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Optimal antitrust enforcement: Competitor suits, entry, and post-entry competition
Journal of Public Economics 95 (2011) 967–972
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Journal of Public Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j p u b e
Optimal antitrust enforcement: Competitor suits, entry, and post-entry competition☆ Warren F. Schwartz a,⁎, Abraham L. Wickelgren b a b
Georgetown University Law Center, 600 New Jersey Ave. NW, Washington, DC 20001, United States University of Texas at Austin School of Law, 727 E. Dean Keeton St., Austin, TX 78705 United States
a r t i c l e
i n f o
Article history: Received 4 February 2010 Received in revised form 1 September 2010 Accepted 19 January 2011 Available online 4 February 2011 Keywords: Antitrust enforcement Competitor suits
a b s t r a c t We consider the effect of competitor suits in a model in which an incumbent can take an action that deters the entry of a rival. The option to sue the incumbent can provide a subsidy for entry which can maintain competition even when the incumbent takes this action. Liability for the entrant's lost profits, however, can soften post-entry competition. If the incumbent's action is potentially efficient, taking market structure as given, e.g. it reduces her costs, then competitor suits can generate some post-entry competition without deterring this efficient cost-reduction. If the incumbent's action is inefficient, e.g. it increases the rival's costs (but does not reduce the incumbent's costs), then competitor suits (even with maximal antitrust liability) cannot deter the incumbent from increasing the rival's costs by at least a small amount. Thus, the paper suggests that while competitor suits have advantages for efficient actions that deter efficient entry, they do not work well for inefficient actions that deter entry. © 2011 Elsevier B.V. All rights reserved.
1. Introduction While antitrust enforcement is almost exclusively a government responsibility in Europe and Canada, in the United States private antitrust suits outnumber government suits by nearly nine to one.1 While many of these suits are initiated by customers or groups representing customers, many are also competitor suits. In this paper, we address the question of what the proper role is for competitor suits. Antitrust enforcement is designed to deter firm behavior that reduces competition or efficiency while not deterring behavior that increases competition or efficiency, often judged by courts and governments by its effect on consumer welfare and by economists by its effect on total welfare. For most of our analysis, this distinction is not critical. Because competitors objectives frequently may be poorly aligned with social objectives, much of the literature on private antitrust enforcement has focused on how to better align competitors incentive to sue (or, at least, the results of those suits) with the goals of a social planner. This literature, which we discuss below, has made important contributions. In this paper, however, we take a different, complementary, approach. We abstract from the information and
☆ We thank the participants at the American Law and Economics Association Annual Meeting, the Triangle Law and Economics Conference, and the University of Texas at Austin. ⁎ Corresponding author. Tel.: +1 512 232 1904. E-mail addresses: [email protected] (W.F. Schwartz), [email protected] (A.L. Wickelgren). 1 NAFTA Working Group, Private Actions for Violations of Antitrust Laws, Appendix A. 0047-2727/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jpubeco.2011.01.006
incentive problems of prior work and focus, instead, on the effect of antitrust liability on subsequent competitive interactions. In so doing, we highlight two special effects that competitor suits can have. First, competitor suits provide a subsidy for entry or continued operation in a market. If an incumbent firm is taking an action that is designed to deter entry or induce exit by making it unprofitable for a rival to compete, allowing this rival to sue for damages can undo this effect. Notice, however, that for this to be maximally effective, suits should be limited to actual competitors, not simply potential competitors. Second, because suits by competitors are for damages for lost profits, this provides the incumbent with an incentive to reduce those damages. This means that the incumbent is effectively a partial shareholder in its rival. This generates an incentive toward softer (less aggressive) competition, often through charging higher prices. Thus, at first glance, it might appear that there is not much role for competitor suits. Some acts that might deter entry, however, might also be efficient, taking market structure as given. For example, exclusive dealing or exclusive territory arrangements might lower an incumbent's costs through inducing more efficient distribution while also making it more difficult for a new entrant. Even incumbent investments in marginal cost reduction can make entry unprofitable for a firm that faces a fixed entry cost. Because entry promotes competition which often (though, not necessarily) improves social welfare, the ideal solution would be to both not deter the incumbent's efficient actions and induce the entrant to enter. The entry subsidy that competitor suits provide can accomplish both goals. As we show below, competitor suits can induce an incumbent to undertake an efficient action, while
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eliminating the entry-deterring effect of that action. While competitor suits do not achieve the first best, since prices are elevated as a result of the competition-softening effect of competitor suits, they do accomplish the goal of deterring neither the incumbent's efficient action nor the rival's entry. Unfortunately, in situations where the incumbent's action is clearly inefficient and entry-deterring in the absence of antitrust liability, competitor suits can induce entry but cannot necessarily deter this inefficient action. Consider an action by the incumbent that raises the entrant's costs but does not appreciably affect its own costs (certain tying or exclusive dealing or exclusive territories contracts might have this effect in some situations). We show that, even if the threat of competitor suits induce the incumbent to raise its price so high that its rival's profits are unchanged as a result of its increased costs, the incumbent still can profit from at least a small increase in its rival's costs. Thus, while the threat of a competitor suit might deter an action that raises rivals' costs by a large amount, it cannot eliminate any incentive to raise rivals' costs. These results suggest that while competitor suits may have a valuable role to play for actions that both lower the incumbent's cost and deter entry, they may not be the best vehicle for deterring the incumbent from taking actions that are unambiguously inefficient because they increase the costs of rivals. The general literature on public versus private enforcement was pioneered by Becker and Stigler (1974). Important subsequent contributions were made by Landes and Posner (1975), Polinsky (1980), Shavell (1984), Shavell (1993) among others. Much of this literature focuses on the incentives of public versus private actors to enforce the law and the differences in access to information of both groups. Much of the (limited) literature specifically on private antitrust enforcement also focuses on these issues.2 McAfee et al. (2008), for example, assumes that competitors get more accurate information than the government about whether or not their rival has violated the antitrust laws and also have socially perverse incentives to sue to block pro-competitive actions of a rival that reduce their own profits.3 Similarly, Martini and Rovesti (2004) show that private enforcers who care only about their surplus will spend more resources on antitrust enforcement than will public enforcers who care about social surplus, which is often smaller. Bourjade et al. (2009) analyze optimal rules for facilitating the screening of anti-competitive from pro-competitive defendants in private antitrust actions with the possibility of settlement. These papers do not model how antitrust liability affects the competitive interactions, so they do not consider the tradeoff between the entry subsidy effect and the competition softening effect of competitor suits. Because we assume perfect information and perfect courts, however, our model does not capture the information and incentive issues in those papers. Our competition softening effect is related to the increased consumption effect in the treble damages literature. Salant (1987) and Baker (1988) show that because consumers view the prospect of receiving treble damages as equivalent to a coupon off the stated price, the prospect of consumer suits cannot induce a monopolist to sell more than the monopoly quantity. Besanko and Spulber (1990) show that if consumer information is imperfect, then consumer suits do increase social welfare. Our paper also models optimal pricing of the incumbent under potential antitrust liability. We do not, however, allow the competitor to alter its behavior to increase damages because 2 The paper is also related to the literature on optimal antitrust enforcement more generally, such as Wickelgren (2009) and Ottaviani and Wickelgren (2009). 3 Baumol and Ordover (1985) and Snyder and Kauper (1991) also argue that competitors often initiate socially perverse suits. Page and Blair (1992) argue that the antitrust injury doctrine often stops these suits from having much effect. On the other side, Brodley (1995) claims that this doctrine has unduly discouraged legitimate competitor suits, while Page and Lopatka (1996) argue that public enforcement may be superior if the antitrust injury requirement is not satisfied.
of the requirement that plaintiff's have to mitigate damages. As Hamilton and Cone (1987) have shown, courts have consistently been moving towards enforcing this requirement in antitrust cases.4 Segal and Whinston (2007) provide an excellent survey of many important issues involved in analyzing public versus private antitrust enforcement. 2. Model An incumbent (she) and an entrant (he) produce differentiated but competing products at constant marginal cost. The firms compete in prices. If both firms are active, then demand for product j is given by q(pj,p-j) where j = {I,E}. If only I, the incumbent, is active, then demand for I is given by qm(pI). Let subscripts for q denote partial derivatives. We assume that q1, qm′ b 0, q2 N 0 and that q11, qm″ b 0. To ensure that prices are strategic complements, we assume q12 N −2 q2 / (pj−cj) for all pj, p− j . The entrant, E, must expend a fixed cost of F to enter (I does not). Before E's entry decision, I has the option of taking action A, which affects the marginal costs of either player, or both. We assume that in the absence of A that E finds it profitable to enter. A could reduce E's profits below F, causing him not to enter in the absence of antitrust liability. The sequence of events is as follows.
