Comparative Advantage
Content
comparative advantage
Abstract
This article traces the evolution of the theory of comparative advantage and the gains
from trade from the pioneering work of David Ricardo to the factor proportions
approach of Eli Heckscher and Bertil Ohlin. Extensions of the basic models to many
goods, factors and countries, and to the long run are noted, as well as the attempts at
empirical testing of the predictions derived from them.
Keywords
absolute advantage; comparative advantage; Corn Laws; distributive justice; division
of labour; factor price equalization; factor proportions; fixed factors; free trade; gains
from trade; Haberler, G.; Heckscher, E. F.; Heckscher–Ohlin trade theory; human
capital; international trade; intra-industry’ trade; labour mobility; Leontief, W.;
Lerner, A. P.; monopolistic competition; neoclassical general equilibrium theory;
Ohlin, B. G.; product differentiation; returns to scale; specialization; specific factors;
stationary state; Stolper–Samuelson theorem; terms of trade; time preference; wages
fund
JEL classifications
F1
Article
The modern economy, and the very world as we know it today, obviously depends
fundamentally on specialization and the division of labour, between individuals,
firms and nations. The principle of comparative advantage, first clearly stated and
proved by David Ricardo in 1817, is the fundamental analytical explanation of the
source of these enormous ‘gains from trade’. Though an awareness of the benefits of
specialization must go back to the dim mists of antiquity in all civilizations, it was
not until Ricardo that this deepest and most beautiful result in all of economics was
obtained. Though the logic applies equally to interpersonal, interfirm and
interregional trade, it was in the context of international trade that the principle of
comparative advantage was discovered and has been investigated ever since.
The basic Ricardian model
What constituted a ‘nation’ for Ricardo were two things – a ‘factor endowment’, of a
specified number of units of labour in the simplest model, and a ‘technology’, the
productivity of this labour in terms of different goods, such as cloth and wine in his
example. Thus labour can move freely between the production of cloth and wine in
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Ronald Findlay
From The New Palgrave Dictionary of Economics, Second Edition, 2008
Edited by Steven N. Durlauf and Lawrence E. Blume
The gains from trade
Viewed as a ‘positive’ theory, the principle of comparative advantage yields
predictions about (a) the direction of trade: that each country exports the good in
which it has the lower comparative opportunity cost ratio as defined by the
technology in that country, and about (b) the terms of trade: that it is bounded above
and below by these comparative cost ratios. From a ‘normative’ standpoint the
principle implies that the citizens of each country become ‘better off’ as a result of
trade, with the extent of the gains from trade depending upon the degree to which
the terms of trade exceed the domestic comparative cost ratio. It is the ‘normative’
part of the doctrine that has always been the more controversial, and it is therefore
necessary to evaluate it with the greatest care.
In Ricardo’s example the total labour force in each country is presumably
supplied by an aggregate of different households, each having the same relative
productivity in the two sectors. Thus all households in each country must become
better off as a result of trade if the terms of trade lie strictly in between the domestic
comparative cost ratios. The import-competing sector in each country simply
switches over instantaneously and costlessly to producing the export good (moving
to the opposite corner of its linear production-possibilities frontier, in terms of the
familiar geometry), obtaining the desired level of the other good by imports, raising
utility in the process. When one country is incompletely specialized, then all
households in that country remain at unchanged utility levels, all of the gain from
trade going to the individuals in the ‘small’ country. Thus we have a situation in
which everybody gains, in at least one country, while nobody loses in either country,
as a result of trade.
This very strong result depends upon Ricardo’s assumption of perfect
occupational mobility in each country. Suppose we take the opposite extreme of
completely specific labour in each sector, so that each country produces a fixed
combination of cloth and wine, with no possibility of transformation. In this case,
labour in the import-competing sector in each country must necessarily lose, as a
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England and in Portugal, but each labour force is trapped within its own borders.
Suppose that a unit of labour in Portugal can produce one unit of cloth or one unit of
wine, while in England a unit of labour can produce four units of cloth or two units
of wine. Thus the opportunity cost of a unit of wine is one unit of cloth in Portugal
while it is two units of cloth in England. On the assumption of competitive markets
and free trade, it follows that both goods will never be produced in both countries
since wine in England and cloth in Portugal could always be undermined by a
simple arbitrage operation involving export of cloth from England and import of
wine from Portugal. Thus wine in England or cloth in Portugal must contract until at
least one of these industries produces zero output. If both goods are consumed in
positive amounts, the ‘terms of trade’ in equilibrium must lie in the closed interval
between one and two units of cloth per unit of wine. Which of the two countries
specializes completely will depend upon the relative size of each country (as
measured by the labour force and its productivity in each industry) and upon the
extent to which each of the two goods is favoured by the pattern of world demand.
Thus Portugal is more likely to specialize the smaller she is compared with England
in the sense defined above and the more world demand is skewed towards the
consumption of wine relative to the consumption of cloth.
