1.(28 total points) Suppose there are two consumers, A and B, and two goods, X and Y.Consumer A is given an initial endowment of 3 units of good X and 6 units of good Y.Consumer B is given an initial endowment of 5 units of good X and 6 units of good Y.Consumer A's utility function is given by:

U_A(X,Y) = X²*Y,

And consumer B's utility function is given by

U_B(X,Y) = X*Y.

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

MU_X = 2XY

MU_Y = X²

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

MU_X = Y

MU_Y = X

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.

b) (4 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: