Countervailing Power and Upstream Innovation

Transcription

1 & Antitrust and Innovation Friday, Oct. 27, 2006 Session Ia Vertical Issues 09:45-10:30 14 th WZB Conference on Markets and Politics in collaboration with CEPR and sponsored by the Fritz Thyssen Stiftung and LEAR Conference Paper: Countervailing Power and Upstream Innovation Roman Inderst (Goethe University Frankfurt, London School of Economics and CEPR) Wissenschaftszentrum Berlin für Sozialforschung Reichpietschufer 50, Berlin, Germany Telefon +(49) 0(30) Telefax +(49 0(30) Internet:

2 Countervailing Power and Upstream Innovation Roman Inderst Christian Wey October 2006 Abstract We challenge the view that the presence of powerful buyers stifles suppliers incentives to innovate. Following Katz (1987), we model countervailing (or buyer) power as the ability of, in particular, large buyers to substitute away from a given supplier. We employ a bargaining framework and find that the presence of larger and more powerful buyers increases a supplier s incentives to reduce marginal costs. We identify two main forces. First, we show that while the supplier s total profits decrease in the presence of larger buyers, the supplier can extract a larger fraction of any incremental profits. Second, we find that by lowering its own marginal costs a supplier can reduce the value of buyers outside options and that this effect is also stronger if there are fewer but larger buyers. Keywords: Buyer Power; Countervailing Power; Dynamic Efficiency. Roman Inderst acknowledges financial support from the ESRC grant on Buyer Power in Retailing. A previous version of this paper was circulated under the title How Stronger Buyers Spur Upstream Innovation (CEPR DP 5365). We thank participants at various seminars, the 2006 IIO conference in Boston and EARIE, as well as Paul Dobson for helpful comments. Goethe University Frankfurt and London School of Economics. r.inderst@lse.ac.uk. Deutsches Institut für Wirtschaftsforschung Berlin (DIW), Technische Universität Berlin, CEPR, London. cwey@diw.de. 1

3 1 Introduction Any purely static view of how market structure affects welfare is likely to be misleading. Antitrust authorities are thus well advised to take a more dynamic perspective, as they increasingly do, thereby incorporating firms incentives to invest and innovate. Traditionally, the focus has been squarely on how horizontal market power affects investment incentives. Lately, however, antitrust authorities around the world have become increasingly concerned about the exercise of power in vertical relations. Retailing, in particular in fast-moving consumer goods, provides a prominent example. There, the formation of multinational retail companies and the introduction of ever larger store formats have arguably put increasing pressure on suppliers, as documented in numerous recent policy reports. 1 One key concern is that the exercise of buyer power could stifle suppliers incentives to invest and innovate. 2 As we argue in this paper, this may not be the case. To the contrary, we identify several effects that all point in the opposite direction, implying that a supplier s incentives could increase following the formation of larger and more powerful buyers. The presumption that buyer power reduces suppliers incentives seems to rest on the notion that by extracting a larger share of total profits, a powerful buyer can also extract a larger share of any incremental profits from a supplier s investment. 3 More formally, this argument seems to make implicitly the following joint assumptions. First, a given buyer can extract a fixed fraction of the profits that it jointly realizes with a given supplier. Second, a more powerful buyer can command over a higher fixed fraction of joint profits. Though convenient, to our 1 These include Buyer Power and its Impact on Competition in the Food Retail Distribution Sector of the European Union (European Commission, 1999), Buying Power of Multiproduct Retailers (Series Roundtables on Competition Policy DAFFE/CLP(99)21, OECD, 1999), Report on the Federal Trade Commission Workshop on Slotting Allowances and Other Marketing Practices in the Grocery Industry (FTC 2001), and Supermarkets: A Report on the Supply of Groceries from Multiple Stores in the United Kingdom (Competition Commission, 2000). 2 For instance, a report by the FTC (FTC 2001, p. 57) raises concerns that when facing increasingly powerful buyers, suppliers respond by under-investing in innovation or production. Likewise, a report on buyer power prepared for the European Commission suggests that when facing powerful buyers, suppliers may reduce investment in new products or product improvements, advertising and brand building (EC 1999, p. 4). Pitofsky (1997) expresses similar concerns for the health industry. One possible countervailing force, though arguably only applicable to highly concentrated industries, is that the presence of dominant buyers can overcome free-rider problems (as in, for instance, Fumagalli and Motta (2000)). 3 We restrict attention to investments where incentives can not be adequately provided through contractual means. Similar to much of the related literature, this may be the case as it is hard to specify the investment ex ante in sufficient detail. Likewise, with a large number of buyers free-rider problems may also limit the extent to which incentives can be provided through multilateral contracts. 2