Period 1 I chooses whether or not to take action A at a cost of k. If I does nothing, period 3 marginal costs are cI and cE. If I does A, period 3 marginal costs are c′I and c′E. Period 2 E chooses whether or not to enter at a cost of F. Period 3 Active firms choose prices and earn profits. Period 4 If I took action A in period 1, then E can sue I for antitrust injury at a cost of KE for E and KI for I. E prevails with probability q. If E prevails, then its expected damages are γ times its lost profits.5 Under current treble damage rules, γ = 3. We consider arbitrary γ to determine the optimal level of liability, though we do assume it continues to be, as under current law, tied to the damages suffered by the plaintiff. If E does not enter in period 3, then I's profits are π
m;0
m
=maxp ðp−cI Þ q ðpÞ or π
m;A
m
=maxp ðp−c′I Þ q ðpÞ
ð1Þ
If E enters and I did not do action A, then period 3 profits are π′I =maxpI ðpI −cI Þ qðpI ; pE Þ and πE =maxpE ðpE −cE Þ qðpE ; pI ÞNF 0
0
ð2Þ
If E enters and I did A, then I's and E's profits are given by π′I = ðp′I −c′I Þ qðp′I ; p′E Þ and πE =maxp′E ðp′E −c′E Þ qðp′E ; p′I Þ A
A
ð3Þ
p′I will in general not maximize π′AI (p′I) because I is also concerned with its potential antitrust liability.6 I and E choose prices taking the other's price as given. Competition is imperfect, so prices exceed marginal costs in any post-entry market configuration. 4 It is worth noting that our results suggest that the mitigation principle should not extend to the entry or market participation decision since the main benefit of competitor suits in our model is to create competition by subsidizing entry or market participation. 5 In principle, E could sue whether or not it entered. Of course, it is harder to prove lost profits if one is not in the market. More importantly, as we will see, in our model the main role for competitor suits is that they encourage entry, thus our model implicitly suggests requiring entry for competitors to have standing to sue. 6 We do not allow E to consider the effect of its price on its expected damage award should it sue due to the general requirement of mitigation of damages, which holds in antitrust law as well as other areas of law (Hamilton and Cone, 1987).
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2.1. Antitrust liability and post-entry competition If E enters and sues, expected damages are qγ(πE0−πEA(p′I)). Because damages depend on lost profits, the higher the price that I sets price the lower the damages she pays if she did A. Letting α = qγ, there is a p** such that α (πE0−πEA(p**)) = KE. So, if p′I ≥ p**, then E does not sue because I's period 3 price is high enough that E's expected recovery does not exceed its litigation costs. We assume that p** N argmaxpI′π′I A (p'I). Clearly, p** is increasing in α. To see this, totally differentiate the implicit definition of p** with respect to α to obtain: 0 A A dp =dα= π E −πE ðpÞÞ=α πE ′ðpÞN0
ð4Þ
The numerator is positive as long as KE N 0 by the definition of p**. The denominator is positive since higher prices by the incumbent increase the entrant's profits. If I did A and E entered, then I chooses p′I to maximize h A 0 A πI ðp′I Þ−Z α πE −πE ðp′I Þ + KI
=
A A απE ″ðpÞ + πI ″ðpÞ N 0
deter E from suing. I's expected profits from choosing A are πIA(p**)−k. Her profits from not choosing A are π′0I . Thus, she chooses A if and only if k b πIA(p**)−π′0I . Let k** = πIA(p**)−π′0I , then we have A dk=dα =π I ′ð pÞ dp=dα=
n o 0 A A A π E −π E ðpÞ =α π I ′ðpÞ=π E ′ðpÞb0
ð7Þ The term in curly braces is the amount by which E's profit must increase when α increases in order to keep E's expected payoff from suing at zero. The πIA′(p**) / πEA′(p**) term reflects how much I's profit decreases for every dollar increase in E's profit that occurs due to an increase in I's price. If I chooses to price at p* after doing action A, then she chooses A if and only if kb πIA ð pÞ− α π0E −πEA ðpÞ + KI −π;0I : Let k =πIA ðpÞ− α π0E − 0 π A ð pÞÞ+K −π′ : E
I
I
A A 0 A dk=dα = πI ′ðpÞ+ απE ′ðpÞ dp=dα− π E −πE ðpÞ 0 A =− πE −πE ðpÞ b0
ð8Þ
ð5Þ
Z is an indicator variable that equals one if p′I b p**. Let p* be defined implicitly by α πEA′(p*) + πIA′(p*) = 0.7 So, p* is I's optimal price taking into account antitrust liability if she does not deter suit entirely. Clearly, p* is increasing in α also. To see this, totally differentiate the implicit definition of p* with respect to α to obtain: A dp = dα = −πE ′ðpÞ
969
ð6Þ
This is positive because both the numerator and the denominator are negative. If p* ≥ p**, then I chooses p = p** since both p* and p** exceed the direct profit-maximizing price. So, if p** deters suit entirely, there is no further reason to price higher than that. Otherwise, I chooses either p* or p**.8 Lemma 1. If greater antitrust liability (larger α) does not deter I from action A, then (A) I's price increases almost everywhere with greater liability and (B) if prices are strategic complements, then E's price increases almost everywhere with greater antitrust liability. Proof. (A) We have already proved that both of the incumbent's possible prices, p* and p**, increase in α. It is possible, however, that an increase in α could cause the incumbent to shift from p** to p*, resulting in a one-time decrease in price. Everywhere else, however, I's price must increase in α. (B) The entrant's price will increase whenever the incumbent's increases as long as prices are strategic complements. Q.E.D. This lemma shows that we get a potentially perverse effect from greater antitrust liability. If greater liability does not deter the action, greater antitrust liability results in both firms charging higher prices. There is one potential exception. It is possible that increasing liability could at one point cause the incumbent to shift from pricing to deter suit entirely, charging p**, to pricing optimally given suit, p*. If this happens, then prices may drop at this point. 2.2. Antitrust liability and deterrence Greater antitrust liability can also deter the incumbent from undertaking action A. First, consider the case where I chooses p** to
7 We assume απ AE ″(p)+ πAI ″(p) = α(p′E−cE)q22 + 2q1 + (p−cI)q11 b 0 ∀ p, p′E to insure an interior maximum. 8 p** might be optimal because there is a fixed legal cost that I must pay if E sues.
The dp*/dα term drops out because πIA′(p*)+ α πEA′(p*) = 0 by the first order condition for p*. This is negative since πE0−πEA(p*) N 0. Thus, we have the following result. Lemma 2. As antitrust liability increases (larger α), the maximum cost of action A for which the incumbent will undertake the action decreases. Proof. Since k* and k** decrease with greater antitrust liability, it only remains to show that if greater antitrust liability causes I to shift from p* to p** or vice versa that the cost of A must decrease to make undertaking A profitable. If this were not the case then there would exist some α″ N α′ such that πIA(p*(α″))−[α″ (πE0−πEA(p*(α ″))) + KI] N πIA(p**(α′)) or πIA (p*(α′))−[α″ (πE0−πEA(p*(α′))) + KI] b πIA(p**(α″)). If either of these were the case, then since I's payoff is strictly decreasing in α it would have had a greater payoff at α′ charging the price it charged at α″. This contradicts the fact that it changes its price when α changes from α′ to α″. Q.E.D. Increasing antitrust liability does in fact lead to greater deterrence of action A even as it also leads to price increases in the event that I does action A in spite of greater antitrust liability. Whether or not this greater deterrence of action A is desirable depends on whether or not A is socially efficient. In the next subsection, we examine a case in which A is likely to be efficient (it reduces I's costs). In the following subsection, we examine a case in which A will be inefficient (it increases E's costs). 2.3. Purely cost reducing actions: cI N c′I, cE = c′E We first consider the baseline case of an action that only reduces the incumbent's costs, but does not affect the entrant's. That is, cI′b cI, cE = cE′. 2.3.1. Maximal antitrust liability To examine competitor suits at their most effective in influencing the incumbent's behavior, we consider the limit as α goes to infinity. We do this not because we view this as a realistic value for α, rather it is provides a valuable baseline for our analysis of finite α. In this case, the incumbent will price to deter suit entirely. p** is given by πEA(p**) = πE0; the incumbent must price so that the entrant's profits do not decrease as a result of action A. A cannot deter entry since we have assumed that entry is profitable in the absence of action A. Since the entrant's marginal cost has not changed, its profit function does not depend on A. To keep E's profit unchanged, I chooses p′I = p**= pI and then E will also choose pE′ = pE (since its costs and its rival's price have not changed). Since I's costs have fallen as a result of action A, I's profit must increase.
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That is, I will choose action A if and only if π′AI (pI)−π′0I = (cI − c′I)q(pI, pE) N k. Taking the pricing decisions as given, I will make the socially optimal choice since choosing action A does not change E's profits or consumer surplus. Thus, we have proved the following result. Lemma 3. If action A reduces I's costs but does not change E's costs, then in the limit as α → ∞, I chooses action A if and only if doing so raises social welfare. 2.3.2. Non-maximal antitrust liability Lemma 3 does not imply that maximal antitrust liability is optimal. The reason is that, as we have seen in Lemma 1, larger antitrust liability actually leads to higher prices. That said, even though A is potentially efficient,9 some antitrust liability may be optimal. This will be the case only if α N 0 is necessary to induce entry and entry is socially efficient. Let p A = argmaxp′Iπ′AI (p′I), that is p A is I's profit-maximizing price given action A (and ignoring antitrust liability). Then, if πEA(p A) b F, then it is possible that action A would reduce social welfare without antitrust liability because it would reduce competition. Notice, however, that this isn't necessarily the case since if c′I b b cI it might be more efficient to have a monopoly than a duopoly. From here on, however, we will assume that duopoly is socially desirable, otherwise zero antitrust liability is clearly optimal in this case. Before proceeding, it is worth commenting on this assumption. As Mankiw and Whinston (1986) have demonstrated, even if A does not result in a large cost reduction, entry can be profitable and reduce total surplus. This effect is more pronounced in our setting because the threat of competitor suits softens price competition, reducing the consumer benefit from entry. That said, unlike Mankiw and Whinston, we do not have a free entry model. We focus on monopolization, so there could be socially excessive incentives to enter in a free entry model but socially insufficient incentives for one entrant to enter to change a monopoly to a duopoly.10 Furthermore, even if there are socially excessive incentives to enter, entry may still increase social surplus if entry costs are not too great and the negative externality from entry is small. So, while entry is always socially efficient, it is a relevant case to consider. In addition, since almost all competition authorities and courts in the world use a consumer rather than a total welfare standard, this assumption is always relevant if competition authorities or courts are setting policy under that standard. We now consider the optimal level of antitrust liability when A only reduces I's costs. Starting from the baseline of maximal antitrust liability, reducing α has three effects. First, taking the choice of A and entry as given, Lemma 1 shows that it reduces I's and E's price almost everywhere. This increases welfare since we have assumed that p** and p* exceed the duopoly price without liability, which already exceeds the socially optimal price (price equals marginal cost).11 Second, given I's choice of A, reducing α reduces E's profit because it reduces the profit that I must ensure that E obtains to deter E from suing. Third, reducing α increases I's benefit from choosing A. One might think that the optimal α is the lowest α that does not deter entry, which we will call α*. That is not necessarily true. When α is less than maximal, I's incentive to choose A is not necessarily socially optimal. It may be insufficient, in which case lower α clearly increases social welfare. I may also have a socially excessive incentive 9 We say potentially efficient because we have not considered the cost of the investment nor the (potential) efficiency loss from the prevention of entry. 10 The online appendix demonstrates this for the case of linear demand. 11 This is admittedly not the whole story since there is the question of consumers buying the right product. If the entrant is charging above marginal cost, then it is not generally socially optimal for the incumbent to charge marginal cost since that may induce consumers to purchase from the incumbent even though purchasing from the entrant would maximize social surplus. That said, because we are considering situations in which the incumbent is charging above the duopoly price and typically social welfare would be increased with one firm reducing its price slightly below the duopoly price, reducing p** should increase social welfare in almost any model.
to choose A at finite α , in which case a larger α that deters I from choosing A is optimal. To see this, notice that if I prices at p**, then the only effect of lowering α, taking entry and action A as given, is to lower p**. I could have an excessive incentive to choose A if reductions in p** increase I's profit more than they increase social welfare.12 Proposition 1. If entry is socially efficient then the optimalα is either α*, the lowest α that does not deter entry, if A is socially efficient at α*, orα → ∞, if A is not socially efficient at α*. If KE ≥ π0E −F, then α*∈ (1,KE / (πE0−F)]. If KE b πE0−F, then α*∈[KE / (πE0−F),1). Proof. See Appendix. A could reduce welfare by deterring entry or if A increases I's profit largely through business stealing (which can only happen at finite α). Proposition 1 says that if this business stealing effect drives I to undertake action A even though it reduces total welfare, then it is optimal to make antitrust liability maximal deter I from taking action A.13 On the other hand, if action A is efficient, then it is optimal to make antitrust liability low to ensure that prices are low. That said, there must be some antitrust liability to keep entry profitable for E in spite of I's lower costs. Setting α = KE / (πE0−F) if I prices to deter suit, or somewhere in between this and one if I does not price to deter suit, ensures that I's prices are just high enough to induce E to enter, but no higher. This is a second best solution that ensures efficient cost reduction and some, though not complete, competition. 2.4. Purely cost increasing actions: cI = c′I, cE b c′E In the absence of antitrust liability, actions that raise a rival's costs can be profitable for the incumbent, either by deterring entry or by increasing the entrant's optimal price. The question is whether in the presence of substantial antitrust liability, it can ever be privately optimal for I to increase E's costs. 2.4.1. Maximal antitrust liability As before, we start by considering the case of maximal antitrust liability. If I benefits from increasing E's costs in this case, then she certainly benefits with less antitrust liability. I sets price to keep E's profit identical to what it would have been without action A, while E chooses its price to maximize its profit. Thus, p′E and p′I are implicitly determined by E's first order condition and this equal profit constraint: q p′E; p + ðp′E −c′E Þq1 p′E ;; p =0 πE ðpÞ=πE A
0
ð9Þ ð10Þ
Given these constraints, we analyze if I's profit, π′I A(p**) = (p**−cI) q(p**,p′E), is increasing in cE. If so, then competitor suits may not deter cost increasing actions. We determine the effect of cE on prices under maximal antitrust liability by differentiating (9) and (10) with respect to cE. Solving for dp′E / dc′E and dp** / dc′E yields: h i 2q2 p′E ;; p + ðp′E −c′E Þq12 p′E ;; p dp′E=d′E =q1 p′E ;; p
ð11Þ
h i q2 p′E ;; p 2 q1 p′E ;; p + ðp′E −c′E Þq11 p′E ;; p dp=dc′E = −q1 p′E ;; p q2 p′E ;; p
=
ð12Þ
12 The online appendix more precisely establishes how the private and social incentives to choose A are different with finite α. 13 A large but finite α would also accomplish this goal.
