北京大学中级微观经济学课件Ch36

ChapterThirty-SixAsymmetricInformationChapterThirty-SixAsymmetricI1InformationinCompetitiveMarketsInpurelycompetitivemarketsallagentsarefullyinformedabouttradedcommoditiesandotheraspectsofthemarket.Whataboutmarketsformedicalservices,orinsurance,orusedcars?InformationinCompetitiveMar2AsymmetricInformationinMarketsAdoctorknowsmoreaboutmedicalservicesthandoesthebuyer.Aninsurancebuyerknowsmoreabouthisriskinessthandoestheseller.Ausedcar’sownerknowsmoreaboutitthandoesapotentialbuyer.AsymmetricInformationinMark3AsymmetricInformationinMarketsMarketswithonesideortheotherimperfectlyinformedaremarketswithimperfectinformation.Imperfectlyinformedmarketswithonesidebetterinformedthantheotheraremarketswithasymmetricinformation.AsymmetricInformationinMark4AsymmetricInformationinMarketsInwhatwayscanasymmetricinformationaffectthefunctioningofamarket?Fourapplicationswillbeconsidered:adverseselectionsignalingmoralhazardincentivescontracting.AsymmetricInformationinMark5AdverseSelectionConsiderausedcarmarket.Twotypesofcars;“lemons”and“peaches”.Eachlemonsellerwillaccept$1,000;abuyerwillpayatmost$1,200.Eachpeachsellerwillaccept$2,000;abuyerwillpayatmost$2,400.AdverseSelectionConsideraus6AdverseSelectionIfeverybuyercantellapeachfromalemon,thenlemonssellforbetween$1,000and$1,200,andpeachessellforbetween$2,000and$2,400.Gains-to-tradearegeneratedwhenbuyersarewellinformed.AdverseSelectionIfeverybuye7AdverseSelectionSupposenobuyercantellapeachfromalemonbeforebuying.Whatisthemostabuyerwillpayforanycar?AdverseSelectionSupposenobu8AdverseSelectionLetqbethefractionofpeaches.1-qisthefractionoflemons.ExpectedvaluetoabuyerofanycarisatmostAdverseSelectionLetqbethe9AdverseSelectionSupposeEV>$2000.Everysellercannegotiateapricebetween$2000and$EV(nomatterifthecarisalemonorapeach).Allsellersgainfrombeinginthemarket.AdverseSelectionSupposeEV>10AdverseSelectionSupposeEV<$2000.Apeachsellercannotnegotiateapriceabove$2000andwillexitthemarket.Soallbuyersknowthatremainingsellersownlemonsonly.Buyerswillpayatmost$1200andonlylemonsaresold.AdverseSelectionSupposeEV<11AdverseSelectionHence“toomany”lemons“crowdout”thepeachesfromthemarket.Gains-to-tradearereducedsincenopeachesaretraded.Thepresenceofthelemonsinflictsanexternalcostonbuyersandpeachowners.AdverseSelectionHence“tooma12AdverseSelectionHowmanylemonscanbeinthemarketwithoutcrowdingoutthepeaches?Buyerswillpay$2000foracaronlyifAdverseSelectionHowmanylemo13AdverseSelectionHowmanylemonscanbeinthemarketwithoutcrowdingoutthepeaches?Buyerswillpay$2000foracaronlyif

