Final exam Labor economics Preparation Questions
1.
How many hours will a person allocate to leisure activities if her indifference curves between
consumption and goods are concave to the origin?
Answer
When the indifference curve is concave to the origin the labor would either work for all the available time or will
not work at all. The same can be explained with the help of a diagram.
In the diagram we see that the given budget line is BE. Here two concave utility
curves are drawn. The point P is on a lower utility curve so the labor would move
to a higher utility curve which is either intersects with the higher utility curve that
is U1. Keeping the budget constraint we can see from the figure that the U1 curve
touches the budget line at point B and E. B is the point where the labor is working
for all the hours available and not spending any time for the leisure. Similarly being
on the point E the labor is not working at all and enjoying the same utility curve
that he was enjoying at point B. Thus with a concave curve the employer is
indifferent by either working for all the hours or for not working even a single hour.
This theory cannot be true as the two points B and E can never give the same utility thus we can justify that the
indifference curve is convex to the origin and not concave to the origin. And if we assume to have a concave
indifference curve then either the labor will work for all the hours available or not work at all.
What is the effect of an increase in the price of market goods on a worker’s reservation wage,
probability of entering the labor force, and hours of work?
Answer
Market price is the price which is charged in the market for the exchange of goods and services. The prices charged
by the producers in the economy will depend on the factors of production as well as the various market conditions
of the supply side dynamics.
2.
3.
Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for every hour
in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care expenses for each
hour he works. Tom receives $80 in child support payments each week. There are 168 hours in the
week. Graph Tom’s weekly budget line.
Answer
In order to know the effect of rise in the market goods, let us assume that the price of the market goods increases.
It can be better understood by the diagram that is provided as follows:
It is assumed that the price of market goods rises from p to p and the non-labor
income of the person is V. If she chooses leisure over work, she can buy V/p units
of consumption after the change in the prices, and V/p units of consumption before
the price increase.
The endowment point also changes from E to E’. When leisure is considered a
normal good, the indifference curve is steeper as one moves up a vertical line,
Therefore, an upsurge in the price of goods shrinks the reservation wage and makes
the person more prospective to work.
To determine the effect of prices of market goods on hours of work, it is assumed that the non-labor income V =
0. The rise in the price of goods shifts the budget line from FE to GE which can be seen in the below diagram
which further shifts the worker from P to R. It leads to both substitution effect and income effect.
1
As seen from the above diagram, due to the increase in the prices, the real wages
rate of the individual falls which induces them to demand more for leisure and
work for less number of hours. It shifts the point from P to Q.
Due to the increase in the prices of market goods, the wealth of the individual also
falls which leads to lowers the demand for leisure and work for more number of
hours which is the income effect from Q to R.
Here, the income effect is greater than the substitution effect which leads to fall in
the demand for leisure and compels to work for a greater number of hours. And when the substitution effect is
greater than the income effect, the work for hours falls.
4.
Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given
week is 168 hours. Her utility function is 𝑼(𝑪, 𝑳) = 𝑪 × 𝑳. This functional form implies that Cindy’s
𝑪
marginal rate of substitution is . Cindy receives $630 each week from her great-grandmother—
𝑳
regardless of how much Cindy works. What is Cindy’s reservation wage?
Answer
Cindy’s reservation wage is the wage she would need to work her first hour. That, is it is her marginal rate of
substitution when she is working no hours (L=168). At this point her consumption is only the amount she receives
from her great-grandmother: $630. 𝑀𝑅𝑆 =
𝐶
𝐿
=
630
168
= 3.75. Her reservation wage is $3.75.
It has been provided that C will receive $630 each week from her great-grandmother irrespective of whether she
works or not. In other words, her minimum consumption (C) per week will be $630 even though she is using all
110 hours for leisure (L).
As one knows that reservation wage is the minimum wage that will induce a person to accept a job or devote his
or her time towards work instead of leisure. In other words, reservation wage is the MRS of the said person when
he or she is not working at all. 𝑀𝑅𝑆 =
𝐶
𝐿
=
$630
168
= $3.75. As stated above reservation wage is equal to MRS when
all the available hours are devoted to leisure. In case of Cindy, MRS is $3.75. Thus, the reservation wage of Cindy
will be $3.75 per hour.
5.
Explain why a lump-sum government transfer can entice some workers to stop working (and entices
no one to start working) while the earned income tax credit can entice some people who otherwise
would not work to start working (and entices no one to stop working)
Answer
A sudden lump-sum transfer raises some people’s lifetime income (very slightly). Since they are richer, they will
work less and may retire earlier. Since this transfer is not conditional on working, there is only this lifetime income
effect, and no other effect to induce anyone to start working. In contrast, the earned income tax credit raises the
wage for people who are not currently working: a positive substitution effect that will lead some of them to start
working. On the other hand, everyone who is currently working chose to work over not working before the EITC.
The amount they can earn working has increased or stayed the same while their income from not working stays
constant. Thus, no one who worked before will choose not to work after the EITC is implemented.
6.
Suppose there are two inputs in the production function, labor and capital, and these two inputs are
perfect substitutes. The existing technology permits one machine to do the work of three workers. The
firm wants to produce 100 units of output. Suppose the price of capital is $750 per machine per week.
What combination of inputs will the firm use if the weekly salary of each worker is $300? What
combination of inputs will the firm use if the weekly salary of each worker is $225? What is the elasticity
of labor demand as the wage falls from $300 to $225?
Answer
2
Because labor and capital are perfect substitutes, the
isoquant for producing 100 units of output is linear and the
firm will use only labor or only capital, depending on
which is relatively cheaper in producing 100 units of
output.
The (absolute value of the) slope of the isoquant (
𝑀𝑃𝐸
𝑀𝑃𝐾
) is
1/3 because 1 machine does the work of 3 workers. When
the wage is $300, the slope of the isocost is
300
. The isocost
750
curve, therefore, is steeper than the isoquant, and the firm only hires capital (at point A). To calculate this in a
different way, one machine does the work of three workers. The one machine costs $750; the three workers cost
$300 × 3 = $900. Clearly the firm should hire only machines.
When the weekly wage is $225, the isoquant is steeper than the isocost and the firm hires only labor (at point B).
To calculate this in a different way, one machine does the work of three workers. The one machine costs $750;
the three workers cost $225 × 3 = $675. Clearly the firm should hire only workers.
The elasticity of labor demand is defined as the percentage change in labor divided by the percentage change in
the wage:
𝑎−0
𝛥𝐸
0
𝐸
𝛿=
=
≈ 𝑎, 𝑎 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑛𝑢𝑚𝑏𝑒𝑟
𝛥𝑤
225 − 300
𝑤
300
Because the demand for labor goes from 0 to a positive quantity when the wage drops to $225, the (absolute value
of the) elasticity of labor demand is infinity.
7.
What happens to employment in a competitive firm that experiences a technology shock such that at
every level of employment its output is 200 units per hour greater than before?
Answer
As the output increases by the same amount i.e. 200 units per hour at every level of employment, the marginal
product of labor remains same and so does the value of marginal product (VMP). The value of marginal product
(VMP) is the dollar increase in revenue generated by an additional worker, and is calculated by following formula:
𝑤 = 𝑉𝑀𝑃𝐸 = 𝑝 × 𝑀𝑃𝐸 ⇒ 𝑊 ×
1
= 𝑝 = 𝑀𝐶𝐸
𝑀𝑃𝐸
The law of diminishing marginal returns tells us that if the quantity
of a factor is increased while other inputs are held constant, its
marginal product will eventually decline. The firm expands as long
as the marginal product of labor exceeds the marginal cost of labor.
