非对称信息英文

AsymmetricInformationECON370:MicroeconomicTheorySummer2004–RiceUniversityStanleyGilbert1Econ370-AsymmetricInformationAsymmetricInformationUptonow,wehaveassumedEveryoneisfullyinformedOrequallyuninformedInmanycasesonepartyhaseconomicallyrelevantinformationthatanotherpartydoesnothaveWetermthis“AsymmetricInformation”Itcanproduceeconomicinefficiency2Econ370-AsymmetricInformationExampleSupposetherearetwotypesofumbrellasGoodandBadTheycannotbedistinguisheduntilaftertheyhavebeenusedBadumbrellasdisintegrateafteralittleuseUmbrellasarevaluedasfollowsGoodBadValuetoConsumerCostto

Produce$11.50$14$11$83Econ370-AsymmetricInformationExample:FullInformationUnderfullinformation,onlygoodumbrellaswouldbesoldSincethecosttomakeabadumbrellaexceedsthebenefititprovidesGoodBadValuetoConsumerCostto

Produce$11.50$14$11$84Econ370-AsymmetricInformationExample:AsymmetricInformationIf⅔umbrellasaregoodPeoplearewillingtopay:⅔(14)+⅓(8)=$12perumbrellaWhichisgreaterthanthecosttoproducethemGoodBadValuetoConsumerCostto

Produce$11.50$14$11$85Econ370-AsymmetricInformationExample:AsymmetricInformationButfirmsmakemoremoneysellingbadumbrellasIfallfirmsaresmall,theyhaveincentivetoswitchtomakingbadumbrellasOnce⅔offirmsmakebadumbrellas:Peoplearewillingtopay⅓(14)+⅔(8)=$10WhichislessthanitcoststomakeanyumbrellaGoodBadValuetoConsumerCostto

