1. (exam question from Fall 2019) Consider a standard Edgeworth box economy with two consumers Tom and Jerry, where Tom's utility function is given by Urat, cr) = Vater and Jerry's utility function is given by U,(aj,cy) = min{2aj, 3cy}. Here, a is Tom's consumption of apples, ct is Tom's con- sumption of cheese, a, and c, are Jerry's consumption of apples and cheese, respectively. Tom has an endowment of 6kg apples and 5kg of cheese. Jerry has an endowment of 6kg apples and 3kg of cheese. (a) Illustrate the exchange in an Edgeworth box, and identify the endowment point. (b) Identify the set of Pareto optimal allocations for this economy, and plot it in the Edge- worth box (Show how you find it). (c) Identify the core. (d) At the competitive (general) equilibrium, if the price of apple is $1/kg, what could be an equilibrium price for cheese? Find them all, as well as the corresponding allocation in general equilibrium. (e) Suppose the social welfare function is W(Ur, U) = (Ur)?U;. Find the social welfare maximizing allocation in this economy