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Consider an exchange economy with two goods and two agents. Agent A likes to consume more...

Consider an exchange economy with two goods and two agents. Agent A likes to consume more of either good, but when she consumes a bundle, she dislikes mixing her consumption of both goods. Therefore she only cares for the maximal amount of either good contained in a bundle. Her preferences are represented by ui(xA1 , xA2 ) = max{xA1 , xA2 }. Agent B has preferences represented by ui(xB1 , xB2 ) = (xB1 )^2 + (xB2 )^2. Both agents have endowments (1, 1).

(1) Consider agent B. Is it true that the more of a good she consumes, the larger the extra utility she gets from an additional unit of that good?

(2) Given (1) and the above description of agent A’s preferences, what is your intuition about what should happen in this economy (after exchange)?

(3) Draw some indifference curves for both agents.

(4) Represent this economy in an Edgeworth box with the initial endowment and the indifference curves through the endowment.

(5) Which allocations are in the core of this economy?

(6) Is it possible that the price ratio be different from 1 in a Walrasian equilibrium? Why? Draw the budget line in the diagram.

(7) What are the Walrasian equilibria of this economy?

(Hint: Given (6), you will see that there cannot be a unique Walrasian equilibrium.)

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