4. Yusuf only cares about utility and has a utility of income given by U(I) = I/2. (I/2 is the square root of I.) (17 points total) a. Fill out the following chart by calculating his utility from each level of income and his marginal utility of each $2,500. Is his marginal utility from each $2,500 increasing, decreasing, or staying the same as income rises? (3 points) Utility Income $0 $2,500 $5,000 $7,500 $10,000 $12,500 Marginal utility of $2,500 Not applicable b. Suppose Yusuf has an income of $10,000. Suppose also that Yusuf may develop a medical issue that costs $7,500 to treat with a probability of p. Calculate Yusuf's expected utility if he is not insured for the following probabilities: p=0, p=1/3, p=2/3, and p=1. (3 points) c. If Yusuf's probability of developing the disease is p=1/3, what is his actuarially fair, full insurance premium? (3 points) d. e. Would Yusuf purchase health insurance at the actuarially fair, full insurance premium price with a probability of developing the disease of p=1/3? Why or why not? (4 points) Suppose the insurer adds $275 to the health insurance premium to cover its cost of administering the policy. Would Yusuf still purchase the insurance? Why or why not? (4 points)