Given that the firm’s budget is fixed, profit maximization is
achieved when wage and employment reach their maximum and
minimum levels, respectively. If marginal product of labor is
falling, marginal product of revenue product must be falling as
well. Consequently, cost minimization is achieved when wage and
employment reach their minimum and maximum levels,
respectively. The two rectangle areas are equal.
And as long as the price (p) remains same the value of marginal product also remains same at each level of
employment. As we know the firm hires workers up to the point where the value of marginal product equals wage
3
rate. Therefore, as the value of marginal product remains equal to wage rate at every level of employment, the
firm will not change the level of employment, it will remain same.
8.
Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is
constant at $50 per unit. The production function is
𝟏
𝟏
𝒇(𝑬, 𝑲) = 𝑬𝟐 𝑲𝟐
𝟏
𝟏
𝑲 𝟐
so that the marginal product of labor is 𝑴𝑷𝑬 = ( ) ( ) . If the current capital stock is fixed at 1,600 units,
𝟐
𝑬
how much labor should the firm employ in the short run? How much profit will the firm earn?
Answer
The firm’s labor demand curve is its value of marginal product curve, 𝑉𝑀𝑃𝐸 , which equals the marginal
productivity of labor, 𝑀𝑃𝐸 , times the price (which is also the marginal product revenue):
𝑉𝑀𝑃𝐸 = 𝑝 × 𝑀𝑃𝐸 = 50 ×
1
1,600 1000
×√
=
2
𝐸
√𝐸
Since 𝑉𝑀𝑃𝐸 = 𝑤, then
10 =
1000
√𝐸
⇒ √𝐸 = 100 ⇒ 𝐸 = 10,000
The firm then makes
𝑓(𝐸, 𝐾) = √1,600 √10,000 = 4,000
units of output and earns a profit of
𝜋 = 𝑝 × 𝑓(𝐸, 𝐾) − 𝑤 × 𝐸 − 𝑟 × 𝑘 = $50 × 4,000 − 25$ × 1,600 − $10 × 10,000 = $60,000
9.
Suppose a firm purchases labor in a competitive labor market and sells its product in a competitive
product market. The firm’s elasticity of demand for labor is -0.4. Suppose the wage increases by 5
percent. What will happen to the amount of labor hired by the firm? What will happen to the marginal
productivity of the last worker hired by the firm?
Answer
Given the estimates of the elasticity of labor demand and the change in the wage, we have
𝜂=
%𝛥𝐸
%𝛥𝐸
⇒
= −0.4 ⇒ %𝛥𝐸 = −2%
%𝛥𝑤
5%
An elasticity of -2% implies that a 1% (5%) increase in the wage rate results in only a 0.5% (2%) decrease in the
quantity of labor demanded (since elasticity is a percentage change in quantity demanded in response to a 1%
change in price). This indicates that changes in wages have a relatively small effect on labor demand. In a
competitive labor market setting, the marginal worker is paid the value of his marginal product. Since the output
price does not change, the marginal productivity of the marginal worker increases by 5% as well.
10.
a) What happens to wages and employment if the government imposes a payroll tax on a monopsonist?
Compare the response in the monopsonistic market to the response that would have been observed in
a competitive labor market.
4
Suppose a firm is a perfectly discriminating monopsonist. The government imposes a minimum wage
on this market. What happens to wages and employment?
Answer
a) Monopsony can be defined as the market structure where a single buyer has the market power over the
employees as the sole employer in the market. When the government imposes a payroll tax on a monopsonist,
it can significantly affect wages and employment.
b)
Initially, the monopsonist hires EM workers at a wage of wM. The
imposition of a payroll tax shifts the demand curve to VMP′, and lowers
employment to E′ and the wage to w′. Thus, the effect of imposing a
payroll tax on a monopsonist is qualitatively the same as imposing a
payroll tax in a competitive labor market: lower wages and employment
because the employer shifts some of the tax burden to workers. In
competitive labor markets, tax pass-through is less aggressive because
employers may be less inclined to pass on the full burden of payroll taxes
to workers in the form of reduced wages. So, employers may absorb a
portion of the tax costs to remain competitive, resulting in more stable
wages and potentially less severe employment impacts.
b) When the government imposes a minimum wage on a perfectly
discriminating monopsonist, it can significantly affect wages and employment. A
perfectly discriminating monopsonist faces a marginal cost of labor curve that is
identical to the supply curve. As a result, the employment level of a perfectly
discriminating monopsonist equals the employment level that would be observed
in a competitive market (at E*) The imposition of a minimum wage at wMIN leads
to the same result as in a competitive market: the firm will only want to hire ED
workers as wMIN is now the marginal cost of labor, but E S workers will want to
find work at the minimum wage. Thus, the wage increases, but employment falls.
11. A firm faces perfectly elastic demand for its output at a price of $6 per unit of output. The firm,
however, faces an upward-sloped labor supply curve of
𝑬 = 𝟐𝟎𝒘 − 𝟏𝟐𝟎
where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the firm faces
an upward-sloped marginal cost of labor curve of
𝑴𝑪𝑬 = 𝟔 + 𝟎. 𝟏𝑬
Each hour of labor produces five units of output. How many workers should the firm hire each hour
to maximize profits? What wage will the firm pay? What are the firm's hourly profits?
Answer
Price per unit of output: 𝑃 = $6
Labor supply curve: 𝐸 = 20𝑤 − 120
Marginal cost curve: 𝑀𝐶𝐸 = 6 + 0.1𝐸
Marginal product of labor: 𝑀𝑃𝐸 = 5
First, we need to know how many workers should the firm hire to maximize profits: A firm maximize profits
where value of marginal product of labor (𝑉𝑀𝑃𝐸 ) is equal to the marginal cost of labor.
𝑉𝑀𝑃𝐸 = 𝑃 × 𝑀𝑃𝐸 = 6 × 5 = $30
Then
5
𝑉𝑀𝑃𝐸 = 𝑀𝐶𝐸 ⟹ 30 = 6 + 0.1𝐸 ⟹ 𝐸 = 240
Therefore, the firm will hire 240 workers to maximize profits. To get the wage which the firm will pay, let's put
the value of E in the equation of labor supply curve.
240 = 20𝑤 − 120 ⟹ 𝑤 = $18
So, the firm will pay $18 to the hired workers. Firm's hourly profits: total revenue – total cost = number of workers
value of marginal product of labor - number of workers wages rate. Therefore, the firm's hourly profits are:
(240 × 5 × 6) − (240 × 18) = $2,800
12. Politicians who support the green movement often argue that it is profitable for firms to pursue a
strategy that is “environmentally friendly” (for example, by building factories that do not pollute and
are not noisy) because workers will be willing to work in environmentally friendly factories at a lower
wage rate. Evaluate the validity of this claim
Answer
Compensating wage differentials refers to the idea that individuals may receive higher or lower wages depending
on the risks and undesirability associated with a particular job or working conditions. In a two-commodity
framework – wage is considered a good commodity; furthermore, risk of job injury is considered a bad
commodity. However, safety is costly and if firm invest in green technology and provide a safe work environment
to the workers then worker will be working in lesser wages, and depending on the productivity differential it can
be worked out whether it is becoming profitable for firm or not. The claim that workers are willing to accept lower
wages in environmentally friendly factories is valid in some circumstances but not universally applicable. The
decision is influenced by a combination of personal values, local economic conditions, industry specifics, and
overall compensation considerations.
