課件大綱中級微觀經(jīng)濟學李力行1011

Statecontingentconsumption依情形而定的消費，或PreferencesunderExpectedutilityUseexpectedutilityfunctiontodescribeattitudestowardriskDemandforBudgetInsuranceDiversificationandrisk2UncertaintyisPervasiveWhatisuncertainineconomicfuturefutureavailabilityofpresentandfutureactionsofotherUncertaintyisWhatarerationalresponsestobuyinginsurance(health,life,aportfolioofcontingentconsumptiongoods.StatesofPossiblestatesof“caraccident”“nocaraccident”Accidentoccurswithprobabilitya,doesnotwithprobabilityna;a+na=AccidentcausesalossofAcontractimplementedonlywhenaparticularstateofNatureoccursisE.g.theinsurerpaysonlyifthereisanaccident.Astate-contingentconsumptionplanisimplementedonlywhenaparticularstateofNatureoccurs.E.g.takeavacationonlyifthereisnoEach$1ofaccidentinsurancecostsConsumerhas$mofCnaisconsumptionvalueintheno-accidentstate.Caisconsumptionvalueintheaccidentstate.WithoutCa=m-Cna= Theendowmentm Buy$KofaccidentCna=m-Ca=m-L-K+K=m-L+(1-SoK=(Ca-m+L)/(1-AndCna=m-(Ca-m+L)/(1- mL 1 1 m 1 1mm m

WhereisthemostpreferredThinkofaWin$90withprobability1/2and$0withprobabilityU($90)= U($0)=ExpectedutilityEU1U($90)2

21122

122ThinkofaWin$90withprobability1/2and$0withprobabilityExpectedmoneyvalueofthe EM1$902

2

EU=7andEM=U($457$45forsureispreferredtothelotteryrisk-averse規(guī)避風險.U($45)<7thelotteryispreferredto$45forsurerisk-loving喜愛風險.U($45)=7thelotteryispreferredequallyto$45forsurerisk-neutral

U($45)>EUrisk-MUdeclinesaswealth2 2

U($45)<EUrisk-MUrisesaswealth

U($45)=EUrisk-MUconstantaswealth2 EU1U(c12U(c2期望效用函數(shù)State-contingentconsumptionplansthatgiveequalexpectedutilityareequallypreferred. EU1<EU2<EU3WhatistheMRSofanindifferenceGetconsumptionc1with1andc2withprobability1+2=EU=1U(c1)+EU1U(c1)2U(c2dEU1MU(c1)dc12MU(c21MU(c1)dc12MU(c2dc21MU(c1) EU1<EU2<EU3dcnaaMU(ca

ChoiceUnderQ:Howisarationalchoicemadeunderuncertainty?A:Choosethemostpreferredaffordablestate-contingentconsumptionplan.m

State-ContingentBudgetMostpreferredaffordableMRS=slopeofconstraint; m m

Supposeentrytotheinsuranceindustryisfree.Expectedeconomicprofit=i.e.K-aK-(1-a)0=(-a)K=i.e.freeentry=Ifpriceof$1insurance=accidentprobability,theninsuranceisfair公Wheninsuranceisfair,rationalinsurancechoicessatisfy aMU(ca Marginalutilityofincomemustbethesameinbothstates.Howmuchfairinsurancedoesarisk-averseconsumerbuy?Risk-averseMU(c)asc cacnai.e.full-Supposeinsurersmakepositiveexpectedeconomicprofit.I.e.K-aK-(1-a)0=(-a)K>Then>a

Rationalchoice

Risk-averseMU(c)ascca<cna arisk-averterbuyslessthanfull“unfair”insurance.UncertaintyisWhatarerationalresponsesto–buyinginsurance(health,life, aportfolioofcontingentconsumptiongoods.Twofirms,AandB.SharescostWithprob.1/2A’sprofitis$100andB’sprofitis$20.Withprob.1/2A’sprofitis$20andB’sprofitis$100.Youhave$100toinvest.BuyonlyfirmA’s$100/10=10Youearn$1000withprob.1/2$200withprob.Expectedearning:$500+$100=BuyonlyfirmB’s$100/10=10Youearn$1000withprob.1/2$200withprob.Expectedearning:$500+$100=Buy5sharesineachYouearn$600forDiversificationhasmaintainedexpectedearningandloweredrisk.Typically,diversificationlowersexpectedearningsinexchangeforloweredrisk.100personseachindependentlyriska$10,000loss.Lossprobability=