Quantitative Techniques for Competition and Antitrust Analysis_8 docx

Quantifying Damages of a Cartel 375which in turn means, given the demand equation, we can calculate the implied levelof prices since the inverse demand curve describes p D P .Q/.. The co

7.1 Quantifying Damages of a Cartel 373

Figure 7.8. Pass-on with elastic and inelastic demand

For a formal demonstration, consider a price-taking firm, solving

max

q pq
C.qI c/;

where C.qI c/ represents the total cost function and c represents a cost driver Fromthis problem we derive the firm supply function q D s.p; c/ and from that in turn,given N identical firms, we derive an industry supply curve S.pI c/, increasing in

p and decreasing in c We may now define a function

F pI c/  D.p/
S.pI c/ D 0;

which implicitly defines the equilibrium price as a function of our cost driver, c

We can then apply the Implicit Function Theorem to get an expression for thepass-through @p=@c Specifically, totally differentiating gives

374 7 Damage Estimation

and thirdly by multiplying top and bottom by minus one Finally, note that (i) thedemand elasticity is negative while the supply elasticity is positive so that the denom-inator will be positive and (ii) supply will decline as costs increase so that the numer-ator is also positive, making the ratio positive so that equilibrium prices increasewith cost, @p=@c > 0 Furthermore, we conclude that the pass-on depends on boththe demand and supply elasticities as well as on the cost elasticity of supply Bothelastic demand or elastic supply make the denominator large and hence reduce thepass-through down toward zero Similarly, and intuitively, when the cost elasticity ofsupply is small so that costs tend not to impact on ability to supply the downstreamgood, the rate of pass-through will be small

Verboven and Van Dijk (2007) derive the analytical formulas for the pass-on rateunder perfectly competitive markets and under markets with oligopolistic competi-tion Furthermore, they evaluate the relative importance of the pass-on and outputeffects for a variety of settings They note that the pass-on effect should be appliedand the amount of the overcharge discounted by this effect when the claimant oper-ates in a fully competitive setting But when the claimant’s industry—the down-stream industry—is less competitive, the output effect and the loss of sales volume

by the claimant starts mitigating the effect of the pass-on on the claimants profits.The output effect should in such cases limit the discount in the damages granted by

a pass-on defense Their paper provides analytical expressions for the total discount

to be applied to the overcharge of the cartel, taking into account both the pass-onand the output effects

Cournot competition in quantities the pricing function has the form

7.1 Quantifying Damages of a Cartel 375which in turn means, given the demand equation, we can calculate the implied level

of prices since the inverse demand curve describes p D P Q/ First, recall that if

@P Q/

@Q

:Rearranging gives

so that canceling terms gives

@p

QN

1

;where  is the price elasticity of demand Note that in the Cournot model the sensi-tivity of the price elasticity of demand to the output level affects the pass-through.The expression does not allow us to predict whether the pass-on under Cournot will

be lower or higher than under perfect competition

376 7 Damage Estimation

7.1.4 Timing the Cartel

An area we have not yet considered is the timing of the cartel We need to understandthe time when the cartel was active since damages will accrue over that period Infact, getting the period sufficiently approximately correct may be at least as importantfor the final damages number as pinning down exactly what the difference betweencollusive and competitive prices would have been in any given time period Inaddition, most methodologies rely at least to some extent on pre-cartel or post-cartel data to extract information about the competitive scenario and it is thereforerather important that the data deemed to be the result of competition are in factgenuinely the result of competition, or something very close to it

Most commonly investigators use direct data from company executives to timethe cartel: notes from diaries, records of meetings, emails referring to meetings orexchange of information, and memos describing pricing schemes All these are thebest sources for timing the cartel, as well as proving it existed in the first place.Because they are generally simple and less controversial pieces of evidence, it is

by far the preferred source of information Such information may be obtained fromraiding company offices or executives’ home addresses Alternatively, it may emergefrom the now widespread use of leniency programs, where leniency (particularlyfor second and subsequent leniency applications in a given case) can sometimes beconditional on providing evidence about the workings of a cartel

