Problem 3 Endowment equilibrium - Perfect substitutes (42 points) Consider individuals A and B. They have preferences over two-dimensional consumption bundles x = (z1,x2) where goods consumption must be non-negative, z; > 0 and zy > 0. Individuals A and B have perfect substitutes preferences where u4 (z) = 221 + x2 and ug () = z1 + z3. A has goods endowment e4 = (8,3) and B has endowment eg = (2, 7). This question is going to involve exceptions to our standard solution methods which will help solidify your understanding of concepts of efficiency and equilibrium. 1. 2. o In an Edgeworth Box, show the endowment allocation, (e4,ep). In the same Edgeworth box, draw each agent's indifference curve that runs through the agent's endowment point. In the same Edgeworth box, sketch the set of allocations that Pareto dominate the endowment allocation. Denote the set by PD. . Remember the definition of the Contract Curve: The contract curve is the set of feasible Pareto optimal allocations. A Pareto optimal allocation is an allocation such that nobody can be made strictly better off without making somebody strictly worse off. Determine the contract curve and illustrate it in the Edgeworth Box. Let's move to the analysis of what the market equilibrium will look like. For this, let good 2 be the numeraire good, so p; = 1. (a) For a given price of good 1, p; determine each agent's optimal consumption choice given their respective endowments. (b) [Hard] Determine the equilibrium price and the equilibrium allocation. [Note: There is only one]. (c) Verify that the equilibrium outcome is efficient, that is Pareto optimal