Download Absolute and Comparative Advantage, Reconsidered: The Pattern

Review of International Economics, 10(4), 645–656, 2002
Absolute and Comparative Advantage,
Reconsidered: The Pattern of International Trade
with Optimal Saving
Richard A. Brecher, Zhiqi Chen, and Ehsan U. Choudhri*
Abstract
The paper obtains new results about absolute and comparative advantage, by introducing international technological differences into the three-sector Findlay–Komiya and two-sector Oniki–Uzawa–Stiglitz models of
open-economy growth with optimal saving. For example, if a country has the same Hicks-neutral advantage
in all industries, it exports the capital-intensive tradable, even though the technological advantage is only
absolute rather than comparative. Alternatively, even a small comparative advantage in some good is sufficient for the advanced country to export this product, regardless of relative factor supplies. In either case,
the fundamental reason for trade is technological superiority rather than factor abundance.
1. Introduction
Why countries trade with each other is a central question in international trade theory.
The celebrated Heckscher–Ohlin model views international differences in relative
factor endowments as the fundamental cause of trade. This view is questionable,
however, when the stock of capital is endogenously determined in the long run. The
basic two-dimensional Heckscher–Ohlin model (with capital and labor as the two
factors) has, in fact, been extended to allow for capital accumulation as a process of
optimal saving and investment within the neoclassical growth framework. There
are two approaches towards such an extension: one, based on the contributions of
Oniki and Uzawa (1965) and Stiglitz (1970), treats one of the two goods as a capital
good; and the other, arising from Findlay’s (1995) adaptation of Komiya’s (1967)
framework, adds a nontraded capital good to the two traded consumption goods. To
provide a reason for international trade, these optimal-accumulation versions of the
Heckscher–Ohlin model assume intercountry variation in discount rates. There is,
however, no compelling argument that such variation is an important source of trade.1
An alternative assumption is that technology differs between countries.This assumption is appealing in view of recent evidence that technological differences need to be
added to the fixed-endowment version of the Heckscher–Ohlin model to explain crosscountry data on the factor content of trade (Trefler, 1993, 1995; Davis and Weinstein,
1998) and on the pattern of production (Harrigan, 1997).2 The implications of such
differences for international trade in the presence of optimal accumulation, however,
are not well understood. To explore these implications, this paper examines the effects
of various types of technological advantage in both the Findlay–Komiya and
* Brecher, Chen, Choudhri: Carleton University, 1125 Colonel By Drive, Ottawa, ON, Canada K1S 5B6.
Tel: (613)520-2600, ext. 3765 (Brecher), 7456 (Chen), 3754 (Choudhri); Fax: (613)520-3906; E-mail:
[email protected], [email protected], and [email protected]. We wish to thank
an anonymous referee for helpful comments and suggestions. Our research was supported by the Social
Sciences and Humanities Research Council of Canada under grants 804-96-0036 (Brecher and Choudhri)
and 410-99-0844 (Chen).
© Blackwell Publishers Ltd 2002, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA
646
Richard A. Brecher, Zhiqi Chen, and Ehsan U. Choudhri
Oniki–Uzawa–Stiglitz models. Our analysis yields new results about the pattern of
trade, which are in sharp contrast to those of traditional models.
A well-known implication of the Ricardian model is that uniform absolute advantage does not cause international trade.3 This proposition carries over to the fixedendowment version of the Heckscher–Ohlin model if the advantage is in the form of
Hicks-neutral superiority and countries are identical in all other respects. In the
optimal-accumulation versions, however, the present paper shows that uniform advantage does cause trade. It also shows that the technologically superior country exports
the capital-intensive good but may be labor-abundant in the steady state. Thus, uniform
advantage causes international trade, but need not lead to a trade pattern associated
with the standard Heckscher–Ohlin model (in which the capital-abundant country
exports the capital-intensive good). The case of uniform Hicks-neutral superiority is
especially interesting in light of its empirical support from Trefler (1995) and Davis
and Weinstein (1998).
This paper also examines the role of comparative technological advantage. In
the fixed-endowment version of the Heckscher–Ohlin model, the influence of such
an advantage on the pattern of international trade is not decisive, since the effect
of superior technology in a sector can be offset by a relative scarcity of the factor
used intensively in this sector. No such ambiguity arises, however, in the optimalaccumulation versions. Indeed, the paper shows that in these versions, even a small
technological advantage in a single tradable good is sufficient for this good to be
exported. The paper derives, as well, conditions under which such an advantage can
lead to relative abundance of capital in the country that exports the labor-intensive
product. Thus, capital accumulation in the presence of nonuniform advantage can
violate the Heckscher–Ohlin pattern of trade, and suggest a possible explanation for
the Leontief Paradox.