4 knowledge there exists, however, no theory that would support such a hard-wired link between buyer power and a buyer s share of total profits. In particular, it is not obvious why this should apply to a larger buyer, i.e., why a larger buyer should be able to extract a larger fixed fraction of any incremental profit that is generated by a supplier s investment. If to answer a given question it is only important to know how a supplier s total profits change following the formation of more powerful buyers, then the precise way in which this takes place may indeed not matter for the analysis. In contrast, in order to study a supplier s investment incentives it seems crucial to distinguish between the impact buyer power has on total profits and the impact it has on incremental profits. We build a model where buyer power arises from first principles. Buyers that compete in a downstream market negotiate with a supplier over bilateral contracts, where we allow for twopart tariffs. Our focus will be on a supplier s incentives to invest in a reduction of marginal costs. In our model, buyers have to spend resources in order to generate alternative supply options after a breakdown of negotiations. As large buyers are able to distribute these costs over a larger number of units, they will ultimately have a more valuable alternative supply option when negotiating with a supplier. Consequently, while for very small buyers the alternative supply options may not represent a credible option, for very large buyers the alternative supply option may be so attractive that it already fully pins down the outcome of negotiations. 4 We find that even though the supplier s total profits are lower if there are fewer but larger buyers, its incentives to reduce marginal costs are higher. This has the following reasons. First, as the outcome of negotiations with large buyers is pinned down by the value of their more attractive alternative supply opportunity, the supplier can retain a larger fraction of the incremental profits that are generated by a reduction in marginal profits. The second effect that we identify derives the fact that buyers compete in the downstream market. We find that the value of a given buyer s alternative supply option decreases the lower the supplier s own marginal costs. This follows in turn as this reduces the marginal input price of competing buyers that still purchase from the same supplier. As a supplier can extract more of the joint profits the lower a buyer s outside option in negotiations, this provides additional incentives for the supplier to 4 In the parlance of bargaining theory, we thus use the well-known outside option principle. Seminal references for this are Shaked and Sutton (1984) and Binmore, Rubinstein, and Wolinsky (1989). We have more to say on this below. 3

5 reduce marginal costs. Importantly, we show that this effect is also stronger if there are fewer but larger buyers. Our analysis provides a formal underpinning for the view that large buyers can have a beneficial impact on consumer surplus and welfare by basically keeping suppliers on their toes. 5 Our paper does, however, not intend to provide a carte blanche for the creation and exercise of buyer power. Instead, we would like to emphasize the following broader implications of our analysis. First, our results show that buyer power need not invariably lead to lower welfare and consumer surplus by stifling upstream investment incentives. Second, our analysis shows that it is essential to make precise the sources of buyer power. In our model, it is buyers size that translates into more attractive alternative supply options, which then have an impact on how joint profits are shared and, thereby, finally on a supplier s incentives to invest. Other ways of enhancing buyer power such as private-label goods in retailing or the adoption of specific purchasing techniques (e.g., the use of electronic buying platforms) may well have different implications. There is a growing literature on buyer power. 6 Almost all of these papers focus on shortrun implications for prices on the downstream market, typically in a model where only linear contracts between up- and downstream firms are feasible. 7 To our knowledge, there are only a few exceptions that consider the long-run implications for investment incentives. Both Chen (2004) and Inderst and Shaffer (forthcoming) consider the impact of mergers among buyers on product diversity. In Inderst and Wey (2003, forthcoming) a merger of buyers may induce suppliers to choose a less convex and potentially welfare improving production technology. 8 In 5 To our knowledge, such a possibly positive incentive effect has not been analyzed so far. One argument that we encountered in discussions is that incentives may increase as suppliers have to stretch higher in order to land on the shelves of larger retail chains. This argument suggests some kind of tournament. Being listed at a retailer is associated with some fixed payoff, while a larger retailer can draw on more competing suppliers. While even in a tournament it is far from obvious that incentives to invest increase in the number of participants, the implicit assumption of a fixed price seems not realistic. Instead, the winning supplier will have to offer terms that are competitive vis-a-vis all other potential substitutes. 6 Snyder (2005) and Inderst and Mazzarotto (2006) provide recent surveys. 7 Dobson and Waterson (1997) is an early example of models that study countervailing or buyer power under linear contracting. Chen (2003) uses linear contracts only for transactions with a (downstream) market fringe. Still other papers focus exclusively on distributional issues and derive conditions for when downstream or upstream mergers are profitable (e.g., Horn and Wolinksy (1988) or Chipty and Snyder (1999)). 8 The intuition is that larger buyers negotiate less at the margin of a supplier s strictly convex production technology, which allows a supplier to recoup less of its incremental costs at high production volumes when negotiating with fewer but larger buyers. For a related insight concerning a supplier s choice of capacity see Vieira-Montez (2005). Inderst and Wey (2002) also discuss product innovation, showing that in the presence of 4

