Download CHAPTER 7 7-1. Evaluate the validity of the following claim: The

Chapter 07 - The Wage Structure
CHAPTER 7
7-1. Evaluate the validity of the following claim: The increasing wage gap between highly
educated and less educated workers will itself generate shifts in the labor market over the
next decade. As a result of these responses, much of the “excess” gain currently accruing to
highly educated workers will soon disappear.
(discussion question)
7-2. What effect will each of the following proposed changes have on wage inequality?
(a) Indexing the minimum wage to inflation.
reduce wage inequality (discuss)
(b) Increasing the benefit level paid to welfare recipients.
reduce wage inequality (discuss)
(c) Increasing wage subsidies paid to firms that hire low-skill workers.
reduce wage inequality (discuss)
(d) An increase in border enforcement, reducing the number of illegal aliens entering the
country.
reduce wage inequality (discuss)
7-3. From 1970 to 2000, the supply of college graduates to the labor market increased
dramatically, while the supply of high school (no college) graduates shrunk. At the same
time, the average real wage of college graduates stayed relatively stable, while the average
real wage of high school graduates fell. How can these wage patterns be explained?
(discuss using graphs)
7-4.
(a) Is the presence of an underground economy likely to result in a Gini coefficient that
over-states or under-states poverty?
over-state (discuss)
(b) Consider a simple economy where 90 percent of citizens report an annual income of
$10,000 while the remaining 10 percent report an annual income of $110,000. What is the
Gini coefficient associated with this economy?
0.45
(c) Suppose the poorest 90 percent of citizens actually have an income of $15,000 because
each receives $5,000 of unreported income from the underground economy. What is the
Gini coefficient now?
0.349
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Chapter 07 - The Wage Structure
7-6. Consider an economy with the following income distribution: each person in the bottom
quartile of the income distribution earns $15,000; each person in the middle two quartiles
earns $40,000; and each person in the top quartile of the income distribution earns
$100,000.
(a) What is the Gini coefficient associated with this income distribution?
0.327.
(b) Suppose the bottom quartile pays no taxes, the middle two quartiles pay 10 percent of its
income in taxes, and the top quartile pays 28 percent of its income in taxes. Two-thirds of
all tax money is redistributed equally to all citizens in the form of military defense,
government pensions (social security), roads/highways, etc. The remaining one-third of tax
money is disturbed entirely to the poorest quartile. What is the Gini coefficient associated
with this redistribution plan? Would you consider this tax and redistribution plan to be a
particularly aggressive income redistribution policy?
First, we must determine total taxes: 500(40,000)(0.10) + 250(100,000)(0.28) = $ 9 million are
paid in total taxes. This comes from each person in the lowest quartile paying $0; each person in
the middle two quartiles paying $4,000 in taxes; and each person in the top quartile paying
$28,000 in taxes. Of this $9 million, $6 million is repaid to all people equally in the form of
defense, social security, road, etc. So, each person claims $6,000 of this pool of taxes. The
remaining one-third of taxes, which equals $3 million, is divided among the poorest quartile.
Thus, the poorest 250 people each receive an income transfer of $12,000. New incomes,
therefore, are $33,000 for the bottom quartile, $42,000 for the middle two quartiles, and $78,000
for the top quartile. Given these new numbers, the analysis from part (a) can be repeated.
The bottom quartile receives $8.25 million of income, or 16.9% of $48.75 million.
The middle two quartiles receive $21 million of income, or 43.1% of $48.75 million.
The top quartile receives $19.5 million of income, or 40.0% of $48.75 million.
And the Gini coefficient is 0.173245.
This appears to be a fairly substantial redistribution scheme as it cuts the Gini coefficient in half.
It also has the richest person earning 2.36 times that of the poorest person (78/33) whereas this
ratio was 6⅔ times (100/15) without the redistribution.
7-7. The two points for the international income distributions reported in Table 7-1 can be
used to make a rough calculation of the Gini coefficient. Use a spreadsheet to estimate the
Gini coefficient for each country. Which three countries have the most equal income
distribution? Which three countries have the most unequal income distribution?
The three countries with the most inequality are Chili (0.288), Guatemala (0.266), and the
Dominican Republic (0.244). The three countries with the most equality are Sweden (0.014),
Hungary (0.014), and Germany (0.021). It should be emphasized that these are very crude
measures as they rely on only two points in the income distribution.
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Chapter 07 - The Wage Structure
7-8. Consider the following (highly) simplified description of the U.S. wage distribution and
income and payroll tax schedule. Suppose 50 percent of households earn $40,000, 30 percent
earn $70,000, 15 percent earn $120,000, and 5 percent earn $500,000. Marginal income tax
rates are 0 percent up to $30,000, 15 percent on income earned from $30,000 to $60,000, 25
percent on income earned from $60,000 to $150,000, and 35 percent on income earned in
excess of $150,000. There is also a 7.5 percent payroll tax on all income up to $80,000.
(a) What is the marginal tax rate and average tax rate for each of the four types of
households? What is the average household income, payroll, and total tax bill? What
percent of the total income tax is paid by each of the four types of households? What
percent of the total payroll tax bill is paid by each of the four types of household?
Marginal tax rates:
households earning $40,000 is 15 percent + 7.5 percent = 22.5 percent.
households earning $70,000 is 25 percent + 7.5 percent = 32.5 percent.
households earning $120,000 is 25 percent + 0 percent = 25 percent.
households earning $500,000 is 35 percent + 0 percent = 35 percent.
Income tax bill:
households earning $40,000 is 15 percent of $10,000 = $1,500.
households earning $70,000 is $4,500 + 25 percent of $10,000 = $7,000.
households earning $120,000 is $4,500 + 25 percent of $60,000 = $19,500.
households earning $500,000 is $27,000 + 35 percent of $350,000 = $149,500.
Payroll tax bill:
households earning $40,000 is 7.5 percent of $40,000 = $3,000.
households earning $70,000 is 7.5 percent of $70,000 = $5,250.
households earning $120,000 is 7.5 percent of $80,000 = $6,000.
households earning $500,000 is 7.5 percent of $80,000 = $6,000.
Total tax bill and average tax rates:
households earning $40,000 is $4,500 => ATR = 11.25 percent.
households earning $70,000 is $12,250 => ATR = 17.5 percent.
households earning $120,000 is $25,500 => ATR = 21.25 percent.
households earning $500,000 is $155,500 => ATR = 31.10 percent.
Average tax bills over all households are:
Income: .5(1,500) + .3(7,000) + .15(19,500) + .05(149,500) = $13,250
Payroll: .5(3,000) + .3(5,250) + .15(6,000) + .05(6,000) = $4,275.
Total: $17,525.
Percent of the total income tax collected by the government that is paid by each household group:
$40,000 households pay .5(1,500) / 13,250 = 5.67 percent.
$70,000 households pay .3(7,000) / 13,250 = 15.85 percent.
$120,000 households pay .15(19,500) / 13,250 = 22.08 percent.
$500,000 pay .05(149,500) / 13,250 = 56.42 percent.
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Chapter 07 - The Wage Structure
Percent of the total payroll tax collected by government that is paid by each household group:
$40,000 households pay .5(3,000) / 4,275 = 35.09 percent.
$70,000 households pay .3(5,250) / 4,275 = 36.84 percent.
$120,000 households pay .15(6,000) / 4,275 = 21.05 percent.
$500,000 pay .05(6,000) / 4,275 = 7.02 percent.
(b) What is the Gini coefficient for the economy when comparing after-tax incomes across
households? (Hint: assume there are 1,000 households in the economy.) What happens to
the Gini coefficient if all taxes were replaced by a single 20 percent flat tax on all incomes?
Suppose there were 1,000 households. Total after-tax income is 500($35,500) + 300($57,750)
+150($94,500) +50($344,500) = $66,475,000.
The cumulative gross income shares of the four income groups, therefore, are:
500($35,500) / $66.47m = 26.7 percent.
26.7 percent + 300($57,750) / $66.47m = 52.8 percent.
52.8 percent + 150($94,500) / $66.47m = 74.1 percent.
74,1 percent + 50($344,500) / $66.47m = 100.0 percent.
The area under the Lorenz curve, therefore, is (.5) (½)(.267) + (.3)[.267+(½)(.528–.267 )] +
(.15)[.528+(½)(.741–.528 )] +(.05)[.741+(½)(1–.741 )] = 0.6675 + 0.11925 + 0.95175 +
0.043525 = 0.3247. The Gini coefficient, therefore, is [ .5 – ..3247 ] / .5 = .3506.
Suppose there was a flat tax of 20 percent. Total after-tax income is 500(.8)($40,000 +
300(.8)($70,000) +150(.8)($120,000) +50(.8)($500,000) = $67,200,000.
The cumulative gross income shares of the four income groups, therefore, are:
500($32,000) / $67.2m = 23.8 percent.
23.8 percent + 300($56,000) / $67.2m = 48.8 percent.
48.8 percent + 150($96,000) / $67.2m = 70.2 percent.
