How would David Ricardo have taught the principle of comparative advantage?

1. Introduction

Assume that David Ricardo's life had extended beyond the age of 51, that he became a professor of political economy in his later years, and was invited to lecture on comparative advantage. (l) Against all odds, he displays a remarkable intuition of future developments in economic theory and is able to use the standard tools and graphical techniques found in present-day economics textbooks. In his lecture, Ricardo recalls the numerical example contained in his Principles of Political Economy and Taxation (Ricardo 1951b, chapter 7) where cloth and wine are traded between England and Portugal. He reminds his audience that England's exports of cloth embody the labor of 100 men, whereas 120 men would be needed to produce its wine imports. The corresponding numbers for Portugal are 80 for wine exports and 90 for cloth imports. England's comparative advantage in cloth is explicitly implied by the numbers 100 and 120 pertaining to its two traded commodities, even before Ricardo mentions the corresponding numbers for Portugal. Because the amounts of Portuguese labor associated with the quantities of wine and cloth actually traded are lower than those of English labor, Portugal has an absolute advantage in producing both commodities. However, the fact that 801120 < 90/100 shows that Portugal has a comparative advantage in wine and hence will exchange wine for cloth when trade begins (Ruffin 2002, Maneschi 2004). (2)

This paper aims to present Ricardo's illustration of the gains from trade in both algebraic and graphical form, using first a linear then a nonlinear model of production. Section 2 shows how Ricardo makes a gradual transition to a complete trade model by quantifying the gains from trade as the amount of labor saved by trade in the case where the two countries' transformation curves happen to be linear. In section 3 he generalizes his illustration of the gains from trade by using a concave transformation curve. In section 4 Ricardo proves that the liberalization of trade in wheat raises England's profit rate and reduces rental income, and shows these results diagrammatically. This effect on profits (neglected by contemporary trade textbooks) is the second main source of gains from trade. Section 5 concludes that the resulting representation of the gains from trade does greater justice to Ricardo's original trade model than that found in most textbooks.

2. The Linear Ricardian Model

After his painstaking elaboration of diminishing returns to labor leading to the theory of rent in chapter 2 of his Principles, Ricardo would have had little reason to argue that an economy's production possibility frontier is a straight line, choosing instead a production structure marked by diminishing returns to labor in agriculture that lead to a concave transformation curve. However, in this lecture he decides for pedagogical reasons to make a gradual transition to the latter by starting, as a temporary working hypothesis, with the linear "Ricardian" production model familiar to students of present-day textbooks.

Consider the production possibility line BE in the left-hand quadrant of Figure 1, where the horizontal axis measures the quantity of cloth to the left of the origin O and the vertical axis that of wine. In the right-hand quadrant, the horizontal axis measures the workforce in the wine sector, [L.sub.w]. Given a constant labor coefficient in wine production, the linear production function OQ shows wine output as a function of [L.sub.w]. If OF measures England's labor force L, GF (= OE) is its maximum output of wine. In response to the opportunity to trade with Portugal at terms of trade given by the slope of CB, England specializes in cloth production at B and consumes at C, trading BH units of cloth for CH of wine. According to chapter 7 of Ricardo's Principles, the labor required to produce the export of cloth BH is 100 men, whereas England would require the labor of 120 men to produce the quantity CH of wine it imports. Ricardo argues that the gains of trade are therefore 20 men, and wishes to represent these gains graphically. He notes that points B and T are located on England's production possibility frontier (or transformation curve), so that the output bundles they represent utilize the same amount of labor. Hence, the labor needed to produce BH cloth is the same as that needed to produce TH wine, which can be read in the right quadrant as the amount OR required to produce PR wine. The number of workers that England would need to produce its wine imports CH, equal to QS in the right quadrant, is OS. Hence, England's gains from trade GT in terms of the amount of labor it saves by trading are (3)

[FIGURE 1 OMITTED]

GT= OS - OR = 120-100 = RS = 20 men.

