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Sample
Test
Gains and Losses from Trade
in the Specific-Factors Model
Notes to Instructor
Chapter Summary
Chapter 3 examines the gains and losses from trade for labor, capital, and
landowners. We no longer assume that labor is the only factor production.
The model presented is the specific-factors model, in which labor and land
are used in agriculture whereas labor and capital are used in manufacturing.
Comments
The video Is Wal-Mart Good for America?, available through PBS. org, provides
an excellent example of winners and losers of trade. It begins with an annual
shareholders meeting where everyone in attendance is excited about Wal-
Mart. Then it takes a look at the impact on American suppliers and workers
when Wal-Mart switches to Chinese suppliers in efforts to lower cost.
Discussions
after the video could be stimulated by asking questions such as
whether Wal-Mart and other American businesses should be restricted from
purchasing from foreign suppliers. Although some students may comment
that most consumers at Wal-Mart are from lower-income households, it may
be useful to remind them that the video also mentions that Chinese-made
televisions are also sold in retail stores such as Best Buy and Circuit City.
33
3
of production.
Lecture Notes
Introduction
The chapter begins with an example of violent protests against Bolivia’s export
of natural gas by its indigenous Indians. The protests led to the replacement
of the president and a referendum ensuring more benefits to Bolivia’s
people at the expense of foreign companies. The example brings up the issue
that in the real world there are both winners and losers when a country engages
in trade even though the overall gains from those who benefit from
trade generally exceed the losses of those who are harmed.
1 Specific-Factors Model
The Home Country
The specific-factors model consists of two industries, agriculture and
manufacturing.
Agriculture uses labor and land whereas manufacturing uses labor
and capital. In the short run, land is specific to the agriculture sector,
whereas
capital is specific to the manufacturing sector. Unlike land and capital, labor
is
used in both sectors, meaning that it is not specific to either one. With
diminishing
returns, an increase in the amount of labor used in either sector results
in the decline of the marginal product of labor as depicted in Figure
3-1. Because of the diminishing returns to labor in agriculture and
manufacturing,
the economy’s production possibilities frontier (PPF) is bowed-out, or
concave, as shown in Figure 3-2.
Production Possibilities Frontier The slope of the PPF gives the opportunity
cost of manufacturing in terms of the amount of food the economy has
to give up to produce an additional unit of the manufacturing good. The
slope between any two points on the PPF is given by the ratio MPLA / MPLM,
where MPLA is the marginal product of labor in agriculture and MPLM is the
marginal product of labor in manufacturing.
Opportunity Cost and Prices In addition, the slope of the PPF equals the
price of manufacturing relative to the price of agriculture or the relative
price
of manufacturing, PM / PA. To see this, recall that wage W in a competitive
market is equal to the price of the good times the marginal product of labor
in the producing the good or the value of the marginal product. Because labor
is mobile between the two sectors, the wage in agriculture, W PA
MPLA, must equal to the wage in manufacturing, W PM
MPLM. If this is
not the case, labor will continue to flow to the high-wage sector until the
wages are equalized across the industries.
The Foreign Country
We will forego a discussion on Foreign in this chapter and assume that the notrade
relative price of manufacturing at Home is lower than the Foreign relative
price, (PM / PA)
(P*M / P*A). In other words, Home has a comparative
advantage in producing manufactured goods relative to the foreign country.
34 Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model
Overall Gains from Trade
In the absence of international trade, the economy produces and consumes at
the point on the PPF where the relative price of manufacturing is equal to
the slope of the PPF and the slope of the indifference curve for a representative
consumer as shown in Figure 3-3. Suppose the country engages in trade
that leads to an increase in the relative price of the manufacturing good. The
higher relative price of manufacturing, given by the steeper international
price, line BC in Figure 3-3, attracts workers to the manufacturing sector and
an increase in the production of manufactures from point A to point B. With
the higher relative price of manufacturing, the country exports manufactures
in exchange for agricultural products and consumes at a higher indifference
curve given by U2 at point C.
APPLICATION
How Large Are the Gains from Trade?
The United States experienced the reversal of gains from trade when the
U. S. Congress imposed an embargo on trade with Britain between December,
1807, and March, 1809. The gains from trade for the United States would
have been at least 5% of GDP without the embargo. Put another way, the embargo
cost the United States more than one third of the value of exports.
In another example, Japan experienced gains from trade when it engaged
in international trade in 1859 after 200 years of self-imposed autarky. Japan’s
gains from trade are estimated to be about 4% to 5% of GDP. ■
2 Earnings of Labor
Determination of Wages
To determine the impact of international trade on wages in the two sectors,
we put the marginal product of labor for agriculture and manufacturing on
the same graph, as shown in Figure 3-4. The horizontal axis denotes the total
amount of labor, L, with the amount of labor used in manufacturing, LM,
measured from left (0M) to right, and the amount of labor used in agriculture,
LA, measured from right (0A) to left.
Equilibrium Wage The equilibrium wage is given by the intersection of the
marginal product of labor in each sector multiplied by its respective price.
With the equilibrium wage at point A, the economy uses 0ML units of labor
in manufacturing and 0AL units of labor in agriculture.
Change in Relative Price of Manufactures
We next examine how the higher relative price of manufactures resulting
from trade affects the wage and earnings of capital owners in manufacturing
and landowners in agriculture.
Effect on the Wage Suppose the higher relative price of manufactures is due
to an increase in the price of manufacturing, PM. This shifts PM
MPLM up to
PM
MPLM, where the vertical rise is PM
MPLM, as shown in Figure 3-6.
The intersection of PM
MPLM and PA
MPLA gives the new equilibrium
Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model 35
wage, W, at point B.With the new equilibrium wage, the amount of labor
used in manufacturing increases from 0ML to 0MLand the amount of labor
used in agriculture falls from 0AL to 0AL.