However, if there is not enough hard documentary evidence to time the cartelprecisely, investigators may want to consider looking for a structural break in thedata The idea is to look for a change in the competition regime prevailing in theindustry and the intuition is that we expect changes in conduct to be associated withotherwise unexplained changes in the levels of prices and/or quantities being sold.One way to do this is to specify dummy variables that allow for multiple possiblestarting and finishing dates For instance, one might run the following regression:

pt D x0tˇ C ˛1DApril 06 to May 06t C ˛2DJune 06 to July 06t C "t:

This specification nests two timing options with two different starting dates If

˛1D 0 and ˛2> 0, then the starting date of the cartel is June 2006 If ˛1D ˛2> 0,then the starting date of the cartel is April 2006

One can undertake a similar exercise for the end dates of the cartel but end datesare often trickier to pin down than start dates Reversion to competition can be agradual process and is not always marked by a discrete event such as a meetingamong executives Cartels often collapse little by little due to cheating, entry, adiversion of interests, or due to scrutiny by a competition authority One may observeprices falling with several attempts to re-establish coordination having some limitedsuccess Documenting and incorporating these data into the analysis may not bestraightforward

7.2 Quantifying Damages in Abuse of Dominant Position Cases 377Additionally, there are reasons to think that the cartel may be replaced by acompetition regime that is not necessarily genuine competition The fact that acartel had explicitly solved the problem of agreeing what it meant to be colludingmeant that the first of Stigler’s conditions for tacit collusion may be satisfied, namelyagreement (see the discussion in chapter 6) There are numerous indications that tacitcollusion may be more likely after periods of explicit collusion and examples that arewidely cited include those which followed the breakdown of the electrical cartels inthe late 1950s.14Alternatively, firms in the previously cartelized industry which arebeing exposed to damage claims may sometimes have an incentive to price abovethe noncollusive level in the post-cartel period in order to minimize the size of theirpenalty (Harrington 2003).

Finally, it is worth noting that the focus on claims made by downstream firms inthe discussion of cartel damages reflects, in part, a legal reality, at least in Europe.The fact is that groups of final consumers often find it very difficult to coordinatetogether to generate a successful damages claim Legal fees in a damages case can

be substantial, even if a regulator has already put together a civil case establishingthere was a cartel, while each consumer’s damage may be small For example, in thefootball shirt case in the United Kingdom (JJB Sports) that consumer organization

Which? took to the Competition Appeals Tribunal on behalf of consumers, each

consumer was awarded £20 in damages from the company However, since in theUnited Kingdom this kind of private action requires consumers to opt into the group

of consumers that were represented by Which?, only approximately 1,000 consumers

were expected to receive £20 each in compensation while almost one million shirtswere estimated to have been affected by the cartel.15 The possibility for a limitedform of U.S.-style class-action suits, where groups of consumers would need toopt out of an action rather than opt into it, is under consideration in a number ofEuropean jurisdictions.16

Damages are mostly explicitly calculated for cartel infringements However, olization cases (or in EU language abuse of a dominant position cases) may alsoharm the process of competition and ultimately consumers Because the tradition of

monop-14 Specifically, the General Electric–Westinghouse case provides an example where it was subsequently alleged that tacit collusion replaced the explicit collusion of the late 1950s (see Porter 1980).

15 See, for example, “Thousands of football fans win ‘rip-off’ replica shirt refunds” (http://business timesonline.co.uk/tol/business/law/article3159958.ece) The other aspect of the incentive to take such cases on behalf of consumers is the allocation of costs If a case is won by a consumer organization, it can seek its costs; however, this “loser-pays” principle puts a considerable risk of a large downside on consumer organizations if the court decides that a claim for damages is without merit.

16 See www.oft.gov.uk/news/press/2007/63-07 for the United Kingdom and http://ec.europa.eu/comm/ competition/antitrust/actionsdamages/index.html for the European Commission’s consultation on private actions.

378 7 Damage Estimation

private litigation is not yet fully developed in Europe, there are not many examples

of calculated damages for individual misconduct unrelated to price fixing This tion only briefly introduces the topic and draws from Hall and Lazear (1994) andthe Ashurst (2004) study for the European Commission

sec-7.2.1 Lost Profits

Abuses of dominant position hurt consumers directly through exploitative abuses(high prices) but additional harm to consumers often also occurs because competitionhas been impaired in some way For example, rivals have been prevented fromoperating in the market either entirely or perhaps their scale of operation has beenreduced In either case, we will say they have suffered from an exclusionary abuse.Who, if anybody at all, is entitled to claim damages is a matter of law and differs