Soifoverone-thirdofallcarsarelemons,thenonlylemonsaretraded.AdverseSelectionHowmanylemo14AdverseSelectionAmarketequilibriuminwhichbothtypesofcarsaretradedandcannotbedistinguishedbythebuyersisapoolingequilibrium.Amarketequilibriuminwhichonlyoneofthetwotypesofcarsistraded,orbotharetradedbutcanbedistinguishedbythebuyers,isaseparatingequilibrium.AdverseSelectionAmarketequi15AdverseSelectionWhatifthereismorethantwotypesofcars?SupposethatcarqualityisUniformlydistributedbetween$1000and$2000anycarthatasellervaluesat$xisvaluedbyabuyerat$(x+300).Whichcarswillbetraded?AdverseSelectionWhatifthere16AdverseSelectionSellervalues10002000AdverseSelectionSellervalues17AdverseSelection100020001500SellervaluesAdverseSelection100020001500S18AdverseSelection100020001500Theexpectedvalueofanycartoabuyeris$1500+$300=$1800.SellervaluesAdverseSelection100020001500T19AdverseSelection100020001500Theexpectedvalueofanycartoabuyeris$1500+$300=$1800.Sosellerswhovaluetheircarsatmorethan$1800exitthemarket.SellervaluesAdverseSelection100020001500T20AdverseSelection10001800ThedistributionofvaluesofcarsremainingonofferSellervaluesAdverseSelection10001800Thed21AdverseSelection100018001400SellervaluesAdverseSelection100018001400S22AdverseSelection100018001400Theexpectedvalueofanyremainingcartoabuyeris$1400+$300=$1700.SellervaluesAdverseSelection100018001400T23AdverseSelection100018001400Theexpectedvalueofanyremainingcartoabuyeris$1400+$300=$1700.Sonowsellerswhovaluetheircarsbetween$1700and$1800exitthemarket.SellervaluesAdverseSelection100018001400T24AdverseSelectionWheredoesthisunravelingofthemarketend?LetvHbethehighestsellervalueofanycarremaininginthemarket.TheexpectedsellervalueofacarisAdverseSelectionWheredoesth25AdverseSelectionSoabuyerwillpayatmostAdverseSelectionSoabuyerwi26AdverseSelectionSoabuyerwillpayatmost

Thismustbethepricewhichthesellerofthehighestvaluecarremaininginthemarketwilljustaccept;i.e.AdverseSelectionSoabuyerwi27AdverseSelectionAdverseselectiondrivesoutallcarsvaluedbysellersatmorethan$1600.AdverseSelectionAdverseselec28AdverseSelectionwithQualityChoiceNoweachsellercanchoosethequality,orvalue,ofherproduct.Twoumbrellas;high-qualityandlow-quality.Whichwillbemanufacturedandsold?AdverseSelectionwithQuality29AdverseSelectionwithQualityChoiceBuyersvalueahigh-qualityumbrellaat$14andalow-qualityumbrellaat$8.Beforebuying,nobuyercantellquality.Marginalproductioncostofahigh-qualityumbrellais$11.Marginalproductioncostofalow-qualityumbrellais$10.AdverseSelectionwithQuality30AdverseSelectionwithQualityChoiceSupposeeverysellermakesonlyhigh-qualityumbrellas.Everybuyerpays$14andsellers’profitperumbrellais$14-$11=$3.Butthenasellercanmakelow-qualityumbrellasforwhichbuyersstillpay$14,soincreasingprofitto

$14-$10=$4.AdverseSelectionwithQuality31AdverseSelectionwithQualityChoiceThereisnomarketequilibriuminwhichonlyhigh-qualityumbrellasaretraded.Isthereamarketequilibriuminwhichonlylow-qualityumbrellasaretraded?AdverseSelectionwithQuality32AdverseSelectionwithQualityChoiceAllsellersmakeonlylow-qualityumbrellas.Buyerspayatmost$8foranumbrella,whilemarginalproductioncostis$10.Thereisnomarketequilibriuminwhichonlylow-qualityumbrellasaretraded.AdverseSelectionwithQuality33AdverseSelectionwithQualityChoiceNowweknowthereisnomarketequilibriuminwhichonlyonetypeofumbrellaismanufactured.Isthereanequilibriuminwhichbothtypesofumbrellaaremanufactured?AdverseSelectionwithQuality34AdverseSelectionwithQualityChoiceAfractionqofsellersmakehigh-qualityumbrellas;0<q<1.Buyers’expectedvalueofanumbrellais

