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

U_A(X,Y) = X³*Y

U_B(X,Y) = X*Y

Therefore:

• For consumer A: MU_X = 3X²Y; MU_Y = X³
• For consumer B: MU_X = Y; MU_Y = X

The initial endowments are:

A: X = 40; Y = 80

B: X = 60; Y = 120

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?