# Utility Maximization

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This question is about Walrasian equilibrium in an exchange economy with 2 goods and 2 consumers. Taxes are introduced in the question to solve for the equilibrium and allocation under Pareto theorem.

Question (2)

Consider an exchange economy with 2 goods and 2 consumers . Consumer 1's initial endowment is and consumer 2's endowment is . In each case , the first entry in the endowment vector denotes the initial endowment of good 1, and the second entry the initial endowment of good 2 . Both consumers have the same consumption set: , and the same utility function: Suppose that consumer 1's expenditure on good 1 is taxed at a rate of 50%, and that the revenue from this tax is paid as a lump-sum transfer to consumer 2.

Find the Walrasian equilibrium of this economy . Then find another allocation which Pareto-dominates the equilibrium allocation.

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Question (2)

Consider an exchange economy with 2 goods and 2 consumers . Consumer 1's initial endowment is and consumer 2's endowment is . In each case, the first entry in the endowment vector denotes the initial endowment of good 1, and the second entry the initial endowment of good 2. Both consumers have the same consumption set: , and the same utility function: Suppose that consumer 1's expenditure on good 1 is taxed at a rate of 50%, and that the revenue from this tax is paid as a lump-sum transfer to consumer 2.

Find the Walrasian equilibrium of this economy. Then find another allocation which Pareto-dominates the equilibrium allocation.

Walrasian equilibrium is an economic equilibrium notion based on market clearing, mediated by prices. Consumers choose the consumption vector which maximizes utility over their budget sets. A ...

#### Solution Summary

Utility Maximization is discussed for exchange economy.