Public Good. Suppose there are two goods X and Y in the economy where X is a public good and Y is a private good. Let X + Y = 100 denote the Production Possibility Frontier (PPF). There are two individuals A and B with utility functions uA(X, YA) = XYA and uB(X, YB) = XYB. Note that X does not have a subscript because it is a public good and the two individuals have to consume the same amount. Y is a private good so Y = YA + YB. (a) Suppose A is to achieve a utility of ¯uA. Find the amount of YB available to individual B as a function of different values of X. (b) Find the amount of X and YB that will maximize individual B’s utility. This could depend on ¯uA. Find individual A’s consumption of YA as well. (c) What is the condition for Pareto efficient allocation in such a case? Is the answer you find in part (b) Pareto efficient.