Coaseconjecture CoaseJLawEconomicsOrganizaexibilityaordedbytheabilitytochargedipricesovertimewillhurtthemonopolistConsumerswilltendtowaitforlowerpricesinthefutureThiswillforcethemonopolisttocha ID: 124695
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Supposeamonopolisthastheexibilitytochargedientpricesovertime(intertemporalpricediscrimination).Downwardslopingmarketdemandcurveforthedurablegoodwithpricetakingconsumers(forexample,contin-uumofconsumers).Asamonopolist,ifyousellalottoday,youreducethedemandforyourowngoodtomorrow.Ifthedemandislowertomorrow,youwillhaveincentivetoreduceyourpricetomorrow. Coaseconjecture [Coase(J.LawEconomics&Organiza-exibilityaordedbytheabilitytochargedipricesovertimewillhurtthemonopolist.Consumerswilltendtowaitforlowerpricesinthefuture.Thiswillforcethemonopolisttochargelowerpricesto-day.Asthetimeintervalbetweensuccessivepricerevisionsgoestozero,monopolistlosesallmarketpower.Inthelimit,youhaveacompetitiveoutcome. Themonopolistcanalsodobetterifheleasesthegoodinsteadofsellingit.Leasingconvertsamarketforadurablegoodintoamar-ketforthecurrentservicefromthegoodwhichis,bynition,non-durable. Demandforuseofthegoodeachperiod:[Thinkofthisasif:-thereisaunitmassofconsumers-eachconsumerusesatmostoneunitofthisgoodeachperiod-dollarvaluationofthisuseperperiodisdistributeduniformlybetween Sellingwithpre-commitmenttonotlowerpriceinperiod2(Nointertemporalpricediscrimination).Consumerswhobuydosoinperiod1.Ifquantityissoldthenthemarginalconsumerisonewhoseperperiodusevalueisandsothepricechargedmustbe:=(1+Themonopolistsolves(1+whichyields, 2=) andthetotaldis-countedsumofprotsis (1+Samemarketoutcomeasleasing. So,ifisthequantityofgoodssoldbythemonopolistinperiodisthequantityofgoodssoldinperiod2,thenthepriceinperiod2must Now,wegotoperiod1.Ifmonopolistsellsinperiod1,thenthemarginalcon-sumer(thelowestvaluationconsumerthatbuys)istheonewithutilizationvaluationequaltoThehighestpriceatwhichhecansellisapricesuchthatthismarginalconsumerisindierentbetweenbuyingthegoodinperiod1(andenjoyingitfortwope-riods)orwaitingtobuyitinperiod2atapriceandusingitforoneperiod)(1+[(1 sothat)=(1+ 21) Thetotaldiscountedsumofpro 4 whichisstrictlylessthan (1+thetotaldiscountedsumofprotswhenthemonopolistleasesorsellswithpre-commitmenttonotlowerprices. Result:Astheintertemporal(discountedsumof)protofthemonopolistandallpricesconvergeInthelimit,almostalltradestakeplaceattheinitial Mainarguments:Continuumofconsumersimpliesconsumersarepricetak-Theydecideaccordingtotheirexpectationoffuturepriceswhichtheytakeasgiven.Rationalexpectationsequilibrium:*consumersanticipatethepricepathtobechosenbymonopolist,takethisasgivenandbuyaccordingly;*giventhisbuyingbehavior,thereshouldnoincentiveforthemonopolisttodeviatefromthepricepathatanypoint. Foranyequilibriumpricepathisnon-increasingovertime.Ifpriceincreasestomorrow,noonewillbuytomorrow. ifcurrentp>>c,thenpeopleanticipatepricedeclineinverynearfutureandwait. *Ingeneral,monopolistcandomuchbetterbypre-committingtoasequenceofprices(theoptimalpre-commitmentturnsouttobeaconstantpricesequenceequaltothestaticmonopolyprice).Thelatteralsogeneratessameprotastheleasingout- Mainargument:highervaluationbuyersrealizehowtheirbuyingdecisioninuencesfuturepricesandthatiftheywaittobuyatalowerprice,themonop-olistwillnothaveincentivetochargelowerprice(untiltheyhaveboughtandleftthemarket). Therearetwo *ahighvaluationconsumerwhosevaluationofperiodsuseofoneunitis*alowvaluationconsumerwhosevaluationofonepe-riodsuseofoneunitisCostofproduction Sellingwithpre-commitmentaboutpriceinperiodHere,monopolisthastopre-committoinperiodandcannotconditiononwhathappensinperiod Ifmonopolistwantstoselltobothconsumersinperiod,hisprotis2(1+(1+ Therefore,optimalprotundersellingwithpre-commitment:SPC=(1+ Considerthefollowingstrategies:Monopolist:*charge=(1+inperiod*inperiod2,chargeapriceequaltothehighestvaluationofthebuyersremaininginthemarket.Buyeroftypebuyintherstperiodif(1+H,O.Ifnot,waitforperiodandbuyif Proof:Workbackwards.Firstconsiderperiodandcheckthatnoplayerhasanincentivetodeviate.Giventhebuyersbuyingstrategy,forthemonopolist,itisoptimaltochargeifthehighvaluationbuyerisleftinthemarket(withorwithouttheotherbuyer)andtocharge,ifonlythelowvaluationbuyerisleft.So,theabovementionedstrategyisclearlyoptimalforthemonopolistinstage2. Now,gobacktoperiodEachbuyerknowsthatgiventhestrategyofthemonop-olist,shecangetatmostzeronetsurplusinperiodwillexceedhervaluationorwillexactlyequalhervaluation.So,if(1+,itisoptimalforabuyerwithtobuyinperiod1.(Note:thisisthecriticalargument,thehighvaluationbuyercannotreducethepriceatwhichshebuysbywait- Whenthisequilibriumisplayed,themonopolistpricedis-criminatesovertime(andtherefore,acrossconsumers)andtheprotis=(1+SPC=(1+ Moregenerally,ithasbeenshownthatwithanynumberofconsumers,thereareequilibriawheretheCoaseconjecturedoesnothold.Indeed,intheinnitehorizoncase,thereareequilibriasuchthatasdiscountfactorgoestoone,themonopolistexercisesalmostperfectmarketpowerextractingalmostallsocialsurplus. *Fixedopportunitycostofstayinginthemarket:-monopolistexitsifremainingdemandisnothighenough-sopricecannotfalltoomuchinthefuture. *Increasingmarginalcostovertime(costcongestionforexample,whenproductionovertimeinvolvesuseofanitestockofnecessaryinputsuchasanexhaustiblenaturalresource). *Inowofnewcohortsofbuyers(Conlisk,GerstnerandSobel,QuarterlyJ.ofEcon,1984)-identicalcohortsenterovertime-lowervaluationbuyershavehigherincentivetowait.Thestockofconsumerswaitingtobuyareontheaverageoflowervaluationthannewcohort.Monopolisthasincentivetonotlowerpricetoomuchandselltohighervaluationnewconsumers,untilthestockofoldlowervaluationconsumersbecomelargeandatthatpointtohaveabigsalewhich,inturn,reducesthestockofconsumerssharplyandthenreturntohighpricesagain.Pricecycles. *Reputation:Themonopolistmayestablishareputationfornotcuttingprices.Initially,consumersexpectmonopolistcharginghighpricetobe"honorable"¬tocutpricesinfutureifhedoescutpriceinanyperiod,theyrevisetheirexpec-tationto"heisactuallyascoundrelrationalseller"i.e.,onewhowillcutpricesifitsuitshimandtherefore,theCoaseconjectureworksfromthatpointonanddriveshisprottonearzero.So,eventhougharationalmonopolistmightwanttocutprices,hemayndheisbetteropretendingtobeanhonorableguyandnotcutprices(asthatmightspoilhisreputation&willmakehimearnclosetozeroprotfromthatpointonwards). *PlannedObsolescence:Reducingdurabilityreducesthequantityofgoodscarriedoverandthusconvincesbuyersthatthepricewontfalltoomuch.Textbookproducersfrequentlybringoutneweditionstokillusedbooks. *Oligopolisticcollusion:Thesamemechanismthatal-lowsoligopoliststocolludemayalsoallowthemtopre-committonotcuttingpricesrapidlyovertime.