The present paper focuses primarily on the three-good Findlay–Komiya model,
which is more complex than the two-good Oniki–Uzawa–Stiglitz model, but provides
a richer range of possibilities. Section 2 sets up the three-good model, and section 3
discusses its key results. The set-up and results of the two-good model are briefly
outlined in section 4. Section 5 offers some concluding remarks.
2. The Three-Good Model
This section extends the Findlay–Komiya model to incorporate international differences in technology. First consider a single competitive economy that uses capital and
labor services to produce two tradable consumption goods, 1 and 2, in addition to
capital itself as nontraded good 3. The production function for each good is given by
Yi (t ) = a i Fi [Ki (t ), l (t )Li (t )], i = 1, 2, 3,
(1)
where Yi(t) units of output are produced by Ki(t) and Li(t) units of capital and labor
inputs in industry i at time t. Parameter ai is a Hicks-neutral measure of technological
efficiency for good i, and l(t) represents the number of efficiency units per natural unit
of labor at time t. Assume that l(t) = l(0)egt, where the constant g (>0) is the rate of
labor-augmenting technical progress. Each production function exhibits constant
returns to scale with positive but strictly diminishing marginal products, and satisfies
the Inada conditions. Thus, suppressing the time argument henceforth (except when
needed for clarity), and defining ki ∫ Ki/lLi, rewrite (1) as
Yi = lLi a i fi (ki ), i = 1, 2, 3,
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(2)
ABSOLUTE AND COMPARATIVE ADVANTAGE
647
where fi(ki) ∫ Fi(ki, 1), fi¢ > 0, fi≤ < 0, fi¢(0) = •, and fi¢(•) = 0.
The nominal wage and rental rates, W and R, are determined by the marginal productivity conditions as follows:
W = Pi la i [ fi (ki ) - ki fi ¢(ki )], i = 1, 2, 3,
(3)
R = Pi a i fi ¢(ki ), i = 1, 2, 3,
(4)
where Pi is the price of good i. Good 1 is capital-intensive relative to 2, in the sense
that k1 > k2 for any given values of W and R. Then, as well-known implications of (3)
and (4), each ki is an increasing function of W/lR, while this factor-reward ratio is a
decreasing function of a1P1/a2P2 if Y1 and Y2 are both positive. Thus, when all three
goods are produced,4 we have
r = a 3j ( pa 1 a 2 ),
(5)
where p ∫ P1/P2; r ∫ R/P3, which equals the rate of interest; and j¢ > 0 by the
Stolper–Samuelson theorem.
Let K and L represent the economy’s aggregate amounts of capital and labor at a
point in time. Assume, for simplicity, that L is constant over time. The productionpossibility frontier for the tradable sector, comprising the two consumption goods,
depends on the quantities of capital and labor (in efficiency units) available to this
sector and on the Hicks-neutral measures of technological efficiency. Thus, outputs of
goods 1 and 2 are given by
Y1 = Q1 ( p, KT , lLT , a 1 , a 2 ),
(6)
Y2 = Q2 (1 p, KT , lLT , a 1 , a 2 ),
(7)
where KT ∫ K - K3, LT ∫ L - L3, ∂Q1/∂p > 0, ∂Q2/∂(1/p) > 0, while the other partial
derivatives of Q1 and Q2 are signed by the well-known theorems of Rybczynski (1955)
and Findlay and Grubert (1959). Given constant returns to scale: functions Q1 and Q2
are homogeneous of degree one in KT and lLT, as well as in a1 and a2; Q1 is homogeneous of degree zero in a2 and p; and Q2 is homogeneous of degree zero in a1
and 1/p.
Making use of these homogeneity properties while defining yi ∫ Yi/lL, kT ∫ KT/lL,
and lT ∫ LT/L, express (6) and (7) as
yi = a i qi ( pa 1 a 2 , kT , lT ), i = 1, 2,
(8)
where q1(•) ∫ Q1(pa1/a2, kT, lT, 1, 1) and q2(•) ∫ Q2(a2/pa1, kT, lT, 1, 1), with ∂qi/∂(pa1/a2)
0, ∂qi/∂kT 0, and ∂qi/∂lT 0 as i = 1 or 2, respectively, when both consumption
goods are produced. To see how kT and lT in turn depend on k ∫ K/lL, use (2) to
obtain
kT = k - k3 y3 a 3 f3 (k3 ),
lT = 1 - y3 a 3 f3 (k3 ).