Effect on Real Wages To understand the impact of the new equilibrium
wage on the labor, we note that workers can afford to buy more food because
its price has not changed although wage has increased. Namely, the real wage
has increased for labor in terms of food, W / PA W / PA.
To see whether labor gains or loses in terms of manufactures, we need
to compare the increase in wage relative to the increase in the price
of manufacture, PM. From Figure 3-5 we see that the increase in wage
from W to Wis less than the vertical increase of PA
MPLA given by
PM
MPLM or W
PM
MPLM. Dividing both sides by the initial
wage W gives
W
W
P
P
M
W
M
M
P
P
L
L
M
M
P
P
M
M
,
where the term on the left-hand side is the percentage change in wages and
the term on the right-hand side is the percentage change in the price of manufactured
goods. Because the percentage increase in wage is less than the percentage
increase in the price of manufactured goods, the amount of manufactured
goods workers can now purchase is less than that before the country
engaged in trade. This means that the real wage has fallen for labor in terms
of manufactures, W/ PM
W / PM.
Overall Impact on Labor Whether labor is better off or worse off due to
the increase in the price of manufactures depends on whether the individual
prefers to purchase more manufacturing goods or food. The key point
is that with the specific-factors model, an increase in the price of manufactured
goods results in an ambiguous effect on the well-being of labors since
the effect on real wage is undefined.
Unemployment in the Specific-Factors Model Although it is often cited in
the news that international trade causes unemployment, we do not see this result
in the specific-factors model. One possible reason is that this model does
not incorporate unemployment, a macroeconomic phenomenon caused by
business cycles. Another reason could be that people who lose their jobs due
to import competition are able to find new jobs within a reasonable frame of
time such that unemployment is not an issue.
APPLICATION
Manufacturing and Services in the United States:
Employment and Wages across Sectors
In most industrial countries such as the United States, the service sector is
large relative to manufacturing, particularly compared with agriculture. For
the United States, employment continues to shift away from manufacturing
and into the service sector. As shown in Figure 3-6, whether measured in
terms of the number of workers or as a percentage of total employment, employment
in manufacturing has been on the decline since the 1970s. From
Figure 3-7 we see that, although the real hourly earning of production/
manufacturing workers is higher than those of services as a whole, this is
36 Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model
not the case if we disaggregate information service from overall general services,
which includes retail.
Moreover, a closer look at employment in manufacturing and services
shows that between 2003 and 2005, 0. 8 million workers were displaced or laid
off in manufacturing as compared with 2. 3 million in services. More notably,
Table 3-1 shows that of the 64% of the manufacturing workers that were reemployed
by January 2006, about half (49%) earned less in their new jobs,
whereas 68% of the displaced workers in services that were re-employed by
January 2006, 56% of them earned the same or more in their new jobs. ■
APPLICATION
Trade Adjustment Assistance Programs:
Financing the Adjustment Costs of Trade
We often talk about how an economy can benefit by engaging in international
trade. However, it is clear that not all sectors within the economy enjoy
the overall gains from trade. The question then is whether it is the role of
the government to temporarily assist those who lose their jobs due to foreign
competition. In the United States, workers displaced by import competition
may qualify for compensation through the Trade Adjustment Assistance (TAA)
program. In addition, there is a special TAA program for those laid off due to
competition from Canadian or Mexican imports under the North American
Free Trade Agreement (NAFTA). ■
H E A D L I N E S
Service Workers Are Now Eligible for Trade Adjustment
Assistance
The Trade Adjustment Assistance (TAA) program, which was introduced by President Kennedy
in 1962, was brought into the twenty-first century by the stimulus bill passed in 2009. TAA
was changed in three major ways: more workers are now eligible and service workers are now
fully eligible; training support was raised from $220 to $575 million; and the bill created a
special Labor Department TAA office to ensure eligible workers are aware of their options.
3 Earnings of Capital and Land
In this section, we examine the effect of an increase in the relative price of
manufactures on the rental of capital and land. In particular, which of the two
specific factors gain when the economy engages in international trade according
to the specific-factors model?
Determining the Payments to Capital and Land
Denoting QA as the output in agriculture and multiplying by its price gives
revenue earned in the industry. To determine the total payment to the specific
factor, we subtract the wage payment, W
LA, from the revenue. Using
the same method we obtain the payment to capital as follows:
Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model 37
Payments to capital PM
QM – W
LM
Payments to land PA
QA – W
LA.
Letting T represent the quantity of land in acres and K signifying the number
of physical capital, we can use the preceding equations to show the rental
on capital (earning per capital), RK, and the rental on land (earning per acre),
RT, by the following:
RK
Payments
K
to capital
PM
QM
K
W
LM,
RT
Paymen
T
ts to land
PA
QA
T
W
LA.
Alternatively, we could calculate the rentals by multiplying the marginal
product of the specific factor by its price,
RK PM
MPKM, and RT PA
MPTA.
Similar to the formulation for wage, MPKM is the marginal product of capital
in manufacturing although MPTA is the marginal product of land in agriculture.
Change in the Real Rental on Capital To understand the effect of an increase
in the price of manufactures on the rental on capital, holding agriculture
price fixed, recall that due to the change in the relative price of manufactures,
the wage rises throughout the economy. With the higher wage labor
shifts from agriculture into manufacturing, which increases the marginal product
of capital. Rewriting in notational format we have,
LM ↑, so that MPKM RK / PM ↑
PM ↑ ⇒
LA ↓, so that MPTA RT / PA ↓
where the increase in the marginal product of capital implies that the real
rental on capital in terms of the manufactured good, RK / PM, also goes up.
In addition to their gains in terms of manufactured good, capital owners enjoy
a raise in the real rental on capital in terms of food, RK / PA, because RK
has increased although PA is fixed. Therefore, capital owners are clearly better
off when the price of the good using their specific factor rises.
