Two agents meet to trade two goods. Agent 1 has preferences representable by utility func- tion ul(x(1)) = x,(x2 ))3, while agent 2's preferences are representable by utility function u2 (2(2)) = (2,2))3x,". Agent 1 brings 1 unit of each good to trade, while agent 2 brings 2 units of each good.. Find a competitive equilibrium of this economy. . Depict this equilibrium in an Edgeworth box. Your diagram should include the endow ment, the equilibrium allocation, each agent's indifference curve through their equilib rium allocation, and a budget constraint. . A social planner proposes splitting the aggregate endowment of each good equally between the two agents in an attempt to achieve a fair outcome. Add this allocation and the corresponding indifference curves to the diagram from the previous part. . Is the allocation proposed by the planner efcient? If not, propose a trade between the two agents that would make both better off. (Your trade should include specic quantities of each good and specify who gives and who receives each good.) . Suppose that the planner reallocates endowments as in part 3 and then allows agents to trade via a decentralized price mechanism. Find a competitive equilibrium of this economy. Add this allocation and the corresponding budget constraint and indifference curves to your diagram. Comparing this allocation to the one you found in part 1, who wins and who loses