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?

Q: Answer-Consider an exchange economy with two agents, 1 and 2, and two goods, X and Y. Each agent's consumpt...

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.