Change in the Real Rental on Land Contrary to the case for capital, the
loss of labor to manufacturing leads to a fall in the marginal product of agriculture.
It follows that the decline in MPTA means that the real rental on land
in terms of food has fallen. Moreover, landowners additionally suffer in terms
of their ability to purchase manufactures because the price of the manufactured
good has gone up. Consequently, landowners are clearly worse off
when the price of the good not specific to their factor rises.
Summary The general conclusion is given by the following: An increase in the
relative price of an industry’s output will increase the real rental earned by the factor specific to
that industry, but will decrease the real rental of factors specific to other industries.
In other words, the factors specific to the export industries are winners
when an economy engages in trade whereas the specific factors used in
import industries are losers following the fall in the relative price of
imports.
38 Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model
⎧⎪⎪⎨⎪⎪⎩
Numerical Example
Suppose the payments to labor and capital in manufacturing and agriculture
are given by the following:
Manufacturing: Sales revenue PM
QM $50
Payments to labor W
LM $30
Payments to capital RK
K $20
Agriculture: Sales revenue PA
QA $50
Payments to labor W
LA $30
Payments to land RT
T $20
We will maintain the preceding assumption that the increase in the relative
price of manufactures, PM / PA, is because of a rise in PM, holding PA constant.
Suppose the following price changes:
Manufacturing: Percentage increase in price PM / PM 20%
Agriculture: Percentage increase in price PA / PA 0%
Percentage increase in the wage W / W 10%
Change in the Rental on Capital Using the information given, we will
determine the impact of the increase in the price of manufactures on the
rentals on capital and land. We begin by rewriting the previous formula for
the rental on capital in percentage change. Recall that the rental on capital
is given as
RK .
By including the percentage changes in the price of manufacturing (PM / PM),
wage (W / W), and rental on capital (RK / RK) to this equation we obtain:
R
R
K
K
.
Substituting the information above gives,
R
R
K
K
MMMMMMMMMM 35%.
We get that the percentage increase in the rental on capital, 35%, is far
greater
than the percentage increase in the relative price of manufacturing, 20%.
Change in the Rental on Land To obtain the change in the rental on land,
we start with its formula,
RT
PA
QA
T
W
LA,
and in a similar approach for the rental on capital, we include the percentage
changes for the price of agriculture (PA / PA), wage (W / W), and rental
PM
QM W
LM
K
Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model 39
P
PM
PM
QM
W
W
W
LM
RK
K
20%
50 10%
30
20
on land (RT / RT). Given our assumption that the price of agriculture remains
fixed, we can substitute in zero for the percentage change in the agriculture
price and rewrite the equation for the percentage change in rental on
land as
R
R
T
T
.
Using the data for agriculture, we get that the fall in the land rent (15%)
exceeds the percentage increase in the wage (10%) as follows:
R
R
T
T
10
2
%
0
30
15%.
Note that had the share of revenue received by labor been lower than the
share of revenue received by land, the decrease in the rental on land would
have been smaller.
General Equation for the Change in Factor Prices We can summarize
our finding of the impact of a short-run change in factor prices with the
following,
RT / RT
0
W / W
PM / PM
RK / RK, for ↑ PM
and
RK / RK
PM / PM
W / W
0
RT / RT, for ↓ PM.
In other words, due to an increase in the relative price of manufacturing, capital
owners are better off because the real rental on capital rises by more than
the hike in the percentage change in the price of manufactures. Wages also
increase but by less than the percentage increase in the price of the manufactured
goods, whereas the rental on land falls by a greater percentage than the
rise in wages, which means that landowners are worse off with trade.
If instead the price of manufactures was to fall, the situation would be reversed
such that landowners would be better off although capital owners
would be worse off. Furthermore, landowners would also be better off if the
price of agricultural good rises. In particular, we can summarize the effect as,
RK / RK
0
W / W
PA / PA
RT / RT, for ↑ PA.
What It all Means
These general equations show that the specific factor in the sector whose
price has increased gains, while the specific factor in the other sector loses.
Moreover, the factor “caught in the middle,” namely labor, gains on one hand
in terms of its ability to purchase one good and loses in terms of the other.
W
W
W
LA
RK
T
40 Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model
Real rental
on land falls
⎧⎪⎪⎨⎪⎪⎩
Real rental
on capital falls
⎧⎪⎪⎨⎪⎪⎩
Change in the real
wage is ambiguous
⎧⎪⎪⎨⎪⎪⎩
Real rental
on land rises
⎧⎪⎪⎨⎪⎪⎩
Change in the real
wage is ambiguous
⎧⎪⎪⎨⎪⎪⎩
Real rental on
capital rises ⎧⎪⎪⎨⎪⎪⎩
Real rental
on capital falls
⎧⎪⎪⎨⎪⎪⎩
Change in the real
wage is ambiguous
⎧⎪⎪⎨⎪⎪⎩
Real rental
on land rises
⎧⎪⎪⎨⎪⎪⎩
In other words, the changes in the earnings of the specific factors are dramatic
when relative prices fluctuate due to international trade. The reason is that,
unlike labor, which is mobile between the sectors, the specific factors can only
be employment in the particular industry.
APPLICATION
Prices in Agriculture
The prices of agriculture products such as cotton, palm oil, rice, sugar, rubber,
wheat, and wool have declined as countries become productive in growing
crops, which results in an increase in the global supply. The specific-factors
model predicts that landowners, like the farmers, lose in real terms due to the
decrease in the relative price of agriculture. ■
Coffee Prices The price of coffee fluctuates greatly because the beans are
only grown in developing countries. Shown in Figure 3-8, the real, wholesale
prices of coffee often fluctuate. The world coffee prices reached as high
as $3. 00 per pound in 1986 to a low of 50¢ per pound in 2001. The swing
in the world coffee prices is due to excess exports from Vietnam and Brazil.
