4
The Heckscher-Ohlin
Model
1
H-O Model
2
Empirical
Evidence
3
Conclusions
Introduction
• The Heckscher-Ohlin model (HO) shows how
trade occurs because countries that have different
resources.
• They wanted to explain this increase in trade
during the “golden age” of international trade.
• H-O assumed that technologies were the same
across countries, but had an uneven distribution
of resources.
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Introduction
• The specific factors model in the last chapter was
a short run model since capital and labor could
not move between industries.
• The HO model is a long run model because all
factors of production can move between the
industries.
• Generalizations
 Many factors and goods
 Differing productivities
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Heckscher-Ohlin Model
• Two countries: Home and Foreign.
• Two goods: computers and shoes.
• Two factors of prod’n: labor (L) and capital (K).
• Resource constraint equations:
 Capital in each good for each country
 K = KC + KS and K* = K*C + K*S
 Labor in each good for each country
 L = LC + LS and L* = L*C + L*S
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Assumptions of the Heckscher-Ohlin Model
1. Both factors can move freely between industries.
 R and W must be the same in both industries.
2. Shoe production is labor-intensive; it requires
more labor per unit of capital to produce shoes
than computers, so that LS/KS > LC/KC.
 This means that computer production is capitalintensive.
 Figure 4.1 shows relative demand curves for labor in
each industry.
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Assumptions of the Heckscher-Ohlin Model
Figure 4.1
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Assumptions of the Heckscher-Ohlin Model
3. Foreign is labor abundant. Equivalently, Home is
capital abundant
 L*/K* > L/K and K/L > K*/L*
 Here, we do not consider why the amount of
resources differs across countries. Take as given.
4. The final outputs, shoes and computers, can be
traded freely, without restrictions, between
nations, but labor and capital do not move
between countries.
 Latter assumption will be relaxed in the next chapter.
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Assumptions of the Heckscher-Ohlin Model
5. The technologies used to produce the two goods
are identical across the countries.
 This is opposite of the assumption in the Ricardian
model.
6. Consumer tastes are the same across countries,
and preferences for computers and shoes do not
vary with a country's level of income.
 These are not realistic assumptions, but they allow us
to focus on differences in factor endowments as the
basis for trade.
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Are Factor Intensities the Same Across Countries?
APPLICATION
• As part of our assumptions, we assume that factor
intensities in each industry are the same in both
countries.
 E.g. shoes are labor intensive in both countries
• Although all countries may have access to the
same technologies, the machines used in the U.S.
are different from those used in Asia and
elsewhere.
• While the U.S. still produces some shoes, the
production is different from the production in Asia.
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Are Factor Intensities the Same Across Countries?
APPLICATION
• Asian production uses old technology and workers earn
relatively little compared to the U.S.
 Labor intensive in Asia.
• In call centers, technologies and therefore factor
intensities are similar across countries.
• So, shoes in India are labor intensive compared to the call
center—the opposite of the U.S.
• This illustrates Reversal of Factor Intensities between
the two countries.
 Holds for all Wage/Rental ratios.
 We will ignore the possibility of “factor intensity reversals.”
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Heckscher-Ohlin Model
No Trade Equilibrium
• As always, start with the no-trade equilibrium.
• Factor abundance and intensity (combined with total
endowments) determine the shape of the PPFs:
 Home is capital abundant and computer production is capital
intensive.

Home is capable of producing more computers than shoes.
 Foreign is labor-abundant and shoe production is laborintensive.