13. Consider two identical jobs, but some jobs are located in Ashton while others are located in Benton.
Everyone prefers working in Ashton, but the degree of this preference varies across people. In
particular, the preference (or reservation price) is distributed uniformly from $0 to $5. Thus, if the
Benton wage is $2 more than the Ashton wage, then 40 percent (or two-fifths) of the worker population
will choose to work in Benton. Labor supply is perfectly inelastic, but firms compete for labor. There
are a total of 25,000 workers to be distributed between the two cities. Demand for labor in both
locations is described by the following inverse labor demand functions:
𝑨𝒔𝒉𝒕𝒐𝒏: 𝒘𝑨 = 𝟐𝟎 − 𝟎. 𝟎𝟎𝟐𝟒 𝑬𝑨
𝑩𝒆𝒏𝒕𝒐𝒏: 𝒘𝑩 = 𝟐𝟎 − 𝟎. 𝟎𝟎𝟎𝟒 𝑬𝑩
Solve for the labor market equilibrium by finding the number of workers employed in both cities, the
wage paid in both cities, and the equilibrium wage differential.
Answer
Given:
1) 𝑤𝐴 = 20 − 0.0024 𝐸𝐴 ,
2) 𝑤𝐵 = 20 − 0.0004 𝐸𝐵
3) 𝛥 = 𝑤𝐵 − 𝑤𝐴 ,
4) 𝐸𝐴 + 𝐸𝐵 = 25,000,
5) 𝐸𝐵 =
25,000𝛥
5
= 5,000𝛥
Equation (5) is the most difficult for most students to see. And once they see it, they wonder why a sixth equation
of EA = 25,000 – 5,000Δ isn’t also included. Of course, this sixth equation plus (4) and (5) are perfectly collinear,
so only two of the three can be used. Now consider the following algebraic manipulations:
(2) − (1) → 𝑤𝐵 − 𝑤𝐴 = 𝛥 = (20 − 0.0004 𝐸𝐵 ) − (20 − 0.0024 𝐸𝐴 ) = 0.0024 𝐸𝐴 − 0.0004 𝐸𝐵
6
Substituting in (4) yields:
𝛥 = 0.0024(25,000 − 𝐸𝐵 ) − 0.0004 𝐸𝐵 = 60 − 0.0028𝐸𝐵
Substituting (5) into this last equation yields:
𝛥 = 60 − 0.0028(5,000𝛥) ⇒ 𝛥 = 60 − 14𝛥 ⇒ 𝛥 = $4
The entire equilibrium is given by:
(1) → 𝐸𝐵 = 5,000𝛥 = 5,000(4) = 20,000
(4) → 𝐸𝐴 = 5,000
(2) → 𝑤𝐵 = 20 − 0.0004 𝐸𝐵 = 20 − 0.0004 (20,000) = $12
(1) → 𝑤𝐴 = 20 − 0.0024 𝐸𝐴 = 20 − 0.0024 (5,000) = $8
Thus, the labor market equilibrium is for 20,000 workers to work in Benton, each being paid $12 per hour; for
5,000 workers to work in Ashton, each being paid $8; and for the equilibrium wage differential to be $4.
14. The hedonic wage function is the locus of points that illustrates the relationship between the wage that
workers get paid and job characteristics. All else equal, the more pollutants miners breathe while
working in a mine, the worse off the miners are. However, miners vary in their degree of dislike for
breathing in pollutants. Given the current distribution of perfectly competitive firms (that is, mines)
and technologies for cleaning up pollutants, a hedonic wage function comes about. Suppose the
distribution of mines and technologies remains fixed, but, due to a public relations campaign by the
American Cancer Society, all potential miners change their preferences so that they dislike breathing
in pollutants even more.
a) What will happen to the hedonic wage function after the public relations campaign?
b) What will happen to where each individual miner locates on the hedonic wage function?
Answers
a) As the public relations campaign has no effect on technology or competition, the hedonic wage function does
not change. At best, the “dirtiest” firms may no longer find anyone willing to work there, and therefore these
firms go out of business.
b) Each miner becomes less tolerant of breathing in pollutants. That is, each worker’s preferences change –
graphically, indifference curves in wage-pollutant space become steeper. Therefore, as a result of the
campaign, each worker locates further down (toward the origin) the hedonic wage function, meaning that
each worker accepts a lower wage in order to work at a cleaner environment.
15. In a particular industry, labor supply is 𝑬𝒔 = 𝟏𝟎 + 𝒘 and labor demand is 𝑬𝑫 = 𝟒𝟎 − 𝟒𝒘, where E is
the level of employment and w is the hourly wage.
a) What are the equilibrium wage and employment if the labor market is competitive? What is the
unemployment rate?
b) Suppose the government sets a minimum hourly wage of $8. How many workers would lose their jobs?
How many additional workers would want a job at the minimum wage? What is the unemployment
rate?
Answer
7
a) In equilibrium, the quantity of labor supplied equals the quantity of labor
demanded:
𝐸𝑠 = 𝐸𝐷 ⇒ 10 + 𝑤 = 40 − 4𝑤 ⇒ 𝑤 ∗ = $6
Given the equilibrium wage, equilibrium employment is (let’s use arbitrarily
labor supply equation)
𝐸 ∗ = 10 + 6 = 16
so, 16 persons are employed. There is no unemployment because the number of persons looking for work equals
the number of persons employers are willing to hire at the going wage rate of $6 per hour
b) If employers must pay an hourly wage of $8, employers would only
want to hire 𝐸𝐷 = 40 − 4(8) ⇒ 𝐸𝐷 = $8 workers, while
𝐸𝑠 = 10 + 8 ⇒ 𝐸𝑠 = 18 persons would like to work. Thus, 8 workers
lose their job following the minimum wage as 16 workers used to be
employed but now only 8 are; and 2 additional people enter the labor
force following the minimum wage as 16 workers used to want a job but
now 18 do. Under the minimum wage, the unemployment rate would be
%𝑈 =
𝐸𝑠 − 𝐸𝐷 18 − 10 10
=
=
⇒ %𝑈 = 55.6%
𝐸𝑠
18
18
16. Suppose the supply curve of physicists is given by 𝒘 = 𝟏𝟎 + 𝟓 ∙ 𝑬∗ , while the demand curve is given by
𝒘 = 𝟓𝟎 − 𝟑 ∙ 𝑬∗ . Calculate the equilibrium wage and employment level. Suppose now that the demand
for physicists increases to 𝒘 = 𝟕𝟎 − 𝟑 ∙ 𝑬∗ . Assume the market is subject to cobwebs. Calculate the
wage and employment level in each round as the wage and employment levels adjust to the demand
shock. What are the new equilibrium wage and employment level? (calculate the values of the wage
and employment for the first two rounds)
Answer
Let a be the equilibrium point of supply and demand curves. The equilibrium employment can be found by
equating the demand and supply curves:
𝑆 = 𝐷 ⟹ 10 + 5 ∙ 𝐸 ∗ = 50 − 3 ∙ 𝐸 ∗ ⟹ 𝐸 ∗ = 5
We plug the equilibrium employment 𝐸 ∗ = 5 e find equilibrium either in
supply equation or demand equation (equilibrium) to find the equilibrium
wage:
𝑤 ∗ = 50 − 3 ∙ (5) ⟹ 𝑤 ∗ = $35
Therefore, equilibrium employment 𝐸 ∗ = 5, and wage 𝑤 ∗ = $35
8
The physicists labor demand curve increases: 𝐷 = 50 − 3 ∙ 𝐸 → 𝐷𝑁 =
70 − 3 ∙ 𝐸. The slope of the demand remains the unchanged, so we have
an upward shift of the demand curve with demand curve 𝑤𝑁 = 70 − 3 ∙
𝐸. Equating new demand curve with initial supply curve at the new
equilibrium point b:
𝑆 = 𝐷𝑁 ⟹ 10 + 5 ∙ 𝐸 = 70 − 3 ∙ 𝐸 ⇒ 𝐸1 = 7.5
𝑤1 = 70 − 3 ∙ (7.5) ⇒ 𝑤1 = 70 − 3 ∙ (7.5) ⇒ 𝑤1 = $47.5
Therefore, the new equilibrium wage is 𝑤1 = $47.5, and new equilibrium employment 𝐸1 = 7.5.
