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Studies in the Theory of International Trade
Chapter VI
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WILSON'S EXAMPLE I: NO PRICE CHANGES NECESSARY | ||||
---|---|---|---|---|
Commodity | Paying country |
Receiving country | ||
Purchases before payment | Purchases after payment if no price changes occurred | Purchases before payment | Purchases after payment if no price changes occurred | |
P... | 60 | 54 | 30 | 36 |
Dp... | ... | ... | ... | ... |
Dr... | ... | ... | ... | ... |
R... | 30 | 27 | 15 | 18 |
Total... | 90 | 81 | 45 | 54 |
Granted Wilson's assumptions, his example I is an adequate demonstration of the possibility that payments can be transferred without resulting in any movement of the terms of trade. Under the conditions given, the receiving country is willing in the absence of price changes to increase its purchases of each of the commodities to an extent just sufficient to offset the decreases in purchases by the paying country, and therefore no price changes are necessary for the restoration of equilibrium. This example suggests a general principle already formulated by a previous writer in this connection that "If the borrower wants what the lender does without, no change in prices is necessary."*86 It is to be noted, however, that in example I one of the countries spends a substantially larger amount on foreign than on native commodities. It will be found upon experimentation that, given the assumption that in the absence of price changes the international loan or tribute will not cause either country to desire a change in the proportions in which it had hitherto distributed its expenditures between native and imported commodities, the transfer of the loan or tribute will necessarily result in a movement of the terms of trade unfavorable to the paying country unless before reparations the unweighted average ratio of expenditures on native to expenditures on foreign commodities for the two countries combined is unity or less, an improbable situation when there are domestic commodities.
In example I there were assumed to be no domestic commodities. To show that his conclusion—that the transfer of payments will not necessarily involve a movement of the terms of trade against the paying country and may even involve a movement of the terms of trade in its favor—is not dependent on the assumption that there are no domestic commodities, Wilson presents his example IV, in which domestic commodities are introduced for both countries but otherwise the same assumptions are followed as for example I.
Comparing separately for each commodity the amounts which in the absence of price changes the two countries combined would be willing to purchase after the payments with the amounts they purchased before the payments, Wilson concludes that while the price of the receiving country's domestic commodity would rise, and the price of the paying country's domestic commodity would fall, the aggregate demand for the receiving country's export commodity will at unaltered prices have fallen more (from 60 to 58) relatively than the aggregate demand for the paying country's export commodity (from 50 to 49) and therefore the price of the former will probably have to fall relatively to the price of the latter to restore equilibrium. For the relations of the price levels of the internationally-traded commodities, he reaches the general conclusion that: "No matter what be the original proportions of total demand, that class of goods will be higher relatively in price to the other, for which the borrowing country has the greater relative demand as compared with the lending country."*87
No significance can be attached, for constant cost conditions, to the results derived by Wilson from his example IV, since it fails to take into consideration the necessary relationship between the prices in each country of domestic and export commodities resulting from their competition for the use of the same factors of production. If in either country the prices of domestic commodities rose or fell relative to export commodities, factors of production would be diverted from the low-price to the high-price industry until the earning power of the factors in the two industries was equalized, and under constant costs this would mean that in neither country could there be relative changes between the prices of domestic and export commodities. What the direction of relative change of the prices of the products of the respective countries will be as the result of international payments will depend on what effect the payments have on the relative aggregate demands of the two countries for all the products, and therefore for the factors of production, of the respective countries. In Wilson's example IV, the payment results, in the absence of price changes, in an increase in the aggregate demand for the products of the receiving country (275 after the payment as compared to 270 before the payment) and in a decrease in the aggregate demand for the products of the paying country (85 after the payment as compared to 90 before the payment). The prices of the factors, and consequently the commodity terms of trade, must therefore move against the paying country if equilibrium is to be restored.
WILSON'S EXAMPLE IV: TERMS OF TRADE MOVE AGAINST RECEIVING COUNTRY | ||||
---|---|---|---|---|
Commodity | Paying country |
Receiving country |
||
Purchases before payment | Purchases after payment if no price changes occur | Purchases before payment | Purchases after payment if no price changes occur | |
P... | 20 | 18 | 30 | 31 |
Dp... | 40 | 36 | ... | ... |
Dr... | ... | ... | 210 | 217 |
R... | 30 | 27 | 30 | 31 |
Total... | 90 | 81 | 270 | 279 |
To an objection to his analysis made by some unspecified person*88 to the effect that the flow of gold from lending to borrowing country, by raising money prices and incomes generally in the borrowing country, and lowering them generally in the lending country, will make the prices of the productive services and therefore also of their products, in domestic and export industries alike, rise in the borrowing country and fall in the lending country, Wilson replies that: "mere changes in money costs of production are not sufficient in themselves to cause a change in prices. If prices are to be affected by changes in costs of production, it can only come about through a change in the relative demand and supply of those goods whose money costs of production are affected," and that the relative changes in price which such changes in cost would tend to produce would tend to be checked by diversion of expenditures to or from other classes of goods not so affected.*89 This reply bears only on the degree of relative price changes needed, whereas the issue is whether any price changes are needed, and if so, in what directions. It, moreover, misses the character of the valid objection to which his analysis is open, which is not the common but fallacious argument that relative changes in the amounts available for expenditure in the two countries must necessarily result in changes in the same direction in the prices of the productive services and therefore also in the money costs of production of the two countries,*90 but that changes in the relative aggregate demands for the commodities of the respective countries will do so. If, as is possible, but, as will later be shown, improbable, a transfer of funds on loan from country A to country B results in an increase in the aggregate demand of the two countries for A's products and a decrease in their aggregate demand for B's products, it will be the prices of A's, and not of B's, factors of production which will rise.
Yntema applies to the problem a powerful mathematical technique, and analyzes it on the basis of a wide range of assumptions.*91 For cases such as those contemplated by the older writers, he reaches conclusions substantially in accord with theirs, especially with reference to the relative movement of the prices of the domestic commodities of the two countries and of their double factoral terms of trade.*92 But Yntema's analysis rests throughout on certain assumptions which seriously limit the significance of his results. He assumes that when a relative change in the amount of money in two countries occurs as a result of loans or tributes or other disturbances in the international balances, there will occur in the country whose stock of money has increased a rise not only in all of that country's demand schedules (in the simple Marshallian sense), but also in the prices of the factors of production and in the supply schedules of that country's products, and that there will similarly occur in the country whose stock of money has decreased a fall not only in all of that country's demand schedules, but also in the prices of its factors of production and in the supply schedules of that country's products, though these rises or falls need not be uniform in degree within each country. But a rise in all the demand schedules of a country does not necessarily lead to or require a rise in its supply schedules or in the prices of its factors of production. What will be the effect of an international transfer of income on the direction of the relative movement of the prices of the factors in the two countries is itself the question relating to the equilibrating process awaiting solution, but in Yntema's analysis it is unfortunately decided by arbitrary assumption. Yntema's conclusion that under constant cost the terms of trade must necessarily shift in favor of the receiving country results from his assumption that the prices of the factors and the money costs of production will necessarily rise in the receiving country. As had been argued above, this is not a valid assumption.
In his important treatise,*93 Ohlin gives an elaborate account of the mechanism, whose most important contribution is the convincing demonstation that not price changes only but also relative shifts in demands resulting from the transfer of means of payment, are operative in restoring a disturbed equilibrium in the balance of payments. On the question immediately at issue, i.e., the specific mode of operation of relative changes in sectional price levels in the mechanism of adjustment, he is extremely critical in tone in his treatment of the older writers, although as long as he adheres to the traditional assumptions he follows the traditional reasoning and conclusions only too closely. Ohlin claims that the older writers exaggerated the importance of relative price changes in the equilibrating process both because they overlooked the direct influence on purchases of the shift in means of payment and because the ordinarily high elasticity of foreign demand for a particular country's exportable products makes a small change in price exert a large influence on the volume of trade. Subject to the qualification that I believe I have shown that recognition of its validity was not nearly as rare among the classical expositors of the theory of international trade as he appears to take for granted, I concede his first point. But on the second point, at least a partial defense can be made of the position of the older writers. When two factors are necessarily associated in a complex economic process, there is rarely a satisfactory criterion for measuring their relative importance, even if all the quantitative data that could be desired were available. Ohlin appears to regard the relative degree of price change as between different classes of commodities as an appropriate measure of the importance of such price changes in the equilibrating process. A more appropriate criterion, if it could be applied, would be the proportion of (1) the equilibrating change in the trade balance which results from relative price changes to (2) the total change in the trade balance necessary to restore equilibrium. Since foreign demands for a particular country's products ordinarily have a high degree of elasticity, small price changes in the right direction can exert great equilibrating influence. But the emphasis which Ohlin gives to the question of the degree of change seems to me a novel one, as far as discussion of mechanism is concerned, and I cannot recall a single instance in the older literature where a definite position was taken as to the extent of the price changes necessary to restore a disturbed equilibrium.