As predicted by the specific-factors model, the dramatic fluctuation in the
world price of coffee causes huge swings in the real incomes of land owners
in coffee-growing regions in Central America and Asia.
Fair-Trade Coffee To assist the coffee growers in the developing countries,
TransFair USA, an import group, engages in “fair-trade coffee” by avoiding
the middlemen and ensuring a minimum price for the farmers. The
fixed–fair-trade price is a form of insurance against large fluctuations in the
world price, thereby allowing the farmers a more stable source of income.
The fair-trade price protects the farmers in a manner similar to the government
policy in industrialized countries except that consumers have the option
to purchase the higher-priced product.
H E A D L I N E S
Rise in Coffee Prices—
Great for Farmers, Tough on Co-ops
Fair-trade cooperatives had difficulties obtaining deliveries from member farmers when the
price of coffee beans rose above their agreed fair-trade price of $1.26 per pound. The coop’s
leader convinced the farmers to deliver the coffee by drawing on their sense of loyalty.
4 Conclusion
The specific-factors model is a short-run model in which labor is perfectly
mobile between industries although other inputs such as land and capital are
specific to the industry in which the factor is used. Under these assumptions,
the factor specific to the import-competing industry loses in terms of its ability
to purchase the goods produced because of the drop in its relative price
from opening to trade. Because the factor facing import competition is immobile,
owners of the specific factor experience a fall in the real rental. By
Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model 41
contrast, the factor specific to the export industry gains in real terms because
its relative price rises when the economy opens to trade. Unlike the specific
factors, labor avoids extreme changes in wage because it is able to move between
industries. However, when an economy engages in trade, the impact of
the change in the relative price has an ambiguous effect on labor. More
specifically, for labor, whether there are gains or losses from international trade
depends on its preferences because the real wage rises in terms of one good
but falls in terms of the other good.
TEACHING TIPS
Tip 1: Coffee Prices and Factor Returns in the Real World
In this chapter, we discuss the affect of goods’ prices on returns to both fixed
and mobile factors of production. Have students look up the most recently
available world coffee prices published by the International Coffee Organization
(http://www. ico. org/coffee_prices. asp). Ask your students to use this
data to predict what has happened to factor return on land in coffee exporting
countries.
Tip 2: U.S. Employment Since the Global Recession
A major part of this chapter focuses on unemployment and Trade Adjustment
Assistance. When this book was written, the global economy was just beginning
to recover from a major global recession that greatly affected international
trade. Have students investigate the current characteristics of U. S. employment
and unemployment. Ask students to visit the Bureau of Labor
Statistics and investigate the Labor Force Statistics from the Current Population
Survey at http://www. bls. gov/news. release/disp. toc. htm. Here students
can explore the most current data on the characteristics of the U. S. employed
and unemployed. Have students investigate this data and then discuss
their findings in class.
Tip 3: Discussion about the Global Economy
Beginning in Chapter 1, there has been a focus on the changing face of trade.
This emphasis was continued with our discussion of the TAA being extended
to the service industry. Have students discuss why they think this change is
important, and how greater global competition in services will affect them.
42 Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model
Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model 43
I N – C L A S S P R O B L E M S
1. Use the following information to answer the questions
below.
Computers: Sales revenue PC
QC 150
Payments to labor W
LC 75
Payments to capital RK
K 75
Barley: Sales revenue PB
QB 150
Payments to labor W
LB 70
Payments to land RT
T 80
Holding the price of computers constant, suppose
the percentage increase in the price of barley is
10% and the percentage increase in wage is 5%.
a. Determine the impact of the increase in the
price of barley on the rentals on land.
Answer:
R
R
T
T
R
R
T
T
14. 4%.
b. Determine the impact of the increase in the
price of barley on the rentals on capital.
Answer:
RK
R
R
K
K
W
W
W
RK
L
K
C
R
R
K
K
5%
7
7
5
5
5%.
c. Determine the impact of the increase in the
price on the welfare of labor.
Answer: The impact of the increase in the
price of barley on the welfare of labor is ambiguous
because labor gains in terms of computers
because the price of computers remained
constant, while wages increased by
5% but lost in terms of barley because the
percentage increase in barley is higher than
the percentage change in wage.
2. Summarize your finding in problem 1 using notational
format.
RK / RK
0
W / W
PB / PB
RT / RT,
for PB
3. If, instead of the situation given in problem 1, the
price of computers was to fall, would landowners
or capital owners be better off? Explain. How
would the decrease in the price of computers effect
labor? Explain.
Answer: Similar to the situation given in problem
1, capital owners would be worse off because the
rental on capital would fall by more than the decrease
in the computer price. Landowners would
be better off as the rental on land rises even without
the increase in the price of barley. The effect
on labor because of the decrease in the price of
computers is also ambiguous. Wages fall, so labor is
worse off in terms of barley, but because the drop
in wage is less than the percentage decrease in the
manufactured good, labor gains in terms of computers.
RK / RK
PC / PC
W / W
0
RT / RT,
for PM.
4. What is fair trade?
Answer: Fair trade is the process by which nongovernmental
organizations such as TransFair USA
assist farmers in developing countries by selling
agricultural commodities such as coffee beans directly
to consumers in industrial countries. By
avoiding the local buyers, millers, shippers, and
other middlemen, these import groups are able to
ensure a minimum price for the farmers.
10%
150 5%
70
80
(PB / PB)
PB
QB (W / W)
W
LB
RT
T
0
QC W
LC
K
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
⎧⎪⎪⎨⎪⎪⎩
44 Chapter 3 ■ Gains and Losses from Trade in the Specific-Factors Model
5. Ashland is considering whether to engage in the
international trade of rice and furniture. Suppose
that the world price of rice is lower than Ashland’s
no-trade price but its no-trade furniture price is
lower than the world price. Assume that land is
specific to the production of rice and that labor is
free to move across sectors. Do you think the
landowners will support the move to free trade?