70.2 percent + 50($400,000) / $67.2m = 100.0 percent.
The area under the Lorenz curve, therefore, is (.5) (½)(.238) + (.3)[.238+(½)(.488–.238 )] +
(.15)[.488+(½)(.702–.488 )] +(.05)[.702+(½)(1–.702 )] = .0595 + .1089 + .08925 + .04255 =
.3002. The Gini coefficient if there was a 20 percent flat tax, therefore, would be [ .5 – ..3002 ] /
.5 = .3996.
(c) A presidential candidate wants to remove the cap on payroll taxes so that every
household would pay payroll taxes on all of its income. To what level could the payroll tax
rate be reduced under the proposal while keeping the total amount of payroll tax collected
the same?
Suppose there are 1,000 households: 500 pay $3,000, 300 pay $5,250, and 200 pay $6,000. The
total payroll tax receipts, therefore, are $4,275,000, while total income is $84 million. Thus,
generating $4.275 million of tax on $84 million of income requires a tax rate of 5.089 percent.
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Chapter 07 - The Wage Structure
7-10. Ms. Aura is a psychic. The demand for her services is given by Q = 2,000 – 10P, where
Q is the number of one-hour sessions per year and P is the price of each session. Her
marginal revenue is MR = 200 – 0.2Q. Ms. Aura’s operation has no fixed costs, but she
incurs a cost of $150 per session (going to the client’s house).
(a) What is Ms. Aura’s yearly profit?
$6,250 per year.
(b) Suppose Ms. Aura becomes famous after appearing on the Psychic Network. The new
demand for her services is Q = 2500 – 5P. Her new marginal revenue is MR = 500 – 0.4Q.
What is her profit now?
$153,125.
(c) Advances in telecommunications and information technology revolutionize the way Ms.
Aura does business. She begins to use the Internet to find all relevant information about
clients and meets many clients through teleconferencing. The new technology introduces an
annual fixed cost of $1,000, but the marginal cost is only $20 per session. What is Ms.
Aura’s profit? Assume the demand curve is still given by Q = 2500 – 5P.
$287,000.
(d) Summarize the lesson of this problem for the superstar phenomenon.
(discuss)
7-11. Suppose two households earn $40,000 and $56,000 respectively. What is the expected
percent difference in wages between the children, grandchildren, and great-grandchildren
of the two households if the intergenerational correlation of earnings is 0.2, 0.4, or 0.6?
(straightforward)
7-12. Suppose 50 percent of a population all receive an equal share of p percent of the
nation’s income, where 0 ≤ p ≤ 50.
(a) For any such p, what is the Gini coefficient for the country?
0.5 – p.
(b) For any such p, what is the 90 – 10 wage gap?
(1–p)/p.
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Chapter 07 - The Wage Structure
7-13. Consider two developing countries. Country A, though quite poor, uses government
resources and international aid to provide public access to quality education. Country B,
though also quite poor, is unable to provide quality education for institutional reasons. The
distribution of innate ability is identical in the two countries.
(a) Which country is likely to have a more positively skewed income distribution? Why?
Plot the hypothetical income distributions for both countries on the same graph.
(discuss)
(b) Which country is more likely to develop faster? Why? Plot the hypothetical income
distributions in 20 years for both countries on the same graph.
(discuss)
7-14. File sharing software threatens the music industry in part because artists will not be
fully compensating for their recording of songs. Suppose that the government decides that
file sharing software products are legal anyway.
(a) The almost immediate result will be that artists start earning very little money for their
recordings but they continue to earn money for live performances. How will income change
for the music industry? How does your answer relate to the superstar phenomenon?
Musicians who are also great performers will continue to make new music and will continue to
earn a lot of money. Musicians who are good at making new music but not good at giving live
performances will see a reduction in their income. For example, rumor has it that Steely Dan and
the Steve Miller Band are fairly horrible in concert, although their music is loved by many
people. These bands would struggle to earn money under the policy. Other artists that are known
to put on great shows (The Rolling Stones) will continue to earn a lot of money. Thus, the public
policy doesn’t choose which superstars will continue to do well; it simply redefines what talents
are going to be rewarded.
(b) Although one would expect lower prices to benefit the music-listening public if the
government decides that file sharing software products are legal, but in what way(s) could
the music-listening public also be hurt from the policy?
The most obvious way such a policy would hard the music-listening public is that fewer people
make music as it is less profitable. Thus, the public will have fewer choices of music to listen to.
This is analogous to if the government removed the patent system from new drugs, which would
results in fewer new drugs being developed.
7-6