Front Page Titles (by Subject) X. An Alternative Solution - Studies in the Theory of International Trade
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X. An Alternative Solution - 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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X. An Alternative Solution
That it is possible to attack the problem without resort to utility analysis is demonstrated in chart VI in terms of a two-country case, based on the assumptions that in each country before reparations more is spent on native than on imported commodities, that the proportions in which expenditures are distributed between native and imported commodities remain unaltered in both countries, in the absence of relative price changes, as the amount available for expenditures changes, that production is carried on under constant cost conditions, and that there are no trade barriers or transportation costs. The “amount available for expenditure,” it is to be noted, is measured not in money but in units of the native commodity, or their equivalent in value, which can be bought with the money available at the prevailing prices.
Through any point,e, on a vertical line mn draw a horizontal line df, such that the distance df, represents the aggregate number of units of commodities which England can purchase with her national income before reparations at the prevailing prices, when the physical units of the commodities are so chosen that the English
and the German commodity are equal in price, and such that de, and ef, represent the amounts of German commodities, respectively, which the English would consume before reparations at the prevailing prices. Through any point on mn below e draw another line gj such that, in the absence of price changes, gj—df would represent the amount of reparations received by England, and gh and hj would represent the amounts of English and of German commodities, respectively, which the English would consume after reparations. Draw lines connecting g with d and j with f, and project them until they intercept mn. If a change in the amount England has available for expenditure does not, in the absence of price changes, and within the range of observation, change the proportions in which England would divide her expenditures between English and German commodities, i.e., if gh:hj::de:ef, then the projections of gd and jf will intercept mn at some common point a, above e.
Through any point e1 on another vertical line m1n1 draw a horizontal line d1f1 such that the distance d1f1 represents the aggregate number of units of commodities which Germany can purchase before reparations at the prevailing prices when the physical units of the commodities are the same as in the other part of the diagram, and such that d1e1 and e1f1 represent the amounts of German and English commodities, respectively, which the Germans would buy before reparations at the prevailing prices. Through any point on m1n1 above e1 draw another line g1j1 such that, in the absence of price changes, d1f1 — g1j1 would represent the amount of reparations paid by Germany, and g1h1,h1j1, would represent the amount of German and of English commodities, respectively, which the Germans would buy after reparations. Draw lines connecting d1 with g1 and f1 with j1 and project them until they intercept m1n1. If a change in the amount Germany has available for expenditure does not in the absence of price changes change the proportions in which Germany divides her expenditure between German and English commodities, i.e., if, then g1h1:h1j1::d1e1:e1f1 and d1g1 when extended upward will intercept f1j1 at some common point a1 above h1.
Suppose now that de > ef, and that d1e1 > e1f1, i.e., that before reparations each country spent more money on its own than on the other country's commodities. To show that on these assumptions reparations must turn the terms of trade against Germany, it is necessary to show that, in the absence of relative price changes, the two countries combined would, after reparations, want to buy more of England's commodities and less of Germany's commodities than before reparations, i.e., that, in the absence of relative price changes: (1) the amount by which England would want to increase her consumption of English commodities was greater than the amount by which Germany would want to decrease her consumption of English commodities, or that gk > l1f1 (2) that the amount by which Germany would want to decrease her consumption of German commodities was greater than the amount by which England would want to increase her consumption of German commodities, or that d1k1 > lj.
Since reparations results in an increase in England's spendable funds equal to the decrease in Germany's spendable funds,
Reparations payments will, therefore, in the absence of relative price changes, result in this case in a shortage, relative to demand, of English commodities, and a surplus, relative to demand, of German commodities, and the establishment of a new equilibrium, adjusted to the reparations payments, will require a relative rise in the prices of English commodities, i.e., a movement of the commodity terms of trade against Germany.
If in either or in both countries the proportion in which expenditures between native and imported commodities, in the absence of relative price changes, varies with variations in the aggregate amount of spendable funds, such variations will operate favorably or unfavorably for Germany's terms of trade according as, in the case of Germany, the proportion spent on German goods increases or decreases with a decrease in the amount of spendable funds and as, in the case of England, the proportion spent on German goods increases or decreases with an increase in the amount of spendable funds. Deviation in the proportions of the expenditures in a direction favorable to Germany in either or in both countries will not suffice, however, to turn the terms of trade in favor of Germany, given an excess before reparations in the expenditures of each country (or in both combined) on native commodities over their expenditures on imported commodities, unless such deviations are sufficiently marked to make reparations payments result in the aggregate for both countries, in the absence of relative changes in prices, in a relative increase in the demand for German commodities over the demand for English commodities.1
A concrete case may be cited to illustrate the type of situation in which the terms of trade might turn in favor of the paying country as the result of reparations. First, suppose that the paying country, Germany, produces two kinds of commodities, one a “domestic” commodity, primarily a necessary, and the other a luxury, which is exported but is not consumed heavily at home, and imports from England what is essentially a luxury commodity. As the spendable funds of Germany are cut down by reparations payments, there would probably occur, in the absence of relative price changes, a proportionately greater reduction in the German purchases of the luxury import than of the necessary “domestic” commodity. Suppose, in turn, that England also produces two kinds of commodities, one a “domestic” commodity, primarily a necessary, and the other a luxury, which is exported but is not consumed heavily at home, and imports from Germany what is a luxury commodity. As the spendable funds of England are increased by the reparations receipts, there would probably occur, in the absence of relative price changes, a proportionately greater increase in the English purchases of the imported luxury than of the necessary “domestic” commodity. These deviations from proportionality, both working in favor of Germany, could conceivably be sufficiently marked to make the terms of trade turn in favor of Germany as the result of reparations, even if before reparations each country spent much more on native than on foreign commodities. This would be certain to be the situation if the English demand for native commodities was such that, with prices unchanged, the English purchases of native commodities would fall absolutely when the English incomes increased, and if the German demand for native commodities was such that, with prices unchanged, the German purchases of native commodities would rise absolutely when the German incomes decreased, demand phenomena which are no doubt highly improbable, but are not inconceivable.2
Demand and supply curves in terms of money prices of the ordinary Marshallian type cannot legitimately be used in the solution of the reparations transfer problem, since they abstract from the interrelationships between demands, supplies, and incomes.3 Nor can the problem be solved through the use of Marshallian reciprocal-demand curves without additional information, since the problem turns on what happens as the result of reparations payments to the position and shape of the reciprocal-demand curves, and this depends on the utility functions in both countries, and cannot be determined without reference, direct or indirect, to these functions.4
It has so far been assumed that in every industry production is carried on under conditions of constant costs. By virtue of this assumption, it has been possible to carry out the analysis without explicit reference to costs without impairing the validity of the conclusions reached. Under constant technological costs money costs can change only as the prices of the factors of production change, and, assuming no change in the supplies of the factors, their prices can change only as the aggregate demands for them from all the industries using them change. It was therefore necessary to take account only of the apportionment by the two countries of their expenditures as between their own products and foreign products, and their mode of apportionment of their expenditures as between their “domestic” and their export commodities had no bearing on the problem. Under constant costs, moreover, the double factoral terms of trade would be affected by reparations payments in precisely the same way, both as to direction and as to degree, as the commodity terms of trade. But if some, or all, industries operate under varying costs as their output is varied, it is possible in each country for the prices of domestic and of export commodities, respectively, to move in different degrees and even in different directions as the result of a change in the volume of expenditures, so that the movement of the prices of the “domestic” commodities of the two countries may differ in direction or in degree from the movement of their export commodity prices, and the factoral terms of trade may move differently, in degree, and when the commodity terms of trade move against the receiving country, even in direction, from the commodity terms of trade. This will hold even if there is effective mobility of the factors within each country, i.e., if the marginal value productivity and the rate of remuneration of each factor are equal in all industries in which it is employed, provided different industries use the factors in different and variable combinations. But if prices at which any factor is available are for any reason not uniform in all industries, or if there are factors which are specialized for certain industries, then the range of possible relative variation of the prices of “domestic” and of export commodities in each country will be still greater.
The task of tracing the effect of international payments on the terms of trade when production is carried on under conditions of varying cost as output is varied appears to be one of discouraging complexity. Even after resort to the utmost simplification of which the problem admits there remain more variables to be dealt with than either arithmetical illustrations or ordinary graphic methods can effectively handle. Though general solutions may be obtainable by algebraic methods, it seems evident that they are not easily obtainable, and in any case they are not within my power. There seems no good a priori reason to suppose, however, that any of these additional factors has an inherent tendency to operate more in favor of the paying than of the receiving country, as far as the terms of trade are concerned.
I venture the prediction, therefore, that when the problem is solved for more complex cases involving varying costs as output is increased, the following conclusions derived from analysis of the simpler cases dealt with above will be found not to require substantial modification: (1) that a unilateral transfer of means of payment may shift the commodity terms of trade in either direction, but is much more likely to shift them against than in favor of the paying country; (2) that the double factoral terms of trade will ordinarily shift in the same direction as the commodity terms of trade, but under increasing costs in all industries, when the commodity terms of trade shift in favor of the paying country, the double factoral terms of trade will nevertheless shift in favor of the receiving country, or will shift in less degree than the commodity terms of trade in favor of the paying country; and (3) that the tendency of the terms of trade to move against the paying country will be more marked, caeteris paribus, the greater the excess in each country, prior to the transfer, of consumption of native products to consumption of imported products, to the extent that such excess is not due to trade barriers or to higher international than internal transportation costs.
Le., unless in chart VI, the deviations in the two countries from the proportions in which they originally distributed their expenditures between German and English goods would, in the absence of price changes, be sufficiently favorable to Germany to make lj > d1k1 and gh < l1f1.
In this case, in terms of chart VI, although gj > df, and g1j1 < d1f1, in each instance by the amount of reparations payments, nevertheless gh < de, and g1h1 > d1e1.
Cf. infra, pp. 582 ff.
Cf. D. H. Robertson, “The Transfer Problem,” in Pigou and Robertson, Economic essays and addresses, 1931, p. 171: “they [i.e., Keynes, Pigou, Taussig] have nowhere, so far as I know, explained clearly the reactions of a reparation payment on the shape and position of the Marshall [reciprocal-demand] curves.”