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      Question

      Consider an exchange economy with two agents, 1 and 2,

      and two goods, X and Y. Each agent's consumption set is in +R2. The endowments of agents 1 and 2 are (10, 1) and (0, 9) respectively. In any commodity bundle, the first entry is the quantity of X, and the second entry is the quantity of Y. If a>c, or a=c and b>d, then Agent 1 strictly prefers bundle (a,b) to (c,d). If b>d, or b=d and a>c, then Agent 2 strictly prefers bundle (a,b) to (c,d). Which of the following allocations is a competitive equilibrium allocation?
      A Agent 1 gets (10,1) and Agent 2 gets (0,9) Correct Answer Incorrect Answer
      B Agent 1 gets (10,10) and Agent 2 gets (0,0). Correct Answer Incorrect Answer
      C Agent 1 gets (5,5) and Agent 2 gets (5,5). Correct Answer Incorrect Answer
      D None of the above. Correct Answer Incorrect Answer

      Solution

      A competitive equilibrium allocation is one where no agent can be made better off without making the other agent worse off, given their initial endowments and preferences.

      • Agent 1 prefers bundles with more of good X (and possibly good Y), while Agent 2 has a preference for bundles with more of good Y (and possibly good X).
      • The initial endowments (10,1) for Agent 1 and (0,9) for Agent 2 align with their preferences, making the initial distribution optimal.
      • Any redistribution would leave at least one agent worse off, thereby violating the conditions for a competitive equilibrium.
      Thus, the allocation where Agent 1 gets (10,1) and Agent 2 gets (0,9) is indeed a competitive equilibrium allocation.

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