6 all of these papers, buyer power has different origins than in the current model, where it is linked to buyers outside option. This approach follows closely Katz (1987), which analyzes the implications of imposing uniform pricing. Other channels to create a link between, in particular, size and buyer power include risk aversion (e.g., Chae and Heidhues (2004), DeGraba (2003)) or collusion among suppliers (Snyder (1996)). Finally, some of the more general insights on bargaining and incentives in this paper are shared with the recent literature on the hold-up problem. De Meza and Lockwood (1998) and Chiu (1998) show how results of the theory of ownership change if one adopts a bargaining concept that embodies the logic of the outside option principle, as we do in the current paper. There are, however, several important differences between their work and ours. In our model, a supplier negotiates with multiple buyers, which further compete on a downstream market. Also, we study the role of buyers size and are interested in what impact it has on welfare and consumer surplus by affecting upstream investment incentives. The rest of the paper is organized as follows. Section 2 presents the model and derives some preliminary results. Section 3 analyzes how the formation of larger and more powerful buyers affects investment incentives. Section 4 discusses and extends these results. Section 5 concludes. 2 The Model and Preliminary Analysis 2.1 The Industry We analyze a supplier s incentives to reduce marginal costs. The supplier provides an input to an intermediary industry. Firms in the intermediary industry use the input to produce a homogeneous final good. All firms in the intermediary industry have identical production functions. As in Katz (1987), which considers the case where a monopolistic supplier serves two competing downstream firms, we assume that firms transform one unit of the input into one unit of the output. 9 The intermediary firms compete in a number of independent markets. We allow for N 2 independent markets, in each of which two competing firms are active. The 2N downstream firms are owned by a number I 2 of intermediaries, to which we simply refer to larger buyers a supplier may choose a product that generates more demand. 9 Given symmetry of production functions, this specification is not important for our results. A natural example where this specification is reasonable is that of retailing. 5

7 as buyers. A given buyer i, where1 i I, can only own firms in separate markets. This rules out standard monopolization effects. It also allows us to treat all N markets symmetrically, regardless of the number and size of buyers. After presenting our results, we comment more on these assumptions in the light of a particular application, namely retailing. The number of firms n i that buyer i owns will be our measure of the buyer s overall size. As in Katz (1987), larger buyers will be able to extract a better deal from the supplier. Our focus is on analyzing how the presence of more powerful buyers affects the supplier s investment incentives, with buyer power being derived endogenously from buyers size. In each independent market, downstream firms offer a homogeneous good and compete in quantities. All N independent markets are symmetric. If in a given market one of the two active firms chooses the quantity q and the other firm the quantity bq, thefirst firm s revenues are given by R(q, bq) :=qp(q + bq), where P ( ) denotes the inverse demand function. The supplier has constant marginal costs of production c 0. It is convenient to assume that P is twice continuously differentiable where positive. We assume that standard stability conditions are satisfied and that best responses are downward sloping. With constant marginal costs, this is ensured by the following assumption. 10 Assumption 1. The inverse demand P that characterizes the downstream markets satisfies P 0 < min{0, qp 00 } whenever P is positive. We will find that in equilibrium all buyers are supplied at a constant per-unit price that equals marginal costs c. (We formally introduce supply contracts further below.) Under Assumption 1, the Cournot game where two firms can procure at constant input prices equal to c has a unique equilibrium. In this equilibrium, both firms produce symmetric quantities, which we denote by q S. From our assumptions on differentiability and by Assumption 1, we further have that q S is continuously differentiable in c (where q S > 0) withdq S /dc < See, for instance, Vives (1999). 6

8 2.2 The Two Stages of the Model There are two stages in our model. In the first stage, the supplier can choose a non-contractible action to reduce marginal costs. Subsequently, the supplier negotiates simultaneously with all buyers i I. We may think of a situation where the supply contracts for all buyers i are up for renewal. Alternatively, our model may capture the introduction of a new product. 11 In the first stage, the supplier can choose a reduction of marginal costs S 0 such that c = c S,where0 S c and c>0. The associated costs are given by the function K S ( S ), which is strictly increasing and satisfies K S (0) = 0. ItisconvenienttoassumethatK S is twice continuously differentiable and that its derivative satisfies KS 0 (0) = 0 and K0 S ( S) for S c. We want to make sure that production is always profitable in equilibrium. A sufficient condition for this is that there exists some q>0 such that P (q) > c. Negotiations take place in the second stage of the model. There, buyers and the supplier negotiate over an (only privately observed) two-part tariff of the form t i (q) =τ i + qw i. The useoftwo-parttariffs deserves some comments. First, with two-part tariffs we can abstract from well-known issues relating to the presence of double-marginalization. Second, in the set of non-linear tariffs the further restriction to two-part tariffs is relatively innocuous. As will become clear in what follows, our unique equilibrium with two-part tariffs would also be an equilibrium if we allowed for more general menus t i (q). 12 In this respect, the two-part tariffs should also not be interpreted too literally. Though in equilibrium the buyer will make a fixed lump-sum transfer τ i to the supplier, this does not suggest that we should necessarily observe such transfers in practice. 13 We postpone a further description of the bargaining game until the next section. The remainder of this section is dedicated to a definition of buyers alternative supply options. Though our model allows for a broader interpretation, we closely follow Katz (1987) and specify that after disagreement buyers have the option to integrate backwards. When integrating 11 This could also justify why there is only a single (potential) supplier. 12 Itcouldalsobearguedthatnon-linearcontractsmaytosome extent be more realistic if bilateral negotiations allow for third-degree price discrimination. The opposite case is that where supply contracts are determined in a market interface that operates between suppliers and buyers (e.g., an organized commodity exchange). See also Inderst and Shaffer (2005) for a more detailed discussion of the difference between bilateral negotiations and a market interface and the implications for the analysis of buyer power. 13 It is well-known that retailers sometimes charge suppliers up-front transfers in the form of slotting fees. 7

