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Chapter 19: Taxes: Equity versus Efficiency
Solutions Manual
Learning Objectives for Chapter 19
After reading this chapter, you should know
LO 19-01. How the U.S. tax system is structured.
LO 19-02. What makes taxes more or less progressive.
LO 19-03. The nature of the equity-efficiency trade-off.
Questions for Discussion
1. What goods or services do you and your family receive without directly paying for them?
How do these goods affect the distribution of economic welfare? (LO 19-02)
2. Why are incomes distributed so unevenly? Identify and explain three major causes of
inequality. (LO 19-03)
3. Do inequalities stimulate productivity? In what ways? Provide two specific examples.
(LO 19-03)
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© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
4. What loopholes reduced President Obama’s 2010 tax bill (See the News, p. 413)? What’s the
purpose of those loopholes? (LO 19-01)
5. How might a flat tax affect efficiency? Fairness? (LO 19-03)
6. If a new tax system encouraged more output but also created greater inequality, would it be
desirable? (LO 19-03)
7. If the tax elasticity of supply were zero, how high could the tax rate go before people reduced
their work effort? How do families vary the quantity of labor supplied when tax rates
change? (LO 19-03)
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© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
8. Is a tax deduction for tuition likely to increase college enrollments? How will it affect
horizontal and vertical equities? (LO 19-03)
9. What share of taxes should the rich pay (see Figure 19.4)? Should the poor pay any taxes?
(LO 19-03)
10. If U2’s tax bill falls by $1 million when the band relocates to the Netherlands (World View,
p. 411), who really pays for the band’s charitable contributions? (LO 19-03)
Problems
1. How much more income tax would President Obama have paid in 2010 (News, p. 413) if he
had used no “loopholes”? (Use the tax rates in Table 19.1.) (LO 19-02)
**Note the tax tables that are to be used for this problem do not appear in the text.
Please use the following:
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manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Feedback: President Obama would have paid an additional $159,392 in taxes if his family
had not taken advantage of “loopholes” in 2010. The “loopholes” created by exemptions,
deductions, adjustments, and tax credits cause a distinction between gross economic income
2. If there were no deductions for charitable contributions, how much more would the Obamas
have paid in 2010? (LO 19-02)
**Note the tax tables that are to be used for this problem do not appear in the text.
Please use the following:
Answer: $85,776.25
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© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Feedback: President Obama would have paid an additional $73,616 in taxes if the charitable
contributions deduction did not exist in 2010. The charitable contributions deduction is an
example of a “loophole” created by exemptions, deductions, adjustments and tax credits
cause a distinction between gross economic income and taxable income. Without this
deduction, the Obamas would have paid taxes on their 2010 income without the charitable
deduction (= $1,550,593) and not their 2010 taxable income (= $1,340,207). Since the
Obamas earnings were very high in 2010, their earnings above $373,650 were taxed at the
highest marginal rate in 2010 (= 35%). This $245,075 difference in income would have been
taxed at that highest marginal tax rate. This means the Obamas would have paid an additional
$85,776 in taxes (= $245,075 × 35%).
3. In 2010 what was the Obamas’
(a) Nominal tax rate?
(b) Effective tax rate?
(LO 19-02)
Feedback:
(a) A nominal tax rate is tax paid divided by taxable income. In 2010 the Obamas paid
(b) An effective tax rate is tax paid divided by total economic income (total gross income).
4. Use Table 19.1 to compute the taxes on a taxable income of $200,000.
(a) What is the marginal tax rate?
(b) What is the average tax rate?
(LO 19-01)
Answers:
Feedback:
(a) The marginal tax rate is the tax rate imposed on the last (marginal) dollar of income. In
this case, the last dollar of income ($200,000) is within the 33 percent tax bracket.
(b) The average tax rate is tax paid divided by total income. Tax paid is calculated as
follows:
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© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
5. Using Table 19.1, compute the taxable income and taxes for the following taxpayers:
Which taxpayer has
(a) The highest nominal tax rate?
(b) The highest effective tax rate?
(c) The highest marginal tax rate?
(LO 19-01)
Answers:
Taxpayer Gross Income Exemptions and Taxable Tax
Deductions Income
A $20,000 $4,000 $16,000 $1,946.25
Feedback:
"Taxable income" is gross income minus exemptions and deductions. For example, the
taxable income for Taxpayer A in the table above is $20,000 - $4,000 = $16,000.
To compute "tax" use the tax bracket table provided. For example, Taxpayer D has a taxable
income of $90,000. Her "tax" paid is calculated as follows:
(a) Nominal tax rate is tax paid divided by taxable income. According to the information
provided below, Taxpayer D has the highest nominal tax rate at 20.4 percent.
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© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Taxpayer Nominal Tax Rate Effective Tax Rate Marginal Tax Rate
A 12.2% 9.7% 15%
(b) Effective tax rate is tax paid divided by gross income. According to the table provided
(c) Marginal tax rate is the tax rate imposed on the last (marginal) dollar of income.
