assume that both X and Y are goods

9. (20 pts. In total) Consider Frederick, whose preferences are represented by the daily utility function U(X,Y) = x3y3, and who each day chooses a combination of X and Y that maximizes that day's utility, subject to a daily monetary budget, all of which must be spent each day. Frederick can buy (but not sell) X and Y each day in a nearby market where Px = $12 and Py= $4. Initially, Frederick has $120 to spend each day. Some months later, two friends of Frederick (Albert and Riley) decide that Frederick is not consuming enough X and Y. (They want Frederick to live like a King.) Albert wants to encourage Frederick to consume more X and so each day gives Frederick one unit of X plus $6 for every unit of X that Frederick consumes. (Frederick even receives $6 for consuming the one unit of X that Albert provided!) Riley wants to encourage Frederick to consume more Y and so each day gives Frederick three units of Y plus $1 for every unit of Y that Frederick consumes. (Frederick even receives $1 for each of Riley's three units of Y that he consumes!) RANG c) (5 pts.) How much of the change in X is due to the substitution effect as measured by Slutsky? d) (5 pts.) Draw a well-labeled diagram that illustrates your answer in part (c)