Taking the case of international loans,*94 Ohlin assumes, as a first approximation, that "all goods produced in a country require for their manufacturing 'identical units of productive power' consisting of a fixed combination of productive factors." The lending country B must make initial remittances to the borrowing country A. The assumptions as to the effects on demands are not clearly stated, but seem to be as follows: the aggregate demands in terms of money prices of the two countries combined (1) for the export goods of A and (2) for the export goods of B, are each assumed to remain unaltered;*95 (3) the demand in A for A "domestic" goods increases; (4) the demand in B for B "domestic" goods decreases. This "implies" a shift in demand from B factors to A factors, which "raises the [relative] scarcity of the A unit, which means that every commodity produced in A becomes dearer than before compared with every commodity produced in B. The terms of exchage between A's export goods and B's change in favor of A."*96 So far, therefore, there is no correction of the older doctrines with respect to the kind of price changes necessary to restore equilibrium. But Ohlin attributes these results to the assumption that all industries use identical "units of productive power," and remarks that it is because they have expressed costs in such units that "men like Bastable, Keynes, Pigou, and Taussig have stopped at the preliminary conclusion in §5 and have found a variation in the terms of trade certain in all cases, at least where the direction of demand is not of a very special sort."*97
These results, however, arise not from the assumption of the use in each country of identical "units of productive power," but from Ohlin's assumption that the transfer of funds does not of itself lead to any alteration in the aggregate monetary demand for the export commodities of the respective countries. Even with both these assumptions, they are not necessary results, if it be granted that, without price changes, the increase in funds in A may lead to a decrease in the demand for A "domestic" goods, or that the decrease in the funds in B may lead to an increase in the demand for B "domestic" goods, or both, consequences by no means inconceivable, as, for instance, if A's and B's domestic goods are both predominantly low-grade necessaries of the sort heavily consumed only when there is economic pressure.*98 But Ohlin would probably regard—and not without justification—such movements of demand as "of a very special sort" and therefore not calling for consideration.
Abandoning the assumption of identical "units of productive power" and substituting the assumption that different industries use different factors, and use the same factors in different proportions, Ohlin shows that by introducing additional assumptions of non-competing factoral groups, the existence of idle resources, the tendency of the prices of the products to rise more rapidly than the prices of the factors in an expanding industry, and so forth, instances are possible where the commodity terms of trade turn against rather than in favor of the borrowing country.*99
It is to be noted that some of these assumptions are of a non-equilibrium nature, i.e., can be valid only temporarily. But granted that Ohlin has shown the possibility that the terms of trade, when such assumptions are made, will turn against the borrowing country, what about the probabilities? Every one of these added factors is as likely, a priori, to accentuate the movement of the terms of trade in favor of the borrowing country as to operate to move them against the borrowing country. Take only one example, sufficiently representative of the others: Ohlin argues that the factors used relatively largely in expanding industries are likely to rise in price, while those used relatively largely in declining industries are likely to fall in price; in the borrowing country, the domestic commodity industries will be expanding, because of the increased demand for their products, while the export commodity industries will be declining, presumably because of decreased demand in the lending country for their products; the prices of the factors used largely in the domestic commodity industries therefore will rise, while those used largely in the export commodity industries will fall. In the lending country, reverse trends will be operating. The export commodities of the borrowing country therefore will decline in price relative to the prices of the export commodities of the lending country; i.e., the terms of trade will move against the borrowing country. But the export commodity industries of the borrowing country are not, a priori, more likely to decline than to expand. The foreign demand for their products, it is true, will tend to fall, but Ohlin overlooks that the home demand for their products will tend to rise, and that there is no obvious reason why the latter tendency should be expected to be less marked than the former and to be insufficient to offset the former.
The "orthodox" conclusions as to the kind of price change which would tend to result from international borrowing thus emerge from Ohlin's critical scrutiny almost unscathed. When he adheres to the usual assumptions, Ohlin reaches the same conclusions. When he departs from them, he succeeds in showing that different results are possible. But he does not succeed in showing that they are probable, or even that they are not improbable.
In a recent article Pigou has attacked the problem in terms of marginal utility functions, and has reached the conclusion that, under constant costs, there is a strong presumption, but not a necessity, that the commodity terms of trade (which he calls the "real ratio of international interchange") will turn against the paying country as the result of reparations.*100 Pigou's results, it will later be shown, can in part at least be reached by an alternative procedure which is simpler and has the additional virtue that it does not involve resort to utility analysis. But Pigou's analysis can be made to serve the useful function of bringing into clear view the utility implications of this alternative procedure, and thus warrants detailed examination and elaboration.
Pigou assumes a paying country, Germany, and the rest of the world, which he calls "England," but since the existence of neutral countries, neither paying nor receiving reparations, gives rise to complications which this procedure disregards, I will proceed, for the time being, as if there are only two countries, Germany, the paying country, and England, the receiving country. Pigou makes the following additional assumptions: only one commodity produced in each area; "constant returns" (i.e., constant technological costs); dependence of the utility of any commodity on the quantity of that commodity alone; and linear utility functions throughout.
Pigou writes X/Y for the commodity terms of trade before reparations, and for the terms of trade after reparations, where: X, Y, represent the annual pre-reparations physical quantities of English exports and imports, respectively; X + P—P being negative—represents the annual quantity of English exports (or German imports) after reparations payments have been initiated; R represents the annual reparations payments measured by their value in English goods; and Y + Q represents the annual quantity of English imports (or German exports) after reparations payments have commenced. He further writes nX, nY, for the "representative" Englishman's pre-reparations exports and imports, respectively, and mX, mY, for the "representative" German's pre-reparations imports and exports, respectively. He then writes:
φ(nY) for the marginal utility of (nY) German goods to the representative Englishman;
ƒ(nX) for the marginal disutility to him of surrendering (nX) English goods;
F(mX) for the marginal utility of (mX) English goods to the representative German;
ψ(mY) for the marginal disutility to him of surrendering (mY) German goods.
Then, in accordance with Jevon's analysis,
In order that the new terms of trade should be equal to the old, it would therefore be necessary that
which, for linear functions, implies*101 that
It can similarly be shown that reparations will cause the terms of trade to turn in favor of Germany if and to turn against Germany if
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 d1f1axis, to the left from the oa or o1a1axis, 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 a1b1and a1c1are 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, a1b1and 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 ø = 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 > efand d1e1 > e1 f1 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(f') 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 utilities, 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 occurred 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.
Duties on imports, however, whether levied by the paying or the receiving country, and a fortiori when levied by both, do tend to result in higher initial utilities in each country for native than for imported commodities, and although they also tend to result in an excess of expenditures on native over expenditures on foreign commodities, they operate to make reparations turn the terms of trade in favor of, instead of against, the paying country. Import duties, regardless of which country levies them, operate to make the imported commodity relatively dearer than the native commodity in each country, as compared to what the situation would be in the absence of the duties. If in each country the units of the two commodities are so chosen as to be equal in price before the imposition of the duty, then, with the units used for the English commodity in England and the German commodity in Germany left unaltered, after the imposition of the duty the size of the unit used for the German commodity in England and the size of the unit used for the English commodity in Germany will both have to be decreased if the units used for the two commodities within each country are to be kept equal to each other in price. In terms of the graphical illustrations here used, it will follow that the initial utility of the imported commodity will be lower in each country after the duty than before, the initial utility of the native commodity remaining unaltered. A situation with respect to "dissimilarities" of the utility functions within each country corresponding in kind to that illustrated in chart IV will thus tend to result.
This reasoning is illustrated, for the case of an English import duty, in chart V. It is there assumed that initially there are no trade restrictions in either England or Germany, that there are no "domestic" commodities, and that in each country the representative consumer spends as much on imported as on native commodities. It is also assumed that in each country the utility functions are linear and originally "similar," so that when commodity units are so chosen as to be equal in their original prices, the utilities of initial units are also equal. Then so that Germany could make reparations payments to England without affecting the terms of trade.
Suppose, however, that before the obligation to pay reparations comes into effect, England imposes a revenue import duty of 50 per cent ad valorem on the German commodity. Let us assume that as a result the price of the German commodity to the English consumer rises by one-third relative to the price of the English commodity, i.e., one unit of the English commodity now has the same price in England as three-fourths of a unit of the German commodity, duty-paid. If, while the unit used for the English commodity in England is left unchanged, a new unit three-fourths as large as the old one is now used for the imported commodity so as to make units of the two commodities equal in value at the new relative prices, there will be a new utility function, a'c', for the imported commodity, with oa' 75 per cent of oa, and oc' 33 1/3 per cent greater than oc.
If the levy of a 50 per cent duty on the German commodity
causes its price in England duty-paid to rise by one-third relative to the price of the English commodity in England, then in Germany, with units unchanged, the price of the English commodity must rise one-eighth relative to the price of the German commodity, i.e., one unit of the German commodity now has the same price in Germany as eight-ninths of a unit of the English commodity.*103 If the unit used for the German commodity in Germany is left unchanged, but a new unit eight-ninths as large as the original one is now used for the English commodity in Germany so as to make the units of the two commodities equal in value at their new relative prices, there will be a new utility function, a'1c'1, for the English commodity in Germany, with o1a'1 eight-ninths of o1a1, and o1c'1 nine-eighths of o1c1. Since ø' and F' are now both smaller numerically and therefore greater algebraically than they were before the imposition of the duty, while ƒ' and ψ' are unaltered, therefore in the new situation, and, even in the case illustrated by chart V, where the imposition of the duty causes the representative consumer in each country to spend more on native than on imported commodities,*104 the levy of the duty creates a situation in which reparations payments would make the terms of trade turn in favor of Germany.
It can be similarly shown that export taxes levied by either or both countries and an excess of international over internal transportation costs for the commodities of either or both countries, even when they result in an excess in each country of expenditures on native over expenditures on foreign commodities, by tending to make native commodities relatively cheap in each country and thus tending to make the initial utility of native commodities greater in each country than the initial utility of imported commodities of equal price, tend likewise, given linear functions, to create a situation in which reparations payments will turn the terms of trade in favor of the paying country. Export or import subsidies, granted by either or by both countries, and an excess of internal over international transportation costs for the commodities of either or both countries, tend, on the other hand, by making native commodities dear in each country relative to imported commodities, to create a situation in which reparations will turn the terms of trade in favor of the receiving country in spite of an excess in each country of expenditures on foreign over expenditures on native commodities.
The existence of "domestic" commodities also operates to create a presumption that reparations payments will turn the terms of trade against the paying country, but in this case by increasing the proportion of expenditures in each country on native commodities without affecting the relative utilities of initial units of native and imported commodities. To adapt Pigou's analysis to the existence of domestic commodities, the utility functions for a representative consumer of the products of his own country must be interpreted as representing the marginal utility curve of a composite commodity made up of one or more units of each of the different native commodities, with the units so chosen as to be equal in pre-reparations price, and with the number of units of each commodity entering into the composite commodity made proportional to their respective importance in domestic consumption. If the assumptions of constant costs and of similarity and linearity of utility functions for "representative" consumers are adhered to, and if the possibility that reparations payments may change the identity of the "representative" consumer is disregarded, the weighting of the different native commodities in making up the composite native commodity presents no difficulty, since under these assumptions relative variations in the prices or the volume of consumption of the constitutent items of the composite native commodity cannot result merely from a change in the total expenditures of the representative consumer. The introduction in either country of domestic commodities will operate with respect to that country to reduce the slope of the curve of marginal utility to a representative individual of the composite native commodity, i.e., the existence of domestic commodities will operate to reduce the relevant ƒ' and/or ψ'. Since and
it follows, therefore, that where there are only two countries, the existence of "domestic" commodities in either country will tend to make
and therefore will tend to make reparations payments turn the terms of trade against the paying country.
If either of the countries is incompletely specialized, i.e., if it imports a portion of its consumption of some commodity, say cloth, which it also produces at home, a special case arises where the ratio of to
does not suffice to determine the effect of reparations on the terms of trade even on the assumptions of linearity and "similarity" within each country of the various utility functions. Regardless of the ratio of
to
the incompletely specialized country, whether it be the paying or the receiving country, can check any tendency for the terms of trade to move against it by cutting down on its exports and shifting the productive resources thus freed to the production of cloth. Under constant costs the prices of other foreign commodities could not rise relative to cloth as long as cloth was still being produced abroad, and the prices of other native commodities could not fall relative to cloth as long as more cloth could be produced at home. Before the terms of trade could turn against the country which before reparations had been incompletely specialized, it would be necessary therefore that she should be producing nothing except ("domestic" commodities and) cloth and that the other country should have completely abandoned the production of cloth.*105
If the assumption of linearity of the utility functions is abandoned the solution of the problem becomes much more difficult. But in the two-country case, the departures from linearity are as likely a priori to be in directions strengthening the presumption that reparations payments will cause the terms of trade to turn against the paying country as to weaken it, and Pigou has shown in effect that if is much greater numerically than
it will take substantial deviations from linearity in directions working favorably for the terms of trade of the paying country to keep reparations payments from turning the terms of trade against her.*106
The use of the concept of a "representative" German or Englishman in utility analysis raises familiar difficulties. Its use in this particular problem involves a tacit evasion of the difficulty arising if the payment of reparations results in a redistribution of the available spending power within either or within both communities of such a nature that the individual who could reasonably be taken as "representative" before the payments began was no longer "representative" after they had begun. Any redistribution in spending power in Germany resulting from the making of reparations payments would operate to make the terms of trade move unfavourably or favorably to Germany according as the reduction in spending power fell relatively more heavily or less heavily on individuals for whom, as compared to other Germans, the ratio, or the ratio of the slope of their utility curve for German goods to the slope of their utility curve for English goods, was large or small numerically. Similarly, any redistribution in spending power in England resulting from the receipt of reparations payments would operate to make the terms of trade move favourably or unfavourably to Germany according as the increase in spending power accrued more heavily or less heavily to individuals for whom, as compared to other Englishmen, the
ratio, or the ratio of the slope of their utility curve for German goods to the slope of their utility curve for English goods, was small or large numerically. In the absence of special information, it is hard to see any basis for any presumption that the changes in distribution of spending power in either country would be in one direction rather than the other.
I have so far assumed that there are only two countries. If in addition to the countries directly participating in the reparations payments there are other countries connected with them through trade relations, additional complications arise which Pigou, who does not differentiate "England" from "non-Germany," but takes his "representative Englishman," with his significant ratio as representative of all non-Germany, fails to mention. If there are three or more countries, there is no longer only one significant set of commodity terms of trade, but there are at least four distinct sets, namely, the terms of trade: (1) between Germany and the rest of the world, including England; (2) between England land and the rest of the world, including Germany; (3) between Germany and England, and (4) between the neutral area and the rest of the world.
Since the reparations payments go only to Englishmen proper, the change in the relative distribution of spending power as between Englishmen and other non-Germans as the result of reparations will, even with the assumptions of linearity and of "similarity" of the utility functions within the entire non-German area, prevent Pigou's ratio, although adequately representative of the utility functions of all non-Germany before reparations, from being representative after reparations, and will render inadequate Pigou's criterion for the effect of reparations payments on the terms of trade of Germany, unless before reparations the ratios corresponding to Pigou's
ratio were identical for both the representative Englishman and the representative neutral. If before reparations the ratio for the representative Englishman corresponding to Pigou's
for all non-Germany was smaller algebraically than the similar ratio for the representative neutral, then the terms of trade would turn against Germany as the result of reparations not only when before reparations Pigou's condition of
was met, but also if
and even, within limits, if
On the other hand, if before reparations the ratio for the representative Englishman corresponding to Pigou's
was greater algebraically than the similar ratio for the representative neutral, the terms of trade would turn in favor of Germany as the result of reparations not only when before reparations
, but also if
, and even, within limits, if
. But since, a priori, the probability that the ratio corresponding to Pigou's
will be greater algebraically for the representative Englishman than for the representative neutral is no greater than the probability that it will be smaller, and, because of the existence of "domestic" commodities, Pigou's
is likely to be much smaller algebraically than
the presumption that the terms of trade will turn against the paying country survives the introduction of third countries into the problem. If England and the third country produce the same commodity (or commodities), there is no basis for trade between these two countries, and the terms of trade between Germany and the outside world as a whole must be identical with those between Germany and England. The third country, therefore, will share with England any improvement or impairment in the terms of trade with Germany which may result for England as the result of her receipt of reparations from Germany.
If the third country produces the same commodity (or commodities) as Germany, similar conclusions would be reached as in the preceding case, except that the fortunes of the neutral country would now be pooled with those of the paying country instead of with those of the receiving country. If either England or Germany produces "domestic" commodities as well, this would operate, in the manner already explained, to make reparations payments result in the terms of trade turning against Germany, but whether or not the neutral country produced "domestic" commodities would not affect the direction of change in the terms of trade of Germany with the outside world as the result of reparations.
If the third country, however, produces distinctive exportable commodities of its own, the method of approach needs to be modified somewhat. To take first the terms of trade of Germany with the outside world, "non-German" data are to be used wherever in the case of only two countries English data would be used, and the problem will then correspond to the case where England and the neutral country produce identical commodities, except that given the pre-reparations ratio of representative of all non-Germany, the greater numerically the slope of the representative Englishman's utility curve for the neutral country's commodity as compared to the slope of his curve for the German commodity, the more favorable will be the situation for Germany with respect to the terms of trade. Similarly, for the terms of trade of England with the rest of the world, "non-English" data are to be used wherever in the case of only two countries German data would be used, and the problem will then correspond to the case where Germany and the neutral country produce identical commodities, except that, given the pre-reparations ratio
representative of all non-England, the greater numerically the slope of the representative German's utility curve for the neutral country's commodity as compared to the slope of his curve for the English commodity, the less favorable will be the situation for England with respect to the terms of trade. To take next the terms of trade of England with Germany, they will remain unchanged, move in favor of England, or move in favor of Germany, given Pigou's assumptions, according as
= , < , or >
where φ' and ƒ' relate to the slopes of the utility curves of the representative Englishman for English and German commodities, respectively, and ψ' and F' relate to the slopes of the utility curves of the representative German for English and German commodities, respectively, i.e., regardless of the slopes of their respective utility curves for neutral country commodities or of the slopes of the utility curves of the representative neutral for the commodities of England and Germany.
To take, finally, the terms of trade of the neutral country with the rest of the world, the payment of reparations by Germany to England will leave them unchanged, will move them in favour of the neutral country, or will move them against the neutral country, caeteris paribus, according as the slope of the utility curve for the neutral country's commodity is numerically equal, smaller, or greater for the representative Englishman than for the representative German, and, caeteris paribus, according as the pre-reparations volume of imports of neutral commodities is equal, greater, or smaller for England as a whole than for Germany as a whole, in proportion to their total expenditures.
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 g1h1:h1j1::d1e1:e1f1, then d1g1 and f1j1 and when extended upward will intercept m1n1 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.
By assumption,
gh:hj::de:ef; (1)
de = kh; ef = hl; (2)
∴ gk:lj::de:ef. (3)
By assumption,
de > ef; (4)
∴ gk > lj, and, similarly, d1k1 > l1f1. (5)
Since reparations results in an increase in England's spendable funds equal to the decrease in Germany's spendable funds,
gk + lj = d1k1 + l1f1 (6)
∴ gk > l1f1, and d1k1 > lj (7)
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.*107
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.*108
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.*109 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.*110
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.
