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Econ 432 Westerhold Name:__________________________________ HW #6: Taxation due Tuesday, July 27th (Grad Students have additional work in questions 4B, and 7) 1. Suppose that income tax is levied at a flat rate of 5%, but no tax is levied above $50,000 in taxable income. Taxable income is the individual’s income minus a $10,000 exemption. What are the marginal and average tax rates for the following three workers? a. A part-time worker with annual income of $9,000. b. A retail salesperson with annual income of $45,000. c. An advertising executive with annual income of $600,000. d. Is the tax progressive, proportional, or regressive with respect to income? 2. Consider the following tax system for two individuals: Person A has an income of $300,000 and Person B has an income of $30,000. Assume that under the current system, Person A pays $90,000 in taxes and Person B pays $3,000 in taxes. Suppose a new tax reform bill is passed that results in the taxes of Person A being reduced by $5,000 and taxes being reduced for Person B by $500. Is the new system more or less progressive than the old system? A. Determine the degree of progressivity using the average tax measurement: B. Determine the degree of progressivity using the elasticity of tax revenue measurement: C. Is the tax cut progressive? Briefly explain. 3. Use the table below (provided by the Congressional Budget Office 2007) to answer all parts of question 3: Lowest Second Third Fourth Highest All Top 1% Quintile Quintile Quintile Quintile Quintile Households Average Tax Rates (Percent) All Federal Taxes 4.0 10.6 14.3 17.4 25.1 20.4 29.5 Individual Income Taxes -6.8 -0.4 3.3 6.2 14.4 9.3 19.0 Social Insurance Taxes 8.8 9.5 9.4 9.5 5.7 7.4 1.6 Corporate Income Taxes 0.4 0.5 0.8 1.1 4.6 3.0 8.8 Excise Taxes 1.6 1.0 0.8 0.7 0.4 0.6 0.1 Share of Tax Liabilities (Percent) All Federal Taxes Individual Income Taxes Social Insurance Taxes Corporate Income Taxes Excise Taxes Income (Dollars) Average Pretax Income Average After-Tax Income Share of Pretax Income Share of After-Tax Income Number of Households (millions) 0.8 -3.0 4.8 0.6 11.0 4.4 -0.3 10.8 1.4 14.1 9.2 4.6 16.6 3.3 18.1 16.5 12.7 24.7 6.8 22.2 68.9 86.0 42.9 86.8 34.3 100 100 100 100 100 28.1 39.5 4.1 57.0 4.7 18,400 17,700 4.0 4.9 42,500 38,000 8.4 9.4 64,500 55,300 13.1 14.1 94,100 77,700 19.3 20.0 264,700 198,300 55.9 52.5 96,000 76,400 100 100 1,873,000 1,319,000 19.4 17.1 24.6 22.2 22.9 23.0 23.7 116.9 1.2 A. In 2007, what is the overall average tax rate according to the table? B. Which tax constitutes the largest share of household income for the middle class? For all households? Briefly explain. C. For the lowest-resource households, which tax has the lowest average tax rate? Briefly interpret the number. D. Which tax constitutes the largest share of tax liability for the top 1% income earners? E. Do any of the tax categories appear to be regressive? Briefly explain. F. In general, how would you characterize the federal tax system in terms of progressivity? Briefly explain. 4. A. Assume that in a given country, tax revenues, T, depend on income, I, according to the following formula: T= -4000 + 0.20I Is this a progressive tax schedule? Hint: you could calculate average and marginal tax rates at varying income levels such as $5,000; $10,000; and $30,000 to see a pattern. B. Grad Students Only: Now, let’s generalize the tax schedule in this example to T = a + tI where a and t are numbers. Write down a formula for the average tax rate as a function of the level of income. Show that the tax system is progressive if a is negative and regressive is a is positive (Hint: the average tax rate is T/I). 5. In an effort to reduce alcohol consumption, the government is considering a $1.25 tax on each unit of liquor sold. Suppose that demand for alcohol is given by Qd=500,000 – 20,000P and the supply equation is Qs=-5000 + 7500P. A. Show the market for alcohol and determine the equilibrium price and quantity prior to the tax. B. Determine the price elasticity of demand (Ed) and price elasticity of supply at the equilibrium. Categorize your numbers as elastic or inelastic. C. Determine the value of consumer surplus, producer surplus, and total surplus at this original equilibrium. D. Show the new supply curve on your graph in part A with the $1.25 excise tax and determine the new equilibrium price paid by consumers, the net price received by producers, and the new equilibrium quantity. E. Determine the amount of tax revenue generated by the excise tax. Determine the relative tax burden of each economic agent. Who bears the burden of this tax? Why? F. Determine the new consumer surplus, producer surplus, and total surplus values after the tax. Determine the value of the deadweight loss. Is society better off or worse off with the tax? Briefly explain. 6. The government of Byngia has introduced a new tax on airline travel. They have two types of travelers: business and leisure. Business travelers have a price elasticity of demand of -1.2 while leisure travelers have an elasticity of -3.0. The airlines may price discriminate by charging different prices to different people. Which group will bear the larger burden of the tax? Briefly explain. 7. Graduate Students Only: Show mathematically that if an excise tax has statutory incidence placed on the consumer (instead of the seller) that the change in price will be equal to: