Demand-driven integration and divorcement policy

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Contentslistsavailableat ScienceDirect

International

Journal

of

Industrial

Organization

www.elsevier.com/locate/INDOR

Demand-driven

integration

and

divorcement

policy

✩

Patrick

Legros

a,b,∗

,

Andrew F.

Newman

b,c

a_{Université libre de Bruxelles (ECARES), Belgium; and Northeastern University,} United States

b_CEPR,_London,_UK c

BostonUniversity,UnitedStates

a r t i c l e i n f o Articlehistory: Availableonlinexxx JELclassiﬁcation: D23 D43 L2 L4 L5 Keywords: Theoryoftheﬁrm Reversecausality Verticalintegration OIO Regulation Antitrust a bs t r a c t

Traditionally, vertical integration has concerned industrial economists only insofar as it aﬀects market outcomes, par-ticularly prices. Thispaperconsiders reversecausality, from

prices– andmoregenerally,fromdemand– tointegrationin amodelofadynamicoligopoly.Ifintegrationiscostlybut en-hancesproductiveeﬃciency,thenatrendofrisingpricesand increasing integration could be due to growing demand, in whichcaseadivorcementpolicyofforceddivestituremaybe counterproductive.Divorcementcanonlyhelpconsumersifit underminescollusion,butthentherearedominatingpolicies. We discuss well-known divorcement episodes in retail gaso-lineandBritishbeer,aswellasotherevidence,inlightofthe model.

✩ _This _paper _has _beneﬁted _from _comments _by _seminar _participants _at _{Université libre} _{de Bruxelles,}

CRESSE 2014,Tilburg university(TILEC)and ParisDauphine.The authorsare grateful tothe Editor and the referees fortheir comments.Legros gratefully acknowledges support of the European Research Council (AdvancedGrant339950).

∗_{Corresponding}_author_at:_{Université libre}_de_Bruxelles_(ECARES),_Belgium._Tel.:₊₃₂_26504219;_fax:₃₂

26504475.

E-mailaddress:[email protected] (P.Legros).

http://dx.doi.org/10.1016/j.ijindorg.2016.04.007

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1. Introduction

A regulator observes that the firms in an industry he suspects of being imperfectly competitivehavebeenverticallyintegratingovertime.Armedwiththetraditionaltools ofindustrialeconomics,hereckonsthateitherintegrationisoccurringbecauseitenhances theproductiveorallocativeefficiencyofthefirmsintheindustry,orbecausethefirmsare attemptingtoenhancetheirmarketpower.Efficiencygainscanarisebecauseintegration orverticalrestraintshelptheverticalchaintointernalizesomeexternalities(e.g.,double marginalizationorfreeridingbydistributors),inwhichcasepricesoughttofall. Market powerenhancementcouldbeduetoforeclosure (increaserivals’costs,refusaltosupply) ortoincreasedabilityforverticalchainstocollude;eitherway,pricesshouldriseeitherat thewholesaleorretaillevel.1_Hence,_theory_suggests_that_integration_may_lead_to_higher or lower prices depending on whether the dominant effect is foreclosure or efficiency. Telling the differenceis straightforward: if prices arefalling with integration, efficiency effectspredominate.Iftheyarerising,likely thefirms aresucceedinginenhancingtheir marketpower.

Inthecaseofdecreasingprices,theregulator,whosemainconstituencyisconsumers, has little reason to be concerned. In the other case, though, the regulator might be temptedtoinvokea divorcementpolicyinordertolimittheapparenteffectsof integra-tion,either byinterveningin thecontrol structureoftheproductionchain (forinstance byorderingfranchisegasolineretailersratherthantheirsupplyingrefinerstomake pric-ingdecisions)or,moredrastically,byorderingassetdivestitures(asintheforced saleof pubs bythe brewersthat own and supply them).2 _Being _a _practical _person _mainly in-terestedin effectivepolicyimplementation,theregulatorisnotapttoasktheseemingly academic question of why integration hasincreased recentlyrather than some time in the distant past;the issue is how to actgiven the risein prices.(Inthe case offalling prices,the regulator mighttake reasonable comfort in chalking itup to changes in the technologyofproductionordistribution.)

Butasisoftenthecase,therearedangersinavoidingtheacademicquestions.Indeed, inoft-studiedcasesinUSretailgasolineandBritishbeer,regulatorsimposeddivorcement policies following long periods of increasingintegration and risingprices. Whatensued

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Seee.g.,LafontaineandSlade(2007);ReyandTirole(1997);Riordan(2005).Onbalance,theempirical literature tends to provide support for the eﬃciency eﬀect of vertical integration or vertical restraints (Cooperetal.,2005;LafontaineandSlade,2008).

2_The_terms_dissolution,_divestiture_and_divorcement_are_often_used_{interchangeably.}_The_following_excerpt

fromOppenheim(1948)– citedinAdams(1951) – clarifiesusage:“divestiturereferstosituationswherethe defendantsarerequiredtodivestthemselvesofproperty,securitiesorotherassets.Divorcementis[...]used toindicatetheeffectofadecreewherecertaintypesofdivestitureareordered.Itisespeciallyapplicableto caseswherethepurposeoftheproceedingistosecurereliefagainstanti-trustabusesflowingfrom[vertically] integratedownershipandcontrol.Theterm‘dissolution’isgenerallyusedtorefertoanysituationwherethe dissolvingofanallegedlyillegalcombinationorassociationisinvolved,includingtheuseofdivestitureand divorcementasmethodsofachievingthatend.Whiletheforegoingdefinitionsdifferentiatethree aspects ofremedies,thetermsarefrequentlyusedinterchangeablywithoutanytechnicaldistinctionsinmeaning.” WethankYossiSpiegelforsuggestingthisreference.

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wasasurprisingcontinuation ofrisingpricesinsteadoftheexpectedfall. Whatismore, ﬁrms’proﬁtabilityfell,despitethepriceincreases.

Standardindustrialeconomictheorieshaveahardtimeexplainingtheseepisodes,but they make sense in the light of more recent developments in organizational economics, which has traditionally been concerned with the causes of integration more than its consequences (at least for the market). Ina nutshell, the combination of rising prices, increasingintegration,andreducedprofitswithcontinuedrisingpricespost-divorcement canallbeattributedtoefficiencyeffects along with rising demand :inthisview,causality runs from demand to integration, rather than from integration to market outcomes. The basisforthis explanationis verysimple.Ifintegration indeed increasesproductive efficiency– aviewthatalsohasseveral,sometimescompeting,sometimescomplementary, foundationsinorganizationaleconomics– thenitfollowsfrommaximizingbehaviorthat demand conditions must influence the integration decision. For if integration is costly, as ithastobe,else firmswouldalwaysintegrateto themaximumpossible extent,then theproductivitygainitoffersisonlyworththecostwhentheextraoutputproducedis sufficientlyvaluable,namelywithhighdemand.Ifdemandislow,thecostofintegrating outweighs thebenefit,andthefirmremainsnon-integrated.