EV=14q+8(1-q)=8+6q.High-qualitymanufacturersmustrecoverthemanufacturingcost,

EV=8+6q

³11Þ

q

³1/2.AdverseSelectionwithQuality35AdverseSelectionwithQualityChoiceSoatleasthalfofthesellersmustmakehigh-qualityumbrellasfortheretobeapoolingmarketequilibrium.Butthenahigh-qualitysellercanswitchtomakinglow-qualityandincreaseprofitby$1oneachumbrellasold.AdverseSelectionwithQuality36AdverseSelectionwithQualityChoiceSinceallsellersreasonthisway,thefractionofhigh-qualitysellerswillshrinktowardszero--butthenbuyerswillpayonly$8.Sothereisnoequilibriuminwhichbothumbrellatypesaretraded.AdverseSelectionwithQuality37AdverseSelectionwithQualityChoiceThemarkethasnoequilibriumwithjustoneumbrellatypetradedwithbothumbrellatypestradedAdverseSelectionwithQuality38AdverseSelectionwithQualityChoiceThemarkethasnoequilibriumwithjustoneumbrellatypetradedwithbothumbrellatypestradedsothemarkethasnoequilibriumatall.AdverseSelectionwithQuality39AdverseSelectionwithQualityChoiceThemarkethasnoequilibriumwithjustoneumbrellatypetradedwithbothumbrellatypestradedsothemarkethasnoequilibriumatall.Adverseselectionhasdestroyedtheentiremarket!AdverseSelectionwithQuality40SignalingAdverseselectionisanoutcomeofaninformationaldeficiency.Whatifinformationcanbeimprovedbyhigh-qualitysellerssignalingcrediblythattheyarehigh-quality?E.g.warranties,professionalcredentials,referencesfrompreviousclientsetc.SignalingAdverseselectionis41SignalingAlabormarkethastwotypesofworkers;high-abilityandlow-ability.Ahigh-abilityworker’smarginalproductisaH.Alow-abilityworker’smarginalproductisaL.aL<aH.SignalingAlabormarkethastw42SignalingAfractionhofallworkersarehigh-ability.1-histhefractionoflow-abilityworkers.SignalingAfractionhofallw43SignalingEachworkerispaidhisexpectedmarginalproduct.Iffirmskneweachworker’stypetheywouldpayeachhigh-abilityworkerwH=aHpayeachlow-abilityworkerwL=aL.SignalingEachworkerispaidh44SignalingIffirmscannottellworkers’typestheneveryworkerispaidthe(pooling)wagerate;i.e.theexpectedmarginalproduct

wP=(1-h)aL+haH.SignalingIffirmscannottell45SignalingwP=(1-h)aL+haH<aH,thewageratepaidwhenthefirmknowsaworkerreallyishigh-ability.Sohigh-abilityworkershaveanincentivetofindacrediblesignal.SignalingwP=(1-h)aL+haH46SignalingWorkerscanacquire“education”.Educationcostsahigh-abilityworkercHperunitandcostsalow-abilityworkercLperunit.cL>cH.SignalingWorkerscanacquire“47SignalingSupposethateducationhasnoeffectonworkers’productivities;i.e.,thecostofeducationisadeadweightloss.SignalingSupposethateducatio48SignalingHigh-abilityworkerswillacquireeHeducationunitsif

(i)wH-wL=aH-aL>cHeH,and

(ii)wH-wL=aH-aL<cLeH.SignalingHigh-abilityworkers49SignalingHigh-abilityworkerswillacquireeHeducationunitsif

(i)wH-wL=aH-aL>cHeH,and

(ii)wH-wL=aH-aL<cLeH.(i)saysacquiringeHunitsofeducationbenefitshigh-abilityworkers.SignalingHigh-abilityworkers50SignalingHigh-abilityworkerswillacquireeHeducationunitsif

