University of California, Berkeley
Department of Economics
Fall 2007
Professor Andrea Weber
Economics 152 – Wage Theory and Policy
Problem set #4 - Solutions
- Updated 11/05/07 1. (a) The 1986 Immigration Reform and Control Act (IRCA) made it illegal for employers in the United
States to knowingly hire illegal aliens. The legislation, however, has not reduced the flow of illegal aliens
into the country. As a result, it has been proposed that the penalties against employers who break the law
be substantially increased. Suppose that illegal aliens, who tend to be less skilled workers, are
complements with native workers. What will happen to the wage of native workers if the penalties for
hiring illegal aliens increase?
(b) In class we discussed an article from The New York Times – “Crackdown upends
Slaughterhouse’s Work Force” NYT October 12, 2007 – which reports how law enforcement
actions against illegal immigrants affected a large firm in North Carolina. Does this article
provide evidence for your predictions from point (a)? What other labor market effects related to
the outflow of immigrant workers are discussed in this article?
(c)What does this article say about a wage compensation for the unpleasant working conditions
in the slaughterhouse.
(a) A substantial increase in the penalties associated with hiring illegal aliens will likely reduce the
number of illegal aliens entering the United States. The effect of this shift in the size of the illegal alien
flow on the marginal product (and hence the demand curve) of native workers hinges on whether illegal
aliens are substitutes or complements with natives. As it is assumed that natives and illegal aliens are
complements, a cut in the number of illegal aliens reduces the value of the marginal product of natives,
shifting down the demand for native labor, and decreasing native wages and employment.
(b) No, the article does not offer evidence in the direction of the prediction in (a). The article describes
the scenario where the immigrants and natives are substitutes. Other problems described in the article
point to an increase in the compensating wage differential, greater provision of job amenities (like
transportation to work), declining union power, a higher turnover of natives, and an increase in the
training costs.
(c) The article describes that the slaughterhouses do pay higher wages for the unpleasant working
conditions. Moreover, the article also says that the wage differential paid to natives is substantially
different from that paid to immigrants, which may be due to the fact that they have different preferences.
2.
Consider the case when the labor market is not perfectly competitive, specifically the case when a
firm can influence wages.
(a) What is a monopsony? What is the difference between a perfectly discriminating monopsonist and a
non-discriminating monopsonist?
(b) Suppose a firm is a perfectly discriminating monopsonist. The government imposes a minimum wage
on this market. What happens to wages and employment?
Econ 152 – Problem set #4 – Solutions
2
(c) 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.
(d) Consider a nondiscriminatory monopsonist firm which faces a perfectly elastic demand for its product
at a price of $4. This firm also faces an upward sloping labor supply curve E = 10w - 50. This implies
that the firm faces a marginal cost of labor curve given by MC = 0.2E + 5. Assume further that each
worker can produce 3 units of output per hour, and that there are no other costs of production. How
many workers will the firm hire per hour to maximize profits? What is the hourly wage? What are the
firm’s hourly profits?
(a) A monopsonistic market is a market where there is only one buyer of labor. A monopsony is a firm
that faces an upward-sloping demand curve, i.e. in contrast to the competitive firm – which can hire as
much labor as it wants at the going price – a monopsonist must pay higher wages in order to attract more
workers. A perfectly discriminating monopsonist can hire different workers at different wages (essentially
corresponding to each workers reservation wage), whereas a non-discriminating monopsonist must pay all
workers the same wage, regardless of the worker's reservation wage.
(b) 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 ES workers will want to find work at the minimum
wage. Thus, the wage increases, but employment falls.
Dollars
S
w MIN
A
w*
VMPE
ED
E*
ES
Employment
(c) 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. (It is interesting to note that the same result comes about if the
payroll tax is placed on workers, so that the labor supply and marginal cost of labor curves shift as
opposed to labor demand.)
(d) Optimal employment under profit maximization is determined by equating marginal cost and the value
of marginal product, which is given by the output produced by the last worker hired times output price:
0.2E + 5 = 3*4. So the firm hires E = 12*5 – 25 = 35 workers. The hourly wage is given by the supply
curve w = 3.5 + 5 = $8.5. The firm’s hourly profit per worker is 3*4 – w = 12 – 8.5 = $3.5. Total profit
per hour is 3.5 * 35 = $122.5.
Econ 152 – Problem set #4 – Solutions
3
Suppose that the market for labor economists is subject to a cobweb adjustment process, because
3.
it takes time to train new labor economists. Specifically, suppose that the supply curve is given by
w = 10 + 5E and the demand curve by w = 50 − 3E .
(a) What is the initial equilibrium wage and employment level?
(b) Now suppose the government urgently needs labor economists to evaluate a new training program.
This sudden demand shock shifts the demand curve up to w = 70 − 3E . Calculate the wage and
employment levels in each "round" of the cobweb game as the wage and employment levels slowly adjust
to the shock [you can stop with the 6th round].
(c) Sketch the adjustment process in a graph.
(d) What is the new equilibrium level of wage and employment?