Theinﬂuence ofdemandonintegrationisat theheartofa recentpaper(Legrosand Newman,2013),whichconsidersthecaseofperfectcompetition,wherethelogicismost transparent. Inthiscase, therole ofdemand isrepresented entirely bytheprice ofthe ﬁnal product that aperfectly competitivesupply chainfaces. Thegist of theargument can be madeinthefollowing reducedformmodel.Supposethat achain’s technologyis represented bythecostfunction

φ( d )c (q) + h (d ),

where q isoutputand c (q )isastandard costfunction;weassumethatthereare eventu-allydiminishingreturnstoscalesothatthischain isnotabletoserve theentiremarket at constant marginal cost. Thechoice variable d isthe d egree or d epthof vertical inte-gration,forinstance,thenumberofunitsinthesupplychainthatbelongtoasinglefirm withtherestremainingstand-alonefirms.3_The_function_φ(_d₎_represents_how_integration affectsproductiveefficiency; h (d )representscostsofintegration.Examplesoftheformer include improved coordination(Hart andHolmström, 2010);bettermultitasking incen-tives (Holmström and Milgrom, 1991); alignment of control and incentives (Grossman andHart,1986;HartandMoore,1990);orreductionsinthecostsoftransactions, adap-tation,oropportunism(Kleinetal.,1978;Williamson,1971;1975).Inmanycases,costs

h (d ) can be generated by the same factors: incentives over multipletasks are diﬃcult to balance, and ceding control often means exchanging one incentive problem for an-other, resultingindecisions that arediﬃcultforsome partiesto achievegiventraining,

3_This_is_a_drastic_{simpliﬁcation,}_since_combinations_of_the_members_of_the_supply_chain_into_several

non-singletonﬁrms,letalonerecombinationsacrosssupplychains,arenotallowed.Butitisenoughtomake thepoint.

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priorinvestments,orvision.Ortheymayresultfrom maintainingacommunicationand monitoring infrastructurewithinthefirm.4 _Assuming_that _the_chain _chooses_d_and_q_to maximizeits(joint)profits P q − φ(d )c (q) − h(d )givenmarketprice P ,afirstobservation is that P affects the choice of integration level, justas it affects the choice of quantity produced, because itis a parameter of anoptimization problem. To be more concrete, assumethat φ( d )is decreasing and h (d ) increasing.Then profitis supermodular in the choices(d , q )andhasincreasingdifferencesin(P , q ).Asaresult,optimal q andtherefore optimal d increasewith P :whenoutputismore valuable,andthechainthereforewants toproducemore ofit,itisworthinvestingmorein thereducedcostsofdoingso.5

Now consider the policy maker’s conundrum. If demand was increasing over time (and not compensated by entry), then price would be rising. This wouldinduce firms to integrate more; their costs would be lower and profits (both net and gross of the integrationcost)higher.Eachfirmwouldsupplymore(butnotsomuchthattheindustry price would be reduced to its previous level, else firms wouldreturn to their previous integrationandsupplylevelsleadingtoexcessdemand).Thenewequilibriumpricewould behigher,butrather despite integrationthanbecauseofit.Forifthepolicymakerforced firmstoreduceintegrationtosomepriorandlowerlevel,theircostswouldrise,industry supply would be lower and the price even higher. This outcome is evocative of what happenedinthegasolineandbeerepisodesthat wedocumentinSection 4.

Of course, there are important diﬀerences, notleast that neither of these industries appearedtobe prima facie competitive.Extendingtheperfectlycompetitiveframework toanoligopolisticoneisthetaskofthispaper.Wearenotattemptinganysortof gener-alityhere,onlyenoughto highlightsome oftheissues.Weconsider amodel ofCournot competitionamongsupplychainsthatcan choosethelevelofverticalintegration,which reducestheirmarginalproductioncost.Thisisanappropriatesettingtoaddressanother policy concern – expressed for example by policy makers in the British beer case – of whetherandhowintegrationfacilitatescollusionamongthesechains,aswellhowpolicies that regulatehowintegratedaﬀectindustryperformance.

1.1. Summary of ﬁndings

Thefirstobservationisthatthereisaconflictofinterestbetweenfirmsandconsumers concerning thelevel of integration: as in other efficiency models, consumers wouldlike

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Typically in organizationalmodels, at least partof the costs or benefits of integrating are private, unobservable,andinanycasenon-contractible.Practicallyspeakingthismaymeanthattheywillbedifficult forthe empirical investigatoror policymakerto observe. Inparticular adistinction between gross(i.e. revenueminuscostsofmeasuredinputs)profitabilityandnetprofitability(grossprofitsminusintegration costs)isworthbearinginmind.

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Tobesure,insomemodels,particularlythoseinwhichincentivesplayarole,theextentoftheefficiency gains, orthe costs ofintegrating, may depend onother variables besidesd, suchas theprice Por the distributionoftheprofitsamongthevariousproductionunits.ForinstanceinLegrosandNewman(2013), boththeintegrationbenefitandtheintegrationcostdisplaydecreasingdifferencesin(d, P), butthenet effectisthatdisalwaysincreasinginP.Othermodelsoffirmsmayhavenon-monotonicpredictions;indeed, thedifferencesacrossmodelscouldenablemarketdatatoserveasaprovinggroundfororganizationtheory (LegrosandNewman,2014).

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there tobeahigh degreeofintegration,sincethattendstowardlowcostsandtherefore low prices. But from the point of view of the firms in the market, there is too much integration: each firm confers a negative externality on its rivals when it integrates, because thecost reduction resultsin business stealing. In equilibrium, while measured profits may be substantial due to low marginal production costs,net profits that take account ofthecostofintegration(butat leastinsome oftheinterpretationsalluded to above wouldbedifficulttomeasure),will below.

Second, asin theperfectlycompetitivecase,demand plays a rolein determiningthe integration decisions that ﬁrms make. Increasing demand always increases integration. But whether itis accompaniedby rising or falling prices depends on whichparameter ofthe(linear)demandisshifting.Consistentwiththemodel,co-variationofintegration and price is notalwaysobserved: indeed the beer and gasoline casesappear somewhat unusual inthetrendsthatledto thepolicyresponses.