Foreign is capable of producing more shoes.
• Indifference Curves
 Consumer tastes are the same across countries, so the
shape of the indifference curves is the same in each country.
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Heckscher-Ohlin Model
No Trade Equilibrium
Figure 4.2
No-Trade Equilibria in Home and Foreign
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Heckscher-Ohlin Model
• No Trade Equilibrium Price
 The no-trade prices reflect the differing amounts of
resources found in the two countries.
 Foreign has abundant labor.
 Shoe production is labor intensive.
 The no-trade relative price of shoes is lower in Foreign.
 People in Foreign are willing to give up more shoes for
one computer since they have a lot of shoes.
 The same logic applies to Home.
 Home has abundant capital.
 Computer production is capital intensive.
 The no-trade relative price of shoes is lower in Home.
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Heckscher-Ohlin Model
Free Trade Equilibrium
• Three steps to finding free trade equilibrium
 Trace out the Home export supply of computers.
 Trace out the Foreign import demand for computers.
 Put together the export supply and the import demand
to determine equilibrium relative price of computers.
• Home Equilibrium with Free Trade (Figure 4.3)
 The Home PPF will show a free trade or world relative
price of computers that is higher than the no-trade
Home relative price.
 They will produce more computers and fewer shoes.
 Home specializes in and exports computers.
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Heckscher-Ohlin Model
Figure 4.3
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Heckscher-Ohlin Model
• We can use the Home trade information to graph
the exports of computers against the relative
price.
 Trace out the quantity of exports at each relative price.
 This gives the Home export supply curve for
computers.
 It is upward-sloping since at higher relative prices,
Home is willing to specialize further in computers and
export more of them.
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Heckscher-Ohlin Model
Figure 4.3
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Heckscher-Ohlin Model
• Foreign Equilibrium with Free Trade
 The Foreign PPF will show a free trade or world
relative price of computers that is lower than
the no-trade Foreign relative price.
• Foreign can now consume on any point along
the world price line through point B*.
• We can now define the Foreign “trade triangle”
which is the triangle that connects points B*
and C*.
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Heckscher-Ohlin Model
Figure 4.4
• Next, we run through
the same steps for
the Foreign country.
• Foreign specializes
further in shoes and
produces fewer
computers.
• B* is where Foreign
produces and C* is
where Foreign
consumes.
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Heckscher-Ohlin Model
Figure 4.4
• We can use the Foreign
trade information to
graph the import of
computers against the
relative price.
• It is downward-sloping
since at higher relative
prices, Foreign is willing
to specialize further in
shoes and import more
computers.
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Heckscher-Ohlin Model
• The equilibrium free trade price is determined by the
intersection of the Home export supply curve and the foreign
import demand curve: Point D.
• At that relative price,
the quantity that Home wants
to export equals the amount
that Foreign wants to import.
Figure 4.5
• This is a free-trade
equilibrium since there is no
reason for the relative price
to change.
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Heckscher-Ohlin Model
• Pattern of Trade
 This is the 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.
• When trade opens:
 The relative price of computers in Home rises from the
no-trade price.
 This gives Home an incentive to produce more computers and
export the difference.
 The relative price of computers in Foreign falls from the
no-trade price.
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Heckscher-Ohlin Model
• Testing the HO Theorem: Leontief’s Paradox
 Wassily Leontief performed the first test of the HO
theorem in 1953 using data for the U.S. from 1947.
 He measured the amounts of labor and capital used in
all industries needed to produce $1 million of U.S.
exports and to produce $1 million of imports into the
U.S.
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Heckscher-Ohlin Model
• Leontief used labor and capital used directly in the
production of final good exports in each industry.
• Capital is high because we are measuring the whole
capital stock—not the part actually used to produce
exports.
• It was impossible for Leontief to get information on the
amount of labor and capital used to produce imports.
• He used data on U.S. technology to calculate estimated
amounts of labor and capital used in imports from abroad.
 Remember the HO model assume technologies are the same
across countries.
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Heckscher-Ohlin Model
• Leontief assumed correctly that in 1947 the U.S.
was capital abundant relative to the rest of the
world.
 From the HO model, Leontief expected that the U.S.
would export capital intensive goods and import labor
intensive goods.
• Leontief, however, found the opposite.
 The capital labor ratio for U.S. imports was higher than
for exports.
• This contradiction came to be called Leontief’s
paradox.
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Heckscher-Ohlin Model
• Why would this paradox exist?
• U.S. and foreign technologies are not the same as
assumed.
• By focusing only on labor and capital, land abundance
in the U.S. was ignored.
• No distinction between skilled and unskilled labor.
• The data for 1947 could be unusual due to the recent
end of WWII.
• The U.S. was not engaged in completely free trade as
is assumed by the HO model.
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Heckscher-Ohlin Model
• Several of the explanations depend on having
more than two factors of production.
 The U.S. is land abundant, and much of what it was
exporting might have been agricultural products which
use land intensively.
 It might also be true that many of the exports used
skilled labor intensively.
• More current research was aimed at redoing the
Leontief test.
 The “extended” HO model works much better for the
same year of data.
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Effects of Trade on Factor Prices
• How do the changes in pre-trade and post-trade relative
prices affect the wage paid to labor in each country and
the rental earned by capital?
 Remember the relative price of computers in Home increase,
causing them to export computers.
 The relative price of computers in Foreign decreases, causing
them to import computers.
• Effect of Trade on the Wage and Rental rate of Home
 Derive an economy-wide relative demand for labor.
 Compare it to the economy-wide relative supply of labor, L/K.
 This will determine Home’s relative wage and what happens after
the relative price of computers changes.
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Effects of Trade on Factor Prices
• Economy-Wide Relative Demand for Labor
 K = KC + KS and L = LC + LS
 We can divide total labor by total capital to get the
relative supply equal to the relative demand.
• The relative demand is a weighted average of the
labor-capital ratio to each industry.
LC  LS
LC  KC
L



K
K
KC  K
Relative Supply
 LS  K S 



 KS  K 
Relative Demand
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Effects of Trade on Factor Prices
• The relative demand curve is an average of the labor
demand curves for each industry.
• The relative demand
curve therefore lies
between these two
curves.
Figure 4.6
• Where the curves
intersect gives the
wage to rental rate
ratio: W/R.
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Effects of Trade on Factor Prices
The increase in Pc/Ps
causes a shift in resources
from shoes into computer
production. This puts more
weight on the computer
sector.
Figure 4.8
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Effects of Trade on Factor Prices
• How does this happen?
 More labor per unit of capital is released from shoes than is
needed to operate that capital in computers.
 As the relative price of computers rises, computer output
rises while shoe output falls.
 Labor is “freed up” to be used more in both industries.
LC  KC  LS  K S 
L





K KC  K  K S  K 
Relative Supply
Relative Demand
No change
No change in total
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Effects of Trade on Factor Prices
• Determination of the Real Wage and Real Rental
Rate.
 Who gains and who loses from the change in the
relative price of computers?
 We need to determine the change in the real wage and
real rental.
 The change in the quantity of shoes and computers that
each factor of production can purchase.
 Real rental rate: R/PS and R/PC
 Real wage: W/PC and W/PS
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Effects of Trade on Factor Prices
• Change in the Real Rental Rate
 Because the labor/capital ratio increases in both
industries, the marginal product of capital increases.
 There are more people to work with each unit of capital.
 The rental rate of capital is determined by its marginal
product.
 R = PC*MPKC and R = PS*MPKS
 Rearranging we get:
 MPKC = R/PC and MPKS = R/PS
An increase in the relative price of a good will benefit the
factor of production used intensively in producing that
good.
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Effects of Trade on Factor Prices
• Change in the Real Wage
 Since the labor/capital ratio increases in both
industries, the marginal product of labor must decrease
in both industries.
 As before the wage is determined by the marginal
product of labor and the price of goods.
 W = PC*MPLC and W = PS*MPLS
 Rearranging
 MPLC = W/PC and MPLS = W/PS
 Labor is clearly worse off due to the increase in the
price of computers.
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Effects of Trade on Factor Prices
• The 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.
• Therefore, in the Heckscher-Ohlin model:
The abundant factor gains from trade, and the
scarce factor loses from trade.
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Effects of Trade on Factor Prices
• A Numerical Example
 Suppose we have the following data:
 Computers
Sales Revenue = PCQC = 100
Earnings of labor = WLC = 50
Earnings of capital = RKC = 50
 Shoes
Sales Revenue = PSQS = 100
Earnings of labor = WLS = 60
Earnings of capital = RKS = 40
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Effects of Trade on Factor Prices
• Shoes are more labor-intensive than computers.
 The share of total revenue paid to labor in shoes (60%)
is more than the share in computers (50%).
• When trade opens, the relative price of computers,
PC, increases while the price of shoes, PS, does not
change.
 Computers: % increase in price = ΔPC/PC = 10%
 Shoes:
% increase in price = ΔPS/PS = 0%
• Our goal is to see how the increase in the relative
price of computers translates into long run changes in
the wage and rental.
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Effects of Trade on Factor Prices
• The rental rate on capital
is calculated by taking
payments to capital and
dividing by the amount of
capital:
• Apply the following
assumptions:
ΔPC > 0 and ΔPS = 0,
to the last equations:
PC  QC  W  LC
R
KC
PS  QS  W  LS
R
KS
PC  QC  W  LC
R 
KC
0  QS  W  LS
R 
KS
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Effects of Trade on Factor Prices
• Rewrite the last
equation in
percentage
changes:
• Plugging in data
from before:
R  PC  PC  QC   W   W  LC 





R  PC  R  KC   W   R  K C 
R
W   W  LS 

 


R
W
R

K


S 
R
 100   W  50 
 10%

 
R
 50   W  50 
R
 W  60 
 
 
R
 W  40 
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Effects of Trade on Factor Prices
• After solving we get:
 (ΔW/W) = -(20%/0.5) = -40%
 When the price of computers increases by 10%, the
wage falls by 40%
 The real wage, measured in terms of either good, has
fallen, so labor is worse off.
• We can also see:
 (ΔR/R) = -(ΔW/W)(60/40) = 60%
 Rental on capital increases by 60% when the price of
computers rises by 10%
 The real rental measured in terms of either good has
gone up, and capital owners are clearly better off.
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Effects of Trade on Factor Prices
• General Equation for the Long-Run Change in Factor
Prices
 In summary, for an increase in PC
 ΔW/W < 0 < ΔPC/PS < ΔR/R
 Real wage falls, real rental increases
• We see what is referred to as a ‘magnification effect’
 They show how changes in the prices of goods have
magnified effects on the earnings of factors.
 Even modest fluctuations in the relative prices of goods
on world markets can lead to exaggerated changes in
the long-run earnings of both factors.
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Opinions Toward Free Trade
APPLICATION
• A survey was conducted in the U.S. by the
National Elections Studies (NES) in 1992 to see
how citizens viewed trade.
 Respondents could either answer that they favor
placing limits on imports, not supporting free trade, or
they could oppose limits on imports, supporting free
trade.
 How do these answers compare with characteristics of
the respondents, such as their wages, skills, or the
industries they work in?
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Opinions Toward Free Trade
APPLICATION
• If labor earns some of the return to capital, then workers in
exporting (importing) industries will support (oppose) free
trade.
• In the short run, the industry of employment of workers will
affect their attitudes toward free trade.
• In the long run HO model, the industry of employment
should not matter.
• In the long run then, the skill level of workers should
determine their attitudes toward free trade.
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Opinions Toward Free Trade
APPLICATION
• In the NES survey, the industry of employment was
somewhat important in explaining respondents’ attitudes
toward free trade, but skill level was much more important.
 Workers in export-oriented industries are somewhat more likely to
favor free trade.
 Those in import-competing industries favoring import restrictions.
• A much more important determinant of the attitudes
toward free trade is the skill level of workers, measured by
wages or years of education.
 This suggests respondents are considering long run earnings as
predicted by HO and Stolper-Samuelson.
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Opinions Toward Free Trade
APPLICATION
• Respondents were also asked if they owned a home.
• People who owned homes in communities where the local
industries face a lot of import competition are much more
likely to oppose free trade.
• People who owned homes in communities where the
industries benefit from export opportunities are more likely
to support free trade.
• People are concerned about the asset value of their
homes, just like the owners of specific-factors in our model
are concerned about the rental earned by the factor of
production they own.
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Extending the Heckscher-Ohlin Model
• We need to make the HO model more realistic by
allowing for more than two goods, factors, and
countries.
• As the second modification, we will allow the
technologies used to produce each good to differ across
countries.
• Many Goods, Factors, and Countries
 The predictions of the HO model depend on knowing what
factor a country has in abundance, and which good uses
that factor intensively.
 When there are more than two goods, it is more complicated
to evaluate factor intensity and factor abundance.
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Extending the Heckscher-Ohlin Model
• Measuring the Factor Content of Trade
 How do we measure the factor intensity of exports and
imports when there are thousands of products traded
between countries?
 How can we use this to test the HO model?
• Measuring the Factor Content of Trade
 Using Leontief’s test, we can look at similar data.
 We can multiply his numbers shown in Table 4.2 by the
actual value of U.S. exports and U.S. imports.
 This gives values for “total exports” and “total imports.”
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Extending the Heckscher-Ohlin Model
• These values are called the factor content of exports
and factor content of imports.
• By taking the difference between the factor content of
exports and factor content of imports.
 This gives factor content of net exports, shown in the final
column of 4.2.
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Extending the Heckscher-Ohlin Model
• Measuring the Factor Content of Trade
 Since both these factor contents are positive, we see
that the U.S. was running a trade surplus.
• Measuring Factor Abundance
 How should we measure factor abundance when there
are more than two factors and two countries?
 Compare the country’s share of that factor with its
share of world GDP.
 If the share of a factor > share of world GDP.
 The country is abundant in that factor.
 If the share of factor < share of world GDP.
 The country is scarce in that factor.
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Extending the Heckscher-Ohlin Model
Country Factor Endowments, 2000
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Figure 4.9
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Extending the Heckscher-Ohlin Model
• Capital Abundance
 For example, 24% of the world’s physical capital is located in the
U.S., which had 21.6% of world GDP.
 We can conclude that the U.S. was abundant in physical capital in
2000.
• Labor and Land Abundance
 U.S. is abundant in R&D scientists: 26.1% of the world’s total as
compared to 21.6% of the world’s GDP.
 The U.S. is also abundant in skilled labor but is scarce in lessskilled labor and illiterate labor.
 India is scarce in R&D scientists: 2.5% of world’s total as
compared to 5.5% of the world’s GDP.
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Extending the Heckscher-Ohlin Model
• Labor and Land Abundance
 The U.S. is also scarce in arable land which is
surprising since we think of the U.S. as a major
exporter of agriculture.
 Another surprise is that China is abundant in R&D
scientists.
 These findings seem to contradict HO model.
 It is likely that the productivity of R&D scientists and
arable land are not the same in both countries.
 We need to allow for differences in productivity.
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Extending the Heckscher-Ohlin Model
• Differing Productivities Across Countries
 Remember that Leontief found that the U.S. was
exporting labor-intensive products even though it was
capital-abundant at that time.
 One explanation is that labor is highly productive in the
U.S. and less productive in the rest of the world.
 Then the effective labor force in the U.S. is much larger than if
we just count people.
 Effective labor force is the labor force times its productivity.
 We can now look at differing productivities into the HO
model.
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Extending the Heckscher-Ohlin Model
• Measuring Factor Abundance Once Again
 Effective Factor Endowment is the actual factor
endowment times the factor productivity.
 To determine if a country is abundant in a certain factor,
we compare the country’s share of that effective factor
with share of world GDP.
 If share of an effective factor is less than its share of world GDP
then that country is abundant in that effective factor.
 If share of an effective factor is less than its share of world GDP,
then that country is scarce in that effective factor.
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Extending the Heckscher-Ohlin Model
• Effective R&D Scientists
 On way to measure this is through a country’s R&D spending per
scientist.
 Take the total number of scientists and multiply that by the R&D
spending per scientists
 With these productivity corrections, the U.S. is more abundant in
effective R&D scientists and China is lower.
• Effective Arable Land
 Effective arable land is the actual amount of arable land times the
productivity in agriculture.
 The U.S. has a very high productivity in agriculture where China
has a lower productivity.
 The U.S. is neither scarce nor abundant in effective arable land.
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Extending the Heckscher-Ohlin Model
“Effective” Factor Endowments, 2000
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Figure 4.10
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Food Imports Close to Matching
Level of Exports
HEADLINES
• It is expected that by about 2010, U.S. imports of
agricultural goods will be about equal to exports.
