Chapter Five:
Factor Endowments and the
Heckscher-Ohlin Theory
By Rajkumar, Assistant Professor
College of Vocational Studies
5.2 Assumptions of the Theory
A. The Assumptions
1) There are two nations (1&2), two commodities
(X&Y), two factors of production (labor & capital).
Used to illustrate the theory in a two-dimensional figure.
2) Both nations use the same technology in production.
Means both nations have access to and use the same
general production techniques.
3) Commodity X is labor intensive and Y is capital
intensive in both nations.
Means the labor-capital ratio (L/K) is higher for X than Y
in both nations at the same relative factor prices.
4) Both commodities are produced under constant
returns to scale in both nations.
Means that increasing the amount of L and K will
increase output in the same proportion
5) There is incomplete specialization in production in
both nations.
Means that even with free trade both nations continue
to produce both commodities. This implies neither
nation is very small.
6) Tastes are equal in both nations.
Means demand preferences are identical in both
nations. When relative prices are equal in the two
nations, both consume X&Y in the same proportion.
7) There is perfect competition in both commodities
and factor markets in both nations.
Means that producers, consumers, and traders of X&Y
in both nations are each too small to affect prices of
commodities. Also, in the L-R commodity prices
equal their costs, leaving no economic profit.
8) There is perfect factor mobility within each
nation but no international factor mobility.
Means K&L are free to move from areas and
industries of lower earnings to those of higher
earnings until earnings are the same in all areas, uses
and industries of the nation. International differences
in earnings persist due to zero international factor
mobility in the absence of international trade.
9) There are no transportation costs, tariffs, or other
obstructions to the free flow of international trade.
Means specialization in production proceeds until
relative (and absolute) commodity prices are the same in
both nations with trade. If transportation costs and tariffs
were allowed, specialization would proceed only until
prices differed by no more than the costs and tariffs on
each until of the commodity traded.
10) All resources are fully employed in both nations.
Means there are no unemployed resources in either
nation.
11) International trade between the two nations is
balanced.
 Means that the total value of each nation’s exports
equals the total value of the nation’s imports.
5.3 Factor Intensity, Factor Abundance, and the
Shape of the Production Frontier (PF)
A. Factor Intensity
 In a world of 2 commodities and 2 factors, Y is capital
intensive if its (K/L) is greater than (K/L) of X.
 If production of Y requires 2K and 2L, then K/L=1.
 If production of X requires 1K and 4L, then K/L=1/4.
 We say that Y is K intensive and X is L intensive.
 Measuring K and L intensity depends on K/L rather
than the absolute amount of K and L.
 In fig. 5-1, Nation 1 can produce 1Y using 2K-2L, and
2Y using 4K-4L. Thus, K/L=1, this gives the slope of
Y in Nation 1.
FIGURE 5-1 Factor Intensities for Commodities X and Y
in Nations 1 and 2.
 Nation 1 can produce 1X using 1K-4L, and 2X using
2K-8L. Thus, K/L=1/4, this gives the slope of the ray of
X in Nation 1.
