《健康经济学》课件Chapter9

IntroPreviously,westudied:DemandforinsuranceRiskaversionbutnoinformationasymmetryAkerlof’smarketforlemonsinformationasymmetrybutnoriskaversionTheRothschild-StiglitzModel(1976)putsthesetwotogether.Ch9|AdverseSelection:TheRothschild-StiglitzmodelTheIH-ISspaceIH-ISspaceRecalltheincome-utilityspaceTakeHEandSEpointsandbundlethemtoonepointE(endowmentpoint)inIH-ISspacePointEshowstheincomeofanindividualinboththehealthyandthesickstateIH-ISspacePointCrepresentsapartialinsurancecontractHorizontalshift=premium(r)Verticalshift=payoutifsick(q-r)IH-ISspaceGivenC1,C2,C3,C4,andendowmentpointEwecanmakesomeassumptions:IndividualprefersC2toC1PrefersC1toC3CannotcomparepreferencebetweenC1toC4CannotcomparepreferencestoECh9|AdverseSelection:TheRothschild-StiglitzmodelINDIFFERENCECURVESINIH-ISSpaceIndifferencecurvesinIH-ISspaceDownwardslopingWillingtogiveupincomeinonestateifcompensatedformoreincomeintheotherstateConvexMoredownward-slopingatlowlevelsofIHbutflatterathighlevelsISandIHareimperfectsubstitutesResultofriskaversionCh9|AdverseSelection:TheRothschild-StiglitzmodelTHEFULL-INSURANCELINEThefull-insurancelineThe45%lineisthefull-insurancelineWhy?Whatdoesthishavetodowithstateindependence?

Anypointonthislinerepresentsafullinsurancecontract.Ch9|AdverseSelection:TheRothschild-StiglitzmodelTHEZERO-PROFITLINEThezero-profitlineRepresentsthesetofcontractssuchthatthepremiumisexactlythesameastheexpectedpayout(noprofitsforinsurancecompany)Zero-profitlinerunsthroughendowmentpointEAlsocanbethoughtofastheactuarially-fairlineThezero-profitlinedividesIH-ISspaceintoprofitableandunprofitablezonesC1liesbelowthezero-profitlineandresultsinprofitsforinsurancecompaniesC3liesabovethezero-profitlineandresultsinalossofmoneyforcompaniesNocompanywillofferpointsabovezero-profitlineWillcustomersbewillingtotakesomethingbelowthezero-profitline?Ch9|AdverseSelection:TheRothschild-StiglitzModelTHEFEASIBLECONTRACTWEDGEThefeasiblecontractwedgeR1=overfullinsuranceGetmoreincomeifyouaresick(implausiblecontract)R2=underindifferencecurvegoingthroughEIndividualprefersEtoanycontractofferedinthisregionR3=northeastofzero-profitlineCompanieswilllosemoneyonthesecontractsF=feasiblecontractwedgeOnlyareawherebothcustomersandinsurancecompanieswanttomeetCh9|AdverseSelection:TheRothschild-StiglitzModelFINDINGANEQUILIBRIUMEquilibriumAsetofcontractsisinequilibriumif:Allindividualsselectthecontractthatoffersthemostutility.Nocontractinthesetearnsnegativeprofitsforthefirmofferingit.Thereexistsnocontractorsetofcontractsoutsidethesetthat,ifoffered,wouldattractcustomersandearnatleastzeroprofit.Case#1:symmetricinformation,homogeneouscustomersIstheset{E,α}anequilibrium?αliesonahigherindifferencecurve(satisfiesequilibriumcondition1)αisbelowthezero-profitline(satisfiescondition2)Butβcanattractcustomersawayfromαandstillmakepositiveprofits(condition3violated)Case#1:symmetricinformation,homogeneouscustomersTheonlyvalidequilibrium:Ch9|AdverseSelection:TheRothschild-StiglitzModelHETEROGENEOUSRISKTYPESHeterogeneousrisktypesRobusttypeshavealowprobability,p,ofgettingsickFrailtypeshaveahigherprobabilityofgettingsickSlopeofzero-profitlinedependsonprobabilityofsicknessWhohasasteeperzero-profitline?Why?Thepopulationzero-profitlinewillfallbetweenthefrailzero-profitlineandtherobustzero-profitline.Ch9|AdverseSelection:TheRothschild-StiglitzModelINDIFFERENCECURVESFORTHEROBUSTANDFRAILHeterogeneousrisktypesHowdotheindifferencecurvesvaryforrobustandfrailindividuals?WhovaluesISmorerelativetoIH?Case#2:symmetricinformation,heterogeneouscustomersIdealcontractpointliesonanindividual’srespectivezero-profitlineIndifferencecurveslietangenttozero-profitlineThesecontractsareofferedwhenfirmscantellfrailandrobustindividualsapartandcanlegallyexcludecertainrisktypesfromcertaincontractsThisidealcontractiscalledthe“symmetricinformationequilibrium”Ch9|AdverseSelection:TheRothschild-StiglitzModelINFORMATIONASYMMETRYANDTHEPOOLINGEQUILIBRIUMPoolingequilibriumDefinition–acontractthatattractsbothrobustandfrailindividualswhilealsosatisfyingequilibriumconditions

