1. Consider an economy with J E N consumers whose utility functions Uj : C' - R are defined by Uj(c) = U(c - a'), C' = {ceRN: czaj}, where the {a'};-, C RN are parameters, and where U : RN - R is a strictly increasing and sufficiently smooth utility function with strictly convex better-than sets {c E RN : U(c) 2 u}. And U(0c) = OU(c) for any c E RN, and 0 > 0. The endowments are {y}- C a. Suppose this economy has a competitive equilibrium. Show how to construct it and argue that it must be unique. b. What do you have to assume about the {(a', y')}=1 to ensure that the economy does in fact have an equilibrium