Third,wecanaddressthequestionofwhetherintegrationservestofacilitatecollusion, which seems to have been a particular concern for regulators in the British beer case (Spicer et al., 2012). A first answer is not at all: as we have suggested, the industry notonlyhasacollectivemotivetorestrictoutput,but alsotoreduce integrationlevels. Indeed,iftheyareabletosustaincollusionthroughrepeatedinteraction,thentheywill choosea lower integrationlevelthantheywouldinthenon-collusiveCournotequilibrium. Inthismodel,atleast,highlevelsofintegrationserveassignsoflowlevelsofcollusion.6 But there is a sense in whichintegration can support collusion. Forthe punishment inflicted ona deviatorfrom acollusivestrategyprofileinwhichlowlevelsofintegration andoutputarebeingsustainedistoreverttothehigherintegrationandoutputlevelsof Cournotequilibrium.Ifintegrationwereexogenous,oratleastcappedatalowlevel,this punishmentwouldnotbesosevere,andcollusionmoredifficulttosustain.Bythreatening the very low Cournot payoffs that integration affords, it is the possibility, rather than thereality, ofmoreintegrationthat helpssustaincollusion.

Our fourth finding concerns theeffects of divorcement policy, modeled as a binding cap on integration that is below the current level, and therefore requires divestment of assets.It follows from the over-investment result that if the industryis in the non-collusiveequilibrium, thendivorcementtypically helpsfirms.Consumersarenothelped bythis, ofcourse,becausemarginalcostsandthereforepricesrise.

If,however,theindustrywascolludingbeforethedivorcementpolicyimplementation, thentwothingscanhappen.Eithercollusioncontinuesanyway,inwhichcaseconsumers are harmed relative to the pre-divorcement outcome because marginal costs have in-creased,oritisundermined, becausetheCournotpayoﬀ isnowrelativelyhighanddoes not constitute an adequatethreat against deviation. This provides a potential beneﬁt to consumersthat wouldin generalhave tobeweighedagainsttheincreasein marginal

6_To_be_sure,_a_collusive_industry_that_experiences_rising_demand_would_increase_its_level_of_integration,

justasamonopolistwould.Butanon-collusiveindustrywoulddothesame,andwouldalwayshavehigher levelsofintegrationthanthecollusiveone.

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costsresultingfrominefficientorganization.However,asdiscussedinthefinalsectionof the paper, which considers the gasolineand beer divorcement episodes in more depth, itdoesnotappear ineithercasethatthetrade-off betweencollusionandorganizational inefficiencywasmanagedtoconsumers’benefit.

This is not to say that leaving industries unregulated is optimal. We discuss more generalintegration regulationsthat place caps onintegration that neednotforce firms to divest. These may still destabilize collusion by increasing the Cournot payoff, but wouldhavelessdetrimentaleffectsoncostsincasetheydonot.7

1.2. Links to the literature

Ourmodel is similarto models of investmentin costreduction,where thereduction inthemarginalcostofproductioncomesattheexpenseofahigherfixedcost(seeVives, 2008forarecentsurvey),andinastaticworld,therewouldbeindeedverylittledifference in interpreting d as an investment in process innovation or degree of integration. The differenceofinterpretation isimportantwhenweconsider dynamicsandcollusionsince we willassume thatthe costreduction istemporary and thereforereversible:firms can choosethelevelofintegrationeachperiod.Thisassumptionofreversibilitywouldbehard torationalizeinamodelwherethecostreductionisduetoinnovation.Theassumptionis natural,however,in anorganizational contextsincefirms candivest assets,or integrate more assetseachperiod.8

Thechoice of d affectstheabilityoffirms to compete,sinceitmodifiesthemarginal cost,butdoesnotmodifythedemandfortheproduct.If d couldalsomodifythequality oftheproducts,therewouldbeademandeffect,asinSutton(1991),withtheimportant caveatthat thecost h (d )isnotsunkbut fixed.

There issurprisingly little literatureontacit collusionwhenﬁrms make investments thataﬀectcosts(ordemand)beforecompetitionontheproductmarket.Anexceptionis Nocke(2007)whichconsiderscollusioninasunkcostindustry;investmentspermanently modifythedemand fortheproducts.Thisisnotthecasein ourworldsinceintegration decisions arereversible.SeealsoSchinkelandSpiegel(2016) inthis volume.

Our resultshelp us understand the role that organizational design can play in tacit collusion,andhighlightthattheremaybecostsandfewbenefitsofforcingfirmstodivest even after observing covariation of prices and integration. They should not, of course, beinterpretedasimplyingthatdivestmentandotherformsofintegrationregulationare never desirable. For instance when vertical integration may lead to input foreclosure, divestitures may be pro-competitive (Sibley and Weisman, 1998; Vickers, 1985). But policymakersoughttobe awarethat upwardtrendingpricesand profitsin thewakeof

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Thepossibilitythatregulationmayenhancewelfarebylimitingcollusionthroughrestrictionsthatonly bindoﬀ theequilibriumpathhasbeenobservedinothercontexts;seeChassangandOrtner(2015).

8_Clearly,_transaction_costs_in_the_market_for_trading_assets_will_limit_{reversibility;}_something_we_ignore_here

butwouldberelevantinageneralanalysis.Theassumptionwemakeisinlinewithorganizationaltheories suchasthe“propertyrights” literature,whichemphasizetheprivate andincentivecostsofrelinquishing controlrightsunderintegration.

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integration need not be the resultof foreclosure. As has been notedin other contexts, caution must be exercised in the design of policies that regulate vertical relationships (Cremer etal.,2007;Fiocco,2011;HöﬄerandKranz,2011;KarlandLegros,2015). 2. Amodelofintegration

We consider an industry populated by vertical supply chains that are isolatedfrom each other exceptat thefinal downstream stage, where theysellin a commonmarket. Intermediategoodsalongthesupplychainhavenomarket.Thisportraitoftheindustryis mainlyforsimplicity,butitisalsointhespiritofmuchoftheorganizationliteraturethat emphasizes “relationshipspecificity.” Anexamplewouldbecoal-firedelectricgenerating station locatednextto a coalmine: coaliscostly totransport and lowin value,so the mine’smarketislimitedprimarily tothepowerplant,buttheelectricitycan besoldin a nationalmarketviathepowergrid.Ourreducedformmodel isconsistent withricher theoriesofintegration, e.g.,LegrosandNewman(2013).

Thetiming ofthemodel isasfollows:

• Thereare n downstreamproducersindexedby i or j ,andeachmakesadecision d to integratewithsuppliers(wedonotconsiderhorizontalintegration).

• Integrationdecisions areobservedandﬁrmschoose thequantitytoproduce.

• Theproductmarketclears,thatisif Q isthetotalquantityproducedbytheﬁrmsthe priceonthemarketis P (Q ):= a − Q, thepriceequaltovalueoftheinversedemand functionat Q ,where a > 0.

If thedegreeofintegration ina firmis d ∈[0, d ], andthequantityproducedis q ,the cost borne by the firm is C (q ; d ), where to simplify the analysis we use the following specification:

C( q; d ):=(c − d)q +d 2.

