in the theory of value and prices. 37 



whence, since the marginal utility of money to I is the same in each 

 case, 



(?U ^ cm _ 



d\' dB/' cm, ^l\:ih- Pra 



Since this is true for every individual and the prices to all individ- 

 uals are the same, we may write : 



_ d^ dV d^ 



Pa'lh' ^^"^ - dA^' dB^' 'dM^ 



_dTJ_ d^ d\] 



- Ia/'Ib/' 'dW^ 



_d\l dV^ dU 



~~ dA„ ' dB„ dMn 



These equations express in the most general way the theory of 

 marginal utilities in relation to prices. This theory is cot, as some- 

 times stated, "the marginal utilities to the same individual of all 

 articles are equal," much less is it " the marginal utilities of the same 

 article to all consumers are equal," but : The marginal utilities of 

 all articles consumed hy a given individual are proportional to the 

 marginal utilities of the same series of articles for each other con- 

 sumer^ and this unifor^n contiJiuous ratio is the scale of prices of 

 those articles. 



The idea of equality is inadequate and must be replaced by the 

 idea of proportionality. The problem which confronts the individ- 

 ual must be figured as to so adjust his consumption of all commodi- 

 ties that the utilities of the last pound, yard, gallon, etc., shall bear 

 the ratio which he finds their prices do, while the market as a whole 

 must cause such prices to emerge as will enable each individual to 

 solve this problem and at the same time just take off the supply. 



§ 4. 



This notion of a ratio is introduced into the following more com- 

 plicated mechanism (fig. 8). Fig. 9 (an elevation of fig. 8) shows 

 the various cisterns of various commodities for the individual I. 

 The ordinates represent marginal utility per unit of commodity. 

 It corresponds to fig. 6, except that in the latter the utility is jyer 

 dollar'^s worth of commodity. The tops of the cisterns are no longer 

 at the same level. The cisterns are now to fioat like boats in a 



