Naked Exclusion, Efficient Breach, and Downstream Competition

Transcription

1 Naked Exclusion, Efficient Breach, and Downstream Competition John Simpson and Abraham L. Wickelgren 1 Federal Trade Commission July This paper does not represent the views of the Federal Trade Commission or any individiual Commissioner. We thank Patrick DeGraba and seminar participants at the North American Summer Meetings of the Econometric Society for helpful comments.

2 Abstract Previous papers by Eric B. Rasmusen et. al. (1991) and Ilya R. Segal and Michael D. Whinston (2000) argue that exclusive contracts can inefficiently deter entry in the presence of scale economies and multiple buyers. We show that these results no longer hold when buyers are final consumers who, as contract law requires, can breach these contracts and pay expectation damages or renegotiate these contracts. If buyers are downstream competitors, however, then exclusive contracts can inefficiently deter entry provided the degree of competition is great enough. Scale economies, however, are not necessary for this result.

3 1 Introduction Whether or not an incumbent firm can use an exclusive contract to inefficiently deter entry is an important issue in competition policy. While United States antitrust law currently treats exclusive contracts under a rule of reason standard in which economic efficiencies are balanced against possible anticompetitive harm, Chicago School scholars (Richard Posner (1976, p. 212) and Robert Bork (1978, p. 309)) contend that antitrust law should treat exclusive contracts as per se legal. These scholars correctly note that a firm that monopolizes a market by getting buyers to sign exclusive contracts imposes harm on consumers equal to its monopoly profit plus some deadweight loss. They then assume that the excluding firm cannot get buyers to sign these exclusive contracts except by fully compensating buyers for this harm. Given this assumption, they note that the excluding firm cannot profitably induce buyers to sign exclusive contracts since the excluding firm only gains the monopoly profit from using the exclusive contracts but must pay buyers the monopoly profit plus the deadweight loss to induce them to sign the exclusive contracts. Based on this, they conclude that efficiency considerations, rather than anticompetititve motives, explain the use of exclusive contracts. Eric B. Rasmusen et al. (1991) and Ilya R. Segal and Michael D. Whinston (2000) (henceforth RRW-SW) have challenged this analysis by showing that an incumbent monopolist can sometimes use exclusive contracts to deter efficient entry when production exhibits scale economies. 1 The RRW-SW model analyzes several different cases. In one case, the monopoly profit from all buyers exceeds the compensation payments (monopoly profit plus deadweight loss) needed to sign a sufficiently large number of buyers to block entry. In this case, an incumbent monopolist can always deter entry if it can offer discriminatory contracts. Realizing this, buyers conclude that entry will not occur. The incumbent monopolist is then able to deter entry at no cost to itself because competition among buyers to sign exclusive contracts drives to zero the payment needed to get buyers to sign the exclusive contracts. This result requires that production scale economies be large relative to the size of the market. In a second case, the monopolist can use discriminatory contracts, but the monopoly profit from 1 Other articles that challenge the Chicago School view include Phillippe Aghion and Patrick Bolton (1987), Kathryn E. Spier and Whinston (1995), and B. Douglas Bernheim and Whinston (1998). Robert Innes and Richard J. Sexton s (1994) article argues that the Chicago School claim that exclusive contracts are necessarily efficient can be resurrected if one allows coalitions between all buyers and the incumbent and the entrant and price discrimination is prohibited. None of these papers consider the case where buyers may compete with each other in a downstream product market. 1

4 all buyers does not exceed the compensation payments needed to sign a sufficiently large number of buyers to block entry. In a third case, the monopolist cannot use discriminatory contracts. In these two cases, the RRW-SW model finds that an incumbent monopolist can sometimes get enough buyers to sign exclusive contracts to deter entry. However, such an equilibrium requires that buyers be unable to coordinate on their most preferred equilibrium, which is entry by another firm. This result requires that there economies of scale at production levels that exceed the demand of the largest buyer. While the RRW-SW results cover an important benchmark case, two key assumptions deserve further exploration. The first is the assumption that the incumbent can offer exclusive contracts that cannot be renegotiated or breached if a rival firm enters. Relaxing this assumption dramatically affects the results; in the RRW-SW model, exclusive contracts cannot deter entry in any subgame perfect equilibrium when final consumers can renegotiate the exclusive contract or breach the exclusive contract and pay expectation damages. Upstream economies of scale do not affect this result. The second assumption is that buyers are final consumers rather than downstream competitors. Relaxing this assumption also affects the results; if downstream competition is sufficiently intense, exclusive contracts can deter entry. This result also holds whether or not there are upstream economies of scale, suggesting that downstream competition, rather than economies of scale, are the crucial factor that determines the ability of exclusive contracts to deter efficient entry. The intuition for these results is straightforward. If another supplier enters, a buyer that has signed an exclusive contract can obtain a lower price by breaching the exclusive contract. While the buyer must pay to the incumbent monopolist damages equal to the monopoly profit (under the expectation damages rule, the dominant rule for breach of contract cases), the buyer saves this monopoly profit plus the deadweight loss by purchasing at the lower price. Thus, a buyer who is a final consumer will breach the exclusive contract to save the deadweight loss. Since the entrant can now make sales to this buyer, the exclusive contract does not prevent the entrant from attaining scale economies. If the buyer is a downstream competitor, then the buyer and its customers share the savings from obtaining a lower price. Where downstream competition is limited, the buyer retains most of the savings from breaching the exclusive contract and thus finds that breaching the exclusive contract is profitable. However, where downstream competition is intense, competition forces the buyer to pass along to its customers most of the savings from obtaining a lower price. In these 2

