Trade and Resources: The
Heckscher-Ohlin Model
Professor Ralph Ossa
33501 International Commercial Policy
International Commercial Policy
The Heckscher-Ohlin Model
Introduction
Remember that countries trade either because they are
different from one another or because of increasing
returns to scale.
Countries may differ from one another in terms of
technology, endowments, or preferences.
The Ricardian model emphasized technological
differences but abstracted from endowment differences.
The Heckscher-Ohlin model instead emphasizes
endowment differences but abstracts from technological
differences.
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International Commercial Policy
The Heckscher-Ohlin Model
Introduction (cont.)
This is interesting because factor endowments certainly
play a role in shaping the pattern of trade. For example,
the U.S. exports orange juice to Canada not because its
Orange farmers are inherently more productive but
because it is endowed with good weather in Florida.
It is also interesting because it introduces distributional
issues without which it is hard to make sense of
protectionism. While there will still be overall gains from
trade, there will now be individual winners and losers
from trade.
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International Commercial Policy
The Heckscher-Ohlin Model
Overview of the lecture
Develop the Heckscher-Ohlin model: (i) setup, (ii)
autarky equilibrium, (iii) free trade equilibrium, (iv) gains
from trade.
Provide some empirical evidence on the HeckscherOhlin model.
Along the way, consider some real-world applications of
the Heckscher-Ohlin model.
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International Commercial Policy
The Heckscher-Ohlin Model
Setup
There are two countries: Home and Foreign, two goods: food
and cloth, and two factors of production: labor and land.
Countries differ in their factor endowments. Home is labor
abundant relative to Foreign, in the sense that Home is
endowed with relatively more labor:
L/T > L*/ T*.
Countries share the same technology. Cloth production is
labor intensive relative to food production, in the sense that
cloth production uses relatively more labor for all factor
prices:
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aLC/aTC > aLF/aTF
International Commercial Policy
The Heckscher-Ohlin Model
Setup: Application
By assuming that technologies are the same across
countries, we rule out factor intensity reversals across
countries.
If the production of one good is labor intensive relative
to the production of another good in one country we
also assume the same to be the case in the other
country.
However, this assumption does not always hold in
practice. For example, shoe production is capital
intensive relative to call center service production in the
U.S. while the opposite is true in India.
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International Commercial Policy
The Heckscher-Ohlin Model
Setup (cont.)
Technology features constant returns to scale and
diminishing marginal products.
All markets are perfectly competitive.
As one consequence, food and cloth producers take
prices and wages as given.
As another consequence workers are paid a
competitive wage and land-owners are paid a
competitive rent.
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: PPF
One can show that the opportunity cost of producing
cloth in terms of food is not constant in this model.
It is low when the economy produces a low amount of
cloth and a high amount of food.
It is high when the economy produces a high amount of
cloth and a low amount of food.
As a consequence, the PPF becomes curved.
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The Heckscher-Ohlin Model
Autarky: PPF (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Production and prices
The production possibility frontier describes what an
economy can produce, but to determine what the
economy does produce, we must consider the prices of
goods.
Perfect competition and profit maximization imply that
the economy produces at the point that maximizes the
value of production, V:
V = P C Q C + P FQ F
where PC is the price of cloth and PF is the price of food.
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Autarky: Production and prices (cont.)
Define an isovalue line as a line representing a
constant value of production, V.
V = P C Q C + P FQ F
 P FQ F = V – P C Q C
 QF = V/PF – (PC /PF)QC
The slope of an isovalue line is – (PC /PF).
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Production and prices (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Production and prices (cont.)
For given prices, production at point Q thus yields the
highest feasible value of production. This is where the
economy will produce.
At that point, the slope of the PPF equals – (PC /PF), so
the opportunity cost of cloth equals the relative price of
cloth.
In other words, the trade-off in production equals the
trade-off according to market prices.
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Autarky: Production and prices (cont.)
Notice that an increase in the price of cloth relative to
the price of food therefore leads to an increase in the
production of cloth relative to the production of food.
This relationship between relative prices and relative
production can again be captured by a relative supply
curve.
Notice, however, that the relative supply curve is no
longer kinked as it was in the Ricardian model since the
PPF is no longer a straight line in the Heckscher-Ohlin
model.
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The Heckscher-Ohlin Model
Autarky: Production and prices (cont.)
Relative price
of cloth, PC/PF
RS
Relative domestic
quantity of cloth, QC
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QF
International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Preview comparative advantage
Ultimately, we want to understand how cross-country
differences in endowments influence the pattern of
trade.
Recall that countries export the good in which they have
a comparative advantage. Recall also that having a
comparative advantage means having lower opportunity
costs or production. Recall finally that having lower
opportunity costs of production comes along with having
a lower autarky relative price.
Hence, to understand how cross-country differences in
endowments influence the pattern of trade we need to
understand how such differences influence autarky
relative
prices.
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Preview comparative advantage (cont.)
