Chapter Five
Factor Endowments and the
Heckscher–Ohlin Theory
5.1 Introduction
In this chapter we extend our trade model in two important directions.
First,we explain the basis for comparative advantage,that is,what
determines comparative advantage.Second,we analyze the effect that
international trade has on the earnings of factors of production in the
two trading nations.
5.2 Assumptions of the Theory
As with other economic theories,the H–O theory presumes a
number of simplifying conditions.We present together the
presumptions that underlies the theory and offer brief explanations
to some of them.
• the assumptions and their meanings
1. 2N×2C×2F
2. Same technology in production
3. X and Y are labor intensive and capital intensive respectively
4. Under constant returns to scale in both nations
5. Incomplete specialization
6. Equal tastes in both nations
7. Perfect competition in both commodity and factor markets
8. Perfect factor mobility
9. No idle resources
About the meanings of the assumptions, see page 117-118.
5.3 Factor Intensity, Factor Abundance, and the
Shape of the Production Frontier
Since H–O theory is expressed in terms of factor intensity and
factor abundance,we deem it crucial to make these meanings clear
and precise.
5.3A Factor Intensity
• Factor intensity is described as the proportion of two factors of
production in which they are used in producing different
commodities.
• For nation 1, K/L (means the ratio of capital to labor ) are ¼ and 1
for commodity X,Y respectively. Commodity X is L–intensive ,
Commodity Y is K–intensive .
For nation 2 ……
• Note that even though commodity Y is K–intensive in
relation to commodity X in both nations,Nation 2 uses a
relatively higher K/L in the production of both X and Y.
• The obvious question is:Why does nation 2 use more K–
intensive production techniques in both commodities
than in nation 1?
The answer is capital must be relatively cheaper in
nation 2 than in nation 1, so that producers in nation 2
will respond to use relatively more capital in producing
both commodities to minimize their costs of production
by substituting the cheaper factor of production（K）for
the more expensive one (L).
• Another question:Why is capital relatively cheaper in
nation 2?
To answer this question,we must define factor abundance
and examine its relationship to factor prices.
• Before we explain factor abundance ,I’d like to,at the
end of this section,draw your attention to a point of
crucial importance which,however,is not explicitly stated
in average domestic textbooks:Strictly speaking ,only if
K/L in the production of Y exceeds that in the production
of X at all possible relative factor prices can we say
unequivocally that commodity Y is the K–intensive
commodity.
5.3B Factor Abundance
There are two ways to define factor abundance:
• One way is in terms of physical units (i.e., in terms of the overall
amount of capital and labor available to each nation), defined as:
Nation 2 is capital abundant if the ratio of the total amount of
capital to the total amount of labor is greater than that in
nation 1(i.e., TK/TL for N2 exceeds TK/TL for N1).
Note that it is not the absolute amount of capital and labor
available in each nation that is important,but what really matters is
the relative amount (the ratio of the total amount of capital to the
total amount of labor)—a notion in relative sense.
According to this definition, a nation can still be K abundant even if
it has less capital.
• Another way is in terms of relative factor prices (i.e., in terms of
rental price of capital,r and the price of labor time,w in each
nation. ),defined as:
Nation 2 is capital abundant if the ratio of the rental price of
capital to the price of labor time is lower than that in nation 1
(i.e.,PK/PL is smaller in nation 2 than in nation 1).
Note once again that it is not the absolute level of r that determines
whether or not a nation is K abundant,but the relative level r/w.
• The relationship between the two definitions is clear: the former
considers only the supply of factors while the latter both the supply
and demand. Since we assume equal tastes or demand preference
in both nations, the two definitions give the same conclusions
from different angles.
• Direct Vs. derived demand
• But this case is not always true in real world. There does
exist a strong or week demand biased in favor of this or
another commodity, which distorts the relative price
levels.
• If the spending pattern or consumption pattern in N2 is
strongly biased in favor of commodity Y which is capitalintensive, the derived demand for capital could be higher
in N2 and the price of capital r2could be higher
enough.As a result, nation 2 is otherwise labor- abundant.
This is how a biased spending pattern will distort the
relative factor prices.
In such situations it is the definition in terms of
relative factor prices that should be used. That is,a
nation is K abundant if the relative price of capital is
lower in it than in the other nation.
