4. Yusuf only cares about utility and has a utility of income given by U(I) =...

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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) 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)