A cobweb labor market is characterized by labor supply adjustments which lag behind changes in demand because
of the lengthy training periods required. The path of wages and employment in such models traces out a spiral
pattern when plotted on a supply and demand diagram. The calculation of the wage and employment in each round
is level adjusted to the demand shock. According to theory, the physicists' supply is inelastic. Each round occurs
on the new demand curve.
First round: an increase of labor demand, D, shift the labor demand line
to the new labor demand, DN. Given the original employment, 𝐸 ∗ = 5,
we find the new wage on the new labor demand, DN, at point c.
𝑤2 = 70 − 3 ∙ (5) ⇒ 𝑤2 = $55
Therefore, in first round 𝐸 ∗ = 5, and 𝑤2 = $55.
Second round: at wage rate 𝑤2 = $55, the supply of labor is at point d
corresponds to adjusted employment 𝐸2 :
$55 = 10 + 5 ∙ 𝐸 ⟹ 𝐸2 = 9
Inserting the value of employment 𝐸2 = 9 to new demand curve, DN, we
find the adjusted employment 𝑤3 :
𝑤3 = 70 − 3 ∙ (9) ⟹ 𝑤3 = $43
Therefore, in second round 𝐸2 = 9, and 𝑤3 = $43
And so on...
Round
1
2
3
4
5
6
7
8
Wage Employment
$55.0
5
$43.0
9
$50.2
6.6
$45.9
8.0
$48.4
7.2
$46.9
7.7
$47.8
7.4
$47.2
7.6
The table gives the values for the wage and employment levels in each round.
The values in the table are calculated by noting that in any given period the
number of physicists is inelastically supplied, so that the wage is determined
by the demand curve. Given this wage, the number of economists available
in the next period is calculated. By round 7, the market wage rate is within
30 cents of the new equilibrium.
9
17. Consider two identical jobs, but some jobs are located in Ashton while others are located in Benton.
Everyone prefers working in Ashton, but the degree of this preference varies across people. In
particular, the preference (or reservation price) is distributed uniformly from $0 to $5. Thus, if the
Benton wage is $2 more than the Ashton wage, then 40 percent (or two-fifths) of the worker population
will choose to work in Benton. Labor supply is perfectly inelastic, but firms compete for labor. There
are a total of 25,000 workers to be distributed between the two cities. Demand for labor in both
locations is described by the following inverse labor demand functions:
𝑨𝒔𝒉𝒕𝒐𝒏: 𝒘𝑨 = 𝟐𝟎 − 𝟎. 𝟎𝟎𝟐𝟒 𝑬𝑨
𝑩𝒆𝒏𝒕𝒐𝒏: 𝒘𝑩 = 𝟐𝟎 − 𝟎. 𝟎𝟎𝟎𝟒 𝑬𝑩
Solve for the labor market equilibrium by finding the number of workers employed in both cities, the
wage paid in both cities, and the equilibrium wage differential.
Answer
Given:
6) 𝑤𝐴 = 20 − 0.0024 𝐸𝐴 ,
7) 𝑤𝐵 = 20 − 0.0004 𝐸𝐵
8) 𝛥 = 𝑤𝐵 − 𝑤𝐴 ,
9) 𝐸𝐴 + 𝐸𝐵 = 25,000,
10) 𝐸𝐵 =
25,000𝛥
5
= 5,000𝛥
Equation (5) is the most difficult for most students to see. And once they see it, they wonder why a sixth equation
of EA = 25,000 – 5,000Δ isn't also included. Of course, this sixth equation plus (4) and (5) are perfectly collinear,
so only two of the three can be used. Now consider the following algebraic manipulations:
(2) − (1) → 𝑤𝐵 − 𝑤𝐴 = 𝛥 = (20 − 0.0004 𝐸𝐵 ) − (20 − 0.0024 𝐸𝐴 ) = 0.0024 𝐸𝐴 − 0.0004 𝐸𝐵
Substituting in (4) yields:
𝛥 = 0.0024(25,000 − 𝐸𝐵 ) − 0.0004 𝐸𝐵 = 60 − 0.0028𝐸𝐵
Substituting (5) into this last equation yields:
𝛥 = 60 − 0.0028(5,000𝛥) ⇒ 𝛥 = 60 − 14𝛥 ⇒ 𝛥 = $4
The entire equilibrium is given by:
(1) → 𝐸𝐵 = 5,000𝛥 = 5,000(4) = 20,000
(4) → 𝐸𝐴 = 5,000
(2) → 𝑤𝐵 = 20 − 0.0004 𝐸𝐵 = 20 − 0.0004 (20,000) = $12
(1) → 𝑤𝐴 = 20 − 0.0024 𝐸𝐴 = 20 − 0.0024 (5,000) = $8
Thus, the labor market equilibrium is for 20,000 workers to work in Benton, each being paid $12 per hour; for
5,000 workers to work in Ashton, each being paid $8; and for the equilibrium wage differential to be $4.
18. Suppose Peter lives for three periods. He is currently considering three alternative education work
options. He can start working immediately, earning $100,000 in period 1, $110,000 in period 2 (as his
work experience leads to higher productivity), and $90,000 in period 3 (as his skills become obsolete
and his physical abilities deteriorate). Alternatively, he can spend $50,000 to attend college in period 1
and then earn $180,000 in periods 2 and 3. Finally, he can receive a doctorate degree in period 2 after
completing his college education in period 1. This last option will cost him nothing when he is attending
graduate school in the second period as his expenses on tuition and books will be covered by a research
assistantship. After receiving his doctorate, he will become a professor in a business school and earn
10
$400,000 in period 3. Peter's discount rate is 20 percent per period. What education path maximizes
Peter's net present value of his lifetime earnings?
