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In a dictatorship, the incomes of the poor and the rich are yp=$100 and yr=$600, respectively. The size of the society is 1, the share of the poor is 1-8=0,8. The rich may introduce a new income tax (T) from which the revenue is distributed evenly among the citizens. The cost of taxation is C(T) = t 22. After this step, the poor may decide whether to start a revolution or not. In case of revolution, half of the income will be destroyed forever, and the rich will be expelled from the country. The utilities of both the poor and the rich are determined by their actual incomes. a) What is the average income in the economy? b) How high is inequality (the share of the rich from total income)? c) What will be the tax rate by which revolution can be just avoided? d) Compute the resulting after-tax incomes!

In a dictatorship, the incomes of the poor and the rich are yp=$100 and yr=$600, respectively. The size of the society is 1, the share of the poor is 1-8=0,8. The rich may introduce a new income tax (T) from which the revenue is distributed evenly among the citizens. The cost of taxation is C(T) = t 22. After this step, the poor may decide whether to start a revolution or not. In case of revolution, half of the income will be destroyed forever, and the rich will be expelled from the country. The utilities of both the poor and the rich are determined by their actual incomes. a) What is the average income in the economy? b) How high is inequality (the share of the rich from total income)? c) What will be the tax rate by which revolution can be just avoided? d) Compute the resulting after-tax incomes!

Microeconomics: Private and Public Choice (MindTap Course List)
Microeconomics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506893
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter4: Demand And Supply: Applications And Extensions
Section: Chapter Questions
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In a dictatorship, the incomes of the poor and the rich are yp=$100 and yr=$600, respectively. The size of the society is 1, the share of the poor is 1-8=0,8. The rich may introduce a new income tax (T) from which the revenue is distributed evenly among the citizens. The cost of taxation is C(T) = t 22. After this step, the poor may decide whether to start a revolution or not. In case of revolution, half of the income will be destroyed forever, and the rich will be expelled from the country. The utilities of both the poor and the rich are determined by their actual incomes. a) What is the average income in the economy? b) How high is inequality (the share of the rich from total income)? c) What will be the tax rate by which revolution can be just avoided? d) Compute the resulting after-tax incomes!
Transcribed Image Text:In a dictatorship, the incomes of the poor and the rich are yp=$100 and yr=$600, respectively. The size of the society is 1, the share of the poor is 1-8=0,8. The rich may introduce a new income tax (T) from which the revenue is distributed evenly among the citizens. The cost of taxation is C(T) = t 22. After this step, the poor may decide whether to start a revolution or not. In case of revolution, half of the income will be destroyed forever, and the rich will be expelled from the country. The utilities of both the poor and the rich are determined by their actual incomes. a) What is the average income in the economy? b) How high is inequality (the share of the rich from total income)? c) What will be the tax rate by which revolution can be just avoided? d) Compute the resulting after-tax incomes!
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