Consider the following (highly) simplified description of the U. S. wage distribution and income and payroll tax schedule. Suppose 50 percent of households earn $40,000, 30 percent earn $70,000, 15 percent earn $120,000, and 5 percent earn $500,000. Marginal income tax rates are 0 percent up to $30,000, 15 percent on income earned from $30,000 to $60,000,25 percent on income earned from $60,000 to $150,000, and 35 percent on income earned in excess of $150,000. There is also a 7.5 percent payroll tax on all income up to $80,000. Required:

a. What are the marginal tax rate and average tax rate for each of the four types of households? What are the average household income, payroll, and total tax bill? What percent of the total income tax is paid by each of the four types of households? What percent of the total payroll tax bill is paid by each of the four types of households?
b. What is the Gini coefficient for the economy when comparing after-tax incomes across households? (Hint: Assume there are 1,000 households in the economy.) What happens to the Gini coefficient if all taxes were replaced by a single 20 percent flat tax on all incomes?
c. A presidential candidate wants to remove the cap on payroll taxes so that every household would pay payroll taxes on all of its income. To what level could the payroll tax rate be reduced under the proposal while keeping the total amount of payroll tax collected the same?