Explain.
Answer: Landowners will not support the move
because the world price of rice is lower than Ashland’s
no-trade price. By engaging in trade, the
landowners would be worse off because the rental
on land will fall due to the decrease in the price of
rice.
6. When labor shifts from agriculture to manufacturing,
why does the marginal product of capital increase
while the marginal product of land falls?
Answer: When labor shifts from agriculture to
manufacturing, the marginal product of land falls
because there are fewer laborers to work on each
acre of land. By contrast, the increase in the quantity
of labor used in manufacturing will raise the
marginal product of the capital because there are
more laborers available to work on the machinery.
7. Between 2005 and 2007, displaced workers in the
service industries are better off relative to those in
the manufacturing industries. Comment.
Answer: According to Table 3-1, although the
number of workers displaced between 2005 and
2007 is significantly higher (more than double) in
the service industries relative to the manufacturing
industries, 68% of the workers in the service industry
found employment by January 2008, with 56% of
those newly employed workers earning the same or
more in their new jobs. By contrast, 64% of the displaced
workers in manufacturing were re-employed
by January 2006 and only 51% received the same or
higher pay in their new positions.
8. Assuming that labor is mobile, is it true that wages
always must be equal across the sectors in the
specific-factors model?
Answer:Yes, labor will continue to shift from the
low-wage sector to the high-wage sector until the
wages are equalized.
9. Home, a small, open economy, uses a mobile factor
(labor) and two specific factors (drylands and
wetlands) to produce two goods, cactus and rice.
Dryland is only productive in growing cactus and
wetlands can only grow rice. Suppose the worldrelative
price of cactus is higher than Home. Determine
the effect of this price increase on the real
wage and real returns on the different types of
land.
Answer: Because the world-relative price of cactus
is higher than Home, the small country will export
cactus, which will lead to an increase in the
real rental on drylands. Real wage will increase in
terms of rice because of the increase in the price
of cactus but will fall in terms of cactus because the
percentage rise in the price of cactus is higher than
the percentage increase in wage.
45
4 Trade and Resources:
The Heckscher-Ohlin Model
Notes to Instructor
Chapter Summary
This chapter presents the Heckscher-Ohlin model with two factors (capital
and labor), two goods (computers and shoes), and two countries (Home and
Foreign). A test of the model is discussed with Leontief ’s paradox.
Additionally
this chapter, like the last, discusses the affect of trade on factor prices.
The
“sign test” in the Heckscher-Ohlin model is discussed in the Appendix.
Comments
Note that this chapter covers only two theorems of the Heckscher-Ohlin
model—the Heckscher-Ohlin theorem and the Stolper-Samuelson theorem.
The other two theorems—the Rybczynski theorem and Factor Price
Insensitivity—are deferred to the next chapter, in an effort to break the
material
into smaller pieces.
Unlike the previous chapters, a discussion of the theory is followed by an
empirical test. This concept is possibly new to students and could be
highlighted
to generate interest in the topic. Moreover, although students are
quite familiar with graphing supply and demand from their principles course,
place emphasis on teaching the export supply and import demand curves,
particularly because the derivation of these curves requires an understanding
of the relationship between the no-trade and free-trade relative prices.
Similarly,
the topic of relative demand and supply may also benefit from additional
attention as the shift of the curves due to changes in the relative price
may not be immediately obvious to the students because the curves are in ratios
(i. e. , horizontal axis gives the ratio of labor to capital and the vertical
axis has the ratio of wage to rental on capital).
Lecture Notes
Introduction
We begin the chapter with a comparison between the Ricardian model, in
which trade occurs due to differences in technology between countries giving
rise to their comparative advantage, and the Heckscher-Ohlin model,
in which uneven distribution in resources leads countries to trade with one
another. The Heckscher-Ohlin model also differs from the specific-factors
model in that factors of production can move between industries because the
model is set in the long run. The model was developed to explain the “golden
age” of international trade between 1890 and 1914, during which there was
an increase in the ratio of trade to gross domestic product (GDP) coinciding
with improvements in transportation.
1 Heckscher-Ohlin Model
The Heckscher-Ohlin model consists of two factors (capital and labor), two
goods (computers and shoes), and two countries (Home and Foreign). The
total amount of capital (K) in an economy is given by the sum of the capital
used in shoes, KS, and computers, KC. The total available labor (L) in the
economy is synonymously equal to the labor used in shoes, LS, and computers,
LC.
Assumptions of the Heckscher-Ohlin Model
The six assumptions of the Heckscher-Ohlin model are as follows:
Assumption 1: Both factors can move freely between the industries.
The implication of the first assumption is that the rental on capital, R, is
identical across the two industries. If one industry has a higher rental, it
would
attract capital from the industry with the lower rental, leading the rates to
adjust
until they are equal between the industries. The same reasoning also implies
that the wage earned by labor, W, is the same across the industries.
Assumption 2: Shoe production is labor-intensive, that is, it requires more
labor per unit of capital to produce shoes than computers, so that LS / KS
LC / KC.
The second assumption states how intensive the factors are in the production
of each good. Namely, computer production is capital-intensive, requiring
more capital per worker than the production of shoes. Because shoe
production is labor-intensive, the relative demand curve in shoes, LS / KS, is
to the right of the relative demand curve in computers, LC / KC, in Figure 4-1,
46 Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model
where the horizontal axis gives the ratio of labor to capital used in
production
and the vertical axis denotes the ratio of the labor wage to the capital
rental.
Assumption 3: Foreign is labor abundant, by which we mean that the labor/
capital ratio in Foreign exceeds that in Home, L* / K* L/ K. Equivalently,
Home is capital abundant, so that K/ L K* / L*.
The third assumption distributes the resources unevenly across the two
countries, with Home being capital-abundant whereas Foreign is laborabundant.
Assumption 4: The final outputs, shoes and computers, can be traded
internationally,
but labor and capital do not move between countries.
The forth assumption allows the final goods to move between the countries
but not the factors of production.
Assumption 5: The technologies used to produce the two goods are identical
across the countries.
From the fifth assumption, we see that each good is produced using the
same technology across the two countries. In other words, across both
countries,
each industry has the same factor intensity.
Assumption 6: Consumer tastes are the same across countries, and preferences
for computers and shoes do not vary with a country’s level of income.
The sixth assumption implies that although the poorer country would consume
less of both goods than the richer country, the ratio of shoes to computers
expenditure is the same across both countries.
APPLICATION
Are Factor Intensities the Same across Countries?
In the United States, footwear production is more capital-intensive than call
centers because of the expensive automated-manufacturing machines used
by a New Balance plant. However, there is a “reversal” of factor intensities
in India, where call centers are more capital-intensive than footwear
production
using labor-intensive sewing machines. Another example of a reversal
of factor intensities between countries is in the agriculture sector.
Although farmers in the United States use costly computerized equipment
to cultivate their farms, their counterparts in developing countries use little
or no mechanized equipment because labor is cheap relative to the cost of
capital. ■
Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model 47
N E T W O R K
The New Balance Web site can be found through the following link:
http://www.newbalance.com. In addition to producing shoes, the company makes
apparel,
eyewear, headwear, sport bags, fitness equipment, and shoe- and apparel-care
products.
No-Trade Equilibrium
Production Possibility Frontiers Figure 4-2 shows the production possibility
frontiers (PPFs) for Home in panel (a) and Foreign in panel (b). The
bowed-out PPF is biased toward computer (on the horizontal axis) for Home
because Home is capital-abundant and the production of computers is capital
intensive. For Foreign, the PPF skews more toward shoes (on the vertical axis)
because shoe production is labor intensive and Foreign is labor abundant.
Indifference Curves With the assumption of common consumer tastes
across the countries, we add an identical indifference curve to each country’s
PPF. The tangency of the indifference curve and the PPF gives the relative
price of computers for Home, (PC / PS)A, and Foreign, (PC * / PS
* )A*, in panels
(a) and (b), respectively.
No-Trade Equilibrium Price The no-trade equilibrium for Home is at point
A, with production of computers and shoes given by QC1 and QS1. The notrade
equilibrium for Foreign is shown by point A*, at which outputs are denoted
by Q*
C1 for computers and Q*
S1 for shoes. The slope of the price line
is relatively steeper for Foreign than for Home, reflecting the higher relative
price of computers in the labor-abundant country.
Free-Trade Equilibrium
Home Equilibrium with Free Trade With free trade, the equilibrium relative
price of computers is between the no-trade relative prices found at Home and
Foreign. More specifically, panel (a) of Figure 4-3 shows that the free-trade
equilibrium price of computers, (PC / PS)W, is steeper than the no-trade price
at Home (see Figure 4-2) because its no-trade price is lower than that of the
foreign country. Given the higher world relative price, Home further
specializes
in the production of computers by moving from point A to point B, where
QC2 QC1 and QS2
QS1. By engaging in trade, Home can consume on a
higher indifference curve at point C. Using points B and C, we can create a
“trade triangle,” where the height represents the amount of shoes imported
(QS3
QS2) by Home and the base gives export of computers (QC2
QC3).
Panel (b) of Figure 4-3 shows the Home exports of computers versus the relative
price. The Home relative price without trade given by point A in panel
(a) corresponds to point A in panel (b) with zero computer exports. Given the
higher free-trade relative price, Home exports the difference between the
amounts produced and consumed, shown by point D in panel (b). Home export
supply curve of computers is derived from connecting points A and D.
Foreign Equilibrium with Free Trade In panel (a) of Figure 4-4, the Foreign
no-trade equilibrium is at point A*. Because the Foreign no-trade relative
price is higher than at Home, the world equilibrium price of computers, (PC /
PS)W, is flatter than the no-trade Foreign price, (PC * / PS
*)A*. Facing a lower relative
price of computers under free trade, Foreign will increase the production
of shoes by moving from point A*, (Q*
C1, Q*
S1), to point B*, (Q*
C2, Q*
S2), such
that Q*
S2 Q*
S1 and Q*
C2
Q*
C1. Engaging in trade at the world relative price,
Foreign consumes at a higher indifference curve at point C*, (Q*
C3,
Q*
S3). Connecting points B* and C*, we form a “trade triangle” similar to that
at Home except now the base is Foreign’s imports of computers and the height
48 Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model
is Foreign’s export of shoes. Foreign’s import demand curve for computers is
given in panel (b) of Figure 4-4.
Equilibrium Price with Free Trade Putting together Home’s export supply
curve for computers and Foreign’s import demand curve for computers gives
the equilibrium relative price of computers with free trade as shown in Figure
4-5. At the world relative price of computers, the amount of computers
imported by Foreign is exactly equal to the quantity exported by Home,
(QC2
QC3)(Q*
C3
Q*
C2). This implies that the trade triangles of the two
countries are of identical size.
Pattern of Trade The pattern of trade can be determined from the free-trade
equilibrium. Namely, a country will export the good that uses intensively the
factor of which it has an abundance. This means that Home will export the capital-
intensive good (computers) and Foreign will export the labor-intensive good
(shoes) because Home is capital-abundant whereas Foreign is labor-abundant.
This finding is summarized by the following Heckscher-Ohlin theorem.
Heckscher-Ohlin Theorem With two goods and two factors, each country
will export the good that uses intensively the factor of production it has in
abundance and will import the other good.
2 Testing the Heckscher-Ohlin Model
In this section, we investigate different methods to empirically test the
Heckscher-Ohlin Model. We begin with one of the first such tests, and then
move to more recent attempts.
