Download 432HW06

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: