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Gains and Losses from Trade
in the Specific-Factors Model
1. Why is the specific-factors model referred to as a short-run model?
2. Figure 3-7 presents wages in the manufacturing and services sectors for the period
1973 to 2012. Is the difference in wages across sectors consistent with either the
Ricardian model studied in Chapter 2 or the specific-factors model? Explain why or
why not.
3. In the gains from trade diagram in Figure 3-3, suppose that instead of having a rise
in the relative price of manufactures, there is a fall in that relative price.
a. Starting at the no-trade point A in Figure 3-3, show what would happen to
production and consumption.
Answer:
S-19
U2
A
B
C
Output of manufacturing,
Q
M
3
b. Which good is exported and which is imported?
c. Explain why the overall gains from trade are still positive.
4. Starting from equilibrium in the specific-factors model, suppose the price of manu-
factured goods falls so that wages fall from W9 to W in Figure 3-5.
a. Show that the percentage fall in the wage is less than the percentage fall in the
price of manufacturing, so that the real wage of labor in terms of manufactured
goods goes up.
Answer:
S-20 Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model
Wage
W
P
M ·
MPL
M
P
M
·
MPL
M
0
M
L
M
0
A
L
A
LL
b. What happens to the real wage of labor in terms of agriculture?
c. Are workers better off, worse off, or is the outcome ambiguous?
5. Use the following information to answer the questions below:
Manufacturing: Sales revenue 5 PM ? QM 5 150
Payments to labor 5 W ? LM 5 100
Payments to capital 5 RK ? K 5 50
Agriculture: Sales revenue 5 PA ? QA 5 150
Payments to labor 5 W ? LA 5 50
Payments to land 5 RT ? T 5 100
Holding the price of manufacturing constant, suppose the increase in the price of
agriculture is 10% and the increase in the wage is 5%.
a. Determine the impact of the increase in the price of agriculture on the rental on
land and the rental on capital.
Answer: Rental on land can be calculated as follows:
D
R
_
T
R
T
100
Recalling that the price of manufacturing remained constant, we get the rental
on capital as
0 ? QM 2
DW ? LM
R
K
5
0
Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model S-21
b. Explain what has happened to the real rental on land and the real rental on
capital.
6. If, instead of the situation given in Problem 5, the price of manufacturing were to
fall by 10%, would landowners or capital owners be better off? Explain. How would
the decrease in the price of manufacturing affect labor? Explain.
The rental on capital is found by calculating the following:
D
R
K
R
T
1
0
0
Putting it together we get
S-22 Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model
Real rental
on capital falls
Change in the real
wage is ambiguous
Real rental
on land rises
Real rental
on capital falls
Change in the real
wage is ambiguous
Real rental
on land rises
7. Read the article by Lori G. Kletzer and Robert E. Litan, “A Prescription to Re-
lieve Worker Anxiety,” Policy Brief 01-2, (Washington, D.C.: Peterson Institute for
International Economics), available online at http://www.iie.com/publications/pb/
pb.cfm?researchid=70, which refers to the U.S. recession of 2000 and 2001. Then
answer the following:
a. Under the most recent version of Trade Adjustment Assistance (TAA) in the
United States that they refer to, how many extra weeks of unemployment insur-
ance are workers eligible for? What two criteria must workers meet to qualify
for this extra unemployment insurance?
b. Consider the proposal for “wage insurance” that Kletzer and Litan make in their
article. What criteria would workers need to qualify for this insurance? What
amount of extra income would they receive from the insurance?
c. If Kletzer and Litan’s new plan for “wage insurance” had been adopted by the
United States, what would have been the budgetary cost in 1999 when unem-
ployment was 4.2%? How does this compare with the amount that is now spent
on unemployment insurance?
8. In the specific-factors model, assume that the price of agricultural goods de-
creases while the price of manufactured goods is unchanged (DPA/PA , 0 and
DPM/PM 5 0). Arrange the following terms in ascending order:
DRT/RT DRK/RK DPA/PA DPM/PM DW/W
Hint: Try starting with a diagram such as Figure 3-5 but change the price of agricul-
tural goods instead.
Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model S-23
9. Suppose two countries, Canada and Mexico, produce two goods: timber and tele-
visions. Assume that land is specific to timber, capital is specific to televisions, and
labor is free to move between the two industries. When Canada and Mexico engage
in free trade, the relative price of televisions falls in Canada and the relative price of
timber falls in Mexico.
a. In a graph similar to Figure 3-5, show how the wage changes in Canada due to
a fall in the price of televisions, holding constant the price of timber. Can we
predict that change in the real wage?
S-24 Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model
Wage
Labor
B
A
P
TV · (
MPL
TV )
P
TIM ·
MPL
TIM
0
TV
L
TV
0
TIM
L
TIM
LL
L
Vertical distance
b. What is the impact of opening trade on the rentals on capital and land in Can-
ada? Can we predict that change in the real rentals on capital and land?
c. What is the impact of opening trade on the rentals on capital and land in
Mexico? Can we predict that change in the real rentals on capital and land?
d. In each country, has the specific factor in the export industry gained or lost and
10. Home produces two goods, computers and wheat, for which capital is specific to
computers, land is specific to wheat, and labor is mobile between the two industries.
Home has 100 workers and 100 units of capital but only 10 units of land.
a. Draw a graph similar to Figure 3-1 with the output of wheat on the vertical axis
and the labor in wheat on the horizontal axis. What is the relationship between
the output of wheat and the marginal product of labor in the wheat industry as
more labor is used?
Answer: See the following graph.
Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model S-25
Labor in wheat,
L
W
1
MPL
W
Wheat output,
Q
W
b. Draw the production possibilities frontier for Home with wheat on the horizon-
tal axis and computers on the vertical axis.
Answer: See the following graph.
c. Explain how the price of wheat relative to computers is determined in the ab-
sence of trade.
d. Reproduce Figure 3-4 with the amount of labor used in wheat measuring from
left to right along the horizontal axis and the amount of labor used in computers
moving in the reverse direction.
Answer: See graph below.
S-26 Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model
Wheat output,
Q
W
Computer
output,
Q
C
Production possibilities
frontier, PPF
Wage
Computer
labor
Labor
market
equilibrium
Value of
marginal product
of computer
Wheat labor
W
A
P
C ·
MPL
C
0
W
L
W
0
C
L
C
L
L
e. Assume that due to international trade, the price of wheat rises. Analyze the ef-
fect of the increase in the price of wheat on the allocation of labor between the
two sectors.
Answer:
11. Similar to Home in Problem 10, Foreign also produces computers and wheat using
capital, which is specific to computers; land, which is specific to wheat; and labor,
which is mobile between the two sectors. Foreign has 100 workers and 100 units of
land, but only 10 units of capital. It has the same production functions as Home.
a. Will the no-trade relative price of wheat be higher in Home or in Foreign?
Explain why you expect this outcome.
Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model S-27
Wage
Computer
labor
Wheat labor
Vertical
distance
P
W · (
MPL
W
)
0
W
L
W
0
C
L
C
L
L
L
b. When trade is opened, what happens to the relative price of wheat in Foreign
and to the relative price of wheat in Home?
c. Based on your answer to (b), predict the effect of opening trade on the rental
on land in each country, which is specific to wheat. What about the rental on
12. In the text, we learned that workers displaced by import competition are eligible for
compensation through the Trade Adjustment Assistance program. Firms are also eli-
gible for support through Trade Adjustment Assistance for Firms, a federal program
that provides financial assistance to manufacturers affected by import competition.
Go to http://www.taacenters.org to read about this program, and answer the follow-
ing questions:
a. What criteria does a firm have to satisfy to qualify for benefits?
b. What amount of money is provided to firms, and for what purpose?
S-28 Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model
Wheat output,
Q*
W
Computer
output,
Q*
C
c. Provide an argument for and an argument against the continued funding of this
Solutions n Chapter 3 Gains and Losses from Trade in the Specic-Factors Model S-29
Trade adjustment assistance centers’ total expenditures, cooperative agreement years 1995-99
$6,000,000
$5,000,000
Note: Operations and administrative costs include staff time spent assisting
firms with the certification process and preparing adjustment plans,
in addition to the cost of funding day-to-day operations.
Source: GAO derived from TAA Centers’ data.
