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titive Insurance ?When insurance is fair, rational insurance choices satisfy ?. M U ( c ) M U ( c )a na???????1 1? ? ? ?aaanaM U ( c )M U ( c )anaCompetitive Insurance ?When insurance is fair, rational insurance choices satisfy ?. ?Marginal utility of ine must be the same in both states. ??????1 1? ? ? ?aaanaM U ( c )M U ( c )anaM U ( c ) M U ( c )a na?Competitive Insurance ?How much fair insurance does a riskaverse consumer buy? M U ( c ) M U ( c )a na?Competitive Insurance ?How much fair insurance does a riskaverse consumer buy? ?Riskaversion ? MU(c) ? as c ?. M U ( c ) M U ( c )a na?Competitive Insurance ?How much fair insurance does a riskaverse consumer buy? ?Riskaversion ? MU(c) ? as c ?. ?Hence M U ( c ) M U ( c )a na?c c .a na?Competitive Insurance ?How much fair insurance does a riskaverse consumer buy? ?Riskaversion ? MU(c) ? as c ?. ?Hence ?. fullinsurance. M U ( c ) M U ( c )a na?c c .a na?“ Unfair” Insurance ?Suppose insurers make positive expected economic profit. ?. ?K ?aK (1 ?a)0 = (? ?a)K 0. “ Unfair” Insurance ?Suppose insurers make positive expected economic profit. ?. ?K ?aK (1 ?a)0 = (? ?a)K 0. ?Then ? ? ?a ? ????1 1? ? ?aa.“ Unfair” Insurance ?Rational choice requires ????1 ? ?anaM U ( c )M U ( c )ana“ Unfair” Insurance ?Rational choice requires ?Since ????1 ? ?anaM U ( c )M U ( c )ana????1 1? ? ?aa,M U ( c ) M U ( c )a na“ Unfair” Insurance ?Rational choice requires ?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