Suppose there are two possible outcomes of a gamble: Under outcome A, you get $321 and under outcome B you get $222, where 222 > 321. Outcome A happens with a probability of 6 = 0.5 and outcome B happens with probability (1 6) = 0.5. Suppose we can use the function 3(1) 2 I\" for the consumption/utility relationship that allows us to represent indifference curves over risky outcomes using an expected utility function. a) What values can a take if you are risk averse? risk neutral? risk loving? b) Write down the equations for the expected consumption level as well as the expected utility from the gamble. Which one depends on a and why? c) What is the equation for the utility of the expected consumption level? (:1) Suppose you are offered 35: to not face this gamble. What equation would you have to solve to nd 5:? e) Suppose a = 1. Solve for 2: and explain your results. f) Suppose that, instead of two outcomes, there are actually three possible outcomes: A, B, and C, with associated consumption levels x1, x2, and 2:3 occurring with probabilities 61, 62, and (1 61 62). How would you write the expected utility of this gamble