Testing the Heckscher-Ohlin Theorem: Leontief’s Paradox
Using 1947 data for the United States, Leontief measured the amount of capital
and labor required to produce $1 million worth of U. S. exports. The measurement
indicated that the capital–labor ratio used in export production was
$14,000 per worker. Applying U. S. technology to measure the labor and capital
used in producing imports, Leontief found that the capital–labor ratio for
imports was $18,200 per worker. Because the United States is believed to be
abundant in capital in 1947, the Heckscher-Ohlin theorem predicts that the
United States would export capital-intensive goods and import labor-intensive
goods. Leontief ’s findings, called the “Leontief’s paradox,” indicated that the
U.S. imports were capital-intensive and U. S. exports were labor-intensive.
Explanations Many explanations have been offered to explain Leontief ’s
paradox, including the following:
• Technologies in the United States and rest of the world may not have
been the same as the Heckscher-Ohlin Theorem assumes.
• Leontief ’s test ignored other factors of production, such as land, in which
the United States may have been abundant.
• Leontief did not distinguish between skilled and unskilled labor.
• The data for 1947 might be unusual due to World War II just ending and
the rebuilding of Europe, in which the United States was engaged.
• The United States was not completely open to trade, as the Heckscher-
Ohlin Theorem assumes.
Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model 49
Many of these explanations focus on the importance of more than two factors
or the ability of factors (such as skilled vs. unskilled labor). In the remainder
of this section, we discuss research aimed to redo Leontief ’s test to
incorporate these additional complexities.
Endowments in the New Millennium
The method for measuring factor abundance differs when we consider more
than two factors of production. The general definition of factor abundance is
given by the country’s share of that factor as compared with its share of world
GDP. A country is abundant in that factor if its share of that factor exceeds
its share of world GDP. Conversely, if its share of world GDP is greater
than its share in the factor, the country is scarce in that factor.
Capital Abundance Using the general definition and data from Figure 4-6,
we see that in 2000 the United States was physical-capital abundant because
its share of the world’s capital was 24% and its share of world GDP was
21. 6%. Of the seven selected countries, three were abundant in capital
(United States, Japan, and Germany) and the other four were scarce in capital
(China, India, France, and Canada).
Labor and Land Abundance Using a similar comparison, Figure 4-6 shows
that the United States is abundant in research and development (R&D)
scientists and skilled labor, but is scarce in less-skilled labor, illiterate labor, and
arable land. As with the United States, China is abundant in R&D scientists.
By contrast, India is scarce in R&D scientists but abundant in skilled labor,
semiskilled labor, and illiterate labor. Relative to the other six countries,
Canada is abundant in arable land.
Differing Productivities across Countries
Although the extended Heckscher-Ohlin model is better at predicting the
pattern of international trade by allowing for many goods, factors, and countries,
we can further examine the accuracy of the model by dropping the assumption
of identical technologies across countries. By allowing for differences
in productivities, we can calculate a country’s effective labor force,
which measures how much output the labor force can produce.
Measuring Factor Abundance Once Again Measuring whether a country
is abundant in that effective factor or scarce in that effective factor is
similar to the method we used earlier except that we now compare its share
of the effective factor endowment, defined as the actual amount of a factor
found in a country multiplied by its productivity, with its share of world GDP.
Effective R&D Scientists To account for the differences in productivities
across countries due to the availability of laboratory equipment, we measure
effective R&D scientists by multiplying the actual number of R&D scientists
by the amount of R&D spending per scientist. The first two columns of Figure
4-7 show each country’s share of world R&D scientists where the productivity
differences are corrected for in the second bar. With the correction,
the share of effective R&D scientists in the United States increases along with
Japan and India. However, this share falls by half for China, suggesting that it
is scarce in effective R&D scientists.
50 Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model
Effective Arable Land The effective amount of arable land is defined as the
actual arable land in a country times its productivity in agriculture. After accounting
for the differing productivities in arable land, we find that the
United States is neither abundant nor scarce in effective arable land because
its share of the world total is about equal to its share of the world’s GDP. This
conclusion is verified by the data. From Table 4-2 we can see that even
though the U. S. is a net exporter of agricultural goods, it is some years a net
exporter and some years a net importer of food.
H E A D L I N E S
China Drawing High-Tech Research from the
United States
Applied Materials, a U.S. firm that is currently the world’s largest supplier of equipment used
to make semiconductors, has built its newest and largest research labs in Beijing, China. Applied
Materials is just one of many firms tapping into China’s huge markets and its abundant,
cheap, and highly skilled engineers.
Leontif’s Paradox Once Again
Going back to data from the time periods studied by Leontief, with our newly
developed concepts of effective abundance we can redo Leontief ’s factor calculations,
taking into account the productivity of the U. S. workforce. To do
this we estimate productivity with wages, which we can see from Figure 4-9
is a defensible strategy. By this method, we see that in 1947 the United States
actually had 43 percent of the worlds “effective” labor and only 37 percent of
world GDP, making the United States abundant in effective labor, and thus
solving Leontief ’s Paradox.
3 Effects of Trade on Factor Prices
In this section, we determine the impact of trade on the wage and rental
earned by labor and capital, respectively, when a country faces the world relative
price, which differs from the no-trade relative price.
Effect of Trade on the Wage and Rental of Home
Economy-Wide Relative Demand for Labor Recall that the total amount
of labor (capital) in an economy is equal to the sum of the labor (capital) in
each industry, i. e. , LC LS L (KC KS K). Dividing total labor by total
capital, we get the supply of labor relative to capital or relative supply:
Relative Supply Relative Demand
The relative demand or demand for labor relative to capital, shown on the
right-hand side, is a weighted average of the labor/capital ratio in each industry.
The weighted average is calculated by multiplying the labor/capital ratio
LK
LC LS
K
LC
KC
KC
K
LS
KS
KS
K
Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model 51
⎧⎨⎩
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
52 Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model
for each industry (LC / KC and LS / KS) by the shares of total capital employed
in each industry (KC / Kand KS / K).