ToinsureaninteriorsolutioninthechoiceofintegrationintheCournotgame,weassume that c isnottoo smallwithrespectto a :

c < a < (n +1) 2

n c. (1)

Thecost d 2_is_best_thought_of_as_{“ﬁxed” and}_independent_of_output_or_price._Firms_make

a decisiononthedegreeofintegration d andthehigher d isthelarger aretheﬁxedcost

d 2 andthereductionofmarginal cost c − d.Thekeyfeatureof ourspeciﬁcationforour resultsis that thecostfunctionhasnegative crosspartials in d , q ,that is themarginal costofproductionisa decreasingfunctionofthedegreeofintegration.

2.1. Cournot equilibrium

Weconsidersubgameperfectequilibriainintegrationdecisions{d i},whicharefollowed

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choicesofintegrationbyallfirmsin theindustrybecausethemarginalcostsoffirms are affectedbythese organizationalchoices.

For a given proﬁle of integration decisions d :=(d 1, . . . , d n), the continuation game

is a standard Cournot game with marginal costs {c − di, i =1, . . . , n }. Therefore the

quantities, price, and proﬁt levels are (sums are over j =1, . . . , n inclusive of i unless otherwisenoted): q _i∗(d )=a − c− jd j+(n +1)d i n +1 , Q ∗₍_d₎₌ n (a − c)+ jd j n +1 , P (Q ∗(d ))=a +nc − jd j n +1 .

TheequilibriumCournotprofit(grossprofitlessthefixedintegrationcost d 2

i)is: π_i∗(d )= a − c−_jd j+(n +1)d i 2 (n +1)2 − d 2 i. (2)

Notethattheorganizationalchoicesarestrategicsubstitutesinthefirststagesinceπ∗_i(d ) hasnegativecrosspartialsin(d i, d j).Henceiffirm i expectsotherfirmstointegrateless,

itwillintegratemore.

Whenfirms choose theirintegrationstructure, theyanticipate theequilibrium profit function(2).Because themarginal grossprofitis ₍_n₊₁₎2n 2(a − c−

jd j)+2nnd+1i, as long

as a − c is positive, some ﬁrms will choose positive integration in equilibrium because the marginal ﬁxed cost is equal to zero when d =0. Equilibrium is characterized by a non-singularlinearsystem,forwhichtheuniquesolutionissymmetric:

d ∗= n (a − c)

n 2₊_n₊₁; (3)

assumption(1)ensuresthat d ∗ < c .

Lemma1. Under assumption (1), there exists a unique subgame perfect equilibrium. Each ﬁrm chooses a degree of integration

d ∗= n (a − c)

n 2₊_n₊₁,

produces q ∗= _n2n₊+1_n₊₁(a − c) and the industry market price is P ∗=

a+n(n+1)c n2₊_n₊₁ .

Theintegration decisionbyan individual firmimposes anexternality ontheothers. To see this, consider Π∗(d ), the per-firm profit when all firms use the same degree of integration d andthenplayCournot:

Π∗(d )= (a − c+ d )

2

(n +1)2 − d

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A “Cournot planner” whochooses the(common) levelofintegration d P _for_each_chain,

assuming they go on to play Cournot equilibrium in quantities, regards the marginal beneﬁt ofintegration as 2(₍a_n−c₊₁₎+d2P), andequatesthisto themarginalcost ofintegration

d P_:

d P = a − c

n (n +2).

But from (2), eachfirm regards the marginal benefit as n times larger, because a cost reduction notonlyexpandsthemarketfortheindustry, butincreases themarketshare ofthatfirm.Thisbusiness-stealingeffectimpliesthatCournotcompetitorsover-investin integration(fromtheirpointofview,ofcourse– consumerswouldnotagree),whichisan additionalmotiveover andabove theusualoutputrestrictionmotiveforcollusion.The business-stealing effect is especially severe in ourspecification, as simplealgebra shows that Π∗(0) > Π∗(d ∗).Other properties of thefunctionΠ∗(d ∗)are summarizedhere, as theywillbe usefullater.

Proposition1. Cournot-competing supply chains over-invest in integration in equilibrium: the net proﬁt Π∗(d ) they obtain when integrating at a common level d is a strictly concave function on [0, d ∗] with interior maximum at d P _{< d}∗ _{and minimum at d}∗_.

2.2. Collusive outcome

We think ofcollusionas sustained in a repeatedgame with commondiscount factor

δ, whereﬁrmschooseintegrationaswellasquantitydecisions(d i, q i)everyperiod,since

theyareboth reversibleand costlyforaslong asthesupplychain isoperating.Wewill assumethatcollusionleadstothemaximumper-firmprofitabsentside-payments.That is, weassumethat firmscolludeon

(d M, q M):=argmax

d,q (a − nq− c+d )q − d

2_,

Thetwo ﬁrstorder conditionsare q = a−c₂_n+d and q =2d, implyingthat

d M = a − c 4n − 1, q M ₌ 2(a − c) 4n − 1 , P M ₌2n − 1 4n − 1a + 2n 4n − 1c, (5)

and themaximumcollusiveproﬁtis

ΠM(d M):= (a − c+ d

M₎2

4n − (d

M₎2₌(a − c)2

4n − 1 .

Observethat d M_>_dP_:_the_reason_is_that_marginal_returns_to_integrating_under_monopoly

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The repeated game in (d M_,_qM₎ _is _somewhat _{non-standard,}_since _the _stage _game _is

itself dynamic: firms choose integration first and then, upon observing the integration structure in theindustry, choose theirquantities. Forthis reasonwe are explicitin the waythetrigger strategyisdefined.

• Attime 1,

• Eachﬁrm i chooses d i.

• Ifforeach i , d i= d M, ﬁrmsplay q i= q M.

• Ifforsome i , d i = d M,ﬁrms playtheCournotequilibriumaction q i(d).

• Fortime t ≥ 2, deﬁne a historyto be collusive ifateachpreviousperiod,every ﬁrm chose(d M_,_qM_);_otherwise_the_history_is_{non-collusive.}

• Ifthehistoryiscollusive,play d M_._Once_d_is_observed_play_qM_if_d

i = d M foreach

i ;otherwiseplaytheCournotquantity q ∗_i(d ).

• Ifthehistory isnon-collusive,play d i= d ∗.Foreachobserveddplay theCournot

quantity q _i∗(d ).

Therearetwoincentivecompatibilityconditions:ﬁrst,aﬁrmmustnotwanttochange its organization (degree of integration) to d i = d M and immediately face the Cournot

proﬁts π∗_i(d M_e

−i, d i) and, second, a ﬁrm must not want to change its output given

(d M_e_,_qM_e

−i).Hereeisavectorof1’s;thenotation x e(x e −i)denotesthatallﬁrms(all

ﬁrms but i )areplayingthesameaction x .

Let Πdev_d (d ˆ):=maxdπi(d ˆe −i, d )=maxd{(a−c−(n−1)dˆ+nd) 2 (n+1)2 −d

2_} _be _the _maximum _proﬁt

withina period a firmcouldhave bydeviating to d =d ândfacingimmediate Cournot competition when all other firms choose d ˆ. From the remark following Eq. (2) about thestrategicsubstitutabilityoftheintegrationdecisions,theoptimaldeviationifd < d ˆ ∗

exceeds d ∗andtherefored ˆ.

LetΠdev_q (d ˆ):=maxq(a − c+d ˆ− (n − 1)q ˆ− q)q − ˆd 2 bethemaximumproﬁtwithina

period a firm can achieve by integrating to the level d ˆbut subsequently deviating in quantityfrom thecollusivequantityq ˆchosenbytheother firms.(Thenotationreflects thatthedeviationprofitonlydependsond ˆ, becausewealwaystake q ˆtobetheoptimal monopolyquantitygiventheintegrationleveld ˆ.)

Whena firmdeviatesupward from d ˆ= d M, it gainsa competitive advantagedueto alowermarginalcost,butthisbenefitissignificantlyreducednotonlybytheadditional fixed cost, but also by an immediate change of conduct by the other firms: following this deviation in integration, firms will immediately shift to Cournot play, so that the cost reduction benefit is obtained only over the relatively small Cournot quantity. By contrast, by going along with thecollusive integration decision d M_, _a _firm_can _deviate

inquantity,temporarilygaining alargeshareofthemarket,whilefacingonlyadelayed punishmentbytheotherfirms.Indeed,explicitcomputationofthevaluesofthedeviation profitsdefinedaboverevealsthatdeviatinginquantitywhilebeingobedientinintegration

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bringsa highergainthandeviatingin integration: Πdev_d (d M)≤ 9n 2 (2n +1)(4n − 1)2(a − c) 2 ₍₆₎ Πdev_q (d M)= n (n +2) (4n − 1)2(a − c) 2_. ₍₇₎

(In(6),therighthandsideiscomputedforaninteriorsolution,whichisnotguaranteed by(1);theinequalityallowsforthepossibilitythattheoptimaldeviationisatacorner.) Because Πdev

q (d M) > Πdevd (d M) and following either type of deviation ﬁrms play (d ∗,

q ∗) in all subsequent periods, the binding incentive constraint is the one for quantity deviation.

Lemma 2. The maximum proﬁt a ﬁrm can obtain when deviating is Πdev_q (d M).

Inequilibrium,ﬁrmsproduceq M ₌ a−c+dM

2n , andthereforethebestdeviationfromthis

outputistheonethatachievesΠdev

q (d M).ThereisanincentivetodeviateifΠM(d M) <

(1− δ)Πdev q (d M)+δΠ∗(d ∗), that iswhen: δ < δno(d M, d ∗):= Π dev q (d M)− ΠM(d M) Πdev q (d M)− Π∗(d ∗) , (8)

wherewemakeexplicitthefactthatthecutoﬀ discountfactordependsontheintegration level chosenundercollusionand underCournotbehavior. Itis straightforwardto check that thecriticaldiscount factor δno₍_dM_,_d₎_is_decreasing _in_its_second _argument_for_{d >}

d P _(since_Π∗₍_d₎_is_decreasing_in_that_range)._This_property_of_the_critical_discount_factor

plays akeyrolein ouranalysisofpolicyinthenextsection. 3. Demandchanges anddivorcementpolicy

Inspection of the outcomes under Cournot and collusion (Lemma 1 and expression (5)) shows that when ﬁrms do not expect to collude, they will integrate more: d ∗=

n(a−c)

n2₊_n₊₁ > d M = ₄a_n−c₋₁ for n > 1. In addition to this level eﬀect on integration, ﬁrms’

conduct modiﬁeshow sensitiveintegration is todemand shocks,and Cournot behavior leads tolarger changesin integrationthancollusivebehavior since dd_da∗ > dd_daM.

However, while increases in a result in higher integration levels, they generate two opposite forcesonprices.By themselves,these demand shiftswouldincreaseprice.But thereisacountervailingeﬀectbroughtonbytheinducedreductioninmarginalcost. Nev-ertheless,itisclearfrom theequilibriumvaluesinLemma1andexpression(5)thatthe demandeﬀectdominates,andthepricesunderCournotcompetitionandundercollusion tomonopolyarebothincreasingin a – thevariationis _n2₊1_n₊₁ forCournotand 2₄n_n−1₋₁ for

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Cournot). Because integration also increases when a increases, we have a co-variation betweenprice leveland integration. Noticethat in the standard model withexogenous marginalcost,thevariationinpricedueto a wouldbe larger thanitishere: _n₊₁1 inthe Cournot case, 1

2 under collusion. Thus price increases in our model are notcaused by

integrationatall,and indeedbecauseofitaresmallerthantheywouldotherwisebe. Proposition2.

(i) Rising demand in the form of increasing a generates a higher degree of integration, both under Cournot and under collusion.

(ii) Price and integration co-vary in response to changes in a.

(iii) Integration is more responsive, and price less so, under Cournot than under collu- sion.

Note that in terms of elasticities rather than rates of change, price is more elastic under monopolythanCournot, butintegrationisequally elasticin thetwocases.

If the demand curve is P = a − bQ, the eﬀects of changes in a are as before. But increases in demand that take the formof reductions in the“market size” parameter b

have somewhatdiﬀerent eﬀects. On the one hand,integration increases, as long as in-teriorsolutions exist (thisrequires b > ₍_n₊₁₎n 2 in thecaseofCournot and b >

1 4n in the

case of collusion). On the other hand, in neither casedoes price increasewhen b falls: if integration were held ﬁxed, thefall in b wouldnot leadto a pricechange (as in the standard modelwith lineardemand andconstant marginalcosts),but sinceintegration does increase, costs fall, and therefore both the monopoly and Cournot prices fall in equilibrium. Thus changingdemand doesnotalways generateco-variationin priceand integration. Of course, neither is such co-variation universally observed. It is the pos-sibility of such co-variation under demand-driven integration that we are pointing out here.

Tosimplifytheremainderoftheexposition,weassumethatthereisaone-timedemand shift in the form of an increase in a .9 _We _also _assume _there _is _no _change _in _conduct following thedemand increase.10 _Let_us_assume _that_upon _observing_this _joint_increase in price and integration, the regulator puts more weight on the potential foreclosure effect ofintegration thanonitsefficiency benefits, and decidesto regulate theindustry by preventingany integration above some level d r that we always take to be less than

d ∗ (else the policy hasno bite). In other words, the regulator believes that the causal relationship ﬂowsfromintegrationtoprices.

9_A_full_analysis_of_collusion_under_general_shifts_in_demand,_b_o_oms_or_busts,_in_the_context_of_a_two_stage

staticgamelikeoursisbeyondthescopeofthispaper.SeeforinstanceRotembergandSaloner(1986) and

Kandori(1991) forananalysis ofrepeatedgameswithvariabledemandwhenthereisa one-dimensional strategicvariable.

10_One_can_check_that,_as_each_of_the_three_net_proﬁt_expressions_in_Eq.₍₈₎_are_expressible_as_functions_of ntimes(a− c)2_,_δno₍_dM_,_d∗₎_is_independent_of_a_._Thus_increasing_demand_has_no_impact_on_the_feasibility

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We willfirst considerhow theregulationaffects play assuming there isno changein conduct (i.e.,collusionorCournot).Usingtheseobservations,wederivehowthecritical discountfactor δno(·,·)isaffectedbypolicy,whichallowsustodeterminewhetherthere can bea changeofconduct.Finally,weput thesepiecestogethertoassesstheeffectsof divorcement andotherpoliciesthatregulate thedegreeofintegration.

SupposeﬁrstthatﬁrmsplayCournotbeforeandafterthepolicy.Since d r_{< d}∗_,_they

are constrained toplay d i ≤ dr, and will allchoose d r in equilibrium: sinceintegration

strategies aresubstitutes, whenthe otherﬁrms are constrainedto choose d j ≤ dr,ﬁrm

i willwant tochoose d i > d ∗ but is alsoconstrained andtherefore chooses d r. Thenet

CournotproﬁtisΠ∗(d r_),_which_by_Proposition₁_exceeds_Π∗₍_d∗_)._In_eﬀect,_the_regulation

moves inthedirectiontheCournotplannerwouldwantbyhelpingtolimittheeﬀectsof thebusiness-stealing externality.

If firms arecolluding before and after regulation,the policy hasdiffering effects de-pendingonwhether d r _is_smaller_than_dM_._If_dr _{≥ d}M_,_the_p_olicy_do_es_not_bind_on_what

thefirms doinequilibrium, but doesbind onwhattheycanachieveoff the equilibrium path: thepermanentCournot punishmentfor quantitydeviationnow yieldsa payoff of Π∗(d r₎_>_Π∗₍_d∗_)._However,_colluding_firms_can_still_try_to_play_dM_in_equilibrium,_and_the

punishmentwithintheperiodofplayingCournotatcosts c − dM _is_unchanged,_while_the

gain,whichisnowconstrainedby d ≤ dr_,_cannot_be_larger_than_before_the_regulation._On

the otherhand,theone-shotgain fromdeviating in quantitywhileintegrating at d M is unaﬀectedbythepolicy:Lemma2stillholdsinthiscase,andasbefore,theno-quantity deviation constraintistheonethat binds.

If thepolicy is more severe, with d r _{< d}M_, _then _ﬁrms _are _constrained _in _the _levels

of integration they can maintain on path as well as off. Since the integration profit is concave in d , the cartel will wish to collude on d r_. _The _maximum _profit _level _under

collusionandthemaximalquantitydeviationproﬁtare:

ΠM(d r)=(a − c+d r₎2 4n − (d r₎2_;_Πdev q (d r)= (n +1)2 16n 2 (a − c+ d r₎2_{− (}_dr₎2_. ₍₉₎

Asintheunregulatedcase,therearetwoincentivecompatibilityconditionsforstability, and again the condition with respect to deviations from d r _can _be _sustained _within_a

periodbythethreatofimmediatereversiontoCournotplay.11 _As_before,_then,_it_is_the quantitydeviation incentivecompatibility conditionthat binds.

11

Toseethis,letd∗(dr):=argmaxdπi(dre,d)denotetheunconstrainedoptimaldeviationforiwhenthe

otherﬁrmsplaydr.Sincedr<dM,strategicsubstitutabilityoftheobjectiveimpliesd∗(dr)>d∗(dM)>dM, wherethesecondinequalitywasshownearlierinthediscussionleadingtoLemma2.Concavityofπi(dre,d)

indthenimpliesthattheobjectiveisincreasingon[0,d∗(dr_)],_so_the_solution_to_the_constrained_problem

withd ≤ dr_is _dr_._Thus_the_ﬁrm_can_do_no_better_by_deviating_than_the_Cournot_planner’s_{payoﬀ at}_dr_,

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Tosummarize:

Lemma 3. Suppose the regulator imposes d r < d ∗. If ﬁrms collude before and after the policy change, they play d M if d r ≥ dM, and d r if d r < d M. The permanent Cournot punishment following any deviation leads to a per-period payoﬀ of Π∗(d r₎_.

Todeterminetheeffectsofthepolicyontheabilityoffirmsto collude,weneedonly check howit affectsthecritical discountfactor δno₍_·, _·)._When_dr _{≥ d}M_, _the_sustained

profitis ΠM(d M)and deviationprofit isΠdev_q (d M). TheCournotprofit isΠ∗(d ∗). Thus collusionissustainablewhen

δ≥ δno(d M, d r)= Π dev q (d M)− ΠM(d M) Πdev q (d M)− Π∗(d r) ,

whichisa decreasing functionof d r,sincebyProposition 1, Π∗(d )is decreasingon(d P,

d ∗),whichcontains(d M, d ∗).When d r ≤ dM,collusiveﬁrmsintegratetothelevel d r and thecriticaldiscountfactortosustaincollusionis

δno(d r, d r)= Π dev q (d r) − ΠM(d r) Πdev q (d r)− Π∗(d r) .

From (9) and (4), this ratio is a constant , equal to δno(d M, d M) forany d r ≤ dM; this is because ﬁrms always bear the same ﬁxed cost d r2 _whether _they _collude, _deviate _or

play Cournot and therefore the numerator and the denominator are proportional to (a − c+d r₎2_._Thus_the_minimum_discount _factor_that_sustains_collusion_is_a_continuous,

non-increasingfunctionof d r_, _constant_on_[0,_dM_],_and_decreasing _on₍_dM_,_d∗_].

Wearenowinpositiontoanalyzetheeﬀectsofpolicy.Therearethreecases,depending onthevalueofthediscountfactor δ. Forsimplicity,weassumethatﬁrmscolludeaslong as theirdiscount factorexceedsthecriticallevel.

3.1. Low discount factors, δ < δno_(dM_{, d}∗₎

Inthiscase,ﬁrmsareunabletosustaincollusionbeforethepolicy,andsinceimposing thepolicyraises thecriticaldiscount factor,theywillnotcolludeafter.Theanalysis of Cournotplay applies,andtheresultis

• integrationfallsfrom d ∗ to d r _and_marginal_costs_rise; • productpricerises– consumerslose;

• grossproﬁts(revenuelessproductioncosts)fall;

• netprofit(gross profitlessintegrationcosts)increase– firmsarebetter off.

3.2. High discount factors, δ≥ δno_(dM_{, d}M₎

Here ﬁrms are able to sustain collusion both before and after the policy, regardless of how severe it is (how low d r₎ _and _thus _the _policy _itself _would _have _no _impact _on

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conduct. A policy d r _{≥ d}M _would _have _no _impact _on _market _outcomes, _but _neither _is

it meaningfully a divorcement policy, sinceit does notforce ﬁrms to divest any of the assetstheyown.Atruedivorcementpolicyhas d r < d M,inwhichcase

• integrationfallsfrom d M_to_dr _and_marginal _costs_rise; • productpricerises– consumerslose;

• grossproﬁts(revenue lessproductioncosts)fall;

• netprofits(grossprofitlessintegrationcosts)fall– firmsareworse off.

3.3. Moderate discount factors, δ∈ ( δno_(dM_{, d}∗_{), δ}no_(dM_{, d}M₎₎

The principlediﬀerence between this caseand the two others is thepossibility that the regulations engenders a change of conduct, by raising the critical discount factor above theexisting one.Let d r₍_δ)_∈ ₍_dM_,_d∗_),_solve_δno₍_dM_,_dr₎₌_δ._Given_δ,_this_is _the

minimumlevelofintegrationatwhichcollusionissustainable.Ifd r_{≥ d}r₍_δ),_then_collusion

ispossibleafteraswellasbeforethepolicychange,andthepolicyhasnoimpact(again, since theintegration ceiling is above thelevel that was being sustainedin equilibrium, this policy isnotreally divorcement). Butif d r < d r(δ), collusionis notpossible under the policy. Integration now goesfrom d M to d r, and theﬁrms will deliverthe Cournot quantitygiven d r_._Hence,_if_dr _∈₍_dM_,_dr₍_δ))_the_result_is

• integrationrises from d Mto d r andmarginal costsfall;

• productpricefalls– consumersgain

• grossproﬁts(revenue lessproductioncosts)fall;

• netprofits(grossprofitlessintegrationcosts)fall– firmsareworse off.

Notice that the change of conduct in this regime is generated by the eﬀect of d r _on

oﬀ-path play:there is no constraint on on-path integration levels as long as d r _{≥ d}M_.

Compliance withthepolicythendoesnotactuallyrequirefirms toselloff assets. A divorcement policy in this case wouldreally amount to setting d r < d M,which is inefficient, becauseit doesnomore tochange firms’conduct thansetting d r _just_under

d r₍_δ),_but _does_force _ﬁrms _to _engage _in _Cournot _competition _at _{higher-than-necessary}

costs.Tobesure,itstillbeneﬁtsconsumersrelativetonoregulation,becausedestabilizing collusionalwayslowersthemarketpriceinthismodel.Eveniftheregulatorimposesthe strongestdivorcementpolicybypreventinganyintegration(d r=0),themonopolyprice at d M exceeds Cournot price at d r=0. But he would do better to cap integration at above d M_and_below_dr₍_δ):_it_also_destroys _collusion_but _allows_a _greater_degree_of

cost-reduction – andthereforea lowerCournotprice. Combiningthethreecases,weconclude: Proposition 3.

(i) Following divestiture, the price consumers pay decreases if, and only if, the ﬁrms’ conduct changes from collusion to Cournot competition.

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(ii) Firms beneﬁt from divorcement if and only if they are not colluding.

(iii) If ﬁrms collude on d M _and_the_conduct_of_ﬁrms_can_change_with_an_integration

ceiling, a policy that dominates divorcement limits integration to just under d r₍_δ)

∈(d M_,_d∗₎_.

The policy described in Proposition 3 (iii) is near-optimal in d r _(the_change _of

con-ductat d r₍_δ)_introduces_a _{discontinuity,}_so _an_optimum_does_not_exist). _It_would_result

inashiftinconductfromcollusiontoCournotandconsequentlyan increase inthelevel of integration from d M to d r. Weare not aware of any policy episodes resembling this possibility; note that itrequires information onthediscount factor δ, whichisunlikely to beavailable.There is,however, a policythat economizes oninformationfor the reg-ulator and will dominate divorcement. This soft policy simply caps integration at the existing levelrather thanforcing divestment:it willbreak collusionwhenevera stricter divorcement policywould,is neutralwithrespect to prices andintegrationwhenever it doesnot,butallows largercostreductionsin caseﬁrms doswitchtoCournot.12

Onethingwehavenotconsideredsofaristheeffectsofdivorcementonexit,andwhile a full treatmentis beyondthescope ofthis paper,we makesome observations. Iffirms incuranadditionalfixedcosttooperate,thena fallinnetprofitsfollowingdivorcement mayleadsometoexit.ThereisevidencethishappenedintheBritishbeercase.Exitmay notbe harmfulofcourseiffirms were makingmonopolyprofitspriorto theregulation. But if they were not colluding, the regulation will force costs to be higher, and after exit, thesmaller number of firms combined with higher costswill drive prices upeven further. What is more, with fewer firms left, collusion may be more sustainable than before,raising thepossibilitythat divorcementmightfacilitatecollusion.

4. Some evidencefordemand-drivenintegration

Evidence for the eﬀects of demand on integration is starting to be collected. Some suggestiveevidencecomesfromsomesingle-industrystudies(e.g.ForbesandLederman, 2010),whichshowsthatairlinesaremoreapttointegratewithregionalcarriersonmore “valuable” routes(speciﬁcallythosewherefailuresaremorecostly);ForbesandLederman (2009) alsoshow that integrated relationships are more productive, whichbolsters the keyassumptionin thispaper.

Afewpaperstrysystematicallyto testfordemandeffects onintegrationbyfocusing on ostensibly competitive industries wherein the influence of demand would manifest itself through the price level. An empirical challenge is to find exogenous sources of price variation and look for correlation with integration. One approach is provided in Alfaro et al. (2016), which uses variation in the Most-Favored-Nation (MFN) tariffs

12_If_ﬁrms_are _not_colluding,_the_regulator_caps_integration _at_what _is_actually_d∗_,_(though _he_does_not

knowthis),whichhasnoimpact.Ifﬁrmsarecolluding,thenheiscappingatdM_;_either_this_has_no_impact

becauseweareinthehighdiscountfactorcase,oritbreakscollusionandﬁrmswillmaintainthecurrent costc− dM_.

