Assume that Alegra and Blake are the only two people in an economy and total available income is fixed at $100. Alegra's utility is given by UA = (yA 20) 2 3 where yA is Alegra's income and Blake's utility is UB = (yB 10) 2 3 where yB is Blake's income. 2 (a) What distribution of income maximizes social welfare when the social welfare function is W1 = UA UB? (b) What distribution of income maximizes social welfare when the social welfare function is W2 = 6UA 3UB? (c) What distribution of income maximizes social welfare when the social welfare function is W3 = min(UA, UB)? (d) Are your solutions to (a), (b), and (c) Pareto efficient outcomes? (e) State a Pareto efficient outcome that does not maximize any of the above social welfare functions