Consider an individual with $10,000 in initial wealth that faces a potential loss of $3,600. (Wealth...

 

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Consider an individual with $10,000 in initial wealth that faces a potential loss of $3,600. (Wealth would then be S6,400 if the loss occurs and the individual does not buy insurance.) The probability of the loss is 25%. The individual has expected utility preferences with the utility function u=Vw a. What is the actuarially fair premium per unit of coverage? b. If any amount of insurance were offered (from no insurance to full insurance) at an actuarially fair price, how much would the individual buy? c. If given the choice of any amount of insurance between zero and full insurance, if insurers charge a cost per unit of coverage c=two-sevenths (c=2/7= 0.28571...), how much will the individual choose? (Warning: The algebra will get a little bit messy at the end, even if you do the problem right. Sorry.) Consider an individual with $10,000 in initial wealth that faces a potential loss of $3,600. (Wealth would then be S6,400 if the loss occurs and the individual does not buy insurance.) The probability of the loss is 25%. The individual has expected utility preferences with the utility function u=Vw a. What is the actuarially fair premium per unit of coverage? b. If any amount of insurance were offered (from no insurance to full insurance) at an actuarially fair price, how much would the individual buy? c. If given the choice of any amount of insurance between zero and full insurance, if insurers charge a cost per unit of coverage c=two-sevenths (c=2/7= 0.28571...), how much will the individual choose? (Warning: The algebra will get a little bit messy at the end, even if you do the problem right. Sorry.)