32 



Irving Fisher — MathematiGal investigations 



§2. 



Let the individual I distribute his income over the commodities 



A, B, C, M. Let the thickness of each cistern in fig. 6 be 



proportional to the price of the commodity it contains. Thus if A 

 bears a price of $2 per yard, B %\ per gallon and C %^ per pound, the 

 thickness of cistern B is 2, of B 1, and of C|-. 



Let the unit of area on the front surface of each cistern represent 

 a unit of commodity, yards for A, gallons for B, etc. 



Then the volume of liquid will evidently indicate the money value 

 of the commodity, for it equals the front area times the thickness, 

 that is, the quantity of commodity times its price. Moreover the 

 sum of all the water will indicate the whole* income in dollars. 

 The unit of volume thus represents not a yard, gallon, pound, etc., 

 but a dollar^ loorth in each case. For A it would be \ yard, for B 

 1 gallon, for C 2 lbs., etc. 



Accordingly let the curves which limit the cisterns be so con- 

 structed that the ordinate s shall represent marginal utility per 

 dollar'' s loorth not per yard, gallon, etc. 



The liquid will seek its own level corresponding to the economic 

 proposition : A consumer loill so arrange his consumption that the 

 marginal utility per dollar^ s loorth of each commodity shall he the 

 same. 



* Saving is here regarded as a form of spending, tlie commodity purchased 

 being capital. The analysis implies that the marginal utility of saving a dollar 

 equals the marginal utility of the dollar spent in other ways. This •would be 

 elaborated from another standpoint in a theory of distribution. Cf . Launhardt ; 

 Volkswirthschaftslehre ; Bohm-Bawerk ; Kapital und Kapitalzins. 