Answer
The present discounted values of Peter's earnings associated with each of the alternatives are
𝑃𝑉𝐻𝑆 = 100,000 +
110,000
90,000
+
= $254,167
1 + 0.2 (1 + 0.2)2
𝑃𝑉𝐶𝑂𝐿 = −50,000 +
180,000
180,000
+
= $225,000
1 + 0.2 (1 + 0.2)2
and
𝑃𝑉𝑃ℎ𝐷 = −50,000 +
0
400,000
+
= $227,778
1 + 0.2 (1 + 0.2)2
Thus, the best option for Peter is to start working upon completely high school.
19. Suppose Carl’s wage-schooling locus is given by
Derive the marginal rate of return schedule. When will
Carl quit school if his discount rate is 4 percent? What if
the discount rate is 9 percent?
Answer
The marginal rate of return is given by the percentage increase in earnings if the worker goes to school one
additional year:
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑃𝑟𝑒𝑠𝑒𝑛𝑡 − 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 =
× 100
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠
𝑀𝑅𝑅9 =
𝑀𝑅𝑅10 =
20,350 − 18,500
1,850
× 100 ⇒ 𝑀𝑅𝑅9 =
× 100 ⇒ 𝑀𝑅𝑅9 = 10%
18,500
18,500
22,000 − 20,350
1,650
× 100 ⇒ 𝑀𝑅𝑅10 =
× 100 ⇒ 𝑀𝑅𝑅10 = 8.1%
20,350
20,350
𝑀𝑅𝑅11 =
23,100 − 22,000
1,100
× 100 ⇒ 𝑀𝑅𝑅11 =
× 100 ⇒ 𝑀𝑅𝑅11 = 5%
22,000
22,000
𝑀𝑅𝑅12 =
23,900 − 23,100
800
× 100 ⇒ 𝑀𝑅𝑅12 =
× 100 ⇒ 𝑀𝑅𝑅12 = 3.46%
23,100
23,100
𝑀𝑅𝑅13 =
24,000 − 23,900
100
× 100 ⇒ 𝑀𝑅𝑅13 =
× 100 ⇒ 𝑀𝑅𝑅13 = 0.42%
23,900
23,900
Schooling
9
10
11
Earnings
$18,500
$20,350
$22,000
11
MRR
10.0
8.1
12
13
14
$23,100
$23,900
$24,000
5.0
3.5
0.4
Marginal rate of return for spending 10 years of schooling is 10%. Marginal rate of return should be equal to or
just exceeds than the discount rate. Since marginal rate exceeds discount rate at schooling 12 years, the person
should quite the schooling after 12 years. If the discount rate is 9%, then the marginal rate of return is just
exceeding the discount rate at schooling 10 years. Thus, the person should quite from the schooling after 10 years
of schooling.
20.
a. Describe the basic self-selection issue involved whenever discussing the returns to education.
b.
Does the fact that some high school or college dropouts go on to earn vast amounts of money (e.g., Bill
Gates dropped out of Harvard without ever graduating) contradict the self-selection story?
c.
Most government-provided job training programs are optional to the worker. Describe how the selfselection issue might be used to call into question empirical results suggesting there are large economic
benefits to be gained by requiring all workers to receive government-provided job training.
Answer
People choose their level of education knowing their own abilities, preferences, and financial situation.
Highly capable people would likely earn a large salary even if they didn’t attend college, but they choose to
attend because they earn even more (net of the cost of college) by doing so. Likewise, less capable people
know they are less capable and that they will not get very high paying jobs even with a college degree.
Consequently, highly capably people tend to go to college while less capable people are less likely to go to
college, and the average wage of college graduates is higher than the average wage of non-college graduates
largely because of self-selected education levels due to innate skills or abilities.
a.
b.
No. One, there are always exceptions. And two, if the cost of education gets large enough (or the returns to
education get small enough), even high ability people will forego college.
c.
As job training programs are optional, and willingness to work or try to get a new job or to get retrained is
probably the most important factor in a person’s success, there is certainly a self- selection story to be told.
In particular, the successful people coming out of job training programs would likely have been successful
even if left on their own because of their innate ability/motivation. Similarly, the people who did not choose
job training and failed to get a job would likely have failed to get a job even if the government required them
to pursue job training.
21. What effect will each of the following proposed changes have on wage inequality?
a) Indexing the minimum wage to inflation.
b) Increasing the benefit level paid to welfare recipients.
c) Increasing wage subsidies paid to firms that hire low-skill workers.
d) An increase in border enforcement, reducing the number of illegal immigrants entering the
country.
e) Workers' Rights Amendment sets new bar for state worker power policy.
Answer
a) Indexing the minimum wage to inflation should reduce wage inequality because the minimum wage because
the real value of the minimum wage keeps pace with the cost of living. As a result, low-wage workers'
earnings will increase in line with inflation, providing them with a more stable income. This helps to narrow
the wage gap between low-wage and higher-wage workers. Since only the minimum wage is inflation
adjusted whereas high-wages remained constant, losing actually value in real terms. Indexing the minimum
12
wage implies an indirect increase in the minimum that 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 for welfare recipients can have mixed effects on wage inequality. On one hand,
it may reduce wage inequality by providing financial support to those with low or no income, potentially
lifting them out of poverty. On the other hand, if the increase in benefits is substantial and without work
requirements, it could create disincentives for some individuals to seek employment or pursue higher-paying
jobs, which might exacerbate wage inequality in the long term.
c)
Wage subsidies would increase the demand for less skilled workers, reducing wage inequality. Wage
subsidies for low-skill workers incentivize firms to hire and retain low-wage employees. This can boost the
incomes of low-wage workers, narrowing the wage gap. It also encourages employers to invest in their
employees' skills, potentially increasing their productivity and earning potential.
d) The impact of increased border enforcement on wage inequality is complex and depends on various factors.
Reduction in illegal immigration can lead to a tighter labor market for low-skilled jobs, potentially increasing
wages for native and legal immigrant workers in these sectors. This might have a positive impact on wage
equality. However, it may also lead to labor shortages in some industries, potentially increasing wage
disparities in those sectors. Additionally, the actual effects would depend on the scale of the change in
immigration policy.
e)
The amendment may strengthen the collective bargaining power of workers, enabling them to negotiate for
higher wages and better working conditions. This can lead to increased wages for unionized workers,
potentially reducing wage inequality within unionized sectors. However, not all workers are part of unions.
22. Explain why the intergenerational correlation of earnings would likely be higher or lower than average
for the following groups or as a consequence of policy changes in the United States:
a. Improved educational outcomes for all populations (e.g., minority, low-income, rural) as hoped for
by No Child Left Behind.
b. The elimination of legacy admits to colleges and universities.
c. The implementation of a federal inheritance tax.
d. The economic elite.
Answer
a.
If educational reforms, such as those envisioned by No Child Left Behind, are successful in improving
educational outcomes for all populations, including minority, low-income, and rural communities, we would
likely see a positive impact on income mobility. Higher-quality education can equip individuals with the
skills and opportunities to pursue higher-paying jobs, potentially reducing the influence of parental income
on their own future earnings. This could lead to a lower intergenerational correlation of earnings.
b.
Legacy admissions, where children of alumni receive preferential treatment in college admissions, can
reinforce existing advantages and result in a higher intergenerational correlation of earnings. Eliminating such
policies can create a fairer system where college access is based on merit rather than family connections. In
the long term, this policy change could contribute to lower income mobility and a lower intergenerational
correlation of earnings.
c.
