Economics
0401
Homework
Problems #1: Answers
NOTE: * Indicates
that a graph is required.
1. Using
the material from the chapter on Supply and Demand, analyze the following:
*a. Assume
there are two markets for labor - a military market and a civilian market - and
there is a wage differential between these two markets. Show and explain the
difference between a volunteer army and a conscript army.
The
basic principle here involves the opportunity cost of labor in its civilian
capacity. Assuming that a term of service in the military involves some
hardships or other undesirable features, the military will have to pay more to
recruits than they receive in civilian employment if it wishes to attract
enough recruits. That is, the wage differential compensates recruits for the
undesirable features of military life. Notice here that the cost of a volunteer
army is borne by all the taxpayers.
What
would happen to this differential if a shooting war required the army to
increase its troop strength? What would happen if everyone saw military life as
more desirable than civilian life?
L1 - L3
= L0 - L2
The
military recruiters ignore the opportunity cost of labor by conscripting
workers (anyone between the ages of 18 and 21). This occurs because Congress
does not want to pay recruits very much, so at the wage mandated by Congress
there is an excess demand. The military must then make up this difference
between supply and demand by conscription. Conscription will then increase the
military supply curve and decrease the civilian supply curve.
Note
that (1) civilian wages will be higher in this example than in the volunteer
example, (2) a welfare loss from the forcible conscription of teenagers occurs
(can you explain why?), and (3) there is an implicit tax burden on recruits who
are conscripted as well as those who volunteer. There is one other cost to
using the method of conscription: conscripted soldiers are not very productive
soldiers (unit cohesion suffers, many more men are needed to do a given number
of tasks, etc.), and the military uses labor intensive solutions to problems
that might otherwise be mechanized (because labor is artificially cheap). Such
conditions would probably make our soldiers less effective in combat (compare
Vietnam War to the Gulf War).
NOTE:
In the Military Market (1) Conscript Gains from Trade taxed away, (2) Part of
the Conscript Supply Price taxed away, and (3) Volunteer Gains from Trade taxed
away.
*b. How
would a decrease in the unemployment rate affect the supply of military
recruits? The military wage?
The
explanation here involves the idea of opportunity cost once again. Presumably
when the unemployment rate is high (especially for teenagers), the possibility
of earning a given wage in the volunteer army looks very attractive (relative
to the alternative of being unemployed or employed part-time--thus the
opportunity cost of taking a job in the military would appear to be lower in
times of high unemployment). Thus high unemployment would cause the supply of
recruits in the military market to increase. Reversing this reasoning would
lead to the implication that a falling unemployment rate would shift the supply
curve of recruits to the left and increase the wage because the opportunity
cost of foregoing civilian employment has risen. Note that these supply shifts
would be much smaller for the conscription case. Can you explain why?
*c. Graph
and explain what might happen when the government puts a ceiling on CEO pay for
public corporations which reduces CEO pay below its current level. Assume that
there are two labor markets, one for public corporate CEOs and one for private
corporate CEOs and that the initial wage differential between the two markets
is zero. Explain how a welfare loss and a misallocation of labor resources
occurs because of this policy.
When
a ceiling on CEO pay is imposed on public corporations this reduces the
quantity supplied of CEOs while increasing the quantity demanded thereby
creating a shortage of CEOs in the public corporation labor market. CEOs whose
supply price (wage) was above the ceiling but below the old equilibrium wage will move to the private corporation CEO labor
market and increase the supply there until the equilibrium wage differential
between the two labor markets is again zero. A misallocation of labor occurs
because these CEOs could have generated higher value (and therefore receive
higher wages) in the public corporation labor market before the ceiling was
imposed but must move to the private corporation labor market where they
generate lower value as reflected by the lower wage that they receive. What
would you expect to happen to the quality of CEOs hired by public Corporations?
d. EXTRA
CREDIT: Show and explain what happens to the wage differential between ice road
truckers in Alaska and truckers in the lower 48 states when oil production is
expanded in Prudhoe Bay and more truckers are needed in Alaska. Assume the two
markets are initially in equilibrium.
