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1、14.127Lecture5XavierGabaixMarch4,20040.1Welfareandnoise.Acompliment•Twofirmsproduceroughlyidenticalgoods•Demandoffirm1isD1=P(q−p1+σε1>q−p2+σε2)whereε1,ε2areiidN(0,1).•Thus�√�D1=P(p2−p1>σ(ε1−ε2))=Pp2−p1>σ2η����p2−√p1¯p2−√p1=P>η=Φσ2σ2whereηisN(0,1)andΦ=1¯−Φ,withΦcdfofN(0,1)•Unlikeinε≡0case,herethede
2、mandisnotdramaticallyelastic•Slopeofdemandatthesymmetricequilibriump1=p2����∂∂¯p2−√p1p2−√p1√1−D1=−Φ=φ∂p1∂p1σ2σ2σ21=φ(0)√σ2and“modified”elasticity√1∂1πη=−D1=φ(0)√=D1∂p1σ2σbecauseD1.1=2•Whenσ→0thenη→∞.Eventhoughthe“true”elasticityis∞themeasuredelasticityislowerη<ηtrue.•Openquestion:howtocorrectthat
3、bias?0.2Howtomeasurethequantityofnoiseσ?•—Givepeoplenmutualfundsandaskthemtopicktheirpreferredandnextpreferredfund.—AssumethatallthosefundshavethesamevalueqA=qB—Peopledomaxqi−pi+σεi=si—CallAthebestfund,Bthesecondbestfund,sA≥sB≥allotherfunds.—IncreasepAby∆p.Atsomepointtheconsumerisindifferentbetwe
4、enAandB.qA−pA+σεA−∆p=qB−pB+σεB—IfpA=pBthen∆p=σ(εA−εB)or��∆p=σε(1:n)−ε(2:n)—Proposition.Forlargen∆p=BnσwhereBnistheparameterofGumbelattraction,1Bn=����nfF¯1n0.3Couldthefeesbeduetosearchcosts?•AliHortacsuandChadSyverson,QJE2004,forthcoming.—Supposeyouhavex=$200,000andyoukeepitfor10years.—Youpay1.5
5、%/yearandthuslose200,000×1.5%=3,000ayear.•Competingexplanation—peopledon’tknowthattwoindexmutualfundarethesamething.0.4Openquestions•Whataretheregulatoryimplicationsofconsumerconfusion?•Wheredoesconfusionσεicomesfrom?Forinstance,provideacognitivemodelthatgivesamicrofoundationforthis“noise”•Finda
6、modelthatpredictstheleveloftheconfusionσ?e.g.,inthemutualfundmarket,giveamodelthatpredictsthereasonableorderofmagnitude.•Findamodelthatpredictshowσvarieswithexperience?•Howdofirmsincrease/createconfusionσ?•Empirically,howcouldwedistinguishwhetherprofitscomefromtrueproductdifferentiation,searchcosts
7、,orconfusionnoise?•Deviseanovelempiricalstrategytomeasureaneffectrelatedtothematerialoflectures3to5.0.5Competitionandconfusion•Proposition.Firmshaveanincentivetoincreasetheconfusion.Theeffectisstronger,thestrongeriscompetition
