Contested Mergers and Equilibrium Antitrust Policy - CiteSeerX

JLEO. V9 N1 1

Contested Mergers and Equilibrium Antitrust Policy

David Besanko and Daniel F. SpulberNorthwestern University

Although the Guidelines should improve the predictability of the Agency's merger en-forcement policy, it is not possible to remove the exercise of judgement from the evalua-tion of mergers under the antitrust laws. Because the specific standards set forth in theGuidelines must be applied to a broad range of possible factual circumstances, mechanicalapplication of those standards may provide misleading answers to the economic questionsraised under the antitrust laws. Moreover, information is often incomplete and the pictureof competitive conditions that develops from historical evidence may provide an in-complete answer to the forward-looking inquiry of the Guidelines. Therefore, the Agencywill apply the standards of the Guidelines reasonably and flexibly to the particular factsand circumstances of each proposed merger.

— 1992 Merger Guidelines

1. IntroductionHorizontal mergers can have significant effects on the structure of industries.The size and types of firms that contemplate mergers are determined not onlyby the anticipated economic returns from the merger but also by antitrustmerger policy and enforcement. In the United States, merger policy is shapedby legislation passed by the Congress, by presidential appointments to theenforcement agencies, and by judicial interpretation of antitrust statutes. Theenforcement of merger policy is carried out by the Department of Justice

The authors would like to thank Mark Bagnoli, Jeff Banks, JQrgen von Hagen, Mike Meurer,John Morris, Marty Perry, Ivan P'ng, David Sappington, Mark Zupan, Oliver Williamson, and ananonymous referee for their comments and suggestions. We especially would like to thank JoelFishkin for his valuable research assistance. Spulber gratefully acknowledges the support of theNational Science Foundation, Grant No. SES-90-%205.

© 1993 by Oxford University Press. All rights reserved. 8756-6222/93/S5.00

at Penn State University (Paterno L

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(DOJ) and the Federal Trade Commission (FTC) who must give their approvalto certain mergers. The theoretical literature in economics has generally fo-cused on the profit and welfare effects of horizontal mergers (e.g., Perry andPorter, 1986) and has not emphasized the policy-making and enforcementaspects of antitrust. By contrast, in this article, we present a model of antitrustpolicy-making and enforcement toward horizontal mergers. In the model,there is a potential trade-off between market power and cost savings from themerger. However, the merging firms are assumed to have better informationabout the cost savings than the antitrust authority. Our aim in this article is toanalyze the consequences of this information asymmetry for the formulationand enforcement of policy toward horizontal mergers.'

Williamson (1968) points out that modest cost savings from an anticom-petitive horizontal merger often can lead to an increase in social welfare, butnotes that merging firms are likely to have better information than the govern-ment about prospective cost savings. Given this, Williamson urges that costsavings should be used to justify an anticompetitive horizontal merger only ifthe increase in social welfare from the merger exceeds a positive thresholdthat depends on the quality of the government's information about the costsavings.

Our model supports this argument. It is shown that under asymmetricinformation, expected social welfare is maximized when the antitrust authori-ty makes the challenge decision using a standard that is tougher than the socialwelfare criterion. In other words, only some of the mergers that increasesocial welfare will be approved. The result depends upon the strategic interac-tion between the antitrust authority and the firms contemplating a merger, andthe ability of the antitrust authority to make credible commitments to enforce-ment. Ideally, if the antitrust authority could precommit to a challenge proba-bility, it could choose a challenge level that maximized expected social wel-fare. We refer to this as the ex ante optimal challenge probability. However, aprecommitment to this rule is not credible because ex post—that is, after therule is announced—an antitrust authority employing a social welfare standardwould approve any merger that would be proposed conditional on the rule.2

The reason is that the ex ante optimal challenge rule induces firms to mergeonly if the merger is sufficiently profitable; if it were not, firms would not haveincurred the costs of putting together the merger and risked the likelihood ofits not being approved. Because the profitability of the merger is positivecorrelated with the cost savings the merger generates, the fact that the mergeris proposed conveys "good news" to the antitrust authority about the prospec-tive cost savings from the merger.3 This makes approval of the merger a much

1. The present article is related to our 1990 article on private antitrust enforcement in thatboth articles explore the implications of asymmetric information on antitrust enforcement. How-ever, unlike the present one, the earlier article does not analyze the endogenous formation ofantitrust policy.

2. This is formally demonstrated in Section 3.2 below.3. In the formal model below, "good news" is represented as a Bayesian updating that

increases the enforcement authority's expectation of the cost saving from the merger. Of course,


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more attractive course of action for the enforcement authority than would havebeen the case ex ante. In effect, self-selection by the merging firms means thatthe antitrust authority is likely to be confronted with a better-than-average-quality merger proposal, which the enforcement authority will want to ap-prove. Of course, all of this will be anticipated by rational firms. Therefore, asequential equilibrium analysis is needed to capture fully the informationaland strategic interaction between the enforcement authority and the mergingfirms.

At a sequential equilibrium, it is shown that an enforcement authority thatmakes the ex post challenge decision using a social-welfare criterion willunderenforce as compared to the ex ante social optimum—that is, will choosea probability of challenge that is less than the probability of challenge thatmaximizes ex ante social welfare. Put another way, equilibrium enforcementbased on a social-welfare standard will be biased toward avoiding type Ierrors—challenging mergers that increase social welfare—at the expense ofmore type II errors—approving mergers that reduce social welfare. A welfarestandard that gives relatively more weight to consumers' surplus works tocounteract this bias and moves the equilibrium enforcement outcome closer tothe ex ante first-best solution.

Our model is consistent with the merger enforcement process. The U.S.DOJ issued merger guidelines in 1968, 1982, 1984, and 1992. The guidelinesare a general set of policies that do not specify fully the conditions underwhich mergers will be challenged or approved. Rather, the guidelines leaveconsiderable discretion to antitrust enforcement authorities in evaluatingmergers after they are proposed. Our model follows this institutional frame-work by representing the stringency of merger policy as a welfare standardand by allowing the antitrust authority to determine whether to challenge orapprove the merger after it has been proposed.

Our model is also consistent with the evolving treatment of consumers'surplus and production efficiencies in the U.S. merger guidelines. Each set ofguidelines has specified the extent to which efficiencies should be consideredin evaluating a merger. The 1968 guidelines specified a set of concentrationthresholds above which horizontal mergers would be challenged. The guide-

the fact that the merger is proposed may also convey "bad news" to the enforcement authorityabout its anticompetitive effects as well, since profitability is also likely to be correlated withpost-merger market power. But the received wisdom in the antitrust literature is that the enforce-ment authority is likely to know more about the market power effects of the merger—whichdepend largely on industry characteristics that are publicly observable—than it does about thecost savings effects of the merger—which depend on internal operating characterisUcs of themerging firms and are more likely to be private information to the merging firms. If so, informa-tion about the market power impact of mergers will have already been impounded in the enforce-ment authority's priors, and the fact that two firms have proposed a merger is likely have a muchgreater impact on the enforcement authority's beliefs about cost savings than on its beliefs aboutthe anticompetitive effects of the merger. In the model below, for simplicity we assume that theenforcement authority's priors impound all relevant information about the market power effects ofthe merger, so the fact of merger conveys no information to the enforcement authority aboutmarket power effects.


