A graduated income tax is proposed in Borduria to replace

Chapter 3, Problem 3.4.8

(choose chapter or problem)

A graduated income tax is proposed in Borduria to replace an existing flat rate of 8% on all income. The new proposal states that persons will pay no tax on their first $20,000 of income, 5% on income over $20,000 and less than or equal to $100,000, and 10% on their income over $100,000. (Note: Borduria is a fictional totalitarian state in the Balkans that figures in the adventures of Tintin.) a. Construct a table of values that shows how much tax persons will pay under both the existing 8% flat tax and the proposed new tax for each of the following incomes: $0, $20,000, $50,000, $100,000, $150,000, $200,000. b. Construct a graph of tax dollars vs. income for the 8% flat tax. c. On the same graph plot tax dollars vs. income for the proposed new graduated tax. d. Construct a function that describes tax dollars under the existing 8% tax as a function of income. e. Construct a piecewise function that describes tax dollars under the proposed new graduated tax rates as a function of income. f. Use your graph to estimate the income level for which the taxes are the same under both plans. What plan would benefit people with incomes below your estimate? What plan would benefit people with incomes above your estimate? g. Use your equations to find the coordinates that represent the point at which the taxes are the same for both plans. Label this point on your graph. h. If the median income in the state is $27,000 and the mean income is $35,000, do you think the new graduated tax would be voted in by the people? Explain your answer.