2. Using
the material from the chapter 3, do the following:
*a. In
a recent survey of health economists, 90% of them agreed with the statement
“Workers pay for employer-sponsored health insurance in the form of lower wages
or reduced benefits.” If President Obama’s compulsory health plan (mandated
universal health insurance) passes Congress it will also have a provision for
penalizing employers who do not comply with the law (do not offer health
insurance). The CBO has warned that these fines will also be passed on to
workers in the form of lower wages. Show and explain how labor markets for
primary and secondary workers will be affected by this and explain why such a
program would produce welfare losses. (Hint: Be sure to explain what a welfare
loss is.) NOTE: President Obama claims this is not a tax. Is he correct?
Explain.
Primary
workers have very inelastic supplies and when the health mandate (tax) is
imposed on employers most of the tax burden will be passed along to primary
workers in the form of much lower wages. Primary workers who are employed in
firms which don’t/can’t comply with the mandate face even steeper declines in
their wages as employers pass along most of the fines they incur to these
workers. Employment losses will be minor as will welfare losses (because with
relatively few workers being displaced by the tax and moving to lower valued
uses the welfare losses or misallocations of labor will be small).
Secondary
workers have much more elastic supplies and will simply drop out of the labor
force rather than take a wage cut. This implies a relatively small drop in the
wage (with employers thereby bearing most of the burden of the tax) but a very
large drop in employment (implying very large welfare losses as a very large
number of workers are displaced and move to a lower valued use). Employers may
seek to screen out any future employees who don’t seem to have a strong
attachment to the labor force so that they don’t have to bear such a large
burden of the tax.
Any
government policy that lowers wages for workers (such as an employer mandate to
provide health insurance for all workers) must be considered a tax. Maybe President
Obama does not understand that a mandate
is a tax (although this tax is not collected by the government). Or he is confusing
the legal burden of the tax with the economic burden of the tax. Legally, this is a tax on employers but tax
burdens can and will be shifted by employers onto workers.
Question:
What happens to the workers who are displaced by the health mandate?
*b. Assuming unskilled labor and capital are gross
substitutes and skilled labor and capital are gross complements, show and
explain how an investment tax credit will affect these two labor markets.
Explain how the skill composition of employment changes.
An
investment tax credit of 10% means that an employer making a $1m investment
today will be able to reduce his tax payments to the government by $100,000. In
effect, a $1m piece of capital equipment only costs $900,000 which is a fall in
the price of capital. This change in the price of capital will affect both the
skilled and the unskilled labor markets.
In
the skilled labor market, a reduction in the price of capital will cause the
demand for skilled labor to increase when skilled labor and capital are gross
complements-the scale effect dominates the substitution effect. More
precisely, a fall in the price of capital will decrease the cost of production
and hence increase output (the supply of output increases) which causes the
demand for skilled labor to increase. When the relative price of capital falls,
more capital is gradually substituted for skilled labor causing the demand for
skilled labor to decrease. Since the scale effect dominates the substitution
effect demand for skilled labor ultimately increases.
In
the unskilled labor market, a reduction in the price of capital will cause the
demand for unskilled labor to decrease because unskilled labor and capital are gross
substitutes. More precisely, a fall in the price of capital will decrease
the cost of production and hence increase output (the supply of output
increases) which causes the demand for unskilled labor to increase. When the relative
price of capital falls, more capital is gradually substituted for unskilled
labor causing the demand for unskilled labor to decrease. Since the substitution
effect dominates the scale effect demand for unskilled labor ultimately decreases.
As
a result of the increase in demand for skilled labor and decrease in demand for
unskilled labor, the wage differential between the two types of labor widens.
Since this larger differential is larger than the equilibrium differential, it
should induce some unskilled labor to obtain training which raises their skill
level (and allows them to work in the skilled labor market). That is, the
supply of unskilled labor should gradually decrease and the supply of skilled
labor should gradually increase in the long-run until the equilibrium wage
differential is reestablished.
In
summary, the investment tax credit increases the skill composition of the labor
force (supposing that skilled and unskilled labor conform to the assumptions
made above).
*c. Assume
the minimum wage is imposed on the seamless hosiery workers labor market in the
South in 1938 (see Example 4.2 on page 113 in the text). Show and explain how
this affected the introduction of certain machinery into the seamless hosiery
industry and explain whether workers and machines were gross substitutes or
gross complements.
According
to the text, the passage of the Minimum Wage Law speeded up the introduction of converted
transfer knitting machines—in the first 2 years, there was a 69% increase in
converted transfer machines and a 10% increase in fully automated machines.
Moreover, machines were used more intensively. Meanwhile, total employment decreased
by an average of 5.5% in southern mills but fell by 17% in those mills that had
previously paid less than the minimum wage. Apparently, the increase in wages
for southern mill workers resulted in an overall increased demand for capital
(knitting machines). This means that mill workers and knitting machines were gross
substitutes. In particular, the increased wages resulted in an increase in
production costs which, in turn, caused output to fall when the supply of
output decreased. The scale effect decreased the demand for knitting machines.
By contrast, the increased wage reduced the quantity demanded of labor,
increased the relative wage of labor (relative to machines) and therefore increased
the demand for the relatively cheaper substitute-- knitting machines. In this
case, the overall demand for knitting machines increased as the above data
show.
*d. EXTRA
CREDIT: Show and explain what happens when the corporate income tax is
abolished. (Hint: Start with a tax in place in the capital market and show what
happens in both labor and capital markets when the tax is abolished.) Are
capital and labor gross substitutes or gross complements? Explain.
e. EXTRA
CREDIT: Is technological change a threat to unskilled workers in particular and
total employment in general? Explain the text’s answer to this question and how
Baird’s article on “Recycling Labor” is an important part of the answer.
3. Using
the material from the chapter 4, do the following:
*a. Assume
two groups of workers A and B where workers in group A are relatively unskilled
16-19 year olds and workers in group B are relatively more skilled 20-24 year
olds with more schooling and experience. Also assume that these two markets
start with an equilibrium wage differential before the minimum wage is imposed.
Then impose the minimum wage in the market for group A (assuming group B’s
wages are above the minimum wage). Show and explain what happens in these two
markets when group A and B are gross substitutes.
In
this case we get a labor-for-labor substitution which partially explains why
imposition of the minimum wage seems to have rather minimal impacts on
employment. Here’s how it works. With the introduction of the minimum wage for
group A, employers of workers in group A will experience increased costs of
production which will cause output to fall (because the supply of output
decreases). The scale effect causes the firm to decrease its demand for all
other inputs including the demand for group B workers. However, the
substitution effect works in the opposite direction: the relative wage of group
A has increased (relative to Group B’s wage) causing employers to increase
their demand for substitutes in group B. With the substitution effect being
greater than the scale effect, the overall demand for labor in group B
increases, meaning groups A and B are gross substitutes.(Note: W1
> Wmin > W0 )
*b. When
the minimum wage law was first introduced in 1938 the seamless hosiery industry
which was one of the largest manufacturing industries in the South was
significantly affected by this law. See Example 4.2 in the text on page 113 for
details. Northern manufacturers who paid their workers higher wages (because
their opportunity costs were higher) strongly supported this law in order to
hamper competition from their lower cost competitors in the South (where wages
were lower). Assume two labor markets for seamless hosiery workers, one in the North
(N) and one in the South (S) before passage of the law with a wage differential
between them. Then impose the minimum wage law which only affected the Southern
labor market. Show and explain what happened to these two markets after the law
was passed using information from Example 4.2. (Hint: What happened to the
output markets in both the North and South?)
Data
from the example indicate that employment in Southern mills fell by 5.5% (employment
fell 17% in mills that paid wages below the minimum) while employment in
Northern mills expanded by 4.9%. The increased cost of production for Southern
mills caused the supply of output to decrease thereby decreasing output and
raising the price of hosiery made in the South. This caused the demand for
Northern hosiery output to expand, causing demand for hosiery workers to expand
as well (remember the demand for labor is a derived demand). This example
suggests that support for the minimum wage can arise from those firms which
want to cripple their lower-cost rivals.
*c. "Each
time the minimum wage has been raised total employment has continued to grow.
Therefore, those who claim that the minimum wage causes job loss are simply not
correct." Graph and analyze this statement. Is it true or false? Why?
This
statement is false. The reason why employment growth occurs arises from
economic growth in the economy. This growth means that ouput demands are
increasing and causing the demand for labor in most markets (including the
covered minimum wage markets) to increase. The job growth occurs because of the
increasing demand for labor, not because the minimum wage has been raised. Note
that job growth in the minimum wage market will only occur if the rate of
growth of demand exceeds the rate of growth in the minimum wage. Why might this
be the case?
*d. Using
some of the Hicks-Marshall laws, explain why unions (1) oppose repealing import
quotas, (2) attempt to organize an entire industry (instead of part of it) and
(3) try to limit the substitution of other inputs.
