Practice Problem Set - Solutions
ECON2800 Labour Economics
University of Queensland
Part A: Multiple Choice Questions
For each question, choose one and only one answer.
1. Which of the following statements is correct?
(a) In the taste-based discrimination model that we discussed in class, a dis-
criminating firm earns lower profit by employing labor and producing output
over the optimal level.
(b) If potential employers could observe the productivities of different individ-
uals, but still offer different salaries to man and women, the employers are
having statistical discrimination.
(c) The findings of Charles & Guryan (2008) suggest that the black-white wage
gap in the U.S. is unaffected by the prejudices of the most prejudiced persons
in a state, which provides evidence against the taste-based discrimination
in the U.S. labor markets.
(d) None of above is correct. X
2. Evaluate the following statement “In a simple signaling model of education,
human capital increases as a result of education.”
(a) True
(b) False X
(c) Only true in industrialized economies.
(d) Uncertain
3. Evaluate the following statement “Education of a worker increases his/her pro-
ductivity, which could spill over to other workers. This is the only justification
for government to subsidize education.”
(a) True
(b) False X
(c) Only true in non-democratic countries.
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(d) Uncertain
4. Suppose that there are two countries, A and B. Comparing the two countries,
all but one factors affecting their labor markets are the same. Country A is
relatively more open so that capital could flow in and out of Country A quicker
than in and out of Country B. Imagine that there is a positive shock of labor
supply due to the same sudden increase of unskilled immigrants into Country A
and Country B. Assuming that unskilled immigrants are perfect substitutes of
unskilled native workers, which of the following statements is correct?
(a) Capital will flow out of Country A and Country B after the shocks.
(b) In the short run, unskilled wage will increase in Country A but decrease in
Country B.
(c) In the short run, unskilled wage will decrease in both Country A and Coun-
try B. But wage recovers quicker in Country A than in Country B. X
(d) In the long run, Country A would experience an increase in unskilled wages
while unskilled wage would not change in Country B.
5. Filling in the blanks indicated by X, Y, Z, J, K and H, which of the following is
correct?
(a) (X, Y, Z) = (Quits, Job Loss, Job Creation)
(b) (X, Y, Z) = (Job Loss, Job Creation, Quits)
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(c) (X, Y, Z) = (Job Destruction, Job Creation, Quits)
(d) (X, Y, Z) = (Recession, Graduation, Minimum Wage Hikes)
(e) (X, Y, Z) = (Start-up Firms, Part-time Jobs, Parental Leaves)
(f) (Z, K, J) = (Unemployment, New Hiring, Quits)
(g) (J, K, H) = (Unemployment, Vacancies, New Hiring) X
(h) (J, K, H) = (Vacancies, New Hiring, Unemployment)
6. Which of the following best described a Beveridge curve?
(a) Figure:
(b) Figure:
(c) Figure:
X
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(d) Figure:
(e) Figure:
(f) Figure:
7. In recent years, which of the following countries has the lowest income inequality
as measured by the Gini coefficient?
(a) China
(b) South Africa
(c) United States
(d) Sweden X
8. Which of the following statements is incorrect?
(a) In both U.S. and Australia, female workers on average earn less than male
workers.
(b) In the U.S., female workers with a college degree on average earn less than
male workers with a college degree.
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(c) In the U.S., female workers without a college degree on average earn less
than male workers without a college degree .
(d) In the U.S., unemployment rate of the black population is similar to the
unemployment rate of the white population. However, the average earnings
of the black population is lower than the average earnings of the white
population. X
9. Suppose an individual has a utility function U = C + 2L, where C is the con-
sumption level and L is the leisure hours. Suppose the individual has 100 hours
in total for work and leisure and no non-labor income. The wage rate is 1.75.
Which feasible consumption level maximizes the individual’s utility?
(a) 0 X
(b) 17.5
(c) 87.5
(d) 175
According to the utility function, 1 unit of L give utility 2. But giving up a
unit of leisure to work gives extra earning 1.75, which translates to 1.75 higher
utility from the consumption. Thus, giving up 1 unit of leisure is not worth it
and this is true at what ever leisure level. So to maximize utility, it must be the
case that work and hence consumption must be zero to maximize utility for this
individual.
10. Suppose firms use skilled labor (H) and unskilled labor (L) to produce according
to the following production function
Q = min{H,L}
where Q is the output quantity. The supply curve of skilled labor is given by H =
wH − 0.5. And unskilled labor is supplied inelastically at price wL = 1. Output
market is competitive and output price is 2. Input markets are competitive as
well. Which of the following input combination gives the greatest profit?
(a) H = 0, L = 0
(b) H = 2, L = 0
(c) H = 0, L = 2
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(d) H = 0.25, L = 0.25 X
(e) H = 1, L = 1
(f) H = 2, L = 2
(g) H = 3, L = 1.5
Why H = 0.25, L = 0.25? Since output Q is the minimum of H and L, profit
maximizing input choice must have H = L. Otherwise, some input would be
wasted without generating extra output. So the profit pi is:
pi = PQ−HwH − LwL
= 2H −H(H + 0.5)−H
= 0.5H −H2
where P is just the output price and we substitute prices wH and wL using the
supply function of skilled labor wH = H + 0.5 and the price of unskilled labor
wL = 1. The first order condition for profit maximization is
dpi
dH
= 0.5− 2H = 0,
which gives us the optimal choice of input H = L = 0.25.
11. Suppose a firm only uses labor to produce. The firm’s production function is
Y = ln(1 + 2L)
where Y is the output quantity and L is the hours of labor input. The firm is
in a competitive product market where the price is p = 11 and a competitive
labor market where the wage rate is w = 2. Which of the following labor hours
maximizes the firm’s profit?
(a) 1
(b) 3
(c) 5 X
(d) 11
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The firm’s profit is:
pi = pY − wL
= 11 ln(1 + 2L)− 2L
The first order condition of profit maximization is:
dpi
dL
=
11× 2
1 + 2L
− 2 = 0
Solving this equation gives L = 5 as the profit-maximizing labor input.
12. Oreopoulos et al. (2012) study the short- and long-term career effects of gradu-
ating in a recession. Their main findings could be summarized by the following
figure.
Which of the following statements is correct?
(a) Oreopoulos et al. (2012) shows that the labor market of university graduates
in the United States is perfectly competitive.
(b) Oreopoulos et al. (2012) shows that graduating at a time when unemploy-
ment rate is high has a permanent impact on earning.
(c) Oreopoulos et al. (2012) suggests that the matching between workers and
firms has limited implications on the earnings.
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(d) None of the above. X
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Part B: Short Answers
Please answer all of the following questions. There are four questions and each ques-
tion may have several parts. The marks for each part of a question are stated in
parentheses. For a successful attempt to a question, clearly show your reasoning and
related calculation. Please also circle or highlight your final answers and start a
question on a new page.
1. Consider two hypothetical countries X and Y. In the following graph, the income
distribution of country X is described by the Lorenz curve that is represented by
the solid line between area A and area B; the income distribution of country Y
is described by the Lorenz curve that is represented by the dashed line between
area B and area C.
(a) Which country has a more equal distribution of income?
ANSWER: Country X.
(b) Suppose the areas of A and C are 0.12 and 0.27 respectively. The Gini
coefficient of Country X is 0.24. What is the Gini coefficients of country Y?
ANSWER:
Gini(X) =
A
A+B + C
=
0.12
0.12 +B + 0.27
= 0.24
0.12+B + 0.27 = 0.5
⇒ B = 0.11
Gini(Y ) =
A+B
A+B + C
=
0.12 + 0.11
0.12 + 0.11 + 0.27
= 0.46
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2. Suppose the bottom 60 percent of a population (in terms of earnings) all receive
an equal share of p percent of the nation’s income, where 0 ≤ p ≤ 60. The top
40 percent of the population all receive an equal share of 1 − p percent of the
nation’s income.
(a) For p = 40, what is the 50-10 earning gap ratio, i.e. the ratio of the 50
percentile of earnings to the 10 percentile of earnings.
ANSWER: Since the bottom 60 percent of the population all have the
same income, the 50 percentile of earnings is the same as the 10 percentile
of earnings. Therefore, the 50-10 earning gap ratio is 1.
(b) For p = 20, what is the 90-50 earning gap, i.e. the ratio of the 90 percentile
of earnings to the 50 percentile of earnings.
