The certainty equivalent of a gamble is defined to be the amount of money which, if you were promised it with certainty, would be indifferent to the gamble.

a. If an expected utility maximizer has a utility function U(W) = w^1/2(where W is wealth) and if the probability of events 1 and 2 are both 1/2, write a formula for the certainty equivalent of a gamble that gives you x if event 1 happens and y if event 2 happens.

b. Generalize your formula in part (a) to the case where the probability of event 1 is p and the probability of event 2 is 1 ? p.

c. Generalize the formula in part (a) to the case where U(W) = W^afor a > 0.