Since we assume that preferences are the same in both
countries so that the relative demand curves are the
same in both countries, cross-country differences in
endowments only influence autarky relative prices if
they are associated with differences in the countries’
relative supply curves.
Hence, to understand how cross-country differences in
endowments influence the pattern of trade, we need to
understand how they are reflected in cross-country
differences in the relative supply curves.
To that end, we simply consider one country’s relative
supply curve and see how it shifts in response to
changes
in that country’s endowment.
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Preview comparative advantage (cont.)
To understand how a country’s relative supply curve
shifts in response to changes in that country’s
endowment, we proceed in a number of steps.
First, we show that relative goods prices determine
relative factor prices.
Second, we show that relative factor prices determine
factor intensities.
Finally we show how, for given factor intensities,
endowment changes affect relative production.
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Goods prices and factor prices
In competitive markets, the price of a good should be
reduced to the cost of production. In our model, the cost
of production depends on the wage rate w, and the land
renting rate r.
The effect of changes in the wage rate depend on the
intensity of labor services in production. The effect of
changes in the land renting rate depend on the intensity
of land usage in production.
An increase in the wage rate should affect the price of
cloth more than the price of food since cloth is the labor
intensive industry. Changes in w/r are therefore directly
related to changes in PC/PF .
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The Heckscher-Ohlin Model
Autarky: Goods prices and factor prices (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Factor prices and factor intensities
Producers may choose different amounts of factors of
production to make cloth or food.
Their choice depends on the wage rate and the land
renting rate. As the wage rate increases relative to the
land renting rate, producers use less labor services and
more land in the production of food and cloth.
However, since food production is land intensive and
cloth production is labor intensive, producers are using
relatively more land for food production for all wage
rental ratios.
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Factor prices and factor intensities (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Relative endowments and relative
production
Since the economy produces at the point that
maximizes the value of production, all resources are
employed in equilibrium.
The allocation of resources to sectors can be
represented in the following diagram:
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The Heckscher-Ohlin Model
Autarky: Relative endowments and relative
production (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Relative endowments and relative
production (cont.)
For given output prices, how do outputs change if
endowments change?
Recall that holding output prices constant, means
holding factor prices constant, which in turn means
holding factor intensities constant.
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Relative endowments and relative
production (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Relative endowments and relative
production (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Relative endowments and relative
production (cont.)
Rybczynski theorem: For given relative goods prices,
an increase in the endowment of a factor will increase
output in the sector that uses this factor intensively, and
will decrease output in the other sector.
Together with constant returns to scale, this implies
that, for given relative goods prices, a higher labor-land
ratio comes along with a higher relative cloth
production.
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The Heckscher-Ohlin Model
Autarky: Putting the pieces together
Recall that Home is labor abundant and Foreign is
land abundant, in the sense that Home is endowed
with relatively more labor than Foreign: L/T > L*/ T*.
Hence, Home’s relative cloth supply will be larger than
Foreign’s relative cloth supply for any relative cloth
price.
As a consequence, Home’s autarky relative cloth price
will be below Foreign’s relative cloth price so that Home
will have a comparative advantage in cloth production.
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International Commercial Policy
The Heckscher-Ohlin Model
Autarky: Putting the pieces together (cont.)
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International Commercial Policy
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Autarky: Putting the pieces together (cont.)
Heckscher-Ohlin theorem (first variant): A country
has a comparative advantage in the good that uses its
abundant factor intensively.
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The Heckscher-Ohlin Model
Trade: Pattern of trade
Again, prices must be equalized with trade to rule out
arbitrage opportunities.
Hence, the relative price of cloth rises in the labor
abundant country (Home) and falls in the labor scarce
country (Foreign) if trade is liberalized.
 In Home, the rise in the relative price of cloth leads to a
rise in the relative supply of cloth and a fall in relative
demand of cloth; Home becomes an exporter of cloth and
an importer of food.
 The decline in the relative price of cloth in Foreign leads it
to become an importer of cloth and an exporter of food.
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Trade: Pattern of trade (cont.)
Heckscher-Ohlin theorem (second variant): A
country exports the good that uses its abundant factor
intensively.
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International Commercial Policy
The Heckscher-Ohlin Model
Trade: Goods prices and factor prices
The close relationship between goods prices and factor
prices discussed earlier, has two important additional
implications.
The first is summarized by the Stolper-Samuelson
theorem.
The second is summarized by the factor prize
equalization theorem.
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International Commercial Policy
The Heckscher-Ohlin Model
Trade: Stolper-Samuelson theorem
Stolper-Samuelson theorem: An increase in the
relative price of a good will increase the real return to
the factor used intensively in the production of that
good, and will decrease the real return to the other
factor, in terms of both goods.
Notice that, together with the Heckscher-Ohlin theorem,
this implies that the owners of the abundant factor gain
but the owners of the scarce factor lose if trade is
liberalized. Hence, trade can have important
distributional consequences.
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Trade: Stolper-Samuelson theorem (cont.)
For example, an increase in the relative price of cloth
will increase the real return to labor and decrease the
real return to land, in terms of both cloth and food.