ANSWER: Let the national income be 1. Then, the earnings of the
bottom 60 percent add up to p = 0.2. The income of an individual of the
bottom 50 percent is
yB =
0.2
0.6
=
1
3
The earnings of the top 40 percent add up to 1 − p = 0.8. The income of
an individual of the top 40 percent is:
yT =
0.8
0.4
= 2
Since the top 40 percent all have the same earnings, the 90 percentile of
earnings is 2. Since the bottom 60 percent all haev the same earnings, the
50 percentile of earnings is 1
3
.
The 90-50 earning gap ratio is:
yT
yB
=
2
1/3
= 6
(c) Suppose a firm uses capital (K) and labor (L) to produce. The firm’s
production function is
Q = ln(K) + 2 ln(L)
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where Q is the output quantity; K is units of capital input; and L is number
of workers. Let the wage rate of workers is w = 4 and the rental price of
capital is r = 2. The output price is p = 1 per unit. The firm operates
in competitive input and output markets. What is the profit maximizing
combination of K and L? Show your calculation.
ANSWER:
The profit function is
pi = p[ln(K) + 2 ln(L)]− rK − wL
F.O.C. of profit maximization:
∂pi
∂K
=
p
K
− r = 0
∂pi
∂L
=
2p
L
− w = 0
i.e.
∂pi
∂K
=
1
K
− 2 = 0
∂pi
∂L
=
2
L
− 4 = 0
which give
K = 0.5 = L
3. Suppose that Emi has utility function U(C,L) = ln(C) + L, where C is con-
sumption and L is leisure hours. Emi has 10 hours in total and no non-labor
income. The wage rate is 5. What would be Emi’s labor supply decision?
ANSWER:
Emi’s budget constraint is given by:
5(10− L) = C
Substitute this back to Emi’s utility function gives:
U = ln[50− 5L] + L
F.O.C. of utility maximization:
U ′ =
−5
50− 5L + 1 = 0
11
U ′ =
−1
10− L + 1 = 0
Therefore, utility maximizing choice is L = 9
4. Suppose a firm’s production function is given by:
q = 2 ln(Ew + Eb)
where Ew and Eb are the number of whites and blacks employed by the firm
respectively. Suppose the market wage for black workers is $8, the market wage
for whites is $10, and the price of each unit of output in $20.
(a) Are black workers and white workers perfect substitutes in the production
process?
ANSWER:
Yes, because only the total number of workers matters for the output level
and the racial composition of the work force does not matter at all.
(b) What is the marginal product of black workers? What is the marginal prod-
uct of white workers? (hint: apply chain rule; see math review)
ANSWER:
∂q
∂Ew
=
2
Ew + Eb
∂q
∂Eb
=
2
Ew + Eb
(c) How many workers would a firm hire if it does not discriminate? How much
profit does this nondiscriminatory firm earn if there are no other costs?
ANSWER:
Profit maximizing requires that marginal revenue equals to marginal cost.
Since black wage is lower and black and white workers are perfect substi-
tutes, a non-discriminating firm would hire all black workers to maximize
profit.
MR = MC ⇒MP × p = w
2
0 + Eb
× 20 = 8
⇒ Eb = 5
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Maximum Profit then is:
pi = 20 ∗ q − 8Eb
= 20× 2 ln(5)− 8 ∗ 5
≈ 24.38
(d) Consider a firm that discriminates against blacks with a discrimination
coefficient of 0.5. The total for each black worker it hires is the wage rate
plus a dis-utility cost equivalent to 50% of the wage rate How many workers
does this firm hire? How much profit does it earn?
ANSWER:
Since
10 < 8× (1 + 0.5) = 12
The black wage is not sufficiently lower than the white wage. Thus, this
discriminatory firm only hire white workers. To maximize profit, it set
MR = ww
where ww is the white wage. Profit maximizing for this firm means:
2
Ew + 0
× 20 = 10
⇒ Ew = 4
Maximum Profit then is:
pi = 20 ∗ q − 10Ew
= 20× 2 ln(Ew + 0)− 10Ew
= 20× 2 ln(4 + 0)− 10× 4
≈ 15.45
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