Public Finance 2010 Problem Set 1 Taxation and income distribution April 20, 2010 Task 1 Suppose that the demand for cigarettes in a hypothetical country is given by QcD=2000-200Pc, where QcD is the number of packs demanded and Pc is the price per pack. The supply of cigarettes is QcS=200Pc a) Find the price and quantity of cigarettes, assuming the market is competitive b) In an effort to reduce smoking, the government levies a tax of $2 per pack. Compute the quantity of cigarettes after the tax, the price paid by consumers, and the price received by producers. How much revenue does the tax raise for the government? Task 2 Suppose that the demand curve for a particular commodity is QD=a-bP, where QD is the quantity demanded, P is the price, and a and b are constants. The supply curve for the commodity is QS=c-dP, where QS is quantity supplied and c and d constants. Find the equilibrium price and output as functions of the constant a, b, c and d. Suppose now that a unit tax of u dollars is imposed on the commodity. Show that the new equilibrium is the same regardless of whether the tax is imposed on producers or buyers of the commodity. Task 3 Suppose that the income tax in a certain nation is computed as a flat rate of 5 percent, but no tax is levied above $50,000 in taxable income. Taxable income, in turn, is computed as individual’s income minus $10,000; that is, everyone gets a $10,000 deduction. What are the marginal and average tax rates for each of the following three workers? (Evaluate the marginal tax rate at each person’s current income level.) 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. Is the tax progressive, proportional or regressive with respect to income? Task 4 Assume that in a given country, tax revenues, T depend on income, I, according to the formula T = a + tI 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 if a is positive. Task 5 In 2002, New York City increased the tax rate on cigarettes from 8 cents a pack to $1.50 a pack. A month after the increase, a spokesman for the mayor noted that “fewer cigarettes are being sold, and the city is making more money”. Assume for simplicity that the supply of cigarettes to New York City is perfectly elastic. a. Assuming that the spokesman’s facts are correct, what must be true of the elasticity of the demand for cigarettes in New York City? b. Recall that the spokesman’s comment was made just one month after the tax increase was enacted. As more time passes, what do you expect to happen to the elasticity of the demand curve, and how this affect tax revenues for New York City?
