# Tax Progressivity and Partial Equilibrium Tax Analysis

Tax Progressivity and Partial Equilibrium Tax Analysis

Economics 436
Papke/Sayer
515
This problem set is due February 2 at the beginning of class. Please work with others, but you must hand in your own work. Problem sets must be stapled or they will not be accepted.
1. Consider the following tax system. You pay 25 percent of your income after a deduction of \$5000.
Complete the following table:
Income Tax Liability average tax rate lATRl marginal tax rate lMTRl
\$8,000
\$15,000
\$30,000
\$40,000
\$80,000
Is this tax system progressive, regressive, proportional? Explain.
2. Suppose 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 is computed as the 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 retain salesperson with annual income of \$45,000.
c. An advertising executive with an annual income of \$600,000.

3. Consider the following demand and supply equations:
QD=20-5P Q5=2p-2
where Q is in thousands and P is in dollars.
a. Re-write each equation in graphical (y = mx+b) form.
b. Graph the two equations on the same graph.
c. Calculate the market equilibrium price and quantity.
d. Calculate the elasticity of demand and the elasticity of supply at the price found in part (c). If a
tax were levied in this market, which side of the market would pay the most tax?
3. Consider the competitive market where demand is P = 20 – .25Q and supply is P = 3 + .5Q.
a. Analyze the effects on the equilibrium quantity, producer price Pn, and consumer price Pg of a
\$1 per unit tax on producers. What is the tax revenue?
b. Analyze the effects on the equilibrium quantity, producer price Pn, and consumer price Pg of a
20% ad valorem tax on producers. What is the tax revenue?
c. Analyze the effects on the equilibrium quantity, producer price Pn, and consumer price Pg of a
\$1 per unit subsidy to consumers. What is the cost to the government?