The implementation of a federal inheritance tax could have a mixed impact. On one hand, it might reduce the
transfer of wealth across generations, potentially leading to greater income mobility and a lower
intergenerational correlation of earnings. On the other hand, wealthy families often use estate planning
strategies to minimize tax liability, which can limit the effectiveness of such a tax. The overall effect would
depend on the specifics of the tax policy and its enforcement.
d.
The influence of the economic elite on the intergenerational correlation of earnings depends on various
factors. Policies that address income and wealth inequality could potentially reduce the concentration of
13
resources within a small, privileged group, leading to greater income mobility. In contrast, policies that
protect and exacerbate wealth disparities might reinforce the influence of the economic elite and result in a
higher intergenerational correlation of earnings.
23.
Use the two wage ratios for each country in Table 7-4
to calculate the percent increase in the 90-10 wage ratio from 1984
to 1994. Which countries experienced a compression in the wage
distribution over this time? Which three countries experienced the
greatest percent increase in wage dispersion over this time?
Answer
Thus, Germany, Canada, and Norway (with Japan holding
constant) all experienced a compression in the wage
distribution over this time. The United Kingdom, New
Zealand, and Italy experienced the largest percent increases in
wage dispersion.
24. Consider the Roy model of potential immigrant flows as discussed in the chapter.
a) Why is it that a source country can experience both an outflow of low-skill workers and an outflow
of high-skill workers at the same time?
b) Provide a graph of the returns to skills in the destination and source countries that would suggest
both behaviors occur simultaneously.
c) How do the social and economic (that is, tax) policies of the United States encourage both types of
flows?
Answer
a) In reality a source country will experience an outflow of low-skill and high-skill workers at the same time
because of individual preferences – some people will want to immigrate regardless of the skills issue. In
theory and in practice, however, a source country can experience an outflow of low-skill and high-skill
workers at the same time because the returns to skills in the two countries are not linear as the model in the
text suggests. In the United States, for example, the returns to low-skills may be much greater than in Mexico.
At the same time, the returns to high-skills may also be much greater in the United States than in Mexico. In
the middle, though, the returns may be relatively higher in Mexico. If so, then Mexico will experience an
outflow of low-skill and high-skill workers.
b)
Figure illustrates the level of return (Wage)
for the low skill, medium skill and high skill
labor in the domestic country and foreign
country. It reveals that the returns for the high
skill and low skill in the foreign country are
greater than the domestic country. Thus,
there would be a simultaneous outflow of
high skill and low skill labor to the foreign
country.
14
c)
The policy of social safety net, working condition in the foreign country would be better than the domestic
country. Highest tax rate in the foreign country is less than the domestic country. Also, wealth, freedom of
individual rights is well protected in the foreign country. Thus, these policies would encourage the
simultaneous outflow of high skill labor and low skill labor.
25. An economy consists of two regions, the North and the South. The short-run elasticity of labor demand
in each region is -0.5. Labor supply is perfectly inelastic within both regions. The labor market is
initially in an economywide equilibrium, with 600,000 people employed in the North and 400,000 in the
South at a wage of $15 per hour. Suddenly, 20,000 people immigrate from abroad and initially settle in
the South. They possess the same skills as the native residents and also supply their labor inelastically.
a) What will be the effect of this immigration on wages in each of the regions in the short run
(before any migration between the North and the South occurs)?
b) Suppose 1,000 native-born persons per year migrate from the South to the North in response to
every dollar differential in the hourly wage between the two regions. What will be the ratio of
wages in the two regions after the first-year native labor responds to the entry of the
immigrants?
c) What will be the effect of this immigration on wages and employment in each of the regions in the
long run (after native workers respond by moving across regions to take advantage of whatever
wage differentials may exist)? Assume labor demand does not change in either region.
Answer
a) The effect of migration of 20,000 people in the south (who possess the same skill as the native workers) on
the wages in both south and north region. As there is no migration between south and north, and the workers
have only migrated to south, therefore there would be no changes in the employment and wage level in the
north.
There were 400,000 workers initially working in the south, and 20,000 additional workers migrated, so the
total workforce is now 420,000. Therefore, there is
20,000
400,000
= 5% increase in labor supply in the south region.
Now, we know that as the labor supply increases the wage rate will fall, and since the short run elasticity of
labor demand is -0.5:
420,000 − 400,000
𝛥𝐸
%𝛥𝐸
5%
400,000
𝐸
𝛿𝑆𝑅𝑆 =
=
⇒ −0.5 =
⇒ %𝛥𝑤 =
⇒ %𝛥𝑤 = −10%
%𝛥𝑤 𝛥𝑤
%𝛥𝑤
−0.5
𝑤
Therefore, the wage rate will fall by 10%. The equilibrium wage in south would be 15 × 0.90 = $13.50
b) As it is given that 1000 native born persons per year migrate from south to north in response to 1-dollar
differential in the hourly wages between the two regions. Now, the wages in south have fallen to $13.50, while
the wages in north are $15, so there is a difference of $1.5. This difference of $1.5 therefore will call cause a
migration of 1500 persons from south to north. The total employment in the north region is (600,000+1500 =
601,500), which means there is
1,500
600,000
= 0.25% increase in labor supply. Since the elasticity of labor supply
is -0.5, we have
601,500 − 600,000
𝛥𝐸
%𝛥𝐸
0.25%
600,000
𝐸
𝛿𝑆𝑅𝑁 =
=
⇒ −0.5 =
⇒ %𝛥𝑤 =
⇒ %𝛥𝑤 = −0.5%
%𝛥𝑤 𝛥𝑤
%𝛥𝑤
−0.5
𝑤
Therefore, the wage rate will fall by 0.5%. The equilibrium wage in south would be 15 × 0.995 = $14.9250.
Now, after the migration of 1,500 labor from south to north, the labor supply in south is 418,500 (420,000-1500).
Which means the employment is decreased by 0.358 %. As the elasticity of labor supply is -0.5, therefore the
15
wage in south increases by
south wages is:
14.93
13.60
0.358
0.5
= 0.715% . Which means the wages in south is $13.60. So, the ratio of north
= 1.098
1. Well, in the long run there will be a movement of labour from south to north, because the wage rate in the
north is higher than that of the south. As elasticity of labour is same in both the region therefore in the long
run this movement of labour from south to north will bring about the same proportion of employment (60:40)
and same level of wages in both the regions.
As we know initially 600,000 workers were employed in north region and 400,000 were employed in the south
region, so the additional 20,000 labour which had migrated in south will also get distributed in ratio of 60:40
in both north and south regions in the long run. Hence 60% of 20,000 i.e. 12,000 workers will migrate to north
region, and as result the total employment level in the north would be (600,000+12,000) 612,000 in the long
run. Similarly, 40% of 20,000 i.e. 8000 workers will remain in south region, so in the long run the total
employment in south would be 408,000 (400,000+8,000).
Therefore, in the long run there has been 2% increase in the employment in both the regions i.e. 12000 is 2%
of 600,000, and 8000 is 2% of 400,000. So, overall there is 2% increase in the employment level in both the
regions. Now, as the elasticity of labour supply is -0.5 in both the regions, therefore the fall in wages in both
the regions would be
2
0.5
= 4% . Thus a 4% fall in the initial wage of $15 in both the regions would bring a
wage of $14.40.
Therefore in the long run equilibrium employment of north region is 612,000, of south region is 408,000, and
the wage rate in both the regions would be $14.40.