(a) The initial equilibrium is given by
10 + 5E = 50 − 3E
⇒ w 0 = 35, E 0 = 5
(b) We start at the initial equilibrium given in part (a). As the demand curve shifts up due to the
sudden shock, and short-run supply is perfectly inelastic at the employment level E0 (because it
takes time to produce a new labor economist), in the 1st round we move up to the new demand
curve at the old employment level (point A in the figure in part (c)). In the second round we
move on a horizontal line (to the unchanged supply curve) as now a large number of labor
economist enters the labor market due to the higher wage (point B), and so on, until we slowly
move towards the new equilibrium.
The following table gives the values for wage and employment in each round. As already
outlined in the previous paragraph, the values in the table are calculated by noting that in any
given period the number of labor economists is inelastically supplied, so that the wage is
determined by the demand curve. Given the wage, the number of labor economists available in
the next round is calculated. By the 6th round, the market begins to converge around the new
equilibrium.
Round
1
2
3
4
5
6
7
8
Wage ($)
55.0
55.0
43.0
43.0
50.2
50.2
46.0
46.0
48.4
48.4
46.9
46.9
47.8
47.8
47.2
47.2
Employment
5
9
9
6.6
6.6
8
8
7.2
7.2
7.7
7.7
7.4
7.4
7.6
7.6
7.44
Point
A
B
C
D
E
etc.
Econ 152 – Problem set #4 – Solutions
4
(c)
(d) The new equilibrium wage and employment level will be:
70 − 3E = 10 + 5E
⇒ E1 = 7.5, w 1 = 47.5
4. Consider a competitive economy that has four different jobs that vary by their wage and risk level. The
table below describes each of the four jobs.
Job
A
B
C
D
Risk ( r )
1/5
1/4
1/3
1/2
Wage ( w )
$3
$12
$23
$25
All workers are equally productive, but workers vary in their preferences. Consider two workers X and Y
who value wage and the risk levels according to the following utility functions:
Econ 152 – Problem set #4 – Solutions
u X ( w, r ) = w +
5
1
2
and uY ( w, r ) = 0.5 * w + 2 .
2
r
r
(a)
Where does each worker choose to work? What is the relationship between the observed wage
and risk levels in the economy called?
(b)
Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5
(that is, all jobs become A jobs). What wage would each worker now need to earn in the A job to be
equally happy following the regulation?
(a) Calculate the utility level for each job by using the wage and the risk level:
UX(A) = 28, UX (B) = 28, UX (C) = 32, and UX (D) = 29. Therefore, worker X chooses a type C job and
receives 32 units of happiness.
UY(A) = 51.5, UY (B) = 38, UY (C) = 29.5, and UY (D) = 20.5. Worker Y chooses a type A job and receives
51.5 units of happiness.
The relationship between observed wage and risk bundles is called the Hedonic Wage Function.
(b) If the government regulation is imposed worker X is forced to work a type A job, the worker would
need to receive a wage of $7 in order to maintain her 32 units of happiness as 7 + 25 = 32.
Worker Y is not affected by the regulation.
Suppose a firm must employ 20 workers in order to produce 2000 units of output that the firm has
5.
contracted to supply to the government for $1.4 million. The firm must choose how much to invest in
safety. The firm can choose any level of safety, S, from 0 to 100. The cost of safety is C(S) = 50S2. Given
the firm’s choice of safety, it must pay an annual salary of 60,000 - 300S. Thus, a firm that chooses S =
30 pays $45,000 for this level of safety and pays each worker $51,000. What level of safety will the firm
choose, and how much does this cost? How much will each worker earn? How much profit will the firm
earn?
Econ 152 – Problem set #4 – Solutions
6
The calculus solution:
Profit = $1.4 million – 50S2 – 20(60,000 – 300S) = 200,000 + 6,000S – 50S2.
The first order condition is: 6,000 = 100S. Thus, S* = 60.
In summary, the firm installs a safety level of 60 at a cost of $180,000 and pays each of its 20
workers an annual salary of 60,000 – 300(60) = $42,000. Doing so, yields a profit of 1,400,000 –
180,000 – 20(42,000) = $380,000.
The Excel solution:
S
0
1
2
C(S)
$0
$50
$200
W(S)
$60,000
$59,700
$59,400
Profit
$200,000
$205,950
$211,800
55
56
57
58
59
60
61
62
63
64
65
$151,250
$156,800
$162,450
$168,200
$174,050
$180,000
$186,050
$192,200
$198,450
$204,800
$211,250
$43,500
$43,200
$42,900
$42,600
$42,300
$42,000
$41,700
$41,400
$41,100
$40,800
$40,500
$378,750
$379,200
$379,550
$379,800
$379,950
$380,000
$379,950
$379,800
$379,550
$379,200
$378,750
98
99
100
$480,200
$490,050
$500,000
$30,600
$30,300
$30,000
$307,800
$303,950
$300,000
S=A102
=50*A102^2
=60000-300*A102
=1400000-B102-20*C102