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exchange economy

The attached question is about 2 consumers with 3 goods in an exchange economy, the consumer's utility functions are given. The question asks to find demand functions for each consumer as well as finding Walrasian equilibrium under certain assumptions.

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Question (1)
Consider an exchange economy with two consumers and three goods
Let be the amount of good ( )consumed by consumer . Each consumer consumption set is Suppose that each consumer has an endowment of one unit of each good. Suppose consumer 1's utility function is and consumer 2's utility function is . Suppose that the price of good 1, , is normalized to one, and that the prices of goods 2 and 3 are denoted by and , and are strictly positive.
(a) Explain why consumer 1's utility maximization implies that . Then find consumer 1's demand as a function of and .
(b) Derive consumer 2's demand.
(c) Find a Walrasian equilibrium in which consumer 2 buys strictly positive quantities of all goods. Describe both consumers' consumption in this equilibrium.

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Solution Summary

This job examines an exchange economy.

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