Preferences Toward Risk Think of a lottery. Win $90 with probability 1/2 and win sO with probability 1/2 U($90)=12,U($0)=2 Expected utility is EU=×U(S90)+×U(S0) 212 2 =×12+-×2=7 2
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 is EU = U($90) + U($0) = + = 1 2 1 2 1 2 12 1 2 2 7. Preferences Toward Risk
Preferences Toward Risk Think of a lottery. Win $90 with probability 1/2 and win sO with probability 1/2 Expected money value of the lottery s EM=×S90+×S0=$45 2
Think of a lottery. Win $90 with probability 1/2 and win $0 with probability 1/2. Expected money value of the lottery is EM = $90 + $0 = 1 2 1 2 $45. Preferences Toward Risk
Preferences Under Uncertainty E=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 is preferred to $45 for sure→risk- oVing(喜爱风险) U($45)=7= the lottery is preferred equally to $45 for sure risk-neutrality 风险中性)
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 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 Utility 12 EUF7 $0 $45 $90 Wealth
Risk Averse $0 $90 Wealth 2 12 $45 EU=7 Utility
Risk Averse Utility U($45>EU 3 risk-aversion 12 mu declines as wealth U($45) rises U<0. EUF7 $0 $45 $90 Wealth
Risk Averse $0 $90 Wealth 12 U($45) U($45) > EU risk-aversion. 2 EU=7 $45 MU declines as wealth rises. U”<0. Utility