Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = X2*Y UB(X,Y) = X*Y2 Therefore: . For consumer A: MUx = 2XY; MUY = X2 . For consumer B: MUx = Y2; MUY = 2XY The initial endowments are: A: X = 45; Y = 15 B: X = 60; Y = 25 a) (16 points) Suppose the price of Y, Py = 1. Calculate the price of X (Px) that will lead to a competitive equilibrium. Put this equilibrium price of X in the blank below. PX = b) (8 points) How much of each good does each consumer demand in equilibrium? Consumer A's demand for X is Consumer A's demand for Y is Consumer B's demand for X is Consumer B's demand for Y is c) (4 points) What is the marginal rate of substitution (MRS) for consumer A at the competitive equilibrium? MRS =