5.3C Factor Abundance and the Shape of the
Production Frontier
We plot the production frontiers of nation 1 and nation 2
on the same set of axes in fig.5.2..There is a biased
expansion of production frontier, i.e., the production
frontier shifts out much more in one direction than in the
other.
• Since nation 1 is L abundant nation and commodity X is
L–intensive,its production frontiers is skewed toward the
horizontal axis,which measures commodity X, indicating
that nation 1 can produce relatively more of X than
nation 2.
• Since nation 2 is K abundant nation and commodity Y is
K–intensive,its production frontiers is biased toward the
vertical axis, which measures commodity Y production,
indicating that nation 2 can produce relatively more of Y
than nation 1.
5.4 Factor Endowment and the Heckscher–
Ohlin Theory
• Having clarified the meaning of factor intensity and factor
abundance,we are now ready to present the modern theory of
international trade: the H–O theory. This theory is also referred
to as factor-proportions theory, because it emphasizes the
interplay between the proportions in which different factors of
production are available in different nations (factor abundance)
and the proportions in which they are used in producing
different goods (factor intensity).
• In a nutshell, the Heckscher–Ohlin theory can
be presented in the forms 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
5.4A The Heckscher–Ohlin Theorem
• We state the Heckscher–Ohlin theorem as follows: 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 expensive factor. In
short, the relatively labor–rich nation exports the relatively labor–
intensive commodity and imports the relatively capital–intensive
commodity.
• Of all the possible reasons (technologic gap, differences
in tastes, economy to scale and imperfect competition etc.)
for differences in relative commodity prices and
comparative advantage among nations, the H–O theorem
singles out the differences in factor abundance or
factor endowments, among nations as the basic cause or
determinant of comparative advantage and international
trade. Thus, the H–O theorem goes one step forward to
explain the comparative advantage rather than assuming
the existence of it ,as was the case for classical
economists.
5.4B General Equilibrium Framework of the H–O
Theorem
We say the H–O model is a general equilibrium model
for the reason that it takes all economic forces into
considerations, these forces are at work together to
determine the prices of final commodities. See fig.5.3. on
page 126.
5.4C Illustration of the Heckscher–Ohlin Theory
• Since we assume the two nations have equal tastes or demand
preferences, they face the same indifference map.For simplicity,
we assume the two nations are on the same indifference curve Ⅰ
in isolation and end up on the same indifference curve Ⅱ of the
indifference map.We only did so in order to facilitate the graphic
illustration of fig.5.4. (this leaves the conclusion unaffected).
Though, it need not be the case.
• In fig.5.4., the production frontiers of nation 1 and nation 2 are
the very same ones as we have discussed in previous sections.
• At any other relative price other than PB, trade is in imbalance and
pressure from demand and supply will give rise to the fall or rise
of relative price, causing it to gravitate toward the equilibrium PB.
• Explain the pattern of trade and gains from trade. Since the
indifference curve Ⅱ is higher than curve Ⅰ, both nations’
welfares are improved.
5.5 Factor–Price Equalization and
Income Distribution
• In the section 3.5B Equilibrium–Relative
Commodity Prices with Trade, we learned that
free trade tends to equalize commodity prices
among trading partners.
Can the same be said for factor prices?
The answer is invariably “can”.
• To answer it, we carry on to this section and
examine the other form of theorem of the H–O
theory, the factor–price equalization theorem,
which is really a corollary of H–O theorem.
5.5A The Factor–Price Equalization Theorem
• We state it as follows: International trade will bring
about equalization in the relative and absolute returns
to homogeneous factors across nations. As such,
international trade is a substitute for the international
mobility of factors.
• What this means is that international trade will cause the
wage rates of homogeneous labor and the interest rates
of homogeneous capital to be the same in all trading
nations (i.e., w1=w2…, r1=r2). It also implies that both
relative and absolute factor prices will be equalized(r1/
w1= r2 / w2).
• Homogeneous labor and homogeneous capital
• Have a look into the process of the following example to see how
wages are equalized by trade in two nations. In the absence of trade,
the relative price of X is lower in nation 1 than in nation 2 because
the relative price of labor or wage rate (w) is lower in nation 1 than
in nation 2.