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applied byGATT/WTO members as a proxy for pricevariation. Theidea is that tar-iffs affect prices,and throughthat integration, but (vertical) integration is unlikely to affect tariffs.The argument forexogeneity ofMFN tariffs comes partly from the insti-tutional structure by which they are set: long rounds of multilateral bargaining and a non-discriminationprinciplethatforcesuniformapplicationoftariffstoalltrading part-ners makestheMFNtariffs muchmore resistant to lobbyingthanother formsof trade barriers.Becausetariffsraiseproductpricesinthedomesticmarket(ascomparedtothe worldprice),reversecausalitysuggeststhattheyshouldleadtomoreintegrationamong firms sellinginthat market.

Alfaro et al. (2016) defines the degree of integration to be the fraction of inputs (in value-added terms) that are produced within the firm(this measure is due to Fan and Lang, 2000); in the data, the average is about 6%, though there is considerable variation across as well as within (4-digit SIC) industries. Tariffs should have stronger effects on firms that do not sell abroad, since exporters face the world price, not the justthedomesticone.Focusingonthisdifferentialeffectoftariffsondomesticfirmsand exporters,andusingcountry-sectorfixedeffectstocontrolforpossibleomittedvariables that mightbedrivingintegrationandtariffs,thepaperreportsstrongeffectoftariffson the degreeofintegration. Theestimated tariff elasticityofvertical integration isin the range0.02–0.09,which,sincetariffsaveragearound5%,translatesintoapriceelasticity in therange0.4–2.

An exampleof a single-industry study that tries to identify price eﬀects on vertical integration isMcGowan(2015),whichlooks atchanges inthevertical structureofU.S. coalprocessingplantsandtheminesthatsupplythem.TheStaggersRailroadActof1980 deregulatedrailroadpricing;greatercompetitionamongrailroadsledtofallingshipping costs,whichenabledelectricpowerplants,particularlyintheEast, toproﬁtablysource coalfromanywhereinthecountry.CheapcoalfromthePowderRiverBasininMontana andWyoming wasnowabletocompete withEasterncoalamong Easternpowerplants, reducing coal prices there. However, in the West, there was little change in shipping costs,mainlyduetotherelativesparsenessofrailnetworks.Asourmodelhypothesizes, thedatarevealapositivecorrelationbetweenprocessingplantproductivityandvertical integration. And consistent with its predictions, by the mid-1980s,vertical integration (thefractionofminesownedbyprocessingplants)intheEasthadfallen28%relativeto theWest.

Inboth theBritishbeerand USgasolinedivorcementepisodes,theregulatorsforced divestituresinverticalchains,admittedlybecausetherewasanincreasingtrendinprices andthefearwasthatthiswasduetoforeclosureeffectsfacilitatedbyverticalintegration. The econometric challenge to identify the effect of divorcement on prices is to con-trol for thepossibility that other factors,such as changesin accountingconventions or tax rulesfor the beer industry, contributed to theincrease in prices. If theforeclosure story wastherightone,divorcementshould have ledto adecrease inprices.If divorce-ment led to anincreasein prices, thereis support for anefficiency view of integration. Slade(1998a)documentstheeffectsoftheBeerOrdersofthe1980s,aUKMonopoliesand

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MergersCommissiondecisiontoforce divestitureof14,000 publichouses.She contrasts four typesof organizationinthevertical chain brewer-pub:companyowned, franchised pubs withor without ﬁxed fees,and arms-length relationship.Company owned is akin tointegration, whilethetwo otherformsareweak andstrongforms ofnon-integration.

The upstream segment of the industry was relatively concentrated at the time of thedecision,withseven largenational brewersanda largernumber ofmicro-breweries. Thedivorcement effectivelyputceilings onthenumberofpubs(licenses) thata brewer could have. The divestitures led to the emergence of public-house chains, which have long-term contractual agreements with national brewers, as well as decisions by some brewers to stop production and shift to retailing. Themain findingwas that following thedecision,retailprices increased(in thehousescloselytiedtothebrewers,but notin thefreehouses), andprofitsofbrewersdecreased.Consistentwithourresults,following thepolicy,somebrewersexitedtheindustry.

Interestingly,somecommentatorsonthebeercase(e.g.Spiceretal.,2012)notethat demandforpubbeerwasgrowingoverthedecadeleadingtoBeerOrders,duetoincome growth andgreaterleisuretime. Theyalsodocument thestrongindustryoppositionto the policy.Interms ofour model,theevidence ﬁts thescenario in which collusionwas sustainedbothbeforeandaftertheintervention:thisaccountsfortheincreasedprice,the fallen proﬁts,and theindustryopposition.If collusionhad beenstoppedbythe policy, mostlikely prices wouldhave fallen, at leastfor a while,as suggested in Section 3.3. If therehadbeennocollusion,brewersshouldhavewelcomedsomeversionofthepolicyas a checkontheirover-investment.

BarronandUmbeck(1984)studiestheeffectsofthedivorcementlawenactedin1974 in Maryland that prohibited refiners’ control of gasoline stations, and reallocated con-trol rights for hours of operation and retail pricing to the stations.13 _Contrary _to _the beerexample,here therefinerswere notobliged todivest theirassetsbut to movetoa franchisingsystem where thegasstation franchisees wouldhave control over operation decisions,includingtheretailprice.Asinthepreviousexample,theeffectofthe divorce-menthasbeenanincreaseinretailprices.BarronandUmbeck(1984)citeevidencethat the supportersof thelegislationincluded ownersof independentgasolinestations, who areindeed likely to gainfrom thedivorcement sincepricecompetitionwillbe softenat the retail level, while opponents to thelegislation included, obviously, refinersaffected bythedivorcementpolicybut also consumers .

These results are consistent with an eﬃciency view of integration, a point that has beenmadeinmanyotherempiricalstudiesofverticalrelationships(LafontaineandSlade, 2007),butareespecially pertinentforourdiscussion.Aregulatorstepped inandforced divorcementfollowinganupwardtrendinbothretailpricesandverticalintegration,yet pricescontinuedtorise.Thisisconsistentwiththeviewthatthepre-divorcementupward trendinpriceswasdueprimarilynottointegrationbuttochangesindemandthatwere drivingboth integrationandprice.

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5. Conclusion

One ofthe challengingtasks in evaluating mergersor the performanceof integrated firms is to disentangle the efficiency and market power effects of integration. Our un-derstanding of the causal relationship between price levels and degrees of integration not only guides econometric efforts to separate these effects but also influences policy decisions. In the divorcement episodes discussed here, making allowance in the policy discussion for thepossibility of demand-driven integrationmay have led tomore satis-factory outcomes. In terms of our model, a simple cap on integration at then-current levelswouldhavehadthesamepotentialbenefitasdivorcementintermsofdestabilizing collusion, but without thedamage to firms’cost structures that ultimatelykept prices high.

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