第12章讲义不确定性

chaptertwelveuncertaintystructurestatecontingentconsumption(依情形而定的消费）state-contingentbudgetconstraintpreferencesunderuncertaintychoiceunderuncertaintyriskaversiondiversificationandriskspreadinguncertaintyispervasivewhatisuncertainineconomicsystems?tomorrow’spricesfuturewealthfutureavailabilityofcommoditiespresentandfutureactionsofotherpeople.uncertaintyispervasivewhatarerationalresponsestouncertainty?buyinginsurance(health,life,auto)aportfolioofcontingentconsumptiongoods.statesofnaturepossiblestatesofnature:“caraccident”(a)“nocaraccident”(na).accidentoccurswithprobabilitya,doesnotwithprobabilityna;

a+

na=1.accidentcausesalossof$l.contingenciesacontractimplementedonlywhenaparticularstateofnatureoccursisstate-contingent.e.g.theinsurerpaysonlyifthereisanaccident.contingenciesastate-contingentconsumptionplanisimplementedonlywhenaparticularstateofnatureoccurs.e.g.takeavacationonlyifthereisnoaccident.state-contingentbudgetconstraintseach$1ofaccidentinsurancecosts.consumerhas$mofwealth.cnaisconsumptionvalueintheno-accidentstate.caisconsumptionvalueintheaccidentstate.state-contingentbudgetconstraintscnacastate-contingentbudgetconstraintscnaca2017astate-contingentconsumption

with$17consumptionvalueintheaccidentstateand$20consumptionvalueintheno-accidentstate.state-contingentbudgetconstraintswithoutinsurance,ca=m-lcna=m.state-contingentbudgetconstraintscnacamtheendowmentbundle.state-contingentbudgetconstraintsbuy$kofaccidentinsurance.cna=m-k.ca=m-l-k+k=m-l+(1-)k.state-contingentbudgetconstraintsbuy$kofaccidentinsurance.cna=m-k.ca=m-l-k+k=m-l+(1-)k.sok=(ca-m+l)/(1-)state-contingentbudgetconstraintsbuy$kofaccidentinsurance.cna=m-k.ca=m-l-k+k=m-l+(1-)k.sok=(ca-m+l)/(1-)andcna=m-(ca-m+l)/(1-)state-contingentbudgetconstraintsbuy$kofaccidentinsurance.cna=m-k.（k为premium(保费)）ca=m-l-k+k=m-l+(1-)k.sok=(ca-m+l)/(1-)andcna=m-(ca-m+l)/(1-)i.e.state-contingentbudgetconstraintscnacamtheendowmentbundle.state-contingentbudgetconstraintscnacamtheendowmentbundle.state-contingentbudgetconstraintscnacamtheendowmentbundle.whereisthemostpreferred

state-contingent

consumptionplan?preferencesunderuncertainty2statesofnature:atprobabilitya,consumptioniscaatprobabilityna,consumptioniscnaa+na=1.utilityisu(ca,

cna,

a,na).preferencesunderuncertaintyexpectedutilityfunctionvon-neuman-morgensternutilityfunctionpreferencesunderuncertaintystate-contingentconsumptionplansthatgiveequalexpectedutilityareequallypreferred.preferencesunderuncertaintycnacaeu1eu2eu3indifferencecurves

eu1<eu2<eu3preferencesunderuncertaintywhatisthemrsofanindifferencecurve?forconstanteu,deu=0.preferencesunderuncertaintypreferencesunderuncertaintypreferencesunderuncertaintypreferencesunderuncertaintypreferencesunderuncertaintypreferencesunderuncertaintycnacaeu1eu2eu3indifferencecurves

eu1<eu2<eu3choiceunderuncertaintyq:howisarationalchoicemadeunderuncertainty?a:choosethemostpreferredaffordablestate-contingentconsumptionplan.state-contingentbudgetconstraintscnacamtheendowmentbundle.whereisthemostpreferred

state-contingent

consumptionplan?state-contingentbudgetconstraintscnacamtheendowmentbundle.whereisthemostpreferred

state-contingent

consumptionplan?affordable

plansstate-contingentbudgetconstraintscnacamwhereisthemostpreferred

state-contingent

consumptionplan?morepreferredstate-contingentbudgetconstraintscnacammostpreferredaffordableplanstate-contingentbudgetconstraintscnacammostpreferredaffordableplanstate-contingentbudgetconstraintscnacammostpreferredaffordableplanmrs=slopeofbudget

