1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X, Y) = X*Y UB(X,Y) = X*Y3 Therefore: For consumer A: MUx = Y; MUy = X For consumer B: MUx = Y3; MUy = 3XY2 The initial endowments are: A: X = 12; Y = 10 B: X = 12; Y = 10 a) (40 points) Suppose the price of Y, Py = 1. Calculate the price of X, Px that will lead to a competitive equilibrium.b] [16 points) How much of each good does each consumer demand in equilibrium? Consumer A's Demand for X: Consumer A's Demand for '1' Consumer B's demand for X Consumer B's demand for Y c) (8 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium