Lectures, 4
THE FACTOR ENDOWMENTS THEORY
The factor endowments theory (a.k.a. Heckscher-Ohlin theory, and the Modern Theory of
International Trade) is a “modern” extension of the classical approach and attempts to explain the
pattern of comparative advantage.
Does this by hypothesizing that comparative advantage is ultimately due to international
differences in relative factor endowments. Done for 4 reasons:
1. Natural extension of the classical theory which sees international factor immobility as
the basis for trade.
2. Can define “factor” broadly.
3. Seems important in practice.
4. Very useful theoretically for linking trade to internal income distribution, growth, factor
movements, and so on.
The basic vehicle for developing this theory is the Heckscher-Ohlin-Samuelson model, a twocountry version of the standard two-sector neoclassical model.
This model dominated international trade theory from the fifties into the eighties and remains
central today, but its practical relevance has always been a central controversy in the field.
I.
The Heckscher-Ohlin-Samuelson Model
2x2x2 model. Two goods (A and B), two factors (K and L) and two countries (home and foreign).
The Factor Endowments Theory
Page 2
1. The production function. Consider the production process for one of the goods in one of the
countries: A = FA(KA,LA), where FA is a neoclassical production function (CRS, strictly quasiconcave, etc.). Can utilize CRS to express FA in two other normalized forms.
intensive
Figure 4.1
extensive
Figure 4.2
2. Economics. Factors are paid the value of their marginal products, and profits are zero, i.e.,
prices = costs.
so
since {...} = 0 by cost minimization.
W ilfred J. Ethier
Page 3
and
Figure 4-3
Figure 4-4
Figure 4-5
Figure 4-6
The Factor Endowments Theory
Page 4
Duality between ù and kA.
Duality between F and c.
3. Two sectors: Factor-market clearing. Let B denote the second good, with an analogous
production sector. Then
RAkA + RBkB = k
aKA A + aKB B = K
or
RA + RB = 1
aLA A + aLB B = L
where RA / LA/L and RB / LB/L.
4. Two sectors: Relative factor intensity. A is relatively capital intensive [B is relatively labor
intensive] if:
kA(ù) > kB(ù).
Factor intensity reversal:
Figure 4-7
Figure 4-8.
W ilfred J. Ethier
Page 5
So reversals are associated with different degrees of substitutability of inputs across sectors.
Note that a given k can correspond to only one pattern of relative factor intensities, and therefore
so can a given PPF. In this sense reversals are global but not local phenomena.
At a factor intensity reversal, k = kA = kB, so the capital and labor constraints are identical to each
other and to the PPF, which is therefore linear.
Figure 4-9
The Factor Endowments Theory
Page 6
5. Two sectors: Relative commodity prices.
so:
Figure 4-10
Figure 4-12
Figure 4-11
W ilfred J. Ethier
Page 7
6. Two sectors: Comparative statics of price changes.
where èij denotes factor i's distributive share in sector j.
Thus:
Therefore
THE BASIC THEOREMS OF THE HECKSCHER-OHLIN-SAMUELSON MODEL
Theorem I (Stolper-Samuelson): A (small) change in relative prices and in factor rewards will
increase the real reward of the factor intensive in the production of the good whose relative
price has risen and reduce the real reward of the other factor, provided that the economy
remains diversified.
i.e., if we call good A the relatively capital-intensive one, then
The theorem has already been proved by deriving:
Show geometric derivations in Figure 10, Figure 11 and Figure 12.
The Factor Endowments Theory
Page 8
Can also be intuitively understood by the reasoning underlying the algebra.
[Explain in detail]
Note that although the statement of the theorem and the algebra were in terms of differential
changes, the basic reasoning and all the geometry could accommodate finite changes. Also factor
endowments were not referred to, so they could be changing as well.
But factor intensity reversals were excluded (by small changes in factor prices):
A movement from A to B produces the opposite
redistribution from a movement from A to B'
[though still have magnified price changes for
factors].
Constant endowments will prevent a FIR from
being encountered.
Figure 4-13
Theorem II (Global Stolper-Samuelson): Theorem I applies to finite price changes leaving the
economy diversified, provided that endowments are held fixed or that the technology does not
exhibit factor intensity reversals.
Expand on the significance of the SS theorem. Contrast with the effect of price changes when the
economy is specialized.
Theorem III (Factor Price Equalization): For each P consistent with both goods being
produced, there exists a cone H(P) of endowments such that all countries with endowments in
H(P), and with the given technology, will have identical factor prices when freely trading at
world prices P. The cone H(P) is of full dimensionality as long as it does not coincide with a
factor-intensity reversal.
W ilfred J. Ethier
Page 9
Proof is by construction of H(P). Since P is consistent with both goods being produced, P =
WA(W) for some W $ 0. Then let H(P) = {v | v $ 0 and v = A(W)x for some x $ 0}. If W is not at a
factor intensity reversal, A(W) is non-singular, so H(P) is two dimensional; if this is a reversal,
H(P) is a ray through the origin.
Illustrate and show how H(P) need not be unique if there are factor-intensity reversals.
