Problem 2. Carol's risk preference is represented by the following expected utility formula: U (1,01;1 – 71, C2) = 7+(1 – ) VC2. T C1 T i) Suppose Carol is indifferent between the following two options: the first option A returns $100 with probability į and $49 with probability ż, and the second option B returns $X for sure. Determine X. Is X smaller than the expected return of A? Explain why. = = 2 ii) Consider the following three lotteries: L1 = (0.8, $100; 0.2, $25), L2 (0.6, $100; 0.4, $25), and L3 = (0.5, $225; 0.5, $0). What is the ranking of these lotteries for Carol? Calculate the risk premiums of these lotteries for Carol.