9 backwards, a buyer must incur the fixed costs F 0. The attractiveness of the buyer s new supply option depends on how much resources the buyer spends. A given buyer i that integrates backwards also controls its (new) marginal costs c i Out. Precisely, by incurring the additional expenditure K B ( i B ) the buyer can reduce marginal costs to ci Out = c Out i B,where0 i B c Out and c Out > 0. We specify that K B (0) = 0, whilek B is twice continuously differentiable with K 0 B (0) = 0 and K0 B ( i B ) for i B c Out. While interpreting the alternative supply option as backward integration is convenient, we need only that generating the alternative supply option involves a certain amount of fixed costs, i.e., F + K B in the chosen setting. 14 Instead of integrating backwards, a switch to an alternative supply option may involve costly search and subsequent expenditures to reorganize the purchasing and distribution system. Some of the latter costs may also arise at a newly chosen supplier, which are then rolled over to the buyer. 2.3 Negotiations For the second stage of the model, where supply contracts are determined, we use the following bargaining model. Bargaining proceeds in pairwise negotiations, where the supplier is represented by I different agents, each negotiating with one buyer. All agents of the supplier form rational expectations about the outcome in all other pairwise negotiations, while their objective is to maximize the supplier s payoff. Our approach to the individual pairwise negotiations is axiomatic, though we provide a non-cooperative foundation in Appendix B. 15 We employ the axiomatic Nash bargaining solution. We need not write down the Nash solution in its generality. Several features of our model ensure that the solution has a very simple characterization. Recall first that contracts can specify a fixed fee τ i. This allows to fully disentangle the issue of maximizing joint profits from that of how to share the realized surplus. 16 Next, as firms compete in quantities in each of the N markets and as contracts are not observable, the choice of w i does not affect the supplier s payoff with all other buyers but i. Ifamutuallybeneficial agreement with buyer i is feasible, it is thus 14 In particular, we could also introduce without changing results a linear component, which depends on the subsequently produced quantity. 15 We use this setting, where the supplier is represented by I agents, also in the non-cooperative game in Appendix B. It should be noted that in the characterized equilibrium the supplier could not profitably orchestrate a multilateral deviation by all of its agents. 16 Strictly speaking, we need also risk neutrality to make utility transferable. 8

10 uniquely optimal to set w i = c. Lemma 1. The requirement that joint surplus is maximized in each bilateral negotiation implies that w i = c. Lemma 1 is a restatement of a well-known result. The supplier faces a problem of opportunism when dealing with multiple competing buyers. This problem has been analyzed, though with a different focus, in a number of papers, including Hart and Tirole (1990), McAfee and Schwartz (1994), or O Brien and Shaffer (1994). 17 In these papers, the supplier typically makes simultaneous offers to all downstream firms. 18 Consequently, a downstream firm must form beliefs about the (non-observable) offers that the supplier made to all other firms. The outcome where w i = c is obtained under passive beliefs. There, when receiving an unanticipated offer a firm believes that the supplier did not simultaneously adjust its offer to other firms. Our specification that the supplier negotiates through I agents has the same implications. By Lemma 1, the supplier s total profit is just equal to the sum of all agreed fixed transfers τ i. One implication of this is that an individual agreement does not affect the supplier s profits from all other potential agreements. If all other negotiations are successful, an agreement with buyer i, whichcontrolsn i firms, then generates the joint profits 19 n i [R(q S,q S ) q S c], (1) where we substituted the respective equilibrium quantities q S. Suppose now first that buyer i would cease to operate when negotiations break down. (For instance, the fixed costs F from integrating backwards could be too high.) According to the general Nash bargaining solution, τ i would then be determined by the requirement that the profits of buyer i are equal to some fraction 0 ρ i 1 of the joint profits (1). As noted in the Introduction, it is common to model an increase in buyer power by increasing ρ i. The shortcoming of this approach is that there is no theory to support this. Non-cooperative models of bargaining - as the one we present in Appendix B - allow to endogenize ρ i from 17 We follow these papers in assuming that contractual ways to achieve the monopoly outcome (e.g., by granting exclusivity) are not credible or not feasible, e.g., as they would constitute a non-permissible vertical restraint. 18 A notable exception is O Brien and Shaffer (1994), who adopt an axiomatic Nash bargaining approach. 19 The axiomatic approach does not allow for renegotiations following an unanticipated disagreement with other buyers. However, with w i = c there would clearly be no scope for bilaterally efficient renegotiations. 9