by jurisdiction

The calculation of damages arising from an abuse of dominant position is a fairlyuncommon activity for competition authorities, far rarer than damage calculationsare for cartels One reason may be that the damage inflicted by a dominant firm oncustomers and the extra profits generated by the abusive conduct can be very difficult

to calculate whenever there is a significant element of exclusionary abuse Indeed,there are few well-understood methodologies for evaluating the damage caused byexclusionary abuses, although a simulation model could be used in principle Byits very nature estimating what competition would have been like with additionalfirms active is a very difficult exercise The quantification of the additional profitsgenerated by the abuse, on the other hand, may be of interest if the authority wants

to assess the incentives that firms face for engaging in abusive behavior of somekind The methods presented here could also be used for such a purpose

When the injured party is a rival and not a customer, the damage calculation is evenless straightforward Typically, damages will be expressed as the additional profitsthat would have been obtained if the abuse had never taken place The counterfactual

is more difficult to establish than the effect on consumers since it will involve theperformance of a particular firm if it had faced different conditions on the market.While our current generation of simulation models might be used to incorporateindividual abusive conduct and to produce comparative static results of outcomeswith and without the conduct, the data required to undertake such an exercise robustlywould quite possibly rarely be available

The design of a counterfactual and the quantification of the profit differentialwith and without the conduct is the most essential and also the trickiest part ofsuch a damage estimation exercise There are, however, other empirical issues thatwill also be relevant For example, if plaintiffs can recover interest from their pastlosses, there will have to be a calculation of the present value of past damages.Similarly, future losses due to irreparable damage will have to be divided by asuitable discount rate in order to be expressed in net present value The choice of the

7.2 Quantifying Damages in Abuse of Dominant Position Cases 379interest rate and the discount factor theoretically appropriate will take into accountthe characteristics of the firm and the risk of the investment While such generalstatements are widely acknowledged to be standard practice, they are not the same

as stating the right number for any given context Doing so with any confidencewould require a substantial endeavor Finally, the timing of injury may not coincidewith timing of the infringement since injury can extend beyond the infringement andthe claimant may not have been directly affected by the abuse since it took place

7.2.2 Valuation of Lost Profits

The quantification of lost profits due to an abuse of dominant position by another firmmay well mostly involve using accounting data and accounting concepts to constructthe profitability that would have occurred in the counterfactual world where noabuse took place One approach is to base the damage calculations on the claimantcompany’s earnings: the damages will be the discounted estimated change in thecash flow The cash flow is defined as the firm’s earnings actually received minusthe costs actually incurred The calculation of cash flow would exclude depreciationsince the cost of depreciation is not actually paid Assumptions must be made abouthow costs would have changed with different output and revenues The calculation

of “but for” cash flow will have to be carefully based on information about thecompany situation before the injury and its likely prospects on the market Thelatter, in particular, means that a sufficiently deep knowledge of the firm and industry

is required for such an exercise, and/or at least a willingness to make reasonableassumptions

A second approach to evaluating lost profits is to use a market-based approach.Damages could be estimated by calculating the loss of sales due to injury andmultiplying that by the stock market valuation of a similar company as a multiple

of its sales If a similar company’s stock price implies a valuation of double thesales revenues, the damage to lost sales will be double This approach eliminates theneed to discount the loss in profits over time but the calculation of the loss in salesraises the same issues as the calculation of the “but for” cash-flow or the “but for”scenario in general A related assets-based approach would calculate the damages asthe change in the book value of assets before and after the infringement Of course,for such an approach to be a sensible one, the analyst must be confident that thechange in asset valuation is a consequence of the abuse and reflects the value ofdamage

Each of these techniques has advantages and disadvantages and they all raise thechallenge of constructing a credible “but for” world Case handlers may have to draw

on the knowledge and industry expertise of an array of professionals such as try experts, accountants, and strategy managers in order to construct a reasonableestimate of such damages

indus-380 7 Damage Estimation

 Cartels increase prices and diminish output causing both a loss in total welfareand also a transfer of welfare from customers to producers Profits go upand consumer surplus will generally go down under a cartel relative to acompetitive market

