Download Assignment 9

İnsan Tunalı
Econ 320: Labor Economics
27 April 2017
Answers to Assignment 9
Problems from Borjas, Ch.7
7-2. What effect will each of the following proposed changes have on wage inequality?
(a) Indexing the minimum wage to inflation.
Indexing the minimum wage to inflation should reduce wage inequality because the minimum wage helps
prop up the wages of less skilled workers. Note that an increase in the minimum wage may have negative
employment effects, but the proposed policy is not to increase the minimum wage but rather simply to
prevent it from falling in real terms.
(b) Increasing the benefit level paid to welfare recipients.
Wage inequality measures the dispersion of wages in the working population. An increase in welfare
benefits would likely induce less-skilled workers out of the labor force, and would reduce measured wage
inequality by effectively eliminating the bottom of the wage distribution.
(c) Increasing wage subsidies paid to firms that hire low-skill workers.
Wage subsidies would increase the demand for less skilled workers, reducing wage inequality.
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?
The graphs below show equilibrium movements in the market for high school graduates and in the market
for college graduates. The decrease in labor supply among high school graduates and the increase in labor
supply among college graduates is taken as given. The analysis, therefore, focuses on labor demand for each
type of labor.
Given a lower supply of high school graduates, the only way for their average wage to fall is for labor
demand for high school graduates to have decreased (shifted in).
Labor Market for
High School Graduates
LS2000
LS1970
w1970
w2000
LD1970
LD2000
L2000
L1970
Given a greater supply of college graduates, the only way for their average wage to stay the same is for labor
demand for college graduates to have increased (shifted out).
Labor Market for
College Graduates
LD1970
LS1970
LS2000
LD2000
w1970 = w2000
L1970
L2000
7-4. (a) Is the presence of an underground economy likely to result in a Gini coefficient that overstates or under-states poverty?
The larger the underground economy, the more the Gini coefficient is likely to over-state poverty as the
underground economy tends to employ low-skill, low-income workers.
(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?
As all citizens in each group receive an equal income, the actual Lorenz curve will be a straight line within
each group. Let’s suppose there are 1,000 citizens. The 90% of poorest citizens, therefore, receive 0.90 x
1000 x $10,000 = $9 million. The entire economy, though, earns 0.9(10,000)+0.1(110,000) = $20 million.
Therefore, the bottom 90% receives 9 ÷ 20 = 45% of total income. The perfect and actual Lorenz curves can
now be drawn rather easily.
Share of Income
1.00
Perfect-Equality
Lorenz Curve
Actual Lorenz
Curve
0.45
0.00
0
0.9
Share of Citizens
1.00
The Gini coefficient is now easily calculated by seeing that the area beneath the actual Lorenz curve is two
triangles and one rectangle.
Gini =
(1 / 2) − [(1 / 2)(0.9)(0.45) + (0.1)(0.45) + (1 / 2)(0.1)(0.55)]
= 0.45 .
(1 / 2)
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(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?
The problem is identical to that above, but the income levels change. In this case, per capita GDP is 0.9 x
15,000 + 0.1 x 110,000 = $24,500 so total income of the 1,000 citizens is $24,500,000. Lastly, the total
income share of the poorest 90% of citizens is 900 x 15000 ÷ 24.5 million = 55.1%. (That is, in the graph on
the previous page, the income share at 90% of citizens increases from 45% to 55.1%.) The Gini coefficient
is not calculated as it was before:
Gini =
(1 / 2) − [(1 / 2)(0.9)(0.551) + (0.1)(0.551) + (1 / 2)(0.1)(0.449)]
= 0.349
(1 / 2)
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?
Find the number of sessions that Ms. Aura will provide by equating the marginal revenue to the marginal
cost of a session: setting MR = MC yields 200 – 0.2Q = 150 which solves as Q* = 250. The price that would
generate demand for 250 sessions is $175 as 2,000 – 10(175) = 250. Thus, her annual profit is 175(250) –
150(250) = $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?
