comparative advantage

Ronald FindlayFrom The New Palgrave Dictionary of Economics, Second Edition, 2008Edited by Steven N. Durlauf and Lawrence E. Blume

Abstract

This article traces the evolution of the theory of comparative advantage and the gainsfrom trade from the pioneering work of David Ricardo to the factor proportionsapproach of Eli Heckscher and Bertil Ohlin. Extensions of the basic models to manygoods, factors and countries, and to the long run are noted, as well as the attempts atempirical testing of the predictions derived from them.

Keywords

absolute advantage; comparative advantage; Corn Laws; distributive justice; divisionof labour; factor price equalization; factor proportions; fixed factors; free trade; gainsfrom trade; Haberler, G.; Heckscher, E. F.; Heckscher–Ohlin trade theory; humancapital; 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; wagesfund

JEL classifications

F1

Article

The modern economy, and the very world as we know it today, obviously dependsfundamentally on specialization and the division of labour, between individuals,firms and nations. The principle of comparative advantage, first clearly stated andproved by David Ricardo in 1817, is the fundamental analytical explanation of thesource of these enormous ‘gains from trade’. Though an awareness of the benefits ofspecialization must go back to the dim mists of antiquity in all civilizations, it wasnot until Ricardo that this deepest and most beautiful result in all of economics wasobtained. Though the logic applies equally to interpersonal, interfirm andinterregional trade, it was in the context of international trade that the principle ofcomparative 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 aspecified number of units of labour in the simplest model, and a ‘technology’, theproductivity of this labour in terms of different goods, such as cloth and wine in hisexample. Thus labour can move freely between the production of cloth and wine in

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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 ofwine, while in England a unit of labour can produce four units of cloth or two unitsof wine. Thus the opportunity cost of a unit of wine is one unit of cloth in Portugalwhile it is two units of cloth in England. On the assumption of competitive marketsand free trade, it follows that both goods will never be produced in both countriessince wine in England and cloth in Portugal could always be undermined by asimple arbitrage operation involving export of cloth from England and import ofwine from Portugal. Thus wine in England or cloth in Portugal must contract until atleast one of these industries produces zero output. If both goods are consumed inpositive amounts, the ‘terms of trade’ in equilibrium must lie in the closed intervalbetween one and two units of cloth per unit of wine. Which of the two countriesspecializes completely will depend upon the relative size of each country (asmeasured by the labour force and its productivity in each industry) and upon theextent 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 Englandin the sense defined above and the more world demand is skewed towards theconsumption of wine relative to the consumption of cloth.

The gains from trade

Viewed as a ‘positive’ theory, the principle of comparative advantage yieldspredictions about (a) the direction of trade: that each country exports the good inwhich it has the lower comparative opportunity cost ratio as defined by thetechnology in that country, and about (b) the terms of trade: that it is bounded aboveand below by these comparative cost ratios. From a ‘normative’ standpoint theprinciple implies that the citizens of each country become ‘better off’ as a result oftrade, with the extent of the gains from trade depending upon the degree to whichthe 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 thereforenecessary to evaluate it with the greatest care.

In Ricardo’s example the total labour force in each country is presumablysupplied by an aggregate of different households, each having the same relativeproductivity in the two sectors. Thus all households in each country must becomebetter off as a result of trade if the terms of trade lie strictly in between the domesticcomparative cost ratios. The import-competing sector in each country simplyswitches over instantaneously and costlessly to producing the export good (movingto the opposite corner of its linear production-possibilities frontier, in terms of thefamiliar geometry), obtaining the desired level of the other good by imports, raisingutility in the process. When one country is incompletely specialized, then allhouseholds in that country remain at unchanged utility levels, all of the gain fromtrade going to the individuals in the ‘small’ country. Thus we have a situation inwhich 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 perfectoccupational mobility in each country. Suppose we take the opposite extreme ofcompletely specific labour in each sector, so that each country produces a fixedcombination 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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result of trade, while labour in each country’s export sector must gain. It can beshown, however, that trade will improve potential welfare in each country in theSamuelson (1950) sense that the utility-possibility frontier with trade will dominatethe corresponding frontier without trade, so that no one need be worse off, and atleast some one better off, if lump-sum taxes and transfers are possible (Samuelson,1962).

International factor mobility and world welfare

Another very important normative issue is the question of the relationship betweenthe free-trade equilibrium and world efficiency and welfare. In the Ricardian modelworld welfare in general will not be maximized by free trade alone. In the numericalexample considered here Ricardo stresses the fact that England can still gain fromtrade even though she has an absolute advantage in the production of both goods,her productivity being greater in both cloth and wine, though comparatively greaterin cloth. Suppose that labour in Portugal could produce at English levels, if it movedto England; that is, the English superiority is based on climatic or other‘environmental’ factors and not on differences in aptitude or skill. Then, if labourwas free to move, and in the absence of ‘national’ sentiment, all production would belocated in England, and Portugal would cease to exist. The former Portuguese labourwould be better off than under free trade, since their real wage in terms of wine willnow be two units instead of one. The English labour would be worse off, if the termsof trade were originally better than 0.5 wine per unit of cloth, but it is easy to showthat they could be sufficiently compensated since the utility-possibility frontier forthe 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 moreinteresting. As is easy to see, from Findlay (1982), this case will involve amovement 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 thelower-wage country under free trade. The terms of trade turn against the higher-wagecountry until eventually the real wage is equalized. The terms of trade that achievethis equality of real wages will be equal to the ratio of labour productivities in eachcountry’s export sector; that is, the ‘double factoral’ terms of trade will be unity. Thissolution of free trade combined with perfect labour mobility will achieve not onlyefficiency 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 andRawlsian criteria of distributive justice would be satisfied as well, as pointed out inFindlay (1982). Despite all this, it still seems utopian to expect a policy of ‘openborders’, 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 andcountries by a number of subsequent writers, whose efforts are described in detail byHaberler (1933) and Viner (1937). In the case of two countries and n goods theconcept of a ‘chain of comparative advantage’ has been put forward, with the goodslisted in descending order in terms of the relative efficiency of the two countries inproducing them. It is readily shown that with a uniform wage in each country allgoods from 1 to some number j must be exported, while all goods from ( j + 1) to n

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must be imported. The number j itself will depend upon the relative sizes of the twocountries and the composition of world demand. Dornbusch, Fischer and Samuelson(1977) generalize this result to a continuum of goods in an extremely elegant andpowerful model that has been widely used in subsequent literature. An analogouschain concept applies to the case of two goods and n countries, this time ranking thecountries in terms of the ratio of their productivities in the two goods, with country 1having the greatest relative efficiency in cloth and country n in wine. World demandand the sizes of the labour forces will determine the ‘marginal’ country j, withcountries 1 to j exporting cloth and ( j + 1) to n exporting wine.

The simultaneous consideration of comparative advantage with many goods andmany countries presents severe analytical difficulties. Graham (1948) consideredseveral elaborate numerical examples, his work inspiring the Rochester theoristsMcKenzie (1954) and Jones (1961) to apply the powerful tools of activity analysis tothis particular case of a linear general equilibrium model. It is interesting to note inconnection with mathematical programming and activity analysis that Kantorovich(1965) in his celebrated book on planning for the Soviet economy worked out anexample of optimal specialization patterns for factories that corresponds exactly tothe Ricardian model of trade between countries.

The three-factor Ricardian model

While most of the literature on the Ricardian trade model has concentrated on themodel of Chapter 7 of the Principles in which it appears that labour is the solescarce factor, his more extended model in the Essay on Profits has been curiouslyneglected, though the connections between trade, income distribution and growthwhich that analysis explores are quite fascinating. The formal structure of the modelwas 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 oflabour and the emergence of output. Labour thus has to be supported by a ‘wagefund’, 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 diminishingreturns to successive increments of labour. The wage-rate is given exogenously interms of corn, and manufactures are a luxury good consumed only by theland-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 realwage, which is equal to the marginal product ‘discounted’ by the rate of interest, inthis model equal to the rate of profit, defined as the ratio of profits to the real wagethat has to be advanced a period before. Momentary equilibrium determines therelative price of corn and manufactures, the rent per acre and the rate of profit, aswell as the output levels and allocation of the labour force between sectors. Thegrowth of the system is at a rate equal to the product of the rate of profit and thepropensity to save of the capitalist class. It is shown that the system approaches astationary state, with a monotonically falling rate of profit and rising rents per acre.