 The total harm caused by a cartel to its customers consists of a direct effect

on the customers who buy from the cartel in the form of an increase in pricesand also an indirect effect due to the restriction in output on those customerswho decide not to buy from a cartel given its high prices If the cartel sells

an input to downstream firms who then sell on to final consumers, damages

to the downstream firm may be mitigated by the downstream firm’s ability topass on the increase in its costs to final consumers

 In practice, cartel damages are often approximated by the direct damage orthe total amount of the overcharge to the customers This is the increase inprice times the actual quantity sold during the cartel period

 Quantifying the damages will require estimating the price that would haveprevailed absent the cartel When market conditions do not vary greatly, thiscan be done by looking at historical time series and taking the price of the com-petitive periods as the benchmark competitive price during the cartel period

If market conditions do vary over time, one may nonetheless be able to use aregression framework to predict the “but for” prices during the cartel period.Structural simulations of the market are also possible but require reasonableassumptions on the nature of demand and the type of competition that wouldprevail absent the cartel

 Using the trend in the prices of a similar product to infer the price in thecartelized market is also possible, assuming such a benchmark is available.Applying a “reasonable” margin to the cost of the cartelized industry duringthe cartel can also provide a “but for” price when such “reasonable” margincan be inferred from the industry history or other benchmark markets

 Timing the cartel is a necessary part of damage estimation It is best doneusing documentary evidence but evidence of unexplained structural breaks inthe pricing patterns can sometimes also provide useful guidance

 The treatment of the pass-on effect in the calculation of damages depends onthe legal framework The extent of the pass-on will depend on the sensitivity

of the firm’s supply function to the change in costs and also on the demandand supply elasticities that it faces When the output effect is very large, sothat a downstream firm’s profits suffer as they lose the margins that wouldhave been earned on competitive volumes, the ability to pass on cost increasesmay not successfully mitigate the damage suffered by the downstream firm

7.3 Conclusions 381

 In addition to the difficulties in cartel cases, the exercise of quantifying ages in cases of abuse of dominant position (attempted monopolization) isfurther complicated by the difficulty in defining the “but for” world Dynamicand strategic elements which are difficult to incorporate might be particularlyrelevant in such settings For example, suppose a claim for damages weremade following the EU’s case against Microsoft for abuse of dominance Toevaluate the damages suffered by rival firms, we may need to take a view

dam-on the counterfactual evolutidam-on of the computer industry—by any measure anontrivial task

Merger Simulation

Simulating markets in order to predict the unilateral effect of mergers on priceshas seen considerable growth in popularity since the method was refined duringthe 1990s in a series of papers including the famous papers by Farrell and Shapiro(1990), Werden and Froeb (1993b), and Hausman et al (1994) Such exercises,called merger simulations, are used for two purposes First, they can serve as ascreening device In that case a standard model is usually taken as an admittedlyvery rough approximation to the world with the expectation that the merger simulatedwith that model provides at least as good a screen as the use of market shares orconcentration indices alone and hence is a complementary assessment tool to thesesimple methods The second purpose of merger simulation involves building a moresubstantial model with the explicit aim of providing a realistic basis for a “bestguess” prediction of the likely effects of a merger

Although merger simulation is now familiar to most antitrust economists and hasbeen applied in a number of investigated cases, authorities remain cautious in theuse of the results of these simulations as evidence One important reason is thatmost authorities’ decisions are subject to review by judges and the courts have notuniversally embraced merger simulation as solid probative material In turn, thereason for judicial concern is that merger simulation models are based on importantstructural assumptions regarding the nature of consumer demand, the nature offirm behavior, and the structure of costs Evaluating whether a simulation model

is likely to be accurate therefore implies determining the appropriateness of thoseassumptions Unfortunately, there is usually considerable uncertainty regarding theprice-setting mechanism in the market, the nature of demand, and the nature of costs.Yet a model builder must make explicit assumptions about each of these importantelements of a merger simulation model

The alternative empirical approach is to try to use “natural experiments.” In somecases natural experiments will allow an empirical evaluation with fewer explicitassumptions We discussed this important approach in detail in chapter 4 Such

an approach is, however, not always either available or convincing As a result,many investigations use a mixture of theoretical arguments, quantitative indicators,and qualitative descriptions of industry features to decide whether a merger willlead to a substantial lessening of competition (SLC) causing prices to rise Such

