684 



BEPOET 1889. 



if he obtain Ox in return for 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 Fig. 6 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 Germany 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 displace the supply-curve in the manner indicated by the dotted curve OE'. Let r' 



Fig. 3. 



c 



be the new point of intersection between the Demand- and (displaced) Supply-cui-ve. 

 The gain to Germany in the way of trade is now t'r'. To which is to be added the 

 tax r's accruing to Germany. Since i!'* 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 refer- 

 ence 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 endeavour of one nation to gain 

 by taxing the imports from (or exports to) another. It will be noticed that the 

 particular supposition entertained by Professor Sidgwick (Book iii. ch. 6, § 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 of the ' Indifference- 

 curve' employed by the present writer ('Mathematical Psychics,' p. 21). Also the 