 In Nation 2, K/L=4 for Y and 1 for X.
 Therefore, Y is the K-intensive commodity, and X is the
L-intensive in Nation 2 also. This is shown by the fact
that the ray from the origin for good Y is steeper than
that of X in both nations.
 Even though Y is K-intensive relative to X in both
nations, Nation 2 uses a higher K/L than Nation 1.
 For Y, K/L=4 in Nation 2 but K/L=1 in Nation 1.
 For X, K/L=1 in Nation 2 but K/L=1/4 in Nation 1.
 Q: Why does Nation 2 use more K-intensive production
techniques in both commodities than Nation 1?
 A: Capital must be relatively cheaper in Nation 2 than in
Nation 1, so that producers in Nation 2 use relatively
more capital in the production of both commodities to
minimize their costs of production.
 Q: But why is capital relatively cheaper in Nation 2?
 A: We must define factor abundance and examine its
relationship to factor prices.
 If the price of capital falls, producers would substitute
capital for labor in production of X&Y to minimize
production costs. As a result, both commodities become
K-intensive. If K/L of Y exceeds K/L of X, Y is
considered a K-intensive commodity.
B. Factor Abundance
 Two ways to define factor abundance:
1) In terms of physical units (i.e. overall amount of
K&L (TK/TL) available to each nation).
According to this definition, Nation 2 is capital
abundant if the ratio of total amount of capital to total
amount of labor available in Nation 2 is greater than
that in Nation 1.
The ratio of TK/TL what is important , not the
absolute amount of K&L available in each nation.
Thus, Nation 2 can have less K than Nation 1 and still
be the capital abundant nation if TK/TL in Nation 2
exceeds TK/TL in Nation 1.
2) In terms of relative factor prices (i.e. rental price of K
(PK) and the price of L time (PL) in each nation).
 According to this definition, Nation 2 is K abundant if
(PK/PL) is lower in Nation 2 than in Nation 1.
 Since rental price of K is taken to be the interest rate (r)
and the price of labor time is wage (w), then PK/PL= r/w.
 The ratio r/w what is important , not the absolute level of r
that determines whether a nation is K abundant.
 The first definition considers only the supply of factors,
while the second definition considers both demand and
supply.
 The demand of the factor is derived from demand for the
final commodity that requires the factor in its production.
C. Factor Abundance and the Shape of the
Production Frontier
 Since Nation 2 is K-abundant and Y is K-intensive,
Nation 2 can produce relatively more of Y than Nation
1.
 Since Nation 1 is L-abundant and X is L-intensive,
Nation 1 can produce relatively more of X than
Nation 2.
 This gives a production frontier for Nation 1 that is
relatively flatter and wider that that of Nation 2.
FIGURE 5-2 The Shape of the Production Frontiers of
Nation 1 and Nation 2.
5.4 Factor Endowments and the Heckscher-Ohlin
Theory
 In 1919 Eli Heckscher published “The Effect of
Foreign Trade on the Distribution of Income” .
 In 1933 Berlin Ohlin published “Interregional and
International Trade” in which he clarified and built on
the work of Heckscher.
 The H-O theory can be presented in the form of two
theorems: the H-O theorem (which deals with and
predicts the pattern of trade) and the factor-priceequalization theorem (which deals with the effect of
international trade on factor prices).
5.4 Factor Endowments and the
Heckscher-Ohlin Theory