26. Suppose high-wage workers are more likely than low-wage workers to move to a new state for a better
job.
a) Explain how this migration pattern can be due solely to differences in the distribution of wages.
b) Explain how this migration pattern can take place even if the cost to move is greater for high-wage
workers.
c) Describe how the immigrant flow is chosen from the population of the country of origin. Why are
some immigrant flows positively selected and other immigrant flows negatively selected?
Answer
If high-wage workers are more likely to move to a new state for a better job, then the following points hold true:
a)
The migration of high-wage workers is solely due to wages. In other words, the new state provides better
wages to skilled laborers than the origin state. The movement of skilled labor would be towards a high-paying
job. High-wage workers earn significantly more than low-wage workers in their current location, making
them more motivated to seek better job opportunities elsewhere. This wage differential serves as the primary
incentive for migration. Even when the cost of moving is greater for high-wage workers, the potential for
substantially higher earnings and other benefits, combined with their financial resources and networks, can
drive them to pursue better job opportunities in states with more favorable wage distributions. The economic
incentives and potential for improved living standards often outweigh the challenges and costs associated
with relocation.
b) The migration of a worker from one place to another depends on three factors: (i) Net present value of
continuing the current job; (ii) Net present value of switching the job and location; (iii) The marginal cost of
migration. Labors evaluate their net present value before deciding to change location for better opportunities.
The laborers will migrate if wages' net present value is greater than the migration cost.
c)
If the reward of skills are higher in foreign than at home, then, then, high-skilled worker will move from
home to foreign. If reward for skills is higher in the source country than in the United States, then workers
16
with low level of skills will get higher payoff in the United States and will therefore move to the United
States. These immigrants are called negatively self-selected. If reward for skills is higher in the United States
than in the source country, then workers with high level of skills will get higher payoff in the United States
and will therefore move to the United States. These immigrants are called positively self-selected.
27. Suppose a worker’s skill is captured by his efficiency units of labor. The distribution of efficiency units
in the population is such that worker 1 has one efficiency unit, worker 2 has two efficiency units, and
so on. There are 100 workers in the population. In deciding whether to migrate to the United States,
these workers compare their weekly earnings at home (w0) with their potential earnings in the United
States (w1). The wage-skills relationship in each of the two countries is given by 𝒘𝟎 = 𝟕𝟎𝟎 + 𝟎. 𝟓𝑺 and
𝒘𝟎 = 𝟕𝟎𝟎 + 𝟎. 𝟓𝑺 where s is the number of efficiency units the worker possesses.
a) Assume there are no migration costs. What is the average number of efficiency units among
immigrants? Is the immigrant flow positively or negatively selected?
b) Suppose it costs $10 to migrate to the United States. What is the average number of efficiency units
among immigrants? Is the immigrant flow positively or negatively selected?
Answer
a) Number of migrants to U.S. can be calculated as follows:
𝑤𝑎𝑔𝑒 𝑖𝑛 𝑑𝑜𝑚𝑒𝑠𝑡𝑖𝑐 𝑐𝑜𝑢𝑛𝑡𝑟𝑦 = 𝑤𝑎𝑔𝑒 𝑖𝑛 𝑈. 𝑆. ⇒ 700 + 05. 𝑆 = 670 + 𝑆 ⇒ 𝑆 = 60
People whose efficiency is greater than 60 will migrate to U.S. Thus, number of people to migrate U.S. is 40.
Average number of efficiency (AEF): The 60th person is indifferent in the migration process. Average number
of efficiency can be calculated as follows:
𝐴𝐸𝐹 =
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦61 + 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦62 + ⋯ + 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦100 61 + 62 + ⋯ + 100
=
⇒ 𝐴𝐸𝐹 = 80.5
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑖𝑔𝑟𝑎𝑛𝑡𝑠
40
Thus, average number of efficiency for migrants excluding the 60 th person is 80.5. Thus, there is a positive
migration to U.S. if the 60th person would migrate then the average number of efficiency is 80 (
3,220+60
40+1
).
b) Number of person migrant to U.S. with migration cost.
Number of migrants to U.S. can be calculated as follows:
𝑤𝑎𝑔𝑒 𝑖𝑛 𝑑𝑜𝑚𝑒𝑠𝑡𝑖𝑐 𝑐𝑜𝑢𝑛𝑡𝑟𝑦 = 𝑤𝑎𝑔𝑒 𝑖𝑛 𝑈. 𝑆. −𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 ⇒ 700 + 05. 𝑆 = 670 + 𝑆 − 10 ⇒ 𝑆 = 80
People whose efficiency is greater than 80 will migrate to U.S. Thus, number of people to migrate U.S. is 20.
Average number of efficiency (AEF): The 20th person is indifferent in the migration process. Average number
of efficiency can be calculated as follows:
𝐴𝐸𝐹 =
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦81 + 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦82 + ⋯ + 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦100 81 + 82 + ⋯ + 100
=
⇒ 𝐴𝐸𝐹 = 90.5
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑖𝑔𝑟𝑎𝑛𝑡𝑠
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Thus, average number of efficiency for migrants is 90.5. Thus, there is a positive migration to U.S.
28. Suppose black and white workers are complements in that the marginal product of whites increases
when more blacks are hired. Suppose also that white workers do not like working alongside black
workers.
a) Will discrimination by white employees lead to the firm choosing to completely segregate its
workplace?
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b) Does it create a wage differential between black and white workers?
Answer
a) If black and white workers are complements, then the employers have an incentive to employ both of these
workers together in the firm. Given that when more blacks are hired, the marginal product of whites is
increased. Hence the employers are better-off in mingling them. The additional wage paid to the newly hired
white worker is more than compensated by hiring a black worker.
b) Since whites work more diligently when they work with blacks, their wages are increased. Hence there
generates a wage differential. This wage differential between the two different groups is essential for whites
to perform better. Such discrimination does not lead to a segregated work force since white workers realize
that they are paid heftily alongside the black workers.
29. Suppose a restaurant hires only women to wait on tables, and only men to cook the food and clean the
dishes.
a) Is this most likely to be indicative of employer, employee, consumer, or statistical discrimination?
b) The dropout rate of minority and international students at U.S. colleges and universities is higher
than it is for white American students. Suppose you strongly believe this is due to discrimination.
Is the empirical pattern most likely indicative of employer (college administrations), employee
(college faculty and staff), consumer (students), or statistical discrimination?
Answer
Employer discrimination occurs when recruiter segregates labor based on race, gender, age, and nationality. The
wage differs due to employer discrimination. Employee discrimination occurs when an employee segregates firms
based on prejudice. It does not create a difference in wages. Consumer discrimination occurs when an employer
segregates labor based on the taste and preference of consumers. Statistical discrimination occurs when an
employer segregates labor based on the characteristics of the group they belong to.
a)
A restaurant hires both women and men. Hence, there is no discrimination from the employer’s side. Men
work in the kitchen, cook food and clean the dishes. Women serve the food and take the order. Even though
they do their work separately, the very nature of serving the food makes their interaction inevitable. Hence
there is no discrimination on employees’ part as well.
b) The kind of discrimination here is most likely the type of consumer discrimination. It is unlikely that there is
statistical discrimination simply because the employer can analyze the abilities of women being the chefs and
men being the servers and waiters by switching their roles.