5 cases, the buyer s savings from breaching the exclusive contract are insufficient to compensate the incumbent monopolist for his loss of monopoly rent. Because no buyer will breach an exclusive contract if downstream competition is sufficiently intense, the incumbent can profitably deter entry by signing all buyers to an exclusive contract. Since all buyers sign the exclusive contract, entry is deterred even in the absence of economies of scale. These results complement the RRW-SW results because they better capture the legal and competitive environment faced by firms that use exclusive contracts. While there are undoubtedly many situations where renegotiation is prohibitively costly and reputational considerations may raise the cost of breach far above any damages a court might impose, the assumption that buyers cannot renegotiate or breach exclusive contracts does not accurately describe contract law in the United States or most other common law countries. Courts in these countries will not enforce contractual provisions that prohibit renegotiation (Restatement (Second) of Contracts 311 cmt. a 1981). Even if renegotiation is not feasible, the buyer still has the option of breaching the exclusive contract and buying from a new supplier. In such a case, the standard common law rule gives each contractual party the option of performing her contractual duties or paying expectation damages, which are damages that put the other party in the position it would have been in had the contract been performed (Hatziz 2001). Thus, while an exclusive contract could set damages so high that breach is never profitable, courts in common law countries would be unlikely to enforce such a penalty clause (Hatziz 2001; Restatement (Second) of Contracts 356 & ). Given this, we suspect that in most situations where exclusive contracts are used, the parties recognize that the buyer will either have the option of renegotiating or breaching the contract. 2 Relaxing the assumption that buyers are final consumers also more accurately reflects the environment in which exclusive contracts are used. Exclusive contracts are very uncommon in final goods markets. While, the final consumer assumption does accurately depict the situation where the upstream supplier is selling to buyers who do not compete in the same market, such as to geographically disperse retailers, in many exclusive contracts cases, the buyers do compete with each other to varying degrees. Thus, examining the efficiency and effectiveness of exclusive contracts under these circumstances is important for making judgments about how antitrust law should treat these contracts. 2 Other papers (Scott Masten and Edward Snyder (1989) and Kathryn Spier and Michael D. Whinston (1995) have raised a similar point in reference to the Aghion and Bolton model, which relies on the assumption that an incumbent monopolist and a buyer can sign a contract with liquidated damages. 3

6 The remainder of this paper discusses these main points in greater detail. Section 2 describes a generalized version of the RRW-SW model that allows for both renegotiation and competition among buyers. Section 3 shows why exclusive contracts have little commitment value in this model when buyers are final consumers. Section 4 shows that exclusive contracts will always commit buyers to buy from the incumbent monopolist, and deter entry as a result, when buyers are undifferentiated Bertrand competitors. Section 5 discusses the intermediate case of imperfect competition and provides an example where exclusive contracts will have commitment value when the competition between buyers is intense but not when the competition is slight. Section 6 concludes. 2 The Model Except where necessary to incorporate breach (or renegotiation) and downstream competition, we use the same model as RRW-SW. Everything described below is common knowledge to all agents in the model. There are two upstream producers of a homogeneous input, an incumbent (I) anda rival (R), and N downstream buyers. RRW-SW assume the buyers are final consumers. We relax this assumption so that the buyers can be downstream competitors. In period 1, I offers buyers exclusive contracts. Following RRW-SW, we assume that the precise nature of the good that will be needed is not known until period 3, so we do not allow I to set a price for the good in this period. 3 In period 2, R decides whether or not to enter. R only enters if it expects to make strictly positive sales and non-negative profits. Our model differs from that of RRW-SW in period 3. In particular, we divide period 3 into three stages. In 3.1, the active upstream firms name prices for free buyers (R offers a price of p r,andi offers a price p f )andi sets its price for captive buyers 4 (p s ). In period 3.2, the captive buyers have the opportunity to breach the contract (becoming free buyers) and pay expectation damages to I. 5 In period 3.3, all free buyers purchase inputs from R or I depending on whether p r <p f or vice versa. If p r = p f, buyers purchase equally from each. 3 Of course, the incumbent could offer buyers who signed an exclusive contract a non-discrimination provision (their price will be no higher than the price the incumbent offers to free buyers) even if the good cannot be described in advance. Allowing this would not change any of our results. The reason is that in every result minimum efficient scale is irrelevant. Thus, if the incumbent cannot deter entry without offering a non-discrimination provision, it cannot deter entry with such a provision since the rival can still induce breach by offering a price of c. If the incumbent can deter entry with exclusive contracts because of downstream competition, then it has no need to include a non-discrimination provision. 4 We refer to buyers who have signed an exclusive contract (and have not yet breached it) as captive buyers. 5 Allowing for renegotiation rather than breach would produce similar results. The breach case is somewhat simpler because it is a unilateral decision. 4

