Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

U_A(X,Y) = XY³

U_B(X,Y) = X*Y

Therefore:

• For consumer A: MU_X= Y³; MU_Y= 3XY²
• For consumer B: MU_X= Y; MU_Y= X

The initial endowments are:

A: X = 16; Y = 28

B: X = 54; Y = 12

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