the output-shifting effect of vertical integration. Note that a reduction in w 1 implies a reduction in industry revenue: a lower value of w 1 triggers an increase of 1 that is larger than the conseuent decrease in 2, because 1 / w 1 > 2 / w 1 > 0. This hints that lowering w 1 benefits the integrated firm only to the extent that the fall in industry revenue is compensated by the cost-efficiency of D 1. In light of this discussion, we next ask under which conditions w 1 will be low enough that D 1 produces a positive uantity. PROPOSITION 2. The integrated firm U D 2 sets a unit price w 1 such that the efficient nonintegrated retailer D 1 is active on the market for the final good ( 1 (w 1, c) > 0) if, and only if, µ 1 < µ 2. If µ 1 = µ 2, U D 2 forecloses retailer D 1 s access to the intermediate good. The proposition shows that if the two retailers D 1 and D 2 were eually efficient (µ 1 = µ 2 ), then U D 2 would foreclose D 1 s access to the intermediate good (Hart and Tirole, 1990; Rey and Tirole, 2007). Indeed, turning back to (2), for µ 1 = µ 2 = µ, the euilibrium value of w 1 is eual to P (Q) µ. At this unit price, the marginal costs of D 1 (w 1 + µ 1 ) are eual to the euilibrium price, implying that 1 = 0. This shows that the expression for w 1 in Proposition 1 provides a generalization of the euilibrium unit price obtained in models with eually efficient retailers to the case of asymmetric retailers. 10

12 Proposition 2 also shows that retailer D 1 is active as long as it is strictly more efficient than retailer D 2 (µ 1 < µ 2 ). To understand this, look at the first-order condition for w 1, which, as we show in the Appendix, is given by (P (Q) 2 + w 1 c) 1 w 1 + P (Q) 1 2 w 1 = 0. (4) U can foreclose D 1 s access to the intermediate good by setting w 1 = P (Q) µ 1, so that 1 euals zero. In this case, Q = 2 m, with 2 m implicitly determined by the downstream firstorder condition 2 m = (P (2 m ) µ 2 c)/p (2 m ). Inserting these values into the left-hand side of (4) and simplifying yields (µ 2 µ 1 ) 1 w 1 0, (5) because 1 / w 1 < 0. Therefore, if µ 2 µ 1 > 0 and w 1 = P ( m 2 ) µ 1, U finds it profitable to decrease w 1 from the foreclosure level and induce D 1 to produce a positive uantity. The intuition is as follows. The monopoly uantity m 2 maximizes industry profits when the integrated firm is bound to produce the final good at a marginal cost of µ 2. However, if µ 1 < µ 2, letting D 1 participate in the final good market implies that the final good is produced more efficiently. The latter effect outweighs the decrease in industry revenue because it reflects the direct impact of lower production costs on industry profitability. 11 Then, even if the difference between µ 1 and µ 2 is tiny, it is not optimal for D 1 to foreclose D 1 s access to the intermediate good. A uestion of great importance for competition policy regards the magnitude of the output-shifting effect. Specifically, can the incentive to reduce w 1 be so strong as to induce U to formulate a unit-price offer below its marginal cost of production (i.e., w 1 < c)? This would render vertical integration procompetitive because the sum of the per-unit prices at the wholesale level would be lower than with vertical separation, leading to larger industry output and consumer surplus. Proposition 3 shows that this can indeed occur. PROPOSITION 3. The integrated firm U D 2 sets a unit price w 1 below its marginal cost of production c if, and only if, µ 2 µ 1 > (P (Q) µ 2 c)(p (Q)) 2 (P (Q)) 2 (P (Q) µ 2 c)p (Q). (6) If condition (6) is satisfied, the aggregate uantity with vertical integration is larger than with vertical separation. Proposition 3 shows that the output-shifting effect can induce the upstream unit of the integrated firm to engage in below-cost pricing at the wholesale level. Specifically, the proposition indicates that below-cost pricing is more likely to occur, the more efficient D 1 is 11 Technically, the increase in industry uantity (and the conseuent fall in revenue) is of second-order importance, because 2 is at the euilibrium level when D 2 s marginal cost is µ 2, due to the envelope theorem. 11

13 relative to D 2 (i.e., if µ 2 µ 1 is large). Indeed, the more efficient D 1, the higher the profit increase that the integrated firm obtains when shifting output to D 1. For the intuition behind the result in Proposition 3, recall that the unit price w 1 is set to maximize the bilateral profits of the integrated firm and D 1. The uestion is why a value of w 1 lower than c can maximize these profits. Below-cost pricing produces an expansion of industry output relative to vertical separation, and thus a fall in industry revenue. However, setting w 1 below c induces retailer D 2 to reduce its uantity compared to vertical separation. If D 1 is particularly efficient, the fall in industry revenue is outweighed by the fact that output is produced more efficiently, thereby rendering a strategy of belowcost pricing optimal. Consistent with the intuition for the results above, lowering w 1 acts as a commitment to tame the incentive of the integrated firm s downstream unit to expand its output. In the scenario with vertical separation, lowering w 1 below c was not optimal because retailer D 2 did not observe the offer to D 1, and therefore could not respond to a change of the value of w 1. This last observation explains why the strategy of pricing below cost, although available, does not arise at euilibrium with vertical separation. Regarding the profitability of vertical integration, a revealed preference argument shows that for U, a vertical merger with retailer D 2 is more profitable than remaining separated, even when the value of the unit price w 1 lies below marginal cost c. With integration the intermediate good is traded internally at marginal cost. Therefore, setting also w 1 at marginal cost would allow the monopoly producer U to replicate the outcome with vertical separation (Lemma 1). Yet, U prefers to depart from pricing at cost, which implies that this departure must be profitable. The output-shifting effect can also be linked to the rate of cost pass-through. A cost increase is shifted to consumers at a rate that depends on the curvature of consumer demand (Bulow and Pfleiderer, 1983; Weyl and Fabinger, 2013). Specifically, the pass-through rate is larger if the demand function is relatively convex. These considerations suggest that the below-cost pricing result is more likely to occur when the demand function is concave, because the nonintegrated retailer D 1 then adjusts its uantity only slightly in reaction to a change in w 1. Thus, U must reduce its unit price by a large amount to induce D 1 to expand its uantity. Indeed, in the formula for w1 in (2), w1 is particularly low if the demand function is relatively concave (P (Q) is small). To illustrate these results, we solve an example using the linear demand function P (Q) = α βq, with β > 0 and α > c + µ 2. We find that if the monopoly producer U is integrated with the less efficient retailer D 2, it sets a unit price w1 eual to (α + c + 4µ 1 5µ 2 ) /2. Let us denote by the difference between retailers marginal costs of production (µ 2 µ 1 ). Both D 1 and D 2 are active provided is smaller than the threshold (α c µ 1 ) /3. In line with Proposition 3, we find that vertical integration between U and D 2 is procompetitive (w1 < c) if, and only if, c (α c µ 1 ) /5, whereas it is anticompetitive for values of below c, with c <. 12 Figure 2 plots these conditions using α = β = 1 and c =.25. The shaded area shows when vertical integration between U and D 2 is procompetitive, as the euilibrium value of w 1 lies below the upstream monopolist s marginal cost c. 12 Note that, for all > 0 the profits of U D 2 when the unit price is eual to w 1 are strictly larger than the profits of the integrated firm when foreclosing D 1 s access to the intermediate good. 12

14 Procompetitive Vertical Integration c Anticompetitive Vertical Integration 0.05 Figure 2: Linear Demand Example 4 Model with a Competitive Bottleneck Alternative In the industry structure of Section 2, the upstream producer U is an unconstrained monopolist. In this section, we extend that model to consider an industry in which U competes with a fringe of less efficient firms, denoted by Û. These fringe firms bear unit costs ĉ to produce the intermediate good, with ĉ c, and behave competitively, as they are willing to offer the intermediate good at a unit price of ĉ. 13 Thus, fringe firms Û act as a bottleneck alternative that constrains the market power of the dominant producer (U). The game proceeds as described in Section 2. We introduce an additional piece of notation: ˆπ i c max {(P ( + i ) ĉ µ i ) }, with i = (c, ĉ) as defined in (1). Thus, ˆπ i c is the profit of a retailer D i that buys the intermediate good from the fringe firms at cost ĉ, whereas its rival obtains the same good at marginal cost c. We assume that fringe firms are effective in constraining the market power of U, i.e., ĉ is low enough. This implies that the uantity of retailer D i when buying the intermediate good at ĉ is positive, even if retailer D i obtains the intermediate good at c ( i (ĉ, c) > 0). In what follows, we first show that the competitive conseuences of vertical integration are the same as those obtained in the main model of Section 2. Then, we analyze how information transmission within an integrated company affects the final good s uantity and price. 13 We obtain the same results if the fringe consists of only a single firm competing à la Bertrand with U to serve retailers. Bertrand competition implies that Û would set a per-unit price of ĉ and a fixed payment of zero. 13