11 primitives such as the two sides impatience to come to an agreement. We know of no theory that would suggest how a buyer s size should affect, say, its discount factor. Being agnostic about the sharing rules ρ i, we thus stipulate that buyers and the supplier have equal bargaining power such that ρ i is equal to one half for all buyer i. 20 If one half of the joint profits (1) already exceeds the value of the respective buyer s alternative supply option, the threat to take up this option is not credible. This is the key insight of the outside option principle in bargaining theory. According to this principle, the buyer s outside option only affects negotiations if its value exceeds the payoff that the buyer would realize when negotiating without having such an option. Once the value of the outside option exceeds one half of (1), however, the value of the buyer s alternative supply option fully determines the buyer s payoff from the negotiation. 21 The value of the outside option of buyer i, which we denote by V i Out,isnoweasilyderived as follows. When integrating backwards, the buyer can also decide on the amount K B ( i B ) that it wants to invest in order to reduce its own future marginal costs from c Out down to c i Out = c Out i B. Given its choice of i B and the resulting marginal costs ci Out, buyer i then has to decide which quantity to produce and to sell via its n i firms. Working backwards, if buyer i decides to integrate backwards then the maximum profits from this strategy are equal to 22 ½ vout i := max n i max R(q, qs ) (c Out i i q B)q ¾ K B ( i B) F. (2) B As there is always the option not to be active any longer, the outside option of buyer i hasthusthevaluevout i =max{0,vi Out }. To ensure that there is indeed scope for a mutually beneficial agreement with all buyers, we make the following assumption While this makes all expressions simpler, none of our qualitative results depends on the particular choice, that is as long as 0 <ρ i < 1 for all B i. However, as we later consider the formation of larger buyers through mergers,itwouldthenfalluponustospecifywhichvalueofρ (or, in the non-cooperative model of Appendix B, which discount factor) to use for the merged buyer. Again, there is no theory that could guide our choice. 21 See also Footnote 4. Binmore, Rubinstein, and Wolinksy (1989) derive this from a non-cooperative model with alternating offers and impatient players. (See also Appendix B for a related model.) They also show that the outcome would differ if one assumed that frictions arise due to some exogenous probability by which negotiations break down if there is delay. (One story is that players negotiate on the phone and that the line may get irrevocably interrupted.) This alternative scenario seems less suitable for inter-firm bargaining with professional negotiators and potentially non-negligible sums at stake. 22 We already use that in equilibrium negotiations with all other buyers will be successful. 23 Assumption 2 is stronger than needed as it will have to hold only under the equilibrium choices of c. Invoking the stronger assumption allows, however, to rule out case distinctions when deriving our results. Moreover, while Assumption 2 is not on the primitives, it is straightforward to impose conditions on c Out (in comparison to c) and on K B (in comparison to K S ) that ensure that Assumption 2 holds. 10

12 Assumption 2. For all c c (and thus for all possible q S )andforalln i N, it holds that v i Out <ni [R(q S,q S ) q S c]. Summing up, we have thus arrived at the following results. Proposition 1. Under Assumption 2 and using the symmetric Nash bargaining solution, there is an agreement in all bilateral negotiations. An agreement with buyer i specifies w i = c, while the agreed fixed transfer τ i is determined as follows. If then τ i satisfies Otherwise, we have that 1 2 ni [R(q S,q S ) q S c] V i Out, (3) τ i = 1 2 ni [R(q S,q S ) q S c]. (4) τ i = n i [R(q S,q S ) q S c] V i Out. (5) In what follows, we refer to the case where (3) does not hold, i.e., where τ i is determined by (5), as the case where the outside option of buyer i binds. Notefinally that the chosen bargaining solution allows the supplier to discriminate between different buyers. In the present setting the cause for this discrimination are the different values of the buyers outside option, which in turn derive from buyers different size. 3 Analysis 3.1 Buyer Size and the Outside Option This is the core analysis of our paper. We are interested in how the formation of larger buyers affects the supplier s incentives to reduce production costs in the first stage of the model. As a first step, we ask how the outcome of negotiations change if there are fewer but larger buyers with which the supplier has to negotiate. Suppose firstthatforsomegivenchoiceofc the outside option was not binding for any buyer. This would be the case if high fixed costs F from integrating backwards made this unprofitable regardless of a buyer s size. Note next that the average price that buyer i pays per unit is equal 11

13 to μ i := τ i + n i q S c n i, (6) q S wherewemakeuseofw i = c from Lemma 1. Substituting for τ i from (4), the average purchasing price of buyer i is then μ i =[c + P (2q S )]/2 and thus independent of its size n i. Intuitively, as the outside option does not affect how profits are shared, the buyer receives a fixed fraction, namely one half, of the profits that are realized in each of its n i markets. If the outside option does not bind for any buyer, the supplier s overall profits are thus equal to N[R(q S,q S ) q S c], where we use that there are two competing firms in each of the N independent markets. The number and size of buyers start to matter, however, once buyers outside options become binding. With a binding outside option, the average purchasing price (6) is strictly decreasing in the number of controlled firms n i. The intuition for this is as follows. Integrating backwards involves two types of fixed costs: F and the additional investment costs K B ( i B ), which depend on the (optimally) chosen level of cost reduction i B.Thelargerni, the larger the total quantity over which the buyer can distribute these costs. As a consequence, the ratio V i Out /ni = v i Out /ni is now strictly increasing in n i, which in turn leads to a strictly lower average purchase price. By the same token,the more firms a buyer controls the more the buyer will subsequently invest in order to reduce its own marginal costs c i Out.24 Lemma 2. Holding the supplier s marginal cost c constant, a buyer s size has the following impact on the value of the buyer s outside option V i Out and thereby on the respective bargaining outcome. i) If after disagreement a buyer of size n i = n weakly prefers to integrate backwards, then any larger buyer with n i >nstrictly prefers to do so. Moreover, in case of backward integration the larger buyer invests strictly more to reduce the resulting marginal costs c i Out. ii) Unless the outside option does not bind for any size n i N, there exists a threshold 1 bn N such that for all buyers with size n i < bn the outside option is not binding, while it is binding for all buyers with size n i bn. For all n i < bn the average purchasing price μ i is identical, while μ i is strictly decreasing in n i if n i bn. 24 If the optimal i B is not unique, then assertion i) of Lemma 2 applies to the respective sets: all i B that are optimal for n i = n 00 are strictly larger than any i B that is optimal for n i = n 0 <n 00.Thisismadeformalinthe proof. 12