8.1 Best Practice in Merger Simulation 383

an approach, as the proponents of simulation models point out, will usually notinvolve stating explicitly the structural and modeling assumptions on which an SLCdecision is based Not stating assumptions is clearly not a satisfactory approachscientifically but it does appear unfortunately to have the legal tactical advantagethat it makes the analysis less prone to challenge At least, this seems to be thecurrent state of affairs At the same time, the appropriate standard of proof for aninvestigation should probably not include the requirement to produce a simulationmodel of the industry with absolutely realistic assumptions On many occasionseither peculiar static or dynamic features of a market would make detailed custom-built simulation modeling extremely difficult Indeed, such a process may often beunrealistic on merger inquiry timescales and budgets, particularly when an authority

is investigating relatively small mergers

Most moderate observers think the bottom line is that a well-designed simulationmodel can potentially be very informative and can even in some cases provide asatisfactory approximation of a merger effect By integrating the results in a broaderanalysis of the qualitative aspects of the industry, merger simulation can providefurther evidence of the effect of mergers on competition Qualitative and descriptiveanalysis can be used to go through the vital task of subjecting any output from asimulation model, such as predicted prices, to careful scrutiny and “reality checks,”

or at least “sanity checks.”

The uncertainty over exactly the appropriate modeling assumptions has a number

of implications First, it will mean that one can never claim to have pinned downwith certainty the effect of a merger Second, it means that measures of uncertaintycalculated under the assumption that the class of models considered includes the

“truth” should probably be treated with appropriate caution And third, consequently,

it will usually be necessary to at least explore the robustness of the prediction todeviations in the assumptions made With these important caveats in mind we turn to

a detailed consideration of simulation models We present first the general rationalefor merger simulation exercises and a simple illustrative example We then provide amore involved discussion going into delving further into the technical complexities.Finally, we discuss the potential use of merger simulation techniques to assess theimpact of a merger on the incentives to coordinate

A merger simulation exercise will produce credible results if certain best practicesare followed.1Those practices relate to the choice of assumptions, to the data used,and to the framing of the results within a broader analysis

Practitioners need to justify their choice of modeling assumptions It is not enough

to use one of the “standard models” and claim that its widespread use justifies its

1 For a discussion on the assessment of merger simulations, see Werden et al (2004).

prod-in the prod-industry Similarly, prod-in prod-industries where we have important technological fusion effects, static pricing models may well miss important dynamic dimensions

dif-of competition For example, firms may want to manage diffusion in order to pricediscriminate, charging the high-value “first adopters” high prices before movingprice down to service the mass market Or they may want to accelerate the spread

of the technology by subsidizing the first users In each case, a simple Bertrandmodel would miss the primary economic factors driving economic outcomes in theindustry

Analogously, in industries where customers really care about the identity of theproducer, be it for quality or institutional reasons, the Cournot model would probablyprovide a poor approximation to reality Other factors that may be important forthe choice of model are the nature of contractual relationships, the identity of thebuyers, the extent of innovation, and the nature of competition either upstream ordownstream In his commentary on merger simulation models, Walker (2005) noteshow, in defending their Volvo–Scania merger simulation, the expert economistspointed out that their predicted margins may have been overestimates of the actualmargins because firms may have sold under the equilibrium price to recoup thelower profits with increased aftermarket sales Walker argues that if this argument iscorrect, then perhaps this pricing behavior should have been captured by the pricingequation in the model (see also Crooke et al 1999) And indeed, in building a mergersimulation model investigators need to constantly remind themselves that they aretrying to capture what would actually happen if the proposed change in industrystructure is allowed The best model may well not be a “standard” one That said,there is obviously a limit to the time and resources available to any investigatorand every model anyone has ever built is only an approximation of reality If thelikely bias in predicted prices can be signed, a simulation model may nonetheless

be informative

Each of these examples suggests that some simulation exercises, perhaps many,will require bespoke industry-specific models If building such models with suffi-ciently good explanatory power proves intractable within the time available for amerger inquiry, then it may be that the analysis should rely on careful and informed,broader, qualitative assessment Some of the time, however, given enough resources,

it will be possible to construct a model that fits the market sufficiently

8.1 Best Practice in Merger Simulation 385

If a merger simulation model is built, then the investigator will have to show that

it predicts the facts of the industry reasonably well In particular, predicted prices,costs, and margin behavior must be consistent with the reality of the industry It