(9)
(10)
Assume that all households have the same tastes, and normalize their total number
to equal 1. Subject to their budget constraint (making consumption plus saving equal
to income) at time t, these infinitely lived households maximize the present discounted
•
value of lifetime utility, given by Ú0 logU[C1(t), C2(t)]e-rtdt; where r (>0) is the pure
rate of time preference; C1 and C2 denote the amounts of goods 1 and 2 consumed
at a point in time; while the function U is strictly quasi-concave and first-degree
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Richard A. Brecher, Zhiqi Chen, and Ehsan U. Choudhri
homogeneous in its two arguments.5 For well-known reasons, this intertemporal
optimization implies that r = r + g in the steady state.6 This equality and (5) yield
a 3j ( p a 1 a 2 ) = r + g ,
(11)
when all three goods are produced. In this case, (11) uniquely determines p for given
values of the parameters r, g, and ai (i = 1, 2, 3).7 Thus, in the steady state, relative
product prices are independent of the pattern of consumer preferences described by
the functional form of U(•).
In light of the specified properties of the U function, utility maximization also implies
that Ci = bi(p)(pC1 + C2) for i = 1, 2; where each bi > 0, since we assume that consumption remains diversified. Thus, defining ci ∫ Ci/l, while noting that pc1 + c2 = py1 +
y2 (because of market clearing for nontraded good 3), we obtain
ci = b i ( p)( py1 + y2 ), i = 1, 2.
(12)
For simplicity of exposition, assume that capital does not depreciate. Under this
assumption, y3 [= (dK/dt)/lL] = dk/dt + gk. Thus, in the steady state (where dk/dt = 0):
y3 = gk.
(13)
Define x ∫ y1 - c1, which represents the excess supply of good 1 per efficiency unit
of labor. Then use (4), (5), (8)–(10), (12), and (13) to obtain
x = a 1 c ( p, k, a 1 a 2 , a 3 ).
(14)
As the Appendix shows: ∂c/∂p > 0 in autarky; ∂c/∂k > 0 if y1, y2 > 0; ∂c/∂(a1/a2) > 0;
and ∂c/∂a3 0 as k3 > k1 (>k2) or k3 < k2 (<k1), respectively.8 The positive sign for the
first three of these partial derivatives indicates that the excess supply of good
1 increases (as expected) in response to rises in its relative price, the relative supply
of its intensively used factor, and its relative efficiency. To understand why the sign
of ∂c/∂a3 depends on whether good 3 is most or least capital-intensive, first note
that holding p, a1/a2, and k constant fixes k3 (by (4) and (5)) and y3 (via (13)). Then,
an increase in a3 causes industry 3 to release both capital and labor for transfer
to the traded-goods sector. This transfer raises kT proportionately more or less
than lT and hence increases or decreases x as good 3 is, respectively, most or least
capital-intensive.
Now expand the model to include a foreign country, in addition to the home country
described above. Initially, assume that both countries are identical in every respect, and
normalize their technological parameters to make l(0) = a1 = a2 = a3 = 1. To examine
how international differences in technology determine the pattern of international
trade—as predicted by autarkic discrepancies in product-price ratios—we analyze
various combinations of shifts in the ai and l(0) parameters at home, leaving their
foreign counterparts unchanged (and equal to 1).
3. Results in the Three-Good Model
This section derives results regarding four specific combinations of international technological differences. These results are not only interesting in their own right, but also
sufficient (when suitably combined) to analyze any other possible combination arising
from shifts in the parameters ai (i = 1, 2, 3) and l(0).
First consider the case in which Hicks-neutral technological differences between
countries are the same for all three goods. For this case, in which a country has an
absolute but no comparative advantage in technology, the following result holds.
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649
Proposition 1. Uniform technological advantage of the Hicks-neutral variety causes the
technologically advanced country to export the capital-intensive consumption good.
To prove this proposition, set a1 = a2 = a3 = a in (11), and differentiate the resulting equation to obtain (at the initial point where a = 1) dp/da = -j/j¢ < 0.9 Since the
home country thus has a lower price of good 1 relative to 2 in autarky, it will export
the first (capital-intensive consumption) good when presented with the opportunity to
engage in free international trade. This result can be explained by the intertemporal
optimality condition that requires r (= af3¢(k3)) to remain constant at the level r + g
in steady-state equilibrium. To satisfy this condition, a rise in k3 must accompany
the given increase in a. Thus, W/lR must also rise, implying a fall in p (via the
Stolper–Samuelson theorem).