14 Proof. See Appendix. 3.2 The Supplier s Incentives We turn now to the first stage of our model. Recall for this that the supplier s profit inthe second stage of the model equals the sum of all fixed transfers τ i. Consequently, the supplier optimally chooses its marginal costs c = c S so as to maximize its net profits U := X τ i K S ( S ), (7) i I where the transfers τ i are determined by (4) or (5), respectively. It is now easily checked (and verified in the following proofs) that U is continuous and almost everywhere differentiable in S. To analyze the supplier s incentives, define thus the derivative m := du/d S at all points where U is differentiable. We make now the following additional assumption. 25 Assumption 3. The per-firm Cournot profits R(q S,q S ) cq S are strictly decreasing in c. Assumption 3 ensures that total Cournot profits are decreasing in marginal costs c. If Assumption 3 did not hold, then a supplier would not want to lower c even if he could extract all industry profits and would not have to incur additional investment expenditures. Suppose first that for some choice of c the outside option does not bind for any buyer. Then the supplier s incentives to (marginally) decrease c would be determined by the derivative m = N d dc [R(q S,q S ) cq S ] K 0 S( S ), (8) where we used Proposition 1 and the fact that there are 2N downstream firms. How do incentives change if, instead, the outside option of some buyer, say buyer i, binds? We can isolate three effects that all point in the same direction, that is towards an increase in the derivative m. First, as the outcome of negotiations with buyer i is now fully pinned down by the value of the buyer s outside option, the supplier can pocket the full marginal increase in the respective joint surplus n i [R(q S,q S ) cq S ]. In other words, with a binding outside option there is no longer 25 Vives (1999, p. 105) provides sufficient conditions on the demand function for Assumption 3 to hold. 13

15 a hold-up problem between the supplier and buyer i, at least not for marginal changes in S. 26 Second, once the outside option of buyer i binds there is an additional effect that increases the supplier s incentives to reduce c. Wefind that a reduction in the supplier s marginal costs reduces the value of a buyer s outside option and, thereby, increases the supplier s profits. To see this, note that in each of the n i markets in which firms controlled by buyer i are active the supplier also sells to competing firms. The lower the supplier s marginal costs, the more competitive are these firms. This reduces the value of the buyer s outside option to integrate backwards instead of purchasing from the supplier. Importantly, which is our third observation, the previous effect becomes stronger if there are fewer but larger buyers. More formally, the size of the (negative) effect that a reduction of c has on a buyer s payoff v i Out under the alternative source of supply increases more than proportionally with the buyer s size n i. Consequently, if we merge a subset I 0 of buyers, then this strictly increases the supplier s incentives. The intuition for this is somewhat more involved. It builds again on the insight that a reduction of c will make all other buyers more competitive, inducing them to choose a strictly higher quantity at each of the N markets. To see that the resulting reduction to a buyer s outside option increases therefore more than proportionally with the number of controlled firms n i recall from Lemma 2 that a larger buyer chooses a lower value of c i Out after disagreement. Consequently, the larger buyer will produce a larger quantity under disagreement and will lose more profits if competitors lower their prices following a reduction of their marginal purchasing price. Note now that for the preceding arguments we scaled up the size of one buyer i. To keep the size of the total industry constant, this requires to simultaneously scale down another buyer. In what follows, in order to keep the size of the market constant we focus on mergers between buyers. Lemma 3. Take some level of the supplier s marginal cost c and consider the marginal incentives for the supplier to further decrease c, which are given by the derivative m. Suppose also that a subset of the I independent buyers are merged into one larger buyer. If the outside option of the 26 Recall our convention by which the outside option of B i is binding if (3) does not hold. Consequently, as R(q S,q S) cq S and vout i both change continuously in c, the outside option of B i stays binding after a small change in S. 14