The Heckscher-Ohlin Theorem
 General Equilibrium Framework of the
Heckscher-Ohlin Theory
 Illustration of the Hechscher-Ohlin Theory
16
The Heckscher-Ohlin Theorem
Heckscher-Ohlin (H-O) theory can be presented in
the form of two theorems:
1. The so-called H-O theorem (which deals with and
predicts the pattern of trade)
2. The factor-price equalization theorem (which
deals with the effect of international trade on
factor prices)
In fact, the H-O model has four major components:




Heckscher-Ohlin Trade Theorem ;
Stolper-Samuelson Theorem;
Rybczynski Theorem;
Factor Price Equalization Theorem
17
A. The Heckscher-Ohlin Theorem



Definition: A nation will export the commodity
whose production requires the intensive use of the
nation’s relatively abundant and cheap factor and
import the commodity whose production requires the
intensive use of the nation’s relatively scare and
expensive factor.
Or: the relatively labor-rich nation exports the
relatively labor-intensive commodity and imports the
relatively capital -intensive commodity.
This means that Nation 1 exports X because X is the
L-intensive commodity and L is relatively abundant
and cheap factor in Nation 1.
 Nation 2 exports Y because Y is the K-intensive
commodity and K is relatively abundant and cheap
factor in Nation 2.
 The H-O theorem isolates the difference in relative
factor abundance, or factor endowments, among
nations as the basic cause of comparative advantage
and international trade.
 For this reason, it is known as factor-proportions or
factor endowment theory.
 It postulates that the difference in relative factor
abundance and prices is the cause of pre-trade
difference in relative commodity prices between two
nations.
B. General Equilibrium Framework of the H-O Theory
20
1. The tastes and the distribution in the ownership of factors
of production together determine the demand for
commodities.
2. The demand for commodities determines the derived
demand for
the factors required to produce them.
3. The demand for factors of production, together with the
supply of
the factors, determines the price of factors of production
under
perfect competition.
4. The price of factors of production, together with
technology,
determines the price of final commodities.
5. The difference in relative commodity prices between
nations determines comparative advantage and the
pattern of trade
21
C. Illustration of the Heckscher-Ohlin Theory
 Since the two nations have equal tastes, they face the
same indifference map.
 Indifference curve I is the highest IC that Nation 1
and Nation 2 can reach in isolation, and points A and
A/ represent their equil. points of production and
consumption in the absence of trade.
 The tangency of IC I at points A and A/ defines the
no-trade equil-relative commodity prices of PA in
Nation 1 and PA/ in Nation 2.
 Since PA < PA/ , Nation 1 has a com-adv. in X and
Nation 2 has a com-adv. in Y.
C. Illustration of the Heckscher-Ohlin Theory
FIGURE 5-4 The Heckscher-Ohlin Model.
C. Illustration of the Heckscher-Ohlin Theory
 The right panel shows that with trade Nation 1
specializes in X and Nation 2 in Y.
 Specialization continues until Nation 1 reaches point
B and Nation 2 B/, where the transformation curves
are tangent to the common relative price line PB.
 Nation 1 exports X in exchange for Y and consume at
point E on IC II. Nation 2 exports Y for X and
consume at point E/ (which coincides with point E).
 Note that Nation 1’s exports of X equal Nation 2’s
imports of X (i.e. BC=C / E /).
 Similarly, Nation 2’s exports of Y equal Nation 1’s
imports of Y (i.e. B / C / =C E).
C. Illustration of the Heckscher-Ohlin Theory
 At PX/PY > PB, Nation 1 want to export more of X
than Nation 2 wants to import at this high relative
price, and PX/PY falls towards PB.
 At PX/PY < PB, Nation 1 want to export less of X than
Nation 2 wants to import at this low relative price, and
PX/PY rises towards PB.
 Point E involves more of Y but less of X than point A
 However, Nation 1 gains from trade because E is on
higher IC II.
 Similarly, at E/ which involves more X but less Y than
A/, Nation 2 is better of because E/ is on higher IC II.
C. Illustration of the Heckscher-Ohlin Theory

Conclusion
Both nations gain from trade because they consume on
higher indifference curve Ⅱ.
 Case Study
5-3 (page 133) examines the pattern of revealed
comparative advantage and disadvantage of various
countries or regions
26
Diagram 3.4 v/s Diagram 5.4
FIGURE 3-4 The Gains from Trade with Increasing Costs
27
FIGURE 5-4 The Heckscher-Ohlin Model
28
Differences
 In Fig 3.4, the difference in the production frontiers of
the two nations is reinforced by their difference in
tastes, thus making the autarky relative commodity
price in the two nation differ even more than in Fig
5.4.
29
 The tastes of the two nations could be different in such
a way as to make mutually beneficial trade impossible.
Both nation may requires export and import of same
goods due to demand preferences. So trade is not
possible.
 HO theory does not requires identical tastes in the two
nations. It only requires that if tastes differ, they do not
differ sufficiently to neutralize the tendency of
different factor endowments and production
possibility curves from leading to different relative
commodity prices and comparative advantage in the
two nations.
30
Factor Price equalization and
Income distribution
 The Factor-Price Equalization Theorem
 Relative and Absolute Factor-Price
Equalization
 Effect of Trade on the Distribution of Income
 Empirical Relevance
31
Additional Topics


