(12 points) Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 40 units of good X and 80 units of good Y. Consumer B is given an initial endowment of 40 units of good X and 80 units of good Y. Consumer A's utility function is given by: UA(X,Y) = X1/7*Y6/7, And consumer B's utility function is given by UB(X,Y) = X3/7*Y4/7. 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: