Question 2

1. Joe has a utility function of U(x) = x 3 . He is offered a gamble that pays him 0 X 9 with probability 0.75 and 16 Y 9 with probability 0.25. Joe has $9 that he either can keep or use to buy the bet.

a. Will Joe ever take the bet? Justify your answer mathematically. (Basically find one value of X and Y in the range for which Joe will accept, if such values exist.)

b. Will Joe always take the bet? Justify your answer mathematically. (Basically find one value of X and Y in the range for which Joe will not accept, if such values exist.)