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cost her. Germany, in short, is, in this third case, exactly. in the same situation as England was in the first case; which may easily be verified by reversing the figures. As a general result of the three cases, it may be laid down as a theorem, that under the supposition we have made of a demand exactly in proportion to the cheapness, the law of international value will be as follows:— The whole of the cloth which England can make with the capital previously devoted to linen, will exchange for the whole of the linen which Germany can make with the capital previously devoted to cloth. Or, still more generally, The whole of the commodities which the two countries can respectively make for exportation, with the labour and capital thrown out of employment by importation, will exchange against one another. This law, and the three different possibilities arising from it in respect to the division of the advantage, may be conveniently generalized by means of algebraical symbols, as follows:— Let the quantity of cloth which England can make with the labour and capital withdrawn from the production of linen, be = n. Let the cloth previously required by Germany (at the German cost of production) be = in. Then n of cloth will always exchange for exactly 2m of linen. Consequently if n=m, the whole advantage will be on the side of England. If n=2n, the whole advantage will be on the side of Germany. If n be greater than m, but less than 2m, the two countries will share the advantage; England getting 2m of linen where she before got only n : Germany getting n of cloth where she before got only m. It is almost superfluous to observe that the figure 2 stands where it does, only because it is the figure which ex
presses the advantage of Germany over England in linen as estimated in cloth, and (what is the same thing) of England over Germany in cloth as estimated in linen. If we had supposed that in Germany, before the trade, 100 of cloth exchanged for 1000 instead of 200 of linen, then n (after the trade commenced) would have exchanged for 10m instead of 2m. If instead of 1000 or 200 we had supposed only 150, m would have exchanged for only om. If (in fine) the cost value of cloth (as estimated in linen) in Germany, exceeds the cost value similarly estimated in England, in the ratio of p to q, then will n, after the opening of the trade, exchange for sm.”
* It may be asked, why we have supposed the number n to have as its extreme limits, m and 2 m (or *m)? why may not n be less than m, or greater than 2m ; and if so, what will be the result? This we shall now examine, and when we do so it will appear that n is always, practically speaking, confined within these limits. Suppose for example that n is less than m ; or, reverting to our former figures, that the million yards of cloth, which England can make, will not satisfy the whole of Germany's pre-existing demand; that demand being (let us suppose) for 1,200,000 yards. It would then, at first sight, appear that England would supply Germany with cloth up to the extent of a million; that Germany would continue to supply herself with the remaining 200,000 by home production: that this portion of the supply would regulate the price of the whole; that England therefore would be able permanently to sell her million of cloth at the German cost of production (viz. for two millions of linen) and would gain the whole advantage of the trade, Germany being no better off than before. That such, however, would not be the practical result, will soon be evident. The residuary demand of Germany for 200,000 yards of cloth furnishes a resource to England for purposes of foreign trade of which it is still her interest to avail herself; and though she has no more labour and capital which she can withdraw from linen for the production of this extra quantity of cloth, there must be some other commodities in which Germany has a relative advantage over her (though perhaps not so great as in linen): these she will now import, instead of producing, and the labour and capital formerly employed in producing them will be transferred to cloth, until the required amount is made up. If this transfer just makes up the 200,000 and no more, this augmented n will now be equal to m ; England will sell the whole 1,200,000 at the German values; and will still gain the whole advantage of the trade. But if the transfer makes up more than the 200,000, England will have more cloth than 1,200,000 yards to offer; n will become greater than m, and England must part with enough of the advantage to induce Germany to take the surplus. Thus the case which seemed at first sight to be beyond the limits, is transformed practically into a case either coinciding with one of the limits or between them. And so with every other case which can be supposed.