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lines expressed the view that, in general, efficiencies would not be a defenseto an anticompetitive merger, in part because "there usually are severe diffi-culties in accurately establishing the existence and magnitude of economiesclaimed for a merger' (U.S. DOJ, 1968: X-3). The 1982 guidelines held that amerger would be challenged only if it raised the likelihood of noncompetitivepricing in the industry for a sustained period of time. Consistent with thiswelfare orientation, these guidelines took a somewhat more tolerant view ofefficiencies than did the 1968 guidelines. Nevertheless, efficiencies were stillviewed with skepticism, with the DOJ indicating that in nearly all cases adefense of efficiencies could not reverse the decision to challenge an anticom-petitive merger.4 The 1984 guidelines are somewhat more receptive to effi-ciency defenses than the 1982 guidelines.5 However, like the 1982 guidelines,the 1984 guidelines emphasize that efficiencies do not constitute a defense toan otherwise anticompetitive merger. The 1992 guidelines also allow forefficiency defenses, stating that "some mergers that the Agency otherwisemight challenge may be reasonably necessary to achieve significant net effi-ciencies" (U.S. DOJ, 1992: 55). The 1992 guidelines present an extensive listof cognizable efficiencies, such as economies of scale, plant specialization,and lower transportation costs. However, the 1992 guidelines weigh efficien-cies in much the same way as do the 1984 guidelines and note that the"burden with respect to efficiency . . . continues to reside with the propo-nents of the merger" (1992: 3).

Our article is most closely related to work by Rogoff (1985) on monetarypolicy, Baron (1988) on regulatory mechanism design, and Spulber and Be-sanko (1992) on administrative law. Rogoff shows that the president will wantto select a central banker who places greater weight on controlling inflationthan on unemployment as compared to the president. Rogoff s model illus-trates the crucial effect of delegation on the choice of the enforcer. Our modeldiffers from RogofFs in its emphasis on the effects of asymmetric informationon the design of merger policy. In Baron's model, a legislature delegates to aregulatory commission the job of designing a price regulation mechanism thatinduces the firm to reveal truthfully its private cost information. The legisla-ture chooses the welfare weight that the commission uses to design the reg-ulatory mechanism. Using median voter theory, Baron argues that the legisla-ture would usually be expected to give consumers' interests more weight thanproducers'. In his model, a legislature that consisted entirely of social welfaremaximizers would want the regulatory commission to act as a social welfaremaximizer as well. This would not be the case in our model. The reason for

4. According to the 1982 guidelines: "In the overwhelming majority of cases, the Guidelineswill allow firms to achieve available efficiencies through mergers without interference from theDepartment. Except in extraordinary cases, the Department will not consider a claim of specificefficiencies as a mitigating factor for a merger that would otherwise be challenged. Plausibleefficiencies are far easier to allege than to prove. Moreover, even if the existence of efficiencieswere clear, their magnitude would be extremely difficult to determine" (U.S. DOJ, 1982: 27).

5. In the policy statement issued along with the 1984 guidelines, the DOJ stated: "Thelanguage of the 1982 Guidelines . . . had a restrictive, somewhat misleading tone and indicatedthat the Department would explicitly consider efficiency claims only in 'extraordinary' cases. Inpractice, the Department never ignores efficiency claims" (U.S. DOJ, 1984: 5-16).


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this important difference is that in Baron's model, the regulatory commissioncan commit to an incentive mechanism. Such mechanisms do not apply to theantitrust merger enforcement process, as will be argued below. Spulber andBesanko (1992) consider the consequences of the legislative and executivebranches delegating enforcement to the regulatory agencies. They show howcommitment and timing issues affect administrative appointments, legislativerestrictions on agencies, and oversight activities.

The article is organized as follows. A model of mergers based on theWilliamson trade-off model (Williamson, 1968) is presented in Section 2. Amodel of the merger-enforcement process and a characterization of the equi-librium in that process are presented in Section 3. The optimal welfare stan-dard is analyzed in Section 4, and a specific example illustrating comparativestatics is presented in Section 5. The impact of pre-merger filing fees isexamined in Section 6. Conclusions are in Section 7. Proofs of all proposi-tions appear in the Appendix.

2. The Williamson ModelThe trade-off between market power and production efficiency gains frommerger is illustrated most clearly by Williamson's model of horizontal merg-ers.6 In that model, the pre-merger market structure is a Bertrand duopoly,and the two competitors merge to form a monopoly. Pre-merger marginalproduction cost is c, and the post-merger marginal cost is 6. A cost savingsarises if 6 < c.1

Let market demand be denoted by D(p). The pre-merger price is c, andconsumers' surplus equals So = J™D(p)dp. The two firms earn zero profit andsplit the market demand, Qo = D(c).

After the merger, the market price p(d) maximizes industry profit,

77(0) = maxQ? - O)D(p).P

Note that p(8) can be greater than or less than the pre-merger cost c. The caseof p{6) > c is represented in Figure la. The deadweight welfare loss is L. Thechange in consumers' surplus, S(d), is the transfer to the firm, T, plus L:

S(d) = D(p)dp < 0.JD(6)Jp(.0)

The firm's profit consists of the transfer T plus the realized production effi-ciencies E, that is, 77(0) = T + E. The case of p{0) < c is represented in

6. The main results of this article continue to hold even under fairly general assumptionsabout the pre- and post-merger market structures and industry behavior, including the Coumotmodel. Moreover, the general insight continues to hold even if one allows for efficiency gains thatare realized intertemporally. A discussion of the general assumptions needed to obtain the resultsderived here is available on request.

7. Throughout the analysis, we refer to c - 0 as the cost savings from the merger. However,we do not need to assume that c — 0 is positive.


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P P

D(p)

p(6)

c

e

Q(6)

Figure 1. The Williamson model

D(p)

Figure lb. The change in consumers' surplus, S(0), is positive in this case.In either case, note that both the change in profit, 11(0), and the change inconsumers' surplus, S(0), are decreasing in 6, and the post-merger price p(6)is increasing in 6.8

Under full information, a social-welfare-maximizing merger policy wouldbe to approve the merger if 11(6) + S(d) > 0. However, this is not a feasiblerule if 6 is unobservable to the antitrust authority. It is assumed in our modelthat the post-merger marginal cost is the private information of the mergingfirms. The enforcement authority has beliefs about the post-merger cost pa-rameter given by a continuous density function, h: [0~ ,6 + ] —* (0,°°), and itsassociated distribution function, H: [8~,8 + ] ~* [0,1]. These beliefs areassumed to reflect all of the objective information available about the magni-tude of the cost savings from the merger. Thus, the firm's private informationreflects its residual informational advantage after the enforcement authorityhas solicited and studied all relevant public information about the merger inorder to estimate the prospective cost savings. It is assumed that S(6) < 0 for asubset [B,9 + ] of values of 6 and that for those 6 for which S(6) > 0,11(6) >S(0).9 This assumption is not restrictive and can be shown to hold for anyinverse demand function that is weakly concave in price and has a finite chokeprice.10 This assumption serves to place an upper bound on any consumers'surplus gains from the merger.

8. W(0) = -D(p{0)), and S'(0) = -D(p(0))p'(0).9. This condition clearly must hold when S(0) < 0,

10. Indeed this condition can be shown to hold even for nonconcave demand functions if thefollowing property holds. Suppose the inverse demand function is locally concave at the post-merger monopoly price p{0), and consider the tangent line to the inverse demand curve at thatpoint. If the vertical intercept of that tangent line lies everywhere above the inverse demand curvefor quantities less than the post-merger monopoly output, then for those cases in which S(0) > 0,it will be the case that Tl(0) > 5(0).


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It is also assumed that E[S(6) + 77(0)] < 0, and S{9~) + 11(6') > 0;that is, the unconditional expectation of the change in social welfare dueto the merger is negative, but social welfare change is positive for the mostfavorable realization of 6. These assumptions imply that under full infor-mation the merger-approval decision would depend on the realized valueof 0 and that there exists a critical value 0o £ (6~ ,0 + ) such that S(0o)

+ me0) = o.3. Enforcement of Merger Policy3 1 The Merger Enforcement Process

The antitrust policy and enforcement process has two stages. In the first stage,a welfare standard that will be employed in the evaluation of horizontalmerger cases is chosen. This standard is chosen to maximize expected socialwelfare, taking into account the impact of the standard on firms' mergerdecisions and the antitrust authority's enforcement decision under the stan-dard. In the second stage, given the welfare standard, firms decide whether ornot to propose a horizontal merger. If a merger is proposed, the antitrustauthority decides whether to challenge the merger by applying the welfarestandard chosen in the first stage. This sequence of actions and events isshown in Figure 2.

The welfare standard stipulates a relative weighting a, 0 s d < 1, of

Policymakers

Establish Welfare Standard

Firms

Attempt / \ Do Not AttemptMerger / \ ^ Merger

AntitrustAuthority

Challenges / \ . Does Not ChallengeMerger / \ . Merger

Figure 2. Merger policy-making and enforcement.


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producers' and consumers' surpluses. Given the weight a, the standard re-quires the merger be approved if and only if

a/7 + (1 - a)S 2= 0.

In practice, the decision to challenge a merger is determined by a host offactors. The merger guidelines are certainly one important factor, but so tooare the personal values and preferences of the personnel in the antitrust agen-cies who must interpret and implement those guidelines. While it is true thatthe merger guidelines specify precise quantitative thresholds and tests to beused to determine whether a merger should be challenged, they also give theantitrust authority discretion in choosing whether to challenge the merger.Although other more complicated modeling specifications may be possible, awelfare weight a is a straightforward and tractable way to model the stringen-cy of merger policy. The choice of a welfare weight in practice would bedetermined by the content of the merger guidelines and by the type of indi-viduals who are appointed to run the enforcement agencies.

Note that the welfare standard includes both social welfare maximization(a = i) and consumers' surplus maximization (a = 0) as special cases. If a <i, greater weight is given to consumers' surplus than to producers' surplus,and, implicitly, greater weight is given to the market power consequences ofthe merger than to the production efficiencies. It is important to reiterate thatalthough the welfare standard employed in a proposed merger is endogenousand can span the spectrum between consumers' surplus maximization andproducers' surplus maximization, the ex ante decision to choose the standarda is made on the basis of social welfare maximization.11

When a merger is proposed, the antitrust authority must decide whether tochallenge it. Let/3 £ [0,1] denote the probability that the authority challengesthe merger.12 We assume that decision by the enforcement authority to chal-lenge a merger is sufficient to block it. This assumption is broadly consistentwith merger enforcement experience in the United States during the lastdecade.13 Let

ip(9;a) = £[(1 - a)S(d) + an(d)\0 £ O]

denote the conditional expectation of weighted welfare when O is the set ofmarginal cost realizations for which the merger is proposed. The challenge

11. The basic insights of our analysis continue to hold if the ex ante decision to choose thewelfare standard is itself based on an (exogenously given) weighted welfare function.

12. We assume that there is no enforcement cost involved in challenging the merger. Inclusionof an enforcement cost k would not alter any of the results in the article.

13. Hay (1989) notes that once the DOJ decides to challenge a merger, "in almost all cases theparties to the transaction will either call it off or restructure the transaction to obtain JusticeDepartment blessing" (1989: 233-34). As Oliver Williamson pointed out to us, this is in partreflective of the quality of the current guidelines. Firms that are challenged may have a greaterwillingness to confront rhe challenge if there were a feeling that the guidelines were deficient, aswas the case with the 1968 Merger Guidelines.


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decision 0 is chosen to be consistent with the welfare standard in the mergerguidelines, given the antitrust authority's beliefs about 9. This implies

= 1,e [0,= o,

i ] ,ifV(6>;a)if ip(O;a)if xl>(G\a)

< 0,

= o,> 0 .

In words, the enforcement authority challenges a merger if the expectedwelfare change from the merger, conditional on a merger having been pro-posed, is negative. It approves the merger if this conditional expected welfarechange is positive. When the conditional expected welfare change is zero, anychallenge probability between zero and unity is optimal.

When the firms attempt to merge, they incur a sunk cost Q =f+ t, where/is a filing fee and t is the cost of negotiating the terms of the merger andpreparing the information needed to defend the merger to the enforcementauthority.14 Given the likelihood fi that the merger will be challenged, thefirms will merge if and only if the expected profit exceeds the sunk cost ofmerging, that is,

77(0)(1 -p)-Q>0. (1)

Because 77(0) decreases in 6, (1) is equivalent to 6 < f?(/J), where the cutoff$ is given by

(2)

and 77 ~'(") is the inverse of 77().15 The function #(/J), which is shown inFigure 3, gives the cost parameter for the marginal merger proposal, that is,the merger proposal which, given the challenge probability /?, has an expectedprofit of zero. The cutoff 9(p) is nonincreasing in /?.

For a given a, let fi*(0;a) denote the firm's equilibrium merger decisiongiven the cost savings parameter 6 (with /x* = 1 indicating that the firmsattempt to merge), and let /?*(a) be the equilibrium challenge probability. Atthe equilibrium in the merger enforcement process, the following conditionsmust be satisfied.16

14. In the United States, filing fees have been required since November 1989. The transactioncost ( is not critical to the analysis. All results go through if t = 0.

15. As a regularity condition, we assume 11(6) a p, for all 0 E. [0~,6+]; that is, anuncontested merger is profitable for all 0-types.

16. Formally, the equilibrium being defined is a sequential equilibrium in a game in which aninformed party (the firms) moves first and makes a discrete decision (merge or not), and anuninformed party (the antitrust authority) moves second and makes a challenge decision when thefirms choose to merger. See Kreps and Wilson (1982) for a general definition of sequentialequilibrium.


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0 -•

Figure 3. Merging firms' reaction function

(a) The firms' strategy fi*(9;a) is a best reply to/3*(a); that is, for any 8

if 6 < &($*{a)) = 0*(a),if 0 = 6*(a), (3)if d> (9*(a),

f = 1 'H*(6;a) \ £ {0,1},

1 = 0 ,where 9{p) is the reaction function defined in (2).