In the examination of the probable effects on the terms of trade of a lasting disturbance of a preexistent international equilibrium, there is one basis of distinction between types of disturbances which calls for special emphasis. Disturbances are to be distinguished according as they originate in a relative change in the amounts, measured in units of constant purchasing power over native goods, available for expenditure in the two areas, or as they originate in a relative change in the demands of the two countries for each other's products in terms of their own products resulting from changes in taste or in conditions of production, or from changes in tariffs, subsidies, internal taxes, or transportation costs.*111 The analysis presented above of the effects on the terms of trade of reparations payments is applicable without serious modification to all lasting disturbances of the first class, i.e., involving an initial relative shift in the amounts available for expenditure, whether this shift is due to loans, tribute, or subsidy, but is not applicable to disturbances of the second class, where, however, analysis in terms of reciprocal demand curves is appropriate in most cases.
Whereas in the first class of disturbance a relative change in the amounts available for expenditure in the two countries is the source of the disturbance and a relative change in the demands of the two countries for each other's products is the result of the disturbance, in the second class of disturbance a relative change in the demands is the original cause of the disturbance and a relative change in the amounts available for expenditure is part of the process of adjustment to the disturbance. The case of a new revenue import duty, levied by one of the countries, may be taken as sufficiently illustrative of the effects of disturbances of the second class on the terms of trade. Let us suppose only two countries, only two commodities, no tariffs, no transportation costs, and an even balance of payments between them. One of the countries, England, now imposes a duty on imports of the German commodity. Before the duty the two commodities exchanged for each other at the same rate in both countries. After the duty the German commodity will rise in price to the English consumer relative to the English commodity. Let us assume that this relative rise is at first equal to the amount of the duty. The English will therefore buy smaller physical quantities than before of the German commodity and larger physical quantities than before of the English commodity. Suppose that the reduction in the volume of their sales to England will tend to cause Germans to reduce their total expenditures to the same amount, and that part of this reduction will be applied to German commodities. The willingness to buy German goods at the prevailing price (in England plus duty) will therefore decline in both countries; the willingness to buy English goods will increase in England, and decrease in Germany; with the increase in the former (corresponding to the total decrease in English purchases of German goods and therefore, by assumption, to the total decrease in German purchases of German and English goods combined) exceeding the decrease in the latter country.
Two consequences will follow: (1) Germany will have an adverse balance of payments with England, and specie will move from Germany to England; (2) the price of the German commodity will fall in both countries relative to the English, so that in England it will, without duty, be lower than it was before the duty was imposed, and, including duty, will exceed the pre-duty price by less than the amount of the duty. In other words, the commodity terms of trade will have moved against Germany, with an international transfer of specie as part of the process whereby this comes about. The effect of the duty on the terms of trade is illustrated in chart VII, an application in a slightly modified*112 form of Marshall's foreign trade curves.
The quantity of the English commodity is measured from o on the ox axis, and the relative price of the English commodity, in terms of number of units of the German commodity for one unit of the English commodity, is measured from o on the oy axis. The curve ae represents the quantities of the English commodity which before the duty England would be willing to export at the indicated rates of exchange of the English for the German commodity, and the curve bg represents the quantities of the English commodity which Germany would be willing to import at the indicated rates of exchange of the English for the German commodity. Equilibrium will be established at the terms of trade of mn or ot units of the German commodity for one unit of the English commodity.
If now England should levy a duty of 40 per cent ad valorem on imports of the German commodity, payable by the importer and used by the government to remit other taxes, the English export supply curve adjusted to the duty will be a1e1, with a1e1 uniformly 40 per cent higher than ae with reference to the ox axis. The new equilibrium rate of exchange of English commodities for German will in the English market (i.e., after payment of duty) be m1k, or ol, units of German goods for one unit of English goods. The new terms of trade, or the rate at which Germany will be able to exchange its commodity for the English commodity, will be m1n1, or o1t1, units of the German commodity for one unit of the English commodity, which will also correspond to the relative prices of the two commodities within Germany. The terms of trade will thus be turned against Germany by the English import duty.
It can similarly be shown that an English protective duty, a German export bounty, higher German or English internal taxes on German than on English goods, a shift in taste in either country in favor of English goods, or a relative reduction in the cost of producing the German commodity, will in like manner turn the terms of trade against Germany, whereas a German revenue or protective duty, an English export bounty, lower German or English internal taxes on German than on English goods, a shift in taste in either country in favor of German goods, or a relative reduction in the cost of producing the English commodity, will turn the terms of trade in favor of Germany.
An endless variety of further distinctions between types of disturbances can of course be drawn. Tributes and loans, for instance, are to be distinguished from each other by the fact that, since the former are as a rule involuntary and the latter voluntary, the problem of adjustment in the "paying" country is likely to be more serious in the former than in the latter case. Loans, moreover, call almost immediately for interest payments and eventually for amortization payments in the opposite direction from the loans, whereas this is not true of tributes. Loans are to be distinguished according to whether they are made out of income or out of capital, and according to whether the proceeds are used in the borrowing country for immediate consumption or for investment, since the nature of the source and of the mode of use of the loan will affect the manner in which adjustment is made to the change in the amount of funds available for expenditure, and will affect also the relative availability of the different classes of commodities toward which the expenditures are directed. In actual experience the initial disturbances may come in various combinations, or may originate at home or abroad, or simultaneously in both, and, depending on the nature of the original disturbance and perhaps on other circumstances, what at one time operates as the source of the disturbance and gives rise to the need for adjustment may at other times be the equilibrating factor, with corresponding changes in the time-sequence of phenomena. Thus price changes, capital movements, changes in demand, for example, may at one time be disturbing factors, at other times equilibrating ones, and except when there are drastic disturbances whose origin is fairly obviously to be associated with contemporary events external to the mechanism of international trade itself, it will ordinarily be fruitless to try to distinguish equilibrating from adjusting factors. Some writers have attempted to generalize, however, as to the "disturbing" or "equalizing" character of specific elements in international balances. Thus Keynes, for instance, has maintained that historically the international movement of long-term capital has adjusted itself to the trade balance rather than the trade balance to capital movements,*113 whereas Taussig*114 has supported the opposite, and traditional, view. There is no apparent a priori reason why the dependence should not be as much in one direction as the other, and the question of historical fact can be settled only, if at all, by comprehensive historical investigation. It is possible, however, to set forth theoretically the types of circumstances which would tend to make the one or the other the more probable direction, and to find striking historical illustrations in support of such analysis. It seems clear to me, for instance, that in the case of Canada before the war the fluctuations in the trade balance were much more the effect than the cause of the fluctuations in the long-term borrowings abroad, whereas in the case of New Zealand the fluctuations in her balance of indebtedness since the war seem to be clearly the result rather than the cause of the fluctuations in her trade balance. In New Zealand a marked degree of dependence of the national income on the state of the crops and the world-market prices of a few export commodities, with sharp year-to-year fluctuations in the crops and in prices, makes it necessary to choose between highly unstable expenditures on consumption or domestic investment, on the one hand, and substantial fluctuations in the net external indebtedness of the country, on the other, and the choice seems to be predominantly in favor of the latter. Examination of such data as are readily available strongly confirms, however, the orthodox doctrine that, at times when "fear" movements of capital are not important, short-term capital movements are much more likely than long-term capital movements to be "equilibrating," and that major long-term capital movements have, as Taussig maintains, mainly been "disturbing" rather than "equilibrating" in nature.
The foregoing discussion, it should be repeated, has dealt solely with the long-run effects of a lasting variation in one of the elements of an original equilibrium on the terms of trade. It should be noted also that changes in the terms of trade have been treated as purely objective phenomena, without reference to the differences in hedonic significance which may be attached to them according to the types of disturbance from which they result.
The classical economists were agreed that (abstracting from the process of distribution of newly-mined bullion) there were no specie movements under equilibrium conditions, and that specie moved only to restore and not to disturb equilibrium, or, as Ricardo put it, gold was "exported to find its level, not to destroy it."*115 But on the range of circumstances which could disturb equilibrium in the balance of payments so as to require corrective specie movements they were, as we have seen, not in agreement. Wheatley, as much later Bastable and Nicholson, held that the balance of payments would adjust itself immediately, and without need of specie movements, to disturbances of a non-currency nature, through an immediate and presumably exactly equilibrating relative shift in the demand of the two regions for each other's commodities. Granted that a relative shift in demand as between the two countries may, without the aid of relative price changes, restore an equilibrium disturbed, say, by an international tribute, it is an error to suppose that the shift in demand can ordinarily occur, under the assumption, be it remembered, of a simple specie currency, without involving a prior or a supporting transfer of specie from the paying to the receiving country. The new equilibrium requires that more purchases measured in money be made per unit of time in the receiving country and less in the paying country; as has been shown above, it is by its effect on the relative monetary volume of purchases in the two countries that the relative shift in demands exercises its equilibrating influence. Unless as and because one country becomes obligated to make payments to the other velocity falls in the paying country and rises in the receiving country, these necessary relative changes in purchases and in demands will not occur except after and because of a relative change in the amount of specie in the two countries, and such changes in velocity are at least not certain to occur, nor to be in the right directions if they do occur. Acceptance of the doctrine that a relative shift in demand schedules may suffice, without changes in relative prices, to restore equilibrium in a disturbed international balance does not involve as a corollary that specie movements are unnecessary for restoration of equilibrium, as Wheatley, Bastable, Nicholson, and others seem to have supposed. The error arises from acceptance of a too simple version of the quantity theory of money, in which price levels and quantities of money must move together and in the same direction regardless of what variations may occur in other terms of the monetary equation. In its most extreme application this erroneous doctrine has led to the conclusion that if unilateral payments should perchance result in a relative shift in price levels in favor of the paying country, the movement of specie will be from the receiving to the paying country!*116
It has been generally overlooked, however, that the velocity of money, or the ratio of the amount of purchases per unit of time to amount of money, has an important bearing on the extent of the specie movement which will be necessary to restore a disturbed equilibrium. It is not purchases, or transactions, in general which are significant for the mechanism of adjustment, but only purchases of certain kinds. If, for instance, a particular house has changed ownership as between dealers through purchase and sale three times in one year, and not at all in the next year, neither the transactions in one year nor their absence in the next year have any direct significance for the international mechanism. What matters is only the volume of expenditures which for the unit period operate to remove the purchased commodities from the market. Such purchases we will call final purchases, to distinguish them from transactions which do not consist of purchase and sale of commodities and services or which, if they do involve such purchase and sale, result merely in transfer of ownership from one person to another who will in turn before the unit period of time is over sell or be ready to sell the commodity or service, whether in the same form or not does not matter, to a third person. It is the relative change as between the two countries in the volume of final purchases, so defined, which plays a direct and equilibrating role in the mechanism of adjustment of international balances to disturbances.
