Consider a pure exchange economy with two individuals (call A and B) and two goods (called X and Y ). Individual A has 120 units of good Y but no good X, and A's utility function is given by UA(xA; yA) = ln xA +ln yA. Individual B has 90 units of good X butnogoodY,andB'sutilityfunctionisgivenbyUB(xB;yB)=2lnxB +lnyB.
(a) Find the Walrasian equilibrium prices and the equilibrium allocation, illustrate this Walrasian equilibrium in the Edgeworth box.
(b) Find all Pareto efficient allocations and demonstrate the first theorem of welfare economics