Stolper-Samuelson Theorem;
Rybczynski Theorem;
32
Factor Price equalization Theorem
 It says that “International Trade will bring about
equalization in the relative and absolute returns to
homogenous factors across nations. As such,
International trade is a substitute for the international
mobility of factors.
 The factor-price equalization theorem was
rigorously proved by Paul Samuelson (1970 Nobel
prize in economics) , so it was also called H-O-S
theorem.
33
Factor Price equalization Theorem
Production Adjustment due to International Trade
 As the production of the good using the abundant
resource intensively increases, demand for that
resource will increase; so will the demand for the
scarce resource, but by a smaller amount
 As the production of the good that uses the scarce
resource intensively decreases, both abundant and
scarce resources will be released, but relatively more of
the scarce resource will be released than the abundant
resource
We can show this production adjustment in following
fig.
34
Factor Price equalization Theorem
SK
SL
ro
W2
D1
D2
Do
r2
Wo
Do
L
0
Labor
D2
D1
0
K
Capital
Production Adjustment due to International Trade
35
Factor Price equalization Theorem
 Explanation of H-O-S theorem
1.
2.
In Nation 1 the relative price of commodity X is
lower than in Nation 2, it means that the relative
price of labor or wage rate is lower in Nation1 in the
absence of trade;
With trade, Nation 1 specializes in the production of
commodity X (L-intensive commodity) and reduces
its production of commodity Y(K-intensive
commodity), the demand for labor rises causes the
wages to rise while the relative demand for capital
falls and its rate falls; on the other hand, in Nation 2
wages fall and rate rises;
36
Factor Price equalization Theorem

Conclusion
1.
International trade tends to reduce the pre-trade
difference in w and r between the two nations;
2.
International trade keeps expanding until relative
commodity prices are completely equalized, which
means that relative factor prices have also become
equal in two nations.
37
Factor Price equalization Theorem
Relative and Absolute Factor-Price Equalization
To show the relative factor-price equalization graphically (see
figure 5-5)
38
Factor Price equalization Theorem
Relative and Absolute Factor-Price Equalization
 To explain Figure 5-5
1. The horizontal axis measures the relative price of labor
(w/r) while the vertical axis measures the relative
price of commodity X (PX/PY);
2. Each w/r is associated with a specific PX/PY ratio (due
to the perfect competition and uses the same
technology, one to one relationship between w/r and
PX/PY);
3. Without trade, Nation 1 is at Point A with w/r=(w/r)1
and PX/PY=PA while Nation 2 is at Point A’ with
w/r=(w/r)2 and PX/PY=PA’;
39
Factor Price equalization Theorem
Relative and Absolute Factor-Price Equalization
4. With trade, Nation 1 will produce more of commodity
X due to the PA ﹤PA’ in the relative price of
commodity X in Nation 1 than Nation 2 while Nation
2 will produce more of commodity Y .
5. With trade in Nation 1 , the increase production of
commodity X, the increase demand of labor leads to
the relative higher price of labor compared with the
capital, w/r will rise in the end;
6. With trade in Nation 2 , the increase production of
commodity Y, the increase demand of capital leads
to the relative higher price of capital compared with
the labor, r/w will rise (w/r will fall) in the end;
40
Factor Price equalization Theorem
Relative and Absolute Factor-Price Equalization
7. The upward movement in Nation 1 and downward
movement in Nation 2 will continue until point
B=B’, at which PB=PB’ and w/r=(w/r) ﹡(only at this
point both nations operate under perfection
competition and use the same technology by
assumption)
 To summarize
PX/PY will become equal as a result of trade, and this
will only occur when w/r has also become equal in
the two nations (as long as both nations continue to
produce both commodities).
41
Factor Price equalization Theorem
Relative and Absolute Factor-Price Equalization
 Absolute factor-price equalization
It means that free international trade also equalizes the
real wages for the same type of labor in the two
nations and the real rate of interest for the same
type of capital in the two nations.
42

1.
2.
3.