16 newly formed large buyer binds, then m is strictly higher. Proof. See Appendix. 3.3 Equilibrium Analysis With Lemma 3 at hands, the following result follows now immediately by applying standard comparative statics results. 27 Proposition 2. If there are fewer but larger buyers, then in equilibrium the supplier s marginal costs will never be higher but they may be strictly lower. Note that we do not need for Proposition 2 that there is a unique optimal cost reduction S for any given number and size of buyers. If there is a multiplicity of equilibrium choices for S and thus for the resulting marginal costs c, then Proposition 2 applies to the optimal sets. 28 An application of Proposition 2 could be to retailing, where a larger buyer is formed by the merger of two or more smaller retail chains. When negotiating with a large chain, the resulting average purchasing price μ i is fully pinned down by the chain s attractive alternative supply options. From the perspective of the supplier, this may then very much look like a take-itor-leave-it offer by the large chain, which leaves no room for haggling over a higher price. In contrast, with small chains there is scope for negotiations. Lemma 3 and Proposition 2 show that the formation of larger retail chains can spur upstream investment to reduce marginal costs. Some of the assumptions that we made in order to focus our analysis on the novel results seem also to be particularly suitable to retailing. There, markets are indeed often locally segmented. Though there may be different competing chains, in a given local market consumers may only choose between few different outlets. 29 If two chains operating in different local markets merge, the merger will thus have no implications for downstream competition. In addition, in case 27 See, for instance, Vives (1999). 28 There are essentially two reasons for why the formation of a larger buyer does not always lead to a strictly lower value of c. First, the outside option of the newly formed larger buyer may not be binding over the relevant range of c. Second, even if this is the case such that m increases over the relevant range, then the optimal c may still be unchanged as it lies on a kink of the supplier s profits U. (U is differentiable everywhere with the exception of points at which the outside option of one buyer starts to bind.) 29 In retailing, in particular in the one-stop-shopping segment of super- or hypermarkets, the assumption of a tight local oligopoly (and, in particular, no further entry) is also often realistic given local planning restrictions. In addition, for many goods or services the local market may also often not support more than a very limited number of competing shops. 15

17 there is some overlap, it is relatively easy for antitrust authorities to define and impose adequate structural remedies by forcing the divestiture of outlets in the affected markets. If a merger of chains has thus no impact on downstream competition and does not directly affect marginal input prices, one if not the most important remaining channel by which consumer surplus and welfare can be affected is through the implications for investment incentives and thus long-run efficiency. If the exercise of buyer power leads to lower marginal costs and thus higher quantities in each of the N markets, consumer surplus is unambiguously higher. We study next the effect on total welfare. Suppose first that the outside option does not bind for any buyer. The resulting hold-up problem with any of the I buyers reduces the supplier s incentives, which then leads to a choice of S that lies below the level that would maximize total industry profits (net of the respective investment costs). This is, however, already strictly below the level at which welfare would be maximized. Hence, by increasing the supplier s incentives total welfare can be improved. Consider next the opposite extreme where all outside options bind, making the supplier the residual claimant when (marginally) increasing joint profits. In this case, the equilibrium choice of S will be strictly above the level that would maximize total industry profits. This follows as a further increase in S is still beneficial for the supplier given that it erodes the value of buyers outside option and thus allows the supplier to extract a higher share of joint profits. In principle, the supplier s incentives may thus become too high, implying that S lies even above the level at which welfare is maximized. As we show next, however, in the (most simple) case of linear demand and quadratic investment costs investment incentives are always too low also from the perspective of total welfare, implying that in this case the formation of larger buyers will always increase also welfare. Example: Suppose that each market is characterized by P (x) =a bx, which is derived from the utility function of a representative consumer. Given marginal costs c, the symmetric Cournot (duopoly) quantities are q S = a c 3b. As the wholesale price equals marginal costs, this yields per-firm profits R(q S,q S ) q S c = b a c 2. 3b A marginal reduction of c increases welfare by N 1 (5a 2c). (9) 3b 3 16

18 Likewise, from differentiating total industry profits we have N 2 (a c), (10) 3b 3 which is clearly always strictly lower than (9). If no outside option binds, then the supplier s incentives are given by one half of (10) and are thus clearly too low. In contrast, if all outside options bind, then the supplier receives the full incremental profits. In this case, we know that the supplier s incentives are given by the sum of (10) and P i I dvout i /dc. To calculate the last expression, note firstthatforgivenc i Out the per-firm profits are equal to b µ 2a + c 3c i Out 6b 2. (11) To determine the optimal value of c i Out, we specify that reducing marginal costs from c Out to c i Out = ci Out i B comes at quadratic costs K B( i B )=γ B( i B )2 /2. Moreover, we specify γ B > 1 N c i (2a + c), Out 6b which ensures that there is always a unique interior solution 0 <c i Out < c Out, regardless of a buyer s size. Maximizing for buyer i the difference of n i times per-firm profits (11) and the respective investment costs γ B ( i B )2 /2, weobtain which can then be substituted into from which we finally have that c i Out = 6bγ Bc Out n i (2a + c) 6bγ B 3n i, (12) v i Out = n i b µ 2a + c 3c i Out 6b dv i Out dc 2 γ B 2 (c Out c i Out) 2 F, (13) µ 2a + c 3c = n i i Out. (14) 18b Take now the extreme case where there are only two buyers, each controlling one firm in each of the N markets. Observe also that the difference between (9) and (10). i.e., between the marginal welfare benefits and a marginal change in industry profits, equals Na/(3b). Consequently we have from (14) that the supplier will still have insufficient incentives to reduce c whenever the additional incentives from dvout i /dc are still too low, i.e., whenever µ 2a + c 3c i 2N Out <N a 18b 3b, (15) which transforms to (a c)+3c i Out > 0 and thus always holds. 17