(i)wH-wL=aH-aL>cHeH,and

(ii)wH-wL=aH-aL<cLeH.(i)saysacquiringeHunitsofeducationbenefitshigh-abilityworkers.(ii)saysacquiringeHeducationunitshurtslow-abilityworkers.SignalingHigh-abilityworkers51SignalingandtogetherrequireAcquiringsuchaneducationlevelcrediblysignalshigh-ability,allowinghigh-abilityworkerstoseparatethemselvesfromlow-abilityworkers.SignalingandtogetherrequireAc52SignalingQ:Giventhathigh-abilityworkersacquireeHunitsofeducation,howmucheducationshouldlow-abilityworkersacquire?SignalingQ:Giventhathigh-ab53SignalingQ:Giventhathigh-abilityworkersacquireeHunitsofeducation,howmucheducationshouldlow-abilityworkersacquire?A:Zero.Low-abilityworkerswillbepaidwL=aLsolongastheydonothaveeHunitsofeducationandtheyarestillworseoffiftheydo.SignalingQ:Giventhathigh-ab54SignalingSignalingcanimproveinformationinthemarket.But,totaloutputdidnotchangeandeducationwascostlysosignalingworsenedthemarket’sefficiency.Soimprovedinformationneednotimprovegains-to-trade.SignalingSignalingcanimprove55MoralHazardIfyouhavefullcarinsuranceareyoumorelikelytoleaveyourcarunlocked?Moralhazardisareactiontoincentivestoincreasetheriskofalossandisaconsequenceofasymmetricinformation.MoralHazardIfyouhavefullc56MoralHazardIfaninsurerknowstheexactriskfrominsuringanindividual,thenacontractspecifictothatpersoncanbewritten.Ifallpeoplelookaliketotheinsurer,thenonecontractwillbeofferedtoallinsurees;high-riskandlow-risktypesarethenpooled,causinglow-riskstosubsidizehigh-risks.MoralHazardIfaninsurerknow57MoralHazardExamplesofeffortstoavoidmoralhazardbyusingsignalsare:higherlifeandmedicalinsurancepremiumsforsmokersorheavydrinkersofalcohollowercarinsurancepremiumsforcontractswithhigherdeductiblesorfordriverswithhistoriesofsafedriving.MoralHazardExamplesofeffort58IncentivesContractingAworkerishiredbyaprincipaltodoatask.Onlytheworkerknowstheeffortsheexerts(asymmetricinformation).Theeffortexertedaffectstheprincipal’spayoff.IncentivesContractingAworker59IncentivesContractingTheprincipal’sproblem:designanincentivescontractthatinducestheworkertoexerttheamountofeffortthatmaximizestheprincipal’spayoff.IncentivesContractingTheprin60IncentivesContractingeistheagent’seffort.Principal’srewardisAnincentivecontractisafunctions(y)specifyingtheworker’spaymentwhentheprincipal’srewardisy.Theprincipal’sprofitisthusIncentivesContractingeisthe61IncentivesContractingLetbetheworker’s(reservation)utilityofnotworking.Togettheworker’sparticipation,thecontractmustoffertheworkerautilityofatleastTheworker’sutilitycostofaneffortleveleisc(e).IncentivesContractingLet62IncentivesContractingSotheprincipal’sproblemischooseetosubjectto(participationconstraint)Tomaximizehisprofittheprincipaldesignsthecontracttoprovidetheworkerwithherreservationutilitylevel.Thatis,...IncentivesContractingSothep63IncentivesContractingtheprincipal’sproblemistosubjectto(participationconstraint)IncentivesContractingtheprin64IncentivesContractingtheprincipal’sproblemistosubjectto(participationconstraint)Substitutefor

andsolveIncentivesContractingtheprin65IncentivesContractingtheprincipal’sproblemistosubjectto(participationconstraint)Theprincipal’sprofitismaximizedwhenSubstitutefor

andsolveIncentivesContractingtheprin66IncentivesContractingThecontractthatmaximizestheprincipal’sprofitinsistsupontheworkereffortlevele*thatequalizestheworker’smarginaleffortcosttotheprincipal’smarginalpayofffromworkereffort.IncentivesContractingThecont67IncentivesContractingHowcantheprincipalinducetheworkertochoosee=e*?Thecontractthatmaximizestheprincipal’sprofitinsistsupontheworkereffortlevele*thatequalizestheworker’smarginaleffortcosttotheprincipal’smarginalpayofffromworkereffort.IncentivesContractingHowcan68IncentivesContractinge=e*mustbemostpreferredbytheworker.IncentivesContractinge=e*m69IncentivesContractinge=e*mustbemostpreferredbytheworker.Sothecontracts(y)mustsatisfytheincentive-compatibilityconstraint;IncentivesContractinge=e*m70RentalContractingExamplesofincentivescontracts:

(i)Rentalcontracts:Theprincipalkeepsalump-sumRforhimselfandtheworkergetsallprofitaboveR;i.e.