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Using these two equations, we find that: .n h io A dπ′I ðpÞ=dc′E =q1 p′E ;; p q2 p′E ;; p 2q1 p′E ;; p + ðp′E −c′E Þq11 p′E ;; p ( −½qðp; p′E Þ + ðp−cI Þq1 ðp; p′E Þ h i ð13Þ × 2 q1 p′E ;; p + ðp′E −c′E Þq11 p′E ;; p + ðp−cI Þ q2 ðp ; p′E Þ ) h i × 2 q2 p′E ;; p + ðp′E −c′E Þq12 p′E ;; p
The first line is positive, since the square bracket term is negative as is q1. Thus, dπIA(p**) / dc′E has the sign of the curly braces term on the second and third lines. q(p**,p′E) + (p**−cI) q1(p**,p′E) b 0 since I has to price above its profit maximizing level so that E's profits does not fall due to higher cE, making the second line negative. If prices are strategic complements, the third line is positive, leading to the following result. Proposition 2. As α → ∞, if prices are strategic complements, then there exists an ε N 0 such that if c′E−cE b ε then π′IA(p**) N π′0I if the only effect of action A is to increase E's costs from cE to c'E. That is, even with maximal antitrust liability, competitor suits may not deter I from taking an action to increase E's costs by at least a small amount. Proof. As c′E approaches cE, then p** will approach pI. This makes q (p**,p′E) + (p**-cI) q1(p**,p′E) approach zero, as it is if p** = pI and p′E = pE. Thus, by making c′E close enough to cE, the second line of the (13) can be made arbitrarily close to zero. The third line remains positive and bounded away from zero. Thus, dπ′AI (p**) / dc′E N 0. Q.E.D. Proposition 2 says that even with antitrust liability is so large that I will not reduce E's profit, I gains from raising E's costs. While competitor suits can stop I from deterring entry, they cannot necessarily stop her from taking actions that inefficiently raise E's costs and then accommodating E to deter suit. 2.4.2. Non-maximal antitrust liability This problem is worse with non-maximal antitrust liability. If I prices to deter suit entirely, then the constraint on her price changes from πE0−πEA(p**) = 0 to π0E−πEA(p**) = KE / α. Since KE / α is independent of c′E, as long as this constraint is binding, dπ,A I (p**) / dc′E remains the same as it was under maximal antitrust liability. For c′E very close to cE, the constraint will not be binding, so I can choose a price to maximize its profits knowing that E will not sue. The increase in c′E increases I's profit. Let c′E** be the c′E for which I's profit-maximizing price exactly equals p** so that E is indifferent between suing and not. That is, let c′E** be implicitly defined by: q p′E; p + ðp′E −c′E Þq1 p′E ;; p =0 qðp; p′E Þ + ðp−cI Þ q1 ðp; p′E Þ= 0 and π0E −πEA ðpÞ=K E=α Then dπ′AI (p**) / dc′E is given by (13) for c′E N c′E**. The argument in the proof of Proposition 2 shows that this is positive for c′E N c′E** for c′E is sufficiently close to c′E** since q(p**,p′E) + (p**−cI) q1(p**,p′E) = 0 for c′E = c′E**. Notice that c′E** N cE. That is, I can increase E's costs by a small amount, price to maximize profit, and still deter suit if antitrust liability is non-maximal. We have now proved the following result. Corollary. For α b ∞, if prices are strategic complements, then there 0 exists an ε N 0 such that if c′E− c′E** b ε then π,A I (p**) N π′I if A increases E's costs from cE to c′E. The corollary establishes the intuitive result that if I can profitably increase E's costs with maximal antitrust liability, it can increase these costs even more if antitrust liability is non-maximal. With nonmaximal antitrust liability, there is a region of raising E's costs that is
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completely free in the sense that I can still price to maximize its own profits, ignoring antitrust liability because the loss to E is too small to induce it to sue. The argument in Proposition 2 then says that I can profitably increase E's costs even further since by increasing its own price above the profit-maximizing level, I can still deter suit while increasing its profit relative to what it would have been without A. 3. Conclusion Proposition 1 shows that competitor suits work quite well when the action A is potentially efficient because they can eliminate the entrydeterring effect of the action by providing an entry subsidy. This provides the benefit of lower costs without completely eliminating competition. Unfortunately, we do not achieve the first best because the threat of liability induces the incumbent to increase its prices to minimize the loss to the injurer, which creates losses to final consumers that exceed the benefits to the firms. Note that Proposition 1 assumes entry is efficient. The online appendix examines a linear demand model to show that there is a substantial range of parameter values where this is the case. If A reduces cost by a large enough amount, however, then entry will not be efficient. In this case, a larger damage multiplier will increase the incentive for inefficient entry and suit. Of course, for the vast majority of competition policy authorities this is a non-issue (except for drastic innovations) since they operate under a consumer welfare standard in which entry is never inefficient. Under a total welfare standard, however, suits by inefficient entrants should receive very different treatment than suits by efficient ones. Proposition 2 says that competitor suits are not necessarily effective when the incumbent can take actions that weaken the entrant directly. Even though the incumbent has to compensate the entrant for lost profit, she still has the incentive to increase the entrant's costs somewhat. That is, we cannot rely on competitor suits to deter all actions designed to raise rival's costs. Taken together, these results are quite useful in suggesting the proper role for competitor suits against monopolization or attempted monopolization claims under Section 2 of the Sherman Act. If the complained about action might further monopolization because it makes the incumbent a more efficient competitor, then competitor suits have a valuable role to play because they need not deter these efficient actions (if the damage multiplier is not too large) but will minimize their competitive impact by effectively subsidizing entry. On the other hand, if the monopolizing action is one that directly damages a rival's efficiency, then competitor suits are not the right vehicle to attack this action. Of course, many potentially monopolizing actions, such as exclusive dealing or tying might both increase the incumbent's efficiency and hamper the rival's. Proposition 1 and 2 suggest that if they appear to have substantial (positive) effects on the incumbent's efficiency, competitor suits can have a beneficial role if these suits are necessary to induce entry. If the these actions primarily reduce a rival's efficiency, however, then competitor suits should not be the main avenue of enforcement. While our model assumes a discrete action, the main insights would apply to a continuous action choice. The most significant effect of allowing a continuous action choice would be that the details of the optimal level of antitrust liability in Proposition 1 would change. Instead of trying to set liability to be just large enough to induce entry when some cost reduction is efficient, the optimal level of liability would also have to take into account how liability affects the magnitude of the cost reduction the incumbent would undertake relative to the socially optimal level of cost reduction. Our model also does not consider settlement. In the absence of asymmetric information, this will not affect our results because it will not affect the relationship between the incumbent's pricing and its expected antitrust liability. The settlement amount will vary with the
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incumbent's price in the same way as would the judgment. If the incumbent had private information about the effect of its action, then settlement would act like a damage cap (see Wickelgren, 2004). This would reinforce the result in Proposition 2 that competitor suits do not work well to deter actions that raise rivals' costs. That said, given that the suit occurs after both sides have observed their profits, private information of this type seems unlikely. As we mentioned in the introduction, because we assume courts are perfect, competitors do not initiate suits to decrease competition in our model. If we allowed for court errors, this would, again, reinforce the result in Proposition 2 that competitor suits do not work well in raising rivals' costs cases. Court errors would decrease the average benefit of competitor suits as an entry subsidy in cases where the incumbent has reduced its marginal cost because we would sometimes get softened post-entry competition when this was not necessary to induce entry. Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10.1016/ j.jpubeco.2011.01.006. References Baker, Jonathan B., 1988. Private information and the deterrent effect of antitrust damage remedies. Journal of Law, Economics, and Organization 4, 385–408. Baumol, William J., Ordover, Janusz A., 1985. Use of antitrust to subvert competition. Journal of Law and Economics 28, 247–265. Becker, Gary S., Stigler, George J., 1974. Law enforcement, malfeasance and compensation of enforcers. Journal of Legal Studies 3, 1–18. Besanko, David, Spulber, Daniel F., 1990. Are treble damages neutral? Sequential equilibrium and private antitrust enforcement. American Economic Review 80, 870–887.