Although Proposition 1 predicts unambiguously that the uniformly advanced
country exports the capital-intensive good, we now show that this country might in fact
be labor-abundant. Noting that x = 0 in autarky, while again setting a1 = a2 = a3 = a (=
1 initially), differentiate (11) and (14) to obtain dk/da = [(∂c/∂p)j/j¢ - ∂c/∂a]/(∂c/∂k).
Although ∂c/∂k > 0 and (∂c/∂p)j/j¢ > 0, recall that ∂c/∂a3 (= ∂c/∂a) > 0 if k3 > k1, in
which case it is possible (but not inevitable) to have dk/da < 0.10 This outcome can
arise because a uniform technological improvement has two opposing effects on the
excess supply of good 1 when good 3 is relatively capital-intensive. On the one hand,
this improvement has a positive impact on the excess supply by transferring factors
from good 3 to the traded-goods sector, as explained above. On the other hand, the
induced fall in the price of good 1 (relative to 2) has a negative impact on excess supply.
If the positive impact outweighs the negative one, the aggregate capital/labor ratio
must fall to maintain a zero excess supply in autarky.
Thus, the home country might be labor-abundant in autarky even though it
ultimately exports the capital-intensive tradable. This result differs from the
Heckscher–Ohlin prediction that, in the presence of absolute without comparative
technological advantage, a capital-abundant (labor-abundant) country exports the
capital-intensive (labor-intensive) good. If good 3 is instead labor-intensive (i.e., k3 <
k2), then ∂c/∂a < 0 and hence dk/da > 0. In this case, a Heckscher–Ohlin trade pattern
would be observed. Of course, in both cases (exogenous) technological differences—
rather than (endogenous) factor abundance—are the fundamental cause of trade.
Although dk/da is ambiguous in sign, d(kT/lT)/da > 0 unambiguously. In other words,
regardless of the capital-intensity ranking for good 3, the autarkic capital/labor ratio
of the traded-goods sector as a whole is greater for the home than for the foreign
country. To show this result, use (8) and (12) while noting that y1/y2 = c1/c2 in autarky,
to get
q( pa 1 a 2, kT lT ) a 1 a 2 = b ( p),
(15)
where q(•) ∫ q1(pa1/a2, kT/lT, 1)/q2(pa1/a2, kT/lT, 1), implying that ∂q/∂(pa1/a2) > 0 and
∂q/∂(kT/lT) > 0; and b(p) ∫ b1(p)/b2(p), with b¢ < 0. Autarkic condition (15) simply states
that the tradable-output ratio y1/y2 equals the consumption ratio c1/c2. Setting a1 = a2,
differentiate (15) totally with respect to a while recalling that dp/da = -j/j¢, to obtain
d(kT/lT)/da = (∂q/∂p - b¢)j/j¢[∂q/∂(kT/lT)] > 0.
Although we have been comparing autarkic equilibria so far, it is also possible to
examine how aggregate capital/labor ratios are affected by the introduction of international trade. For this purpose, turn to Figure 1, in which the home excess-supply
curve HH¢ for good 1 relates x to p. At each interior point on this curve’s horizontal
segment, EE¢, all three goods are produced. Throughout this segment, p is fixed (by
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Richard A. Brecher, Zhiqi Chen, and Ehsan U. Choudhri
p
F
H¢
T
E¢
E
F¢
A
H
x
0
Figure 1. Free-Trade Equilibrium
(11)), and changes in x are generated by changes in k (according to (14)). Either y1 or
y2 equals zero at all points on segment HE or E¢H¢, respectively. Along both of these
segments with specialized production, k is fixed,11 but x varies with p (via changes in
c1). Similarly, FF¢ is the foreign excess-demand curve for good 1. The horizontal
segment of this curve lies above EE¢ because a > 1.
Free-trade equilibrium (assumed to be unique) takes place at the point where the
two curves intersect.12 Clearly, at least one country’s production will be specialized at
this point. We illustrate an equilibrium at point T where both countries are specialized.