7 Captive buyers buy from I at p p s. (possibly) differentiated output. Then downstream buyers compete in prices to sell their Like RRW-SW, we allow I to set different prices for captive buyers and for free buyers. However, unlike RRW-SW, we let captive buyers become free buyers by breaching the contract and paying expectation damages. We also allow I to unilaterally lower its price to captive customers in period 3.3. We do this because, if buyers compete in downstream markets, then I s optimal response to breach by some buyers may be to lower its price to its remaining captive customers (who will certainly not object). (We could also allow R and I to both unilaterally lower the price they offer to free buyers, but this is unnecessary since, as we show below, the price to free buyers is marginal cost, p f = p r = c.) Despite the fact that the buyers may sell differentiated output, we assume (for tractability) that they all face symmetric demand functions in order to give the buyers identical demand functions. That is, buyer i s demand can be written as q(p i, p i )=q(p i,z(p i )) where p i is the vector of the input prices offered to all other buyers and z(p i ) represents any possible renumbering of the N 1 other buyers. In other words, demand depends on the firm s own input price and the input prices of all other buyers but does not depend on which buyers receive which input prices. We assume q(p i,p i ) p i < 0. We write the profit function of each buyer as π b (p i, p i )=π b (p i,z(p i )). This corresponds to the consumer surplus function, CS, in SW when buyers are final consumers or retailers who compete in distinct markets. We assume that both q and π b are weakly increasing in every element of p i (other buyers paying a higher price does not decrease a buyer s demand or profits). 6 Following RRW-SW, we assume the upstream production technology is such that average cost for both I and R is given by c(q) =c for Q Q and c 0 (Q) < 0 for all Q<Q. R will enter in period 2 only if it can make nonnegative profits competing only for free buyers. However, because we allow for breach, the free buyers are downstream buyers who did not sign an exclusive contract in period 1 and downstream buyers who did sign exclusive contracts in period 1 but will breach those contracts in period 3.2. change the result that the free market price, given entry, is c. The following lemma shows that downstream competition does not 6 Notice, we follow RRW-SW in allowing upstream firms to offer only per unit prices. One justification for this assumption is that the good can be easily resold, making non-linear contracts easy to circumvent. In the case where buyers are final consumers, as Segal and Whinston point out, this assumption can also be justified when buyers want at most one unit of the good and have a random reservation price. Then q(p i, p i) is the probability that a buyer i buys when prices are given by (p i, p i ). In addition, since exclusive contracts are often used when firms offer only per unit prices, this case is an important one to consider. 5

8 Lemma 1: If R enters in period 2, the free market price in period 3.1 is c (that is, p f = p r = c). Proof. p f < c or p r < c obviously is not optimal. Say p f >p r c. Then all free buyers buy from R at p r and I makes no profit selling to free buyers. I can lower p f to p r without affecting the demand function from its captive buyers since this does not change the price the captive buyers pay. So, doing this does not decrease I s profit from captive buyers and it gives I non-negative profits from free buyers. Thus, p f >p r c is not possible. Similarly, if p r >p f c, thenr makes zero sales. This cannot be optimal, or R would not have entered. Thus, p r = p f. If both charge above c, theni can almost double its profit by reducing its price by an arbitrarily small amount. Thus p r = p f > c is not possible, which proves the lemma. Q.E.D. Because R decided to enter, we know it must expect positive sales. Because it competes in a homogenous Bertrand market with I, it cannot make positive sales if it charges a price greater than I s marginal cost. Of course, R will only enter if it can sell to enough buyers so that its output is at least Q, otherwise, it will have average costs in excess of c and so will make no sales or make negative profits. In the RRW-SW model, the incumbent s optimal price to a buyer who has signed an exclusive contract is arg max p (p c)q(p), which is independent of the number of captive buyers because they assume buyers are final consumers. To cover the general case where a buyer s demand may depend on the price paid by other buyers, such as when buyers are downstream competititors, we define p m P =argmax p (pi c)q(p i, p i ). Because of the buyer symmetry, the optimal monopoly price (p m ) is equal for all buyers. This is the analogue of p m from RRW-SW (which is arg max p (p c)q(p)). Note, however, that these definitions are only identical when either all buyers face a monopoly input supplier (i.e., R has not entered or all buyers are captive) or input demand is only a function of one s own price (buyers are final consumers or operate in completely distinct downstream markets). To cover the more general case where, say, the first n buyers are subject to an exclusive contract. 7 We define p m P (n) = arg max ni=1 p(n) (p i (n) c)q(p i, (p i (n), c N n )). p(n)isandimensional vector of the input prices for the n buyers subject to an exclusive contract. The term (p i (n), c N n )is an N 1 dimensional vector of the input prices for all buyers other than i. This vector has two components: p i (n) isann 1 dimensional vector of the prices faced by n 1 other buyers subject to an exclusive contract and c N n is an N n 1 dimensional vector where every element is c 7 RRW-SW use S forthenumberofbuyerswhosignanexclusive;ourn is their S if all buyers who sign an exclusive abide by this contract. 6