Bourjade, Sylvain, Rey, Patrick, Seabright, Paul., 2009. Private antitrust enforcement in the presence of pre-trial bargaining. Journal of Industrial Economics 57, 372–409. Brodley, Joseph F., 1995. Antitrust standing in private merger cases: reconciling private incentives and public enforcement goals. Michigan Law Review 94, 1–108. Hamilton, Neil, Cone, Virginia B., 1987. Mitigation of antitrust damages. Oregon Law Review 66, 339–372. Landes, William M., Posner, Richard A., 1975. The private enforcement of law. Journal of Legal Studies 4, 1–46. Mankiw, N. Gregory, Whinston, Michael D., 1986. Free entry and social inefficiency. RAND Journal of Economics 17, 48–58. Martini, Gianmaria, Rovesti, Cinzia, 2004. Antitrust policy and price collusion: public agencies vs delegation. Louvain Economic Review 70, 127–151. McAfee, R. Preston, Mialon, Hugo M., Mialon, Sue H., 2008. Public versus private antitrust enforcement: a strategic analysis. Journal of Public Economics 92, 1863–1875. Ottaviani, Marco and Wickelgren, Abraham L. 2009. “Approval Regulation with Learning.” Mimeo. Page, William H., Blair, Roger D., 1992. Controlling the competitor plaintiff in antitrust litigation. Michigan Law Review 91, 111–123. Page, William H., Lopatka, John E., 1996. Antitrust injury, merger policy, and the competitor plaintiff. Iowa Law Review 82, 127–150. Polinsky, A. Mitchell, 1980. Private versus public enforcement of fines. Journal of Legal Studies 9, 105–127. Salant, Steven W., 1987. Treble damage awards in private lawsuits for price fixing. Journal of Political Economy 96, 1326–1336. Segal, Ilya, Whinston, Michael D., 2007. Public vs. private enforcement of the antitrust laws: a survey. European Competition Law Review 28, 306–315. Shavell, Steven M., 1984. Liability for harm versus regulation of safety. Journal of Legal Studies 13, 357–374. Shavell, Steven M., 1993. The optimal structure of law enforcement. Journal of Law and Economics 36, 255–287. Snyder, Edward A., Kauper, Thomas E., 1991. Misuse of antitrust laws: the competitor plaintiff. Michigan Law Review 90, 551–603. Wickelgren, Abraham, 2004. A model of welfare-reducing settlement. Contributions to Economic Analysis and Policy, 3: Article 4. Wickelgren, Abraham L., 2009. “A Simple Mechanism for Improving ‘Up or Down’ Regulation”. Mimeo.
Contents lists available at ScienceDirect
Journal of Public Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j p u b e
Optimal antitrust enforcement: Competitor suits, entry, and post-entry competition☆ Warren F. Schwartz a,⁎, Abraham L. Wickelgren b a b
Georgetown University Law Center, 600 New Jersey Ave. NW, Washington, DC 20001, United States University of Texas at Austin School of Law, 727 E. Dean Keeton St., Austin, TX 78705 United States
a r t i c l e
i n f o
Article history: Received 4 February 2010 Received in revised form 1 September 2010 Accepted 19 January 2011 Available online 4 February 2011 Keywords: Antitrust enforcement Competitor suits
a b s t r a c t We consider the effect of competitor suits in a model in which an incumbent can take an action that deters the entry of a rival. The option to sue the incumbent can provide a subsidy for entry which can maintain competition even when the incumbent takes this action. Liability for the entrant's lost profits, however, can soften post-entry competition. If the incumbent's action is potentially efficient, taking market structure as given, e.g. it reduces her costs, then competitor suits can generate some post-entry competition without deterring this efficient cost-reduction. If the incumbent's action is inefficient, e.g. it increases the rival's costs (but does not reduce the incumbent's costs), then competitor suits (even with maximal antitrust liability) cannot deter the incumbent from increasing the rival's costs by at least a small amount. Thus, the paper suggests that while competitor suits have advantages for efficient actions that deter efficient entry, they do not work well for inefficient actions that deter entry. © 2011 Elsevier B.V. All rights reserved.
1. Introduction While antitrust enforcement is almost exclusively a government responsibility in Europe and Canada, in the United States private antitrust suits outnumber government suits by nearly nine to one.1 While many of these suits are initiated by customers or groups representing customers, many are also competitor suits. In this paper, we address the question of what the proper role is for competitor suits. Antitrust enforcement is designed to deter firm behavior that reduces competition or efficiency while not deterring behavior that increases competition or efficiency, often judged by courts and governments by its effect on consumer welfare and by economists by its effect on total welfare. For most of our analysis, this distinction is not critical. Because competitors objectives frequently may be poorly aligned with social objectives, much of the literature on private antitrust enforcement has focused on how to better align competitors incentive to sue (or, at least, the results of those suits) with the goals of a social planner. This literature, which we discuss below, has made important contributions. In this paper, however, we take a different, complementary, approach. We abstract from the information and
☆ We thank the participants at the American Law and Economics Association Annual Meeting, the Triangle Law and Economics Conference, and the University of Texas at Austin. ⁎ Corresponding author. Tel.: +1 512 232 1904. E-mail addresses: [email protected] (W.F. Schwartz), [email protected] (A.L. Wickelgren). 1 NAFTA Working Group, Private Actions for Violations of Antitrust Laws, Appendix A. 0047-2727/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jpubeco.2011.01.006
incentive problems of prior work and focus, instead, on the effect of antitrust liability on subsequent competitive interactions. In so doing, we highlight two special effects that competitor suits can have. First, competitor suits provide a subsidy for entry or continued operation in a market. If an incumbent firm is taking an action that is designed to deter entry or induce exit by making it unprofitable for a rival to compete, allowing this rival to sue for damages can undo this effect. Notice, however, that for this to be maximally effective, suits should be limited to actual competitors, not simply potential competitors. Second, because suits by competitors are for damages for lost profits, this provides the incumbent with an incentive to reduce those damages. This means that the incumbent is effectively a partial shareholder in its rival. This generates an incentive toward softer (less aggressive) competition, often through charging higher prices. Thus, at first glance, it might appear that there is not much role for competitor suits. Some acts that might deter entry, however, might also be efficient, taking market structure as given. For example, exclusive dealing or exclusive territory arrangements might lower an incumbent's costs through inducing more efficient distribution while also making it more difficult for a new entrant. Even incumbent investments in marginal cost reduction can make entry unprofitable for a firm that faces a fixed entry cost. Because entry promotes competition which often (though, not necessarily) improves social welfare, the ideal solution would be to both not deter the incumbent's efficient actions and induce the entrant to enter. The entry subsidy that competitor suits provide can accomplish both goals. As we show below, competitor suits can induce an incumbent to undertake an efficient action, while
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eliminating the entry-deterring effect of that action. While competitor suits do not achieve the first best, since prices are elevated as a result of the competition-softening effect of competitor suits, they do accomplish the goal of deterring neither the incumbent's efficient action nor the rival's entry. Unfortunately, in situations where the incumbent's action is clearly inefficient and entry-deterring in the absence of antitrust liability, competitor suits can induce entry but cannot necessarily deter this inefficient action. Consider an action by the incumbent that raises the entrant's costs but does not appreciably affect its own costs (certain tying or exclusive dealing or exclusive territories contracts might have this effect in some situations). We show that, even if the threat of competitor suits induce the incumbent to raise its price so high that its rival's profits are unchanged as a result of its increased costs, the incumbent still can profit from at least a small increase in its rival's costs. Thus, while the threat of a competitor suit might deter an action that raises rivals' costs by a large amount, it cannot eliminate any incentive to raise rivals' costs. These results suggest that while competitor suits may have a valuable role to play for actions that both lower the incumbent's cost and deter entry, they may not be the best vehicle for deterring the incumbent from taking actions that are unambiguously inefficient because they increase the costs of rivals. The general literature on public versus private enforcement was pioneered by Becker and Stigler (1974). Important subsequent contributions were made by Landes and Posner (1975), Polinsky (1980), Shavell (1984), Shavell (1993) among others. Much of this literature focuses on the incentives of public versus private actors to enforce the law and the differences in access to information of both groups. Much of the (limited) literature specifically on private antitrust enforcement also focuses on these issues.2 McAfee et al. (2008), for example, assumes that competitors get more accurate information than the government about whether or not their rival has violated the antitrust laws and also have socially perverse incentives to sue to block pro-competitive actions of a rival that reduce their own profits.3 Similarly, Martini and Rovesti (2004) show that private enforcers who care only about their surplus will spend more resources on antitrust enforcement than will public enforcers who care about social surplus, which is often smaller. Bourjade et al. (2009) analyze optimal rules for facilitating the screening of anti-competitive from pro-competitive defendants in private antitrust actions with the possibility of settlement. These papers do not model how antitrust liability affects the competitive interactions, so they do not consider the tradeoff between the entry subsidy effect and the competition softening effect of competitor suits. Because we assume perfect information and perfect courts, however, our model does not capture the information and incentive issues in those papers. Our competition softening effect is related to the increased consumption effect in the treble damages literature. Salant (1987) and Baker (1988) show that because consumers view the prospect of receiving treble damages as equivalent to a coupon off the stated price, the prospect of consumer suits cannot induce a monopolist to sell more than the monopoly quantity. Besanko and Spulber (1990) show that if consumer information is imperfect, then consumer suits do increase social welfare. Our paper also models optimal pricing of the incumbent under potential antitrust liability. We do not, however, allow the competitor to alter its behavior to increase damages because 2 The paper is also related to the literature on optimal antitrust enforcement more generally, such as Wickelgren (2009) and Ottaviani and Wickelgren (2009). 3 Baumol and Ordover (1985) and Snyder and Kauper (1991) also argue that competitors often initiate socially perverse suits. Page and Blair (1992) argue that the antitrust injury doctrine often stops these suits from having much effect. On the other side, Brodley (1995) claims that this doctrine has unduly discouraged legitimate competitor suits, while Page and Lopatka (1996) argue that public enforcement may be superior if the antitrust injury requirement is not satisfied.
