1、Chapter Twelve,Uncertainty不确定性,Structure,State contingent consumption(依情形而定的消费）Preferences under uncertaintyAttitudes toward riskState-contingent budget constraintChoice under uncertaintyDiversification and risk spreading,Uncertainty is Pervasive,What is uncertain in economic systems?tomorrows price
2、sfuture wealthfuture availability of commoditiespresent and future actions of other people.,Uncertainty is Pervasive,What are rational responses to uncertainty?buying insurance(health,life,auto)a portfolio of contingent consumption goods.,States of Nature,Possible states of Nature:“car accident”(a)“
3、no car accident”(na).Accident occurs with probability a,does not with probability na;a+na=1.Accident causes a loss of$L.,Contingencies,A contract implemented only when a particular state of Nature occurs is state-contingent.E.g.the insurer pays only if there is an accident.,Contingencies,A state-con
4、tingent consumption plan is implemented only when a particular state of Nature occurs.E.g.take a vacation only if there is no accident.,Preferences Under Uncertainty,2 states of nature:At probability a,consumption is caAt probability na,consumption is cnaa+na=1.Utility is U(ca,cna,a,na).,Preferences
5、 Under Uncertainty,Expected utility functionVon-Neuman-Morgenstern utility function,Positive affine transformationv(u)=au+b,a0,Preferences Toward Risk,Risk averseRisk neutralRisk loving,Think of a lottery.Win$90 with probability 1/2 and win$0 with probability 1/2.U($90)=12,U($0)=2.Expected utility i
6、s,Preferences Toward Risk,Think of a lottery.Win$90 with probability 1/2 and win$0 with probability 1/2.Expected money value of the lottery is,Preferences Toward Risk,Preferences Under Uncertainty,EU=7 and EM=$45.U($45)7$45 for sure is preferred to the lottery risk-aversion(规避风险）.U($45)7 the lottery
7、 is preferred to$45 for sure risk-loving（喜爱风险）.U($45)=7 the lottery is preferred equally to$45 for sure risk-neutrality（风险中性）.,Risk Averse,Wealth,$0,$90,2,12,$45,EU=7,Utility,Risk Averse,Wealth,$0,$90,12,U($45),U($45)EU risk-aversion.,2,EU=7,$45,MU declines as wealthrises.U”0.,Utility,Risk-Loving,We
8、alth,$0,$90,12,2,EU=7,$45,Utility,Risk Loving,Wealth,$0,$90,12,U($45)EU risk-loving.,2,EU=7,$45,MU rises as wealthrises.U”0.,U($45),Utility,Risk Neutral,Wealth,$0,$90,12,2,EU=7,$45,Utility,Risk Neutral,Wealth,$0,$90,12,U($45)=EU risk-neutrality.,2,$45,MU constant as wealthrises.U”=0.,U($45)=EU=7,Uti
9、lity,Indifference Curves Under Uncertainty,State-contingent consumption plans that give equal expected utility are equally preferred.,Preferences Under Uncertainty,Cna,Ca,EU1,EU2,EU3,Indifference curvesEU1 EU2 EU3,Preferences Under Uncertainty,What is the MRS of an indifference curve?For constant EU
10、,dEU=0.,Preferences Under Uncertainty,Preferences Under Uncertainty,Cna,Ca,EU1,EU2,EU3,Indifference curvesEU1 EU2 EU3,Budget Constraint with Insurance,Each$1 of accident insurance costs.Consumer has$m of wealth.Cna is consumption value in the no-accident state.Ca is consumption value in the accident
11、 state.,State-Contingent Budget Constraints,Cna,Ca,State-Contingent Budget Constraints,Cna,Ca,20,17,A state-contingent consumptionwith$17 consumption value in the accident state and$20 consumption value in the no-accident state.,State-Contingent Budget Constraints,Without insurance,Ca=m-LCna=m.,Stat
12、e-Contingent Budget Constraints,Cna,Ca,m,The endowment bundle.,Buy$K of accident insurance.Cna=m-K.（K 为premium(保费)）Ca=m-L-K+K=m-L+(1-)K.,So K=(Ca-m+L)/(1-),And Cna=m-(Ca-m+L)/(1-)I.e.,Budget Constraint with Insurance,Cna,Ca,m,The endowment bundle.,Where is themost preferredstate-contingentconsumption plan?,Budget Constraint with Insurance,Choice Under Uncertainty,Q:How is a rational choice made under uncertainty?A:Choose the most preferred affordable state-contingent consumption plan.,Cna,Ca,m,The endowment bundle.,Where is themost preferredstate-contingentconsumption plan?,
