44 Irving Fisher — Mathematical investigations 



adjustment of the breadth of each cistern may be represented by one 

 inch. That is, if 100 cu. in. of water are put m each A cistern the 

 ordinate must be one inch. This applies as well to the utility of 

 money, so that the scale U at the left indicates the number of iitils 

 at which the individual values the last dollar of his income. It 

 should, however, be noted that the variation of utils is only valuable 

 in the same register, that is, for the same individual. There is no 

 important meaning attached to the ratio of the scale readings U for 

 two individuals. If that of I is 1 and of II 2 it means simply that 

 II values his last dollar twice as much as his 100th ton of A, while 

 I values his last dollar just as much as his 100th ton of A. It is in- 

 teresting to observe that analogously the price registers are not to 

 be compared, for while one indicates price per ton the other indicates 

 price per yard, etc. Thus the mechanism is independent of any 

 common measure of utility for different individuals and any common 

 measure of prices for different commodities. 



§^- 



It will be observed that the numbers on the various registers are 

 so connected that the product of the register of A by that of its 

 price added to the like products for B, C, etc., will equal the sum 

 of all the income registers. 



Moreover if each cistern is provided with a graduation to show 

 marginal utility, this number will be found to be the product of the 

 number for price in its front-and-back row, by that for valuation of 

 money in its right-and-left row. 



§8- 



The mechanism just described is the phj^sical analogue of the 

 ideal economic market. The elements which contribute to the 

 determination of prices are represented each with its appropriate 

 r61e and open to the scrutiny of the eye. We are thus enabled not 

 only to obtain a clear and analytical picture of the interdependence 

 of the many elements in the causation of prices, but also to employ 

 the mechanism as an instrument of investigation and by it, study 

 some complicated variations which could scarcely be successfully 

 followed without its aid. Its chief uses may be briefly classified as 

 follows : 



1. Arrange the stoppers I, II, III, etc., so that the money incomes 

 of I, II, III, are all equal. The differences of distribution of the 

 commodities will depend on individual characteristics, that is, on 



