3. There are two goods, with quantities denoted by 2 and y. The total amounts available to An and Bob together are a and y and these quantities satisfy * = y. Ann's preferences are given by the utility function (x, y) = vi + vy and Bob's preferences are given by the utility function UB(, y) - min(x, y}. (a) Determine the set of Pareto allocations. (b) Derive the utility frontier for Ann and Bob, and depict the frontier in a diagram for the case y = 16. (c) What allocation(s) maximize the social welfare function "("AJAX ByB) = "A(TAYA) + Up(ByB)? For parts (d) and (e assume that Ann initially owns the bundle (@ , y ) = (9, 4) and Bob initially owns the bundle (TB, yB) = (7, 12). (d) Determine all the Walrasian equilibria