of the requirement that plaintiff's have to mitigate damages. As Hamilton and Cone (1987) have shown, courts have consistently been moving towards enforcing this requirement in antitrust cases.4 Segal and Whinston (2007) provide an excellent survey of many important issues involved in analyzing public versus private antitrust enforcement. 2. Model An incumbent (she) and an entrant (he) produce differentiated but competing products at constant marginal cost. The firms compete in prices. If both firms are active, then demand for product j is given by q(pj,p-j) where j = {I,E}. If only I, the incumbent, is active, then demand for I is given by qm(pI). Let subscripts for q denote partial derivatives. We assume that q1, qm′ b 0, q2 N 0 and that q11, qm″ b 0. To ensure that prices are strategic complements, we assume q12 N −2 q2 / (pj−cj) for all pj, p− j . The entrant, E, must expend a fixed cost of F to enter (I does not). Before E's entry decision, I has the option of taking action A, which affects the marginal costs of either player, or both. We assume that in the absence of A that E finds it profitable to enter. A could reduce E's profits below F, causing him not to enter in the absence of antitrust liability. The sequence of events is as follows.
Period 1 I chooses whether or not to take action A at a cost of k. If I does nothing, period 3 marginal costs are cI and cE. If I does A, period 3 marginal costs are c′I and c′E. Period 2 E chooses whether or not to enter at a cost of F. Period 3 Active firms choose prices and earn profits. Period 4 If I took action A in period 1, then E can sue I for antitrust injury at a cost of KE for E and KI for I. E prevails with probability q. If E prevails, then its expected damages are γ times its lost profits.5 Under current treble damage rules, γ = 3. We consider arbitrary γ to determine the optimal level of liability, though we do assume it continues to be, as under current law, tied to the damages suffered by the plaintiff. If E does not enter in period 3, then I's profits are π
m;0
m
=maxp ðp−cI Þ q ðpÞ or π
m;A
m
=maxp ðp−c′I Þ q ðpÞ
ð1Þ
If E enters and I did not do action A, then period 3 profits are π′I =maxpI ðpI −cI Þ qðpI ; pE Þ and πE =maxpE ðpE −cE Þ qðpE ; pI ÞNF 0
0
ð2Þ
If E enters and I did A, then I's and E's profits are given by π′I = ðp′I −c′I Þ qðp′I ; p′E Þ and πE =maxp′E ðp′E −c′E Þ qðp′E ; p′I Þ A
A
ð3Þ
p′I will in general not maximize π′AI (p′I) because I is also concerned with its potential antitrust liability.6 I and E choose prices taking the other's price as given. Competition is imperfect, so prices exceed marginal costs in any post-entry market configuration. 4 It is worth noting that our results suggest that the mitigation principle should not extend to the entry or market participation decision since the main benefit of competitor suits in our model is to create competition by subsidizing entry or market participation. 5 In principle, E could sue whether or not it entered. Of course, it is harder to prove lost profits if one is not in the market. More importantly, as we will see, in our model the main role for competitor suits is that they encourage entry, thus our model implicitly suggests requiring entry for competitors to have standing to sue. 6 We do not allow E to consider the effect of its price on its expected damage award should it sue due to the general requirement of mitigation of damages, which holds in antitrust law as well as other areas of law (Hamilton and Cone, 1987).
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2.1. Antitrust liability and post-entry competition If E enters and sues, expected damages are qγ(πE0−πEA(p′I)). Because damages depend on lost profits, the higher the price that I sets price the lower the damages she pays if she did A. Letting α = qγ, there is a p** such that α (πE0−πEA(p**)) = KE. So, if p′I ≥ p**, then E does not sue because I's period 3 price is high enough that E's expected recovery does not exceed its litigation costs. We assume that p** N argmaxpI′π′I A (p'I). Clearly, p** is increasing in α. To see this, totally differentiate the implicit definition of p** with respect to α to obtain: 0 A A dp =dα= π E −πE ðpÞÞ=α πE ′ðpÞN0
ð4Þ
The numerator is positive as long as KE N 0 by the definition of p**. The denominator is positive since higher prices by the incumbent increase the entrant's profits. If I did A and E entered, then I chooses p′I to maximize h A 0 A πI ðp′I Þ−Z α πE −πE ðp′I Þ + KI
=
A A απE ″ðpÞ + πI ″ðpÞ N 0
deter E from suing. I's expected profits from choosing A are πIA(p**)−k. Her profits from not choosing A are π′0I . Thus, she chooses A if and only if k b πIA(p**)−π′0I . Let k** = πIA(p**)−π′0I , then we have A dk=dα =π I ′ð pÞ dp=dα=
n o 0 A A A π E −π E ðpÞ =α π I ′ðpÞ=π E ′ðpÞb0
ð7Þ The term in curly braces is the amount by which E's profit must increase when α increases in order to keep E's expected payoff from suing at zero. The πIA′(p**) / πEA′(p**) term reflects how much I's profit decreases for every dollar increase in E's profit that occurs due to an increase in I's price. If I chooses to price at p* after doing action A, then she chooses A if and only if kb πIA ð pÞ− α π0E −πEA ðpÞ + KI −π;0I : Let k =πIA ðpÞ− α π0E − 0 π A ð pÞÞ+K −π′ : E
I
I
A A 0 A dk=dα = πI ′ðpÞ+ απE ′ðpÞ dp=dα− π E −πE ðpÞ 0 A =− πE −πE ðpÞ b0
ð8Þ
ð5Þ
Z is an indicator variable that equals one if p′I b p**. Let p* be defined implicitly by α πEA′(p*) + πIA′(p*) = 0.7 So, p* is I's optimal price taking into account antitrust liability if she does not deter suit entirely. Clearly, p* is increasing in α also. To see this, totally differentiate the implicit definition of p* with respect to α to obtain: A dp = dα = −πE ′ðpÞ
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ð6Þ
This is positive because both the numerator and the denominator are negative. If p* ≥ p**, then I chooses p = p** since both p* and p** exceed the direct profit-maximizing price. So, if p** deters suit entirely, there is no further reason to price higher than that. Otherwise, I chooses either p* or p**.8 Lemma 1. If greater antitrust liability (larger α) does not deter I from action A, then (A) I's price increases almost everywhere with greater liability and (B) if prices are strategic complements, then E's price increases almost everywhere with greater antitrust liability. Proof. (A) We have already proved that both of the incumbent's possible prices, p* and p**, increase in α. It is possible, however, that an increase in α could cause the incumbent to shift from p** to p*, resulting in a one-time decrease in price. Everywhere else, however, I's price must increase in α. (B) The entrant's price will increase whenever the incumbent's increases as long as prices are strategic complements. Q.E.D. This lemma shows that we get a potentially perverse effect from greater antitrust liability. If greater liability does not deter the action, greater antitrust liability results in both firms charging higher prices. There is one potential exception. It is possible that increasing liability could at one point cause the incumbent to shift from pricing to deter suit entirely, charging p**, to pricing optimally given suit, p*. If this happens, then prices may drop at this point. 2.2. Antitrust liability and deterrence Greater antitrust liability can also deter the incumbent from undertaking action A. First, consider the case where I chooses p** to
7 We assume απ AE ″(p)+ πAI ″(p) = α(p′E−cE)q22 + 2q1 + (p−cI)q11 b 0 ∀ p, p′E to insure an interior maximum. 8 p** might be optimal because there is a fixed legal cost that I must pay if E sues.