The same kind of calculations as in part (a) but using the new demand curve yields a profit maximizing
quantity of 875 sessions at $325 per session and an annual profit of $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.
With the new marginal cost, Ms. Aura will provide 1,200 sessions and charge $260 per session. Her annual
profit will equal $287,000.
(d) Summarize the lesson of this problem for the superstar phenomenon.
Borjas: Superstars command an economic rent because they are, in essence, a monopoly with a favorable
demand curve. The greater the demand for the superstar’s product, the higher price the superstar can charge,
and the more profit can be earned. Notice also that, going from part (a) to part (b), is the lesson that when
demand for your services is high, you provide a lot of service, i.e., an upward sloping labor supply curve.
Two excellent answers from last Econ 320:
Emre: First of all, due to being famous, the demand and price of the [service] rises drastically. In addition,
this drastic increase of demand and price is not followed by an increase of marginal costs or does not face
supply limitations. Also, technological advancements decrease costs and also increase potential supply.
Therefore … .she is able to sell to a much wider group… does not have … time constraint due to the nature
of the product and also due to technology; while being able to sell the good at much higher prices because
of the fame.
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Cem: Since all fortune tellers are not easily substitutable (and since we are willing to pay a lot more for an
accurate guess about our future) and their talents can be sold to large crowds with telecommunication we can
see that [while] … fortune tellers with less abilities earn significantly less, their famous counterparts
[earn quite a bit more].
Part II. Old Exam Question
The table below is based on data collected by the Household Budget Survey conducted in Turkey in
2005.
Household Income
Per capita Income
Share of Income
Cumulative Share
of Income
Share of Income
Cumulative Share
of Income
First 20%
6.0
6.0
6.0
6.0
Second 20%
11.2
17.2
12.0
18.0
Third 20%
15.8
33.0
16.1
34.1
Fourth 20%
22.6
55.6
22.2
56.3
Fifth 20%
44.4
100.0
43.7
100.0
Quintiles
1. Use a graph to sketch the Lorenz curve for Household Income. Mark the axes.
Lorenz curve = Cumulative Share of Income as a function of quintiles.
Lorenz Curve for Household Income
Share of income
1
0,8
0,6
0,4
0,2
0
0
0,2
0,4
0,6
Share of households
Perfect Equality Lorenz Curve (45 degree)
0,8
1
Actual Lorenz Curve
2. Use your graph to illustrate how the Gini coefficient is calculated. Explain what the Gini
coefficient measures.
Let A = Area between the 45 degree line and the Lorenz curve, and A + B denote the area of the
triangle. Then G = Gini coefficient = A/(A + B). It measures the degree of inequality. By
construction 0 < G < 1.
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3. Consider the Per capita Income distribution shown in the table. Is that distribution more, or less
equal than Household Income distribution? Defend your answer.
More equal, because the Cum. Share of Per Capita Income ≥ the Cum. Share of HH Income at
every quintile.
Lorenz Curves (LCs)
1
0,9
Share of income
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0
0,2
0,4
0,6
0,8
Share of households/individuals
1
Perf ect Equality Lorenz Curve (45 degree)
LC f or household income
LC f or per capita income
4. Use a separate graph to sketch a log-normal earnings distribution. Is this distribution consistent
with the income distribution data from Turkey? From the USA?
A log-normal earnings distribution is left-skewed (has a long right tail).
For the data from Turkey shown in class, “log-normal” appears to be a good description. See
below.
Daily earnings in Turkey (TLx1000), 1988
Fraction
.2
.1
0
0
10
20
30
gucrety
See Borjas, Figure 7-1 for the U.S. version.
(Statistical definition: A random variable W has the log-normal distribution if log-W has a normal
distribution.)
5. Why does the typical earnings distribution have a long right tail? Discuss.
Higher ability people are more likely to invest in higher levels of education, and post-school
investments are higher at higher levels of education. Both of these factors result in a distribution
which is skewed to the right. Also, the superstar phenomenon (whereby a handful of famous
people dominate the pay scales in every field) and tournament model (or other incentive based) pay
scales stretch the right tail further.
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