Whydoesthiscontractmaximizetheprincipal’sprofit?

RentalContractingExamplesof71RentalContractingGiventhecontract

theworker’spayoffis

andtomaximizethistheworkershouldchoosetheeffortlevelforwhichRentalContractingGiventheco72RentalContractingHowlargeshouldbetheprincipal’srentalfeeR?Theprincipalshouldextractasmuchrentaspossiblewithoutcausingtheworkernottoparticipate,soRshouldsatisfy

i.e.RentalContractingHowlargesh73OtherIncentivesContracts(ii)Wagescontracts:Inawagescontractthepaymenttotheworkeris

wisthewageperunitofeffort.

Kisalump-sumpayment.

andKmakestheworkerjustindifferentbetweenparticipatingandnotparticipating.OtherIncentivesContracts(ii)74OtherIncentivesContracts(iii)Take-it-or-leave-it:Choosee=e*andbepaidalump-sumL,orchoose

e

¹

e*andbepaidzero.Theworker’sutilityfromchoosing

e

¹

e*is-c(e),sotheworkerwillchoosee=e*.Lischosentomaketheworkerindifferentbetweenparticipatingandnotparticipating.OtherIncentivesContracts(iii75IncentivesContractsinGeneralThecommonfeatureofallefficientincentivecontractsisthattheymaketheworkerthefullresidualclaimantonprofits.I.e.thelastpartofprofitearnedmustaccrueentirelytotheworker.IncentivesContractsinGenera76ChapterThirty-SixAsymmetricInformationChapterThirty-SixAsymmetricI77InformationinCompetitiveMarketsInpurelycompetitivemarketsallagentsarefullyinformedabouttradedcommoditiesandotheraspectsofthemarket.Whataboutmarketsformedicalservices,orinsurance,orusedcars?InformationinCompetitiveMar78AsymmetricInformationinMarketsAdoctorknowsmoreaboutmedicalservicesthandoesthebuyer.Aninsurancebuyerknowsmoreabouthisriskinessthandoestheseller.Ausedcar’sownerknowsmoreaboutitthandoesapotentialbuyer.AsymmetricInformationinMark79AsymmetricInformationinMarketsMarketswithonesideortheotherimperfectlyinformedaremarketswithimperfectinformation.Imperfectlyinformedmarketswithonesidebetterinformedthantheotheraremarketswithasymmetricinformation.AsymmetricInformationinMark80AsymmetricInformationinMarketsInwhatwayscanasymmetricinformationaffectthefunctioningofamarket?Fourapplicationswillbeconsidered:adverseselectionsignalingmoralhazardincentivescontracting.AsymmetricInformationinMark81AdverseSelectionConsiderausedcarmarket.Twotypesofcars;“lemons”and“peaches”.Eachlemonsellerwillaccept$1,000;abuyerwillpayatmost$1,200.Eachpeachsellerwillaccept$2,000;abuyerwillpayatmost$2,400.AdverseSelectionConsideraus82AdverseSelectionIfeverybuyercantellapeachfromalemon,thenlemonssellforbetween$1,000and$1,200,andpeachessellforbetween$2,000and$2,400.Gains-to-tradearegeneratedwhenbuyersarewellinformed.AdverseSelectionIfeverybuye83AdverseSelectionSupposenobuyercantellapeachfromalemonbeforebuying.Whatisthemostabuyerwillpayforanycar?AdverseSelectionSupposenobu84AdverseSelectionLetqbethefractionofpeaches.1-qisthefractionoflemons.ExpectedvaluetoabuyerofanycarisatmostAdverseSelectionLetqbethe85AdverseSelectionSupposeEV>$2000.Everysellercannegotiateapricebetween$2000and$EV(nomatterifthecarisalemonorapeach).Allsellersgainfrombeinginthemarket.AdverseSelectionSupposeEV>86AdverseSelectionSupposeEV<$2000.Apeachsellercannotnegotiateapriceabove$2000andwillexitthemarket.Soallbuyersknowthatremainingsellersownlemonsonly.Buyerswillpayatmost$1200andonlylemonsaresold.AdverseSelectionSupposeEV<87AdverseSelectionHence“toomany”lemons“crowdout”thepeachesfromthemarket.Gains-to-tradearereducedsincenopeachesaretraded.Thepresenceofthelemonsinflictsanexternalcostonbuyersandpeachowners.AdverseSelectionHence“tooma88AdverseSelectionHowmanylemonscanbeinthemarketwithoutcrowdingoutthepeaches?Buyerswillpay$2000foracaronlyifAdverseSelectionHowmanylemo89AdverseSelectionHowmanylemonscanbeinthemarketwithoutcrowdingoutthepeaches?Buyerswillpay$2000foracaronlyif

