Suppose there are two consumers, A and B. The utility functions of each consumer are given by:

U_A(X,Y) = X²*Y

U_B(X,Y) = X*Y²

Therefore:

• For consumer A: MU_X = 2XY; MU_Y = X²
• For consumer B: MU_X = Y²; MU_Y = 2XY

The initial endowments are:

A: X = 80; Y = 50

B: X = 120; Y = 60

a) (16 points) Suppose the price of Y, P_Y = 1. Calculate the price of X, P_X 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?