Under the assumption of a simple specie currency, the significant velocity concept for the analysis of the mechanism of international trade is accordingly the ratio of final purchases per unit of time to the amount of specie in the country, which we will call the "final purchases velocity of money." This concept is to be distinguished not only from the familiar velocity concept, or the "transactions velocity of money," but also from the "income" or "circuit" velocity of money concept. This latter is for our purposes a more serviceable concept than the "transactions velocity," since it disregards many kinds of transactions which are of no direct significance for the international mechanism. It is nevertheless not a wholly satisfactory concept for the present purpose. For any limited period of time "income" is not only difficult of measurement but almost incapable of definition. It does not matter, moreover, for the mechanism of international adjustment whether what is spent comes from current net income or from disposable capital funds, borrowings, internal or external, or "negative income" or business losses eventually to be defrayed by the creditors. Nor does it matter whether the expenditures are for consumption or for maintenance or expansion of investment, except indirectly as this may affect the productive resources of the country or the apportionment of expenditures as between different classes of commodities. What matters for present purposes is primarily the ratio to the volume of money of the expenditures per unit of time which, for that unit of time, make an equivalent reduction in the willingness to spend of the purchasers.*117 The final purchases velocity of money will of course necessarily be much smaller than the transactions velocity. It may be smaller or larger than the income velocity. It will tend to be smaller than the income velocity in so far as the latter covers income not spent or invested at home but hoarded or lent abroad. It will tend to be larger than the income velocity in so far as the latter fails to take account of maintenance and replacement expenditures, disinvestment expenditures, or expenditures of the proceeds of external or internal borrowings.
Since the relative change in the amount of final purchases in the two areas is an important equilibrating factor in the process of adjustment to a disturbance in their international balances, then, assuming no change to occur in either country in the final purchases velocity of money, the greater is the weighted average final purchases velocity of money in the two countries combined, the smaller will be the amount of money necessary to be transferred to restore a disturbed equilibrium, other things remaining the same. If, as the result of a transfer of specie to meet the first instalments of new and periodic obligations of one country to the other, a sudden change occurs in the amount of money in each country, and the volume of final purchases in each country does not immediately respond proportionately to the change in the amount of money, the amount of transfer of money to the receiving country will for a time have to be greater than the amount of such transfer ultimately necessary, and after the velocities in the two countries have recovered their normal levels, but before the periodic payments have terminated, a partial return of money to the paying country will occur. If, on the other hand, change in the amount of money tends to be accompanied with change in its velocity in a corresponding direction, a smaller initial transfer of money will suffice for the time being, but as the velocities recede to their normal levels more money will have to be transferred from the paying to the receiving country to maintain their relative volumes of final purchases at the new equilibrium level. In all cases, the amount of specie transfer necessary for adjustment to a disturbance will depend on the velocities of money in the two areas as well as on the manner in which the demands for different classes of commodities behave as the amounts of money are varied. Except under very unusual conditions, however, adjustment of the balance of payments to new and continuing unilateral remittances will require some initial transfer of specie from the paying to the receiving country.
The final purchases velocities in the two countries not only help to determine the amount of specie transfer necessary for adjustment, but they also help to determine what effects the remittances shall have on the absolute price levels in the two countries combined. If in the receiving country money has a higher velocity than in the paying country, the transfer of means of payment will result in a higher level of prices for the two countries combined, and vice versa. It is even conceivable, though not of course probable, that reparations payments may result in higher (or in lower) prices in both of the countries. Failure to take into account the possibility of different velocities in the two countries has led some writers to deny this even as a theoretical possibility.*118
The role of specie movements and of the velocity of money in the mechanism of adjustment to disturbances is illustrated in table V, in which it is assumed that before reparations the unweighted average ratio of expenditures on native to expenditures on foreign commodities for the two countries combined is unity, and that, in the absence of price changes, reparations payments will not disturb the proportions in which expenditures are distributed between native and foreign commodities in either country. Under these conditions reparations payments, as we have seen, would not disturb the terms of trade. The pre-reparations equilibrium is disturbed by the imposition on one of the countries of the obligation to pay reparations to the other for an indefinite period of time at the rate of 600 monetary units per month.
In case A, the final purchase velocity of money per month, both before and after*119 the beginning of the reparations payments is unity in both countries, and prior to the transfer the final purchases per month are 3000 in the receiving country and 1500 in the paying country. There must therefore have been, in the initial equilibrium situation, 3000 monetary units in the former, and 1500 in the latter, country. A transfer of 600 monetary units from the paying to the receiving country takes place when the payments begin, and the resultant shifts in demands bring about an adjustment of the balance of payments of the two countries to the tribute without necessitating any change in prices. In case B the velocity of money per month both before and after the beginning of the tribute payments is 2 in the receiving country and 1 in the paying country, and prior to the transfer there are 1500 units of money in each of the countries. To restore equilibrium; a transfer of only 450 units of money is necessary. But since the transfer of money is from a low-velocity to a high-velocity country, it results in an increase in the world level of prices and of money incomes. As in case A, however, equilibrium is restored without any change in the terms of trade. In case C the velocity of money is ½ in the receiving country and 1 in the paying country, and prior to the transfer there are 6000 units of money in the receiving country and 1500 in the paying country. To restore equilibrium a transfer of 720 units of money is necessary. But since the transfer of money is from a high-velocity to a low-velocity country, it results in a decrease in the world level of prices and of money incomes. As in the previous cases, however, equilibrium is restored without any change in the terms of trade. Whatever other cases were chosen, the same conclusion would be indicated that the effect of a transfer of payments on relative prices is independent of the velocities, provided that such changes in money incomes as are offset by corresponding changes in prices are assumed not to affect the apportionment of expenditures among different classes of commodities.*120
In the older literature, analysis of this sort of the role of velocity of money in the mechanism of adjustment of international balances is to be found, if at all, only by implication. In the more recent literature, also, discussion of this phase of the mechanism is scanty. Ohlin's treatment of velocity is imbedded in his exposition of the mechanism as a whole, but there seems to me to be agreement between our accounts in so far as they cover the same ground. D. H. Robertson, in a short essay,*121 which nevertheless contains in germ much of what has here been more elaborately expounded with reference to the transfer mechanism, also treats the velocity factor, in so far as he carries his analysis, in the same manner in which it is here treated. But concerned presumably more with establishing certain possibilities than with surveying the range of probabilities, he applies his analysis only to assumptions so extreme as to lead him to highly improbable conclusions. In an analysis of the effects of reparations payments by Germany to America on specie movements, terms of trade, and aggregate income in the two countries, he introduces an annual velocity of money factor, assumed to be unity and invariable in each country, and which represents the ratio of annual income, or annual expenditure, to the stock of money. From an arithmetical illustration he concludes that the payment by Germany of reparations need involve no transfer of money, no alteration in the terms of trade, and no change in "gross monetary income" in either country. Substituting "final purchases" for "gross monetary income," and taking only the data which he presents for America, his illustration is as follows:
America
Before Reparations PaymentsFinal purchases of £1,600 buy 900 American goods + 100 German goods and pay £600 taxes.
Gold stock £1,600. V = 1.
Price of American goods = £1.
During Reparations Payments at the rate of £600 per yearFinal purchases of £1,600 buy 900 American goods + 700 German goods.
Gold stock £1,600. V = 1.
Price of American goods = £1.
How extreme the assumptions are on which all of these results depend is not made apparent only because they are not brought clearly into the open in either the illustration or the accompanying text. The illustration assumes that the government of America uses the proceeds of the reparations payments to remit taxation, but it presumably continues to render the same services to the community, for otherwise £600 of spending power would be unaccounted for. As far as final purchases or "gross money incomes" are concerned, the apparent absence of an increase when reparations are received is due solely to the fact that real income in the form of government services for which previously £600 was paid by individuals in taxes is now met by the reparations income of the government and therefore does not appear in the accounts of private monetary income. As far as money stocks are concerned, the absence of any increase in the receiving country can be explained only if the periodic receipt of the reparations payments and their use by the government in hiring personnel and buying materials with which to carry out its functions requires no use of the country's stock of money, whereas collection of taxes equal in amount to the reparations plus use of the tax receipts in the identical fashion in which the proceeds of the reparations are used would involve the use of £600 throughout the year. As far as the commodity terms of trade are concerned, the absence of any change is to be explained by the assumption that although in the receiving country no prices have changed and spending power has increased by £600, no increase will occur in that country in the amount of its own goods or governmental services demanded by its people.
Graham and Feis hold that the explanation of the mechanism of adjustment of international balances to capital borrowings offered by the classical economists and their modern followers omits reference to a factor operating to bring about relative shifts in price levels in the direction opposite to that posited in this explanation. Graham claims that since the effect of a loan is to shift goods from the lending to the borrowing country, the volume of goods relative to the volume of gold will be increased in the borrowing country and decreased in the lending country, and therefore the prices will tend to fall in the former and rise in the latter. On the assumption that the first phase of the mechanism is a transfer of gold from the lending country to the borrowing country unaccompanied by a transfer of goods, and that the transfer of goods is a later phase, Graham, calling the former the "short-range" effect of capital movements and the latter the "long-range" effect, concludes that "the short and long range effects of borrowings will run in opposite directions."*122 He had earlier applied the same reasoning to the problem of the adjustment of international balances to capital imports under an inconvertible paper currency, on the assumption that the quantity of money in each country is held constant.*123 Feis accepts Graham's argument:
The effects of the goods movements upon price levels would, therefore, tend to be in the opposite direction to those produced by changes in the volume of purchasing power in each of the countries concerned, as Professor Graham has pointed out. Apparently, two conflicting tendencies are present in each country during the process of adjustment. These tendencies may or may not be simultaneous and equal in strength.*124
This reasoning seems erroneous to me. The conclusion of these writers results from a mechanical application of the formula of price determination to the international trade mechanism, on the implicit assumptions that the price level is result and not cause, and that the changes in M and the changes in T are unrelated and independent factors in the mechanism,*125 and Feis, at least, explicitly attributes the same assumptions to the classical school.*126 But in the classical theory, as in the preceding exposition, the establishment of international equilibrium is regarded as primarily a problem of international adjustment of prices, and the direction and extent of flow of specie, and therefore also the relative amounts of money in the two countries, instead of being treated as independent factors, are held to be determined by the relative requirements for money of the two countries given their equilibrium price levels and their respective physical volumes of transactions requiring mediation through money. The bearing of the commodity flows in the mechanism, therefore, is not their influence on the relative price levels, but is, instead, their influence on the quantity of specie flow necessary to support the price relations required for equilibrium.
Let us suppose that when the lending first begins the lending country ships sufficient commodities on consignment to the borrowing country to bring its export surplus to equality with its volume of lending per unit period, but that, in consequence of the influx of goods, prices as a whole fall in the borrowing country to a level lower than is consistent with the maintenance of its import surplus at the required amount. A new or intensified flow of specie must thereupon occur from lending to borrowing country, so as to bring prices (and demands) in the borrowing country to a level adequately high to result in a continuing import surplus equal to the borrowings.*127
"Capital" movements, it is true, if they consist of funds which in the absence of such movement would have been invested at home, and if they result in an increase in the amount of investment in the borrowing country as compared to what would have been the situation in the absence of the borrowings, will eventually result in a relative increase in the output of the marketable commodities of the borrowing country as compared to those of the lending country and, therefore, will to this extent tend to result in a relative fall in the price level of the borrowing country. But Graham's and Feis's argument rests on the supposed effect on relative price levels of the relative changes in the output of commodities in the two countries.
Hume conceded that the fall in the exchange value of a country's currency when for any reason there was adverse pressure on its balance of payments tended to exercise an equilibrating influence by providing an extra incentive to commodity export and a deterrent to commodity import. He held, however, that this could be but a minor factor in the process of adjustment, and although he gave no reasons it may be presumed that he saw that under a metallic standard the maximum possible range of variation of the exchanges, i.e., between the specie export and import points, was so limited as to make it extremely unlikely that such variation could exert an appreciable direct influence on the course of trade.*128 Since his time the maximum range of variation has become still narrower under normal conditions because of reduction in the cost of transporting specie, and scarcely anyone today would dispute that under an international metallic standard exchange variations are a negligible factor as far as their direct influence on commodity trade is concerned.*129 It has sometimes been suggested, however, that this narrowing of the range between the gold points has not been an unalloyed benefit, since by its facilitation of specie shipments it has contributed to the instability of national credit structures. Proposals have been made, starting with Torrens in 1819,*130 artificially to widen the margin between the specie points, by seigniorage charges, premiums on gold for export, different buying and selling prices for gold at the Central Bank, generous tolerance for underweight in the internal specie circulation, differential buying or selling prices for the gold of the particular degrees of fineness most in supply or demand abroad, and other similar devices, and such practices have, for this or other reasons, been followed. To the extent that such practices exist, the range of possible exchange fluctuations under a metallic standard, and therefore the possible influence of exchange variations on the course of trade, can of course be somewhat increased. In effect this is an attempt to retain the advantages of an international metallic standard while escaping in part one of its incidents, namely, the direct dependence of the national stock of money, or of the specie reserves upon which it rests, on the state of the foreign exchanges. But the same advantages of partial freedom of the quantity of the circulating medium from dependence on the vagaries of the exchanges can be more safely, and especially for an important financial center whose effectiveness depends largely on its ability to attract foreign short-term funds, more cheaply obtained, by the maintenance of excess specie reserves, than by artificial widening of the range between the gold points. Even with such widening, moreover, unless it were carried to much greater lengths than has ever been customary, the direct influence of exchange rate fluctuations on the course of commodity trade would still be negligible. But even small variations in the exchanges can exert an appreciable influence on the movement of short-term capital funds, and through them on the mechanism of adjustment. This phase of the mechanism is discussed in the next chapter, in connection with the discussion of the relation of banking processes to the mechanism.
In their discussion of the foreign exchanges, the writers on the theory of international trade with apparently almost complete unanimity expound a particular error of minor practical importance but revealing lack of due precision in exposition or thought. They hold that when the balance of payments is even, the exchanges will be at their mint par.*131 The correct statement is that when the balance of payments is even the exchanges will be somewhere within the export and import points. The mint par has significance for the exchanges only as a base point from which to determine the specie export and import points. Equilibrium between the amount of foreign bills demanded and offered is as likely to be reached at any one as at any other rate within the limits of the specie points. Except for the approximately fixed limits to the range of possible fluctuation of the exchanges under an international metallic standard, there is no basis for differentiating the theory of the foreign exchanges between two currencies having a common metallic standard, on the one hand, and between two currencies on different standards, on the other hand.
Owing more, probably, to good fortune than to superior insight, the classical economists escaped almost completely the fatal error of formulating their theory of the international relationships of prices in terms of simple quantitative relationships between average price levels. But since 1916, Professor Gustav Cassel has expounded, and obtained wide acceptance of, a simple formula purporting to express the relationship to each other of national statistical price levels, which he called the purchasing-power parity theory. Some writers have found in this formula nothing but a restatement of the English classical theory, but it differs substantially from any version of the classical theory known to me.
The following citation embodies an early formulation of his theory by Cassel, and the one which first gained for it wide attention:
Given a normal freedom of trade between two countries, A and B, a rate of exchange will establish itself between them and this rate will, smaller fluctuations apart, remain unaltered as long as no alterations in the purchasing power of either currency is made and no special hindrances are imposed upon the trade. But as soon as an inflation takes place in the money of A, and the purchasing power of this money is, therefore, diminished; the value of the A-money in B must necessarily be reduced in the same proportion.... Hence the following rule: when two currencies have been inflated, the new normal rate of exchange will be equal to the old rate multiplied by the quotient between the degrees of inflation of both countries. There will, of course, always be fluctuations from this new normal rate, and in a period of transition these fluctuations are apt to be rather wide. But the rate calculated in the way indicated must be regarded as the new parity between the currencies. This parity may be called the purchasing power parity, as it is determined by the quotients of the purchasing powers of the different currencies.*133
Cassel has expounded the theory primarily in terms of paper currencies and with special bearing on the effects of currency inflation on exchange rates. But if true for paper currencies, there is no apparent reason why it should not apply equally to gold standard currencies. Since under an international gold standard the possible range of variation of the exchanges is narrowly limited by the gold points, it should follow that under such a standard the possibility of substantial divergence of movement of price levels, in direction or in degree, in different countries is correspondingly limited. It would seem further that if substantial relative changes in the purchasing power of two currencies must generally result in corresponding inverse changes in the rates at which these currencies exchange for each other, then under equilibrium conditions metallic standard currencies must have equal purchasing power in terms of units of identical gold content,*134 unless adequate reason can be found for holding that all the factors other than relative price levels capable of exerting an enduring influence on the exchanges were already present in the year arbitrarily chosen as the base year, had already exercised all of their possible influence on the exchange rates, and would never disappear or weaken. It is easy to conceive, however, of changes in cost or demand conditions or both, in one or the other countries, or both, which so change the relative demands of the two countries for each other's products in terms of their own as to bring about an enduring and substantial relative change in their levels of prices, including the prices of domestic commodities and services, even under the gold standard. The existence of non-transportable goods and services in one country which have no exact prototype in the other, moreover, makes it difficult to see not only how there could be any necessity under the gold standard that the price levels be identical in the two countries, but how the two price levels could be compared at all with any approach to precision.
