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There are four questions a,b,c, d. Here a and b are given. I will upload c and d next.

4. Madeline has initial wealth of w= $100,000 and a utility of money function U(w) = ln(w). She faces a risk of a costly illness, where there is a 0.05 probability (5% chance) of an illness with $50,000 in medical bills, and 95% chance of no illness. a. Calculate her utility if an illness doesn't happen, her expected utility when she is uncertain if she will get sick, the certainty equivalent of the health-related gamble, and her willingness to pay for actuarially fair full insurance. b. Suppose that the insurance company is only willing to sell her full insurance coverage for $3,000 due to their costs of doing business. Will Madeline purchase full coverage