Front Page Titles (by Subject) III. Trade in More Than two Commodities - Studies in the Theory of International Trade
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III. Trade in More Than two Commodities - Jacob Viner, Studies in the Theory of International Trade 
Studies in the Theory of International Trade (New York: Harper and Brothers, 1965).
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III. Trade in More Than two Commodities
The problems connected with the doctrine of comparative costs have usually been examined under the simplifying assumptions that there are only two commodities and only two countries, in the belief that while the introduction of more commodities or countries into the problem would complicate the analysis it would require no serious qualitative change in the conclusions reached on the basis of the simple assumptions as to the nature and profitability of international specialization.1 This position seems to me substantially correct, although certain problems relating to foreign trade tend to be neglected when these assumptions are followed.
Graham has, however, put forth the claim that because of its adherence to the assumptions of only two countries and only two commodities, “the classical theory of international values seems ... to be open to grave objections, objections which, while they do not subvert its foundations, nevertheless call for a substantial modification of its conclusions,” 2 and in a later article3 he has expressed his criticism in still stronger terms. Some of his criticisms are well taken, and expose genuine weaknesses in the classical expositions of the theory. As Graham explains, however, his objections are mainly directed against the reciprocal-demand theorizing of J. S. Mill and Marshall, and not against the doctrine of comparative costs, which is alone the concern of this chapter. The classical economists, moreover, departed from the rigid assumption of only two commodities more often than Graham would lead one to suppose. Several instances, in which analysis in terms of more than two countries bore on the relationship between comparative costs and terms of trade, are examined below.
Longfield appears to have been the first to attempt to extend the Ricardian analysis so as to deal explicitly with more than two commodities. Where there are only two commodities, then, given the comparative costs, there is no question as to which commodity each country will respectively import and export. But when there are more than two commodities the question as to what commodities will be exported and what imported by each of the countries cannot be so readily answered. Longfield's solution, although not entirely satisfactory, approached closely to what later became the accepted one. He abstracts from transportation costs, and from all elements in real costs but labor costs, and assumes tacitly that when trade is under way all prices will be identical in the two countries. He then assumes tentatively that wages in each country are uniform in all occupations. He offers, apparently without realizing it, several different and inconsistent solutions. He first asserts that wages in the two countries will be proportional to the average productivities of labor in the two countries. If English labor, presumably before trade, is on the average three times as productive as French labor, and therefore English money wages three times as high as French wages, then in all those industries in which English labor is, say, four times as productive as French labor money costs will be comparatively low, and these commodities will be exported; while in those industries in which English labor is not more than twice as productive as French labor, money costs will be comparatively high, and these commodities will be imported. “Commerce will flow according as the proportion [of labor productivity] in particular trades is below or above the average proportion.” 4
Later he argues that if, while England was exporting the product of industries in which her labor was twice as productive as that of foreign countries, she acquired a threefold superiority in some other new industries, then her greater superiority in the new industries would make the old ones unprofitable. Labor in the old industries would have to be paid at the same rate as in the new, or at three times the rate prevailing abroad, and as its productivity in the old industries was only twice that of foreign labor, foreigners could produce the old products more cheaply in terms of money costs.5
Still later he provides a slightly different solution:
... if a nation enjoyed an immense superiority in the production of two or three articles of very general demand, the wages of her laborers might be, in consequence, so high that she could not compete with the rest of the world in any other manufacture, under a system of free trade. Let us suppose the productiveness of English labor to be ten times as great as that of any other nation, in the production of tin, calico, coals, cutlery, and pottery. The wages of her laborers will, in consequence, be much greater than those in any other nation; suppose them eight times as great, and suppose that English labor is only twice as productive as foreign labor, in the manufacture of other commodities. These latter, therefore, will be fabricated in the rest of the world, at the fourth part of the price which it will cost to make them in England.6
Longfield here presented correctly two important elements of the correct solution, namely, that for each country the commodities exported would be in the upper and the commodities imported would be in the lower range of its potential products with respect to comparative advantage in real costs, and that comparative money wage rates in the two countries would determine the precise line of division between export and import commodities. Where he failed, however, was in not providing a satisfactory explanation of the mode of determination of the ratio between wages in the two countries. His first two solutions are both obviously arbitrary and incorrect. Wages in the two countries would be proportional neither to the average productivities in all pretrade employments, nor to the productivities in the two countries in the relatively most productive employment of one of the countries. His final formula, where he makes the wage rate in England exceed the wage rate abroad by a somewhat smaller ratio than the ratio of superiority of English labor over foreign in those employments in which England is comparatively most efficient, is correct as far as it goes, but is insufficient basis for a definite solution of the problem. This was an important step forward, but Longfield's contribution unfortunately attracted no attention, and other leading writers did not deal at all with the problem of what determines the relative level of money incomes in different countries or accepted an unsatisfactory solution offered by Senior.
