2. (18 points) Suppose there are two consumers, A and B, and two goods, X and Y.Consumer A is given an initial endowment of 6 units of good X and 1 units of good Y.Consumer B is given an initial endowment of 2 units of good X and 7 units of good Y.Consumer A's utility function is given by:

U_A(X,Y) = X*Y,

And consumer B's utility function is given by

U_B(X,Y) = X*Y³.

Therefore, consumer A's marginal utilities for each good are given by:

MU_X = Y

MU_Y = X

Also, consumer B's marginal utilities for each good are given by:

MU_X = Y³

MU_Y = 3XY²

a) (8 points) Suppose the price of good Y is equal to one.Calculate the price of good X that will lead to a competitive equilibrium.

P_X = _____________________

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) (2 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium?

MRS_A = ____________