Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 4 units of X and TOTAL of 4 units of Y. The consumers' utility functions are given by:
UA (X,Y) = X + 2Y
UB (X,Y) = 2X + Y
Consumer A gets 0 units of X and 4 units of Y and Consumer B gets 4 units of X and 0 units of Y. Is the allocation Pareto Efficient?