The opportunity to import corn more cheaply from abroad will have significantdistributional and growth consequences. Just as Ricardo argued in his case for therepeal of the Corn Laws, cheaper foreign corn will reduce domestic rents and raisethe domestic rate of profit, and thus the rate of growth. The approach to thestationary state is postponed, though of course it cannot be ultimately averted, whilethe growth consequences for the corn exporter are definitely adverse. The main

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doctrinal significance of this wider Ricardian model, however, is to reveal the extentto which the subsequent ‘general equilibrium’ or ‘neoclassical’ approach tointernational trade is already present within the Ricardian framework. For one thing,the pattern of comparative advantage itself depends upon the complex interaction oftechnology, factor proportions and tastes. In his Chapter 7 case the pattern ofcomparative advantage is exogenous, simply given by the four fixed technicalcoefficients indicating the productivity of labour in cloth and wine in England andPortugal. The production-possibility frontiers for each country are linear, andcomparative advantage is simply determined by the relative magnitudes of theslopes. As demonstrated in Findlay (1974), however, the Essay on Profits modelimplies a concave production-possibilities frontier at any moment, since there arediminishing returns to labour in corn even though the marginal productivity of labourin manufactures is constant. With two countries the pattern of comparative advantagewill depend upon the slopes of these curves at their autarky equilibria, which areendogenous variables depending upon the sizes of the ‘wage fund’ in relation to thesupply of land and the consumption pattern of landowners, as well as the technologyfor the two goods.

As Burgstaller (1986) points out, however, the steady-state solution of themodel restores the linear structure of the pattern of comparative advantage. The zeroprofit rate in the steady state requires the marginal product of labour to be equal tothe given real wage, and this implies a fixed land–labour ratio and hence output perunit of labour in corn. We thus once again have two fixed technical coefficients, sothat the slope of the linear production-possibilities frontier is once again anexogenous indicator of comparative advantage.

The ‘neo-Ricardian’ approach of Steedman (1979a; 1979b) considers moregeneral time-phased structures of production. Technology alone determinesnegatively sloped wage–profit or factor-price frontiers, any point on which generatesa set of relative product prices and hence a pattern of comparative advantage relativeto another such economy.

Factor proportions and the Heckscher–Ohlin model

While J.S. Mill, Marshall and Edgeworth all made major contributions to tradetheory, the concept of comparative advantage did not undergo any evolution in theirwork beyond the stage at which Ricardo had left it. They essentially concentrated onthe determination of the terms of trade and on various comparative static exercises.The interwar years, however, brought fundamental advances, stemming in particularfrom the work of the Swedes Heckscher (1919) and Ohlin (1933). The developmentof 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 andcomparative advantage as a branch of neoclassical general equilibrium theory.

The essentials of this approach can be expounded in terms of the familiartwo-country, two-good and two-factor model, on which see Jones (1965) for adetailed and lucid algebraic exposition. The given factor supplies and constantreturns to scale technology define concave production-possibility frontiers, on theassumption 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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the same autarky equilibrium price-ratio and so will have no incentive to engage intrade. Countries must therefore differ with respect to at least one of thesecharacteristics for differences in comparative advantage to emerge. With identicaltechnology and factor endowments, a country will have a comparative advantage inthe good its citizens prefer less in comparison to the foreign country, since then thisgood will be cheaper at home. Similarly, if factor endowments and tastes areidentical, differences in comparative advantage will be governed by relativetechnological efficiency; that is, a country will have a comparative advantage in thegood in which its relative technological efficiency is greater, just as in the Ricardianmodel. These differences in technological efficiency could be represented, forexample, 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 infactor proportions that have dominated the explanation of comparative advantage inthe neoclassical literature. The Heckscher–Ohlin theorem, that each country willexport the commodity that uses its relatively abundant factor most intensively, hasbeen rigorously established and the necessary qualifications carefully specified,as in Jones (1956). Among the more important of these is the requirement thatfactor-intensity ‘reversals’ do not take place; that is, that one good is always morecapital-intensive than the other at all wage-rental ratios or at least within the relevantrange defined by the factor proportions of the trading countries.