19 4 Discussion and Robustness 4.1 The Impact of a Merger on Other Buyers So far we have only analyzed how the formation of a larger buyer affects the supplier s profits and thereby the supplier s incentives. Holding c constant, unless the merged buyer s outside option does not bind, the supplier s profits decrease. This holds still if the supplier optimally adjusts c following the merger. 30 Next, if c remains constant, then the merger will be unambiguously profitable for the larger buyer. Interestingly, this may, however, no longer be the case once we take into account the supplier s optimal adjustment of c. Naturally, buyers would, however, only merge if this was profitable. What remains to be analyzed is how the formation of a larger buyer affects all other buyers, i.e., buyers that remain outside the merger. In policy discussions, in particular in the area of retailing, it is sometimes argued that other buyers may be negatively affected by the formation of a larger and more powerful buyer. In our model, we specified that contracts are sufficiently complex to avoid problems of doublemarginalization. An implication of this is that regardless of a buyer s size, each buyer can procure at the same marginal costs c. While a larger buyer can thus procure at better average terms, this does not give the buyer an advantage in the downstream market. 31 Consequently, in our model it is only in the long run that other buyers are affected by a merger, namely through a possible reduction in the supplier s marginal costs. Here, the exercise of buyer power has now quite surprising implications for other buyers. Small buyers that do not have a sufficiently valuable outside option benefit from a merger. This is the case as these buyers can then extract in their negotiations a fraction of the additional profits that are created by a reduction in c. In contrast, other large buyers may be hurt as a reduction in c reduces the value of their binding outside option. Proposition 3. The formation of a larger buyer can never hurt a small buyer whose outside option does not bind, while the small buyer strictly benefits if the merger induces the supplier to 30 Formally, this follows as c is optimally chosen both before and after the merger. 31 We should note, however, that these stark results would not extend to a setting with only linear pricing (and thus double-marginalization). In fact, Inderst (2006) shows that in this case the merged buyer obtains a lower (constant) input price, whereas the input price for competing buyers increases. 18

20 choose strictly lower marginal costs. On the other hand, a large buyer that remains outside the merger may be negatively affected as the value of its binding outside option decreases in case the supplier chooses lower marginal costs. Proof. See Appendix. The result that the exercise of buyer power may in the long run be beneficial for small buyers, who essentially free ride on the supplier s higher incentives, comes, however, with one important caveat. Our analysis focuses essentially on incremental changes on the upstream market, namely the reduction of the chosen supplier s marginal costs. As noted above, what matters for the supplier s incentives is consequently not his absolute level of profits but, instead, only how the formation of a larger buyer affects his incremental profits from a reduction in marginal costs. For other decisions such as, for instance, whether to introduce a new product or whether to stay or exit, the supplier s total profits should, however, be more relevant. The spill-over that a merger can have on other buyers via this channel may then be quite different to that of Proposition 3. We leave a further analysis to future research. 4.2 Observability of Breakdown in Bilateral Negotiations We assumed in our main analysis that a breakdown of negotiations between the supplier and some buyer i was not observed by other buyers. This allowed us to keep their chosen quantity fixed at the symmetric Cournot quantity q S. In what follows, we analyze how our results extend once we relax this assumption. Clearly, whether or not buyers observe a breakdown in another negotiation is inconsequential for our first effect, namely that once a buyer s outside option becomes binding the supplier can pocket the full increase in joint profits from a marginal reduction in c. We can also show that our second effect survives without any qualification, namely that once a buyer s outside option becomes binding then the supplier has additional incentives to reduce marginal costs as this reduces the value of the buyer s outside option. Finally, while a larger buyer s outside option would still decrease more than proportionally to n i in case other buyers increase their quantities by a fixed amount following a reduction of their marginal purchasing price, if disagreement is observable their reaction may now, however, 19

21 depend on the identity and thus on the size of buyer i. By how much competing buyers adjust their quantities, and how this depends on n i,isnowgenerallyaffected by local properties of the demand function, for which Assumption 1 does not provide sufficient structure. In the case of linear demand, however, the result is still unambiguous. Proposition 4. If the breakdown of bilateral negotiations is observable to competing buyers, then our results continue to hold as follows. i) The formation of a larger buyer still strictly increases the supplier s incentives to reduce marginal costs if the respective buyer s outside option did not bind previously but binds after the merger. ii) If the merging buyers outside option was also previously binding, then with linear demand our third effect, namely that dv i Out /dc increases more than proportionally in ni, still holds, implying that incentives are still strictly higher. Proof. See Appendix. 4.3 Heterogeneous Goods So far we assumed that buyers compete in homogenous goods. We show now that this assumption can be relaxed without affecting our results. We thus specify that if one firm in a given market chooses quantity q and the other firm quantity bq, then the price for the first firm s goods is given by P (q, bq). We denote the respective partial derivatives by P 1 and P 2. The following Assumption extends Assumption 1 to the case with heterogeneous goods. Assumption 1. If goods are not perfect substitutes, then whenever P (q, bq) is positive it holds that P 1 (q, bq) < min{0, qp 11 (q, bq)/2} and that P 2 (q, bq) < min{0, qp 12 (q, bq)}. With Assumption 1, we can show that all of our three effects are still present. This gives then rise to the following result. Proposition 5. If goods are heterogeneous and if Assumption 1 is satisfied, then all results still hold. Proof. See Appendix. 20