The movement from autarky to free trade (e.g., from point A to T for the home
country) will cause the aggregate capital/labor ratio to increase at home and decrease
abroad. Nevertheless, if the foreign country is relatively capital-abundant in autarky
(for reasons discussed above), it could remain so under free trade even though
it exports the labor-intensive tradable,13 still in violation of the Heckscher–Ohlin
prediction.14
Next, consider the case in which a Hicks-neutral technological advantage applies
equally to only the two traded goods of a country. Although this advantage generally
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651
leads to trade when all three goods are consumable,15 the situation is quite different
in the present case (with one capital and two consumption goods), as indicated by the
following result.
Proposition 2. No incentive to trade arises from a Hicks-neutral technological advantage that applies equally and only to both traded goods of a country.16
This proposition follows immediately from the fact that (with a3 now constant) the
autarkic value of p clearly remains unchanged when a1 and a2 are subject to an
equiproportionate increase in (11).
Let us now turn to the case in which Hicks-neutral technological differences between
countries are unequal for the two tradables, and absent for the nontradable. In the case
of fixed factor endowments, a country with a relative technological advantage in producing a traded good exports this good, provided that it is not too abundant in the
factor used intensively in the other tradable. No such proviso is needed to ensure an
unambiguous pattern of trade in the present model with optimal capital accumulation,
as established by the following result.
Proposition 3. A country will export the consumption good in which it has a comparative technological advantage of the Hicks-neutral variety, if there is no international
difference in the technology for the capital good.
This proposition follows immediately from (11), which implies that a parametric
increase or decrease in a1/a2 causes a respective fall or rise in the autarkic value of p,
to keep pa1/a2 constant.
Interestingly, a change in a1/a2 causes the autarkic values of kT/lT and k to move
together in a direction that depends only on the elasticity of substitution in consumption. Denoting this elasticity by s(∫ -pb¢/b), differentiate (15) totally with
respect to a1/a2 while recalling that pa1/a2 remains constant, and thus establish
that d(kT lT ) d(a 1 a 2 ) = (s - 1)q [∂ q ∂ (kT lT )] 0 as s 1. To understand this condition, first note that a doubling of a1/a2 will (ceteris paribus) double the left-hand side
of (15), and cause p to be halved (to keep pa1/a2 constant). This halving doubles the
right-hand side of (15) if s equals 1, in which case there is no need for a change in
kT/lT. On the other hand, as s is respectively larger or smaller than 1, the right-hand
side of (15) more or less than doubles, requiring a rise or fall in kT/lT to keep the two
sides of (15) equal. The sign of s - 1 also determines the sign of dk/d(a1/a2), since the
following argument shows that k moves in the same direction as kT/lT. Noting that k3
remains constant (in light of (4), (5), and (11)), substitute (13) into (9) and (10) to
derive the result that dk/d(kT/lT) = klT2 /kT > 0.
This analysis suggests an important role for consumption substitutability in a technology-based explanation of the Leontief Paradox. In particular, if the home country
has a comparative technological advantage in the labor-intensive tradable and s < 1,
it would be relatively capital-abundant in autarky, and could remain so in free trade
(according to the above argument in connection with Figure 1). By similar reasoning,
if the country is comparatively advanced in the other good and s < 1, it could be a
labor-abundant exporter of the capital-intensive tradable.
Finally, consider the case in which there is an international technological difference
of the labor-augmenting variety, in the sense that l differs from its foreign counterpart. When factor supplies are fixed (in natural units), such a l-type difference leads
to trade between otherwise identical countries, by causing the effective endowment of
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Richard A. Brecher, Zhiqi Chen, and Ehsan U. Choudhri
labor (in efficiency units) to differ internationally. In the present model with saving
and investment, however, the following result holds.
Proposition 4. Labor-augmenting technological advantage does not provide an incentive for international trade.
This proposition follows immediately from the fact that the autarkic value of p is
independent of l, as clearly implied by (11).
Trefler (1993) provides empirical support for Leontief’s (1953) conjecture that a
strongly labor-augmenting technological advantage (by making the US labor-abundant
in efficiency units) could explain why exports were more labor-intensive than imports
for the US in 1947. This explanation of the Leontief Paradox is problematic in our
model because, in light of Proposition 4, a labor-augmenting technological advantage
would not give rise to the 1947 (or any other) pattern of trade.
Propositions 1–4 can be used together to analyze the trade pattern caused by any
combination of shifts in the ai and l(0) parameters, from their initial value of 1.
Suppose, for example, that such shifts make a1 = 8, a2 = 4, a3 = 2, and l(0) = 2. This set
of parametric shifts can be conceptually decomposed into the following four steps: (i)
doubling every ai, from 1 to 2; (ii) further doubling a1 and a2, from 2 to 4; (iii) again
doubling a1, from 4 to 8; and (iv) doubling l(0), from 1 to 2. Steps (i) and (iii) cause a
drop in the autarkic value of p, in light of Propositions 1 and 3. As implied by Propositions 2 and 4, steps (ii) and (iv) have no effects on p. Thus, in the present example,
the home country exports good 1. The same four-step decomposition can be used
similarly to analyze how k and kT/lT compare with their foreign counterparts.
4. The Two-Good Model: Set-Up and Results
This section briefly outlines the two-good Oniki–Uzawa–Stiglitz model with optimal
saving, and shows that this model preserves some of the insights generated by the more
complex three-good model analyzed above. For this purpose: drop good 3; reinterpret
good 2 as the (now tradable) output of the capital-producing industry; redefine r ∫
R/P2; replace U(•) by C1, because good 1 is now the only form of consumption; and
relax the assumption that k1 > k2.17
Thus, change subscript 3 to 2 in (5), and rewrite (11) as
a 2j ( p a 1 a 2 ) = r + g ,
(16)
where j¢ 0 as k1 k2 with diversified production. Similarly, replace subscript 3
by 2 in (13), and use the resulting equation with (8)—after noting that kT/lT = k and
lT = 1 without a nontraded good—to obtain
a 2 q2 ( pa 1 a 2, k, 1) = gk,
(17)
where ∂q2/∂k 0 as k1 k2 (and ∂q2/∂(pa1/a2) < 0 as before). Equations (16) and (17)
determine p and k, given a1, a2, r, and g.
To investigate the effects of a uniform technological advantage of the Hicks-neutral
variety, set a1 = a2 = a (= 1 initially), and differentiate (16) and (17) to derive the following results: dp/da 0 but the sign of dk/da is positive or ambiguous as k1 k2,
respectively. Thus, the technologically advanced country exports the capital-intensive
good, but may be labor-abundant if good 2 is capital-intensive. These results are
reminiscent of Proposition 1 and related discussion.
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Suppose, instead, that the home country has a Hicks-neutral advantage in producing good 1, while the technology for good 2 is internationally identical.18 To derive the
implications of this advantage, set a2 = 1 (= a1 initially), and use (16) and (17) to show
that dp/da1 < 0 and dk/da1 = 0. Thus, the home country exports good 1—in consonance
with Proposition 3—and has the same aggregate capital/labor ratio as the foreign
country in autarky. Nevertheless, in free-trade equilibrium, the country that exports
the capital-intensive (labor-intensive) good will be relatively abundant in capital
(labor), for reasons suggested by the discussion of Figure 1.
On the other hand, if the only technological advantage is a Hicks-neutral one in
home production of good 2, set a1 = 1 (= a2 initially) to obtain the following results
with the help of (16) and (17): dp/da2 > 0, and dk/da2 is positive or ambiguous in sign
as k1 k2, respectively.19 Consequently, the home country becomes an exporter of
good 2 (in the spirit of Proposition 3), is capital-abundant (in violation of the
Heckscher–Ohlin prediction) if this good is labor-intensive, and may be abundant
in either factor under the opposite factor-intensity ranking. Especially interesting (in
relation to the Leontief Paradox) is the case in which k1 > k2, since even a small
technological advantage in good 2 then causes the advanced country to export the
labor-intensive good, despite the fact that this country is capital-abundant necessarily
in autarky and possibly in free trade.
Finally, note that a technological advantage of the labor-augmenting variety does
not cause trade, since l does not appear in (16). Thus, Proposition 4 continues to
hold.
5. Conclusion
This paper introduces international technological differences into the Findlay–Komiya
and Oniki–Uzawa–Stiglitz models, which extend the Heckscher–Ohlin framework to
let the stock of (nontraded or traded) capital be endogenously determined through a
process of optimal saving and investment. The paper’s analysis provides a new perspective on the long-run pattern of trade between countries with different types of
technological advantage.
In one basic case, a country has the same Hicks-neutral advantage over its trading
partner in all goods. Although the advanced country has only absolute (but not
comparative) advantage in technology, it still exports the capital-intensive product.
Another interesting case is that of a country with a comparative technological advantage in some good. Even if small, such an advantage is sufficient for the country to
export this good. In either case, the fundamental reason for the resulting pattern of
trade is technological superiority rather than relative factor abundance.
Our results are based on a comparison of steady states. Although capital abundance
does not drive these results, it could play an important role in the transition to longrun equilibrium. Trade-pattern dynamics during the transitional process in the presence of technological differences is an interesting topic for future research.