(b) When faced with a merger, the enforcement authority's challenge deci-sion must be optimal, given its beliefs about the marginal cost of the mergingfirms. These beliefs must be consistent with Bayes's rule and the equilibriumstrategy of the merging firms. Belief consistency implies that the authority'sexpected welfare is given by17

= £1(1 - a)S(d) + ari(d)\d

3.2 The First-Best Enforcement LevelAs a benchmark against which to compare equilibrium outcomes, \hz first-best enforcement mechanism will be analyzed.18 The first-best likelihood of

17. As will be evident from the proof of Proposition I, a specification of off-the-equilibriumpath beliefs is not needed in our model.

18. We use the term "first best" to mean the optimal enforcement policy given the information


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Contested Mergers and Equffiwium Antitrust ftjdcy 11

challenge P maximizes expected welfare, taking into account the firms' merg-er decision as represented by the reaction function #

max H{Q{fi)){xp{6{P)){\ - P) - til},e[ui]

where rp{0) = ip(6;i)- Let (Pf,df) denote the solution to this problem. Weassume that this solution is interior, that is, P? G (0,1).

A serious problem with the first-best solution is that the challenge proba-bility ftf is not subgame perfect. That is, if the antitrust authority announcedthat the likelihood that the merger would be challenged is pf, and the firms—believing the enforcement authority's announcement—attempted to merge,the antitrust authority would have an incentive not to challenge the merger.19

There are two reasons for this result. First, the negotiation cost / enters thesocial welfare function °W and is a marginal cost of merging that is taken intoaccount in the determination of p^. However, once a merger has been pro-posed, this cost is sunk and does not affect the welfare evaluation of achallenge decision. After a merger has been proposed, the authority would bemore "lenient" because it would ignore this sunk cost.

Second, because the antitrust authority does not know the true value of thecost parameter 6, the precommitment to the challenge probability P is avaluable policy instrument for counteracting adverse selection. Specifically,an increase in the challenge probability will increase the average cost savings,c — 9, of a proposed merger. An increase in the challenge probability thusdecreases the risk of making a type II error—not challenging a merger thatreduces social welfare. At the same time, an increase in the challenge proba-bility P increases the chances of making a type I error—challenging a mergerthat increases social welfare. The first-best challenge probability P*optimallytrades off the reduced risk of a type II error against the increased risk of a typeI error. However, once the antitrust authority commits to P? and is presentedwith a merger proposal, circumstances are different. The challenge probabilityP is no longer useful as a self-selection device, since the set of possible valuesof 6, conditional on the merger having been proposed, has now been deter-mined. Indeed, as is shown in the Appendix, this set of 0-types is (from theantitrust authority's perspective) quite favorable; even the marginal mergerproposal 6{Pf) would increase the enforcer's welfare if approved. At thispoint, then, all the antitrust authority cares about is minimizing the risk of atype I error, and this is done by approving the merger proposal with proba-

asymmetry between the enforcement authority and the firms about 0. Without the informationasymmetry, the socially optimal policy toward mergers is immediate: Approve a merger thatresults in an increase in social welfare given the actual value of 6, and challenge a merger thatresults in a decrease in social welfare. The first-best mechanism entails a precommitment to achallenge probability (i(0r) as a function of a reported marginal cost 6r. Because the enforcementauthority has only one sorting instrument (the challenge probability), the incentive compatibilityconstraints in the mechanism design problem can be shown to imply that fi(0r) must be a constantfunction across all 0-typcs thai attempt merger.

19. This is proven in the Appendix.


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1],if V(if V(if V(

6>*(a);a)d*(a);a)

<o,= 0,> 0 .

12 The Journal of Law. Economics, & Organization, V9 N1

bility 1. In effect, the "commitment" to $J has induced very favorable self-selection by the merging firms, but once this self-selection has taken place,the enforcement authority has an incentive to renege on its commitment.

3.3 Equilibrium EnforcementIn equilibrium, the antitrust authority's challenge decision /3*(a) must max-imize the weighted welfare function, given its equilibrium beliefs about thepost-merger marginal cost of the merging firms. This implies

(4)

Deriving the equilibrium of the merger enforcement process involves find-ing a pair of values /?* and &* that simultaneously satisfy (3) and (4). Fornotational simplicity, we suppress the dependence of the equilibrium valueson a throughout the rest of this section. Given the simple structure of thegame, the equilibrium can be displayed graphically, as shown in Figure 4.

The firms' merger decision is summarized by the reaction function $(/J).For a given /?, if the cost parameter is greater than (9(/3), the firms choose notto merge. The enforcement authority's beliefs are summarized by a conjec-tured cutoff d. For a given &, the authority's enforcement decision can berepresented by the correspondence /J(d;a), defined by

)<0,) = 0,:) >0.

That is, the enforcement authority challenges the merger if the expectation ofweighted welfare, rp(d;a), is negative and may challenge the merger if thisexpectation is zero. It is straightforward to show that the expectation \p(0;a) isstrictly decreasing in &.20 Hence, /?(#;a) is nondecreasing in #. The sequen-tial equilibrium (/3*,#*) occurs where #(/3) and /J(#;a) intersect:

6* = W*), (5)

y3* e £(<9*;a). (6)

Depending on the enforcement authority's welfare weight a, we can eitherhave an interior equilibrium (0 < /?* < 1) or a comer equilibrium (fi* = 0 or

20. Differentiating rf/(.9;a) with respect to 0 yields

1)0 L Ja-- [(1 - a)S(S) + an(6)}}h(x)dt

This inequality follows because 11(0) and S(0) are decreasing in 0.


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Figure 4. Equilibrium in the merger-enforcement process

/?* = 1). The expectation xp($;a) is strictly increasing in a.21 Hence, for asufficiently large, the equilibrium will be at the /?* = 0 comer; for asufficiently small, the equilibrium will be at the /J* = 1 corner, and forintermediate values of a, the equilibrium will be interior.

Proposition 1 formally characterizes the equilibrium of the merger enforce-ment process.

Proposition 1. For any a G [0,1], the equilibrium in the merger enforce-ment process can be characterized as follows. Let22

max /7(0-) - S(9pi

. . r -Eis(O)] 1n+ = mm i - -—— I r

I ET n/a\ r//j\i * I *

For a E [0,a~), /3* = 1 and f)* = 0~. For a

rp{6*;a) = 0.

Fora G (a + , l] , /3* = 0 and d* = d+.

21. (dy/da)0,a) = Lf̂ _{/7(r) - JW> S(0) for all 0.

22. It is straightforward to show that a~ < a +.

and 5* solve

(7)

(8)

- ' > 0, given the assumption that 77(0)


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14 The Journal of Lav* Economics, & Organization, V9 N1

The equilibrium in the merger enforcement process depends on the welfarestandard employed by the antitrust authority. When the antitrust authoritygives a sufficiently large weight to producers' surplus, a > a +, the firmsanticipate that the antitrust authority will not challenge a merger, and the firmsmerge for all realizations of 9. Given this, the antitrust authority's decisionnot to challenge a merger is indeed optimal. When the welfare standard a fallsin [a~,a + ], the firms anticipate that the antitrust authority will challenge amerger with probability /J*. Given this conjecture, the firms will merge only ifthe realization of the cost parameter falls below the cutoff d*. Given thisstrategy by firms, challenging the merger with probability fi* is indeed anoptimal decision for the antitrust authority. Finally, when the enforcementauthority follows guidelines that give a sufficiently large weight to consumers'surplus, a < a~, the firms anticipate that the enforcer will challenge themerger with certainty. Given this, the firms' optimal decision is not to merge.The assumption that S(9~) + 77(0 ~) > 0 can be shown to imply a~ < {.The assumption that E[S(6) + 17(6)] < 0 can be shown to imply a+ > iThus, when the welfare standard is social welfare maximization (a = {), theequilibrium is interior.

