Front Page Titles (by Subject) V. Total Net Utility Derived from International Trade: Edgeworth - Studies in the Theory of International Trade
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V. Total Net Utility Derived from International Trade: Edgeworth - 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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V. Total Net Utility Derived from International Trade: Edgeworth
Edgeworth's analysis of the problem of gain from trade,1 the most elaborate and perhaps the least questioned in the literature, is both in method and in its conclusions in some important respects similar to, and in others different from, Marshall's analysis. Edgeworth's exposition is elliptical and cryptical, and is in part expressed in mathematical terms which I can follow only imperfectly. It is, therefore, with considerable trepidation that I present the following interpretation and criticism of his analysis.
Edgeworth uses reciprocal-demand curves of the Marshallian type to examine the direction of the effect on the amount of gain from foreign trade of disturbances of various kinds. He assumes tacitly that the curves in his diagrams represent the situation of typical individuals in the two areas, and bases his conclusions as to the direction of change in the amount of gain from trade on the proposition that movement from the point of origin of a given reciprocal-demand curve along the curve is always movement toward a position of greater total net utility (= consumer's surplus) and therefore of greater advantage, a proposition which he had earlier demonstrated, given his assumptions, for domestictrade demand curves in terms of money,2 and which he here transfers to reciprocal-demand curves without further argument. Edgeworth does not here attempt to deal graphically with the amount of change in gain from trade resulting from particular disturbances, but only with the direction of the change in the amount of gain.3
The proposition that movement along a Marshallian reciprocal-demand curve from its point of origin tends on ordinarily reasonable assumptions to be movement towards a position of greater advantage can be accepted. But Edgeworth derives from it conclusions which differ substantially from those reached in the preceding two sections. These differences in conclusions can be summarized in the proposition that (with the exception of one special case, to be examined later) in Edgeworth's results the direction of change in the amount of gain from trade and the direction of change in the commodity terms of trade always correspond,4 whereas it has here been argued that in many types of situations the commodity terms of trade and the amount of gain from trade may move in opposite directions was due to his failure, in his interpretation of his diagrams, to distinguish between disturbances involving movement along a given reciprocal-demand curve and disturbances involving movement to a new reciprocal-demand curve. One of Edgeworth's diagrams, reproduced here as chart XVIII,5 is supposed to cover all cases where (1) the gain consequences for country E are alone being considered, (2) the disturbance originates in country E, and (3) the specific nature of the disturbance can be described as “H, where the change originates on the side of supply: such as increased facility of producing or exporting native commodities; [or] h, on the side of demand: such as an increased desire for, or facility in admitting foreign commodities.” 6OE is E's reciprocal-demand curve and OG is G's reciprocal-demand curve, and under the original equilibrium conditions OM of E-goods is given by E in exchange for ON of G-goods. A disturbance ensues, which is assumed to be an impediment rather than an encouragement to trade, and to result in the OE curve becoming “transformed” (the term is Edgeworth's) to OE'. Edgeworth traces the effects of the disturbance as follows:
In the new equilibrium indicated by the point Q, RQ of X is given in exchange for QS of Y. But Q cannot be a position of greater advantage than P', where the horizontal through Q cuts the original curve. For, on the most favorable supposition that the impediment
affects only exportation, not production for internal consumption, (for instance, a transit duty imposed by a third country) England's offer in exchange for OR would be reduced by the impediment from OS' to OS, so that Q would be a position of just equal advantage as P'. But P' is a position of less advantage than P (being nearer the origin as you move along the curve). Thus the native country is prejudiced by the change.7
The mistake in this analysis is the identification, from the point of view of gain significance, of point P' with point Q for all cases, including cases where there is no direct utility relationship between the OE and the OE' curves. In the case of a transit tax on country E's exports, levied by a third country, where the horizontal distance between the OE' and the OE curves represents the total amount of tax, OE is still the real reciprocal-demand curve for country E, as seen by its inhabitants, while OE' is the same curve after the tax has been subtracted in E-bales, i.e., is E's curve as seen by importers in country G. Under the new equilibrium, therefore, country E gives up OS' units of E-commodities in exchange for OR units of G-commodities, while country G receives only OS units of E-commodities in exchange for OR units of its own commodities. The point P', therefore, represents the new equilibrium point on country E's unchanged reciprocal-demand curve, and because P' is nearer to O than is P as we move along the curve OE, the new situation is less advantageous to country E than the old. The change in the gain from trade for country E corresponds in direction to the change in the commodity terms of trade for country E, since because P' is nearer to O along the OE curve than is P, and the OE curve is concave upward with respect to OX, the slope of the OP' vector with respect to OX, which equals the new ratio in which G-commodities are obtained by country E in exchange for E-commodities, is smaller than the slope of the OP vector, which equals the old ratio in which G-commodities were obtained by country E in exchange for E-commodities.
But let us suppose that the disturbance which results in the OE curve being transformed to OE' consists of (1) a reduction in the desire of country E for G-commodities, or (2) an increase in the real cost of producing E-commodities, or (3) an increase in the desire of country E itself for E-commodities, all types of disturbances which Edgeworth believes to be covered by the diagram reproduced here as chart XVIII. The OE curve, as the result of any one of these types of disturbances, now has nothing but historical significance, is a quondam curve of reciprocal-demand, and OE' becomes the real reciprocal-demand curve for country E. The utility significance of two points cannot be compared unless both points relate to the same set of utility and disutility functions, whereas, under any of the three assumptions listed above, the change from the OE to the OE' reciprocal-demand curves is associated with a change in these basic utility functions. It is therefore no longer possible to determine from the position of Q with reference to P whether or not the new equilibrium situation is more advantageous to country E than was the equilibrium situation prior to the disturbance, since these are points on different reciprocal-demand curves whose utility relationship to each other cannot be known without more information than the diagram affords.