30. Suppose the firm’s production function is given by
𝒒 = 𝟏𝟎√𝑬𝒘 + 𝑬𝒃
where 𝑬𝒘 and 𝑬𝒃 are the number of whites and blacks employed by the firm respectively. It can be shown
that the marginal product of labor is then
𝑴𝑷𝑬 =
𝟓
√𝑬𝒘 + 𝑬𝒃
Suppose the market wage for black workers is $10, the market wage for whites is $20, and the price of each
unit of output is $100.
a) How many workers would a firm hire if it does not discriminate? How much profi does this
nondiscriminatory firm earn if there are no other costs?
b) Consider a firm that discriminates against blacks with a discrimination coefficient of 0.25. How many
workers does this firm hire? How much profit does it earn?
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c)
Finally, consider a firm that has a discrimination coefficient equal to 1.25. How many workers does
this firm hire? How much profit does it earn?
Answer
a) The wage in North and South would be:
There are no complementarities between the types of labor as the quantity of labor enters the production
function as a sum, 𝐸𝑤 + 𝐸𝑏 . Further, the market-determined wage of black labor is less than the market
determined wage of white labor. Thus, a profit-maximizing firm will not hire any white workers and will hire
black workers up to the point where the black wage equals the value of their marginal product:
𝑤𝑏 = 𝑃 × 𝑀𝑃𝐸 ⇒ 10 =
100 ∙ 5
√𝐸𝑏
⇒ 𝐸𝑏 = 2,500
The 2,500 black workers produce
𝜋 = 𝑝𝑞 − 𝑤𝑏 𝐸𝑏 ⇒ 𝜋 = 100 × 500 − 10 × 2,500 = $25,000
b) The firm acts as if the black wage is 𝑤𝑏 (1 + 𝑏), where d is the discrimination coefficient. The employer’s
hiring decision, therefore, is based on a comparison of ww and 𝑤𝑏 (1 + 𝑏). The employer will then hire
whichever input has a lower utility-adjusted price. As d = 0.25, the employer is comparing a white wage of
$20 to a black (adjusted) wage of $12.50. As $12.50 < $20, the firm will hire only blacks.
As before, the firm hires black workers up to the point where the utility-adjusted price of a black worker
equals the value of marginal product, or
12.50 =
100 ∙ 5
⇒ 𝐸𝑏 = 1,600
√𝐸𝑏
so that 𝐸𝑏 = 1,600 workers. The 1,600 workers produces 400 units of output, and profits are
c)
𝜋 = 𝑝𝑞 − 𝑤𝑏 𝐸𝑏 ⇒ 𝜋 = 100 × 400 − 10 × 1,600 = $24,000
As d = 1.25, the employer compares a white wage of $20 against a black wage of $22.50. Thus, the firm
hires only whites. The firm hires white workers up to the point where the price of a white worker equals
the value of marginal product:
20 =
100 ∙ 5
√𝐸𝑏
⇒ 𝐸𝑏 = 625
so the firm hires 625 whites, produces 250 units of output, and earns profits of
𝜋 = 𝑝𝑞 − 𝑤𝑏 𝐸𝑏 ⇒ 𝜋 = 100 × 250 − 20 × 625 = $12,500
31. Suppose 100 men and 100 women graduate from high school. After high school, each can work in a
low-skill job and earn $200,000 over his or her lifetime, or each can pay $50,000 and go to college.
College graduates are given a test. If someone passes the test, he or she is hired for a high-skill job
paying lifetime earnings of $300,000. Any college graduate who fails the test, however, is relegated to a
low skill job. Academic performance in high school gives each person some idea of how he or she will
do on the test if he or she goes to college. In particular, each person’s GPA, call it x, is an “ability score”
ranging from 0.01 to 1.00. With probability x, the person will pass the test if he or she attends college.
Upon graduating high school, there is one man with x 5 0.01, one with x 5 0.02, and so on up to x 5 1.00.
Likewise, there is one woman with x 5 0.01, one with x 5 0.02, and so on up to x 5 1.00.
a) Persons attend college only if the expected lifetime payoff from attending college is higher than that
of not attending college. Which men and which women will attend college? What is the expected pass
rate of men who take the test? What is the expected pass rate of women who take the test?
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b) Suppose policymakers feel not enough women are attending college, so they take actions that reduce
the cost of college for women to $10,000. Which women will now attend college? What is the expected
pass rate of women who take the test?
Answer
a) Both groups are identical, so the answers are identical. The expected value requirement for attending
college is:
$300,000𝑥 + $200,000(1 − 𝑥) − $50000 > 200,000 ⇒ 𝑥 > 0.5
Thus, the 50 men and 50 women with x = .51 to x = 1.00 all go to college and take the test. The number of test
takers expected to pass is then the sum of expected pass rates: .51 + .52 + … + 1.00 = 37.75. Thus, 75.5 percent
(37.75 of the 50) of men and 75.5 percent of the women who take the test are expected to pass the test.
b) The expected value requirement for attending college for women has changed to:
$300,000𝑥 + $200,000(1 − 𝑥) − $10000 > 200,000 ⇒ 𝑥 > 0.10
Thus, the 90 women with x = .11 to x = 1.00 attend college and take the test. The number of female test takers
expected to pass is the sum of expected pass rates: .11 + .12 + … + 1.00 = 49.95. Thus, 55.5 percent (49.95 of the
90) of the women who take the test are expected to pass the test.
32. Compare two unemployed workers: one is 25 years old while the other is 55 years old. Both workers
have similar skills and face the same wage offer distribution. Suppose that both workers also incur
similar search costs. Which worker will have a higher asking wage? Why? Can search theory explain
why young workers' unemployment rate differs from older workers?
Answer
The 25-year-old worker is likely to have a higher asking wage (or reservation wage) compared to the 55-year-old
worker, despite having similar skills, search costs, and facing the same wage offer distribution. The marginal
revenue of search depends on the length of the payoff period. The 25-year-old worker will likely have a higher
asking wage due to a longer career horizon, greater risk tolerance, and a focus on optimizing lifetime earnings.
Search theory explains why young workers face higher unemployment rates: they tend to have higher reservation
wages, spend more time exploring the labor market, and encounter more mismatches during the early stages of
their careers. These factors collectively lead to longer unemployment spells for younger workers compared to
their older counterparts.
33. Consider three firms identical in all aspects except their monitoring efficiency, which cannot be
changed. Even though the cost of monitoring is the same across the three firms, shirkers at Firm A are
identified almost for certain; shirkers at Firm B have a slightly greater chance of not being found out;
and shirkers at Firm C have the greatest chance of not being identified as a shirker. If all three firms
pay efficiency wages to keep their workers from shirking, which firm will pay the greatest efficiency
wage? Which firm will pay the smallest efficiency wage?
Answer
There is no connection between the cost of monitoring and the efficiency of monitoring, as it is assumed that
monitoring efficiency cannot be changed. Moreover, the value of unemployment is the same for workers
regardless of their employer. Focusing just on the probability of being caught shirking, workers in Firm A have
the least incentive to shirk (as they are most likely to get caught) while workers in Firm C have the greatest
incentive to shirk (as they are least likely to get caught). The idea of efficiency wages is to use wages to buy-off
the incentive to shirk. Therefore, Firm A will pay the lowest efficiency wage, while Firm C will pay the greatest
efficiency wage.
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