(1)
Import quotas are an effective way of reducing the number of substitutes for
the union-produced output. This strategy produces a demand curve for
union-produced output which is more inelastic. A more inelastic demand for
output produces a more inelastic demand for union labor, allowing the union to
restrict the number of workers by a relatively small amount while increasing
the wage a significant amount.
(2)
If only a portion of an industry is organized, the remaining unorganized
portion of the industry produces output which is a perfect substitute for the
union produced output. By organizing the entire industry, unions eliminate this
perfect substitute and make the demand for output (and the demand for labor)
somewhat more inelastic.
(3)
If the elasticity of supply of other inputs is decreased by policies which
limit the ability of employers to substitute one input for union labor
(electronic printing presses for union typesetters, union work rules which
prevent carpenters from doing minor electrical work, requirements to keep
firemen on diesel trains, etc.) then the demand curve for union labor will be
more inelastic, allowing the union to raise wages significantly.
4. Using
the material from lecture, do the following:
a. Suppose
a man and a woman are being considered for a position which requires specific
training. The man will work for six
periods after the training period while the woman will work four periods
(assume the woman drops out of the labor force in period 2 and 3 to have
children and raise them). Explain the
conditions under which: (i) the man will be hired; (ii) the woman will be
hired. Assume that MP = $20,000, W =
$15,000 and i = 10% for both people in all time periods. (NOTE: The wage for
the woman in case ii must change.)
(i)
Assume NCm = NCw
MP1 - W1 MP2 - W2 MP3 - W3 MP4 - W4 MP5 - W5
Gm
= ────────
+ ────────
+ ────────
+ ────────
+ ────────
(1 + i) (1 + i)2 (1 + i)3 (1 + i)4 (1 + i)5
MP6 - W6
+
────────
(1 + i)6
1 1
1 1
Gm = (MP - W)(────────
+ ────────
+ ────────
+ ────────
+
(1 + i) (1 + i)2 (1 + i)3 (1 + i)4
1 1
──────── + ────────)
(1 + i)5 (1 + i)6
MP1 - W1 MP4 - W4 MP5 - W5 MP6 - W6
Gw
= ────────
+ ────────
+ ────────
+ ────────
(1 + i) (1 + i)4 (1 + i)5 (1 + i)6
1 1 1 1
Gw = (MP - W)(────────
+ ────────
+ ────────
+ ────────
)
(1 + i) (1 + i)4 (1 + i)5 (1 + i)6
1 1 1 1
Gm = ($5000)(────────
+ ────────
+ ────────
+ ────────
+
(1.1) (1.1)2 (1.1)3 (1.1)4
1 1
──────── + ────────)
(1.1)5 (1.1)6
Gm
= ($5000)(0.909 + 0.826 + 0.751 + 0.683 + 0.621 + 0.564)
= ($5000)(4.354) = $21,770
Gw
= ($5000)(0.909 + 0.683 + 0.621 + 0.564)
= ($5000)(2.777) = $13,885
Conclusion: Even though the man and the
woman are equally productive, the man will be hired in this case because he
generates more surplus for his employer than the woman does. In other words,
the return on the employer's investment in the man is higher because the man
has a longer employment tenure over which the employer can collect a surplus.
(ii)
The only way the woman can compete in this case is to lower her wage so that
the employer can collect more surplus. This can be represented in the following
way:
Gw
= $21,770 = ($20,000 - W)(2.777) = $55,540 - 2.777W
2.777W = $55,540 - $21,770 = $33,770
W = $33,770/2.777 = $12,160.60
Therefore,
any wage less than $12,160.60 (such as $12,100) will generate more surplus for
the employer and guarantee that the woman will be hired. That is, the woman
must drop her wage from $15,000 to $12,100 if she expects to be employed.
*b. Suppose that women as a group decide to
postpone having and raising children until period 3 and 4. Using the assumptions from part a, explain
what difference this makes in the decision to (i) hire the man and (ii) hire
the woman. Graph and explain what effect this will have on the wage
differential between men and women. (HINT: Use two supply and demand graphs:
one for men and one for women.)
(i)
Assume NCm = NCw
Gm
= ($5000)(4.354) = $21,770
Gw
= ($5000)(0.909 + 0.826 + 0.621 + 0.564)
= ($5000)(2.920) = $14,600
