Solution Key to PS3
ECN 131
Public Finance
US tax structure
Prof. Farshid Mojaver
1. Suppose Arizona establishes an income tax schedule that has a tax rate of 10% on the first $20,000 of
income, then 25% on the next $30,000, and then 40% on all taxable income above $50,000. Arizona
provides a $4,000 exemption per family member.
i) The Wilkening Family has three members (Tom, the sole earner – and his two sons), and
earns $54,000 per year. Calculate their marginal tax rate, average tax rate, and effective tax
rate.
ii) The Didier Family has four members (Tatiana, the sole earner – and her three daughters), and
earns $74,000 per year. Calculate their marginal tax rate, average tax rate, and effective tax
rate.
iii) Suppose that under Arizona’s tax system, taxes are levied at the household level (i.e. the
marginal tax rates apply to combined spousal income). Does this tax system provide Tom and
Tatiana a financial incentive to marry each other – or does it provide a disincentive?
Ans
1. i) Tom’s taxes:
$54,000 Gross Income
-12,000 Exemptions
------------= 42,000 Taxable income
Tom has to pay $2000 for the first 20,000 of his income, then 25% * 22,000=5,500 for
the remainder of his income, for a total of $7500 for $54,000, which is 13.9% average tax
rate. The marginal tax rate equals the tax on his last dollar of income, or 25%.
ii) Tatiana’s Taxes:
$74,000 Gross Income
-16,000 Exemptions
------------= 58,000 Taxable income
Tatiana has to pay $2000 for the first 20,000 of her income, then 7500 for the next
$30,000, then 40%*8,000=3200 for the remainder of her income. Total taxes = $12,700
for $74,000 of income, which is a 17.2% average tax rate. The marginal tax rate equals
the tax on his last dollar of income, or 40%.
iii) Family taxes:
$128,000 Gross Income
- 28,000 Exemptions
------------$100,000 taxable Income
Now, they have to pay
$2,000 for the first 20,000 of taxable income
$7,500 for the next 30,000
$20,000 For the remaining $50,000
----------29,500 Total taxes.
This is considerably larger than the $20,200 total taxes that they would pay if they
weren’t married. Thus, they have no financial incentive to marry.
2. Explain the concepts of vertical and horizontal equity as goals for tax systems. Which of the concepts is
easier to measure in practice? Explain.
Ans)
Vertical equity is the principle that groups with more resources (higher income, higher
wealth, higher profits) should pay higher taxes than groups with fewer resources. There
are standard measures of vertical equity, including the extent to which tax systems are
progressive, which means that the effective average tax rate rises with income.
In contrast, horizontal equity is the principle that similar people (in terms of resources)
who make different economic choices should be treated similarly by the tax system. In
practice, however, horizontal equity is difficult to measure because it is only
unambiguous when taxes differ for reasons independent of choice. Under most tax
systems, however, people of identical underlying resources who make different choices
will pay different amounts of tax.
3) Alternative Minimum Tax
a) What is AMT?
b) Why was it established?
c) How will its application change over time, and why?
Ans)
a) The Alternative Minimum Tax (AMT) is an additional tax schedule that applies to
taxpayers who have a very high ratio of deductions and exemptions to total
income.
b) It was signed into law in 1969 and was strengthened in 1986. It was established to
ensure that all wealthy households paid some amount of income tax.
c) None of the AMT figures in the law were indexed to inflation, so as nominal
wages have risen over time, more and more taxpayers have become subject to the
AMT. By 2010, one-third of all taxpayers will be subject to the AMT for that
reason.
4.What is the difference between the marginal tax rate and the average tax rate? What is the difference
between the statutory tax rate and the effective tax rate? Explain.
Ans
The marginal tax rate is the percentage that is paid in taxes of the next dollar earned. For
example, for all income above $319,000, the marginal tax rate is 35%. In contrast, the
average tax rate is the percentage of total income that is paid in taxes.
Statutory tax rates are the tax rates laid out in the legal tax schedule. However, the
effective tax rates are the tax rates that a person actually pays. Effective tax rates are
different from statutory tax rates because of the host of exemptions and deductions from
taxable income.
5. a. What is the rationale behind allowing people to deduct charitable giving from their taxable income?
b. What are the two reasons given in the text that the government does not simply provide the charitable
good itself? Explain.
Ans
a. The rationale behind making charitable donations tax-deductible is an
externality/public goods rationale. Due to the free rider problem caused when costs are
private but benefits are public, the private market is likely to underprovide charitable
support for many public goods. To induce more private giving, the government may
allow people to deduct those contributions, thus lowering the relative price of charitable
giving relative to other consumption.
b. The first reason that tax subsidies may be superior to direct public provision is that
direct public provision of the public good may crowd out private contributions. In
contrast, when the government tax subsidizes charitable giving, it can increase private
contributions through both the substitution effect and the income effect.
Second, when the government provides spending directly, it imposes its preferences on
how the funds are spent. By offering tax subsidies to private people to donate as they
wish, the government directly respects the preferences of its citizens.
6. Compare and contrast tax deductions and tax credits in terms of both efficiency and vertical equity.
Ans
There are two considerations in determining which tax policy (credit or deduction) is
more efficient. The first is the sensitivity of demand for the good in question. For goods
for which individual demand is not very elastic to small reductions in price but is elastic
for large reductions in price, credits may have a larger marginal effect than deductions.
The second consideration is that regarding the importance of achieving some minimal
level of the behavior. To the extent that achieving some minimal level is important, tax
credits are preferable to tax deductions. However, if it is unclear that achieving some
minimal level of behavior is important, it may be better to use a deduction to subsidize
people as much as they like.
In terms of vertical equity, tax credits are more equitable than deductions since the value
of deductions rises with one's tax rate, making deductions regressive. In contrast, tax
credits are progressive and become even more so to the extent that they are refundable.
7. The Smith family has four members (Marry, Mark and two young children) and earned $125,000 in
2006. They have contributed $14,000 to a 401k plan and $3,000 to an IRA account. They have purchased a
house in Davis for $500,000. The interest part of their mortgage payment is $2,500 per month. The
property tax is $500 per month. Consider the following tax schedule for married people filing jointly in
2006






a)
10% on the income between $0 and $15,100
15% on the income between $15,100 and $61,300; plus $1,510.00
25% on the income between $61,300 and $123,700; plus $8,440.00
28% on the income between $123,700 and $188,450; plus $24,040.00
33% on the income between $188,450 and $336,550; plus $42,170.00
35% on the income over $336,550; plus $91,043.00
 Exemptions = $3,300 per person
 Standard deduction = $10,350 (for married couple filing jointly)
Calculate their taxable income and their tax owed under regular tax
b)
c)
d)
e)
Calculate the Smith’s statutory marginal and average tax rates
Calculate their effective marginal and average tax rates.
Calculate their AMT taxable income assuming an AMT exemption of $62,550.
Calculate their AMT liability (marginal tax rate for AMT taxable income up to $117,000 is 26%)
Answer:
Married Filing jointly
2006
AMT
125,000
2006 Regular Tax
GI
401k
IRA
GAI
Exemp
4*3,300
Ded'n = Max (STD, Itemized)
STD= $10,350
Itemized= $36,000
Mortgage interest
125,000
-14,000
-3,000
108,000
-13200
12*25000
State &Local taxes
12*500
Taxable Income
($108,000-($13,200 +
$36,000))
Tax owed
0.10*15,100+ 0.15*(58,800-15,100)
Credits (CTC if joint income less 110,000)
Mortgage
-30,000 interest
AMT
-6,000 Exemption
58,800
AMT Taxable income
AMT (26%)
8,065
less Regular tax
AMT Liability
a) Taxable Income $58,800 Tax owed $8,065
b) Statutory Marginal Tax rate is 28%
Statutory Average Tax rate is 19.5% (=24404/125000)
c) Effective Marginal Tax rate is 15%
Effective Average Tax rate is 6.5% (=8065/125000)
d) AMT Taxable Income $32,450
e) AMT liability $372
8. Suppose that the U.S. personal income tax system became a “flat tax” system, in which all taxpayers
paid a certain percentage of their incomes in tax, and in which there are no exemptions or deductions. In
which way(s) could this flat tax be more regressive than the present U.S. system? In which ways could it be
more progressive than the present system?
ANS
On its face, this tax is more regressive than the current system, because poorer taxpayers would
pay exactly the same marginal tax rate as wealthier taxpayers. This system might be more
progressive than it looks, however, given the elimination of exemptions and deductions.
Wealthier taxpayers would lose their home interest deductions, tax-preferred savings
mechanisms, and other benefits; wealthy entrepreneurs would lose their business expense
deductions. The anti-progressive nature of tax deductions—the fact that deductions are more
valuable to high-bracket taxpayers—would end. As a result, wealthier taxpayers may be more
harmed by this change than the less wealthy.
-30,000
-62,550
32,450
8,437
-8,065
372
9. The nation of Turan has a tax rate of 10% on the first 20,000 liras (the national currency)
of taxable income, then 25% on the next 30,000 liras, then 40% on all taxable income above
50,000 liras. Turan provides a 4,000-walop exemption per family member.
a. Afrasiab’s family has three members and earns 54,000 liras per year. Calculate their
marginal tax rate, average tax rate, and effective tax rate.
The first step is to reduce Afrasiab’s taxable income by the amount of his exemptions.
Since there are three people in his family, his total exemptions are 4,000 3 = 12,000, so he will
only pay taxes on 54,000 – 12,000 = 42,000. Since this amount is more than 20,000 but less than
50,000, Afrasiab’s marginal tax rate is 25%. To calculate average tax rate, Jamil must first
calculate the total taxes he pays: he pays 10% on the first 20,000 = 2,000, and 25% on the
remaining 22,000 = 5,500, so total taxes paid = 7,500. Dividing this amount by total income
yields 7,500/54,000. Thus Afrasiab’s average tax rate is 13.88%.