The dp*/dα term drops out because πIA′(p*)+ α πEA′(p*) = 0 by the first order condition for p*. This is negative since πE0−πEA(p*) N 0. Thus, we have the following result. Lemma 2. As antitrust liability increases (larger α), the maximum cost of action A for which the incumbent will undertake the action decreases. Proof. Since k* and k** decrease with greater antitrust liability, it only remains to show that if greater antitrust liability causes I to shift from p* to p** or vice versa that the cost of A must decrease to make undertaking A profitable. If this were not the case then there would exist some α″ N α′ such that πIA(p*(α″))−[α″ (πE0−πEA(p*(α ″))) + KI] N πIA(p**(α′)) or πIA (p*(α′))−[α″ (πE0−πEA(p*(α′))) + KI] b πIA(p**(α″)). If either of these were the case, then since I's payoff is strictly decreasing in α it would have had a greater payoff at α′ charging the price it charged at α″. This contradicts the fact that it changes its price when α changes from α′ to α″. Q.E.D. Increasing antitrust liability does in fact lead to greater deterrence of action A even as it also leads to price increases in the event that I does action A in spite of greater antitrust liability. Whether or not this greater deterrence of action A is desirable depends on whether or not A is socially efficient. In the next subsection, we examine a case in which A is likely to be efficient (it reduces I's costs). In the following subsection, we examine a case in which A will be inefficient (it increases E's costs). 2.3. Purely cost reducing actions: cI N c′I, cE = c′E We first consider the baseline case of an action that only reduces the incumbent's costs, but does not affect the entrant's. That is, cI′b cI, cE = cE′. 2.3.1. Maximal antitrust liability To examine competitor suits at their most effective in influencing the incumbent's behavior, we consider the limit as α goes to infinity. We do this not because we view this as a realistic value for α, rather it is provides a valuable baseline for our analysis of finite α. In this case, the incumbent will price to deter suit entirely. p** is given by πEA(p**) = πE0; the incumbent must price so that the entrant's profits do not decrease as a result of action A. A cannot deter entry since we have assumed that entry is profitable in the absence of action A. Since the entrant's marginal cost has not changed, its profit function does not depend on A. To keep E's profit unchanged, I chooses p′I = p**= pI and then E will also choose pE′ = pE (since its costs and its rival's price have not changed). Since I's costs have fallen as a result of action A, I's profit must increase.
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That is, I will choose action A if and only if π′AI (pI)−π′0I = (cI − c′I)q(pI, pE) N k. Taking the pricing decisions as given, I will make the socially optimal choice since choosing action A does not change E's profits or consumer surplus. Thus, we have proved the following result. Lemma 3. If action A reduces I's costs but does not change E's costs, then in the limit as α → ∞, I chooses action A if and only if doing so raises social welfare. 2.3.2. Non-maximal antitrust liability Lemma 3 does not imply that maximal antitrust liability is optimal. The reason is that, as we have seen in Lemma 1, larger antitrust liability actually leads to higher prices. That said, even though A is potentially efficient,9 some antitrust liability may be optimal. This will be the case only if α N 0 is necessary to induce entry and entry is socially efficient. Let p A = argmaxp′Iπ′AI (p′I), that is p A is I's profit-maximizing price given action A (and ignoring antitrust liability). Then, if πEA(p A) b F, then it is possible that action A would reduce social welfare without antitrust liability because it would reduce competition. Notice, however, that this isn't necessarily the case since if c′I b b cI it might be more efficient to have a monopoly than a duopoly. From here on, however, we will assume that duopoly is socially desirable, otherwise zero antitrust liability is clearly optimal in this case. Before proceeding, it is worth commenting on this assumption. As Mankiw and Whinston (1986) have demonstrated, even if A does not result in a large cost reduction, entry can be profitable and reduce total surplus. This effect is more pronounced in our setting because the threat of competitor suits softens price competition, reducing the consumer benefit from entry. That said, unlike Mankiw and Whinston, we do not have a free entry model. We focus on monopolization, so there could be socially excessive incentives to enter in a free entry model but socially insufficient incentives for one entrant to enter to change a monopoly to a duopoly.10 Furthermore, even if there are socially excessive incentives to enter, entry may still increase social surplus if entry costs are not too great and the negative externality from entry is small. So, while entry is always socially efficient, it is a relevant case to consider. In addition, since almost all competition authorities and courts in the world use a consumer rather than a total welfare standard, this assumption is always relevant if competition authorities or courts are setting policy under that standard. We now consider the optimal level of antitrust liability when A only reduces I's costs. Starting from the baseline of maximal antitrust liability, reducing α has three effects. First, taking the choice of A and entry as given, Lemma 1 shows that it reduces I's and E's price almost everywhere. This increases welfare since we have assumed that p** and p* exceed the duopoly price without liability, which already exceeds the socially optimal price (price equals marginal cost).11 Second, given I's choice of A, reducing α reduces E's profit because it reduces the profit that I must ensure that E obtains to deter E from suing. Third, reducing α increases I's benefit from choosing A. One might think that the optimal α is the lowest α that does not deter entry, which we will call α*. That is not necessarily true. When α is less than maximal, I's incentive to choose A is not necessarily socially optimal. It may be insufficient, in which case lower α clearly increases social welfare. I may also have a socially excessive incentive 9 We say potentially efficient because we have not considered the cost of the investment nor the (potential) efficiency loss from the prevention of entry. 10 The online appendix demonstrates this for the case of linear demand. 11 This is admittedly not the whole story since there is the question of consumers buying the right product. If the entrant is charging above marginal cost, then it is not generally socially optimal for the incumbent to charge marginal cost since that may induce consumers to purchase from the incumbent even though purchasing from the entrant would maximize social surplus. That said, because we are considering situations in which the incumbent is charging above the duopoly price and typically social welfare would be increased with one firm reducing its price slightly below the duopoly price, reducing p** should increase social welfare in almost any model.
to choose A at finite α , in which case a larger α that deters I from choosing A is optimal. To see this, notice that if I prices at p**, then the only effect of lowering α, taking entry and action A as given, is to lower p**. I could have an excessive incentive to choose A if reductions in p** increase I's profit more than they increase social welfare.12 Proposition 1. If entry is socially efficient then the optimalα is either α*, the lowest α that does not deter entry, if A is socially efficient at α*, orα → ∞, if A is not socially efficient at α*. If KE ≥ π0E −F, then α*∈ (1,KE / (πE0−F)]. If KE b πE0−F, then α*∈[KE / (πE0−F),1). Proof. See Appendix. A could reduce welfare by deterring entry or if A increases I's profit largely through business stealing (which can only happen at finite α). Proposition 1 says that if this business stealing effect drives I to undertake action A even though it reduces total welfare, then it is optimal to make antitrust liability maximal deter I from taking action A.13 On the other hand, if action A is efficient, then it is optimal to make antitrust liability low to ensure that prices are low. That said, there must be some antitrust liability to keep entry profitable for E in spite of I's lower costs. Setting α = KE / (πE0−F) if I prices to deter suit, or somewhere in between this and one if I does not price to deter suit, ensures that I's prices are just high enough to induce E to enter, but no higher. This is a second best solution that ensures efficient cost reduction and some, though not complete, competition. 2.4. Purely cost increasing actions: cI = c′I, cE b c′E In the absence of antitrust liability, actions that raise a rival's costs can be profitable for the incumbent, either by deterring entry or by increasing the entrant's optimal price. The question is whether in the presence of substantial antitrust liability, it can ever be privately optimal for I to increase E's costs. 2.4.1. Maximal antitrust liability As before, we start by considering the case of maximal antitrust liability. If I benefits from increasing E's costs in this case, then she certainly benefits with less antitrust liability. I sets price to keep E's profit identical to what it would have been without action A, while E chooses its price to maximize its profit. Thus, p′E and p′I are implicitly determined by E's first order condition and this equal profit constraint: q p′E; p + ðp′E −c′E Þq1 p′E ;; p =0 πE ðpÞ=πE A
0
ð9Þ ð10Þ
Given these constraints, we analyze if I's profit, π′I A(p**) = (p**−cI) q(p**,p′E), is increasing in cE. If so, then competitor suits may not deter cost increasing actions. We determine the effect of cE on prices under maximal antitrust liability by differentiating (9) and (10) with respect to cE. Solving for dp′E / dc′E and dp** / dc′E yields: h i 2q2 p′E ;; p + ðp′E −c′E Þq12 p′E ;; p dp′E=d′E =q1 p′E ;; p
ð11Þ
h i q2 p′E ;; p 2 q1 p′E ;; p + ðp′E −c′E Þq11 p′E ;; p dp=dc′E = −q1 p′E ;; p q2 p′E ;; p
=
ð12Þ
12 The online appendix more precisely establishes how the private and social incentives to choose A are different with finite α. 13 A large but finite α would also accomplish this goal.
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Using these two equations, we find that: .n h io A dπ′I ðpÞ=dc′E =q1 p′E ;; p q2 p′E ;; p 2q1 p′E ;; p + ðp′E −c′E Þq11 p′E ;; p ( −½qðp; p′E Þ + ðp−cI Þq1 ðp; p′E Þ h i ð13Þ × 2 q1 p′E ;; p + ðp′E −c′E Þq11 p′E ;; p + ðp−cI Þ q2 ðp ; p′E Þ ) h i × 2 q2 p′E ;; p + ðp′E −c′E Þq12 p′E ;; p
The first line is positive, since the square bracket term is negative as is q1. Thus, dπIA(p**) / dc′E has the sign of the curly braces term on the second and third lines. q(p**,p′E) + (p**−cI) q1(p**,p′E) b 0 since I has to price above its profit maximizing level so that E's profits does not fall due to higher cE, making the second line negative. If prices are strategic complements, the third line is positive, leading to the following result. Proposition 2. As α → ∞, if prices are strategic complements, then there exists an ε N 0 such that if c′E−cE b ε then π′IA(p**) N π′0I if the only effect of action A is to increase E's costs from cE to c'E. That is, even with maximal antitrust liability, competitor suits may not deter I from taking an action to increase E's costs by at least a small amount. Proof. As c′E approaches cE, then p** will approach pI. This makes q (p**,p′E) + (p**-cI) q1(p**,p′E) approach zero, as it is if p** = pI and p′E = pE. Thus, by making c′E close enough to cE, the second line of the (13) can be made arbitrarily close to zero. The third line remains positive and bounded away from zero. Thus, dπ′AI (p**) / dc′E N 0. Q.E.D. Proposition 2 says that even with antitrust liability is so large that I will not reduce E's profit, I gains from raising E's costs. While competitor suits can stop I from deterring entry, they cannot necessarily stop her from taking actions that inefficiently raise E's costs and then accommodating E to deter suit. 2.4.2. Non-maximal antitrust liability This problem is worse with non-maximal antitrust liability. If I prices to deter suit entirely, then the constraint on her price changes from πE0−πEA(p**) = 0 to π0E−πEA(p**) = KE / α. Since KE / α is independent of c′E, as long as this constraint is binding, dπ,A I (p**) / dc′E remains the same as it was under maximal antitrust liability. For c′E very close to cE, the constraint will not be binding, so I can choose a price to maximize its profits knowing that E will not sue. The increase in c′E increases I's profit. Let c′E** be the c′E for which I's profit-maximizing price exactly equals p** so that E is indifferent between suing and not. That is, let c′E** be implicitly defined by: q p′E; p + ðp′E −c′E Þq1 p′E ;; p =0 qðp; p′E Þ + ðp−cI Þ q1 ðp; p′E Þ= 0 and π0E −πEA ðpÞ=K E=α Then dπ′AI (p**) / dc′E is given by (13) for c′E N c′E**. The argument in the proof of Proposition 2 shows that this is positive for c′E N c′E** for c′E is sufficiently close to c′E** since q(p**,p′E) + (p**−cI) q1(p**,p′E) = 0 for c′E = c′E**. Notice that c′E** N cE. That is, I can increase E's costs by a small amount, price to maximize profit, and still deter suit if antitrust liability is non-maximal. We have now proved the following result. Corollary. For α b ∞, if prices are strategic complements, then there 0 exists an ε N 0 such that if c′E− c′E** b ε then π,A I (p**) N π′I if A increases E's costs from cE to c′E. The corollary establishes the intuitive result that if I can profitably increase E's costs with maximal antitrust liability, it can increase these costs even more if antitrust liability is non-maximal. With nonmaximal antitrust liability, there is a region of raising E's costs that is
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completely free in the sense that I can still price to maximize its own profits, ignoring antitrust liability because the loss to E is too small to induce it to sue. The argument in Proposition 2 then says that I can profitably increase E's costs even further since by increasing its own price above the profit-maximizing level, I can still deter suit while increasing its profit relative to what it would have been without A. 3. Conclusion Proposition 1 shows that competitor suits work quite well when the action A is potentially efficient because they can eliminate the entrydeterring effect of the action by providing an entry subsidy. This provides the benefit of lower costs without completely eliminating competition. Unfortunately, we do not achieve the first best because the threat of liability induces the incumbent to increase its prices to minimize the loss to the injurer, which creates losses to final consumers that exceed the benefits to the firms. Note that Proposition 1 assumes entry is efficient. The online appendix examines a linear demand model to show that there is a substantial range of parameter values where this is the case. If A reduces cost by a large enough amount, however, then entry will not be efficient. In this case, a larger damage multiplier will increase the incentive for inefficient entry and suit. Of course, for the vast majority of competition policy authorities this is a non-issue (except for drastic innovations) since they operate under a consumer welfare standard in which entry is never inefficient. Under a total welfare standard, however, suits by inefficient entrants should receive very different treatment than suits by efficient ones. Proposition 2 says that competitor suits are not necessarily effective when the incumbent can take actions that weaken the entrant directly. Even though the incumbent has to compensate the entrant for lost profit, she still has the incentive to increase the entrant's costs somewhat. That is, we cannot rely on competitor suits to deter all actions designed to raise rival's costs. Taken together, these results are quite useful in suggesting the proper role for competitor suits against monopolization or attempted monopolization claims under Section 2 of the Sherman Act. If the complained about action might further monopolization because it makes the incumbent a more efficient competitor, then competitor suits have a valuable role to play because they need not deter these efficient actions (if the damage multiplier is not too large) but will minimize their competitive impact by effectively subsidizing entry. On the other hand, if the monopolizing action is one that directly damages a rival's efficiency, then competitor suits are not the right vehicle to attack this action. Of course, many potentially monopolizing actions, such as exclusive dealing or tying might both increase the incumbent's efficiency and hamper the rival's. Proposition 1 and 2 suggest that if they appear to have substantial (positive) effects on the incumbent's efficiency, competitor suits can have a beneficial role if these suits are necessary to induce entry. If the these actions primarily reduce a rival's efficiency, however, then competitor suits should not be the main avenue of enforcement. While our model assumes a discrete action, the main insights would apply to a continuous action choice. The most significant effect of allowing a continuous action choice would be that the details of the optimal level of antitrust liability in Proposition 1 would change. Instead of trying to set liability to be just large enough to induce entry when some cost reduction is efficient, the optimal level of liability would also have to take into account how liability affects the magnitude of the cost reduction the incumbent would undertake relative to the socially optimal level of cost reduction. Our model also does not consider settlement. In the absence of asymmetric information, this will not affect our results because it will not affect the relationship between the incumbent's pricing and its expected antitrust liability. The settlement amount will vary with the
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incumbent's price in the same way as would the judgment. If the incumbent had private information about the effect of its action, then settlement would act like a damage cap (see Wickelgren, 2004). This would reinforce the result in Proposition 2 that competitor suits do not work well to deter actions that raise rivals' costs. That said, given that the suit occurs after both sides have observed their profits, private information of this type seems unlikely. As we mentioned in the introduction, because we assume courts are perfect, competitors do not initiate suits to decrease competition in our model. If we allowed for court errors, this would, again, reinforce the result in Proposition 2 that competitor suits do not work well in raising rivals' costs cases. Court errors would decrease the average benefit of competitor suits as an entry subsidy in cases where the incumbent has reduced its marginal cost because we would sometimes get softened post-entry competition when this was not necessary to induce entry. Appendix A. Supplementary data Supplementary data to this article can be found online at doi:10.1016/ j.jpubeco.2011.01.006. References Baker, Jonathan B., 1988. Private information and the deterrent effect of antitrust damage remedies. Journal of Law, Economics, and Organization 4, 385–408. Baumol, William J., Ordover, Janusz A., 1985. Use of antitrust to subvert competition. Journal of Law and Economics 28, 247–265. Becker, Gary S., Stigler, George J., 1974. Law enforcement, malfeasance and compensation of enforcers. Journal of Legal Studies 3, 1–18. Besanko, David, Spulber, Daniel F., 1990. Are treble damages neutral? Sequential equilibrium and private antitrust enforcement. American Economic Review 80, 870–887.
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