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Chapter 5
Resources and
Trade: The HeckscherOhlin Model
Introduction
• So far we learned that:
– Free trade leads to higher average real income per capita
– But not everyone within the country is better off
• In the Specific Factors Model opening a country to trade creates
winners and losers:
– The real return to the factor specific to the expanding (or
export) industry increases
– The real return to the factor “stuck” in contracting (or import)
industry decreases
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Introduction
• The specific-factors model is a short-run model because some
factors cannot relocate across sectors.
What is the impact of trade on income
distribution in the long run?
• We develop a long run version of the multi-factor model: the
Heckscher-Ohlin model.
– 2 factors: capital (K) and labor (L)
– Both are perfectly mobile across sectors (long run
assumption)
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Introduction
• Recall that there are potential gains from trade whenever there is
cross-country variation in autarky prices.
• In the Ricardian model, differences in autarky prices come from
differences in technologies across countries.
• In the Heckscher-Ohlin Model (as in the Specific Factors Model):
– Technologies are the same in all countries
– Trade patterns are explained by cross-country differences in
relative factor endowments
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Introduction
• A country is capital-abundant if the ratio of capital to labor
available in the economy is large compared to other countries.
• A good is capital-intensive if the ratio of capital to labor used in
its production is high compared to other goods.
• Cross-country differences in factor abundance interact with
differences in factor intensity to generate cross-country
dispersion in relative autarky prices.
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Introduction
– Countries differ in their capital-abundance
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Introduction
– Goods differ in their capital-intensity
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Heckscher-Ohlin Model
• The Heckscher-Ohlin model is a 2x2x2 model
– 2 countries: Home and Foreign (*)
– 2 goods: Computers (C) and Shoes (S)
– 2 factors of production: Labor (L) and Capital (K)
• The factor market clearing conditions are:
K C + KS = K
and
L C + LS = L
K *C + K *S = K *
and
L*C + L*S = L*
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Heckscher-Ohlin Model
Assumption 1: Both factors can move freely between the industries
(long run assumption) – but cannot move between countries.
Assumption 2: Shoes are labor-intensive (this is without loss of
generality).
L C LS
<
K C KS
This implies that the relative demand for labor is higher in the shoes
sector for any factor prices.
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Heckscher-Ohlin Model
• An increase in the relative price of labor (wage/rental) decreases the
relative demand for labor in both industries.
• Because shoes are labor-intensive, the relative demand for labor is
always higher in the shoe industry.
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Heckscher-Ohlin Model
Assumption 3: Home is capital abundant (again without loss of
generality):
K K*
> *
L L
• We can use assumptions 2 and 3 to derive the PPF for each
country
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Heckscher-Ohlin Model
• Home is capital abundant, and
computers are capital-intensive
Qs
Foreign PPF
• Home is capable of producing
relatively more computers than
shoes compared to Foreign.
• More generally, the PPF of a
country is skewed towards the
good that is intensive in the
abundant factor.
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Home PPF
Qc
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Heckscher-Ohlin Model
Assumption 4: The final outputs (shoes and computers) can be
traded at no cost between countries, but inputs (labor and capital)
cannot move between countries.
Assumption 5: The technologies are the same in both countries.
Assumption 6: Preferences are the same in both countries and can be
represented by well-behaved indifference curves.
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Heckscher-Ohlin Model
In equilibrium, the slope of the PPF (MRT) is equal to the slope of
the indifference curve (MRS) and the relative price:
MRT = MRS = - PC PS
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Heckscher-Ohlin Model
• The autarky relative price of computer is higher in Foreign
• This reflect the variation in relative factor endowment across
countries.
– Home is capital-abundant and has a comparative advantage in
the production of the capital-intensive good (computers).
– Foreign is labor-abundant and has a comparative advantage in
the production of the labor intensive good (shoes).
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Heckscher-Ohlin Model
§ Autarky (point A):
production and
consumption are equal.
QS
Slope = –(PC/PS)W
§ Trade increase the relative
price of computers at
Home: supply (point B)
and demand (point C).
§ Home exports C and
imports S
A
U1
B
PPF
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§ The rise in utility from U1
to U2 is a measure of the
gains from trade for the
QC economy.
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The Four Theorems
• Which good does each country export? (Heckscher-Ohlin
theorem)
• What is the impact of trade on real factors prices (i.e., welfare)?
(Stopler-Samuelson theorem)
• What is the impact of changes in endowments on production?
(Rybsczynski theorem)
• Do factor prices differ across countries? (Factor price
equalization theorem)
• H.O. model notes.
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Theorems
• Heckscher-Ohlin Theorem: An economy will export the good
that is intensive in its abundant factor of production and import
the good that is intensive in its scarce factor of production.
