TRANSACTIONS OF SECTION F. 



683 



«xport, linen. The altered conditions of su]>plj' may be represented by the displaced 

 curve OG', Fig. 3, indicating that whereas before the improvement Germany in ex- 

 change for any quantity, Ox, of cloth offered only xq, slie now offers xq'. The 

 effect of the improvement on the rate of exchange will depend upon the form of the 

 curve OE beyond the point r. If the intersection of the curve OE is at r, vertically 

 above r, we have the case where, as Mill rather awkwardly says, the demand of Eng- 

 land for linen increases 'in the same proportion with the cheapness.' The other cases 

 in which the demand for linen — and accordingly the price, so to speak, of cloth in 

 linen — are increased more or less than the cheapness, are represented by the points of 

 intersection ?%, r^. 



The same construction may be used to represent the effect on the rate of exchange 

 produced by a tax on exports or imports. Let OG' now represent the undisturbed 

 condition of supply, and let OG be what this curve becomes when displaced by a tax 

 on Germany's exports. According to the position of the original intersection, whether 

 at r,, 7*2, or r,, we have the three cases distinguished by Mill. (Book v. oh. 4, § 6.) 



Fig. 2. 



Again the same construction may be used to facilitate the comprehension of the 

 theory of International Trade which Professor Sidgwick has recently proposed. Let 

 the curves OE and OG' represent the conditions of supply and demand, on the hypo- 

 thesis that cost of transport is annihilated, that England and Germany are in juxta- 

 position. Now restore the abstracted sea, and the altered conditions of Supply and 

 Demand in a marhet on the English shore will be represented by the cliange of OG' to 

 OG. According to the form of the curve OE the different effects on the rate of ex- 

 change are Wsible at a glance. (Cf. Sidgwick, ' Pol. Econ.,' Book ii., ch. 2, § 3.) 



((•) Gain of Trade. — To measure the variations in the advantage accruing from 

 trade by the variations of price— or more generally rate of exchange — is a confusion 

 which could hardly have occurred to the mathematical economist. The simplest 

 method of illu-strating the gain of trade is that proposed by Messrs. Auspitz and 

 Lieben. In Fig. 4, let O^t be the locus of a point t, such that a certain individual in 

 exchange for the quantity Oj* of one commodity will just be willing to give the 

 quantity tx of another commodity, will neither gain nor lose by that bargain. Then, 



