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Problem 5. Social Welfare Consider an exchange economy in which there are two agents, Alice and Bob, and two goods, 1 and 2. The two agents have preferences described by the utility functions of\" (3314,3313) = 051113314 + (l 0011135, and HB (33?,3323) = (1 a) 1113:? + alnsz, where a e (1 / 2, 1). Suppose that the consumers start with initial endow- ments (1014,1154) = (1019,1053) = (1, 1). The agents have agreed to share their resources and they have also agreed that the weight that A receives in the economy is 7,4 6 (0, 1) and the weight that B receives is '73 = 1 7,4. (a) For every weight 7,; e (0, 1), nd the allocation which would maximize the social surplus given the weights; that is, we are interested in finding the allocation ((3:14, $124) , (3:19, 3:23)) which maximizes the sum m (we as) +