International factor mobility and world welfare
Another very important normative issue is the question of the relationship between
the free-trade equilibrium and world efficiency and welfare. In the Ricardian model
world welfare in general will not be maximized by free trade alone. In the numerical
example considered here Ricardo stresses the fact that England can still gain from
trade even though she has an absolute advantage in the production of both goods,
her productivity being greater in both cloth and wine, though comparatively greater
in cloth. Suppose that labour in Portugal could produce at English levels, if it moved
to England; that is, the English superiority is based on climatic or other
‘environmental’ factors and not on differences in aptitude or skill. Then, if labour
was free to move, and in the absence of ‘national’ sentiment, all production would be
located in England, and Portugal would cease to exist. The former Portuguese labour
would be better off than under free trade, since their real wage in terms of wine will
now be two units instead of one. The English labour would be worse off, if the terms
of trade were originally better than 0.5 wine per unit of cloth, but it is easy to show
that they could be sufficiently compensated since the utility-possibility frontier for
the world economy as a whole is moved out by the integration of the labour forces.
The case when each country has an absolute advantage in one good is more
interesting. As is easy to see, from Findlay (1982), this case will involve a
movement of labour to the country with the higher real wage under free trade,
increasing the production of this country’s exportable and reducing that of the
lower-wage country under free trade. The terms of trade turn against the higher-wage
country until eventually the real wage is equalized. The terms of trade that achieve
this equality of real wages will be equal to the ratio of labour productivities in each
country’s export sector; that is, the ‘double factoral’ terms of trade will be unity. This
solution of free trade combined with perfect labour mobility will achieve not only
efficiency for the world economy as a whole but equity as well. ‘Unequal exchange’
in the sense of Emmanuel (1972) would not exist, while liberal, utilitarian and
Rawlsian criteria of distributive justice would be satisfied as well, as pointed out in
Findlay (1982). Despite all this, it still seems utopian to expect a policy of ‘open
borders’, in either direction, for the contemporary world of nation-states.
Extensions of the basic Ricardian model
The two-country, two-good Ricardian model was extended to many goods and
countries by a number of subsequent writers, whose efforts are described in detail by
Haberler (1933) and Viner (1937). In the case of two countries and n goods the
concept of a ‘chain of comparative advantage’ has been put forward, with the goods
listed in descending order in terms of the relative efficiency of the two countries in
producing them. It is readily shown that with a uniform wage in each country all
goods from 1 to some number j must be exported, while all goods from ( j + 1) to n
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result of trade, while labour in each country’s export sector must gain. It can be
shown, however, that trade will improve potential welfare in each country in the
Samuelson (1950) sense that the utility-possibility frontier with trade will dominate
the corresponding frontier without trade, so that no one need be worse off, and at
least some one better off, if lump-sum taxes and transfers are possible (Samuelson,
1962).
The three-factor Ricardian model
While most of the literature on the Ricardian trade model has concentrated on the
model of Chapter 7 of the Principles in which it appears that labour is the sole
scarce factor, his more extended model in the Essay on Profits has been curiously
neglected, though the connections between trade, income distribution and growth
which that analysis explores are quite fascinating. The formal structure of the model
was laid out very thoroughly in Pasinetti (1960). The economy produces two goods,
corn and manufactures, each of which has a one-period lag between the input of
labour and the emergence of output. Labour thus has to be supported by a ‘wage
fund’, an initially given stock that is accumulated over time by saving out of profits.
Corn also requires land as an input, which is in fixed supply and yields diminishing
returns to successive increments of labour. The wage-rate is given exogenously in
terms of corn, and manufactures are a luxury good consumed only by the
land-owning class, who obtain rents determined by the marginal product of land.
Profits are the difference between the marginal product of labour and the given real
wage, which is equal to the marginal product ‘discounted’ by the rate of interest, in
this model equal to the rate of profit, defined as the ratio of profits to the real wage
that has to be advanced a period before. Momentary equilibrium determines the
relative price of corn and manufactures, the rent per acre and the rate of profit, as
well as the output levels and allocation of the labour force between sectors. The
growth of the system is at a rate equal to the product of the rate of profit and the
propensity to save of the capitalist class. It is shown that the system approaches a
stationary state, with a monotonically falling rate of profit and rising rents per acre.
The opportunity to import corn more cheaply from abroad will have significant
distributional and growth consequences. Just as Ricardo argued in his case for the
repeal of the Corn Laws, cheaper foreign corn will reduce domestic rents and raise
the domestic rate of profit, and thus the rate of growth. The approach to the
stationary state is postponed, though of course it cannot be ultimately averted, while
the growth consequences for the corn exporter are definitely adverse. The main
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must be imported. The number j itself will depend upon the relative sizes of the two
countries and the composition of world demand. Dornbusch, Fischer and Samuelson
(1977) generalize this result to a continuum of goods in an extremely elegant and
powerful model that has been widely used in subsequent literature. An analogous
chain concept applies to the case of two goods and n countries, this time ranking the
countries in terms of the ratio of their productivities in the two goods, with country 1
having the greatest relative efficiency in cloth and country n in wine. World demand
and the sizes of the labour forces will determine the ‘marginal’ country j, with
countries 1 to j exporting cloth and ( j + 1) to n exporting wine.
The simultaneous consideration of comparative advantage with many goods and
many countries presents severe analytical difficulties. Graham (1948) considered
several elaborate numerical examples, his work inspiring the Rochester theorists
McKenzie (1954) and Jones (1961) to apply the powerful tools of activity analysis to
this particular case of a linear general equilibrium model. It is interesting to note in
connection with mathematical programming and activity analysis that Kantorovich
(1965) in his celebrated book on planning for the Soviet economy worked out an
example of optimal specialization patterns for factories that corresponds exactly to
the Ricardian model of trade between countries.
Factor proportions and the Heckscher–Ohlin model
While J.S. Mill, Marshall and Edgeworth all made major contributions to trade
theory, the concept of comparative advantage did not undergo any evolution in their
work beyond the stage at which Ricardo had left it. They essentially concentrated on
the determination of the terms of trade and on various comparative static exercises.
The interwar years, however, brought fundamental advances, stemming in particular
from the work of the Swedes Heckscher (1919) and Ohlin (1933). The development
of a diagrammatic apparatus to handle general equilibrium interactions of tastes,
technology and factor endowments by Haberler (1933), Leontief (1933), Lerner
(1932) and others culminated in the rigorous establishment of trade theory and
comparative advantage as a branch of neoclassical general equilibrium theory.
The essentials of this approach can be expounded in terms of the familiar
two-country, two-good and two-factor model, on which see Jones (1965) for a
detailed and lucid algebraic exposition. The given factor supplies and constant
returns to scale technology define concave production-possibility frontiers, on the
assumption that the goods differ in factor intensity. This determines the ‘supply side’
of the model, which is closed by the specification of consumer preferences.
Economies that have identical technology, factor endowments and tastes will have
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doctrinal significance of this wider Ricardian model, however, is to reveal the extent
to which the subsequent ‘general equilibrium’ or ‘neoclassical’ approach to
international trade is already present within the Ricardian framework. For one thing,
the pattern of comparative advantage itself depends upon the complex interaction of
technology, factor proportions and tastes. In his Chapter 7 case the pattern of
comparative advantage is exogenous, simply given by the four fixed technical
coefficients indicating the productivity of labour in cloth and wine in England and
Portugal. The production-possibility frontiers for each country are linear, and
comparative advantage is simply determined by the relative magnitudes of the
slopes. As demonstrated in Findlay (1974), however, the Essay on Profits model
implies a concave production-possibilities frontier at any moment, since there are
diminishing returns to labour in corn even though the marginal productivity of labour
in manufactures is constant. With two countries the pattern of comparative advantage
will depend upon the slopes of these curves at their autarky equilibria, which are
endogenous variables depending upon the sizes of the ‘wage fund’ in relation to the
supply of land and the consumption pattern of landowners, as well as the technology
for the two goods.
As Burgstaller (1986) points out, however, the steady-state solution of the
model restores the linear structure of the pattern of comparative advantage. The zero
profit rate in the steady state requires the marginal product of labour to be equal to
the given real wage, and this implies a fixed land–labour ratio and hence output per
unit of labour in corn. We thus once again have two fixed technical coefficients, so
that the slope of the linear production-possibilities frontier is once again an
exogenous indicator of comparative advantage.
The ‘neo-Ricardian’ approach of Steedman (1979a; 1979b) considers more
general time-phased structures of production. Technology alone determines
negatively sloped wage–profit or factor-price frontiers, any point on which generates
a set of relative product prices and hence a pattern of comparative advantage relative
to another such economy.
The Stolper–Samuelson theorem
Associated with the Heckscher–Ohlin theorem is the Stolper–Samuelson theorem
(1941), that trade benefits the abundant and harms the scarce factor while protection
does the opposite, and the celebrated factor price equalization theorem of Lerner
(1952, though written in 1932) and Samuelson (1948; 1949; 1953), which states that
under certain conditions free trade will lead to complete equalization of factor
rewards even though factors are not mobile internationally. The normative
significance of this theorem is that free trade alone can achieve world efficiency in
production and resource allocation, unlike the case of the Ricardian model as pointed
out earlier. The requirements for the theorem to hold, however, are very stringent,
such as that the number of tradable goods produced be equal to the number of
factors. It also requires factor proportions to be sufficiently close to each other in the
trading partners so that the production patterns are fairly similar. Thus it would be
far-fetched to expect the price of unskilled labour to be equalized between
Bangladesh and the United States, for example.
The specific-factors model
An important and popular variant of the factor proportions approach is what Jones
(1971) calls the ‘specific factors’ and Samuelson (1971) the Viner–Ricardo model. In
this model each production sector has its own unique fixed factor, while labour is
used in all sectors and is perfectly mobile internally between them. Trade patterns
still reflect factor endowments but factor price equalization does not hold in this
model since the number of factors is always one greater than the number of goods.
Gruen and Corden (1970) present an ingenious three-by-three extension of this
approach, in which one sector uses land and labour, while the two others use capital
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the same autarky equilibrium price-ratio and so will have no incentive to engage in
trade. Countries must therefore differ with respect to at least one of these
characteristics for differences in comparative advantage to emerge. With identical
technology and factor endowments, a country will have a comparative advantage in
the good its citizens prefer less in comparison to the foreign country, since then this
good will be cheaper at home. Similarly, if factor endowments and tastes are
identical, differences in comparative advantage will be governed by relative
technological efficiency; that is, a country will have a comparative advantage in the
good in which its relative technological efficiency is greater, just as in the Ricardian
model. These differences in technological efficiency could be represented, for
example, by the magnitude of multiplicative constants in the production functions;
that is, ‘Hicks-neutral’ differences.
In keeping with the ideas of Heckscher and Ohlin, however, it is differences in
factor proportions that have dominated the explanation of comparative advantage in
the neoclassical literature. The Heckscher–Ohlin theorem, that each country will
export the commodity that uses its relatively abundant factor most intensively, has
been rigorously established and the necessary qualifications carefully specified,
as in Jones (1956). Among the more important of these is the requirement that
factor-intensity ‘reversals’ do not take place; that is, that one good is always more
capital-intensive than the other at all wage-rental ratios or at least within the relevant
range defined by the factor proportions of the trading countries.
Long-run extensions of the factor proportions model
One limitation of the Heckscher–Ohlin model was that the stock of ‘capital’,
however conceived, should be an endogenous variable determined by the propensity
to save or time preference of each trading community, rather than being taken as
exogenously fixed. Oniki and Uzawa (1965) extended the model to a situation where
the labour force is growing in each country at an exogenous rate and capital is
accumulated in response to given propensities to save in each country. One of the
goods is taken to be the ‘capital’ good, conceived of as a malleable ‘putty–putty’
instrument. They demonstrated that the system converges in the long run to a
particular capital–labour ratio for each country, which will be higher for the country
with the larger saving propensity. In Findlay (1970; 1984), it is shown that as the
capital–labour ratio evolves the pattern of comparative advantage for a given ‘small’
country in an open trading world will also shift over time towards more capitalintensive goods, thus formalizing the concept of a ‘ladder of comparative advantage’
that countries ascend in the process of economic development. Thus comparative
advantage should not be conceived as given and immutable, but evolving with
capital accumulation and technological change. Much of the loose talk about
‘dynamic’ comparative advantage in the development literature, however, is
misconceived since it attempts to change the pattern of production by protection
before the necessary changes in the capacity to produce efficiently have taken place.
Other models which endogenize the capital stocks of the trading countries are Stiglitz
(1970) and Findlay (1978) which utilizes a variable rate of time preference and an
‘Austrian’ point-input/point-output technology, which implies a continuum of capital
goods as represented by the ‘trees’ of different ages, and Findlay (1995, ch. 2),
which addresses the question posed by Samuelson (1965) of whether trade equalizes
not only the marginal product or rental of capital but the rate of interest itself.
Empirical testing
Empirical testing of the positive side of the theory of comparative advantage begins
in a systematic way only with the work of MacDougall (1951) on the Ricardian
theory and the celebrated article of Leontief (1954) that uncovered the apparent
paradox that US exports were more labour-intensive than her imports. Leontief’s
dramatic finding spurred considerable further empirical research motivated by the
desire to find a satisfactory explanation. The increasing scarcity of natural resources
in the USA, by causing capital to be substituted for it in import-competing
production, was stressed as an explanation for the paradox by Vanek (1963). The
role of ‘human capital’ as an explanation was pointed to by Kenen (1965) and a
number of empirical investigators, who found that US exports were considerably
more skill-intensive than her imports, even though physical capital-intensity was only
weakly correlated with exports and imports. This pointed to the need to reinterpret
the simple Heckscher–Ohlin model in terms of skilled and unskilled labour as the
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and labour, thus neatly integrating the ‘specific factors’ model with the regular
two-by-two Heckscher–Ohlin model. Findlay (1995, chs 4 and 6) uses adaptations
and extensions of the Gruen–Corden specification to introduce human capital
formation and the concept of a natural resource ‘frontier’ into the Heckscher–Ohlin
framework.
Increasing returns
Finally, the crucial role of increasing returns to scale in specialization and
international trade has only recently been rigorously investigated, since it implies
departures from perfect competition. Krugman (1979) and Lancaster (1980)
introduced international trade into models of monopolistic competition with
differentiated products, showing the possibility of gains from trade due to the
provision of greater variety of similar goods rather than differences in comparative
advantage, what is referred to as ‘intra-industry’ trade. Helpman and Krugman
(1985) thoroughly examine and extend our knowledge in this area, while Grossman
and Helpman (1991) expertly extend the monopolistic competition approach to deal
with a number of issues involving endogenous technological progress and growth in
the world economy.
See Also
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Heckscher, Eli Filip
Heckscher–Ohlin trade theory
international trade theory
Leontief, Wassily
Ohlin, Bertil Gotthard
Ricardo, David
terms of trade
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MacDougall, G.D.A. 1951. British and American exports. Economic Journal 61,
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Trefler, D. 1995. The case of missing trade and other mysteries. American Economic
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Vanek, J. 1963. The Natural Resource Content of U.S. Foreign Trade 1870–1955.
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Viner, J. 1937. Studies in the Theory of International Trade. New York: Harper.
12
Abstract
This article traces the evolution of the theory of comparative advantage and the gains
from trade from the pioneering work of David Ricardo to the factor proportions
approach of Eli Heckscher and Bertil Ohlin. Extensions of the basic models to many
goods, factors and countries, and to the long run are noted, as well as the attempts at
empirical testing of the predictions derived from them.
Keywords
absolute advantage; comparative advantage; Corn Laws; distributive justice; division
of labour; factor price equalization; factor proportions; fixed factors; free trade; gains
from trade; Haberler, G.; Heckscher, E. F.; Heckscher–Ohlin trade theory; human
capital; international trade; intra-industry’ trade; labour mobility; Leontief, W.;
Lerner, A. P.; monopolistic competition; neoclassical general equilibrium theory;
Ohlin, B. G.; product differentiation; returns to scale; specialization; specific factors;
stationary state; Stolper–Samuelson theorem; terms of trade; time preference; wages
fund
JEL classifications
F1
Article
The modern economy, and the very world as we know it today, obviously depends
fundamentally on specialization and the division of labour, between individuals,
firms and nations. The principle of comparative advantage, first clearly stated and
proved by David Ricardo in 1817, is the fundamental analytical explanation of the
source of these enormous ‘gains from trade’. Though an awareness of the benefits of
specialization must go back to the dim mists of antiquity in all civilizations, it was
not until Ricardo that this deepest and most beautiful result in all of economics was
obtained. Though the logic applies equally to interpersonal, interfirm and
interregional trade, it was in the context of international trade that the principle of
comparative advantage was discovered and has been investigated ever since.
The basic Ricardian model
What constituted a ‘nation’ for Ricardo were two things – a ‘factor endowment’, of a
specified number of units of labour in the simplest model, and a ‘technology’, the
productivity of this labour in terms of different goods, such as cloth and wine in his
example. Thus labour can move freely between the production of cloth and wine in
1
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Ronald Findlay
From The New Palgrave Dictionary of Economics, Second Edition, 2008
Edited by Steven N. Durlauf and Lawrence E. Blume
The gains from trade
Viewed as a ‘positive’ theory, the principle of comparative advantage yields
predictions about (a) the direction of trade: that each country exports the good in
which it has the lower comparative opportunity cost ratio as defined by the
technology in that country, and about (b) the terms of trade: that it is bounded above
and below by these comparative cost ratios. From a ‘normative’ standpoint the
principle implies that the citizens of each country become ‘better off’ as a result of
trade, with the extent of the gains from trade depending upon the degree to which
the terms of trade exceed the domestic comparative cost ratio. It is the ‘normative’
part of the doctrine that has always been the more controversial, and it is therefore
necessary to evaluate it with the greatest care.
In Ricardo’s example the total labour force in each country is presumably
supplied by an aggregate of different households, each having the same relative
productivity in the two sectors. Thus all households in each country must become
better off as a result of trade if the terms of trade lie strictly in between the domestic
comparative cost ratios. The import-competing sector in each country simply
switches over instantaneously and costlessly to producing the export good (moving
to the opposite corner of its linear production-possibilities frontier, in terms of the
familiar geometry), obtaining the desired level of the other good by imports, raising
utility in the process. When one country is incompletely specialized, then all
households in that country remain at unchanged utility levels, all of the gain from
trade going to the individuals in the ‘small’ country. Thus we have a situation in
which everybody gains, in at least one country, while nobody loses in either country,
as a result of trade.
This very strong result depends upon Ricardo’s assumption of perfect
occupational mobility in each country. Suppose we take the opposite extreme of
completely specific labour in each sector, so that each country produces a fixed
combination of cloth and wine, with no possibility of transformation. In this case,
labour in the import-competing sector in each country must necessarily lose, as a
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England and in Portugal, but each labour force is trapped within its own borders.
Suppose that a unit of labour in Portugal can produce one unit of cloth or one unit of
wine, while in England a unit of labour can produce four units of cloth or two units
of wine. Thus the opportunity cost of a unit of wine is one unit of cloth in Portugal
while it is two units of cloth in England. On the assumption of competitive markets
and free trade, it follows that both goods will never be produced in both countries
since wine in England and cloth in Portugal could always be undermined by a
simple arbitrage operation involving export of cloth from England and import of
wine from Portugal. Thus wine in England or cloth in Portugal must contract until at
least one of these industries produces zero output. If both goods are consumed in
positive amounts, the ‘terms of trade’ in equilibrium must lie in the closed interval
between one and two units of cloth per unit of wine. Which of the two countries
specializes completely will depend upon the relative size of each country (as
measured by the labour force and its productivity in each industry) and upon the
extent to which each of the two goods is favoured by the pattern of world demand.
Thus Portugal is more likely to specialize the smaller she is compared with England
in the sense defined above and the more world demand is skewed towards the
consumption of wine relative to the consumption of cloth.
International factor mobility and world welfare
Another very important normative issue is the question of the relationship between
the free-trade equilibrium and world efficiency and welfare. In the Ricardian model
world welfare in general will not be maximized by free trade alone. In the numerical
example considered here Ricardo stresses the fact that England can still gain from
trade even though she has an absolute advantage in the production of both goods,
her productivity being greater in both cloth and wine, though comparatively greater
in cloth. Suppose that labour in Portugal could produce at English levels, if it moved
to England; that is, the English superiority is based on climatic or other
‘environmental’ factors and not on differences in aptitude or skill. Then, if labour
was free to move, and in the absence of ‘national’ sentiment, all production would be
located in England, and Portugal would cease to exist. The former Portuguese labour
would be better off than under free trade, since their real wage in terms of wine will
now be two units instead of one. The English labour would be worse off, if the terms
of trade were originally better than 0.5 wine per unit of cloth, but it is easy to show
that they could be sufficiently compensated since the utility-possibility frontier for
the world economy as a whole is moved out by the integration of the labour forces.
The case when each country has an absolute advantage in one good is more
interesting. As is easy to see, from Findlay (1982), this case will involve a
movement of labour to the country with the higher real wage under free trade,
increasing the production of this country’s exportable and reducing that of the
lower-wage country under free trade. The terms of trade turn against the higher-wage
country until eventually the real wage is equalized. The terms of trade that achieve
this equality of real wages will be equal to the ratio of labour productivities in each
country’s export sector; that is, the ‘double factoral’ terms of trade will be unity. This
solution of free trade combined with perfect labour mobility will achieve not only
efficiency for the world economy as a whole but equity as well. ‘Unequal exchange’
in the sense of Emmanuel (1972) would not exist, while liberal, utilitarian and
Rawlsian criteria of distributive justice would be satisfied as well, as pointed out in
Findlay (1982). Despite all this, it still seems utopian to expect a policy of ‘open
borders’, in either direction, for the contemporary world of nation-states.
Extensions of the basic Ricardian model
The two-country, two-good Ricardian model was extended to many goods and
countries by a number of subsequent writers, whose efforts are described in detail by
Haberler (1933) and Viner (1937). In the case of two countries and n goods the
concept of a ‘chain of comparative advantage’ has been put forward, with the goods
listed in descending order in terms of the relative efficiency of the two countries in
producing them. It is readily shown that with a uniform wage in each country all
goods from 1 to some number j must be exported, while all goods from ( j + 1) to n
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result of trade, while labour in each country’s export sector must gain. It can be
shown, however, that trade will improve potential welfare in each country in the
Samuelson (1950) sense that the utility-possibility frontier with trade will dominate
the corresponding frontier without trade, so that no one need be worse off, and at
least some one better off, if lump-sum taxes and transfers are possible (Samuelson,
1962).
The three-factor Ricardian model
While most of the literature on the Ricardian trade model has concentrated on the
model of Chapter 7 of the Principles in which it appears that labour is the sole
scarce factor, his more extended model in the Essay on Profits has been curiously
neglected, though the connections between trade, income distribution and growth
which that analysis explores are quite fascinating. The formal structure of the model
was laid out very thoroughly in Pasinetti (1960). The economy produces two goods,
corn and manufactures, each of which has a one-period lag between the input of
labour and the emergence of output. Labour thus has to be supported by a ‘wage
fund’, an initially given stock that is accumulated over time by saving out of profits.
Corn also requires land as an input, which is in fixed supply and yields diminishing
returns to successive increments of labour. The wage-rate is given exogenously in
terms of corn, and manufactures are a luxury good consumed only by the
land-owning class, who obtain rents determined by the marginal product of land.
Profits are the difference between the marginal product of labour and the given real
wage, which is equal to the marginal product ‘discounted’ by the rate of interest, in
this model equal to the rate of profit, defined as the ratio of profits to the real wage
that has to be advanced a period before. Momentary equilibrium determines the
relative price of corn and manufactures, the rent per acre and the rate of profit, as
well as the output levels and allocation of the labour force between sectors. The
growth of the system is at a rate equal to the product of the rate of profit and the
propensity to save of the capitalist class. It is shown that the system approaches a
stationary state, with a monotonically falling rate of profit and rising rents per acre.
The opportunity to import corn more cheaply from abroad will have significant
distributional and growth consequences. Just as Ricardo argued in his case for the
repeal of the Corn Laws, cheaper foreign corn will reduce domestic rents and raise
the domestic rate of profit, and thus the rate of growth. The approach to the
stationary state is postponed, though of course it cannot be ultimately averted, while
the growth consequences for the corn exporter are definitely adverse. The main
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must be imported. The number j itself will depend upon the relative sizes of the two
countries and the composition of world demand. Dornbusch, Fischer and Samuelson
(1977) generalize this result to a continuum of goods in an extremely elegant and
powerful model that has been widely used in subsequent literature. An analogous
chain concept applies to the case of two goods and n countries, this time ranking the
countries in terms of the ratio of their productivities in the two goods, with country 1
having the greatest relative efficiency in cloth and country n in wine. World demand
and the sizes of the labour forces will determine the ‘marginal’ country j, with
countries 1 to j exporting cloth and ( j + 1) to n exporting wine.
The simultaneous consideration of comparative advantage with many goods and
many countries presents severe analytical difficulties. Graham (1948) considered
several elaborate numerical examples, his work inspiring the Rochester theorists
McKenzie (1954) and Jones (1961) to apply the powerful tools of activity analysis to
this particular case of a linear general equilibrium model. It is interesting to note in
connection with mathematical programming and activity analysis that Kantorovich
(1965) in his celebrated book on planning for the Soviet economy worked out an
example of optimal specialization patterns for factories that corresponds exactly to
the Ricardian model of trade between countries.
Factor proportions and the Heckscher–Ohlin model
While J.S. Mill, Marshall and Edgeworth all made major contributions to trade
theory, the concept of comparative advantage did not undergo any evolution in their
work beyond the stage at which Ricardo had left it. They essentially concentrated on
the determination of the terms of trade and on various comparative static exercises.
The interwar years, however, brought fundamental advances, stemming in particular
from the work of the Swedes Heckscher (1919) and Ohlin (1933). The development
of a diagrammatic apparatus to handle general equilibrium interactions of tastes,
technology and factor endowments by Haberler (1933), Leontief (1933), Lerner
(1932) and others culminated in the rigorous establishment of trade theory and
comparative advantage as a branch of neoclassical general equilibrium theory.
The essentials of this approach can be expounded in terms of the familiar
two-country, two-good and two-factor model, on which see Jones (1965) for a
detailed and lucid algebraic exposition. The given factor supplies and constant
returns to scale technology define concave production-possibility frontiers, on the
assumption that the goods differ in factor intensity. This determines the ‘supply side’
of the model, which is closed by the specification of consumer preferences.
Economies that have identical technology, factor endowments and tastes will have
5
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doctrinal significance of this wider Ricardian model, however, is to reveal the extent
to which the subsequent ‘general equilibrium’ or ‘neoclassical’ approach to
international trade is already present within the Ricardian framework. For one thing,
the pattern of comparative advantage itself depends upon the complex interaction of
technology, factor proportions and tastes. In his Chapter 7 case the pattern of
comparative advantage is exogenous, simply given by the four fixed technical
coefficients indicating the productivity of labour in cloth and wine in England and
Portugal. The production-possibility frontiers for each country are linear, and
comparative advantage is simply determined by the relative magnitudes of the
slopes. As demonstrated in Findlay (1974), however, the Essay on Profits model
implies a concave production-possibilities frontier at any moment, since there are
diminishing returns to labour in corn even though the marginal productivity of labour
in manufactures is constant. With two countries the pattern of comparative advantage
will depend upon the slopes of these curves at their autarky equilibria, which are
endogenous variables depending upon the sizes of the ‘wage fund’ in relation to the
supply of land and the consumption pattern of landowners, as well as the technology
for the two goods.
As Burgstaller (1986) points out, however, the steady-state solution of the
model restores the linear structure of the pattern of comparative advantage. The zero
profit rate in the steady state requires the marginal product of labour to be equal to
the given real wage, and this implies a fixed land–labour ratio and hence output per
unit of labour in corn. We thus once again have two fixed technical coefficients, so
that the slope of the linear production-possibilities frontier is once again an
exogenous indicator of comparative advantage.
The ‘neo-Ricardian’ approach of Steedman (1979a; 1979b) considers more
general time-phased structures of production. Technology alone determines
negatively sloped wage–profit or factor-price frontiers, any point on which generates
a set of relative product prices and hence a pattern of comparative advantage relative
to another such economy.
The Stolper–Samuelson theorem
Associated with the Heckscher–Ohlin theorem is the Stolper–Samuelson theorem
(1941), that trade benefits the abundant and harms the scarce factor while protection
does the opposite, and the celebrated factor price equalization theorem of Lerner
(1952, though written in 1932) and Samuelson (1948; 1949; 1953), which states that
under certain conditions free trade will lead to complete equalization of factor
rewards even though factors are not mobile internationally. The normative
significance of this theorem is that free trade alone can achieve world efficiency in
production and resource allocation, unlike the case of the Ricardian model as pointed
out earlier. The requirements for the theorem to hold, however, are very stringent,
such as that the number of tradable goods produced be equal to the number of
factors. It also requires factor proportions to be sufficiently close to each other in the
trading partners so that the production patterns are fairly similar. Thus it would be
far-fetched to expect the price of unskilled labour to be equalized between
Bangladesh and the United States, for example.
The specific-factors model
An important and popular variant of the factor proportions approach is what Jones
(1971) calls the ‘specific factors’ and Samuelson (1971) the Viner–Ricardo model. In
this model each production sector has its own unique fixed factor, while labour is
used in all sectors and is perfectly mobile internally between them. Trade patterns
still reflect factor endowments but factor price equalization does not hold in this
model since the number of factors is always one greater than the number of goods.
Gruen and Corden (1970) present an ingenious three-by-three extension of this
approach, in which one sector uses land and labour, while the two others use capital
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the same autarky equilibrium price-ratio and so will have no incentive to engage in
trade. Countries must therefore differ with respect to at least one of these
characteristics for differences in comparative advantage to emerge. With identical
technology and factor endowments, a country will have a comparative advantage in
the good its citizens prefer less in comparison to the foreign country, since then this
good will be cheaper at home. Similarly, if factor endowments and tastes are
identical, differences in comparative advantage will be governed by relative
technological efficiency; that is, a country will have a comparative advantage in the
good in which its relative technological efficiency is greater, just as in the Ricardian
model. These differences in technological efficiency could be represented, for
example, by the magnitude of multiplicative constants in the production functions;
that is, ‘Hicks-neutral’ differences.
In keeping with the ideas of Heckscher and Ohlin, however, it is differences in
factor proportions that have dominated the explanation of comparative advantage in
the neoclassical literature. The Heckscher–Ohlin theorem, that each country will
export the commodity that uses its relatively abundant factor most intensively, has
been rigorously established and the necessary qualifications carefully specified,
as in Jones (1956). Among the more important of these is the requirement that
factor-intensity ‘reversals’ do not take place; that is, that one good is always more
capital-intensive than the other at all wage-rental ratios or at least within the relevant
range defined by the factor proportions of the trading countries.
Long-run extensions of the factor proportions model
One limitation of the Heckscher–Ohlin model was that the stock of ‘capital’,
however conceived, should be an endogenous variable determined by the propensity
to save or time preference of each trading community, rather than being taken as
exogenously fixed. Oniki and Uzawa (1965) extended the model to a situation where
the labour force is growing in each country at an exogenous rate and capital is
accumulated in response to given propensities to save in each country. One of the
goods is taken to be the ‘capital’ good, conceived of as a malleable ‘putty–putty’
instrument. They demonstrated that the system converges in the long run to a
particular capital–labour ratio for each country, which will be higher for the country
with the larger saving propensity. In Findlay (1970; 1984), it is shown that as the
capital–labour ratio evolves the pattern of comparative advantage for a given ‘small’
country in an open trading world will also shift over time towards more capitalintensive goods, thus formalizing the concept of a ‘ladder of comparative advantage’
that countries ascend in the process of economic development. Thus comparative
advantage should not be conceived as given and immutable, but evolving with
capital accumulation and technological change. Much of the loose talk about
‘dynamic’ comparative advantage in the development literature, however, is
misconceived since it attempts to change the pattern of production by protection
before the necessary changes in the capacity to produce efficiently have taken place.
Other models which endogenize the capital stocks of the trading countries are Stiglitz
(1970) and Findlay (1978) which utilizes a variable rate of time preference and an
‘Austrian’ point-input/point-output technology, which implies a continuum of capital
goods as represented by the ‘trees’ of different ages, and Findlay (1995, ch. 2),
which addresses the question posed by Samuelson (1965) of whether trade equalizes
not only the marginal product or rental of capital but the rate of interest itself.
Empirical testing
Empirical testing of the positive side of the theory of comparative advantage begins
in a systematic way only with the work of MacDougall (1951) on the Ricardian
theory and the celebrated article of Leontief (1954) that uncovered the apparent
paradox that US exports were more labour-intensive than her imports. Leontief’s
dramatic finding spurred considerable further empirical research motivated by the
desire to find a satisfactory explanation. The increasing scarcity of natural resources
in the USA, by causing capital to be substituted for it in import-competing
production, was stressed as an explanation for the paradox by Vanek (1963). The
role of ‘human capital’ as an explanation was pointed to by Kenen (1965) and a
number of empirical investigators, who found that US exports were considerably
more skill-intensive than her imports, even though physical capital-intensity was only
weakly correlated with exports and imports. This pointed to the need to reinterpret
the simple Heckscher–Ohlin model in terms of skilled and unskilled labour as the
7
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and labour, thus neatly integrating the ‘specific factors’ model with the regular
two-by-two Heckscher–Ohlin model. Findlay (1995, chs 4 and 6) uses adaptations
and extensions of the Gruen–Corden specification to introduce human capital
formation and the concept of a natural resource ‘frontier’ into the Heckscher–Ohlin
framework.
Increasing returns
Finally, the crucial role of increasing returns to scale in specialization and
international trade has only recently been rigorously investigated, since it implies
departures from perfect competition. Krugman (1979) and Lancaster (1980)
introduced international trade into models of monopolistic competition with
differentiated products, showing the possibility of gains from trade due to the
provision of greater variety of similar goods rather than differences in comparative
advantage, what is referred to as ‘intra-industry’ trade. Helpman and Krugman
(1985) thoroughly examine and extend our knowledge in this area, while Grossman
and Helpman (1991) expertly extend the monopolistic competition approach to deal
with a number of issues involving endogenous technological progress and growth in
the world economy.
See Also
•
•
•
•
•
•
•
Heckscher, Eli Filip
Heckscher–Ohlin trade theory
international trade theory
Leontief, Wassily
Ohlin, Bertil Gotthard
Ricardo, David
terms of trade
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