1.
2.
3.
Assumptions of the relative and absolute factorprice equalization
Perfect competition in all commodities and factor
markets;
The same technology;
The constant returns to scale;
Conclusion
Trade equalizes the relative and absolute returns to
homogeneous factors;
Trade acts as a substitute for the international
mobility of factors of production in its effect on
factor prices;
Trade operates on the demand for factors, factor
mobility operates on the supply of factors.
43
Effect of Trade on the Distribution of income
We will cover after HO theory
44
Factor Price equalization Theorem
Empirical Relevance
 Unreal Assumptions
In reality, the equalization of the returns to
homogeneous factors is not the case said as HO-S model in different nations with trade. The
reasons as follows: Such as same technology, no
transportation cost, free trade, perfect competition
and constant returns to scale.
45
Factor Price equalization Theorem
Empirical Relevance
 Usefulness
The reason is that it identifies crucial forces
affecting factor prices and provides important
insights into the general equilibrium nature of
out trade model and of economics in general.
46
Factor Price equalization Theorem
Empirical Relevance

Shortcoming
It doesn’t say that international trade will eliminate or
reduce international differences in per capita incomes. It
only says that international trade will eliminate or
reduce international Differences in the returns to
Homogeneous factors.
Reason: Per capita incomes depend on other many
forces ( The ratio of skilled to unskilled labor and so on).
Even if real Wages were to be equalized among nations,
their per capita Incomes could be still wider.
47
Factor Price equalization Theorem
Empirical Relevance
Adjustment of H-O-S Model: International trade can reduce
the international difference in the returns to
homogeneous factors.
Reason: even if international trade has operated to reduce
the absolute difference in factor returns among nations,
many other forces were operating at the same time,
preventing any such relationship from becoming clearly
evident (e.g. trade restrictions)
48
5.6 Empirical Tests of the Heckscher-Ohlin Model



Empirical Results-The Leontief Paradox
Explanations of the Leontief Paradox
Factor-Intensity Reversal
49
The Leontief Paradox
 Leontief's paradox in economics is that the country
with the world's highest capital-per worker has a lower
capital-labour ratio in exports than in imports.
 This econometric finding was the result of Professor W
W Leontief's attempt to test the HO theory
empirically. In 1954, Leontief found that the US(the
most capital abundant country in the world by any
criteria) exported labour-intensive commodities and
imported capital-intensive commodities, in
contradiction with Heckscher-Ohlin theory ("H-O
theory").
50
The Leontief Paradox
1. In 1971 Rober Baldwin showed that US importswere
27% more capital-intensive than US exports in the 1962
trade data using a measure similar to Leontief's.
2. In 1980 Leamer questioned Leontief's original
methodology or real exchange rate grounds, but
acknowledged that the US paradox still appears in the
data (for years other than 1947).
3. A 1999 survey of the econometric literature by Elhanan
Helpman concluded that the paradox persists, but some
studies in non-US trade were instead consistent with the
H-O theory.
4. In 2005 Kwok & Yu used an updated methodology to
argue for a lower or zero paradox in US trade statistics,
though the paradox is still derived in other developed
nations
51
Responses to the Paradox
 For many economists, Leontief's paradox undermined the
validity of the H-O theory, which predicted that trade
patterns would be based on countries' comparative
advantage in certain factors of production (such as
capital and labor). Many economists have dismissed the
H-O theory in favor of a more Ricardian model where
technological differences determine comparative
advantage. These economists argue that the U.S. has an
advantage in highly skilled labor more so than capital.
This can be seen as viewing "capital" more broadly, to
include human capital. Using this definition, the exports
of the U.S. are very (human) capital-intensive, and not
particularly intensive in (unskilled) labor.
52
Responses to the Paradox
 Some explanations for the paradox dismiss the importance
of comparative advantage as a determinant of trade. For
instance, the Linder hypothesis states that demand plays a
more important role than comparative advantage as a
determinant of trade--with the hypothesis that countries
which share similar demands will be more likely to trade.
For instance, both the U.S. and Germany are developed
countries with a significant demand for cars, so both have
large automotive industries. Rather than one country
dominating the industry with a comparative advantage,
both countries trade different brands of cars between them.
Similarly, New Trade Theory argues that comparative
advantages can develop separately from factor endowment
variation (e.g. in industrial increasing returns to scale).
53
Explanations of the Leontief Paradox

