in the theory of value and prices. 99 



second by ^^ and since the first members will become identical we 

 have a common continuous equation : 



dA, dB, dh. 



f?U ~ dJS c?U 



= etc. (3) 



dm^ ' ^ " dm^ ' dm^ 



that is, the marginal utilities of all commodities to all consumers are 

 equal when the unit of utility is the marginal utility of money and 

 the unit of commodity the dollar's worth. Hence the total utility 

 in whole market thus measured is a maximum.* 



§4- 



However it may justly be objected that the marginal utilitj^ of 

 money to one person is not equatable to that of another, that is that 

 it is unfair to use the unit of utility for the poor man the high mar- 

 ginal utility of his small income and add the small number of such 

 large units in a poor man's gain to the corresponding rich man's gain 

 in which the unit of measure is small and the number of units large. 



If we suppose by some mysterious knowledge an exact equiv- 

 alence of utilities were possible between different individuals (see 

 Part n, Ch. IV, § 2) and by some equally mysterious device of 

 socialism we could icithout changi7ig the aggregate commodities alter 

 their distribution so as to make the whole market utility a maximum 

 our condition would be 



d\J dJJ 



T\ = dx: = '''- (') 



This could be brought about by a change in the relative incomes, 

 taking from the rich and giving to the poor until 



dJJ __ dJJ _ 



dm^ dm^ 



which applied to equation (3) will evidently aiford the required (4), 

 or by breaking down the condition of uniformity of price and mak- 

 ing each man's price inversely as his marginal utility of money, 

 which applied to (3) will evidently yield (4). 



To interpret equation 4 in the mechanism w^e may alter the posi- 

 tion of the stoppers in fig. 8 until the ordinates in each front and 

 back row are equal. (This will not be when " incomes are equally 

 divided " nor when " gains " are equal, for persons differ in their 

 power of enjoyment, and it would still be true that those whose 



* Cf. Auspitz und Lieben, p. 23 and 435. 