§ 8. We have now arrived at what seems a law of International Values, of great simplicity and generality. But we have done so by setting out from a purely arbitrary hypothesis respecting the relation between demand and cheapness. We have assumed their relation to be fixed, though it is essentially variable. We have supposed that every increase of cheapness produces an exactly proportional extension of demand; in other words, that the same invariable value is laid out in a commodity whether it be cheap or dear; and the law which we have investigated holds good only on this hypothesis, or some other practically equivalent to it. Let us now, therefore, combine the two variable elements of the question, the variations of each of which we have considered separately. Let us suppose the relation between demand and cheapness to vary, and to become such as would prevent the rule of interchange laid down in the last theorem from satisfying the conditions of the Equation of International Demand. Let it be supposed, for instance, that the demand of England for linen is exactly proportional to the cheapness, but that of Germany for cloth, not proportional. To revert to the second of our three cases, the case in which England by discontinuing the production of linen could produce for exportation a million yards of cloth, and Germany by ceasing to produce cloth could produce an additional 1,600,000 yards of linen. If the one of these quantities exactly exchanged for the other, the demand of England would on our present supposition be exactly satisfied, for she requires all the linen which can be got for a million yards of cloth : but Germany perhaps, though she required 800,000 cloth at a cost equivalent to 1,600,000 linen, yet when she can get a million of cloth at the same cost, may not require the whole million; or may require more than a million. First, let her not require so much ; but only as much as she can now buy for 1,500,000 linen. England will still offer a million for these 1,500,000, but even this may not induce Germany to take so much as a million; and if England continues to expend exactly the same aggregate cost on linen whatever be the price, she will have to submit to take for her million of cloth any quantity of linen (not less than a million) which may be requisite to induce Germany to take a million of cloth. Suppose this to be 1,400,000 yards. England has now reaped from the trade a gain not of 600,000 but only of 400,000 yards; while Germany, besides having obtained an extra 200,000 yards of cloth, has obtained it with only seven-eighths of the labour and capital which she previously expended in supplying herself with cloth, and may expend the remainder in increasing her own consumption of linen, or of any other commodity. Suppose on the contrary that Germany, at the rate of a million cloth for 1,600,000 linen, requires more than a million yards of cloth. England having only a million which she can give without trenching upon the quantity she previously reserved for herself, Germany must bid for the extra cloth at a higher rate than 160 for 100, until she reaches a rate (say 170 for 100) which will either bring down her own demand for cloth to the limit of a million, or else tempt England to part with some of the cloth she previously consumed at home. Let us next suppose that the proportionality of demand to cheapness, instead of holding good in one country but not in the other, does not hold good in either country, and that the deviation is of the same kind in both ; that, for instance, neither of the two increases its demand in a degree equivalent to the increase of cheapness. On this supposition, at the rate of one million cloth for 1,600,000 linen, England will not want so much as 1,600,000 linen, nor Germany so much as a million cloth : and if they fall short of that amount in exactly the same degree; if England only wants linen to the amount of nine-tenths of 1,600,000 vol. II.-50
(1,440,000), and Germany only nine hundred thousand of cloth, the interchange will continue to take place at the same rate. And so if England wants a tenth more than 1,600,000, and Germany a tenth more than a million. This coincidence (which it is to be observed, supposes demand to extend cheapness in a corresponding, but not in an equal degree”) evidently could not exist unless by mere accident: and in any other case, the equation of international demand would require a different adjustment of international values. The only general law, then, which can be laid down, is this. The values at which a country exchanges its produce with foreign countries depend on two things: first, on the amount and extensibility of their demand for its commodities, compared with its demand for theirs; and secondly, on the capital which it has to spare, from the production of domestic commodities for its own consumption. The more the foreign demand for its commodities exceeds its demand for foreign commodities, and the less capital it can spare to produce for foreign markets, compared with what foreigners spare to produce for its markets, the more favourable to it will be the terms of interchange: that is, the more it will obtain of foreign commodities in return for a given quantity of its own. But these two influencing circumstances are in reality reducible to one; for the capital which a country has to spare from the production of domestic commodities for its own use, is in proportion to its own demand for foreign commodities: whatever proportion of its collective income it expends in purchases from abroad, that same proportion of its capital is left without a home market for its productions. The new element, therefore, which for the sake of scientific correctness we have introduced into the theory of interna'tional values, does not seem to make any very material dif.
* The increase of demand from 800,000 to 900,000, and that from a million to 1,440,000, are neither equal in themselves, nor bear an equal proportion to the increase of cheapness. Germany's demand for cloth has increased oneeighth, while the cheapness is increased one-fourth. England's demand for linen is increased 44 per cent, while the cheapness is increased 60 per cent.