32

Irving Fisher—Mathematical 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 Abears a price of $2 per yard, B $1 per gallon and C per pound, thethickness of cistern B is 2, of B 1, and of C£.

6 .

Let the unit of area on the front surface of each cistern representa unit of commodity, yards for A, gallons for B, etc.

Then the volume of liquid will evidently indicate the money valueof the commodity, for it equals the front area times the thickness,that is, the quantity of commodity times its price. Moreover thesum 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's worth in each case. For A it would be £ yard, for B1 gallon, for C 2 lbs., etc.

Accordingly let the curves which limit the cisterns be so con-structed that the ordinates shall represent marginal utility perdollar's worth not per yard, gallon, etc.

§ 3 -

The liquid will seek its own level corresponding to the economicproposition : A consumer will so arrange his consumption that themarginal utility per dollar's worth of each commodity shall be thesame.

* Saving is here regarded as a form of spending, the commodity purchasedbeing capital. The analysis implies that the marginal utility of saving a dollarequals the marginal utility of the dollar spent in other ways. This would heelaborated from another standpoint in a theory of distribution. Cf. Launhardt;Volkswirthschaftslehre; Bohm-Bawerk ; Kapital und Kapitalzins.