6. If the tax elasticity of supply is 0.15, by how much will the quantity supplied decrease when
the marginal tax rate increases from 34 to 38 percent? (LO 19-02)
Feedback:
The tax elasticity of supply is calculated using this formula:
Es = (% change in Qs) / (% change in Tax)
7. By how much might the quantity of labor supplied decrease if the tax elasticity of supply
were 0.20 and the marginal tax rate increased from 35 to 45 percent? (LO 19-02)
Feedback:
The tax elasticity of supply is calculated using this formula:
Es = (% change in Qs) / (% change in Tax)
8. If the tax elasticity of labor supply were 0.16, by how much would the quantity of labor
supplied increase among people in the top U.S. tax bracket if the highest marginal tax rate in
the United States were reduced to the level of Hong Kong’s (World View, p. 419)?
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© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
(LO 19-02)
Feedback:
The tax elasticity of supply is calculated using this formula:
Percentage change in tax rate = ([39.6 – 15] / [(39.6 + 15) / 2]) = 0.901
9. What percentage of income is paid in Social Security taxes by a worker earning
(a) $40,000?
(b) $80,000?
(c) $200,000?
(d) What kind of tax is this? (A: progressive; B: regressive; C: proportional)
(LO 19-02)
Answers:
Feedback:
(a) Every worker sees a Social Security (FICA) tax of 7.65 percent taken out for all income
(b) Once again, every worker sees a Social Security (FICA) tax of 7.65 percent taken out for
(c) For an individual who earns $200,000, Social Security taxes are taken out for only the
(d) A regressive tax is a tax system in which tax rates fall as incomes rise. In the case of the
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© 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
rate taxin change Percentage
suppliedquantity in change Percentage
supply of elasticity Tax
10. What is the effective tax rate with Dick Armey’s proposed flat tax (p. 420) for a family of
four with earnings of
(a) $30,000?
(b) $50,000?
(c) $100,000?
(LO 19-03)
Answers:
Feedback:
(a) In the version of the flat tax plan proposed by Dick Armey, the flat tax rate would be 17
(b) A family of four earning $50,000 would pay a flat tax of 17 percent on each dollar earned
(c) A family of four earning $100,000 would pay a flat tax of 17 percent on $63,200. They
11. Following are hypothetical data on the size distribution of income and wealth for each
quintile (one-fifth) of a population:
Quintile Lowest Second Third Fourth Highest
Income 5% 10% 15% 25% 45%
Wealth 2% 8% 12% 20% 58%
(a) On the graph on the next page, draw the line of absolute equity; then draw a Lorenz curve
for income, and shade the area between the two curves.
(b) In the same diagram, draw a Lorenz curve for wealth. Is the distribution of wealth more
equal (“A”) or less equal (“B”) than the distribution of income?
(LO 19-01)
Answers:
(a)
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manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Feedback:
(a) The line of equality represents a society where all incomes are equal. The greater the area
(b) The Lorenz curve for wealth displays graphically the cumulative size distribution of
12. How much more in taxes did a millionaire have to pay when the top marginal tax rate was
increased from 35 to 39.6 percent (use Table 19.1)? (LO 19-01)
Feedback: A millionaire had to pay 4.6% (= 39.6 – 35) more in taxes on their income of
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13. (a) On the accompanying graph, draw the supply and demand for labor represented by the
following data:
Wage
$1 $2 $3 $4 $5 $6 $7 $8 $9 $10 $11 $12
Quantity of labor supplied
1 2 3 4 5 6 8 10 12 14 17 20
Quantity of labor demanded
20 18 16 14 12 10 8 6 5 4 3 2
(b) How many workers are employed in equilibrium?
(c) What wage are they paid?
(d) Now suppose a payroll tax of $2 per worker is imposed on the employer. Draw the
“supply + tax” graph that results.
(e) How many workers are now employed?
(f) How much is the employer paying for each worker?
(g) How much is each worker receiving?
For the incidence of this tax,
(h) What is the increase in unit labor cost to the employer?
(i) What is the reduction in the wage paid to labor?
(LO 33-03)
Answers:
(a), (d)
Feedback:
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(a) LS1 is graphed by simply plotting wage and the associated quantity of labor supplied
(b) Equilibrium is the point at which quantity of labor supplied is equal to quantity of labor
(c) Equilibrium wage is $7 per period. This is the wage associated with the equilibrium
(d) LS2 is graphed by adding $2 to the previous curve LS1. Hence, LS2 is the “supply + tax”
(e) The new equilibrium point is where quantity of labor supplied (6 workers) is equal to
(f) This new equilibrium is associated with a wage rate of $8 per worker. Thus the employer
(g) The worker receives the amount of the wage ($8 per worker) minus the tax. Since the tax
(h) Previous to the imposition of the payroll tax, the employer paid $7 per worker. After the
(i) Previous to the imposition of the payroll tax, each employee received $7. After the
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