• Stopler-Samuelson Theorem: In the long run when all factors of
productions 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.
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Theorems
• Rybczynski Theorem: If the relative commodity prices are
constant and if both commodities continue to be produced, an
increase in the supply of a factor will lead to an increase in the
output of the commodity using that factor intensively and a
decrease in the output of the other commodity.
• Factor Price Equality Theorem: Under identical constant
returns to scale production technologies, free trade in
commodities will equalize relative factor prices through the
equalization of relative commodity prices, so long as both
countries produce both goods.
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Stopler-Samuelson Theorem
§ There is an increase in the
price of shoes
K
I
RB
I
RA
Computer
§ The shoes isovalue shifts
down
ShoesA
B ShoesB
§ The slope of the isocost
tangent to both isoquant is
now steeper –W/R is higher.
A
B
I
WB
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§ The capital-labor ratio goes
up in both sectors
A
I
WA
L
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Rybczynski Theorem
K
L1
Computer
E1
K
L2
E2
KC1
Shoes
KC2
LS1
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L1
LS2 L2
L
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Empirical Evidence
1. Leontief’s Paradox
• HO theorem: Countries export the good that is intensive in their
abundant factor of production.
• Wassily Leontief performed the first test of the Heckscher-Ohlin
theorem in 1953 using data for the U.S. from 1947.
• In 1947 the U.S. was capital abundant relative to the rest of the
world.
– The U.S. should export capital intensive goods and import
labor intensive goods.
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Empirical Evidence
• He measured the amounts of labor and capital (direct and
indirect) used to produce $1 million of U.S. exports and to
produce $1 million of imports into the U.S.
• It was impossible for Leontief to get information on the amount
of labor and capital used to produce imports.
– But the H.O. model assumes that technologies are the same
across countries.
– He used data on U.S. technology to calculate estimated
amounts of labor and capital used in imports from abroad.
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Empirical Evidence
Leontief’s Data
• In 1947, 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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Empirical Evidence
Baldwin’s test
• 1947 is just after the 2nd world war: maybe data is not
representative
• Baldwin tested the Heckscher-Ohlin theory using US trade data
from 1962 and production information from 1958
• His results “confirm” the Leontief paradox
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Empirical Evidence
2. Sign Test
• We can make the HO model more realistic by allowing for more
than two goods, factors, and countries.
• How do we measure factor abundance when there is more than
two inputs?
– We can compare the country’s share of a factor (SF) with its
share of world GDP (SGDP).
– If SF > SGDP, the country is abundant in that factor.
– If SF < SGDP, the country is scarce in that factor.
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Empirical Evidence
• The sign test is based on the idea that trade in goods is an indirect
way of trading factors of production
• Countries should be net-exporter of their abundant factor.
Sign of ( Factor share – GDP share)
=
Sign of factor content of net export
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Empirical Evidence
• Consider a world with 2 countries and 3 factors
– Suppose that the factors are evenly distributed across
countries.
– Since technologies are the same: SF1 = SF2 = SF3 = SGDP = 1/2
– Now suppose we move all of factor 1 to country 1 and all of
factor 2 to country 2 but GDP is still ½
SF2 = 0 < SF3 = ½ = SGDP = ½ < SF1 =1
SF1 = 0 < SF3 = ½ = SGDP = ½ < SF2 = 1
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Empirical Evidence
• Since income is the same and preferences are the same the factor
content of consumption will also be the same in both countries
• but the factor content of production is not the same.
– Country 1 has factor 1
– Country 2 has factor 2
• The factor content of net export will reflect changes in relative
factor endowment across countries
– Country 1 will “export” factor 1
– Country 2 will “export” factor 2
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Empirical Evidence
Bowen, Leamer and Sveikauskas (1987) applied the sign test in a
sample of 27 countries and 12 factors of production.
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Empirical Evidence
3. Relaxing assumptions of the HO model
(A1) The strongest assumption is that technology is the same across
countries
Estimated Technological Efficiency relative to United States
(i.e., US wages = 1), 1983
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Empirical Evidence
• Other assumptions include
(A2) Countries produce the same goods
(A3) Prices are the same across countries (no barriers
to trade)
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Conclusions
• The HO framework is one of the most widely used models to
explain trade patterns.
• It isolates the effect of differences in relative factor endowments
across countries and determines the impact of these differences
on trade patterns, relative prices, and factor returns.
• By focusing on the differences in relative factor intensities among
goods, the HO model also provides clear guidance as to which
factor gains and which factor loses from trade.
• On its own, the HO model does not do a particularly good job of
explaining trade patterns – we need technological differences.
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