is therefore vital to take the time to refine and check the model sufficiently beforeproceeding to the merger forecasting exercise Methods to check the validity ofsimulation models include both the use of “in-sample” and “out-of-sample” predic-tions Consider, for example, a differentiated products Bertrand model On the onehand, checking the fit of the model in terms of predicted prices within sample will

be useful We may also check “out-of-sample” predictions by estimating the model

on a subset of the data and then using the model to predict prices during the rest

of the sample However, such direct checks are not usually the end of the matter.For example, if estimates of price elasticities are wrong, then a Bertrand model willoften produce negative estimates of marginal costs, which obviously cannot be right.Checking such predictions can provide additional important sanity or possibly evenreality checks

When the theoretical framework is chosen, parameters need to be estimated orcalibrated If there are sufficient market data available, econometric estimation may

be possible and good practice for econometric and regression analysis applies Ifthere are insufficient data or indeed insufficient time available for estimation and themodel is being used solely as a rough-and-ready screening device, then underlyingparameters may be calibrated using the predicted structural relationships betweenobserved variables A poor model will not successfully predict the relationshipbetween observed variables and, with sufficient attention to validity and checking,this will usually become very apparent Of course, the other side of cross checking ismaking sure that the data used are representative and correctly measured In particu-lar, data on margins, marginal costs, or demand elasticities, which may be retrievedfrom industry information, must be checked for consistency and plausibility.Finally, one should keep in mind that most merger simulations currently involvestatic models and do not incorporate dynamic effects Firms may respond to a merger

by issuing new products, repositioning their current products, or by innovating (see,for example, Gandhi et al 2005) Each of these reactions will not be captured by amerger simulation If there is a lot of evidence that the market in question has behaved

in the past in a very dynamic fashion and that the competitive environment is subject

to constant change, the merger simulation exercise will certainly lose relevance forthe medium-term prediction of industry outcomes In those cases, appropriate weightneeds to be given to evidence indicating potential dynamic responses of the market,although these may well be beyond the usual time horizon of a merger inquiry sinceoften we expect entry or other competitive responses to at least mitigate the problemsgenerated by mergers within a few years

In summary, merger simulation results will usually only be one part of the totalevidence base when evaluating the effects of a merger Qualitative analysis of theelements that determine pricing behavior and particularly qualitative analysis of

386 8 Merger Simulation

the aspects of competition not captured by any merger simulation exercise must beproperly incorporated Only when the model used in the merger simulation fits thefacts on the ground and the prediction of the effects is consistent with the rest of theevidence, should a merger simulation be used as part of the evidence Ultimately, theanalyst will want to be solidly aware that judges, rightly, do not like “black boxes”generating evidence, so every effort must be made to make the analysis clear andtransparent

The remaining sections in this chapter explain the rationale of merger simulationusing simple and popular models The purpose is both to outline these popularoptions but also to concentrate on the underlying principles that allow investigators

to undertake customized modeling as well as undertake simulations using thesepopular modeling choices There is little doubt that in the future better modelswill emerge for a variety of particular circumstances In addition, better demandsystems and better approaches to cost estimation will be used to generate genuinelydata-driven answers in unilateral effects merger simulation Experience and a goodunderstanding of the underlying economics will help the investigating economistdiscriminate among the various options and select the appropriate models

This section will use a simple framework to introduce the economic rationale ofmerger simulation and the basic methodological foundations of the exercise To easeexposition we will use a familiar framework Indeed, a major aim of this section is

to put simulation models, which tend to be numerical, into the standard economicframeworks that are entirely familiar to all professional economists and ubiquitoustools for analysis Empirical merger simulation primarily puts those models on acomputer and makes estimates/guesses or “guesstimates” of the parameters of themodels Along the way we hope to make clear the contribution, assumptions, andlimitations of this approach for analyzing unilateral effects of a merger

8.2.1 An Introductory Model: Homogeneous Product Cournot

In industries where the product supplied by the firms is homogeneous, firms compete

in quantities with the aim of maximizing profits, and customers do not differentiatebetween suppliers, competition can be modeled as a Cournot game In this setting,firms choose the quantity of the good that they will produce given the quantityalready supplied by competitors and then offer it at the price determined by aggregatedemand and supply Firms can affect prices with their output decisions and areable to raise prices by restricting output or lower them by increasing production

A merger of undertakings in such a market will have effects that can be easilydescribed Farrell and Shapiro (1990) provide a nice discussion of merger analysis

in a Cournot setting Below, we describe a merger simulation for the very simple

8.2 Introduction to Unilateral Effects 387case of a duopoly merging to monopoly in a homogeneous product market Thesimplicity of this scenario will help illustrate the concepts involved in an empiricalmerger simulation exercise.

