Elizabeth is in her seventies and is concerned about her health. Elizabeth has W=$50,000 in wealth. Her utility is given by U(C) = C^1/2, where C is the amount of her consumption. There is a 10% chance that she gets sick. If she gets sick, the medical bill will be $40,000. Her consumption equals her wealth minus any medical expenses and insurance premiums. a. What is the expected value of Elizabeths consumption with no insurance? What is her expected utility? b. Elizabeth is considering buying health insurance. If she bought full coverage, what would be her actuarially fair annual premium? If she bought coverage with a 20% copay, and a $2,000 deductible, what would be the actuarially fair annual premium? c. Elizabeths expected utility with full insurance if the premium was P would be U(W-P). What is the most she would be willing to pay for full insurance? (Note - Find the P that would make expected utility be the same between full insurance and no insurance.) d. There is another person, Bernie, who is also interested in insurance. His probability of getting sick is 13%. What is Bernies actuarially fair premium? If there was asymmetric information, such that the insurance company knew only that one person had a 13% probability and the other 10% but not whether it was Elizabeth or Bernie, could a pooled price be offered?