9 (the prices faced by the buyers not subject to an exclusive). Thus, p m (n) is the optimal monopoly input price vector for the n buyers subject to an exclusive when the remaining buyers pay an input price of c, andp m = p m (N). 8 There is an integer N such that R enters if and only if it believes that no more than N buyers will remain bound by an exclusive contract to purchase only from I. Because R and I will split l m the free market, this critical value is implicitly given by N = N 2Q /q(c, (p m (N ), c N n 1 ) where dye represents the smallest integer greater than or equal to y and where (p m (N ), c N N 1 ) is the N 1 dimensional vector of the input prices paid by the other buyers, N of whom are subject to an exclusive contract and pay p m (n), the remainder each pay c. 3 No Competition: Buyer Independence (The RRW-SW Case) In this section, we show that, when buyers are independent, exclusive contracts cannot deter entry if buyers can breach these contracts and pay expectation damages. Buyer independence means that buyer demand depends only on her price and not on the price that other buyers pay. Examples of buyer independence include buyers who are final consumers and retailers who sell in completely separate markets. Because of buyer independence, in this case, we can adopt the following RRW- SW notation: buyer demand, q(p i, p i ), can be written as q(p i ); CS(p) = R p q(s)ds is the buyer s consumer surplus at a price of p; π m =(p m c)q(p m )isi s monopoly profit from selling to a buyer subject to an exclusive contract; and x = CS(c) CS(p m ) is the extra consumer surplus that a free buyer gets when R enters. Proposition 1: When buyers are independent and can breach exclusive contracts subject only to expectation damages in period 3.2, then in any subgame perfect equilibrium entry occurs and all buyers pay a price of c, evenifn =0(all N buyers must be free buyers for R to enter). Proof. Consider the subgame after n buyers have signed an exclusive contract in period 1 and R enters in period 2. Say buyer i has signed an exclusive contract. If buyer i breaches the contract, then it owes expectation damages of π m, the amount necessary to put I in the position it would be in if buyer i had not breached. 9 Because R has entered, however, if buyer i breaches, 8 When buyers compete with each other in the downstream market, the demand function, q, thatwehaveused is necessarily a reduced form demand function. That is, it assumes the equilibrium downstream prices chosen by buyers in the downstream market given the buyers input prices. 9 We assume a court can calculate π m perfectly. Since everyone is risk neutral, the results only require that the mean value of expectation damages is π m. 7

10 then it gains x from buying at the free market price of c rather than p m. Because there is dead weight loss from monopoly, x > π m. Thus, buyer i gains by breaching the contract and paying expectation damages. Given that every buyer that signed an exclusive contract in period 1 will breach that contract in period 3.2, the free market in period 3.3 consists of N buyers. Thus, R will enter in period 2, and all buyers will pay a price of c. Q.E.D. Proposition 1 shows that the RRW-SW result that an incumbent monopolist can use exclusive contracts to deter entry when buyers are final consumers does not hold when buyers can breach the exclusive contracts and pay expectation damages. Because the exclusive contract creates ex post dead weight loss to the parties of the exclusive contract, R knows it will be breached. As a result, no matter how many buyers have signed exclusive contracts in period 1, R expects to be able to compete for the entire market in period 3, allowing it to reach minimum efficient scale. (Of course, given this result, we would not expect the incumbent to offer exclusive contracts in equilibrium.) Notice that this result holds whether or not I can discriminate between buyers in period 1. All that matters is that once entry has occurred, there is positive joint surplus between I and a buyer when a buyer opts out of an exclusive contract. This result is somewhat sensitive to the assumption of Bertrand competition upstream. If competition between R and I resulted in a price p 0 ( c, p m ), then buyers would not breach when p 0 was sufficiently close to p m. (When a buyer breaches, she is in effect paying p m c + p 0 on the units she would have bought from I at the price of p m, plus she gets the option to buy more units at p 0. When p 0 = c, she does not have to pay any more on the original units to get this option. But the cost of this option gets very large as p 0 approaches p m while the benefit of the option goes to zero.) 10 Of course, if there were an equilibrium where p 0 was large enough that buyers did not breach, so R could not enter, R would want to deviate by reducing its price to a level where breach is optimal. Unless there is some reason why R cannotchooseanypriceitwants,itishard to imagine some other form of competition resurrecting the ability of exclusive contracts to deter entry. 10 We thank Patrick DeGraba for pointing this out. 8