If "real cost" is measured in terms of labor, Ricardo's interpretation is consistent with what Jacob Viner called the "eighteenth-century rule" for the gains from trade, according to which "it pays to import commodities from abroad whenever they can be obtained in exchange for exports at a smaller real cost than their production at home would entail" (Viner 1937, p. 440).

Ricardo points out that there is an alternative and mathematically identical way to measure the gains from trade that highlights their nature: it is the excess of the amount of labor needed to produce the consumption bundle C over England's labor force. He observes that the net export vector (BH, - CH) is mathematically equal to the difference between the production vector (OB, 0) and the consumption vector (OH, CH). The production of CH units of wine would require OS units of [L.sub.w], while OH (= AT) units of cloth required the labor RF because they are equivalent in labor terms to EA wine. Hence, the excess of the total labor required to produce the bundle C over England's labor force is OS + RF - OF = FS + RF = RS, again equal to 20 men.

Comparative advantage is clearly identifiable in Figure 1. If X (=BH) represents the amount of cloth exported and Y (= CH) that of wine imported, the terms of trade given by the slope of BC are Y/X units of wine per unit of cloth. Because England's unit labor coefficients are 100/X for cloth and 120/Y for wine, the opportunity cost of cloth in terms of wine, given by the slope of BE, is (100/X)/(120/Y) = (5/6)Y/X. In Portugal the corresponding unit labor coefficients are 80/Y for wine and 90/X for cloth, so that its opportunity cost of cloth in terms of wine is (9/8) Y/X. In autarky these opportunity costs are equal to the domestic price ratios. As in the textbook Ricardian trade model, these opportunity costs lie on either side of the terms of trade Y/X, and show that Portugal has a comparative advantage in wine while England has it in cloth. However, contrary to the textbook model, these autarky price ratios are expressed in terms of the amounts of commodities traded, X and Y, and not as the ratios of exogenously given unit labor coefficients. Moreover, in his lecture Ricardo derives them almost as an afterthought after postulating a trade equilibrium at given (though unspecified) terms of trade, rather than as the initial step to be taken before considering the trade equilibrium. Robert Torrens and especially John Stuart Mill were the economists who first analyzed the issue of the determination of the terms of trade that Ricardo never addressed. (4)

3. The Ricardian Model in a Setting of Diminishing Returns to Labor

One of Ricardo's primary interests in writing his Principles was to investigate the shares of national income accruing to the various social classes and how these shares varied over time. As he observed in the preface, "In different stages of society, the proportions of the whole produce of the earth which will be allotted to each of these classes, under the names of rent, profit, and wages, will be essentially different... To determine the laws which regulate this distribution, is the principal problem in Political Economy" (Ricardo 1951b, p. 5). In his analysis of rent in chapter 2, Ricardo assumed diminishing returns to labor in the corn sector at both the extensive and the intensive margin (where the term "corn" in his day signified any grain such as wheat, barley, or rye). In chapters 5 and 6 he integrated the determinants of wages and profits with the analysis of rent in chapter 2. Although the paragraphs on comparative advantage in chapter 7 concerning cloth and wine traded by England and Portugal make no explicit reference to land, the use of land is surely implicit in the production of wine. Moreover, in a footnote that he added directly after his comparative advantage example, Ricardo observed that "a country possessing very considerable advantages in machinery and skill, and which may therefore be enabled to manufacture commodities with much less labour than her neighbours, may, in return for such commodities, import a portion of the corn required for its consumption." This implies that some of the corn consumed is produced domestically, so that specialization in the export sector (contrary to the textbook model) is incomplete. Similarly, when Ricardo considered the possibility of a reversal of comparative advantage, he noted: "Suppose England to discover a process for making wine, so that it should become her interest rather to grow it than import it; she would naturally divert a portion of her capital from the foreign trade to the home trade," rather than all her capital (1951b, pp. 136-7; emphasis added).