Nation 1
Nation 2
W1 is low
W1< W2
W2 is high
1. As it specializes in
As it specializes in
producing X and reduces Y:
producing Y and reduces X:
…………………………………………………………………………
2. relative D for labor rises,DL ↗ relative D for labor falls, DL ↘
…………………………………………………………………………
3. As a result, the rise in D for
As a result, the fall in D for
abundant factor L causes its
scarce factor L causes its
price to increase, that is,
price to decrease, that is
wage (w) to rise W1 ↗
wage (w) to fall, W2 ↘
……
4. cheap factor L becomes
expensive factor L becomes
more expensive
W1= W2 cheaper
This process continues until the W in nation
1 and nation 2 become equal. This proves
that international trade tends to reduce
the pre–trade differences in W between
the two nations.
In like manner,we can prove that international
trade tends to equalize the interest rate r in the
two nations, too.
Remember:
This is left for you to do as an extra-class
assignment.
5.5B Relative and Absolute Factor–Price
Equalization
• In the preceding Section 5.5A, we have proved that international
trade tends to reduce the international differences in the returns
to homogeneous factor. In this section we go further to
demonstrate graphically that international trade would in fact
bring about complete equalizations in relative factor prices
when all the assumptions made in section 5.2A hold.
• See fig.5.5. on page 132:Horizontal axis measures the relative
price of labor (w/r), and vertical axis measures the relative price
of commodity X(PX/PY). Since each nation operates under
perfect competition and uses the same technology , there is a
one-to-one corresponding relationship between w/r and PX/PY.
• Since in the absence of trade, w/r is lower in nation 1 than in nation
2, nation 1 has a comparative advantage in X and nation 2 has a
comparative advantage in Y.
Nation 1
Nation 2
(w/r)1 is low
(w/r)1 < (w/r)2 (w/r)2 is high
1. As it specializes in
As it specializes in
producing X and reduces Y:
producing Y and reduces X:
2. DL increases relative to DK ,
DL decreases in relation to DK
3. cause (w/r)1 to rise, (w/r)1 ↗
cause (w/r)2 to fall, (w/r)2 ↘
……
(w/r)1= (w/r)2
• This process continues until PB=PB' ，(w/r)1= (w/r)2 in both nations.
• To summarize, PX/PY will become equal as a result of international
trade,and this will occur only when w/r has also become equal in
the two nations.
So far we have showed the process by which relative
factor prices are equalized.
• We now move on to take a look at how absolute factor
prices becomes equalized by trade. Equalization of
absolute factor prices means 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 (as is
discussed in the Section 5.5A). This, however, presumes
that all the assumptions hold: perfect competition in both
commodity and factor markets, same technology,
constant returns to scale in the production of both
commodities.
• From section 5.5A and 5.5B we can say that trade acts
as a substitute for the international mobility of factors
of production in the sense that they have the same
effects on factor prices. That is, trade serves as an
indirect way of trading factors of production .
• Factors of production, be it labor or capital, is in
constant pursuit of their own interests. Given perfect
mobility, labor would shift or migrate from the lowwage nation to high-wage nation until the returns to the
same type of labor became equal.
Similarly, capital would move from low-interest rate
nation to high-interest nation until returns on….
5.5C Effect of Trade on the Distribution
of Income
• While in previous section we examined the effect
of international trade on the difference in factor
prices between nations, in this section we
analyze the effect of international trade on
relative factor prices and income distribution
within each nation. That is, we examine how
international trade affects the real wages and
real income of labor in relation to real interest
rates and the real income of owners of capital
within each nation.
• Since resources—capital and labor, are assumed to be
fully utilized, both before and after trade, the real income
of labor moves in the same direction as the movement of
the price of labor, and the real income of capital moves in
the same direction as the movement of the price of capital.
• From Section 5.5A on P129, we can reach the conclusion
that:
International trade causes the real income of the
nation’s abundant and cheap factor to rise, and causes
the real income of the nation’s scarce and expensive
factor to fall
—referred to as Stolper-Samuelson theorem (斯托伯－萨
谬尔森定理).
A question for in-class discussion:
Why do labor unions in developed nations generally lobby
against the imports from the developing countries?
While nations generally gains from international trade, however, it
is quite possible that international trade may hurt particular groups
within nations—in other words, that international trade will have
strong and uneven effects on the distribution of income. The
benefits received by owners of capital tends to more than offset
the losses that labor suffer due to trade. Labor union speak for the
labor and lobby for trade restrictions. Should the U.S.
government implement trade restrictions? The answer is no! for
an individual interests group…, for the nation as a whole…With an
appropriate redistribution policy on the part of the gov., both labor
and owners of capital can benefit from free international trade—
to transfer part of the gains to subsidize the labor.
5.5D The Specific-Factor Model
• In the previous section we have discussed the effect that
inter-national trade has on the distribution of income.
But this effect is based on assumption 8( that factors are
perfectly mobile within a nation from one industry or
sector to another).This is likely to be true in the long
run.In the short run, however, it may not be true when
some factors are immobile or specific to some industry
or sector (a factor is industry-specific or sector-specific).
In such a case we have to modify the conclusions of the
H-O theory on the effect of international trade on the
distribution of income.We introduce the specific-factor
model to explain the effect.
• What is a specific factor? A factor is specific to
some industry or commodity if they can be used
only in the production of the particular commodity.
• In practice, factor specificity is not a permanent
condition. Rather, it is a matter of time or a
question of the speed of adjustment and the
distinction between specific and mobile factors is
not a sharp line. The more specific a factor is, the
longer it takes to re-deploy the factor between
industries.
wY
wX
VMPLX
VMPLY
E
·
w
OX
LX
L
L
w
LY
OY
wY
wX
VMPLX
VMPLY
E
·
w
OX
LX
L
L
w
LY
OY
wX
wY
VMPLX
VMPLX
F
wF
PX
w′
w
OX
LX
VMPLY
· E′
·
E
·
L
L
L′
w′
w
LY
OY
• Effect of trade on the short-run distribution of income
within a nation—the specific-factor model
•
From basic microeconomics we know that under perfect
competition and in isolation, the value of the marginal product of
labor in the production of X (VMPLX, the returns to factor ) in
the two industries in Nation 1 are :
VMPLX = PX MPLX
VMPKX = PXMPKX
………………………………………………………………………………………
VMPLY = PY MPLY
VMPKY =PYMPKY
• VMPLX is equal to the price of X (PX)times the marginal product
of labor (MPLX).For producers to maximize profits,they will
employ labor(capital) until the wage(interest rate) they must pay
equals the value of the marginal product of labor(capital)
wx =VMPLX wY =VMPLY ; rX= VMPKX rY =VMPKY
•
And such,we get the following expressions
wx = PX MPLX
rX= PXMPKX
wY = PY MPLY
rY = PYMPKY
• Suppose Nation 1 is labor-abundant nation ,commodity X is Lintensive,labor is perfectly mobile between two industries,but
capital is specific. With the opening of trade, Nation 1 will
specializes in producing X and PX/PY will rise.We suppose again
for simplicity that PX increases while PY remain unchanged.
1.Change in the nominal wage rate or nominal income of labor
• As the increase in PX/PY will increases the demand for and the
nominal wage rate of labor in industry X, wx ↗. Industry Y will
have to pay a higher going nominal wage rate with the transfer
of some of its labor to the production of X, wY ↗.
• Since labor is perfectly mobile ,the wage of labor will be the
same in the production of commodities X and Y. wx = wY =w.
2. Change in the real wage rate or real income of labor
•
w
 MPLX
PX
w
 MPLY
PY
From principles of microeconomics we know the law of
diminishing returns is at work as labor migrates from industry Y to
X.If industry X employs more L with a given amount of K,MPLX
declines(MPLX↘). It follows that although w and PX increase,the
increase in w is less than the increase in PX. The real wage rate
w/ PX declines in industry X.For industry Y, MPLY ↗, the real
wage rate w/ PY rises.
• The effect of this on the real wage rate of labor in nation 1 thus is
ambiguous(depends on their spending pattern). It falls in terms of
X but rises in terms of Y,which means that the real wage rate and
income will fall for workers who consumes mainly X and will
increase for workers who consumes mainly Y.
Let us take some time out to briefly review the law of
diminishing returns before we can turn to the analysis.
The law of diminishing returns holds that we will get
less and less extra output when we add successively
additional units of an input, while holding other inputs
constant.
Or to put it the other way around, the marginal product
(MP) of each unit of input will decline as the amount of
that input increases, all other inputs held fixed.
3. Change in the rewards(returns) to capital-the specific factor
rX
 MPKX
PX
rY
 MPKY
PY
The returns to the specific factor(capital) change unambiguously.
In the production of X,since the specific capital(K) has more labor
to work with, MPKX ↗, i.e., the real income of immobile K
increases, rx/PX ↗in the industry X.
In the production of Y, since the specific capital(K) has less labor
to work with, MPKX ↘, i.e., the real income of immobile K
decreases, rY/PY ↘ in the industry Y.
• We generalize the specific-factors model as follows :trade will
have an ambiguous effect on the nation’s mobile factors,
benefit the immobile factors specific to the nation’s export
commodities or sectors,and harm the immobile factors
specific to the nation’s import-competing commodities or
sectors.
• The long-run VS. the short-run
The conclusion above reached by the specific-factors model is
what we can expect in the short-run when some factors are
specific or immobile.In the long-run, however,all factors are
perfectly mobile,and the conclusion is exactly as the H-O theory
postulates (that is, the opening of trade will lead to an increase in
the real income or return of the factors used intensively in the
nation’s export commodities and to a reduction in the real income
or return of the factors used intensively in the nation’s importcompeting commodities).
5.6 Empirical Tests of the H-O Model
5.6A Empirical Results—The Leontief Paradox
• The first empirical test of the H-O model was made by Leontief.
The results were startling and seemed to conflict with the H-O
theory. Ever since, a large number of empirical tests were
conducted in an attempt to reconcile the results with the model.
• For his test, Leontief utilized the input-output table of the U.S.
economy to calculate the amount of L and K in a “representative
bundle” of $1 million worth of exports and import substitutes
for the year 1947 (the reason why Leontief used U.S. data on
import substitutes was that foreign production data on actual U.S.
imports were unavailable).
• The Leontief Paradox
Since the U.S. was accepted as the most K-abundant
nation in the world, Leontief expected to find that U.S.
would export K-intensive commodities and import Lintensive commodities. But the results went the other
way around— U.S. import substitutes were more Kintensive than U.S. exports, that is, the U.S. seemed to
import K-intensive commodities and export L- intensive
commodities. This was the opposite of what the H-O
model predicted, and the result becomes known as the
Leontief Paradox.
• It is the single biggest piece of evidence against the H-O
theory.
5.6B Explanations of the Leontief Paradox
There are more than one sources of bias as follows
1. Natural resources — oversimplified model of two
factors, K and L.
2. Tariff policy implemented by U.S. government —A
tariff is nothing else than a tax levied when a good is
imported. And such, a tariff reduces imports and stimulates
the domestic production of import substitutes. The fact
biased the pattern of trade that L-intensive industries were
heavily protected, and reduced the L-intensity of U.S.
import substitutes.
3. Physical capital—perhaps the most important source of
bias. Human capital and knowledge capital were
completely ignored in his measurement of capital.
Human capital refers to education, job training, and health
embodied in workers, which increase their productivity.
The implication is that since U.S. labor embodies more
human capital than foreign labor, if we incorporate human
capital component to physical capital, U.S. exports would
be more K-intensive in relation to its import substitutes
5.6 C Factor-intensity reversal
1. Factor-intensity reversal —a situation where a
given commodity is L-intensive in the L-abundant
nation and K-intensive in the K-abundant nation.
K
X Y
kX
kY
·
k Y
·
·
ω1
O
·
k X
ω2
L
2. The elasticity of substitution
The elasticity of substitution of factors in production
measures the degree or ease with which one factor
can be substituted for another in production as the
relative price of the factor declines.
3. The result of factor-intensive reversal
When factor-intensity reversal is present, neither the H-O
theorem nor the factor-price equalization theorem holds.
The H-O model fails because it would predict that Nation
1 (the L-abundant nation) would export commodity X (its
L-intensive commodity) and that Nation 2 (the K-abundant
nation) would also export commodity X (its K-intensive
commodity). Since the two nations cannot possibly export
the same homogeneous commodity to each other, the H-O
model no longer predicts the pattern of trade.