Please answer the following question:

4. Consider two individuals a and b with the utility functions: Ua = (Xa)3 (Va)= (3) Up = (xb)*(VB)2 (4) where x, y are the amount that consumers consume. Suppose that total quantities of goods are fixed at X and Y. In order to purchase these bundles, they must also have something to sell in this two-good exchange economy. (a) Find an expression for Pareto-efficient allocations in this exchange economy in terms of total fixed quantities of goods X and Y, and consumption of consumer a. [Hint: Max U. s.t. U, and solve for the expression; see example 13.3] (b) If X=400, Y=250, and each consumer has 200 units of good X, how much of good Y each consumer will have at this allocation? Draw the Edgeworth box diagram that shows the equilibrium price ratio at the Pareto efficiency allocation? [Hint: Use the expression derived in (a) to find y, and derive MRS=2: ] Py