International Economics. Li Yumei Economics & Management School of Southwest University. International Economics. Chapter 5 Factor Endowments and the Heckscher-Ohlin Theory. Organization. 5.1 Introduction 5.2 Assumptions of the Theory
Economics & Management School
of Southwest University
Factor Endowments and the Heckscher-Ohlin Theory
If factor prices were same, the two nations would use the exactly
same amount of labor and capital in the production of each
commodity; since factor prices usually differ, producers in each
nation will use more of the relatively cheaper factor in the nation to
minimize their costs of production.
It means that commodity X requires relatively more of labor to
produce than commodity Y in both nations. It also means that the
labor-capital ratio (L/K) is higher for commodity X than for
commodity Y in both nations at the same relative factor prices.
This is equivalent to saying that the K/L ratio (capital-labor ratio) is
lower for X than for Y in both nations, but not mean K/L ratio for X
is the same in both nations.
It means that increasing the amount of labor and capital used in
Production of any commodity will increase output of that commodity
in the same proportion.
It means that even with free trade both nations continue to produce
both commodities. This implies that neither of the two nations is “very
It means that demand preferences, as reflected in the shape and
location of indifference curves are identical in both nations.
It means that producers, consumers and traders of commodity X and
commodity Y in both nations are each too small to affect the price of
these commodities. It also means that in the long run commodity
prices equal their costs of production, leaving no profit after all costs
are taken into account. It also means that all producers, consumers
and owners of factors of production have perfect knowledge of
commodity prices and factor earnings in all parts of the nation and in
It means that labor and capital are free to move, and indeed do
move quickly from areas and industries of lower earnings to areas
and industries of higher earnings until earnings for the same type of
labor and capital are the same in all areas, uses, and industries of
the nation. On the other hand, there is zero international factor
It means that specialization in production proceeds until relative
commodity prices are the same in both nations with trade.
It means that there are no unemployed resources or factors of
production in either nation.
It means that the total volume of each nation’s exports equals the
total volume of the nation’s imports.
FIGURE 5-1 Factor Intensities for Commodities X and Y in Nations 1 and 2
1. The horizontal axis refers to the amount of labor while the
vertical axis refers to the amount of capital, and the slope of
the ray measures the capital-labor ratio (K/L) in the
production of the commodity;
2. Nation 1’s slope of the rays (K/L) in the production of
Commodity X and Commodity Y;
1) K/L in Y=1 ( 2 K and 2 L for 1 Y, 4K and 4L for 2Y with constant returns to scale);
2) K/L in X=1/4 (1K and 4L for 1X, 2K and 8L for 2X with constant returns to scale;
3. Nation 2’s slope of the rays (K/L) in the production of
commodity X and commodity Y;
The same meaning in Nation 2, K/L in Y=4 while K/L in X= 1
1. Commodity Y is K-intensive commodity while commodity X
is L- intensive commodity in both nations;
Reason: K/L ratio is higher for commodity Y than commodity X, on
the contrary the L/K ratio is higher for commodity X than
2. K/L ratio in Nation 2 is higher than Nation 1 in both
commodities X and Y;
Reason: the 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. ( factor abundance and its relationship to factor prices later explanation) . In other words, the relative capital price (r/w) is lower in Nation 2 than in Nation1. If r/w declined, producers would substitute K for L in the production of both commodities to minimize their costs of production. As a result, K/L would rise for both commodities, but Commodity Y continues to be K-intensive commodity (assumption).
1. The terms of physical units
It means the overall amount of capital and labor available to
2. The terms of relative factor prices
It means the rental price of capital and the price of labor time in
1. Nation 2 is capital abundant if the ratio of the total amount
of capital to the total amount of labor (TK/TL) available in
Nation 2 is greater than that in Nation 1. (according to
physical units of factor abundance)
2. According to the definition in terms of factor prices, Nation
2 is capital abundant if the ratio of the rental price of capital
to the price of labor time (PK/PL) is lower in Nation 2 than in
Nation 1. Since the rental price of capital is usually taken to
be the interest rate ( r ) while the price of labor time is the
wage rate ( w ), PK/PL= r/w
3. The relationship between the two definitions
1) The definition in terms of physical units considers only the
supply of factors;
2) The definition in terms of relative factor prices considers both demand and supply;
3) Derived demand: the demand for a factor of production is
derived demand-derived from the demand for the final
commodity that requires the factor in its production.
1. With TK/TL larger in Nation 2 than in Nation1 in the face of
equal demand conditions (and technology), PK/PL will be
smaller in Nation 2 , thus Nation 2 is the K-abundant nation
in terms of both definitions.
2. This is not always the case.
Reason: the demand for Y and the demand for capital, could be so
much higher in Nation 2 than in Nation 1 that the relative price of
capital would be higher in Nation 2 than in Nation 1(alrough the
relative greater supply of capital in Nation 2). In this case, Nation 2
would be considered K abundant according to the definition in
physical terms and L abundant according to the definition in terms
of relative factor prices.
In Such situation, it is the definition in terms of relative factor prices
that should be used.
3.Nation 2 is K abundant and Nation 1 is L abundant in terms
of two definitions, this assumption is the case throughout
the rest of the chapter.
1. Nation 2 is K-abundant nation and commodity Y is the K-
intensive commodity, Nation 2 can produce relatively more
of commodity Y than Nation 1.This gives a production
frontier for Nation 2 that is relatively flatter and wider than
the production frontier of Nation 1 (if measures Y along the
2. Nation 1 is L-abundant nation and commodity X is the L-
intensive commodities, Nation 1 can produce relatively
more of commodity X than Nation 2. This gives a production
frontier for Nation 1 that is relatively flatter and wider than
the production frontier of Nation 2 (if measures X along the
FIGURE 5-2 The Shape of the Production Frontiers of Nation 1 and Nation 2
1. Nation 1’s production frontier is skewed toward the
horizontal axis, which measures commodity X.
Reason: Nation 1is a L-abundant nation and commodity X is L-
2. Nation 2’s production frontier is skewed toward the vertical
axis, which measures commodity Y.
Reason: Nation 2 is a K-abundant nation and commodity Y is K-
1. Case study 5-1: the relative resources endowments of various countries and regions. (page 123)
2. Case study 5-2: the capital stock per worker for a number of leading developed and developing countries. (page 124)
He (StockholmNovember 24, 1879 - Stockholm
December 23, 1952) was a Swedishpolitical
economist and economic historian. Heckscher was
born in Stockholm into a prominent Jewish family,
son of the Danish-born businessman Isidor
Heckscher and his spouse Rosa Meyer, and
completed his secondary education there in 1897.
He studied at university in Uppsala and Gothenburg,
completing his PhD in Uppsala in 1907. He was
professor of Political economy and Statistics at the
Stockholm School of Economics from 1909 until 1929,when he
exchanged that chair for a research professorship in economic
history, finally retiring as emeritus professor in 1945.
According to a bibliography published in 1950, Heckscher had as
of the previous year published 1148 books and articles, among
which may be mentioned his study of Mercantilism, translated into
several languages, and a monumental Economic history of
Sweden in several volumes. Heckscher is best known for a model
explaining patterns in international trade (Heckscher-Ohlin model)
that he developed with Bertil Ohlin at the Stockholm School of
Bertil Ohlin developed and elaborated the
factor endowment theory. He was not only
a professor of economics at Stockholm, but
also a major political figure in Sweden. He
served in Riksdag (Swedish Parliament),
was the head of liberal party for almost a
1/4 of a century. He was Minister of Trade
during World War II. In 1979 Ohlin was awarded a Nobel prize jointly with James Meade for his work in international trade theory.
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:
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 scarce and
1. The basis for trade: Relative factor abundance or factor
endowments as the basis for international trade or the basic
cause or determinant of comparative advantage.
2. Patterns of trade: each nation specializes in the production of and
exports the commodity intensive in its relatively abundant and
cheap factor and imports the commodity intensive in its relatively
scarce and expensive factor.
H-O theorem explains comparative advantage rather than assuming
it . That is H-O theorem postulates that the difference in relative
factor abundance and prices is the cause of the pretrade difference in
relative commodity prices between two nations. This difference in
relative factor and relative commodity prices is then translated into a
difference in absolute factor and commodity prices between the two
nations. It is this difference in absolute commodity prices in the two
nations that is the immediate cause of trade.
The H-O theorem predicts the pattern of trade between countries
based on the characteristics of the countries. The H-O theorem
says that a capital-abundant country will export the capital-intensive
good while the labor-abundant country will export the labor-intensive
The H-O theorem demonstrates that differences in resource
endowments as defined by national abundance is one reason
that international trade may occur.
Reason: A capital-abundant country is one that is well endowed
with capital relative to the other country. This gives the country
a propensity for producing the good which uses relatively more
capital in the production process .
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
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
FIGURE 5-3 General Equilibrium Framework of the Heckscher-Ohlin Theory
1. The general equilibrium framework of H-O theory shows clearly
how all economic forces jointly determine the price of final
2. Out of all economic forces working together, H-O isolates the
difference in the physical availability or supply of factors of
production among nations ( in the face of equal tastes and
technology) to explain the difference in relative commodity prices
and trade among nations. And different supply of factors of
production in different nations have different factor prices.
3. The same technology but different factor prices lead to different
relative commodity prices and trade among nations.
FIGURE 5-4 The Heckscher-Ohlin Model
1. Left panel: it shows the production frontier of Nation 1 and 2
1) Nation 1’s production frontier is skewed along the X-axis;
2) Nation 2’s production frontier is skewed along the Y-axis;
3) Indifference curve Ⅰis tangent to Nation 1’s production frontier
at point A while point A’ in Nation 2’s (due to the equal tastes);
4) A represents Nation 1’s equilibrium points of production and
consumption while A’ represents Nation 2’s equilibrium points of
production and consumption in the absence of trade;
5) Since the equilibrium-relative commodity prices of PA﹤PA’,
Nation has a comparative advantage in commodity X while
Nation 2 in Commodity Y.
2. Right panel: With trade the equilibrium point
1) Nation 1 specializes in the production of commodity X while Nation 2
in commodity Y;
2) Specialization in production proceeds until the transformation curves
of the two nations are tangent to the common relative price line PB.
3) After trade, Nation 1 will export commodity X in exchange for
commodity Y and consume at point E on indifference curveⅡ.
Nation 2 will export commodity Y in exchange for commodity X
and consume at point E’ on indifference curveⅡ.
4) PX/PY=PB, equilibrium point; if PX/PY﹥PB, Nation 1 wants to
export more of commodity X than Nation 2 wants to import at this
high relative price of X, and PX/PY falls toward PB; on the
contrary, if PX/PY﹤PB, Nation 1 wants to export less of commodity X
than Nation 2 wants to import , and PX/PY rises toward PB.
Both nations gain from trade because they consume on higher
indifference curve Ⅱ.
5-3 (page 130) examines the pattern of revealed comparative
advantage and disadvantage of various countries or regions.
The factor-price equalization theorem says that when the
prices of the output goods are equalized between countries,
as when countries move to free trade, then the prices of the
factors (capital and labor) will also be equalized between
countries. This implies that free trade will equalize the wages
of workers and the rents earned on capital throughout the
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. ( page 129)
1. 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;
2. 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;
1. International trade tends to reduce the pretrade 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
FIGURE 5-5 Relative Factor–Price Equalization
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
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
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
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).
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
E.G. W rises and r falls in Nation 1 while w falls and r rises in Nation 2.
E.G. 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)
(Details in 8.4c page 251)
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.
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 5-4 page 135)
FIGURE 5-9 Specific-Factors Model
1. Nation 1 is L-abundant nation and the labor is mobile between
industries but capital is not;
2. The wage of labor will be the same in the production of commodities
of X and Y in Nation 1 and given by the intersection of the value of
the marginal product of labor curve in the production of X and Y;
(VMPLY and VMPLX);
3. The horizontal axis measures the total supply of labor available to
Nation 1 while the vertical axis measures the wage rate;
4. No-trade, the equilibrium point is at E with wage rate ED, OD of labor in X and DO’ of labor in Y;
5. With trade, PX/PY rises, VMPLX moves upward to VMPLX’, the
result is that the wage rate increase (from ED to E’D’) less than
the price increase (EF) proportionately, and DD’ is the increased
labor of X, w falls in X and rises in Y (due to the unchanged price of
1. Nation 1 is L-abundant nation and the labor is mobile between
industries but capital is immobile;
2. More labor work for the production of X with given amount of capital,
it means that VMPKX and r increase in terms of both commodities,
while less labor is used with the fixed capital in the production of Y,
VMPKY and r fall in terms of Y;
3. With trade, the real income of the immobile capital (the nation’s
scarce factor) rises in the production of X and falls in the production
of Y while real wages fall in terms of X and rise in terms of Y.
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.
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
In reality, the equalization of the returns to homogeneous
factors is not the case said as H-O-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.
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).
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.
It doesn’t say that international trade will eliminate or reduce
international differences in per capita incomes. It only predicts
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.
American economist, b. Russia, grad. Univ. of Berlin
(Ph.D., 1928). The son of a Russian economist, he and
his family left the Soviet Union in 1925 because of their
opposition to the Bolshevik government. After serving
as an adviser on railroad construction to the Chinese
government (1929), he emigrated to the United States.
He joined the faculty of Harvard in 1931, rising to the
rank of professor in1946. In 1975, he left Harvard to teach at New York
Univ. Leontief is best known for his development of the input-output
method of economic analysis, used by most industrialized nations for
planning and predicting economic progress. He was awarded (1973) the
Nobel Memorial Prize in Economic Sciences.
(Many production process using natural resources)
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)
It means refers to the situation where a commodity is L intensive
in the L-abundant nation and K intensive in the K-abundant
With factor-intensity reversal, both H-O theorem and the factor-
price equalization theorem fail.
Some tests show that factor reversal was fairly prevalent, some tests
provide strong confirmation of the H-O model.
(factor abundance → factor prices →the cost of production →the comparative advantage)
1. Effect on factor prices: the abundant factor’s price will rise while the scarce factor’s price will fall (factor- price equalization);
2. Effect on returns of factors:
(1) In the long run: the abundant factor’s return will rise while the scarce factor’s returns will fall (exported industries’ income will rise while import competing industries will fall );
(2) in the short run: the specific-factor model 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;
Although the theory is controversial in empirical
studies, but most of studies provide strong and
convincing evidence .
Page 148 from 1 to 15 questions
The original sources for the Hechscher-Ohlin theory are:
The original proof of the factor-price equalization theorem is
For the effect of international trade on the distribution of
For excellent surveys of the Heckscher-Ohlin theory, see: