麻省理工行为金融学讲义14127_lec5_c_a_c

14.127Lecture5XavierGabaixMarch4,2004�0.1Welfareandnoise.Acompliment•TwofirmsproduceroughlyidenticalgoodsDemandoffirm1is•D1=P(q−p1+σε1q−p2+σε2)whereε1,ε2areiidN(0,1).Thus•D1=P(p2−p1σ(ε1−ε2))=P�p2−p1σ√2η��¯�p2−p1�σ√2η=Φ=Pp2−p1σ√2whereηisN(0,1)and¯Φ=1−Φ,withΦcdfofN(0,1)Unlikeinε≡0case,herethedemandisnotdramaticallyelastic•Slopeofdemandatthesymmetricequilibriump1=p2�σ√2��p2−p1�•1∂∂¯p2−p1=φσ√2σ√2∂p1D1=∂p1Φ−−1=φ(0)σ√2and“modified”elasticity1∂1η=D1∂p1D1=φ(0)σ√2=√πσ−becauseD1=12.Whenσ→0thenη→∞.Eventhoughthe“true”elasticityis∞the•measuredelasticityislowerηηtrue.•Openquestion:howtocorrectthatbias?0.2Howtomeasurethequantityofnoiseσ?—Givepeoplenmutualfundsandaskthemtopicktheirpreferredandnextpreferredfund.•—AssumethatallthosefundshavethesamevalueqA=qB—Peopledomaxqi−pi+σεi=si—CallA­thebestfund,B­thesecondbestfund,sA≥sB≥allotherfunds.—IncreasepAby∆p.AtsomepointtheconsumerisindifferentbetweenAandB.qA−pA+σεA−∆p=qB−pB+σεB�—IfpA=pBthen∆p=σ(εA−εB)or∆p=σ�ε(1:n)−ε(2:n)—Proposition.Forlargen∆p=BnσwhereBnistheparameterofGumbelattraction,Bn=1�1��nf�F¯n0.3Couldthefeesbeduetosearchcosts?AliHortacsuandChadSyverson,QJE2004,forthcoming.•—Supposeyouhavex=$200,000andyoukeepitfor10years.—Youpay1.5%/yearandthuslose200,000×1.5%=3,000ayear.•Competingexplanation—peopledon’tknowthattwoindexmutualfundarethesamething.0.4Openquestions•Whataretheregulatoryimplicationsofconsumerconfusion?Wheredoesconfusionσεicomesfrom?Forinstance,provideacognitive•modelthatgivesamicrofoundationforthis“noise”Findamodelthatpredictstheleveloftheconfusionσ?e.g.,inthemutual•fundmarket,giveamodelthatpredictsthereasonableorderofmagnitude.Findamodelthatpredictshowσvarieswithexperience?•Howdofirmsincrease/createconfusionσ?••Empirically,howcouldwedistinguishwhetherprofitscomefromtrueprod­uctdifferentiation,searchcosts,orconfusionnoise?Deviseanovelempiricalstrategytomeasureaneffectrelatedtothema­•terialoflectures3to5.0.5Competitionandconfusion•Proposition.Firmshaveanincentivetoincreasetheconfusion.Theeffectisstronger,thestrongeriscompetition.•Example—cellphonepricing.•Symmetryoffirmsisimportanthere.Ifthereisafirmthatismuchbetterthanothers,thenitwantstohaveverylowσtosignalthis.��Proof.•—Considernidenticalfirmsandsymmetricequilibria.D1=P(q−p1+σ1ε1+V(σ1)maxq−pi+σiεi+V(σi))=P(q−p1+σ1ε1+V(σ1)maxq−p∗+σ∗εiV(σ∗))whereV(σi)istheutilityofcomplexityσi(equatedwithconfusion).