There is now a large literature addressing the question of why international disparities in technology arise and persist. No consensus, however, has yet developed on what
are their key sources. Thus, this paper does not attempt to incorporate a particular
explanation of technological differences, but focuses instead on the effect of given differences on the pattern of trade in the long run. Even in a more general model that
endogenizes such differences, the effects highlighted by our analysis would surely
remain relevant.20
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Richard A. Brecher, Zhiqi Chen, and Ehsan U. Choudhri
Appendix
Using (8), (12), and (14), write
c (∑) = q1 (∑) - b 1 ( p) [ pa 1q1 (∑) + a 2 q2 (∑)] a 1 .
(A1)
In light of the well-known formulae for Rybczynski effects (see, e.g., Kemp, 1969,
p. 14):
∂ qi ∂ kT = fi (ki - k j ) , ∂ qi ∂ lT = k j fi (ki ) (k j - ki ) , i, j = 1, 2,
j πi.
(A2)
Use (13) to express (9) and (10) as
kT = k - gkk3 a 3 f3 , lT = 1 - gk a 3 f3 .
(A3)
From (A1)–(A3), we have
∂c ∂ k = f1 (1 - pb 1 ) (1 - gk3 a 3 f3 + k2 g a 3 f3 ) (k1 - k2 )
+ f2 b 1 (1 - gk3 a 3 f3 + k1 g a 3 f3 )a 2 a 1 (k1 - k2 )
> 0,
∂c ∂ (a 1 a 2 ) = p(1 - pb 1 )∂ q1 ∂ ( pa 1 a 2 )
- pb 1 [∂ q2 ∂ ( pa 1 a 2 ) - q2a 2 a 1 ]a 2 a 1 > 0,
∂c ∂a 3 = gk [(1 - pb 1 ) f1 (k3 - k2 ) + a 2 b 1 f2 (k3 - k1 ) a 1 ] a 32 f3 (k1 - k2 )
Ï> k1 (> k2 )
0 as k3 Ì
,
Ó< k2 (< k1 )
∂c ∂ p = (a 1 a 2 ) ∂ q1 ∂ ( pa 1 a 2 )
- [ f1 gk (k1 - k2 ) a 3 f3 ][( f3 - k3 f3¢ + k2 f3¢) f3 ] dk3 dp
- [b 1¢ ( pa1q1 + a 2 q2 ) + b 1a 1q1 ] a 1
> 0 in autarky.
In determining the sign of ∂c/∂k, note that 1 - gk3/a3f3 = kT/k > 0 and 0 < b2 ∫
(1 - pb1). This identity is also used to sign ∂c/∂(a1/a2) and ∂c/∂a3. The following facts,
moreover, help to determine the sign of ∂c/∂p: f ¢3 < f3/k3; dk3/dp < 0; and, at the autarkic equilibrium (where aiqi = ci for i = 1, 2), S ∫ b 1¢(pa1q1 + a2q2) + b1a1q1 < 0 because
this expression equals the consumer’s substitution effect according to the Slutsky
decomposition.
As each good’s elasticity of substitution in production approaches 0 or •, clearly
dk3/dp and (in light of Bhagwati and Srivinasan, 1971) ∂q1/∂(pa1/a2) approach 0 or •,
respectively. Similarly, S approaches 0 (-•) as the elasticity of substitution in consumption approaches 0 (•). Thus, as all of these elasticities approach 0 (•), the above
expression for ∂c/∂p also approaches 0 (•) in autarky.
References
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Response and Factor Price Equalisation,” Journal of International Economics 1 (1971):19–35.
Chen, Zhiqi, “Long-Run Equilibria in a Dynamic Heckscher–Ohlin Model,” Canadian Journal
of Economics 25 (1992):923–43.
Davis, Donald R. and David E. Weinstein, “An Account of Global Trade,” NBER working paper
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———, “Comparative and Absolute Advantage,” Swiss Journal of Economics and Statistics 116
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Stiglitz, Joseph E., “Factor Price Equalization in a Dynamic Economy,” Journal of Political
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Notes
1. Differences in discount rates also cause interest rates to differ between countries, and thus
lead to a number of paradoxical results under free international borrowing and lending. For a
discussion of these results in the context of a one-sector growth model, see Barro and Salai-Martin (1995, ch. 3). International trade could also arise from an initial difference in national
capital/labor ratios, as Chen (1992) shows for the Oniki–Uzawa–Stiglitz model, and Manning
et al. (1993) demonstrate within a model similar to the Findlay–Komiya one. (For a related
paper, see also Markusen and Manning, 1993.) This possibility, however, would be precluded
by even a small barrier to trade.