constraintstate-contingentbudgetconstraintscnacammostpreferredaffordableplanmrs=slopeofbudget

constraint;i.e.riskaversionthinkofalottery.win$90withprobability1/2andwin$0withprobability1/2.u($90)=12,u($0)=2.expectedutilityispreferencesunderuncertaintythinkofalottery.win$90withprobability1/2andwin$0withprobability1/2.expectedmoneyvalueofthelotteryispreferencesunderuncertaintyeu=7andem=$45.u($45)>7$45forsureispreferredtothelottery

risk-aversion(规避风险）.u($45)<7thelotteryispreferredto$45forsure

risk-loving（喜爱风险）.u($45)=7thelotteryispreferredequallyto$45forsure

risk-neutrality（风险中性）.preferencesunderuncertaintywealth$0$90212$45eu=7utilitypreferencesunderuncertaintywealth$0$9012u($45)u($45)>eurisk-aversion.2eu=7$45utilitypreferencesunderuncertaintywealth$0$9012u($45)u($45)>eurisk-aversion.2eu=7$45mudeclinesaswealthrises.u”<0.utilitypreferencesunderuncertaintywealth$0$90122eu=7$45utilitypreferencesunderuncertaintywealth$0$9012u($45)<eurisk-loving.2eu=7$45u($45)utilitypreferencesunderuncertaintywealth$0$9012u($45)<eurisk-loving.2eu=7$45murisesaswealthrises.u”>0.u($45)utilitypreferencesunderuncertaintywealth$0$90122eu=7$45utilitypreferencesunderuncertaintywealth$0$9012u($45)=eurisk-neutrality.2u($45)=

eu=7$45utilitypreferencesunderuncertaintywealth$0$9012u($45)=eurisk-neutrality.2$45muconstantaswealthrises.u”=0.u($45)=

eu=7utilityexample:competitiveinsurancesupposeentrytotheinsuranceindustryisfree.expectedeconomicprofit=0.i.e.k-ak-(1-a)0=(-a)k=0.i.e.freeentry=a.ifpriceof$1insurance=accidentprobability,theninsuranceisfair.competitiveinsurancewheninsuranceisfair,rationalinsurancechoicessatisfycompetitiveinsurancewheninsuranceisfair,rationalinsurancechoicessatisfyi.e.competitiveinsurancewheninsuranceisfair,rationalinsurancechoicessatisfyi.e.marginalutilityofincomemustbethesameinbothstates.competitiveinsurancehowmuchfairinsurancedoesarisk-averseconsumerbuy?competitiveinsurancehowmuchfairinsurancedoesarisk-averseconsumerbuy?risk-aversionmu(c)asc.competitiveinsurancehowmuchfairinsurancedoesarisk-averseconsumerbuy?risk-aversionmu(c)asc.hencecompetitiveinsurancehowmuchfairinsurancedoesarisk-averseconsumerbuy?risk-aversionmu(c)asc.hencei.e.full-insurance.“unfair”insurancesupposeinsurersmakepositiveexpectedeconomicprofit.i.e.k-ak-(1-a)0=(-a)k>0.“unfair”insurancesupposeinsurersmakepositiveexpectedeconomicprofit.i.e.k-ak-(1-a)0=(-a)k>0.then>a

“unfair”insurancerationalchoicerequires“unfair”insurancerationalchoicerequiressince“unfair”insurancerationalchoicerequiressince

henceforarisk-averter.“unfair”insurancerationalchoicerequiressince

henceforarisk-averter.i.e.arisk-averterbuyslessthanfull“unfair”insurance.uncertaintyispervasivewhatarerationalresponsestouncertainty?buyinginsurance(health,life,auto)aportfolioofcontingentconsumptiongoods.uncertaintyispervasivewhatarerationalresponsestouncertainty?buyinginsurance(health,life,auto)aportfolioofcontingentconsumptiongoods.uncertaintyispervasivewhatarerationalresponsestouncertainty?buyinginsurance(health,life,auto)aportfolioofcontingentconsumptiongoods.?diversification(多样化）twofirms,aandb.sharescost$10.withprob.1/2a’sprofitis$100andb’sprofitis$20.withprob.1/2a’sprofitis$20andb’sprofitis$100.youhave$100toinvest.how?diversificationbuyonlyfirma’sstock?$100/10=10shares.youearn$1000withprob.1/2and$200withprob.1/2