Note, however, the different effect on the commodity terms of trade of an impediment to E's trade which involves no change in E's real reciprocal-demand curve as compared to one which does involve such a change. The original commodity terms of trade were
for country E in the case of the transit tax, but become
in the case of a disturbance involving a real change in E's reciprocal-demand curve. But
i.e., the commodity terms of trade change in different directions in the two cases. In the transit tax case, the change in commodity terms of trade and the change in the amount of gain from trade are necessarily in the same direction; in the other type of case the diagram does not afford sufficient information to determine what is the direction of the change in the amount of gain from trade.
Except for one special case, still to be dealt with here, Edgeworth's failure to discriminate in his interpretation of his diagrams between disturbances which result in the movement of the equilibrium point along the given reciprocal-demand curve of the country under consideration and disturbances which result in that country acquiring a new reciprocal-demand curve pervades his entire analysis, and suffices to account for the differences between the conclusions with reference to the relationship between changes in the commodity terms of trade and changes in the amount of gain from trade reached by him, and those presented above. That Edgeworth had noticed the correspondence between his results with respect to the direction of the changes in the amount of gain from trade and his results with respect to the direction of the changes in the terms of trade is indicated by the fact that when he criticized Mill's procedure in accepting the trend of the commodity terms of trade as a criterion of the trend of gain from trade, he added:
However, it may be admitted that his definition is adequate to the purposes for which it is used. Where he says that the whole or none, or more or less, of the advantage will accrue to a certain country, it is generally true, I think, not only in his sense, but in the more correct sense.8
In the special case to which reference was made above, Edgeworth does deal with a disturbance which causes a displacement
of the equilibrium point off country E's reciprocal-demand curve. But in this case, for special reasons, the original reciprocal-demand curve does not lose any of its utility significance, and Edgeworth provides the additional information necessary to make utility comparisons between the new equilibrium point and the original one. The diagram which Edgeworth uses to present this case is reproduced here as chart XIX.9 Country E levies a tax in kind on its exports, the proceeds, by exception, being distributed in such a manner as to offset any influence which the tax would otherwise have on the relative desires of the inhabitants of country try E for the export and the import commodities.10OE and OG are the reciprocal-demand curves of country E and country G, respectively, and the dotted curve is an indifference curve or locus of positions of trade which are of equal advantage to country E as position P. We may call this dotted curve the trade-indifference curve. As Edgeworth says, this trade-indifference curve must touch the OP vector at P. If Q, which by assumption is the new position of equilibrium on the curve OG, is above M, and inside the trade-indifference curve, the inhabitants of country E are benefited by the tax; if Q is below M they are prejudiced by the tax.
Edgeworth is able here to use the position of the new equilibrium point with reference to the trade-indifference curve as test of whether the new trading position is superior or inferior to the old for country E because OE continues to be the reciprocal-demand curve of E as seen by its inhabitants—though not as seen by country G—and therefore the trade-indifference curve on which P is located retains the same significance for the inhabitants of E after the tax as before. This special case, therefore, also fails to deal with a situation where a disturbance takes the form of a change in E's basic utility functions, but while the commodity terms of trade necessarily move in favor of E, it is nevertheless possible for the new trade position to be less advantageous to E than the old one.
“The pure theory of international values,” in Papers relating to political economy, 1925, II, 31–47 (first published in Economic journal, 1894).
Edgeworth, Mathematical psychics, 1881, pp. 115–16.
In an earlier essay, Edgeworth had dealt graphically with the determination of the amount of gain or consumer's surplus accruing from trade before and after a disturbance (in this case an import duty, presumably a revenue duty, levied by the country, Germany, whose gain is being measured). He uses for Germany not only its reciprocal-demand curve, but also a “no-gain from trade” curve, which he calls a “collective utility curve,” and measures the gain from trade for Germany by the distance at the equillibrium point between the German “no-gain from trade” curve and the German reciprocal-demand curve. His construction is free, therefore, from the objection made above against Marshall's procedure of identifying the reciprocal-demand curve with a total-utility curve. I believe that Edgeworth's procedure here and mine in chart XVII, p. 573, supra, amount to the same thing.—Edgeworth, “On the application of mathematics to political economy,” Journal of the Royal Statistical Society, LII (1889), 555–60.
Edgeworth does not himself direct attention to this aspect of his results. Cf., however, infra, pp. 580–81.
This is diagram I in Edgeworth's fig. 4, Papers, II, 37.
Ibid., p. 34. Edgeworth points out that disturbances of the type labeled H by him and disturbances of the type h require a different graphical procedure where OE, or country E's reciprocal-demand curve, is inelastic, but not when OE is elastic. In chart XVIII, OE is elastic, so that this chart is according to Edgeworth applicable to both types of disturbances. (Ibid., p. 38.)
Ibid., p. 36.
Edgeworth, papers, II, 22.
Cf. ibid., p. 39, fig. 6.
Cf. ibid., pp. 38, 71–72. Edgeworth remarks: “It is not contended that the exception is of any practical importance.” (ibid., p. 72.)