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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 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.

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 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).

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 must be imported. The number j itself will depend upon the relative sizes of the two countries and the composition of world demand. Dornbusch et al. (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.

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 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, b) 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.

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 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.

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 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.

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 capital-intensive 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 two factors, rather than labour of uniform quality and physical capital. Since the formation of skill through education is an endogenous variable, a function of a wage differential that is itself a function of trade, we need a general equilibrium model that can 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 Jones and Neary (1984) and Ethier (1984), while Deardorf (1984) and Feenstra (2004) give very incisive accounts of the attempts at empirical testing of the theory of comparative advantage in its different manifestations. Further important progress in empirical testing of the Heckscher–Ohlin model has been achieved by the work of Leamer (1984), Trefler (1995), Harrigan (1997) and Davis and Weinstein (2001).

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