Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X, Y) = X3 + Y UB(X,Y) = X*Y Therefore: . For consumer A: MUx = 3X2Y; MUY = X3 For consumer B: MUx = Y; MUY = X The initial endowments are: A: X = 100; Y = 48 B: X = 60; Y = 60 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 =