Senior argued that within any country the level of money wages in all occupations—proper allowance being made for differences in the attractiveness of different occupations—was determined by the wages which labor could earn in the export industries, and that the comparative levels of wages in the export industries of different countries were determined by the comparative prices which the export products of the different countries could command in the world markets.7 This became standard doctrine, although it left unanswered the question, given more than two commodities, as to how it was determined what would be the export industries. The prevailing level of wages would obviously be a factor in determining which industries could find export markets for their products. But to explain the determination of which industries should be export industries by reference to the general wage level, and to explain the general level of wages by reference to the level of wages prevailing in the export industries, would obviously be reasoning in a circle. Senior's argument sufficed to show that under equilibrium conditions wages in the non-export industries must be equal to wages in the export industries and that wages in different countries must be proportional to the value productivities of labor in the export industries of the respective countries. Senior failed to show, however, that wages in the non-export industries were determined by wages in the export industries instead of both sets of wages being the common product of a number of factors.
In the writings of Ricardo and the two Mills no approach to a solution of this problem is to be found. Torrens, in an elaborate discussion bearing evidence of indebtedness to Senior and Long-field, made some progress. He pointed out that the extent to which a country could confine its exports to the commodities in whose production it was at or near the upper limit of its scale of comparative advantage depended on the extent of the foreign demand for these commodities. The wider the range of commodities which it had to export in order to employ its labor to the best advantage, the lower, other things equal, would be its relative level of money wages as compared to other countries.8 Cairnes also attacked the problem, and reached the correct conclusion that while the general level of wages and foreign trade were intimately connected, the connection was one not of simple cause and effect operating in a single direction, but of joint dependence on the “productiveness of industry” as a whole and on the demands for different commodities.9 He left vague, however, the precise nature of the inter-relationships between productivities, wage levels, and international specialization.
A minor writer, P. J. Stirling, attempted to deal with the problem,10 but did not carry it as far as had Longfield. He claimed that the two countries would find it to their interest to exchange at each other's “par,” or on terms proportional to the cost of production of the exchanged commodities. “The terms of the exchange are regulated by the relative efficiency of the labor of the two countries in the production, not of all commodities, but of those commodities in the production of which their efficiency is most nearly equal.” He thus assimilated the theory of international value to the theory of domestic value, completely where there is some product whose cost is identical in the two countries, and approximately where there is no such product. He presented the following case:
Tin and silver are commodities peculiar to England and Mexico, respectively, and iron has identical costs in both countries. England will export cloth and import wheat, in the ratio of 150 units cloth to 100 units wheat, or the reciprocal of the ratio of their costs of production in the countries where they can be respectively produced at a comparative advantage. Although he does not expressly say so, silver and tin will also presumably exchange in the reciprocal of the ratio of their costs of production, or 400 units silver for 25 units tin, and iron will not move in trade. He says that if the English output of iron should increase to 55 units per 1000 days labor, other things remaining the same, then the rate at which English cloth would exchange for Mexican wheat would be 150 units cloth for 110 units wheat, which, it will be noted, makes the double factoral terms of trade with respect to these two commodities conform to the reciprocal of the ratio between the costs in the two countries of the commodity, iron, in which these costs approach most closely to equality. This is of course a purely arbitrary solution. But it has at least the one point of merit that it posits that the commodities which each country will export and import, respectively, will lie in the upper and the lower range of its series in terms of comparative advantage.
The necessary further step toward a satisfactory solution was taken by Mangoldt.11 He shows that, cost of production being regarded as constant, each country will specialize in the production of a group of one or more commodities, that the commodities within each of these groups will exchange for each other in proportion to their real costs of production, and that the terms on which the commodities belonging to the two different groups will exchange for each other will be determined by the effect of the reciprocal demand of the two countries for each other's export commodities on the relative money rates of remuneration of the productive factors in the two countries. To find a basis for determining which country will export any particular commodity. Mangoldt posits the existence of a commodity such that, when its real costs in each of the respective countries are multiplied by the rates of remuneration prevailing there, there will result a
money cost which is equal in both countries. Mangoldt presents his argument by means of laborious arithmetical illustrations, but it seems preferable to expound it with the aid of Edgeworth's ingenious logarithmic illustration, which, among other advantages, dispenses with the necessity of positing a commodity which is just on the margin of export or import.