Cassel nevertheless accepts readily the corollaries of his doctrine:
Even when both countries under consideration possess a gold standard, the rate of exchange between them must correspond to the purchasing power parity of their currencies. The purchasing power of each currency has to be regulated so as to correspond to that of gold; and when this is the case, the purchasing power parity will stand in the neighborhood of the gold parity of the two currencies. Only when the purchasing power of a currency is regulated in this way will it be possible to keep the exchanges of this currency in their parities with other gold currencies. If this fundamental condition is not fulfilled, no gold reserve whatever will suffice to guarantee the par exchange of the currency. Under stable currency conditions and when no radical alterations in the conditions of international trade take place, no great or lasting deviation from purchasing power parity is possible.*135
Some writers have held that the purchasing-power parity theory is invalid if applied to general price levels, but that it could be made acceptable, and in fact reduced to the status of a truism, if it were confined to the price levels of commodities directly entering into international trade, and if abstraction were made, as does Cassel, from relative changes in transportation costs or tariff rates. The following quotation from Heckscher is representative of this point of view:
The conception that the exchanges represent relative price levels, or, what is the same thing, that the monetary unit of a country has the same purchasing power both within the country and outside it, is correct only upon the never existing assumption that all goods and services can be transferred from one country to another without cost. In this case, the agreement between the prices of different countries is even greater than that which is covered by the conception of an identical purchasing power of the monetary unit; for not only average price levels but also the price of each particular commodity or service will then be the same in both countries, if computed on the basis of the exchanges.*136
Cassel, however, rejects this view, and insists that the doctrine will not hold if applied to international commodities alone, since if the prices of all B's export commodities were doubled, all other prices in B and all prices in A remaining unchanged, the exchange value of B's currency would fall by much less than half. Before the exchange could fall to this level, other commodities hitherto produced only for home consumption could be profitably exported by B, and its imports of A's commodities would have fallen, and thus a further drop in its exchanges would be prevented.*137
Cassel is right in maintaining that the doctrine need not hold if applied to the price levels of a variable range of international commodities. But it need not hold even if applied to a fixed assortment of international commodities. Suppose that there are only two countries, that no new commodities enter into international trade, that no commodities already in international trade change the direction of their flow or disappear from trade, and that there are no tariffs or freight costs, so that all international commodities command idential prices in all markets, in terms of the standard currency when this is uniform and exchange is at par, or in terms of the currency of either of the countries converted from the other, when necessary, at the prevailing rate of exchange. Even in this case, the doctrine that the exchange rates will vary in exact inverse proportion with the relative variations in the index number of prices of international commodities in the two countries would not only not be atruism, but would not necessarily or ordinarily be true if, as would be most appropriate, weighted index numbers were used and the basis for the weighting were, not the relative importance of the commodities in international trade (which, with only two countries, would mean identical weights for both countries) but their relative importance in the consumption or the total trade, external and internal, of the respective countries. In fact, it would be possible for the exchange rate under these conditions to change even if no change occurred in any price, provided there were changes in the weights in the two countries, or even if no change occurred in any weight, provided there were any changes in prices, notwithstanding the necessity under the conditions assumed that any price changes should be identical in both countries.
The only necessary relationships between prices in different countries which the classical theory postulated, or which can be formulated in general terms, are the international uniformity of particular prices of commodities actually moving in international trade when converted into other currencies at the prevailing rates of exchange, after allowance for transportation costs and tariff duties, and the necessity of such a relationship between the arrays of prices in different countries as is consistent with the maintenance of international and internal equilibrium.
The one type of case which would meet the requirement of exact inversely proportional changes in price levels and in exchange rates would be a monetary change in one country, such as a revaluation of the currency, which would operate to change all prices and money incomes in that country in equal degree, while every other element in the situation, in both countries, remained absolutely constant.*138 Cassel, however, argues for at least the practical validity of his theory, as applied to actual history, on the ground that it is substantially confirmed by the facts, since under the gold standard there do not occur even over long periods wide divergences in the trends of the indices of different countries, and under fluctuating paper currencies the divergences between the actual trends of the indices and the purchasing-power parities calculated in accordance with his formula are not great and tend to disappear. He claims that the disturbances such as capital flows or tariff changes which operate to prevent purchasing-power parity from establishing itself are rarely powerful enough, as compared to the influence of the comparative purchasing power of the respective currencies, to result in a wide divergence from purchasing-power parity and are moreover likely to be temporary in character. His defense of the theory is essentially empirical rather than analytical.
It is no doubt true that the comparative purchasing power of two paper currencies in terms of all the things which are purchasable in their respective countries is at least ordinarily the most important single factor in determining the exchange rate between the two currencies and must ordinarily be powerful enough to keep divergences of the exchange rate and purchasing power parity from reaching such lengths as, say, a rate only 50 per cent or as much as 200 per cent of the rate called for by the purchasing-power parity formula. It is also true that the exchange rate, which means approximately the comparative mint prices of gold, is ordinarily the most important single factor in determining the price levels of countries on an international gold standard. But the divergences between actual exchange rates and those required by the purchasing-power parity formula are in fact frequently substantial, and the "disturbances" from which such divergences result need not by any means be temporary in character, so that a longer period would lessen the divergence, but may in fact be progressive in character through time. Nor can these divergences be satisfactorily explained by defects in the available index numbers. On the contrary, the indices ordinarily used are unweighted wholesale price indices, and these are notoriously heavily loaded with the staple commodities of international commerce, whose prices are most likely to have uniform trends in different countries. Examination of such few indices as are constructed on a broad enough basis to give some representation to domestic commodities and services indicates, what is to be expected, that the more comprehensive the index the wider tends to be the divergence of the actual exchange rate from the purchasing-power parity rate. Use of weighted indices also ordinarily results in a widening of the indicated deviation of the exchanges from the purchasing-power parity rate.
Cassel's theory purports to be not merely a statement of relations between quantities, but also an explanation of the order of causation, with exchange rates being determined by relative price levels, rather than vice versa. Under an international metallic standard in the long run, for any one country, and especially if it is a small country, its price level will be determined for it largely by factors external to it and impinging upon it through specie movements.*139 Under paper standards not substantially pegged to gold, whether de jure or de facto, it is impossible to formulate the issue intelligently without reference to the principles on which the quantity of money in each country is regulated, and if, as is, however, rarely the case, there is no clear governing principle, and the play of circumstances, such as the state of the national budget, pressure from business, or more or less arbitrary or traditional discount policies, are allowed to be the determining factors, there will be mutual influence of prices on exchange rates and of exchange rates on prices, with no satisfactory way of apportioning to each set of influences its share of responsibility for the actually resultant situation.
Cassel has defended his failure to give attention to the factors which even in the long run can operate to create divergence between the actual exchange rate and the purchasing-power parity rate on the ground that his theory threw the emphasis on what was during the war and post-war period of extreme inflation overwhelmingly the most important factor in determining exchange rates, namely, currency inflation. Under such circumstances, the proper procedure for the economist apparently is to forget about the minor factors:
The art of economic theory to a great extent consists in the ability to judge which of a number of different factors cooperating in a certain movement ought to be regarded as the most important and essential one. Obviously in such cases we must choose a factor of permanent character, a factor which must always be at work. Other factors which are only of a temporary character and may be expected to disappear, or at any rate can be theoretically assumed to be absent, must for that reason alone be put in a subordinate position.*140
No objection can be made to this, if it is to be understood to mean merely that minor factors should be treated as minor factors. But if it is presented as justification for the omission of mention of minor factors, and even for express denial that they are operative, on the ground that their recognition weakens the persuasive power of one's argument, then this amounts merely to saying that bad theory may make good propaganda, and is a debatable proposition at that.*141
Supposerons-nous qu'un seul État fournisse aux autres plus de marchandises qu'il n'en retire et que toutes les nations soldent avec cet État en argent?... Croit-on de bonne foi que cette situation serait durable, et que cet État absorberait peu à peu tout l'argent qui existe dans le mond? Non, sans doute. L'augmentation de la quantité d'argent en diminuerait le prix; le luxe croitrait et avec lui la consommation des denrées soit nationales, soit étrangères. Il enrésulterait donc que cet État transporterait aux autres une moindre quantité. Ainsi il swerait obligé à sort tour de payer en argent et la circulation ae rétablirait. ("Paradoxes philosophiques sur la liberaté du commerce entre les nations" [ms. 1764], first printed in F. Sauvaire-Jourdan, Isaac de Bacalen et les idées libre-échangistes en France, 1903, p. 43.)
Cf. also Issac Gervaise in 1720, supra, pp. 80-81.
The equilibrium of trade would be disturbed if the imposition of the tax diminished in the slightest degree the quantity of linen consumed...the balance therefore must be paid in money. Prices will fall in Germany, and rise in England; linen will fall in the German market; cloth will rise in the English. The Germans will pay a higher price for cloth, and will have smaller money incomes to buy it with; while the English will obtain linen cheaper, that is, its price will exceed what it previously was by less than the amount of the duty, while their means of purchasing it will be increased by the increase of their money incomes.
It is difficult to explain the decline in the percentage of exports to total [Canadian] commodity production, without reference to the capital borrowings from abroad.... The expansion of manufacturing not only absorbed an increased proportion of the Canadian production of raw materials, but it withdrew labor, from the production of raw materials which otherwise would have been exported, to the construction of plant and equipment and the fabrication, from imported raw materials, of manufactured commodities for domestic consumption. The development of roads, towns, and railroads, made possible by the borrowings abroad, absorbed a large part of the immigration of labor, and these consumed considerable quantities of Canadian commodities which would otherwise have been available for export. Changes in relative price levels resulting from the capital borrowings were also an important factor in restricting exports, operating coordinately with the factors explained above (ibid., pp. 262-63).
