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Chapter 20: Transfer Payments: Welfare and Social Security
Solutions Manual
Learning Objectives for Chapter 20
After reading this chapter, you should know
LO 20-01. The major income transfer programs.
LO 20-02. How transfer programs affect labor supply and total output.
LO 20-03. The trade-offs between equity and efficiency.
Questions for Discussion
1. If we have to choose between compassion and incentives, which should we choose? Do the
terms of the trade-off matter? (LO 20-03)
2. What’s so hard about guaranteeing everyone a minimal level of income support? What
problems arise? (LO 20-02)
3. If poor people don’t want to work, should they get welfare? What about their children?
(LO 20-03)
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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. Once someone has received TANF welfare benefits for a total of five years, he or she is
permanently ineligible for more TANF benefits. Should this person receive any further
assistance? How will work incentives be affected? (LO 20-02)
5. In what ways do younger workers pay for Social Security benefits received by retired
workers? (LO 20-02)
6. Should the Social Security earnings test be eliminated? What are the benefits and costs of
doing so? (LO 20-02)
7. How would the distribution of income change if Social Security were privatized? (LO 20-01)
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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. Who pays the economic cost of Social Security? In what ways? (LO 20-02)
9. Why don’t we give poor people more cash welfare instead of in-kind transfers like food
stamps, housing assistance, and Medicaid? (LO 20-03)
Problems
1. Suppose the welfare benefit formula is
Benefit = $4,800 – 0.67 (Wages > $2,000)
(a) What is the marginal tax rate on
(i) The first $2,000 of wages?
(ii) Wages above $2,000?
(b) How large is the benefit if wages equal
(i) $0?
(ii) $2,000?
(iii) $6,000?
(c) What is the breakeven level of income in this case?
(LO 20-02)
Answers:
Feedback:
(a)(i) Based on the welfare benefit formula provided, there is no marginal tax rate on the first
$2,000 of wages.
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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.
(ii) The marginal tax rate on any wages over $2,000 is 67 percent.
2. A welfare recipient can receive food stamps as well as cash welfare benefits. If the food
stamp allotment is set as follows,
Food stamps = $6,000 – 0.30 (Wages)
(a) How high can wages rise before all food stamps are eliminated?
(b) If the welfare formula in Problem 1 applies, what is the combined marginal tax rate of
both welfare and food stamps for wages above $2,000?
(LO 20-02)
Answers:
Feedback:
(a) To determine how high wages could rise before all food stamps are eliminated, set the
(b) If both formulas apply, the welfare recipient would face a marginal tax rate of 97 percent
3. Draw a graph showing how benefits, total income, and wages change under the following
conditions:
Wage rate = $10 per hour
Welfare benefit = $5,000 – 0.5 (Wages > $3,000)
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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.
Identify here and label on the graph the following points:
A—welfare benefit when wages = 0
(a) How much is that benefit?
B—welfare benefit when wages = $10,000
(b) How much is that benefit?
C—breakeven level of income
(c) What is that income level?
(LO 20-03)
Answers:
0 500 1000 1500
$0
$2,000
$4,000
$6,000
$8,000
$10,000
$12,000
$14,000
An Individual's Welfare Labor Market
Benefits
Wages
Total Income
Hours Worked (per year)
Dollar Amount s (per year)
Feedback:
(a) The marginal tax rate is imposed on only those wages greater than $3,000. In this case
(b) When wages are equal to $10,000, the last $7,000 in wages will be taxed at a rate of 0.5.
(c) The breakeven level of income is the point at which the welfare benefit is equal to zero.
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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.
A
B
C
4. What is the breakeven level of income for Social Security as depicted in Figure 20.6?
(LO 20-03)
Answer: $39,480.
Feedback: According to Figure 20.6, a worker aged 62–64 can earn up to $15,480 (point A)
5. According to the benefit formula in Table 20.2, how large will the Social Security benefit be
for a worker who had prior earnings of
(a) $30,000 a year?
(b) $80,000 a year?
What is the marginal wage replacement rate for
(c) The $30,000-per-year worker?
(d) The $80,000-per-year worker?
(LO 20-03)
Answers:
Feedback:
(a) According to the benefit formula in Table 20.2, the wage replacement rate is 90 percent
(b) According to the benefit formula in Table 20.2, the wage replacement rate is 90 percent
(c) The marginal wage replacement rate is the percentage of base wages paid out in benefits
(d) The marginal wage replacement rate is the percentage of base wages paid out in benefits
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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.
6. How large a monthly Social Security check will a retiree get if her maximum benefit is
$1,600 per month and she continues working for wages of $2,000 per month? (See text p.
434) (LO 20-03)
Feedback:
In 2014 the wage “ceiling” for workers aged 62–64 was $15,480. Hence the benefit formula
7. (a) On the following graph, depict the wages, income, and Social Security benefits at
different hours of work for a worker aged 62–64 who earns $15 per hour and is eligible for
$15,000 in Social Security benefits.
(b) What is the total income if the person works 1,000 hours per year?
(c) What is the breakeven level of income?
(LO 20-03)
Answers:
(a)
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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.
0 500 1000 1500 2000 2500 3000
$0
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
$35,000
$40,000
$45,000
An Individual's Social Security Labor Market
Social Security
Wages
Total Income
Hours Worked (per ye ar)
Dollar Amount s (per mont h)
Feedback:
(a) First, graph wages by computing $15 × hours worked. Second, graph Social Security
(b) Benefit amount = Maximum award – 0.5 (Wages in excess of ceiling)
(c) The breakeven level of income is the point at which the Social Security benefit is equal to
zero.
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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. If older workers have a tax elasticity of labor supply equal to 0.20, by how much will their
work activity decline when they reach the Social Security earnings test limit? (Assume
explicit taxes of 20 percent below that limit.) (LO 20-03)
Feedback:
The tax elasticity of labor supply is equal to the percentage change in quantity of labor
supplied divided by the percentage change in tax rate. The Social Security earnings test limit
is 50 percent with explicit taxes of 20 percent below that limit. Therefore:
9. Suppose the benefit formulas for various welfare programs are
Food stamps: $400 per month – 0.30 (Wages)
Housing assistance: $1,000 per month – 0.25 (Wages)
Cash welfare: $400 per month – 0.67 (wages above $500)
(a) How much will someone earning $800 a month receive in
(i) Food stamps?
(ii) Housing assistance?
(iii) Cash welfare?
(b) What is the cumulative marginal tax rate at
(i) Wages under $500?
(ii) Wages over $500?
(LO 20-01)
Answers:
Feedback:
(a)(i) Food stamps: $400 per month – 0.30(Wages). With monthly earnings of $800, a
(ii) Housing assistance: $1,000 per month – 0.25(Wages). With monthly earnings of
(iii) Cash welfare: $400 per month – 0.67(Wages above $500). With monthly earnings of
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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.
(b)(i) The cumulative marginal tax rate for all wages under $500 is 55 percent (30 percent tax
(ii) The cumulative marginal tax rate for all wages over $500 is 122 percent (30 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.
