Front Page Titles (by Subject) VIII. A Graphical Examination of Pigou\'s Analysis 1 - Studies in the Theory of International Trade
The Online Library of Liberty
A project of Liberty Fund, Inc.
Search this Title:
Also in the Library:
VIII. A Graphical Examination of Pigou's Analysis 1 - Jacob Viner, Studies in the Theory of International Trade 
Studies in the Theory of International Trade (New York: Harper and Brothers, 1965).
About Liberty Fund:
Liberty Fund, Inc. is a private, educational foundation established to encourage the study of the ideal of a society of free and responsible individuals.
The text is in the public domain.
Fair use statement:
This material is put online to further the educational goals of Liberty Fund, Inc. Unless otherwise stated in the Copyright Information section above, this material may be used freely for educational and academic purposes. It may not be used in any way for profit.
VIII. A Graphical Examination of Pigou's Analysis1
The examination of Pigou's algebraic analysis, and especially of its economic implications, can be facilitated by the use of graphical illustrations. In chart III the left-hand diagram relates to the representative Englishman and the right-hand diagram to the representative German. Commodity units of the respective commodities are so chosen, for each country separately, as to be equal in price prior to reparations. For the English and the German “representative” consumer, respectively, the quantity purchased before reparations of his own country's commodity is
measured on the df or d1f1 axis, to the left from the oa or o1a1 axis, and the quantity purchased before reparations of the imported commodity is measured on the same axis but to the right from the oa or o1a1, axis. For the representative consumer in each country the marginal utilities of the different commodities are measured vertically from the bc, or b1c1, axis. The curve of marginal utility to the representative English consumer is, therefore, ab for the native commodity and ac for the imported commodity, and a1b1 and a1c1 are similarly the curves of marginal utility to a representative German of the German and the English commodities, respectively. Since the utility functions are assumed to be linear, ab, ac,a1b1 and a1c1, are all drawn as straight lines.
In chart III there is substituted, for the two “marginal disutility of surrendering” functions which Pigou uses (i.e., ƒ(nX) and ψ(mY)), the corresponding marginal utility curves, ab and a1b1. The substitution does not call for a change in the numerical value of the slope, and by placing the ab and a1b1 curves on the left side of oa, o1a1 axes, i.e., by making their inclinations positive, change of signs is also avoided. Since ⊘ = the slope of ac,ƒ′ = the slope of ab,ψ′ = the slope of a1b1 and F' = the slope of a1c1, Pigou has demonstrated that the terms of trade of Germany will not change, will move against Germany, or will move in favour of Germany according as
Unless, however, some presumptions can be established as to the relative slopes of the various utility curves, no progress has been made toward determining the probable effects of reparations payments on the terms of trade. To establish such presumptions Pigou resorts to two additional sets of presumptions, first, that before reparations each country spends more on native than on imported goods, and second, that the utility functions within each country are “similar.”
The presumption that each country before reparations spends more on its own products than on foreign products is equivalent to making de > ef and d1e1 > e1f1 in chart III. Pigou adopts it, presumably, on the ground that such is almost invariably the actual situation. The general prevalence of this situation results, however, chiefly from restrictions on foreign trade, from the existence—by no means universal—of greater international than internal costs of transportation from producer to consumer, and, above all, from the fact that included in the native commodities of each country are “domestic” commodities, or commodities which because of regional differences of taste or non-transport-ability cannot find a market outside their country of production. But Pigou presumably abstracts from trade restrictions and transportation costs, and he explicitly excludes “domestic” commodities by his assumption that “there is only one sort of good made in the reparation paying country and only one sort made in the rest of the world.” In the absence of these factors, there would be no a priori presumption that there was any difference in either area in the amounts spent for native and for imported commodities if the two areas were equal in size, size being measured in terms of the pre-reparations value of output or of consumption. If the two areas were unequal in size, the most reasonable assumption would appear to be that, at the pre-reparations equilibrium, prices of the commodities would be such as to induce each country to spend more on the larger country's than on the smaller country's product. To justify acceptance of a general presumption that each country spends more on its own than on imported products it is necessary to recognize the existence of trade restriction, transportation costs, and above all, “domestic” commodities. It will be shown, moreover, that while an excess in each country before reparations of expenditures on native over expenditures on imported commodities, of itself, whatever its cause, tends to make , i.e., to contribute toward a situation in which reparations will make the terms of trade turn against the paying country, to the extent that such excess is due to higher international than internal transportation costs or to import duties this tendency unfavourable to the paying country will, given linear utility functions, be more than offset by the counter-tendency of the transportation costs and import duties to cause deviations from “similarity” of the utility functions within each country in directions favorable to the paying country.