Whyisthisdesirable?Case#3:asymmetricinformation,

heterogeneouscustomersAnypossiblepoolingequilibriummustbeonthepopulationzero-profitlineIftotherightofzero-profit,firmlosesmoneyIftotheleftofzero-profit,thenotherfirmscanenterthemarketCase#3:asymmetricinformation,

heterogeneouscustomersContractα:BothfrailandrobustindividualschooseαoverEFirmmakeszeroprofitsbecauseαisonthezero-profitlineCase#3:asymmetricinformation,

heterogeneouscustomersContractα:BothfrailandrobustindividualschooseαoverEFirmmakeszeroprofitsbecauseαisonthezero-profitlineHowever,becauserobustandfrailindifferencecurvesaredifferentslopes,otherinsurancefirmscanenterthemarketatδandappealtotherobustindividualsnopoolingequilibriumcanexist!δcreatesadverseselectionOnlyattractstherobustindividualsGoodforfirmofferingδbecauseexpectedpayoutislowandfirmscanexpectpositiveprofitsBadforfirmofferingαbecauseleftwithfrailindividualsandcanexpecttolosemoneyduetoincreasedpayoutsYoucanfindaδtospoilanypoolingequilibriumanywhereonthezero-profitlineCh9|AdverseSelection:TheRothschild-StiglitzModelFINDINGASEPARATINGEQUILIBRIUM(SOMETIMES)SeparatingequilibriumDefinition:asetofcontractswhereoneattractsfrailindividualsandtheotherattractsrobustindividuals,whilesatisfyingequilibriumconditionsSeparatingequilibriumRecall:Ω1andΩ2cannotco-existbecausefrailindividualswillmovetoΩ2fromΩ1NeedacontractΩ3thatwillnottemptfrailindividualstoleaveΩ1SeparatingequilibriumΩ3liesonthesameindifferencecurveasΩ1forfrailindividualsbutmostlikelychooseΩ1

SeparatingequilibriumΩ3liesonthesameindifferencecurveasΩ1forfrailindividualsbutmostlikelychooseΩ1

RobustindividualspreferΩ3toΩ1

ThusbothrobustandfrailindividualsaremaximizingtheirutilitySeparatingequilibriumR1–attractsthefrailindividualsbutnottherobustandthereforeisunprofitableforafirmR2–bothrobustandfrailareattractedtothisregionbutitisabovethepopulationzero-profitlineandisthereforeunprofitableR3–attractsrobust,butisunprofitableforfirmsΩ3andΩ1areaseparatingequilibriumSeparatingequilibriumscanbreakExample:toomanyrobustcustomersCreatesnewregion,R4Whoisharmed?Whenfirmscannottellfrailorrobustindividualsapart,frailcustomersstillreceivefullinsuranceatanactuariallyfairpriceTherobustreceiveinferiorinsurancecontractsthatarenotasfullastheylike–therobustarequantityconstrainedDoesthissuggesttherobustandthefrailcouldmakeapareto-improvingtrade?Ch9|AdverseSelection:TheRothschild-StiglitzModelCANMARKETSSOLVEADVERSESELECTION?SolvingadverseselectionGovernmentforceseveryonetobuythecontractattheintersectionofthefull-insurancelineandthepopulationzero-profitlineButtherecouldbefreemarketsolutions,underonecrucialassumption:Healthdifferencesbetweenrobustandfrailonlyappearovertimeascustomersage.SolvingadverseselectionLifetimeinsurancecontractTwocustomers