502 



NATURE 



[Sept. 19, 1889 



curve OE is at r, vertically above r, we have the case where, as 

 Mill rather awkwardly says, the demand of England for linen in- 

 creases " in the same proportion with the cheapness." The other 

 cases in which the demand for linen— and accordingly the price, 



Fig. 2. 



Fig. 3. 



so to speak, of cloth in linen — are increased more or less than 

 the cheapness, are represented by the points of intersection 



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 rj, r^, or r.„ we have 

 the three cases distinguished by Mill (book 

 V. ch. iv. § 6). 



Again, the same construction may be used 

 to facilitate the comprehension of international 

 trade which Prof. Sidgwick has recently pro- 

 posed. Let the curves OE and OG' represent 

 the conditions of supply and demand, on the 

 Hypothesis that cost of transport is annihilated, 

 that Eneland and Germany are in juxtaposi- 

 tion. Now restore the abstracted sea, and 

 the altered conditions of supply and demand 

 in a market on the English shore will be re- 

 presented by the change of OG' to OG. Ac- 

 cording to the form of the curve OE the 

 different effects on the rate of exchange are 

 visible at a glance. (Cf. Sidgwick, "Pol. 

 Econ.,"book ii. ch. ii. § 3 ) 



(c) Gain of Trade. — To measure the 

 variations in the advantage acruing 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 illustrating the gain of trade is that pro- 

 posed by Messrs. Auspitz and Lieben. In 

 Fig. 4, let On be the lonis of a point /, such 

 that a certain individual in exchange for the 

 quantity Ox of one commodity will just be 

 willing to give the quantity tx of another 

 commodity, will neither gain nor lose by that 

 bargain. Then, if he obtain Ox in return f jr 

 only rx, he is a gainer by that bargain to the 

 extent of tr. The curve thus defined is called 

 the utility-curve. 



Now add properly the utility-curves for all 

 the individuals of a community, and we obtain 

 what may be called a collective utility-curve. 

 There is a peculiar propriety in taking one 

 axis, say the ordinate, to stand for money. 

 Let ON, then, in P'ig. 5, be the collective 

 utility-curve, in this sense, for the German 

 community with respect to cloth. Let OG 

 represent the demand of Germany for cloth, 

 as before, except that the ordinate now stands 

 for money, not linen. And let OE represent 

 the supply of cloth in exchange for money on 

 the part of England. Then the gain to Ger- 

 many of the trade with England is represented 

 by the vertical distance tr. 



Now let Germany impose a tax on the import 

 of cloth. The effect of the tax will be to dis- 

 place the supply-curve in the manner indicated 

 by the dotted curve OE'. Let r' be the new 

 point of intersection between the demand- and 

 (displaced) supply-curve. The gain to Ger- 

 many in the way of trade is now t'r'. To 

 which is to be added the tax r'S accruing to 

 Germany, bince ^'S may very well be greater 

 than tr, Germany may gain by the imposition 

 of the tax. 



What difficulties the reader may feel about 

 this proposition will disappear on reference 

 to Messrs. Auspitz and Lieben's beautiful 

 and original reasoning ("Theorie der Preise," 

 §§ 80-82). In the light of their constructions 

 it will be at once seen what conditions of 

 supply and demand are favourable to the en- 

 deavour of one nation to gain by taxing the 

 imports from (or exports to) another. It will 

 be noticed that the particular supposition 

 entertained by Prof. Sidgwick (book iii. ch. v. § 2) — that the 

 quantity consumed of the taxed import is constant — is not 

 essential. 



It may be observed that the utility-curve is a particular case 