Intuitively, this is because the increase in the relative
price of cloth leads to an increase in the wage-rental
ratio, which leads to an increase in the land-labor ratio
employed in cloth and food production.
This then increases (decreases) the real return to labor
(land) since real factor returns are given by marginal
products and the marginal product of labor (land) is
increasing (decreasing) in the land-labor ratio.
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International Commercial Policy
The Heckscher-Ohlin Model
Trade: Stolper-Samuelson theorem (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Trade: Factor price equalization theorem
Moreover, the Heckscher-Ohlin model predicts that
factor prices will be equalized among trading countries.
This result is known as the factor price equalization
theorem.
Because output prices are equalized and because of
the direct relationship between output prices and factor
prices, factor prices are also equalized.
Intuitively, trade increases the demand of goods
produced by abundant factors, indirectly increasing the
demand of the abundant factors themselves, raising the
prices of the abundant factors across countries.
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International Commercial Policy
The Heckscher-Ohlin Model
Trade: Factor price equalization theorem (cont.)
Of course, factor prices are not really equal across
countries.
Three counterfactual assumptions are driving this
counterfactual prediction.
First, the model assumes that both countries have the
same technology. Second, the model assumes that
both countries produce both goods. Third, the model
assumes that there are no trade costs.
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Gains from trade
We have already established that the owners of the
abundant factor gain but the owners of the scarce factor
lose if trade is liberalized.
However, the owners of the abundant factor gain more
than the owners of the scarce factor lose in the sense
that the owners of the abundant factor could
compensate the owners of the scarce factor for their
losses and still be better off.
Hence, while some people gain and some people lose
from trade, the economy as a whole still gains from
trade in the Heckscher-Ohlin model.
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Gains from trade (cont.)
The economy as a whole still gains from trade since
trade expands the economy’s consumption possibilities.
Under autarky, domestic consumption has to equal
domestic production.
Under trade, however, domestic consumption can differ
from domestic production, since domestically produced
goods can be exchanged for foreign produced goods at
world market prices.
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Gains from trade (cont.)
Consumption of food, DF
Output of food, QF
Consumption possibilities under trade exceed
consumption possibilities under autarky. The
consumption point no longer coincides with the
production point since the economy can
exchange goods at world prices.
Production and
consumption under
autarky
Production under trade
Slope = -(PC/PF)AUTARKY
Slope = -(PC/PF)TRADE
Consumption of cloth, DC
Output of cloth, QC
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International Commercial Policy
The Heckscher-Ohlin Model
Evidence
At first sight, the evidence on the Heckscher-Ohlin
model is confusing. Some studies seem to find that the
Heckscher-Ohlin model does poorly, while others seem
to find that the Heckscher-Ohlin model does well.
On closer inspection, the following message emerges:
The factor price equalization version of the HeckscherOhlin model does poorly. However, once the
assumptions underlying the factor price equalization
theorem are relaxed, the Heckscher Ohlin model does
well.
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International Commercial Policy
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Evidence: Leontief (1953)
Leontief (1953) was the first to confront the HeckscherOhlin model with the data. He considered the simple
factor price equalization version.
At the time of his study, the U.S. was the most capital
abundant country in the world. Hence, he expected U.S.
exports to be capital intensive and U.S. imports to be
labor intensive.
However, he found exactly the opposite. This result
became known as the Leontief paradox.
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Evidence: Bowen et al. (1987)
While Leontief (1953), tested the basic two-factor, twogood version of the Heckscher-Ohlin model, Bowen,
Leamer, and Sveikauskas (1987) repeated his analysis
using a multi-factor, multi-good version of the
Heckscher-Ohlin model.
However, the multi-factor, multi-good version they
considered also featured factor price equalization.
As a consequence, the empirical performance of the
model was again poor.
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International Commercial Policy
The Heckscher-Ohlin Model
Evidence: Trefler (1995)
Trefler (1995) was the first to consider a non-factor
price equalization version of the Heckscher-Ohlin
model.
Remember that the factor price equalization theorem
rests on three main assumptions: (i) all countries have
the same technology, (ii) all countries produce all
goods, (iii) there are no trade costs.
Trefler (1995) allowed for cross-country differences in
technology and found that the model performed much
better.
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International Commercial Policy
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Evidence: Davis and Weinstein (2001)
Davis and Weinstein (2001) relaxed the second
assumption of the factor price equalization theorem and
allowed for complete specialization.
Again, the model performed much better.
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Evidence: Romalis (2004)
Former Chicago Booth professor John Romalis, relaxed
the third assumption of the factor price equalization
theorem and allowed for costly international trade.
Again, the model performed much better.
His results suggest that countries indeed export
disproportionate amounts in industries that use their
abundant factor intensively.
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International Commercial Policy
The Heckscher-Ohlin Model
Evidence: Romalis (2004) (cont.)
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International Commercial Policy
The Heckscher-Ohlin Model
Evidence: Romalis (2004) (cont.)
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International Commercial Policy
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Evidence: Romalis (2004) (cont.)
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