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a)Write down the budget constraint and solve for the demand functions. Given your answer how much tax revenue was actually raised? Does it differ from hat the mayor expected? If it does can you explain why? Calculate the utility level under this policy.

a)Write down the budget constraint and solve for the demand functions. Given your answer how much tax revenue was actually raised? Does it differ from hat the mayor expected? If it does can you explain why? Calculate the utility level under this policy.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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2) Consider a mayor that oversees a community of 1000 people. The mayor wants to build a local park and she needs to raise $100,000 in tax revenue to do so. Suppose that the mayor wants to raise the revenue by placing a sales tax on good x1. She does not know the preferences of the community members but knows that each resident has an income of $2000 dollars and the community as a whole purchased 1 million units of x1 at $1 per unit. So she figures that if she sets a sales tax of 10% she will be able to raise the $100,000. This would imply that the effective price that people face for xı is $1.10 to take into account the tax. Assume p2 = 1. The preferences and marginal utilities of each member of the community are given by U (*1, 02) = xi"x", 1/2„1/2 MU = 1/2(x2/T1)"/2, MU, = 1/2(x1/x2)/2. (1) a)Write down the budget constraint and solve for the demand functions. b) Given your answer how much tax revenue was actually raised? Does it differ from what the mayor expected? If it does can you explain why? c) Calculate the utility level under this policy. c) Now suppose that instead of using a sales tax the mayor decides to use an income tax of 5% or $100 per person. Write out the new budget constraint in recalculate the demand functions. d) Does the mayor achieve her desired tax revenue? e) Calculate the utility under this scenario. which tax are residents better off under?
Transcribed Image Text:2) Consider a mayor that oversees a community of 1000 people. The mayor wants to build a local park and she needs to raise $100,000 in tax revenue to do so. Suppose that the mayor wants to raise the revenue by placing a sales tax on good x1. She does not know the preferences of the community members but knows that each resident has an income of $2000 dollars and the community as a whole purchased 1 million units of x1 at $1 per unit. So she figures that if she sets a sales tax of 10% she will be able to raise the $100,000. This would imply that the effective price that people face for xı is $1.10 to take into account the tax. Assume p2 = 1. The preferences and marginal utilities of each member of the community are given by U (*1, 02) = xi"x", 1/2„1/2 MU = 1/2(x2/T1)"/2, MU, = 1/2(x1/x2)/2. (1) a)Write down the budget constraint and solve for the demand functions. b) Given your answer how much tax revenue was actually raised? Does it differ from what the mayor expected? If it does can you explain why? c) Calculate the utility level under this policy. c) Now suppose that instead of using a sales tax the mayor decides to use an income tax of 5% or $100 per person. Write out the new budget constraint in recalculate the demand functions. d) Does the mayor achieve her desired tax revenue? e) Calculate the utility under this scenario. which tax are residents better off under?
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