11 4 Perfect Competition: Buyer s Are Homogenous Bertrand Competitors In this section, we assume that buyers are homogeneous Bertrand competitors who simply take the good supplied by an upstream firm and resell it to consumers. Thus, the only expense for these buyers is the cost of the input. In this case, we show that the incumbent, I, canprofitably use exclusive contracts to deter entry. As in the previous section, this result does not depend on the presence or absence of scale economies. Proposition 2: When buyers compete as homogenous Bertrand competitors, in every subgame perfect equilibrium where no one plays a weakly dominated strategy, enough buyers sign an exclusive contract in period 1 and do not breach that contract in period 3.2 if there is entry so that R does not enter in period 2 for any value of Q. Proof. Say R has entered and there is at least one free buyer in period 3.3. We know from Lemma 1 that this buyer has marginal cost of c. Since the marginal cost of the captive buyers is p s, captive buyers will make no sales in the downstream market if p s > c (the free buyer will undercut their price unless they charge below their marginal cost). Because I will make no profits from captive buyers if it sets p s > c, itsetsp s = c in period 3.3. (This will not affect his damages from breach since that is based on the price set in period 3.1, before any buyers have breached.) Because all buyers obtain the input at c in period 3.3, no buyer makes positive profits. Consequently, if all buyers have signed an exclusive contract in period 1, then no buyer can make positive profits by breaching the contract in period 3.2 even if R enters. Since expectation damages for breach are strictly positive if no other buyers breach, breach is a weakly dominated strategy. Given this, if all buyers sign an exclusive contract in period 1, all buyers will be captive in period 3.2. Now, consider period 1, say I offers each buyer ²>0 to sign an exclusive contract. Each buyer will accept this offersinceitearns² in period 1 and at least zero in period 3.3 if it accepts this offer but earns zero in period 1 and zero in period 3.3 if it rejects this offer. Since all buyers accept I s offer in period 1 and do not breach the exclusive contracts in period 3.2, R does not enter. Thus, I makes positive profits in period 3.3 by getting buyers to sign exclusive contracts. Since I makes zero profit in period 3.3 if it does not sign enough buyers to prevent R from entering, every subgame perfect equilibrium must involve R not entering. Q.E.D. When buyers are Bertrand competitors, if one buyer becomes a free buyer by breaching the 9

12 exclusive contract, Bertrand competition between the upstream incumbent and the upstream rival ensures that all buyers get the input at cost. Bertrand competition between the downstream buyers then ensures that final consumers get the downstream product at cost. Thus, all of the benefits that a buyer would get from breaching an exclusive contract are passed on to final consumers in the form of lower prices. Given this, a buyer that breaches an exclusive contract cannot earn enough profit to cover the expectation damages it would owe if it breached. For this reason, a buyer has no incentive to breach the exclusive contract. This setting turns the Posner and Bork argument on its head. In the Posner and Bork argument, the incumbent cannot use exclusive contracts to deter entry because upstream competition maximizes the joint surplus of the incumbent and the buyers. When buyers are Bertrand competitors, however, an upstream monopoly maximizes joint (though, not total) surplus. By using exclusive contracts to eliminate upstream competition, the incumbent can offer a two part tariff that implements this outcome. A negative fixed fee (of ²) allocates some of this surplus to the buyers. 11 Upstream competition undermines this arrangement. While the Posner and Bork argument that upstream competition eliminates the total deadweight loss is still correct, all of this surplus ends up in the hands of final consumers, who are not parties to the exclusive contracts. 5 Imperfect Competition: Buyer s are Differentiated Bertrand Competitors The preceding two sections considered two polar cases. When buyers do not compete at all we showed that an incumbent monopolist cannot use exclusive contracts to deter entry, while when buyers are perfect competitors exclusive contracts can always deter entry. These results suggest that there may be some threshold level of downstream competition below which exclusive contracts cannot deter entry and above which they can deter entry. Since the profit functions for the incumbent, captive buyers, and free buyers all depend on the demand function for the buyers final output, we cannot prove that this is true for all possible demand functions. We can, however, provide an example where such a threshold exists. Moreover, in this example, this threshold is independent of R s minimum efficient scale. This is an important negative result. One might have suspected that the irrelevance of minimum efficient scale on the effectiveness of exclusive contracts in the prior two sections was an artifact of the extreme cases they considered. That is, it could 11 We thank Patrick DeGraba for suggesting this two part tariff interpretation. 10

13 be that, even though no competition is enough and perfect competition is always sufficient, the greater the entrant s minimum efficient scale, the less downstream competition that is needed for exclusive contracts to be able to deter enty. This would suggest that minimum efficient scale and downstream competition work together to determine when exclusive contracts can deter entry. Our example shows that this conjecture is not generally true. Before proceding to the example, consider the general case. We begin by analyzing a buyer s breach decision in period 3.2. Let π I (n; z) bei s equilibrium profit inperiod3wheren is the number of buyers that remain subject to an exclusive contract, and let z be a parameter of the final demand curve that measures the product differentiation of the buyers output (where larger values of z mean the products are closer substitutes, i.e., downstream competition is more intense). 12 Similarly, let π s (n; z) andπ f (n; z) be the equilibrium profit of captive buyers and free buyers respectively given the number of captive buyers and the product differentiation parameter. With these definitions, it is clear that n exclusive contracts are breach proof only if: π I (n; z)+π s (n; z) π I (n 1; z)+π f (n 1; z) (1) ThelefthandsideisthejointsurplusofI and buyer i when i does not breach the exclusive contract (and neither do any other buyers). The right hand side is the joint surplus of I and buyer i when i alone breaches the exclusive contract and becomes a free buyer. If this condition does not hold, then at least one buyer will breach its exclusive agreement with I if R enters in period 2 because it can compensate I for its loss and still be better off. This condition is also sufficient to establish that there exists an equilibrium of the subgame after R has entered in which n exclusive contracts are breach proof. There could be, however, other equilibria in which more than one buyer breaches the exclusive if π I (n 0 ; z) +π s (n 0 ; z) π I (n 0 1; z) π f (n 0 1; z) < 0forsomen 0 <n. 13 From here on, we will consider the case most favorable for exclusive contracts where (1) is sufficient as well as necessary for n exclusives to be breach proof. The following condition (which we call MES-Irrelevance) determines whether minimum efficient scale affects the incumbent s ability to use exclusive contracts to deter entry. 12 This is equilibrium profit inthatitassumesthati has already chosen p m (n), the optimal p s given n and the reduced form demand curve, q, which will necessarily depend on the degree of downstream competition (since this affects the buyers choice of output prices). 13 If we allow renegotiation but not breach, then I can decide whether to renegotiate with any subset of buyers. In this case, the sufficient conditions for n exclusive contracts to be renegotiation proof are more complicated and would depend on one s model for multi-lateral negotiations. 11

14 MES-Irrelevance If there exists an n 0 [0,N] such that π I (n 0 ; z) +π s (n 0 ; z) π I (n 0 1; z) π f (n 0 1; z) 0thenπ I (N; z)+π s (N; z) π I (N 1; z) π f (N 1; z) 0. If MES-Irrelevance holds, then minimum efficient scale will not affect the ability of exclusive contracts to deter entry. This follows because whenever I can sign n 0 firmstoanexclusiveandhave them all remain subject to this exclusive even if R enters, then I can sustain an N firm exclusive regime. A N firm exclusive regime necessarily blocks entry. Deterring entry by signing N firms to an exclusive must be profitable since π I (N; z)+π s (N; z) π I (N 1; z) π f (N; z) 0implies that π I (N; z) π I (N 1; z) π f (N 1; z) π s (N; z). This means that the amount I gains from deterring entry by signing all N buyers to an exclusive as opposed to having one free buyer that could be supplied by R exceeds what one buyer could gain by refusing to sign the exclusive even if R does enter. Recall that in the prior sections, the rival s minimum efficient scale did not affect whether exclusive contracts could deter entry or not. Analyzing these two polar cases using MES-Irrelevance shows why. When buyers are final consumers, π I (n; z)+π s (n; z) π I (n 1; z) π f (n 1; z) < 0 for all n (this is why buyers would always breach an exclusive contract), hence MES-Irrelevance holds. If buyers are Bertrand competitors, then we showed that if all buyers signed an exclusive contract, then it was not in a buyer s interest to breach, assuming no other buyer breached. This is equivalent to showing that π I (N; z)+π s (N; z) π I (N 1; z) π f (N 1; z) 0, guaranteeing MES-Irrelevance. To determine whether there is a critical level of downstream competition such that exclusive contracts can deter entry if and only if the downstream market is at least that competitive, we use the following condition (which we call the Monotone Competition Effect). Monotone Competition Effect (MCE) There exists a z > 0 such that π I (n; z 0 )+π s (n; z 0 ) π I (n 1; z 0 ) π f (n 1; z 0 ) 0forsomen (N,N]ifandonlyifz 0 z. If MCE holds, then the incumbent can use exclusive contracts to deter entry if and only if downstream competition is intense enough (downstream products are not too differentiated). It is in this sense that we say that more downstream competition always makes it easier for exclusive contracts to deter entry We are ignoring the possibility of entry into the downstream market. If there is free entry in the dowsntream market, then the degreee of downstream product differentiation is endogenous. If R enters, this will induce entry, creating more downstream competition and more free buyers. The net effectofthisontheabilityofexclusive contracts to deter entry is left for future research. 12

