Joe's preferences are described by the following utility function U (x, y) = xyB with a > 0 and B > 0. (a) Let I denote Joe's income, and Pr and py denote the prices of good x and y, respectively. Find Joe's optimal consumption bundle. (b) Now, suppose a = 6, B = 2, Px = 2, py = 3 and I = 24. Evaluate Joe's optimal choice. (c) Suppose Pr increases by 50%. What is Joe's new optimal consumption bundle? Calculate both the Income Effect and the Substitution Effect