15 4.1 Vertical Separation Consider first an industry featuring vertical separation. LEMMA 3. The dominant producer (U) offers a contract T i = {c, π c i ˆπ c i } to retailer D i with i = 1, 2. Thus, the euilibrium uantities with vertical separation are given by c 1 and c 2. The result in Lemma 3 follows Hart and Tirole (1990) and Rey and Tirole (2007). We omit the proof because it mirrors the one of Lemma 1. First, note that the euilibrium uantities are the same as in the model without a bottleneck alternative. Because the dominant producer is more efficient than the bottleneck alternative (Û), it supplies both retailers. Moreover, pairwise profit maximization between U and each retailer D i reuires fixing the per-unit price at c, leading to euilibrium Cournot uantities of 1 c and 2. c However, differently from the unrestricted monopoly model, when a bottleneck alternative is available to retailers, U cannot ask for the payment of the full Cournot profit in the fixed component of the two-part tariff, because D 1 and D 2 can buy from Û and secure a profit of ˆπc i. Therefore, U will set a fixed payment of F i eual to πi c ˆπ i c. 4.2 Vertical Integration We now consider the vertically integrated industry. We focus on the case in which U is integrated with the inefficient retailer (D 2 ). The reason is that when U is integrated with the more efficient retailer (D 1 ), it will foreclose the competing retailer s access to the intermediate good to the extent possible. Differently from the analysis in Section 3.2, in a model with a bottleneck alternative, U needs to take into account that retailer D 2 can turn to Û and buy the intermediate good at a unit price of ĉ. Therefore, in euilibrium U D 1 will set w 2 = ĉ, both retailers D 1 and D 2 are active and produce 1 = 1 (c, ĉ) and 2 = 2 (ĉ, c), respectively. 14 We now let the dominant producer U be integrated with the less efficient retailer D 2, leading to the results in the following proposition. PROPOSITION 4. The integrated firm U D 2 sets the same unit price as in the set-up without the bottleneck alternative, that is, w1 BA = w1, if w1 < ĉ, and w1 BA = ĉ otherwise = min{w1, ĉ}). The fixed component of the two-part tariff is eual to (w BA i F BA 1 = 1 (w BA 1, c)(p (Q) µ 1 w BA 1 ) 1 (ĉ, c)(p ( 1 (ĉ, c) + 2 (c, ĉ)) µ 1 ĉ), with 1 = 1 (w BA 1, c), 2 = 2 (c, w BA 1 ), and Q = The proposition shows that, as long as w 1 < ĉ, the optimal unit price is the same with and without a bottleneck alternative. The intuition is as follows. The presence of the bottleneck alternative affects the outside option of retailer D 1 (i.e., the profits D 1 raises when rejecting U s offer). In the scenario without the bottleneck alternative this outside option was zero, whereas with the bottleneck alternative it is given by the profit of D 1 when buying from Û. However, since the downstream affiliate of the integrated firm (D 2 ) knows when D 1 buys 14 The formal proof of this result follows Rey and Tirole (2007). 14

16 the intermediate good at ĉ, the outside option of D 1 does not depend on w1 BA. Therefore, the optimal value of w 1 coincides with the one derived in Proposition 1 as long as w1 < ĉ. When w1 ĉ, the unit price with the bottleneck alternative (w1 BA ) is eual to ĉ. The reason is that raising the unit price above ĉ cannot be profitable for U, because D 1 can then turn to the bottleneck alternative Û. This discussion implies that the competitive implications of vertical integration are as in Section 3. Specifically, the results in Proposition 3 carry over to the model with the bottleneck alternative. 4.3 Information Transmission The results in Proposition 4 rely on the assumption that, as in the main model, the downstream affiliate of the integrated firm is informed about the rival retailer s acceptance decision. However, this information transmission might not be possible, for example, due to the regulatory imposition of an information firewall between the two units of the integrated firm. In fact, the imposition of behavioral remedies of this type is one of the most common forms of conduct relief in merger decisions. For this reason, in this section we propose a variant of the model with a bottleneck alternative to analyze the effects of the imposition of an information firewall on economic outcomes. 15 Following Nocke and Rey (2102), we model the situation in which information transmission is not feasible by assuming that stages 2 and 3 of the game in Section 2 take place simultaneously. When stages 2 and 3 occur simultaneously, the downstream unit of the integrated firm cannot know the rival retailer s decision when it chooses its uantity. Instead, when stages 2 and 3 take place seuentially (as in the main model), the upstream unit of the integrated company can inform the downstream unit about the acceptance decision of the rival retailer before the integrated retailer chooses its uantity. The analysis of the model without information transmission leads to the results in Proposition 5. PROPOSITION 5. If the dominant producer U is integrated with the less efficient retailer D 2, the unit price in the regime with information transmission is lower than the unit price in the regime without information transmission. We find that when information transmission is not possible, the integrated firm has an incentive to raise the unit price w 1 above the one with information transmission. The intuition behind this result is as follows. If information transmission is not possible, D 2 does not know whether D 1 accepted U s offer when setting its uantity. Due to passive conjectures, D 2 believes that D 1 buys from U at w 1, as it does on the euilibrium path. This implies that D 2 produces the euilibrium output 2 (c, w 1 ) even when D 1 buys from Û. Conseuently, the outside option of D 1 decreases in w 1, because an increase of w 1 leads to an increase of D 2 s uantity. Realizing this, the upstream unit of the integrated firm increases w 1 to reduce the outside option of D 1 and demand a higher fixed payment The imposition of information firewalls is typically justified by the possibility that the downstream unit of an integrated firm obtains private information of a rival s production process via its upstream unit. We show that even in a model that abstracts from these considerations, information firewalls affect consumer surplus. 16 This effect is not present when information transmission is possible because the outside option of D 1 does not depend on the value of w 1. 15