—DenoteMn−1=maxi=2,...,nεi.InequilibriumD1=P(p∗−p1+σ1ε1+V(σ1)(σ∗)σ∗Mn−1)ε1σ∗Mn−1−p∗−p1−+VV(σ1)−V(σ∗)=Pσ1σ1=EF¯(c)—Attheequilibrium,p1=p∗,σ1=σ∗,andbysymmetryD1=1.n���—Letuscheckittodevelopflexibilitywithtricksofthetrade.FirstnotethatP(Mn−1x)=P((i)εix)=F(x∀)n−1∗Densitygn−1(x)=G′(x)=(n−1)Fn−2(x)f(x).n−1∗Now1−�1−D1=E�F¯(Mn−1)=E(F(Mn−1))=F(x)gn−1(x)dx=F(x)(n−1)Fn−2(x)f(x)dx=(n−1)Fn−1(x)f(x1=(n−1)�Fn(x)�+∞=n−1=1−nnn−∞∗ThusD1=1n.��—Heuristicremark.E�F¯(Mn−1)=1n.HenceMn=An+Bnη,whereAnBnareGumbelattractionconstants.ThusMn≃An.So,�1Mn≃F¯≃Ann������σ∗—Theprofitπ1=maxp1,σ1EF¯σ1Mn−1−p∗−p1+V(σ1)−V(σ∗)(p1−c1)σ1—FromFOCandenvelopetheoremd0=dσ1π1=(p1−c1)∂∂σ1D1∗Notethat∗∂∂σ1D1=E−f(cn)σ∗Mn−1(p−p1+V(σ1)−V(σ∗))+σ12−−σ12−Inequilibrium,cn=Mn−1,hence∗∂0=∂σ1D1=E−f(Mn−1)−Mn−1V′(σ1)��σ∗σ∗=E�f(Mn−1)Mn−1�+E�f(Mn−1−)V′(σ1)�σ∗σ∗Hence• V′(σ1)=E(f(Mn−1)Mn−1)Ef(Mn−1)−≡−dnConsidersomesimplecases•—Uniformdistributiondn=1−2n—Gumbeldn=lnn+A—Gaussiandn∼√lnnInthosecases,V′(σ1)0.••Thuswehaveexcesscomplexity.•Whathappensascompetitiongrowswhilen→∞?=1−χ12σ−σ∗∗TaketheutilityofnoisetobeV(σ)().—=−(σ−σ∗∗1χThenV′(σ))=−dn,andconsequentlyσ=σ∗∗+χdn—Hence,ifcompetitiongrows,theproblemgetsexarcerbated.•20.5.1Openquestion.Themarketforadviceworksverybadly.Why?—Thefundmanagerwantstoselltheirownfunds.•—Advisorchargesyou1%peryearforadvice:hegivesyoustorieseachmonththatsuggestsomekindoftrade.Otherwise,hecouldloseclient.1Marketing­Introduction•Whyhighpricesofadd­onsandlowpricesofprintersorcars?Oftenthehighadd­onsfeesarepaidbythepoornotrichwhomight•bearguedhavelowmarginalvalueofmoney,e.g.useofcreditcardtofacilitatetransactions.•Manygoodshave“shroudedattributes”thatsomepeopledon’tanticipatewhendecidingonapurchase.Considerbuyingaprinter.•—Someconsumersonlylookatprinterprices.—Theydon’tlookupthecostofcartridges.Shroudedadd­onswillhavelargemark­ups.•—Evenincompetitivemarkets.—Evenwhendemandisprice­elastic.—Evenwhenadvertisingisfree.•�2ShroudedattributesConsiderabankthatsellstwokindsofservices.••Forpricepaconsumercanopenanaccount.Ifconsumerviolatesminimumshepaysfeep.WLOGassumethatthetruecosttothebankiszero.•ConsumerbenefitsVfromviolatingtheminimum.•ConsumeralternativelymayreduceexpendituretogenerateliquidityV.•DonotviolateminimumViolateminimumSpendnormally0pSpendlessV−e0V−�pV−e−��•�2.1Sophisticatedconsumer•Sophisticatesanticipatethefeep.•Theychoosetospendless,withpayoffV−e...ortoviolatetheminimum,withpayoffV−p�•�•�2.2NaiveconsumerNaiveconsumersdonotfullyanticipatethefeep.Naiveconsumersmaycompletelyoverlooktheaftermarketortheymay•mistakenlybelievethatpe.Naiveconsumerswillnotspendatareducedrate.•NaiveconsumermustchoosebetweenforegoingpayoffVorpayingfeep.��•�2.3Summaryofthemodel•Sophistica