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PROBLEM SET:
1. Consider an exchange economy with two agents and two goods. Let xik denote agent i's consumption of good k. Consumption sets are the nonnegative orthant. Agent 1 has utility represented by Ax11 + x12 where A > 0 ; while agent 2's utility is x21x22. Endowments are (e, 0)for agent 1, and (0, e) for agent 2, where e> 0 .
a) Characterize the core allocations for this economy.
b) Let A=1 and either argue directly that the core converges to the Walrasian equilibrium as the economy is replicated k > 1 times, or show that it does not.
2. Consider a two agent and two good exchange economy where agent 1 has preferences represented by u1 (x11, x12) = min(2.x11, x12) , and agent 2 has preferences represented by u2 (x21, x22) = min(x21, x22) . Both agents have endowments (1,1) . The consumption sets of the agents are k+2 . Describe the core allocations of this economy.
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