Suppose that there are two consumers indexed by the subscript i. Each consumer receives a given amount of income wi, pays an income tax at rate t, receives a lump-sum transfer , 0, and consumes ci. Assume that w1 = 1 and w2 = 5. The utility of individual i is given by u(ci) with u > 0 and u < 0. The government chooses an income tax rate t and a uniform lump-sum transfer from the set of feasible policies to maximize social welfare i.e. sum of individual utilities u(c1) + u(c2). (a) Show that the social welfare is maximized when each individual's marginal rate of con- sumption is the same. (7 points) (b) Find the optimal tax and transfer policy (t, ) and the resulting consumption alloca- tions c 1 and c 2. (8 points) (c) How would the results change if the government maximized a weighted sum of utilities u(c1) + (1 )u(c2) where [0, 1]? (5 points