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 protectiondoes the opposite, and the celebrated factor price equalization theorem of Lerner(1952, though written in 1932) and Samuelson (1948; 1949; 1953), which states thatunder certain conditions free trade will lead to complete equalization of factorrewards even though factors are not mobile internationally. The normativesignificance of this theorem is that free trade alone can achieve world efficiency inproduction and resource allocation, unlike the case of the Ricardian model as pointedout 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 offactors. It also requires factor proportions to be sufficiently close to each other in thetrading partners so that the production patterns are fairly similar. Thus it would befar-fetched to expect the price of unskilled labour to be equalized betweenBangladesh 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. Inthis model each production sector has its own unique fixed factor, while labour isused in all sectors and is perfectly mobile internally between them. Trade patternsstill reflect factor endowments but factor price equalization does not hold in thismodel 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 thisapproach, in which one sector uses land and labour, while the two others use capital

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and labour, thus neatly integrating the ‘specific factors’ model with the regulartwo-by-two Heckscher–Ohlin model. Findlay (1995, chs 4 and 6) uses adaptationsand extensions of the Gruen–Corden specification to introduce human capitalformation and the concept of a natural resource ‘frontier’ into the Heckscher–Ohlinframework.

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 propensityto save or time preference of each trading community, rather than being taken asexogenously fixed. Oniki and Uzawa (1965) extended the model to a situation wherethe labour force is growing in each country at an exogenous rate and capital isaccumulated in response to given propensities to save in each country. One of thegoods 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 aparticular capital–labour ratio for each country, which will be higher for the countrywith the larger saving propensity. In Findlay (1970; 1984), it is shown that as thecapital–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 capital-intensive goods, thus formalizing the concept of a ‘ladder of comparative advantage’that countries ascend in the process of economic development. Thus comparativeadvantage should not be conceived as given and immutable, but evolving withcapital accumulation and technological change. Much of the loose talk about‘dynamic’ comparative advantage in the development literature, however, ismisconceived since it attempts to change the pattern of production by protectionbefore 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 capitalgoods as represented by the ‘trees’ of different ages, and Findlay (1995, ch. 2),which addresses the question posed by Samuelson (1965) of whether trade equalizesnot 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 beginsin a systematic way only with the work of MacDougall (1951) on the Ricardiantheory and the celebrated article of Leontief (1954) that uncovered the apparentparadox that US exports were more labour-intensive than her imports. Leontief’sdramatic finding spurred considerable further empirical research motivated by thedesire to find a satisfactory explanation. The increasing scarcity of natural resourcesin the USA, by causing capital to be substituted for it in import-competingproduction, was stressed as an explanation for the paradox by Vanek (1963). Therole of ‘human capital’ as an explanation was pointed to by Kenen (1965) and anumber of empirical investigators, who found that US exports were considerablymore skill-intensive than her imports, even though physical capital-intensity was onlyweakly correlated with exports and imports. This pointed to the need to reinterpretthe simple Heckscher–Ohlin model in terms of skilled and unskilled labour as the

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two factors, rather than labour of uniform quality and physical capital. Since theformation of skill through education is an endogenous variable, a function of a wagedifferential that is itself a function of trade, we need a general equilibrium model thatcan simultaneously handle both these aspects, as in Findlay and Kierzkowski (1983)and Findlay (1995, ch. 4).

Many other extensions of the Heckscher–Ohlin theory are surveyed in Jonesand Neary (1984) and Ethier (1984), while Deardorf (1984) and Feenstra (2004) givevery incisive accounts of the attempts at empirical testing of the theory ofcomparative advantage in its different manifestations. Further important progress inempirical testing of the Heckscher–Ohlin model has been achieved by the work ofLeamer (1984), Trefler (1995), Harrigan (1997) and Davis and Weinstein (2001).

Increasing returns

Finally, the crucial role of increasing returns to scale in specialization andinternational trade has only recently been rigorously investigated, since it impliesdepartures from perfect competition. Krugman (1979) and Lancaster (1980)introduced international trade into models of monopolistic competition withdifferentiated products, showing the possibility of gains from trade due to theprovision of greater variety of similar goods rather than differences in comparativeadvantage, what is referred to as ‘intra-industry’ trade. Helpman and Krugman(1985) thoroughly examine and extend our knowledge in this area, while Grossmanand Helpman (1991) expertly extend the monopolistic competition approach to dealwith a number of issues involving endogenous technological progress and growth inthe 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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