• That is what the HO model would predict, given
our finding that the U.S. is neither abundant nor
scarce in effective land.
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Extending the Heckscher-Ohlin Theorem
• We have now abandoned many of the
assumptions we previously made.
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We allow for many goods, factors, and countries.
We also allow for factors to differ in productivity.
A new version called the “sign test” is available.
If a country is abundant in an effective factor, then the
factor’s content in net exports should be positive.
 If a country is scarce in an effective factor, then that
factor’s content in net exports should be negative.
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Extending the Heckscher-Ohlin Theorem
• The sign test is as follows
 Sign of (country’s % share of effective factor minus the %
share of world GDP) equals Sign of (Country’s factor content
of net exports).
 Using 35 countries, the U.S. share of GDP of those
countries was 33%.
 Given the timing after WWII, we can assume that the U.S.
share of world capital was more than 33%.
 Therefore, the U.S. was abundant in capital and since that
factor’s content of net exports was positive, it passes the
sign test.
 The U.S. share of population for the 35 countries was about
8%.
 Therefore, the U.S. was scarce in labor.
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Extending the Heckscher-Ohlin Theorem
• But labor’s factor content of net exports was positive.
• The sign test seems to fail for the U.S. in 1947 in labor.
• However, the U.S. share of the population is not the right
way to measure the U.S. labor endowment.
• One way to measure productivity is to use wages paid to
workers.
• The effective amount of labor found in each country equals
the actual amount of labor times the wage.
 The amount of labor in each country times the average
wages gives total wages paid to labor.
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Extending the Heckscher-Ohlin Model
Figure 4.11
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Extending the Heckscher-Ohlin Theorem
• Doing this for 30 countries and comparing it to the U.S. we
find that the U.S. was abundant in effective labor.
• Given that the U.S. was abundant in effective factor, then
labor also passes the sign test, in addition to capital.
• There is no “paradox” in the U.S. pattern of trade.
• This explanation for Leontief’s paradox relies on taking
into account the productivity differences in labor across
countries.
 As Leontief himself proposed, once we take into account
differences in the productivity of factors across countries, there is
no “paradox” after all.
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Why does India Import Cotton Textiles?
APPLICATION
• From the 17th century until the early 19th century, India was
a major world producer of cotton textiles and exported
those goods to Britain and elsewhere.
• By the early 19th century, however, Britain had overtaken
India as the world’s dominant producer of cotton textiles
and was exporting to India.
• India still produced raw cotton needed to manufacture
cotton cloth—the raw cotton was exported to Britain.
• A similar trade pattern held for China and Egypt.
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Why does India Import Cotton Textiles?
APPLICATION
• These countries are all labor abundant rather than land
abundant, therefore it is puzzling why they seem to be net
exporters of land and net importers of labor.
• Two explanations
1. Britain’s rise as the world’s leading exporter of cotton
textiles was related to technological improvements.
 However India was able to gain access to this technology.
 Then the importing of textiles is contrary to the HO model.
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Why does India Import Cotton Textiles?
APPLICATION
2. The poor countries used this new technology
to make textiles inefficiently.
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•
•
•
Large differences in efficient use of technology across countries remained. .
This inefficiency applied more strongly to labor than it did to
other factors such as land.
Estimates from 1910 and 1990 show that labor was not
necessarily the abundant factor in India once we take into
account its low productivity.
India could be considered land-abundant if land and labor
are measured by their “effective” amounts.
This can explain the switch from exporter to importer.
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