Questions for Review
1. The rates of job separation and job finding determine the natural rate of unemploy-
ment. The rate of job separation is the fraction of people who lose their job each month.
2. Frictional unemployment is the unemployment caused by the time it takes to match
workers and jobs. Finding an appropriate job takes time because the flow of informa-
tion about job candidates and job vacancies is not instantaneous. Because different jobs
3. The real wage may remain above the level that equilibrates labor supply and labor
demand because of minimum wage laws, the monopoly power of unions, and efficiency
wages.
Minimum-wage laws cause wage rigidity when they prevent wages from falling to
4. Depending on how one looks at the data, most unemployment can appear to be either
short term or long term. Most spells of unemployment are short; that is, most of those
who became unemployed find jobs quickly. On the other hand, most weeks of unem-
ployment are attributable to the small number of long-term unemployed. By definition,
the long-term unemployed do not find jobs quickly, so they appear on unemployment
rolls for many weeks or months.
5. Economists have proposed at least two major hypotheses to explain the increase in the
natural rate of unemployment in the 1970s and 1980s, and the decrease in the natural
rate in the 1990s and 2000s. The first is the changing demographic composition of the
labor force. Because of the post–World-War-II baby boom, the number of young workers
CHAPTER 6Unemployment
Problems and Applications
1. a. In the example that follows, we assume that during the school year you look for a
part-time job, and that on average it takes 2 weeks to find one. We also assume
that the typical job lasts 1 semester, or 12 weeks.
b. If it takes 2 weeks to find a job, then the rate of job finding in weeks is:
2. To show that the unemployment rate evolves over time to the steady-state rate, let’s
begin by defining how the number of people unemployed changes over time. The change
in the number of unemployed equals the number of people losing jobs (sE) minus the
number finding jobs (fU). In equation form, we can express this as:
Ut + 1 – Ut= ΔUt+ 1= sEt– fUt.
Recall from the text that L= Et+ Ut, or Et= L– Ut, where Lis the total labor force (we
will assume that Lis constant). Substituting for Etin the above equation, we find:
ΔUt + 1 = s(L– Ut) – fUt.
52 Answers to Textbook Questions and Problems
The first point to note about this equation is that in steady state, when the unemploy-
ment rate equals its natural rate, the left-hand side of this expression equals zero. This
tells us that, as we found in the text, the natural rate of unemployment (U/L)nequals
(U/L)n.
3. Call the number of residents of the dorm who are involved I, the number who are unin-
volved U, and the total number of students T = I + U. In steady state the total number
of involved students is constant. For this to happen we need the number of newly unin-
volved students, (0.10)I, to be equal to the number of students who just became
involved, (0.05)U. Following a few substitutions:
(0.05)U= (0.10)I
4. Consider the formula for the natural rate of unemployment,
= .
If the new law lowers the chance of separation s, but has no effect on the rate of job
finding f, then the natural rate of unemployment falls.
5. a. The demand for labor is determined by the amount of labor that a profit-maximiz-
ing firm wants to hire at a given real wage. The profit-maximizing condition is
that the firm hire labor until the marginal product of labor equals the real wage,
MPL =.
Chapter 6 Unemployment 53
U
L
W
P
s
s + f
The marginal product of labor is found by differentiating the production function
with respect to labor (see Chapter 3 for more discussion),
Notice that this expression has the intuitively desirable feature that increases in
the real wage reduce the demand for labor.
b. We asume that the 1,000 units of capital and the 1,000 units of labor are supplied
inelastically (i.e., they will work at any price). In this case we know that all 1,000
units of each will be used in equilibrium, so we can substitute them into the above
labor demand function and solve for .
1,000 = 1,000
( )
–3
Notice that workers get two-thirds of output, which is consistent with what we
know about the Cobb–Douglas production function from Chapter 3.
c. The congressionally mandated wage of 1 unit of output is above the equilibrium
wage of 2/3 units of output.
d. Firms will use their labor demand function to decide how many workers to hire at
the given real wage of 1 and capital stock of 1,000:
54 Answers to Textbook Questions and Problems
8
27
W
P
W
P
6. a. The labor demand curve is given by the marginal product of labor schedule faced
by firms. If a country experiences a reduction in productivity, then the labor
demand curve shifts to the left as in Figure 6–1. If labor becomes less productive,
then at any given real wage, firms demand less labor.
b. If the labor market is always in equilibrium, then, assuming a fixed labor supply,
an adverse productivity shock causes a decrease in the real wage but has no effect
on employment or unemployment, as in Figure 6–2.
Chapter 6 Unemployment 55
w/p
Figure 6–1
w/p
LS
Figure 6–2
c. If unions constrain real wages to remain unaltered, then as illustrated in Figure
6–3, employment falls to L1and unemployment equals L– L1.
This example shows that the effect of a productivity shock on an economy depends
on the role of unions and the response of collective bargaining to such a change.
7. Real wages have risen over time in both the United States and Europe, increasing the
reward for working (the substitution effect) but also making people richer, so they want
to “buy” more leisure (the income effect). If the income effect dominates, then people
8. The vacant office space problem is similar to the unemployment problem; we can apply
the same concepts we used in analyzing unemployed labor to analyze why vacant office
space exists. There is a rate of office separation: firms that occupy offices leave, either
w/p
LS
Figure 6–3
56 Answers to Textbook Questions and Problems