E4465 ps2 question1

SUL 1. Suppose that you have a job paying $2500 per month. With 10 percent probability, you may get sick and your monthly earnings will be reduced by $900. Assume that you spend all of your income on consumption and you have no savings. Your utility from consumption is given by u(C) = VC and you are interested in maximizing the expected utility. (a) Suppose that you have no access to insurance. What is your expected income next month? What is your expected consumption? (b) What is the maximum price that you would be willing to pay for the first dollar of insurance? (c) Suppose that you can buy insurance that will cover all of your $900 loss. What is the maximum amount that you would be willing to pay for that insurance? (d) If you divide the amount obtained in part (c) by the amount of coverage purchased ($900), you should get a number that's smaller than the price that you'd be willing to pay for the first dollar of coverage but larger than the actuarially fair price. Explain why. (e) Suppose the dollar of coverage costs q=1/9. How much coverage are you going to buy