Produce$11.50$14$11$86Econ370-AsymmetricInformationExample:ObservationsUnderfullinformationwehavetheefficientresultTotalSurplus=$14–11.50=$2.50perumbrellaUnderAsymmetricinformationthemarketcollapsesTotalsurplus=07Econ370-AsymmetricInformationProblemsAdverseSelectionPeoplewithapoorhiddencharacteristic…takeadvantageofother’signoranceExample:SickpeoplebuyinglifeinsuranceMoralHazardPeoplewhocantakehiddenactions…takeadvantageofother’signoranceExample:MakingpoorumbrellasExample:Employeesshirking8Econ370-AsymmetricInformationAdverseSelectionExampleAcompanyoffersHealthinsuranceEachillnesscosts$100,000Twotypesofpeople:“Healthy”“Sick”InsurancecompanycannotdistinguishthemTypesofpeopledifferinprobabilityofgettingsickandinwillingnesstopayforinsurance9Econ370-AsymmetricInformationAdverseSelectionActuariallyFairinsurancechargesratesexactlyequaltothecosttoinsureAPoolingEquilibriumisoneinwhicheveryoneischargedthesamerates,regardlessoftypeType%ofPopulationRiskofIllnessWillingnesstoPayHealthy90%1/1000$200Sick10%1/100$1,500CosttoInsure$100$1,00010Econ370-AsymmetricInformationPoolingEquilibriumIftheinsurancecompanypoolseverybody,itwouldcharge:0.9×100+0.1×1000=$190WhicheveryoneiswillingtopaySoaPoolingEquilibriumexistsType%ofPopulationRiskofIllnessWillingnesstoPayHealthy90%1/1000$200Sick10%1/100$1,500CosttoInsure$100$1,00011Econ370-AsymmetricInformationExample2Iftheinsurancecompanypoolseverybody,itwouldcharge:0.8×100+0.2×1000=$280WhichonlythesickarewillingtopaySothereisNOPoolingEquilibriumexistsTheinsurancecompanymustcharge$1,000Type%ofPopulationRiskofIllnessWillingnesstoPayHealthy80%1/1000$200Sick20%1/100$1,500CosttoInsure$100$1,00012Econ370-AsymmetricInformationObservationsSincethecompanycannottell“sick”peoplefrom“healthy”peopleItcanonlychargeasingleaveragerateAlthoughitwouldhappilyinsureeveryoneatfairratesAndpeoplewouldwillingpaythoseratesItcannotbecauseitcannottellpeopleapartThereforeamajorityareuninsured13Econ370-AsymmetricInformationResponsesSomemarketplayersloseasaresultofasymmetricinformationSotheyhavedevelopedstrategiesto(partially)overcometheproblemTwomainstrategiesSignallingScreening14Econ370-AsymmetricInformationScreeningScreening:isanactiontakenbytheignorantpartytodeterminetypesofpeopleIngeneral,Itisacostimposedonthe“low-value”partyThatthe“high-value”partiesareunwillingtoendure15Econ370-AsymmetricInformationScreeningExampleAveragecosttoinsureeverybody:0.5×100+0.5×200=$150WhichonlythesickarewillingtopaySincethereisnopoolingequilibrium,theinsurancecompanymustchargeatleast$200Type%ofPopulationRiskofIllnessWillingnesstoPayCosttoInsureCostofPhysicalHealthy50%1/1000$140$100$40Sick50%1/500$250$200$15016Econ370-AsymmetricInformationScreeningPoliciesSupposetheinsurancecompanyofferstwopoliciesOnefor$240withnorestrictionsOnefor$100butyoumustpassaphysicaltogetitAnyonecan“pass”thephysicalBut“sick”peoplehavetobribethedoctortodoitType%ofPopulationRiskofIllnessWillingnesstoPayCosttoInsureCostofPhysicalHealthy50%1/1000$140$100$40Sick50%1/500$250$200$15017Econ370-AsymmetricInformationEquilibriumHealthypeopleAreunwillingtobuythe$240policyButwillpaythe$100+$40togettheotherpolicySickArewillingtobuythe$240policyWouldpaythe$100+$150fortheotherpolicy,But,itismoreexpensivethantheoriginalpolicyType%ofPopulationRiskofIllnessWillingnesstoPayCosttoInsureCostofPhysicalHealthy50%1/1000$140$100$40Sick50%1/500$250$200$15018Econ370-AsymmetricInformationScreeningObservationsTheinsurancecompanyimposesarequirementThatismorecostlyfor“sick”peopletomeetAndsoisabletoseparateout“healthy”from“sick”peopleAndinsureeveryoneSincenoonehasanincentivetochangeThisqualifiesasaseparatingequilibriumNoticethatComparedtothefull-informationsituationThisisinefficient,duetothecostofthephysical19Econ370-AsymmetricInformationSignalingInseveraloftheexampleabove,The“low-cost”peoplestoodtogainbybeingidentifiableWhileScreeningisacostimposedbytheignorantpartytoidentifytypesSignalingisacostvoluntarilyadoptedbyknowledgeablepartiestosignaltheirtypesExample:LemonModel20Econ370-AsymmetricInformationLemonModelOntheusedcarmarketTwotypesofcarsGoodCarsLemonsThetypesareindistinguishabletothebuyersThemarkethasthefollowingcharacteristicsType%ofPopulationValuetoBuyerValuetoSellerGoodCars50%$2,000$1,500Lemons50%$1,000$50021Econ370-AsymmetricInformationPoolingSincebuyerscan’tdistinguishthecarsinadvanceTheyarewillingtopayonly0.5×$2000+0.5×$1000=$1,500AllsellersarewillingtoparticipateatthatpriceSothisisapoolingequilibriumType%ofPopulationValuetoBuyerValuetoSellerGoodCars50%$2,000$1,500Lemons50%$1,000$50022Econ370-AsymmetricInformationSignalingSellersofgoodcarswouldliketosignalthequalityoftheircarsSincedoingsowouldenablethemtocharge$2,000But,ithastobeinawaythatsellersoflemonsareunwillingtoemulateType%ofPopulationValuetoBuyerValuetoSellerGoodCars50%$2,000$1,500Lemons50%$1,000$50023Econ370-AsymmetricInformationInspectingLemonsSellerscansubmittheircarsforinspectionandcertificationProfitsforownersofgoodcarswithinspection:2000–200–1500>1500–1500SoprofitsfromdeviatingexceedpoolingprofitsSothereisnolongerapoolingequilibriumType%ofPopulationValuetoBuyerValuetoSellerCosttopassinspectionGoodCars50%$2,000$1,500$200Lemons50%$1,000$500$1,10024Econ370-AsymmetricInformationSeparatingLemonsEvaluatetheseparatingequilibriumObviously,ownersofgoodcarshavenoincentivetodeviateLemonOwnersprofitsfromdeviating2000–1100–500<1000–500SoLemonownerswillnotdeviateeitherType%ofPopulationValuetoBuyerValuetoSellerCosttopassinspectionGoodCars50%$2,000$1,500$200Lemons50%$1,000$500$1,10025Econ370-AsymmetricInformationObservationsonSignalingInourexample,ownersofgoodcarshaveanincentivetodeviatefromthepoolingcaseSo,thepoolingcaseisnotstableThereisnopoolingequilibriumwhentheinspectionregimeisavailableOntheotherhand,noonehasanincentivetodeviatefromtheseparatingcaseTheonlystableequilibriumhereistheseparatingequilibrium26Econ370-AsymmetricInformationGeneralCommentsDifferentmodelsofthissortmayhavedifferentoutcomesAllthefollowingarepossiblePoolingequilibriumbutnoseparatingequilibriumSeparatingequilibriumbutnopoolingequilibriumBothpoolingandseparatingequilibriaNeitherpoolingnorseparatingequilibria27Econ370-AsymmetricInformationMoralHazardMoralHazardTheknowledgeablepartyactsdifferently…thanwheneveryonepossessesfullinformationMinimizingMoralhazardrequiresprovidingincentivestoactefficientlyExampleIfIdidn’tinsuremycar,IwouldinstallanalarmButsinceitisinsured,IdonotInsurancecompany’ssolution:Provideadiscountforinstallingacaralarm28Econ370-AsymmetricInformationExample:HiringaCEOOurcompany,YZACorporation,ishiringaCEOOurobjectiveistomaximizeprofitsTheCEO’sobjectiveistomaximizeutilityProfitsdependonthe‘effort’theCEOexertsEffortiscostlytotheCEOLetprofitsbe:Π(e)–wWhere‘e’represents‘effort’TheCEO’sutilityis:U=w–f(e)AndcangetworkelsewherewithutilityuA29Econ370-AsymmetricInformationCEORoadmapWewillevaluatethefollowingcases:Full-informationequilibriumAsymmetricinformationequilibriumWhentheCEOisrisk-neutralWhentheCEOisrisk-averseWeseektoidentifyTheoptimalamountofefforttheCEOshouldexertAndanoptimalcontracttoinducethateffort30Econ370-AsymmetricInformationFull-InformationCEOTheCEOmustprovidetheoptimaleffortwillinglyThuswehaveaParticipationConstraintw*–f(e*)≥uAWehavenoreasontowanttopaymore,sosetw*–f(e*)=uAProfitmaximizationmeans:Whichimpliesthattheoptimale*satisfies:31Econ370-AsymmetricInformationFull-InformationObservationsAnoptimalcontractwouldconsistofw*=uA