15 We now proceed to an example where both MES-Irrelevance and MCE hold. While this example certainly does not show that they hold everywhere, it does demonstrate that the irrelevance of minimum efficient scale is not restricted to the two polar cases considered in the prior sections. Linear Demand Example For this example, we consider the following demand function: NX q i =1 P i + z (P j P i ) (2) j=1 Here, P i represents the price that downstream firm i charges to final consumers (as opposed to p i which is its input price). Because we assume that the only cost downstream firms bear is their input cost, their profit function is: π i =(P i p i )q i (3) The Bertrand-Nash equilibrium to the downstream pricing game is the following: P i = 2(1 + p i)+z[2n 1+p T (1 + z(n 1)) + p i (N 1)(3 + z(n 1))] (2 + z(n 1))(2 + z(2n 1)) (4) In this equation, p T = P N j=1 p j. Using (2) and (4), one can find the demand function for I from only those buyer s subject to an exclusive contract as a function of the number of buyers subject to exclusive contracts and the input price, p s, it charges those buyers. We call the total amount of demand by the n firms subject to an exclusive, Q s. n(1 + z(n 1))[2 + z(2n 1) + c(n n)z(1 + (N 1)z) Q s = p s (2 + (3N n 1)z +(N n)(n 1)z 2 )] (2 + z(n 1))(2 + z(2n 1)) (5) I can either choose p s in period 3.1 to deter buyers from breaching the contract or it can set p s to maximize its profits for a given number of buyers that remain subject to an exclusive (assume that n is independent of p s as it is in period 3.3). Notice that if the second approach gives a lower price than the first, then I does not need to consider the effect of p s on n. First, we solve for the 13

16 optimal p s using the second approach. For a given n, I s profits are given by: π I =(p s c)q s (6) Notice that this ignores the profits that I earns from the damages paid by any buyers who are free as a result of breaching an exclusive. Because the injured party has a duty to mitigate damages, I should not have an incentive to choose price to affect the damages it is entitled to receive from breach. Thus, ignoring damage payments in the profit function used to determine p s should give the correct p s. (There is a simple way for a court to enforce the duty to mitigate without full knowledge of the demand function; it can determine the lost profit from losing a free buyer based on the profit I earns from a captive buyer.) Solving I s first order condition for profit maximization, we find that the optimal price that I charges to those subject to exclusive contracts is p s,3 (the second subscript refers to the fact that this is the price I will choose in period 3.3, when n is given): p s,3 = (1 + c)(2 + z(2n 1)) + 2c(N n)z(1 + (N 1)z) 2(2 + (3N n 1)z +(N n)(n 1)z 2 ) (7) Now we determine the highest price I can charge in period 3.1 that will deter a buyer from breaching, given that n other buyers will remain subject to an exclusive contract and given that I will not reduce this price in period 3.3. We call this price p s,1, which is the solution to the following equation: π b (p s,1, (p n s,1, c N n 1 )) {π b (c, (p n s,1, c N n 1 )) [(n +1)(p s,1 c)q(p s,1, (p n s,1, c N n 1 )) n(p s,1 c)q(p s,1, (p n 1 s,1, cn n ))]} =0 (8) Recall that π b (p s,1, (p n s,1, cn n 1 )) is a buyer s profit when it pays an input price of p s,1, n other buyers also pay this input price and the remaining N n 1 buyers pay c. So the first term is a buyer s profit from not breaching when n other buyers remain subject to an exclusive. The second term, in curly braces, is the buyer s profit from breaching. The first term is her profit buying the good at c when n other buyers are subject to an exclusive. The term in square brackets is the expectation damages she must pay for breach, I s profit whenn + 1 buyers are subject to an exclusive minus its profit when only n buyers remain subject to an exclusive. Using (2) and (4), we can get explicit formulas for π b and q as a function of p s,1 and n. Using 14

17 these, we solve (8) for p s,1 : p s,1 = c + (1 c)(n 1)(2 + z(2n 1))z 2 (1 + (N 1)z)(2 + Nz)(2 + (3N 2n 2)z +(N 2n 1)(N 1)z 2 ) (9) When p s,1 <p s,3, I s profits are clearly increasing in p s,1 for any given n. Notice that p s,1 is increasing in n. Thus, if it is profitable for I to set p s,1 to deter n buyers from breaching, it is profitable for I to set p s,1 to deter all N buyers from breaching (assuming they have all signed exclusives in period 1). 15 NowthatwehaveshownthatI can more profitably deter breach from a greater number of buyers than a lesser number of buyers, we turn to the case where p s,1 >p s,3 (the binding price is the price set to maximize period 3.3 profits). We can use (4) and p s,3 to find the equilibrium downstream prices as a function of the number of buyers subject to an exclusive contract (since free buyers pay c). This, in turn, allows us to compute equilibrium profits for the incumbent, buyers subject to an exclusive, and free buyers only as a function of n, the number of buyers who are subject to an exclusive contract, and z, the degree of product differentiation downstream. ˆπ I (n, z) = n(1 c) 2 (1 + z(n 1))(2 + z(2n 1)) 4(2 + z(n 1))(2 + (3N n 1)z +(N n)(n 1)z 2 ) (10) ˆπ s (n, z) = (1 c)2 (1 + z(n 1)) 4(2 + z(n 1)) 2 (11) ˆπ f (n, z) = (1 c)2 (1 + z(n 1))(4 + (6N n 2)z +(2N n)(n 1)z 2 ) 2 4(2 + z(n 1)) 2 (2 + (3N n 1)z +(N n)(n 1)z 2 ) 2 (12) Using these profit functions in condition (1), we find that signing n buyers to an exclusive is breach proof given entry if and only if: ˆπ I (n; z)+ˆπ s (n; z) ˆπ I (n 1; z) ˆπ f (n 1; z) = (1 c) 2 (1 + z(n 1)) n(2 + z(2n 1))(2 + z(n 1)) 4(2 + z(n 1)) 2 {1+ 2+(3N n 1)z +(N n)(n 1)z 2 (4 + (6N n 1)z +(2N n +1)(N 1)z 2 ) 2 (n 1)(2 + z(n 1))(2 + z(2n 1)) (2 + (3N n)z +(N n +1)(N 1)z 2 ) 2 2+(3N n)z +(N n +1)(N 1)z 2 } 0 15 For large n, wecouldhavep s,1 >p s,3. This does not alter the result since we show below that when p s,3 is the binding price the same result holds. 15

