Suppose that your utility function is u(x)5 !x

, and that you are offered a gamble which allows you to win $4 if you are lucky and $1 if you are not.

(a) Suppose that the probability of winning $4 is 1/4 and the probability of winning $1 is 3/4. What is the expected value of this gamble?

(b) Suppose that the probability of winning $4 is still 1/4 and the probability of winning $1 is 3/4. What is the expected utility of this gamble?

(c) Suppose that the probability of winning $4 is still 1/4 and the probability of winning $1 is 3/4. What is the certainty equivalent of the gamble; that is, what is the amount of money X such that you are indifferent between receiving $X for sure and playing the gamble?

(d) Imagine now that the probability of winning $4 is p and the probability of winning $1 is (1 2 p). If the utility of the gamble equals 3/2, what is p?