in the theory of value and prices.

43

5. The marginal utility of each commodity to each individual—represented by the ordinate of each cistern, i. e. by the distancefrom its top to the water level.

6. The money price of each commodity — represented (in anycistern in the same front-and-back-row) by the thickness of the backcompartment, and registered on scales * p„, p b , p c at the rear. (Therelation of price to marginal utility will recur.)

7. The prices of commodities in terms of each other —representedby the ratios of their ordinates.

8. The marginal utility of money to each individual — repre-sented (in any cistern in the same right-and-left-row) by the ratiofof the ordinate of that cistern to thethickness of its back compartmentand registered on scales\ U I, U II,

U III at the right.

The units of these magnitudesare :

L. The unit of commodity is aton, yard, gallon, etc-., and is repre-sented by (say) a cubic inch ofwater.

2. The unit of money is (say) adollar and is represented by (say) acubic inch of water.

3. The unit of price is one dollarper ton, yard, gallon, etc., and isrepresented by one inch.

4. The unit of marginal utilityfor each individual is. the marginalutility of (say) 100 tons of A. Itmay be called a util and by a proper

11 .

* The rods RRR are each connected by a cord and pulley with the pointers ofthe scales p a , p t , p c .

f This ratio is evidently the marginal utility of money (“valuation of money ”)

because as seen in chapter IV, § 2, = Y? . p

r 0 dA dm •

whence :

dU

dm

rtU

dA

Pa

ordinate of cistern

thickness of its hack compartment"i Fig. 11 (which views the outside of the right wall of the tank) shows thedevice by which this is accomplished. Evidently from the labels

x

1

dU

dA dU

— or x = —p dm'

The pointer obviously varies with x. It is so arranged as to register zero whenx = 0.