中级微观-第十二次课件.ppt

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1、Chapter TwelveUncertainty不确定性不确定性StructureuState contingent consumption(依情依情形而定的消费）形而定的消费）uPreferences under uncertaintyuAttitudes toward riskuState-contingent budget constraintuChoice under uncertaintyuDiversification and risk spreadingUncertainty is PervasiveuWhat is uncertain in economic systems?

2、tomorrows pricesfuture wealthfuture availability of commoditiespresent and future actions of other people.Uncertainty is PervasiveuWhat are rational responses to uncertainty?buying insurance(health,life,auto)a portfolio of contingent consumption goods.States of NatureuPossible states of Nature:“car

3、accident”(a)“no car accident”(na).uAccident occurs with probability a,does not with probability na;a+na=1.uAccident causes a loss of$L.ContingenciesuA contract implemented only when a particular state of Nature occurs is state-contingent.uE.g.the insurer pays only if there is an accident.Contingenci

4、esuA state-contingent consumption plan is implemented only when a particular state of Nature occurs.uE.g.take a vacation only if there is no accident.Preferences Under Uncertaintyu2 states of nature:At probability a,consumption is caAt probability na,consumption is cna a+na=1.uUtility is U(ca,cna,a,

5、na).Preferences Under UncertaintyExpected utility functionVon-Neuman-Morgenstern utility functionPositive affine transformationv(u)=au+b,a0Preferences Toward RiskuRisk averseuRisk neutraluRisk lovinguThink of a lottery.uWin$90 with probability 1/2 and win$0 with probability 1/2.uU($90)=12,U($0)=2.uE

6、xpected utility isPreferences Toward RiskuThink of a lottery.uWin$90 with probability 1/2 and win$0 with probability 1/2.uExpected money value of the lottery isPreferences Toward RiskPreferences Under UncertaintyuEU=7 and EM=$45.uU($45)7$45 for sure is preferred to the lottery risk-aversion(规避风险）规避风

7、险）.uU($45)EU risk-aversion.2EU=7$45MU declines as wealthrises.U”0.UtilityRisk-LovingWealth$0$90122EU=7$45UtilityRisk LovingWealth$0$9012U($45)0.U($45)UtilityRisk NeutralWealth$0$90122EU=7$45UtilityRisk NeutralWealth$0$9012U($45)=EU risk-neutrality.2$45MU constant as wealthrises.U”=0.U($45)=EU=7Utili

8、tyIndifference Curves Under UncertaintyuState-contingent consumption plans that give equal expected utility are equally preferred.Preferences Under UncertaintyCnaCaEU1EU2EU3Indifference curvesEU1 EU2 EU3Preferences Under UncertaintyuWhat is the MRS of an indifference curve?uFor constant EU,dEU=0.Pre

9、ferences Under UncertaintyPreferences Under UncertaintyCnaCaEU1EU2EU3Indifference curvesEU1 EU2 0.“Unfair”InsuranceuSuppose insurers make positive expected economic profit.uI.e.K-aK-(1-a)0=(-a)K 0.uThen a “Unfair”InsuranceuRational choice requires“Unfair”InsuranceuRational choice requiresuSince“Unfa

10、ir”InsuranceuRational choice requiresuSinceuHence for a risk-averter.“Unfair”InsuranceuRational choice requiresuSinceuHence for a risk-averter.uI.e.a risk-averter buys less than full“unfair”insurance.Uncertainty is PervasiveuWhat are rational responses to uncertainty?buying insurance(health,life,aut

11、o)a portfolio of contingent consumption goods.?Diversification(多样化）uTwo firms,A and B.Shares cost$10.uWith prob.1/2 As profit is$100 and Bs profit is$20.uWith prob.1/2 As profit is$20 and Bs profit is$100.uYou have$100 to invest.How?DiversificationuBuy only firm As stock?u$100/10=10 shares.uYou earn

12、$1000 with prob.1/2 and$200 with prob.1/2.uExpected earning:$500+$100=$600DiversificationuBuy only firm Bs stock?u$100/10=10 shares.uYou earn$1000 with prob.1/2 and$200 with prob.1/2.uExpected earning:$500+$100=$600DiversificationuBuy 5 shares in each firm?uYou earn$600 for sure.uDiversification has

13、 maintained expected earning and lowered risk.uTypically,diversification lowers expected earnings in exchange for lowered risk.Risk Spreading/Mutual Insuranceu100 persons each independently risk a$10,000 loss.uLoss probability=0.01.uInitial wealth is$40,000.uNo insurance:expected wealth isRisk Spreading/Mutual InsuranceuMutual insurance:Expected loss isuEach of the 100 persons pays$100 into a mutual insurance fund.uMutual insurance:each person has a certain wealth ofuRisk-spreading benefits everyone.