Soifoverone-thirdofallcarsarelemons,thenonlylemonsaretraded.AdverseSelectionHowmanylemo90AdverseSelectionAmarketequilibriuminwhichbothtypesofcarsaretradedandcannotbedistinguishedbythebuyersisapoolingequilibrium.Amarketequilibriuminwhichonlyoneofthetwotypesofcarsistraded,orbotharetradedbutcanbedistinguishedbythebuyers,isaseparatingequilibrium.AdverseSelectionAmarketequi91AdverseSelectionWhatifthereismorethantwotypesofcars?SupposethatcarqualityisUniformlydistributedbetween$1000and$2000anycarthatasellervaluesat$xisvaluedbyabuyerat$(x+300).Whichcarswillbetraded?AdverseSelectionWhatifthere92AdverseSelectionSellervalues10002000AdverseSelectionSellervalues93AdverseSelection100020001500SellervaluesAdverseSelection100020001500S94AdverseSelection100020001500Theexpectedvalueofanycartoabuyeris$1500+$300=$1800.SellervaluesAdverseSelection100020001500T95AdverseSelection100020001500Theexpectedvalueofanycartoabuyeris$1500+$300=$1800.Sosellerswhovaluetheircarsatmorethan$1800exitthemarket.SellervaluesAdverseSelection100020001500T96AdverseSelection10001800ThedistributionofvaluesofcarsremainingonofferSellervaluesAdverseSelection10001800Thed97AdverseSelection100018001400SellervaluesAdverseSelection100018001400S98AdverseSelection100018001400Theexpectedvalueofanyremainingcartoabuyeris$1400+$300=$1700.SellervaluesAdverseSelection100018001400T99AdverseSelection100018001400Theexpectedvalueofanyremainingcartoabuyeris$1400+$300=$1700.Sonowsellerswhovaluetheircarsbetween$1700and$1800exitthemarket.SellervaluesAdverseSelection100018001400T100AdverseSelectionWheredoesthisunravelingofthemarketend?LetvHbethehighestsellervalueofanycarremaininginthemarket.TheexpectedsellervalueofacarisAdverseSelectionWheredoesth101AdverseSelectionSoabuyerwillpayatmostAdverseSelectionSoabuyerwi102AdverseSelectionSoabuyerwillpayatmost

Thismustbethepricewhichthesellerofthehighestvaluecarremaininginthemarketwilljustaccept;i.e.AdverseSelectionSoabuyerwi103AdverseSelectionAdverseselectiondrivesoutallcarsvaluedbysellersatmorethan$1600.AdverseSelectionAdverseselec104AdverseSelectionwithQualityChoiceNoweachsellercanchoosethequality,orvalue,ofherproduct.Twoumbrellas;high-qualityandlow-quality.Whichwillbemanufacturedandsold?AdverseSelectionwithQuality105AdverseSelectionwithQualityChoiceBuyersvalueahigh-qualityumbrellaat$14andalow-qualityumbrellaat$8.Beforebuying,nobuyercantellquality.Marginalproductioncostofahigh-qualityumbrellais$11.Marginalproductioncostofalow-qualityumbrellais$10.AdverseSelectionwithQuality106AdverseSelectionwithQualityChoiceSupposeeverysellermakesonlyhigh-qualityumbrellas.Everybuyerpays$14andsellers’profitperumbrellais$14-$11=$3.Butthenasellercanmakelow-qualityumbrellasforwhichbuyersstillpay$14,soincreasingprofitto

$14-$10=$4.AdverseSelectionwithQuality107AdverseSelectionwithQualityChoiceThereisnomarketequilibriuminwhichonlyhigh-qualityumbrellasaretraded.Isthereamarketequilibriuminwhichonlylow-qualityumbrellasaretraded?AdverseSelectionwithQuality108AdverseSelectionwithQualityChoiceAllsellersmakeonlylow-qualityumbrellas.Buyerspayatmost$8foranumbrella,whilemarginalproductioncostis$10.Thereisnomarketequilibriuminwhichonlylow-qualityumbrellasaretraded.AdverseSelectionwithQuality109AdverseSelectionwithQualityChoiceNowweknowthereisnomarketequilibriuminwhichonlyonetypeofumbrellaismanufactured.Isthereanequilibriuminwhichbothtypesofumbrellaaremanufactured?AdverseSelectionwithQuality110AdverseSelectionwithQualityChoiceAfractionqofsellersmakehigh-qualityumbrellas;0<q<1.Buyers’expectedvalueofanumbrellais

EV=14q+8(1-q)=8+6q.High-qualitymanufacturersmustrecoverthemanufacturingcost,

EV=8+6q

³11Þ

q

³1/2.AdverseSelectionwithQuality111AdverseSelectionwithQualityChoiceSoatleasthalfofthesellersmustmakehigh-qualityumbrellasfortheretobeapoolingmarketequilibrium.Butthenahigh-qualitysellercanswitchtomakinglow-qualityandincreaseprofitby$1oneachumbrellasold.AdverseSelectionwithQuality112AdverseSelectionwithQualityChoiceSinceallsellersreasonthisway,thefractionofhigh-qualitysellerswillshrinktowardszero--butthenbuyerswillpayonly$8.Sothereisnoequilibriuminwhichbothumbrellatypesaretraded.AdverseSelectionwithQuality113AdverseSelectionwithQualityChoiceThemarkethasnoequilibriumwithjustoneumbrellatypetradedwithbothumbrellatypestradedAdverseSelectionwithQuality114AdverseSelectionwithQualityChoiceThemarkethasnoequilibriumwithjustoneumbrellatypetradedwithbothumbrellatypestradedsothemarkethasnoequilibriumatall.AdverseSelectionwithQuality115AdverseSelectionwithQualityChoiceThemarkethasnoequilibriumwithjustoneumbrellatypetradedwithbothumbrellatypestradedsothemarkethasnoequilibriumatall.Adverseselectionhasdestroyedtheentiremarket!AdverseSelectionwithQuality116SignalingAdverseselectionisanoutcomeofaninformationaldeficiency.Whatifinformationcanbeimprovedbyhigh-qualitysellerssignalingcrediblythattheyarehigh-quality?E.g.warranties,professionalcredentials,referencesfrompreviousclientsetc.SignalingAdverseselectionis117SignalingAlabormarkethastwotypesofworkers;high-abilityandlow-ability.Ahigh-abilityworker’smarginalproductisaH.Alow-abilityworker’smarginalproductisaL.aL<aH.SignalingAlabormarkethastw118SignalingAfractionhofallworkersarehigh-ability.1-histhefractionoflow-abilityworkers.SignalingAfractionhofallw119SignalingEachworkerispaidhisexpectedmarginalproduct.Iffirmskneweachworker’stypetheywouldpayeachhigh-abilityworkerwH=aHpayeachlow-abilityworkerwL=aL.SignalingEachworkerispaidh120SignalingIffirmscannottellworkers’typestheneveryworkerispaidthe(pooling)wagerate;i.e.theexpectedmarginalproduct

wP=(1-h)aL+haH.SignalingIffirmscannottell121SignalingwP=(1-h)aL+haH<aH,thewageratepaidwhen