Thus suppose that Germany is normally sending so much of her exports abroad and buying with them so much imports; and that, on the top of this situation, she is subjected to an indemnity whose amount is expressed in English goods. If the indemnity exceeds the previous sum of English exports sent to her by us, so that it cannot be paid by Germany's dispensing with these exports, and if also the English demand for German goods in respect of enlarged quantities has an elasticity less than unity, Germany cannot, however much she increases her exports to us, provide the means of paying the indemnity.
Whether Pigou uses "demand" here in the simple monetary sense or in the reciprocal demand sense, this would not necessarily be true since in either case the English demand for German goods might shift in a direction favorable to Germany as the result of the receipt by England of reparations payments.
In his later Treatise on money (1930, 1, 340-42), Keynes returns to the problem briefly, but without much addition to his earlier argument. He here stresses the difficulty of surrender of gold by Germany; appears to interpret Ohlin's argument, perhaps rightly, as resting on the assumption that neither relative price changes nor specie movements are necessary for transfer of reparations if the proper credit policies are adopted in paying and receiving countries; and takes it for granted that a loss of gold by Germany, in the absence of a change in credit policy, means a lowering of money wages in out relative price changes, without changes in the usual gold reserve ratios in either country, without a fall in money wages in the paying country or a rise in the receiving country, through the mediation of an initial transfer of specie and its effects on relative demands for commodities in terms of money. See infra, pp. 338 ff., 366 ff.
It has indeed been said that we might judge of its value [i.e., the value of money] by its relation, not to one, but to the mass of commodities. If it should be conceded, which it cannot be, that the issuers of paper money would be willing to regulate the amount of their circulation by such a test, they would have no means of so doing; for when we consider that commodities are continually varying in value, as compared with each other; and that when such variation takes place, it is impossible to ascertain which commodity has increased, which diminished in value, it must be allowed that such a test would be of no use whatever.
Cf. also, Malthus, review of Tooke, Quarterly review, XXIX (1823), pp. 234-35: ibid., Principles of political economy, 1st ed., 1820, p. 126; William Jacob, An historical inquiry into the production and consumption of the precious metals, 1831, II, 375-76; Arthur Young, An inquiry into the progressive value of money in England, 1812, p. 134; Tooke, in Report from Select Committee on banks of issue, 1840, p. 337.
Whewell, in 1856, in what was presented as mainly an uncritical mathematical exposition of J. S. Mill's doctrines on international trade, formulated what he called the "principle of uniformity of international prices," to the effect that, transportation costs being abstracted from, "when the international trade has been established, the relative value of all commodities which are exported and imported is the same in the two countries."—"Mathematical exposition of some doctrines of political economy. Second memoir," Transactions of the Cambridge Philosophical Society, IX, part I (1856), 137-39.
See also, for similar reasoning: Longfield, Three lectures on commerce, 1835, p. a5; Cairnes, Essays in political economy, 1873, pp. 70 ff.; ibid., Some leading principles, 1874, p. 409; Marshall, Money credit & commerce, 1923, p. 228; Taussig, "International freights and prices," Quarterly journal of economics, XXXII (1918), 411-12.
To my argument that a substantial range of fluctuation of the relative prices of the same commodity in two different markets is possible if the commodities are bulky or are subject to import duty, Bresciani-Turroni has replied: "Experience however shows that in many cases even for commodities for which transportation costs or import duties are very high there exists an equilibrium between prices in different countries and that goods move from one country to another as soon as the equilibrium is disturbed." (Inductive verification of the theory of international payments, 1932, p. 97. note.) He claims that for international commodities there is a "normal difference" in their prices in two markets, corresponding to the costs of transportation and of duties, and that "When the actual agread in prices is not equal to this 'normal difference,' the disturbed 'parity' will soon be reestablished through movements of goods" (ibid). What he says is, indispetable, and has not been, disputed for commodities which do commodity move in international trade and always move only in one particular direction. But it does not cover adequately the full range of possibilities, and takes no account, in particular, of two possibilities, for, let us say, a commodity, wheat, which has been moving from country A to country B. First, the departure from "parity" in the price of wheat in country B may be such as to stop raffer than to stimulate the movement of wheat, i.e., the price of wheat in B may fall below its import parity, with the result that import ceases, perhaps permanently. Secondly, the fall in the price of wheat in country B relative to its price in country A may be so great as to carry the price in B from import parity with respect to country A to export parity with respect to country A, i.e., may reverse the direction of movement of the wheat.
"Q. Do you mean that you doubt whether an increase of foreign demand has not always a tendency to increase the production and wealth of a nation?
A. In no other way than by procuring for us a greater quantity of the commodities we desire in exchange for a given quantity of our own commodities, or rather for a given quantity of the produce of our land an labor."
Cf. also J. E. Cairnes, Leading principles, 1874, p. 409.
Graham used a similar classification of commodities in the analysis of the mechanism under depreciated paper.—"International trade under depreciated paper. The United States, 1860-1879," Quarterly journal of economics, XXXVI (1922), 290-73.
Expressing costs in terms of "units of productive power" and similar concepts, one cannot, of course, push the analysis beyond a demonstration that this unit, i.e., productive factors as a whole, becomes more scarce in the capital-importing country, less scarce in the capital-exporting country.
And on this premise it is inevitable that the terms of trade will move against the latter country.
From (iii)
and
Marshall, nevertheless, offers a solution by means of his reciprocal-demand curves of what is, for present purposes, a problem identical with that of the effect of reparations payments, namely, the effect of the transfer of interest payments. His solution, must, however, be rejected, as wholly arbitrary. He leaves the receiving country's curve unaltered, and shifts the paying country's curve to the right by an amount, equal at all points of the curve, to the amount of interest payments. Cf. Marshall, Money, credit & commerce, 1923, p. 349, fig. 19.
It is theoretically possible for the terms of trade to change in favor of Germany so that the prices of German exports rise and the prices of German imports fall. This leads to the rather paradoxical result that gold flows into Germany, and the transfer mechanism thus cases the situation of the country paying reparations. This is not a very probable case, but it would arise if the increase of foreign demand were for German exports, and the fall in Germany's demand related to imports. (Theory of international trade, 1936, pp. 75-76.)
ir for the amount available for expenditure in the receiving country before transfer (=3000).
ip for the amount available for expenditure in the paying country before transfer (=1500).
Ir for the amount available for expenditure in the receiving country after transfer.
Ip for the amount available for expenditure in the paying country after transfer.
x for the ratio of the weighted average velocity after transfer to the weighted average velocity before transfer, for the two countries combined.
Then
2Ir + Ip = 2ir + ip = 7500
Ir = xir + 600
Ip = xip - 600
Solving for x, Ir and Ip
x = 69/75 ;Ir = 3360; Ip = 780
Allocation of Ir and Ip to the different classes of commodities in the proportions in which it is assumed each country would distribute its expenditures in the absence of relative price changes yields the remainder of the data necessary to determine whether relative changes in prices are necessary for the new equilibrium, and, if so, in what direction.
There is one circumstance worth attention on account of its tendency to increase the transmission of specie under an adverse exchange. The articles of export which might replace gold and silver are usually few in number, speaking practically, and the increased quantity of such goods received by the creditor country lowers their price in it to an extent which, partially at least, lessens the effect produced by the enlargement of its currency.
If Norman means by this passage that a sufficient large flow of specie must occur to offset any otherwise disequilibrating influence on prices of the flow of commodities, then the position taken here corresponds with his.
If a and b represent two countries, E represents the number of units of b's money which exchanges for one unit of a's money, P represents the index number of prices, and o and r the base and the given years, respectively, then according to Cassel:
...I cannot read the literature of this subject without seeming to feel that in the ordinary explanations of prices by reference to fluctuations in the quantity of money, and of circulation, etc., are not only curious reversals of the true theory, but practical dangers. They concentrate attention on the secondary factor, assign all importance to it, and tend toward the practical doctrine that remedies are to be sought in some artificial manipulation of the money system. I would not deny [sic] for a moment that the money system of a country is without influence on the course of its prices; no two facts can coexist in mutual dependence without some reciprocal influence being exercised, but the influence seems to me to be secondary in its action and relatively insignificant. It only acts because, through deeper lying causes, there is already a determined range of prices. The comparative efficiency of a country as one member of the great trading community is what in the long run determines the scale of prices in it, and it is to the variations in the conditions affecting its efficiency that we must turn for final explanation of the movements which on the surface appear as changes in an independent entity, money.
The purchasing-power parity theorists, of course, overstated their case of unilateral causation (inflation-prices-exchange rates). But it was necessary to do so at a time when the monetary authorities tried to deny any responsibility for the depreciation by maintaining that the intense "need" for imported goods and the misbehavior of wicked speculators were to be blamed. The concession that, under dislocated currencies, certain shifts in the relative intensity of the demand for the other countries' goods may bring about a (slight) change in foreign exchange rates was entirely out of place at a time when foreign exchanges were continuously rising to some fantastic multiple of their original level. (Journal of political economy, XLIII [1935], 395 Italics mine.)
But to recommend a dogma on account not of its inherent validity but of its good practical consequences is dangerous. When people discover its theoretical weaknesses they may not only reject the dogma, but neglect the practical consequences.
Chapter VII
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