2. The different-technology assumption also plays an important role in empirical work on
“levels accounting” (Hall and Jones, 1999) and “conditional convergence” (Islam, 1995) within
the growth literature.
3. See, however, Jones (1980) for a trade-inducing effect of absolute advantage when an internationally footloose input is added to the standard Ricardian model.
© Blackwell Publishers Ltd 2002
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Richard A. Brecher, Zhiqi Chen, and Ehsan U. Choudhri
4. This situation must prevail in autarky if consumer preferences for goods 1 and 2 have the
usual neoclassical properties that lead to diversified consumption.
5. The following analysis easily extends to the more general case in which our instantaneous
utility function, logU(•), is replaced by {[U(•)]1–q - 1}/(1 - q) where q > 0. (The latter function
approaches the former as q approaches 1.) Such a function is needed for the sake of consistency
with steady-state growth in per capita consumption, as explained by Barro and Sala-i-Martin
(1995, p. 64).
6. In this condition, g would be multiplied by q under the generalization discussed in note 5.
7. This solution for p determines a unique value of P3/P2 in accordance with (3) and (4).
8. For the sake of brevity, ignore the remaining possibility that k1 > k3 > k2, without detracting
significantly from the analysis. Regardless of the factor-intensity ranking of good 3, our steadystate equilibria are stable, as we show in a separate paper (in preparation).
9. None of our results depends qualitatively on the simplifying assumption that a country’s
technological advantage is small.
10. This possibility occurs if (for example) ∂c/∂p is sufficiently small. In this regard, the Appendix shows that the autarkic value of ∂c/∂p approaches 0 as the elasticities of substitution in production (of each good) and consumption approach 0, but that these elasticities do not enter the
other partial derivatives in the above formula for dk/da. Note also that j/j¢ depends only on ki
(i = 1, 2, 3), as we can readily show with the help of Kemp (1969, eq. 1.21a) and Komiya (1967,
eqs 2.4).
11. For example, when y2 = 0 and hence kT/lT = k1, use (9), (10), and (13) to solve for k in terms
of k1 and k3 (as well as parameters a3 and g). This solution is independent of p, since k1 and k3
are fixed by r (= r + g) via (3) and (4). Essentially the same analysis applies when y1 = 0, except
that kT/lT = k2 then.
12. Balanced trade per efficiency unit of labor implies aggregate trade balance under present
assumptions, which ensure that both countries have the same number of such units.
13. Of course, since kT/lT exceeds its foreign counterpart in autarky, trade augments this excess.
14. By contrast, Manning et al. (1993) obtain a continuum of free-trade equilibria, each consistent with the Heckscher–Ohlin prediction. Their results arise because they assume the same
technology for both countries.
15. For example, if tastes are homothetic and both tradables have the same cross elasticity of
demand with respect to the price of the nontraded good in the Komiya model, trade will occur
unless: (i) the own-price elasticity of demand for the nontradable is unitary; and/or (ii) the
capital/labor ratio for this good equals the economy’s endowment ratio.
16. Propositions 1 and 2 obviously yield the following corollary. A Hicks-neutral advantage in
production of only the nontraded good will cause the technologically advanced country to export
the capital-intensive consumption good. This unambiguous prediction about the direction of
trade, however, does not characterize the Komiya model.
17. Although this assumption entails no loss of generality in the three-good model, it would be
a serious restriction in the two-good model, since some of our results depend on the relative
factor intensity of the capital good.
18. In the present two-good (unlike the above three-good) model, it matters whether a change
in a1/a2 is due to a shift in the numerator or denominator, because good 2 is now the capital
good. Thus, here we consider changes in a1 and a2 separately.
19. In obtaining these results, use the following facts: (pa1/a2)j¢/j > 1 if k1 > k2, by the “magnification effect” of Jones (1965); ∂q1/∂k < 0 if k1 < k2, by the Rybczynski theorem; and, for wellknown reasons, pa1∂q1/∂k + a2∂q2/∂k = r (= r + g).
20. Our analysis could be extended, moreover, to let each country’s rate of labor-augmenting
technical progress be endogenously determined as a function of variables and parameters in the
model. Under such an extension, Propositions 1–4 would still hold for any free-trade steadystate equilibrium.
© Blackwell Publishers Ltd 2002