An important question is whether the equilibrium in the merger enforce-ment process when the welfare standard is social welfare maximization coin-cides with the first-best solution. Proposition 2 indicates that this is not thecase.

Proposition 2. Suppose the welfare standard employed in the enforcementprocess is social welfare maximization (i.e., a = i). The equilibrium chal-lenge probability is less than the first-best challenge probability, and themarginal merger proposal has a smaller level of cost savings than would be thecase under the first-best solution. That is, /?*(i) < yS^and 0*(±) > QJ.

Proposition 2 implies that the application of merger guidelines based on asocial welfare standard will have a bias toward the avoidance of type I errorsat the expense of type II errors. The result in Proposition 2 is due to twodistinct but reinforcing effects. First, because the transaction cost t is a sunkcost, its magnitude does not influence the antitrust authority's challenge deci-sion. This implies that even if the enforcement authority had complete infor-mation about the cost parameter 9, there would be realizations of 9 for whicha social-welfare-maximizing enforcement authority would approve a merger,even though the merger reduces ex ante social welfare (i.e., social welfareminus the transaction cost). We refer to this effect as the sunk cost effect.Thus, if the antitrust authority were to employ a social welfare standard, thesunk cost effect would result in merger enforcement that is more lenient thanthe first-best solution.23

Second, at an equilibrium in the merger enforcement process, the antitrustauthority chooses the challenge probability fl based on a (correct) conjecture

23. Of course, the sunk cost effect vanishes if the transaction cost I is zero.


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Contested Mergers and Equilibrium Antlliust Ftaflcy IS

[6~ ,#*] about the set of 0-types that would propose a merger. In contrast tothe first-best benchmark, when the enforcement authority computes the mar-ginal benefit of increasing the challenge probability at the equilibrium, it doesnot include the impact that a variation in (i would have on inducing morefavorable self-selection. We refer to this second effect as the self-selectioneffect. The self-selection effect reinforces the sunk cost effect and works tomake the equilibrium challenge probability under a social welfare standard,P*(i), too low relative to the full-commitment challenge probability ftf. How-ever, unlike the sunk cost effect, the self-selection effect operates only whenthe merging firms have private information about the post-merger marginalcost 0.

A key element of our analysis is the impact of the welfare standard a onequilibrium enforcement. This impact is described in Proposition 3.

Proposition 3. The more weight given to consumers' surplus in the welfarestandard—that is, the smaller is a—the greater is the equilibrium probabilityfi*{a) that the merger will be challenged, and the lower is the equilibriumcutoff d*(a); that is, dfi*/da < 0 and d&*/da > 0.

These comparative statics results are illustrated in Figure 5. Note [from (1)]that the reaction function @(p) does not depend directly on a. Hence, as aincreases, the correspondence P(d;a) shifts upward, holding 0(/J) fixed.Varying a traces out an equilibrium locus that coincides with the #(/?) curve.Moving along this locus entails a trade-off: As a decreases, the average costsavings from a merger increase, but the likelihood that the merger is approved

eV1)

eV)

E "

a 1 >

E '

a "

\ e

0 p#(a") PV>Figure 5. Comparative statics on trie welfare weight.


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16 The Journal of Law. Economics, & Organization. V9 N1

goes down. Put another way, as a decreases, the risk of a type I error goes up,but the risk of a type II error goes down. Ex ante, the expected social welfareconsequences of this trade-off are ambiguous. However, as we show in thenext section, ex ante expected social welfare is maximized when the welfarestandard that is employed in the enforcement process gives greater weight toconsumers' surplus.

4. The Optimal Welfare StandardThe optimal welfare standard a maximizes ex ante expected social welfare,taking into account the impact of the standard a on the equilibrium in themerger enforcement process. Specifically, the optimal standard, denoted bya*, solves

max W*(a) = H(d*(a)){ip(d*(a))(l - 0*(a)) - t/2}. (9)a6[0,l]

As indicated in the discussion following Proposition 3, varying the value of acreates a nontrivial welfare trade-off. If a is too low, high-efficiency, welfare-enhancing mergers may be blocked, but if a is too high, mergers that reducesocial welfare may be undertaken and approved in equilibrium. The nextproposition indicates that the ex ante optimal standard errs on the side ofdeterrence by giving more weight to consumers' surplus than to producers'surplus.

Proposition 4. For any a' E (a - ,i) and any a" G [i, 1], W*(a') > W*(a").Thus, ex ante social welfare is maximized by merger guidelines specifying awelfare standard that gives strictly greater weight to consumers' surplus thanto producers' surplus.

The keys to understanding Proposition 4 are Propositions 2 and 3. Recallfrom Proposition 2 that the use of a social welfare standard by the antitrustauthority would result in insufficient enforcement relative to the first-bestlevel. Proposition 3 implies that an increase in the weight given to consumers'surplus in the welfare standard would increase the equilibrium likelihood ofchallenge. Thus, by decreasing a, the equilibrium probability of challenge 0*and cutoff 8* can be moved closer to the first-best solution.

The divergence of the optimal welfare standard from social welfare maxi-mization can be seen by differentiating W*(a) with respect to a and evaluatingat a = i:

dW*(a)da a-l/2

where the inequality follows because drp/dd < 0 and dd*/da > 0. Thisexpression can be understood by tracing through the implications of an infini-


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Contested Mergers and Equilibrium Antitrust Pdflcy 17

tesimal decrease da in the weight given to producers' surplus. This decreaseleads to an infinitesimal decrease dO* in the equilibrium cutoff 6*. The firstterm in curly braces in (10) gives the savings in the expected transaction costdue to the reduction h(6*)dd* in the equilibrium probability of the merger.This term corresponds to the sunk cost effect described in the discussionfollowing Proposition 2. The second term in the curly braces in (10),(dip/d&)(l - 6*)H(6*), represents the marginal increase in the expectation ofsocial welfare due to the improvement in the set of 0-types that will propose amerger at the equilibrium when the welfare standard is (a — da). This termcorresponds to the self-selection effect discussed following Proposition 2.Note that expression (10) contains no terms reflecting the marginal impact ofa on the equilibrium challenge probability. This is because when a = i , theenforcement authority is optimizing along the 6 margin in a manner consistentwith social welfare maximization, and an infinitesimal reduction da in thewelfare weight has a second-order effect on ex ante expected social welfarealong this margin. By contrast, the reduction da leads to a first-order im-provement in ex ante expected social welfare along the 6 margin.

The determination of the optimal a is closely related to the first-best prob-lem discussed in the previous section. To develop this point, consider Figure 5again. Varying a traces out an equilibrium locus that corresponds to thereaction function @(B). By maximizing W*(a), one can, in effect, choose anoptimal (6,6) point along the d(6) locus. Thus, the problem of choosing a tomaximize W*(a) is equivalent to the problem

max //(0(/9)){V(0G8))(l - 6) - t/2}./Se[0,i]

But this problem is just the first-best problem discussed above. Thus wehave the following result.