Let the two columns of letters on either side of the vertical line in chart VIII (a) represent the logarithms of the real costs of the commodities a, b, c, d, e, in the two countries, with the left-hand column representing costs in country I and the right hand column representing costs in country II. Locate the points a, b, c, d, e by marking off from a fixed point o the logarithms of the real costs of the respective commodities in country I. Assume that the right-hand column can be made to slide freely up and down while the left-hand column is held rigid. From any fixed point o′ on this sliding column mark off in the same way and on the same scale as for country I the points a′, b′, c′, d′, e′, representing the logarithms of the real costs of the respective commodities in country II. Slide the right-hand column up or down to make oo′ equal the logarithm of the ratio of wages in country II, (wi), to wages in country I, (wii), so that
putting o′ below o when wages in country II are lower than wages in country I, as in Chart VIII(a), and putting o′ above o when wages in country II are higher than wages in country I, as in chart VIII(b).12 The relative rates of wages in the two countries, and therefore the distance of o′ below or above o, will be determined by the reciprocal demand of the two countries for each other's products, which in turn will be partially determined by the comparative costs. Real costs in the two countries remaining the same, any shift in their reciprocal demand for each other's products would result in a change in relative wages in the two countries and therefore in a corresponding shift, upward or downward, in the movable right-hand column in chart VIII(a). If the demand of country I for country II's products in terms of its own products increased, other things remaining the same, the right-hand column in VIII(a) would slide upward, and vice versa. The vertical distances from o, when the right-hand column is adjusted properly, of the points a, a′, b, b′, etc., will then show the logarithms of the money costs of production of the different commodities in the two countries in terms of a common currency unit.
Since the reciprocal demands are not shown in this chart, it does not show how the comparative wage rates are determined. It shows, however, given the real costs in each country and the comparative wages as determined by reciprocal demand, what commodities each country will export and import, respectively, and on what terms. If the wage rates are as indicated in chart VIII (a), the money costs of production will be higher in country I for commodities a, b, and c, and lower in country I for commodities d and e, then in country II. Country I will therefore export d and e, and import a, b, and c. The commodity terms of trade as between each pair of export and import commodities will be indicated by their comparative prices: e.g., the number of units of commodity a obtained by country I in return for 1 unit of d will be the number of units of b obtained by country I in return for one unit of e will be and so forth. If there were a commodity with equal money costs of production in both countries, that commodity might be exported or imported by either country, might not move at all in foreign trade, or might be exported from one country to the other while being produced in both countries, quite consistently in each case with the conditions stated.
Whatever commodities country I will export and whatever ones she will import, the ratio of the logarithms of the real costs, and therefore also the ratio of the real costs in country I to the real costs in country II, will be lower for each of the commodities exported by country I than for any of the commodities imported by country I. Thus in (a) of the above chart, where country I exports commodities d and e and imports commodities a, b, and c, and are both smaller than or 13 But as Edgeworth points out:14
This theory brings into view an incident which is apt to be masked as long as we confine ourselves to the case of two commodities, ... namely, that it is not in general possible to determine a priori, from a mere observation of the [real] costs of production in the respective countries before the opening of the trade, which commodities will be imported and which produced at home.... Thus if o′ in the figure be pushed up a little, the distances o′a′, o′b′ etc., being preserved constant, e will become an export (from country no. I) instead of an import. But the position of o′ depends not only the cost of production in each country, but also on the law of demand in each country for the different commodities.
This can perhaps be more clearly brought out by a comparison of (a) and (b). The scales of comparative costs are the same in both (a) and (b), but because of different reciprocal demands in the two cases the ratio between wages in country I and wages in country II is higher for (a) than for (b). As a result, country I exports only commodities d and e in case (a), as compared to commodities, b, c, d, and e in case (b).
Cf. J. S. Mill, Principles, Ashley ed., p. 588: “Trade among any number of countries, and in any number of commodities, must take place on the same essential principles as trade between two countries and in two commodities.”
F. D. Graham, “The theory of international values re-examined,” Quarterly journal of economics, XXXVIII (1923), 54-55.
“The theory of international values,” ibid., XLVI (1932), 381-616.
M. Longfield, Three lectures on commerce, 1835, pp. 50-56.
ibid., pp. 63-64.
Ibid., pp. 69-70.
N. W. Senior, Three lectures on the cost of obtaining money, 1830, pp. 11-30.
R. Torrens, Colonisation of South Australia, 1835, pp. 148-74, and especially pp. 169-74. What is here given is to be regarded as an interpretation of the general drift of Torrens's argument rather than a close paraphrase of his actual language.
Some leading principles of political economy, 1874, pp. 334-41. Ohlin also points this out. (Interregional and international trade, 1933, p. 281.)
P. J. Stirling, The Australian and Californian gold discoveries, 1853, pp. 211 ff.
H. von Mangoldt, Grundriss der Volkswirthschaftslehre, 2d ed., 1871, pp. 209-30. I follow here Edgeworth's excellent summary and commentary. Papers relating to political economy, II, 52-58.
Edgeworth presents only chart VIII (a) as drawn above. If wages were equal in both countries, then would be zero, and o and o′ would be on a level with each other.
Cf., for another and in some respects more general method of dealing with this problem. Haberler, “The theory of comparative cost once more,” Quarterly journal of economics, XLIII (1929), 378-80, and The theory of international trade, 1936, pp. 136-39, 150-52.
Papers relating to political economy, II, 55.