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?Since ?Hence for a riskaverter. ????1 ? ?anaM U ( c )M U ( c )ana????1 1? ? ?aa,M U ( c ) M U ( c )a nac ca na“ Unfair” Insurance ?Rational choice requires ?Since ?Hence for a riskaverter. ?. a riskaverter buys less than full “unfair” insurance. ????1 ? ?anaM U ( c )M U ( c )ana????1 1? ? ?aa,M U ( c ) M U ( c )a nac ca naUncertainty is Pervasive ?What are rational responses to uncertainty? –buying insurance (health, life, auto) –a portfolio of contingent consumption goods. Uncertainty is Pervasive ?What are rational responses to uncertainty? –buying insurance (health, life, auto) –a portfolio of contingent consumption goods. ? Uncertainty is Pervasive ?What are rational responses to uncertainty? –buying insurance (health, life, auto) –a portfolio of contingent consumption goods. ? ? Diversification (多樣化) ?Two firms, A and B. Shares cost $10. ?With prob. 1/2 A’s profit is $100 and B’s profit is $20. ?With prob. 1/2 A’s profit is $20 and B’s profit is $100. ?You have $100 to invest. How? Diversification ?Buy only firm A’s stock? ?$100/10 = 10 shares. ?You earn $1000 with prob. 1/2 and $200 with prob. 1/2. ?Expected earning: $500 + $100 = $600 Diversification ?Buy only firm B’s stock? ?$100/10 = 10 shares. ?You earn $1000 with prob. 1/2 and $200 with prob. 1/2. ?Expected earning: $500 + $100 = $600 Diversification ?Buy 5 shares in each firm? ?You earn $600 for sure. ?Diversification has maintained expected earning and lowered risk. Diversification ?Buy 5 shares in each firm? ?You earn $600 for sure. ?Diversification has maintained expected earning and lowered risk. ?Typically, diversification lowers expected earnings in exchange for lowered risk. Risk Spreading/Mutual Insurance ?100 persons each independently risk a $10,000 loss. ?Loss probability = . ?Initial wealth is $40,000. ?No insurance: expected wealth is 0 99 40 000 0 01 40 000 10 00039 900? ? ? ? ??$ , ($ , $ , )$ , .Risk Spreading/Mutual Insurance ?Mutual insurance: Expected loss is ?Each of the 100 persons pays $100 into a mutual insurance fund. ?Mutual insurance: each person has a certain wealth of ?Riskspreading benefits everyone. 0 01 10 000 100? ? ?$ , $ .$ 4 0 , 0 0 0 $ 1 0 0 $ 3 9 , 9 0 0 .?