1. Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

U_A(X,Y) = X^*Y

U_B(X,Y) = X*Y³

Therefore:

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

The initial endowments are:

A: X = 12; Y = 10

B: X = 12; Y = 10

a) (40 points) Suppose the price of Y, P_Y = 1. Calculate the price of X, P_X 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 Y

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?