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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