Man
503 Homework
VII Fall
2009
1. In 1996, the
a.
What will the free
market wage rate and employment level be?
Suppose the government sets a minimum wage of $5 per hour. How many people would then be employed?
In
a free-market equilibrium, LS = LD. Solving yields w = $4 and LS = LD
= 40. If the minimum wage is $5,
then LS = 50 and LD = 30.
The number of people employed will be given by the labor demand, so
employers will hire 30 million workers.
Figure 9.1.a
b.
Suppose that instead of a minimum wage, the
government pays a subsidy of $1 per hour for each employee. What will the total level of employment be
now? What will the equilibrium wage rate
be?
Let w denote the wage received by the employee. Then the employer receiving the $1 subsidy per worker hour only pays w-1 for each worker hour. As shown in Figure 9.1.b, the labor demand curve shifts to:
LD = 80 - 10 (w-1) = 90 -
10w,
where w represents the wage received by the
employee.
The new equilibrium will be given by the intersection of
the old supply curve with the new demand curve, and therefore, 90-10W**
= 10W**, or w** = $4.5 per hour and L** = 10(4.5) = 45 million persons
employed. The real cost to the employer
is $3.5 per hour.
2. About 100 million pounds of jelly beans
are consumed in the United States each year, and the price has been about 50
cents per pound. However, jelly bean
producers feel that their incomes are too low, and they have convinced the
government that price supports are in order.
The government will therefore buy up as many jelly beans as necessary to
keep the price at $1 per pound. However,
government economists are worried about the impact of this program, because
they have no estimates of the elasticities of jelly
bean demand or supply.
a. Could this program cost the government more than $50 million per year? Under what conditions? Could it cost less than $50 million per year?
Under what conditions? Illustrate with a diagram.
If
the quantities demanded and supplied are very responsive to price changes, then
a government program that doubles the price of jelly beans could easily cost
more than $50 million. In this case, the
change in price will cause a large change in quantity supplied, and a large
change in quantity demanded. In Figure
9.5.a.i, the cost of the program is (QS-QD)*$1. Given QS-QD is larger
than 50 million, then the government will pay more than 50 million
dollars. If instead supply and demand
were relatively price inelastic, then the change in price would result in very small changes in
quantity supplied and quantity demanded and (QS-QD) would
be less than $50 million, as illustrated in figure 9.5.a.ii.
b. Could this program cost consumers (in
terms of lost consumer surplus) more
than $50 million per year? Under what conditions?
Could it cost consumers less
than $50 million per year? Under what conditions?
Again, use a diagram to illustrate.
When
the demand curve is perfectly inelastic, the loss in consumer surplus is $50
million, equal to ($0.5)(100 million pounds). This represents the highest possible loss in
consumer surplus. If the demand curve
has any elasticity at all, the loss in consumer surplus would be less then $50
million. In Figure 9.5.b, the loss in
consumer surplus is area A plus area B if the demand curve is D and only area A
if the demand curve is D’.
Figure 9.5.a.i
Figure
9.5.a.ii
Figure 9.5.b
3. In Exercise 4 of Chapter 2, we examined a vegetable fiber
traded in a competitive world market and imported into the
Price |
(million
pounds) |
(million
pounds) |
3 |
2 |
34 |
6 |
4 |
28 |
9 |
6 |
22 |
12 |
8 |
16 |
15 |
10 |
10 |
18 |
12 |
4 |
Answer the following about the
a. Confirm that the demand curve is given by , and that the supply curve is given by .
To
find the equation for demand, we need to find a linear function QD= a + bP
such that the line it represents passes through two of the points in the table
such as (15,10) and (12,16). First, the slope, b, is equal to the “rise” divided by the “run,”
Second, we substitute for b and one point, e.g., (15, 10), into our linear function to solve
for the constant, a:
, or a = 40.
Therefore,
Similarly, we may solve for the supply equation QS= c + dP
passing through two points such as (6,4) and
(3,2). The slope, d, is
.
Solving for c:
or
c = 0.
Therefore,
b. Confirm that if there were no
restrictions on trade, the
If
there are no trade restrictions, the world price of $9.00 will prevail in the
c. If the
With
a $3.00 tariff, the
0.5(12-9)(8-6)+0.5(12-9)(22-16)=$12
million.
d. If the
With
an import quota of 8 million pounds, the domestic price will be $12. At $12,
the difference between domestic demand and domestic supply is 8 million pounds,
i.e., 16 million pounds minus 8 million pounds.
Note you can also find the equilibrium price by setting demand equal to
supply plus the quota so that
The
cost of the quota to consumers is equal to area A+B+C+D in Figure 9.6.d, which
is
(12 - 9)(16) + (0.5)(12 - 9)(22 - 16) = $57 million.
The
gain to domestic producers is equal to area A in
Figure 9.6.d, which is
(12 - 9)(6) + (0.5)(8 - 6)(12 - 9) = $21 million.
Figure 9.6.d