18 This condition will hold if and only if the term in the curly braces is positive. equal to zero and solving for n yields the following solutions: Setting this term n 1 = n 2 = 3z 2 (N 2 1) + 9zN + z +6+ p (1 + z(n 1)) (4 + 8z (N +2)+z 2 (5N 2 +26N 11) + z 3 (N 1) (N 2 +10N +1)) 4(1 + z(n 1)) 3z 2 (N 2 1) + 9zN + z +6 p (1 + z(n 1)) (4 + 8z (N +2)+z 2 (5N 2 +26N 11) + z 3 (N 1) (N 2 +10N +1)) 4(1+z(N 1)) One can easily show that n 1 >N. n = n 2, we get: If we evaluate the derivative of the term in curly braces at q z 2 (1 + z(n 1)) 3 (4 + 8z (N +2)+z 2 (5N 2 +26N 11) + z 3 (N 1) (N 2 +10N +1))> 0 (15) Therefore, we have shown that if the curly braces term is positive for any n<n then it is positive at n = N, that is, we have shown that MES-Irrelevance for any degree of downstream product differentiation. For this linear demand function, minimum efficient scale plays no role in the ability of exclusive contracts to deter entry, no matter how intense the downstream competition is. Because MES-Irrelevance holds, we know that the degree of product differentiation is such that n exclusive contracts are breach proof if and only if N exclusive contracts are also breach proof. Thus, to determine whether MCE holds, it is sufficient to analyze the case where all other buyers adhere to the exclusive. First, consider the case where p s,1 <p s,3. When all other buyers do not breach, p s,1 is: p s,1 (n = N 1) = c + (1 c)(n 1)(2 + z(2n 1))z 2 (1 + (N 1)z)(2 + Nz)(2 + Nz (N 1) 2 z 2 ) (16) It is easy to verify that this is increasing in z. When I chooses p s,1 <p s,3, it can charge a higher price and make more profits the larger z is. This means that if will be profitable to choose p s,1 to deter breach for some z 0,thenitwillbeprofitabletodosoforallz>z 0. Now, consider the case where p s,1 >p s,3. When n = N, the curly braces term from (13) 16

19 becomes: (zn +1)(2+zN z) z3 (N 1) 2 + z 2 N (N 1) z(n +1) 2 (2 + 2zN + z 2 N z 2 ) 2 (17) This expression has the sign of z 3 (N 1) 2 +z 2 N (N 1) z(n +1) 2. Notice that z 3 (N 1) 2 + z 2 N (N 1) z(n +1) 2isconvexinz (given z 0) and at z = 0 it is negative. This means that say this expression is positive for some z 0,thenz 3 (N 1) 2 + z 2 N (N 1) z(n +1) 2 must be strictly increasing in z for all z>z 0. ThisprovesthatMCE holds for this linear demand function. 6 Conclusion Both Rasmusen et al. (1991) and Segal and Whinston (2000) assume that an incumbent monopolist can offer exclusive contracts that prevent buyers from buying from an entrant under any circumstances. In the United States, however, no contracts are that powerful: Courts will neither enforce contractual provisions that prohibit renegotiation nor impose damages that they believe exceed the harm to the seller resulting from breach. Although non-legal enforcement mechanisms (such as reputation) may make renegotiation or breach prohibitively costly for buyers in some circumstances, such circumstances are probably more the exception than the rule. Because of this, a potential entrant knows that buyers will renegotiate or breach their exclusive contract if their benefit from doing so exceeds the ex post harm to the incumbent. In the context of the RRW-SW model, this has the effect of creating an additional period where buyers can choose to renegotiate or breach their exclusive contracts. Once this extra period is added, the RRW-SW result that minimum efficient scale can lead to inefficient exclusion when buyers are final consumers no longer holds. This does not mean, however, that inefficient exclusion can never occur. We show that when the buyers are downstream competitors, inefficient exclusion can occur. We show this by analyzing both the extreme case of perfect competition downstream and a linear demand case with imperfect product substitution. In these cases, whether or not inefficient exclusion occurs is a function only of the degree of downstream competition, not of minimum efficient scale. While these example do not show that minimum efficient scale is always irrelevant to the efficacy of naked exclusion, they do indicate that, unlike downstream competition which is an essential precondition for naked exclusion, naked exclusion can occur even in the absence of any scale economies. 17

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