The equilibrium relative wage at Home is determined by the intersection
of the relative supply and relative demand curves at point A as shown in Figure
4-10. Because the relative supply curve depends on the total amount of factor
resources in the economy and not on the relative wage, it is represented
by a vertical line. The economy-wide relative demand for labor (RD curve)
is an average of the demand for labor relative to capital in each industry.
Increase in the Relative Price of Computers Because of free trade, Home
faces a higher relative price of computers, which drives it to further specialize
in the production of computers, shifting away resources from the production
of shoes. The increase in the production of the capital-intensive good (computers)
leads to a change in the relative demand for labor. More specifically,
for the relative demand for labor in the economy, we put more weight toward
computers, a rise in (KC / K), and less weighted toward the shoe industry, a
fall in (KS / K), because capital has shifted to the computer industry. Figure
4-12 shows this change in the weights as a leftward shift of the relative demand
curve from RD1 to RD2, giving the new equilibrium at point B.
With production specializing in computers, the fall in the relative demand
for labor in the shoe industry causes a decrease in the relative wage from
(W / R)1 to (W / R)2. The lower relative wage in turn induces an increase in
the number of workers hired per unit of capital in each industry, shown by the
movement along the relative demand curves for shoes (from (LS/KS)1 to
(LS/KS)2) and computers (from (LC/KC)1 to (LC/KC)2). Thus, the increase in
the relative price of computers resulting from free trade leads to a rise in the
labor/capital ratio in both industries. The rise in the labor/capital ratio in
both shoes and computers results from labor being “freed up” as production
shifts from shoes to computers. In particular, the additional labor per unit of
capital released from the shoes exceeds the requirement necessary to operate
the capital in computers. The change in the relative supply and relative demand
due to an increase in the relative price of computers can be summarized
by the following:
Determination of the Real Wage and Real Rental
Change in the Real Rental The rental on capital in computers (shoes) is
equal to its marginal product multiplied by the price of computers (shoes):
R PC MPKC and R PS MPKS
Because the labor/capital ratio increases in both industries due to the higher
world relative price of computers, the marginal product of capital also increases
in both shoes and computers. Rearranging the previous equations, we get
MPKC R / PC ↑ and MPKS R / PS ↑,
LK
LC
KC
KC
K
LS
KS
KS
K
Relative Supply
No change
⎧⎨⎩
Relative Demand
No change in total
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩
↑ ↑ ↑ ↓
Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model 53
where R / PC (R / PS) gives the quantity of computers (shoes) a capital owner
at Home can purchase with the rental. Because the marginal product of capital
increases in both industries, we see that the real rental on capital increases
in terms of shoes and computers. Namely, the capital owner benefits from the
increase in the relative price of computers when Home engages in trade.
More generally, an increase in the relative price of a good (computers) will
benefit the factor of production (capital) used intensively in producing that
good (computers are capital-intensive).
Change in the Real Wage Similarly, the wage in computers (shoes) is equal
to its marginal product multiplied by the price of computers (shoes):
W PC MPLC and W PS MPLS
However, unlike the case for capital, the law of diminishing returns tells us
that the increase in the labor/capital ratio (i. e. , more labor per unit of capital)
will lead to a decrease in marginal produce of labor in both industries.
Re arranging the preceding equations gives:
MPLC W / PC ↓ and MPLS W / PS ↓
where we see that labor experiences a decrease in real wage in terms of the
quantity of computers (R / PC) and shoes (R / PS) it can purchase at Home
with its wage. Thus, labor is worse off in real terms as a result of the increase
in the relative price of computers from free trade.
The situation for Foreign would be the opposite because it faces a lower
world relative price of computers. More specifically, by opening up to trade,
Foreign experiences a fall in real terms in rental on capital and a rise in real
terms in wage. This means that labor in Foreign is better off with free trade
and the capital owner is worse off. This finding is summarized by the following
Stolper-Samuelson theorem:
Stolper-Samuelson Theorem In the long run, when all factors are mobile,
an increase in the relative price of a good will increase the real earnings of the
factor used intensively in the production of that good and decrease the real
earnings of the other factor.
An alternative statement is that the abundant factor gains from trade, and
the scarce factor loses from trade.
Changes in the Real Wage and Rental: A Numerical Example
Suppose the following:
Computers: Sales revenue PS QC $150
Earnings of labor W LC $50
Earnings of capital R KC $100
Shoes: Sales revenue PS QS $150
Earnings of labor W LS $100
Earnings of capital R KS $50
Note that shoes are more labor-intensive than computers because the share
of total revenue paid to labor in shoes (100 / 150 66. 7%) is more than that
share in computers (50 / 150 33. 3%). Under free trade, the relative price
of computers rises as follows:
54 Chapter 4 ■ Trade and Resources: The Heckscher-Ohlin Model
Computers: Percentage increase in price PC / PC 5%
Shoes: Percentage increase in price PS / PS 0%
To determine the impact of the higher relative price of computers on the
rental on capital for each industry, we subtract the payments to labor from total
sales revenue and divide the difference by the amount of capital:
R , for computers
R , for shoes
We now add in the information pertaining to the increase in the price of
computers:
R , for computers
R , for shoes
Rewriting the previous equations in terms of percentage changes, we have
the following:
, for computers
0
, for shoes
where PC / PC is the percentage change in the price of computers, W /
W is the percentage change in the wage, and R / R is the percentage change
in the rental on capital.
Substituting the numbers given and subtracting one equation from the
other, we get:
5%
1
1
5
0
0
0
W
W
1
5
0
0
0
,
for computers
Minus: 0
W
W
1
5
0
0
0
,
for shoes
Equals: 0 5%
1
1
5
0
0
0
W
W
1
1
5
0
0
0
,
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