The used data was not representative;

Two-factor model (L, K) , ignoring the natural
resources; (Many production process using natural
resources)

U.S. Trade policy (heavy protection of domestic
labor-intensive industries, so more labor –intensive
goods export);

Only the measure of physical capital and ignoring
the human capital and “knowledge” capital;
At the same time there are many strong and convincing
evidences verifying H-O theory. (See Figure 5-6) Case
Study 5-7 (page 143)
54
FIGURE 5-6 Comparative Advantage with Skills and Land
55
Effect of International Trade on distribution of Income
International trade on the effect of relative factor prices
within each nation
 Trade increases the price of the nation’s abundant and
cheap factor and reduces the price of its scarce and
expensive factor. eg W rises and r falls in Nation 1
while w falls and r rises in Nation 2. International
trade on the effect of income within each nation
 The real income of labor and the real income of
owners of capital move in the same direction as the
movement in factor prices. eg Trade causes the real
income of labor to rise and the real income of owners
of capital to fall in Nation 1 while in Nation 2 the
situation is the opposition. (Stolper-Samuelson
Theorem)
56
Effect of International Trade on distribution of Income
Stolper-Samuelson Theorem:
The theorem postulates that an increase in the relative
price of a commodity raises the return or earnings of the
factor used intensively in the production of the commodity.
Application
 Developed countries
Developed countries are the relatively capital abundant
Factor, international trade tends to reduce the real
income of labor and increase the real income of owners
of capital. This is why labor union generally favor trade
restrictions.( Case study 5-5 page 139)
57
Effect of International Trade on distribution of Income
Conclusion
 International trade on the effect of relative factor prices
and the distribution of income within each nation in the
long run;
 According to H-O-S theorem and Stolper- Samuelson
theorem, international trade causes real wages and the
real income of labor to fall in a capital-abundant and
labor –scarce nation (such as developed countries). On
the contrary, international trade causes real interests and
the real income of capital to fall in a labor-abundant and
capital scarce nation (such as developing countries);
 Unequal distribution of income needs an appropriate
distribution policy of the government. (detail in Chapter 8)
58
The Specific-Factors Model

Conclusion
In the short run when some factors my be immobile Or
specific to some industry or sector. In this case, it
Postulates that trade will have an ambiguous effect
on the nation’s mobile factors : It will benefit the immobile
factors that are specific to the nation’s export
commodities or sectors, and harm the immobile factors
that are specific to the nation’s import-competing
commodities or sectors.
59
The Specific-Factors Model

Conclusion
In the long run when all input are mobile among all
Industries of a nation, the H-O model postulates that the
opening of trade will lead to an increase in the real
income or return of the inputs used intensively in the
nation’s export sectors and to a reduction in the real
income or return of the inputs used intensively in the
production of the nation’s import-competing sectors.
60
Factor-Intensity Reversal

Concept
It means refers to the situation where a commodity is L intensive
in the L-abundant nation and K intensive in the K-abundant
nation.
 This may occur when the elasticity of substitution of factors
in production varies greatly for the two commodities.
With factor-intensity reversal, both H-O theorem and the factorprice equalization theorem fail.

Controversial topic
Some tests show that factor reversal was fairly prevalent, some tests
provide strong confirmation of the H-O model.
61