Because Afrasiab has total income of 54,000, it appears at first glance that his marginal
tax rate is 40% (because that is the rate on income greater than 50,000). As shown above,
however, Afrasiab’s effective marginal tax rate is only 25% because he has been able to reduce
his taxable income by taking three exemptions.
b. Piran’s family has four members and earns 74,000 liras per year. Calculate their
marginal tax rate, average tax rate, and effective tax rate.
Piran’s taxable income is 74,000 – (4,000 x 4) = 58,000. Since this amount is greater than 50,000,
his marginal tax rate is 40%. Total taxes paid by Pirans are (10% 20,000) + (25% 30,000) +
(40% 8,000). This yields 2,000 + 7,500 + 3,200 = 12,700. Thus, his average tax rate is
12,700/74,000 = 17.16%.
Because Piran pays taxes on an amount greater than the cutoff for the highest marginal tax rate,
his effective marginal tax rate and the statutory rate for his income are the same: 40%.
c. Suppose that Turan changed their tax code to a flat tax of 30%, with an 8,000-lira per
family member exemption. Would this change in the tax system make the system more
progressive, more regressive, or neither? Explain.
Holding family size constant, the flat tax would make the system less progressive by eliminating
the increasing marginal tax rate structure currently in place. The higher exemption, however,
would make the effective tax rate paid by large families less than the statutory 30%. If poorer
people tended to have larger families, this aspect of the tax plan would contribute to some
progressivity.
In the case of the two families described above, the plan is much less progressive.
For Afrasiab, taxes would be 30% x (54,000 – [3 x 8,000]) = 30% x 30,000 = 9,000, more than he
pays now. His average tax rate is 9,000/54,000 = 16.67%.
For Piran, taxes would be 30% x (74,000 – [4 x 8,000]) = 30% x 42,000 = 12,600, slightly less
than he pays now. His average tax rate is 12,600/74,000 = 17.03%, only slightly more than the
poorer Afrasiab.
10. Ed and Wendy are a married couple with two children and a combined household
income of $100,000. (Ed earns $30,000 per year and Wendy earns $70,000 per year.)
John and Kristen also have a combined income of $100,000, with each earning $50,000.
They have one child.
Consider the U.S. federal income tax system in 2004, as described in Chapter 18.
Which married couple would benefit more from a change in the tax code that would tax
each spouse separately, regardless of family income? Explain.
John and Kristen would benefit most from a change that would allow computation of taxes
separately. Taxed together, both couples are in the second highest tax bracket, with a 33%
marginal tax rate. Taxed separately, however, John and Kristen face a much lower marginal tax
rate: 15%. Because Wendy’s own income is fairly high, when she is taxed separately she still
occupies a relatively high tax bracket: individually she pays a 28% marginal tax rate. While
Wendy and Ed benefit under separate tax calculations, the benefit Ed enjoys by being in the
lowest bracket is more than offset by Wendy’s position in a high bracket.
11. Your roommate and you had identical high school grade point averages and SAT
scores. In many respects, one would expect that you would be equally successful. But
because you chose economics as a major and your roommate chose geology, you will be
paying a larger amount of tax in the future than your roommate will because your income
will be higher. Is this attribute of the tax code vertically equitable? Is it horizontally
equitable?
Vertical equity requires that the person with the higher income pay the higher tax. If the
economics major earns more than the geology major, then according to this principle the
economics major should pay the higher tax.
Horizontal equity requires that people with similar ability to pay should pay the same tax.
In this case, measuring ability to pay solely by salary, they should pay different tax amounts. The
difference in salaries, though, was generated solely by the choices the roommates made,
presumably with information about the expected return to different majors.
An argument could be made that any difference in their salaries is attributable to
compensating wage differentials: the lower-wage major receives nonmonetary satisfaction from
his or her job sufficient to offset the monetary wage difference. In other words, total
compensation to the two majors (monetary plus nonmonetary) must, by definition, be equal. Any
difference in monetary wage is made up in nonmonetary amenities. That argument supports the
claim that this difference in tax liability is inequitable, as taxes are levied only against monetary
wages.
12. Suppose that the government adopts a Haig-Simons comprehensive income definition.
Will this make employers more likely or less likely to offer employer-provided pension
plans or health insurance coverage? Why?
Adoption of the Haig-Simons definition would require inclusion of employer-provided benefits in
taxable income, because these benefits increase employees’ ability to consume. Taxation of these
benefits would make them less attractive to workers, so employers would not be able to substitute
benefits for wages as easily as they do now. As a result, employers would be less likely to offer
the benefits.
On the other hand, even if these benefits were taxed, employers may be able to provide them
more efficiently—and thus, more cheaply—than employees could obtain them in private markets.
If it were cheaper to obtain group health insurance through an employer than it would be to
purchase private insurance in the market, even when the benefit is taxed, then workers would
remain willing to trade off higher wages for more benefits. And the total cost of hiring a worker
may be less for the firm offering the benefits, in which case employers would still provide the
benefits.