Proposition 5. Merger guidelines specifying a welfare weight a* that max-imizes ex ante expected social welfare W*(a) attains the first-best solution asan equilibrium in the merger enforcement process; that is, (6*(a*),6*(a*)) =

The solution to the problem of choosing an optimal welfare standard isdepicted graphically in Figure 6 as a point of tangency between the 6(6) locusand the indifference curves for expected social welfare in (6,6) in space.24

Figure 6 depicts an interior solution (a* > a~) , but depending on exogenousparameters, a corner solution (a* = a~) is also possible.

The analysis so far has implicitly assumed that the enforcement authorityfaces at most one horizontal merger during its term of office or that all

24. The indifference curves are the contour lines for the function H($){ij>(&)(i - 0) - 112}.Although the indifference curves for the expected social welfare function will not be everywheredownward sloping in (/?,<?) space, a region of downward-sloping indifference curves will oftenexist.


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18 The Journal dt Law. Economics, 4 Organizalion, V9 N1

Increasing ExpectedSocidWHfere

"

Figure 6 Optima) choice of the welfare weight

potential mergers are identical ex ante. Both assumptions are obviously false.The enforcement authority would be expected to face a large number ofpossible mergers with different 5, 77, and H(6) functions. The insight fromProposition 4 continues, however, to be relevant. Suppose it is anticipated thatthere are Tdifferent potential mergers at dates x — \,...,T. Let W*(a) be theexpected social welfare for the rth of these potential mergers when the en-forcement authority's welfare weight is a. The optimal welfare weight a*maximizes the ex ante discounted social welfare W*(a) = 2 J_ , 6TW*(a).Although the aT that maximizes W*(a) may vary across r, Proposition 4implies that a* of W*(a) must be less than i.25 Thus, even though an enforce-ment authority is faced with a large number of possible merger cases, ex antesocial welfare is increased by a welfare standard that gives strictly greaterweight to consumer surplus.

The optimal welfare weight a* will in general differ from the optimalweight a* at any particular date r. In this sense, the welfare weight is a bluntinstrument and, in contrast to Proposition 5, adjusting the welfare weight willnot guarantee attainment of the first-best solution. This opens up the pos-sibility that additional policy tools will be valuable to the antitrust authority.For example, the antitrust authority might approve a merger conditional on thepost-merger price not rising above a certain level or the post-merger outputnot falling below a certain level. A full analysis of the effects of post-mergerprice or output controls is beyond the scope of this article. However, it isimportant to understand that reliance on such controls would significantly

25. The argument is straightforward. If a* < i, then there must exist a t such thai W%a*) >. But this contradicts Proposition 4.


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Contested Mergers and EquSbrium Antitrust PoOcy 19

alter the nature of merger enforcement policy, transforming it from a relativelystraightforward administrative process involving approval or challenge deci-sions to one that would more closely resemble traditional public utilitiesregulation. See Spulber (1989: 474-82) for a related discussion.

5. An ExampleIn general, the optimal a will trade off the risk of type I and type II errors, andthe optimal a can lie between a~ and | . To illustrate this point, a specificexample is presented. Suppose market demand is linear, P = a- bQ, and thedistribution of 8 is uniform on [6~,6 + ], with a > d+ and 6~ < a -2bl/2gin < 6+. Given these assumptions,

77(0) = ^ (a - 0)2,

[(a - 0")2 + (a - 0-)(a - ^) + (a -

_ (1 - a)(g - c p2b

The equilibrium in the merger enforcement process is given by

4gb(a-fjl*)2'

for a G ( a ~ , a + ), where a~ and a + are such that ip(d~;a~) = 0 andV(0+ ;a + ) = 0.

In Table 1, we indicate how a mean-preserving spread of the distribution of0's affects the optimal a. In this example, as the uncertainty about 0

Table 1. Ex Ante Optimal a for Mean-preserving Spread of 6

6-

2018161412

e*

8082848688

E(0)

5050505050

Oe

17.3218.48196320.7821 94

a"

.340

.333

.328

.324321

No«e- a, - variance of 9; a" - ex ante optimal a; parameter values tor the taHe: a = 100. b = 100. c - 50.I - 1 . / - 0 .


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20 The Journal of Law, Economres, & Organization, V9 N1

increases, the social-welfare-maximizing a goes down; that is, the welfarestandard gives increasingly more weight to consumers' surplus. This com-parative statics result is due to self-selection. Firms will not merge for thehighest realizations of 0. Therefore, as far as the challenge decision is con-cerned, the relevant effect of the mean-preserving spread is on the lower tail ofthe distribution of 0's. Specifically, the mean-preserving spread increases theexpectation of weighted welfare, ip(d;a), for any given conjectured cutoff 6.This reduces the equilibrium challenge probability y3* and worsens the mix of0-types that attempt to merge.26 At the same time, the first-best challengeprobability ftf decreases, but at a rate less than the equilibrium challengeprobability. To compensate for the greater-than-preferred reduction in theequilibrium challenge probability, the optimal welfare standard places greaterweight on consumers' surplus.

6. Filing FeesIn November of 1989, the DOJ and the FTC began collecting a $20,000 feefrom firms filing pre-merger notifications. The intent of the filing fees is todefray the costs of enforcing merger policy. The merger enforcement modelanalyzed in the previous sections can be employed to study the effects of filingfees.27 Throughout this section we take the welfare standard a as fixed(though not necessarily at the ex ante optimal level). We begin by establishinga comparative statics result.

Proposition 6. At an interior equilibrium, an increase in the filing feedecreases the equilibrium probability of challenge, /?*, but has no effect onthe mix of 0-types that merge; that is, dfi*/df < 0 and dd*/df = 0.

The comparative statics result in Proposition 6, which is illustrated inFigure 7, reflects the interaction of two effects. First, for a fixed fi, theincrease in the filing fee deters marginally profitable mergers. This effect isreflected by the downward shift in the firms' reaction function #(/J). Second,given a favorable mix of 0-types that merge, the enforcement authoritychooses a lower challenge probability. In equilibrium, the firms correctlyanticipate the enforcement authority's challenge probability, resulting in a lessfavorable mix of 0-types that merge. At a sequential equilibrium, these effectsexactly offset each other. When /?* G (0,1), the filing fee thus has a neutraleffect on the mix of 0-types that attempt to merge.

Proposition 6 does not imply, however, that an increase in the filing fee hasneutral social welfare implications.

26. This result is somewhat more general than our specific example. In particular, the resultholds for the uniform distribution for general consumers' surplus and profit functions, S(0) andfl(9), satisfying the assumptions made in Section 2.

27. Because the amount of the current filing fee is relatively low, one might not expect that itwould have a substantial impact on firms' merger strategies. Thus, the analysis presented here ishypothetical in nature. Nevertheless, we feel this analysis is useful because the filing fee isessentially a tax on merger proposals. Understanding the impact of a merger tax on the enforce-ment equilibrium may reveal the inherent dieoretical limitations of a tax as a policy tool.


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Contested Merge™ and Equilbrium Antitrust Roficy 21

e

e*(f")=e*(f)

9" +

Figure 7. Comparative statics on the filing fee.

Proposition 7. If a is less than (equal to) (greater than) i, and the equi-librium in the merger enforcement process is interior, then an increase in thefiling fee increases (has no effect on) (decreases) ex ante social welfare.

Proposition 7 seems counterintuitive in view of the earlier result that thesocial-welfare-maximizing welfare weight a is strictly less than i. Proposition7 implies that when a < i, ex ante social welfare is increased by increasingthe filing fee, thereby reducing the equilibrium challenge probability. Theresult can be explained with the help of Figure 8. By reducing a below i,ex ante social welfare increases, moving the equilibrium outcome to B inFigure 8. (Here, point B is the optimal a, given the initial filing fee.) But thewelfare weight a is a "blunt" instrument of control, in that variations in aonly move the equilibrium along the 8(fS) locus. The equilibrium outcomecan be "fine tuned" by increasing the filing fee. This shifts the #(/?) locusdownward and, in the range where a < i, places the outcome at point C on ahigher indifference curve.

7. Commitment and Reputation in Merger EnforcementThe analysis in the previous sections rests strongly on the idea that the anti-trust authority is unable to commit to the first-best challenge rule because thatrule is not subgame perfect. One might reasonably question whether ouranalysis takes the requirement of subgame perfection too seriously. At leasttwo questions can be raised in this connection: (i) Do merger guidelinesconstitute a precommitment to a challenge rule? (ii) Assuming that the en-


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e f •• > f

e

e ( f ••) = e ( f •)

0 P(f") p'(f)Figure 8. Welfare effects of the filing fee.

forcement authority cannot credibly precommit to the first-best challengeprobability, will the first-best policy emerge as a result of rational reputationbuilding by the enforcement authority?

7.1 Merger Guidelines as a Precommitment DeviceBecause the merger guidelines state precise concentration thresholds andidentify specific tests for defining markets, some might argue that contrary toour model, merger guidelines constitute a precommitment to a challengeprobability—or at least offer the opportunity by which such a precommitmentcan be made. The government then could achieve the first-best solution bywriting sufficiently detailed guidelines that, in effect, specify a formula asso-ciating market and firm characteristics with a challenge probability, whichwould then be faithfully applied in each merger case by the enforcementauthority. We believe, however, that it is much more reasonable to viewmerger guidelines as an expression of policy that helps shape the welfarestandard used in merger challenges, rather than as a formula for the first-bestchallenge probability. The antitrust authority exercises discretion in choosingwhether to approve or challenge a merger.

We come to this view for several reasons. First, empirical evidence on FTCmerger enforcement decisions by Coate, Higgins, and McChesney (1990)strongly suggests that the FTC does depart from the wording of the guidelinesand exercises discretion in making its enforcement decisions. Second, themanner in which a given set of guidelines is applied changes over time. Forexample, in the first two years of the Bush administration there was muchpublicity given to the DOJ's departure from Reagan administration policy


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Contested Mefgere and Equifibrium Antitrust Fbficy 23

toward horizontal mergers.28 Yet, until 1992, the Bush administration wasbound by the 1984 Merger Guidelines written by the Reagan administration'sJustice Department. This sort of change is inconsistent with the notion thatmerger guidelines represent a precommitment to a strict formula mapping in-dustry and firm actions into enforcement action. It is not inconsistent, however,with the notion that merger guidelines are but one factor that shapes the welfarestandard used in merger cases. According to the latter view, merger guidelinesare sufficiently ambiguous and flexible in their application that, depending onwho interprets them, a different welfare weighting may emerge from the fixedlanguage of the guidelines. The welfare standard in merger enforcementchanged not because the guidelines changed but because the personnel leadingthe enforcement agencies were different in the two administrations.

Finally, a careful reading of the 1984 and 1992 guidelines reveals substan-tial flexibility. (Indeed, the quote from the 1992 guidelines at the beginning ofthis article openly attests to this flexibility.) For example, the precisely statedHerfindahl-Hirschman Index thresholds in the 1992 guidelines are intended tobe only a starting point for the evaluation of mergers. Because of alternativeways in which one might define the relevant market, the enforcement agencieshave considerable leeway in applying the thresholds. Indeed, several antitrustscholars (e.g., Scherer, 1990; Hay, 1989) criticized the 1984 guidelines be-cause they gave the enforcement agencies too much discretion. Scherer writes:"The Guidelines' list of 'other factors' allows the Department of Justice evenmore discretion in choosing not to challenge mergers even when they breachthe quantitative thresholds" (1990: 93). He also notes that the values of theenforcement agency play an important role in assessing "the seriousness of,and relative weight to be placed on avoiding Type I errors . . . as compared toType II errors" (1990: 93). Hay points out that the DOJ is under no obligationto disclose its reasons for not challenging a merger. Moreover, because the1984 guidelines instructed the DOJ to rely on imputed market shares based onthe staffs evaluation of the effects of a hypothetical price increase, it wouldhave been very difficult for Congress or the president to monitor thefaithfulness with which the Department implemented the guidelines. Hay alsopoints out that the 1984 guidelines gave the Justice Department a tremendousamount of discretion in applying them in practice:

. . . the inherent flexibility in those procedures has made it extremely difficult to predicthow the Department will come down on any specific transaction that is proposed. If one ofthe main purposes of the 1968 Guidelines was to enable businessmen to plan with confi-dence about how a given transaction would be received, that ability has been significantlydiminished [by the 1982 and 1984 Guidelines]. If so, one has to ask whether the Guide-lines serve any useful purpose at all except as a training manual for Justice staff." (1989:244)

Our analysis suggests that, to the contrary, the merger guidelines do serve apurpose as an embodiment of antitrust policy. As such, merger guidelines set a

28. See, for example, "More Antitrust Challenges Are Expected Under Bush" (New YorkTimes. November 2, 1989: Cl) or "Justice, FTC Signal Tougher Merger Enforcement Standards"{Antitrust, Summer 1990: 5-8).


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24 The Journal of Law, Economics, 4 Organizallon. V9 N1

general tone that guides merger enforcement in a particular direction, ratherthan provide a fixed prescription for action. Given this, one would expect thelanguage of the guidelines to introduce flexibility and discretion into theenforcement process, so that a given set of guidelines could be applied in adifferent way by different administrations. The combination of merger guide-lines with the personal values and preferences of the enforcement personneldetermines the objective function employed in making a challenge decision.Thus, the guidelines are one—but not the only—lever by which this objectivefunction can be altered.

7.2 Reputation BuildingEven if the antitrust authority cannot make credible precommitments, it mightbe argued that the antitrust authority can achieve the first-best outcome bydeveloping a reputation for "toughness." Even though challenging a givenmerger may not be subgame perfect, the antitrust authority may still decide todo so in order to preserve its reputation. Rational reputation building could bemodeled formally in this context by assuming that there is some positiveprobability that the antitrust enforcer is irrationally tough and will alwayschallenge a merger irrespective of a merger's effects on social welfare or thecosts of undertaking a challenge. A rational enforcement authority mightbenefit from firms' uncertainty about the rationality of the enforcement author-ity in that the prospect of a challenge by an irrational enforcer would deter themerger from being proposed altogether. When actually faced with a merger, arational enforcer will weigh the current welfare effects of challenging themerger against the future loss in reputation if it does not challenge the merger.(It will have been revealed to be rational, thus making it more susceptible towelfare-reducing merger proposals in the future.) We have analyzed the se-quential equilibrium in the model just described, and, as expected, we findthat the desire to build reputation counteracts the enforcer's ex post incentivenot to challenge the merger. However, there is no necessary correspondencebetween the level of enforcement that emerges in equilibrium and the first-bestlevel of enforcement. Given that this is the case, even in a model that allowsfor reputation building, ex ante social welfare can be improved by creating adivergence between the enforcement authority's welfare functions and actualwelfare.

More fundamentally, the argument that reputation building is the primaryforce that drives merger enforcement policy strikes us as implausible. In orderfor reputation building to affect the merger strategies of firms, firms that arecontemplating a merger would have to look back at the enforcement authori-ty's prior record on challenging mergers and update their beliefs about theenforcement authority's "toughness." But the prior record is unlikely to bevery informative if previous challenges occurred in unrelated industries.Moreover, the staffs of the FTC and the DOJ are not obligated to publiclyjustify a decision not to challenge a particular merger or to reveal the informa-tion or analysis used to arrive at that decision. Finally, a reputation will not betransferred to future staffs after a change in administration. Given all of this,


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Contested Mergers and EquiBbrium Antitrust Policy 25

the observation that the antitrust authority has decided not to challenge amerger between two firms in industry B may convey very little information tofirms in industry A about the enforcer's proclivity to challenge a merger in thatindustry.

8. ConclusionAntitrust policy reflects not only the political considerations and preferencesof policy-makers but also the institutional constraints on enforcement. Theanalysis of merger policy formation presented here highlights the effects ofasymmetric information about prospective cost savings. The analysis alsodemonstrates the crucial role that delegated enforcement plays in designingpolicy. We conclude that ex ante social welfare is maximized when the en-forcement authority screening merger proposals makes its enforcement deci-sions on the basis of a welfare standard that gives strictly greater weight toconsumers' surplus than does a social welfare standard. This is consistent withthe current U.S. merger guidelines, which give more weight to adverse mar-ket power consequences than to the production efficiencies that might resultfrom a horizontal merger.

Appendix: Proofs

Proof That the First-Best Solution Is Not Subgame Perfect. Suppose thatthe enforcement authority precommits to the first-best challenge probabilityfif, and the firms—regarding fif as a credible commitment—merge if therealization of 9 is less than or equal to the cutoff fr = &((¥). Faced with thismerger proposal, the enforcer's ex post expected welfare as a function of /? isgiven by

so we have

We now show that xp{6f) is positive, indicating that the enforcer has an expost incentive to reduce the challenge probability to zero. Because the solu-tion to the first-best problem is interior, it is characterized by the first-ordercondition d°W/dfi = 0, which implies

The inequality follows because dipldQ < 0 and dd/dfi < 0, and it impliesw\p) < 0. Q.E.D.


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26 The Journal of Law Economics, & Organization, V9 N1

Proof of Proposition 1. (i) a < a ~: Note that this case can only arise ifS(6~) < 0, for otherwise a~ = 0. When S(6~) < 0, the condition a < a~ isequivalent to

ip(d-;a) < 0.

Since \p(0;a) decreases in 6, it follows that

xp0;a) < 0, for all 0 E [d~,6 + ].

Thus, when a < a~, it is a dominant strategy for the authority to challengethe merger, so /J* = 1 in this case. Given that the antitrust authority chal-lenges the merger with certainty, the firms are better off not merging, nomatter what the realization of the cost parameter 6.

(ii) a £ [a~ ,a + \. We begin by arguing that there exists a unique solutionto (7) and (8). The condition a £ [a~,a + ] is equivalent to

ip(9-;a) > 0, y{6+\a) < 0.

Because rp(Q;a) is strictly decreasing in &, and, 6~ < 9+, there exists aunique & G [0~ ,0 + ] such that (8) holds. Now, 77(0) & Q for 6 £ [d~ ,d + ].Thus, for the d* that solves (8), there exists a unique /J* £ [0,1] that solves(7). Hence, a unique solution (/!*,&*) to the system (7) and (8) exists. Thesolution to (7) and (8) constitutes a sequential equilibrium, because (7) isequivalent to (5), and (8) implies (6). When a £ (a~ ,a + ), this equilibrium isunique because the only (0*,/3*) pair satisfying (5) and (6) is the uniquesolution to (7) and (8).

(iii) a> a + : Note that this case can only arise when a + < 1. When this isso, a > a+ implies

V(0 + ;a) > 0.

Hence a challenge probability /?* = 0 is the antitrust authority's best reply if itbelieves that the merging firm's cost parameter is 6+ or less. Now, for all 6 £[6~ ,0 + ], an uncontested merger is profitable—thus, the firms' strategy ofmerging if and only if 6 £ [6 ~, 6 + ] is optimal given the challenge probability0* = 0. Q.E.D.

Proof of Proposition 2. Since, by assumption, £ £ (a~ ,a + ) , V($*(i)) = 0and \p{&f) > 0, where the latter inequality is derived in the proof that the first-best solution is not subgame perfect. Since drp/dd < 0, it follows that &f <<9*(i). Because (9(#) decreases in 0, 6' = 0(£O, and <?*(i) = 0(/3*(i)), itfollows that fif > /8*(i). Q.E.D.

Proof of Proposition 3. Totally differentiating (8) with respect to a yields

dd* -d\plda


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CortesJod Mergers and Equfibrium Antitrust Ftoflcy 27

The inequality follows because dxplda > 0 and dxpldB < 0. Totally differ-entiating (7) with respect to a yields

because 11(6) is decreasing. Q.E.D.

Proof of Proposition 4. Note that

d*(o')]. (A3)

For a ' G (a~, i ) , we have an interior equilibrium. Rearranging the equi-librium condition (8) yields

( A 4 )

Substituting (A4) into (A3) yields

V(6*(a')) = (1 - l/2a')E[S(d)\d < d*(a')]. (A5)

Substituting (A5) into the expression for W*(a') yields

d*(a')](l - /8*(a')) - r/2}. (A6)

Since 77(0) > 0, (A4) implies

E[S(6)\d ^ &*(a')] < 0.

Moreover, since a ' < i, it follows that

W*(a') > -H(d*(a'))t/2. (A7)

Now, for a" £ [i,a + ] we can derive an expression similar to (A6), but sincea" si,

W*(a") £ -H(6*(a"))t/2. (A8)

From Proposition 3, #*(a') < d*(a"). Thus,

W*(a') > W*(a"), for a ' £ (a" , i ) , a" E [i,a + ].


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For a > a+, W*(a) is constant and can be shown to be less than or equal toW*(a + ). Thus, W*(a') > W*{a") for a ' E (a",4), a" £ [4,1]. Q.E.D.

Proof of Proposition 6. Totally differentiating the equilibrium conditions(7) and (8) (recalling Q = t + f) yields d&*/df = 0 and

~- = -[TI0*)]-1 < 0. Q.E.D.

Proof of Proposition 7. Differentiating W* in (9) with respect t o / a n dnoting from Proposition 6 that dd*/df = 0, we have

Since

V(0*) = tp(6*;a) + (4 - a)E[n(d) - S(0)\9

and ip(@*;a) = 0 at an interior equilibrium,

^ *£. ( i - a)£[/7(0) - S(0)|0 ^ (9*],

which implies dW*/df | 0 as a I i. Q.E.D.

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