Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X, Y) = X2Y UB ( X, Y) = XY Therefore: . For consumer A: MUx = 2XY; MUY = X2 . For consumer B: MUx = Y; MUY = X The initial endowments are: A: X = 90; Y = 12 B: X = 60; Y = 8 a) (20 points) Suppose the price of Y, Py = 1. Calculate the price of X, Px that will lead to a competitive equilibrium. b) (8 points) How much of each good does each consumer demand in equilibrium? Consumer A's Demand for X: Consumer A's Demand for Y: Consumer B's demand for X: Consumer B's demand for Y: c) (4 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium