Consider an economy with two agents and 1 unit of a single good. Both agents prefer more of the good to less. 1. Find the set of Pareto-efficient allocations. 2. Suppose that agents' preferences are represented by the utility functions ui(x(i)) = x(i). (I will write x(i) rather than xi to make clear that i is a superscript and not an exponent.) (a) Find the set of utility pairs (w1,w2) R2 that can be implemented by Pareto- efficient allocations. (A utility pair (w1, w2) is implementable if it satisfies (w1, w2) = (u1(x(1)), u2(x(2))) for some Pareto-efficient allocation x.) (b) Plot the set you found in the previous part. Each implementable utility pair (w1,w2) should be a point on your diagram, with x-coordinate equal to w1 and y-coordinate equal to w2. (c) Based on your diagram in the previous part, identify the subset of Pareto-efficient allocations that can be generated by maximizing a weighted sum of utilities