You are a risk-averse decision maker with a utility function u(x) = I 3200 x '2, where x denotes your income expressed in thousands of dollars. Your income is $100,000 (thus, x = 100). However, there is a 0.2 chance that you will have an accident that results in a loss of $20,000 (then x = 80). (See Uncertainty Practice Problems #3 and Bensako 15.14, 15.6) a. Calculate both the expected value and the expected utility of this lottery. (6 points) b. Calculate your utility of the expected value. How does it compare to the expected utility from part a? Explain what this reveals about preferences. (8 points) Calculate your risk premium. (8 points) d. Suppose you can purchase an insurance policy that fully insures you against loss. What is the highest premium that you would be willing to pay for this insurance policy? (8 points)