+f(e*)ifsheworkse*ZerootherwiseThisisexactlywhatshewouldworkifsheownedthecompanyherselfToseethis,writeanexpressionforherutilityunderthosecircumstancesEffortdoesnotneedtobedirectlyobservableSinceprofitisafunctiononlyofeffort,Wecandeterminehowmucheffortwasexertedsimplybeobservingprofits32Econ370-AsymmetricInformationRisk-NeutralCEOHereletprofitsbeΠ(e,ε)–wWhereεisarandomvariableSincewecannotobserveeffortPaymusttaketheform:w(Π)OurParticipationConstraintisE[w(Π(e*,ε))]–f(e*)≥uASetE[w(Π(e*,ε))]=uA

+f(e*)Profitsbecome33Econ370-AsymmetricInformationRisk-NeutralContractRequirementsAnoptimalcontractwouldsatisfytheIncentiveCompatibilityConstraintThatis,theUtilitymaximizingCEOwillexertexactlytheProfitmaximizingeffortThatis,mathematically:E[w(Π(e*,ε))]–f(e*)≥E[w(Π(e,ε))]–f(e)34Econ370-AsymmetricInformationRisk-NeutralContractsAsbefore,optimaleffortisexactlywhatshewouldworkifsheownedthecompanyOneoptimalcontract(then)istosellherthecompanyAnotheristoallowhertokeepanyamountaboveexpectedprofitsBothhavetheeffectofplacingallriskonher(Sincesheisrisk-neutral,thatdoesn’tbotherher)Andensureshemakestheoptimaldecision35Econ370-AsymmetricInformationRisk-AverseCEOWegreatlysimplifyourmodelforthiscaseTwopossiblestatesoftheworld,ε1,ε2Thestatesoccurwithprobabilityp,1–pTwopossibleeffortlevels,e1,e2ProfitsareΠ(e1,ε1)=1Otherwise,profitsarezeroCEOutilityisU=u(w)–f(e)Weletf(e2)=0,andf(e1)=α,andu(0)=0ReservationwageiszeroWagebecomesw1ifprofitsare1,w0otherwise36Econ370-AsymmetricInformationRisk-AverseCEOAnalysisAssume:e1isoptimale2isoptimalE[u(w(Π(e2,ε)))]–f(e2)≥

uAoru(w0)–0≥0orw0=0Issatisfiedbyw1=w0=0ParticipationConstraint:ParticipationConstraint:orE[u(w(Π(e1,ε)))]–f(e1)≥

uApu(w1)+(1–p)u(w0)–

α≥0IncentiveCompatibility:IncentiveCompatibility:E[u(w(Π(e1,ε)))]–f(e1)≥ E[u(w(Π(e2,ε)))]–f(e2)pu(w1)+(1–p)u(w0)–

α≥u(w0)p(u(w1)+u(w0))≥

αor37Econ370-AsymmetricInformationRisk-AverseCEOSolutionif:e1isoptimale2isoptimalw1=w0=0ParticipationConstraint:pu(w1)+(1–p)u(w0)=

αIncentiveCompatibil