8.2.1.1 Mergers in Cournot Industries

In any game theoretic context including Cournot, economists characterize firmbehavior by their best response functions Consequently, simulating the effect of

a merger involves calculating the best response functions for both the pre-mergerand post-merger scenarios and solving for the corresponding equilibrium prices andquantities In the Cournot model, if firms are symmetric in costs, the only differ-ence between the pre- and post-merger scenarios will be the total number of firmsoperating in the market and so this is the variable that will need to be adjusted in thereaction functions Symmetry assumptions simplify analysis because, with N play-ers, N reaction functions arising from a Cournot model become just one equation

to actually solve since all reaction functions are identical If firms are neous, we will, in general, need to solve for equilibrium quantities by solving all Nreaction functions We will see this process in action a number of times during thisintroductory section

heteroge-Whether firms are assumed symmetric or not, we will need an estimate of marginalcost(s) as well as parameters of the market demand Once these parameters areestimated, we can compute the pre-merger quantities and profits using the reactionfunctions of a market corresponding to the number of firms existing in the pre-merger world We then compute the post-merger quantities and profits To illustrate,consider the case of a merger in an industry with only two firms, we would justcompare the output and prices emerging from a Cournot duopoly, the pre-mergersituation, with the output and prices of the monopoly that would exist post-merger

We develop the analytical model for a two-to-one merger in a homogeneousproduct market where the strategic variable involves quantities

The pre-merger model Let us consider the case of a duopoly Profit maximization

involves choosing the optimal quantity given the demand function, the rival’s output,and the costs facing the firm:

max

q j

˘j.q1; q2/ D max

q j.P q1C q2/
mcj/qj;where the subscript j represents either firm 1 or firm 2 and where we assume constantmarginal costs The first-order condition for maximization is

The post-merger model Suppose now that the two firms merge to form a monopoly

with two plants Profit maximization by the new firm now takes into account theprofits of both plants In assessing the profitability of a price increase, the change inrevenues from the sales at the second plant will now also be taken into account:max

q 1 ;q 2

˘1.q1; q2/ C ˘2.q1; q2/

D max

q 1 ;q 2.P q1C q2/
mc1/q1C P q1C q2/
mc2/q2:

In modeling the post-merger world we must always decide what happens to ferences across firms when they merge Here each plant has a different constantmarginal cost and a monopolist would profitably choose to shut down one plant, theinefficient (high marginal cost) one For simplicity, but also perhaps for realism, inthis first example we therefore set marginal costs to be the same for both plants andequal to the lower of the two, suppose mc1 This would, for example, be the case ifbest practice is transferred across to the second plant or, in this constant marginalcost example, if the second plant were entirely shut down and all production used themore efficient plant (We will see that this is not necessarily true when marginal costsare eventually increasing in output at a plant More generally, if each plant faces

dif-8.2 Introduction to Unilateral Effects 389

an increasing marginal cost function, then a monopolist will allocate productionefficiently across the plants to minimize total costs of any given level of production.Since Cournot is a homogeneous product model there is no demand-side return tokeeping both plants open but there may be a cost advantage in the presence of dis-economies of scale at the plant level.) In that case, the firm’s profit-maximizationproblem simplifies to

This result suggests that post-merger quantities will be lower than pre-mergerquantities and prices will be correspondingly higher post-merger

If firms are not equally efficient pre-merger, the situation is slightly more complex,and quantities will reduce post-merger if a > 2mc2
mc1D mc2C mc2
mc1/.That is, if the consumer’s valuation of the first unit of demand is larger than themarginal cost of producing it at plant 2 plus the efficiency gain from producing it atplant 1 post-merger This particular result is obviously dependent on the linear form

of demand assumed, but it is indicative of the general result that cost reductionsarising from a merger can reverse the general result that mergers result in higherprices and reduced output We explore the effect of this “efficiency defense” below

We also examine the situation where marginal costs increase in output below In that