Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = X2Y UB(X,Y) = X*Y 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) Suppose the price of Y, PY = 1. Calculate the price of X, PX that will lead to a competitive equilibrium. b) 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) What is the marginal rate of substitution for consumer A at the competitive equilibrium