By “similarity” of the utility functions within each country, Pigou must mean that, numerically, φ′ = E(ƒ′) and F′ = G(ψ′), where E is the pre-reparations ratio of the expenditures of a representative Englishman on English goods to his expenditures on German goods, and G is the pre-reparations ratio of the expenditures of a representative German on German goods to his expenditures on English goods. When the commodity units within each country are so chosen as to be equal in price before reparations, this is equivalent to the assumption that within each country first units of the different commodities have equal utilites, i.e., that in chart III the lines ab,ac start from the oa axis at some common point a, and the lines a1b1, a1c1 start from the o1a1 axis at some common point a1.
For the two-country case, the assumptions of linearity and of “similarity” within each country of the utility functions turn out to involve as a corollary the familiar assumption in other discussions of this problem that, in the absence of relative price changes, changes in the amounts available for expenditure in the respective countries resulting from reparations payments will not affect in either country the proportions in which these expenditures are apportioned between native and foreign commodities. Before reparations the representative Englishman bought ed units of English commodities and ef units of German commodities. Since the commodity units in chart III have been so chosen as to make the pre-reparations prices of the two commodities equal, their marginal utilities must have been equal to a representative English purchaser of both, i.e., kd = lf. Therefore, d, e, f, must be points on a horizontal straight line. Suppose that in the absence of relative price changes the representative Englishman, after reparations, buys hg units of English commodities and hj units of German commodities. If no changes have occured in their relative prices, the two commodities must still have equal marginal utilities to him, i.e., g, h, j, must be points on a horizontal straight line. From the geometry of triangles it follows that i.e., that in the absence of relative price changes, changes in the amount of his aggregate expenditures will not affect the proportions in which the representative Englishman distributes them as between English and German commodities. Similarly, i.e., in the absence of relative price changes, changes in the amount of his aggregate expenditures will not affect the proportions in which the representative German distributes them as between German and English commodities.
That for the two-country case the assumptions of linearity and of similarity within each country of the utility functions plus the assumption of an excess before reparations for the representative consumer of each country of his purchases of native over his purchases of foreign commodities suffice to establish Pigou's conclusion that reparations will necessarily cause the terms of trade to turn against the paying country, i.e., that can also readily be demonstrated from chart III. Suppose that in chart III, ed > ef and e1d1 > e1f1. Then, since: numerically, φ′: ƒ′:: ed: ef; numerically, ψ′: F′:: e1f1: e1d1; and
The assumption of “similarity” of the utility functions is a reasonable one, not because “similarity” is in fact probable, but because in the absence of specific information the “dissimilarity” which is likely to exist is, a priori, as likely to be in the one direction as in the other. Given the proportions in which expenditures in each country before reparations are divided between native and imported commodities, dissimilarities existing within either or both countries will tend to make reparations turn the terms of trade against or in favor of the paying country according as they take the form of lower or of higher ratios of the utility of initial units of native to the utility of initial units of imported commodities, the units of the commodities being so chosen, for each country separately, as to be equal in their pre-reparations prices.
Chart IV illustrates the bearing of “similarity” of utility functions on the problem. The proportions in which expenditures in each country are divided before reparations between native and imported commodities are made the same as in chart III, i.e., ed > ef and e1d1 > e1f1. Reparations payments, nevertheless, would leave the terms of trade unaltered, i.e., This results from the assumptions in the chart that, when for each country such commodity units are chosen as will make their pre-reparations prices equal, to the representative Englishman the utility of a first unit of the English commodity is sufficiently greater than the utility of the first unit of the German commodity (i.e., oa > oA) and to the representative German the utility of a first unit of the German commodity is sufficiently greater than the utility of the first unit of the English commodity (i.e., o1a1 > o1A1) to make
It can be seen from chart IV that, other things equal, the greater before reparations the average ratios of excess of the consumption of native over the consumption of imported commodities in the two countries, the greater must be the average ratio of excess in the two countries of the initial utility of the imported commodity over the initial utility of the native commodity if the terms of trade are not to be turned against the paying country by reparations payments. Although the pre-reparations ratios of consumption of native to consumption of imported commodities assumed in chart IV are much lower than would ordinarily be found in practice, the ratio of excess of the initial utility of native over the initial utility of imported commodities had to be substantial for each country (or on the average for the two countries combined) if reparations payments were not to turn the terms of trade against the paying country. If with uniform commodity units in both countries the ratio between the
prices of the two commodities was identical in both countries—as would be the rule for internationally traded commodities in the absence of trade barriers or transportation costs—it would be difficult, if not impossible, to find plausible grounds for holding that such substantial “dissimilarities” of utility functions were likely to prevail in practice.
I have benefited from the criticism of Professor G. A. Elliott, of the University of Alberta, of the diagrams here presented, and chart V, in particular,incorporates a modification made as the result of his criticism. He has since published a treatment of the problem along lines similar to those adopted here, but it unfortunately became available to me too late to permit its use as a check on my results. Cf. G. A. Elliott, “Transfer of means-of-payment and the terms of international trade,” Canadian journal of economics and political science, II (Nov. 1936), 481–92.