Theorem IV (Global Univalence): If there are no factor-intensity reversals, any two countries
with the common technology must have equal factor prices if freely trading at a common world
price and if both countries diversify.
i.e., there is a global univalence between factor rewards and commodity costs in the absence of
factor-intensity reversals. This follows immediately from our earlier result that PB/PA is strictly
monotone in w/r, except at a factor intensity reversal. This also immediately implies the following, since the comparative advantage theorem applies to this model.
Theorem V (Partial Equalization): If there are no factor-intensity reversals and if two
countries share the same technology, relative factor prices will be more nearly equal in free
trade than in autarky, provided that autarky equilibrium is unique in each country.
Theorem VI (Rybczynski): At constant relative commodity prices, a (small) change in factor
endowments will increase, relative to both factors, the output of the good making relatively
intensive use of the factor with the relatively enlarged endowment, and reduce the output of the
other good, relative to both factors, provided that the economy remains diversified.
Thus, if A is relatively capital intensive,
and
Can be proved from the factor constraints:
The Factor Endowments Theory
Page 10
From theorem III, a small change in endowments at constant P cannot change W, because the
economy remains in H(P). Thus the aij are constant, and differentiation gives:
from which the theorem follows at once. (Here ëKA = aKAA/K, so that ëKB + ëKA = 1, etc.)
Give the intuitive argument.
Note that the argument applies to any finite change which leaves E in H(P). If there is no FIR, so
H(P) is unique, this means any finite change leaving the economy diversified.
Theorem VII (Global Rybczynski): Theorem VI applies to any finite change in endowments
leaving the economy diversified, provided that there is no factor intensity reversal.
Geometrically:
Figure 4-14
Figure 4-15
W ilfred J. Ethier
Page 11
Contrast with case of complete specialization. Like SS, a case where more than one sector makes
a big difference.
Path of outputs if the K stock expands, at constant commodity prices, if the A sector is initially Kintensive, and if › FIRs:
Figure 4-16
Figure 4-17
The basic goal of H.O. theory is to explain trade patterns; this is done in the H.O. theorem, which
relates trade to factor abundance. To do this, need a definition of factor abundance. Have two:
Q - Def.: A country is capital abundant relative to another if it has more K
per worker.
P - Def.: A country is capital abundant relative to another if it would have a
higher wage-rental ratio in autarky.
The second definition obviously embodies more information than the first. Have a version of the
H.O. theorem corresponding to each.
The Factor Endowments Theory
Page 12
Theorem VIII (Quantity Version of H. O.): Suppose that two countries have:
(a) Identical homothetic demands,
(b) identical HOS technologies, with
(c) no FIRs.
Then in any free trade equilibrium (with some trade) each country will export the good that
makes relatively intensive use of that country's relatively Q-abundant factor.
Can be proved via the Rybczynski theorem. Suppose that the two countries trade and establish a
common world price P. Then assumption (c) implies at most a unique diversification cone H(P).
Theorem VII implies that the relatively capital abundant country produces a higher A/B ratio, if
both countries' endowments are in H(P) [by assumption (b)], calling the relatively capital
intensive good A. Both countries' endowments cannot lie outside H(P) and on the same side of
H(P), or they would both specialize in the same good and there would be no trade. Thus if a
country's endowment is outside of H(P) it must specialize in the good that makes intensive use of
its abundant factor.
Thus the capital abundant country produces the higher A/B ratio, regardless of the pattern of
specialization. By (a) the two countries consume the two goods in the same proportions. Thus the
theorem follows.
Note that if the two countries are separated by an odd number of FIRs the theorem's conclusion
will hold for one country but not the other; if there are an even number of separating FIRs the
theorem's conclusions may or may not hold. But in all cases each country “exports” its abundant
factor in the sense that its bundle of exports embodies in its production a more intensive bundle
of the services of the abundant factor that did its bundle of imports where produced.
Note also the role of demand. This motivates the “price version” using the P-def. of abundance.
W ilfred J. Ethier
Page 13
Theorem IX (Price Version of H. O.): Suppose that two countries have:
(a) identical (HOS) technologies, with
(b) no FIRs.
Then each country has a comparative advantage in the good making relatively intensive use of
the country's relatively P-abundant factor. Thus each country will export that good in free trade,
if:
(c) Autarky equilibrium is unique in each country.
Proof of the first part follows directly from Theorem IV; the proof of the second part follows
directly from the comparative advantage theorem, since the HOS model satisfies all the other
requirements of that theorem.
A “demand reversal” is said to occur if the two definitions of abundance differ. Note that in this
case theorem IX applies. Also free trade necessarily features factor price equalization and the
presence of FIRs in the technology becomes irrelevant. This requires relative endowments to be
similar, and tastes different. If, on the other hand, K/L in the two countries is sufficiently diverse,
no pattern of tastes can produce a demand reversal, and factor price equalization is impossible.
Discuss the implications of HO + SS for the effects of free trade on the internal distribution of
income in each country and the implications of HO + RYB for the effects of economic growth on
a country's offer curve. Use reciprocal demand to infer the effects on the terms of trade, and
discuss the possibility of immiserizing growth.