41

in the theory of value and prices.

ordinates of the front row are proportional to those of the row nextbehind, also of the second row behind and so on. Remembering

1 O

that each ordinate is a marginal utility we have:

<2U cZU _ rfU (HJ _ dV dJJ _

d A, ' c?B, • • • • — • ^ 3 ^ .... — ....

which is the required condition that marginal utilities must be pro-portional (§3).

Secondly there are the horizontal levers (F34, etc., fig. 10 ) lyingon the surface of the water in the tank. These relate to prices.The sliding pivots 3, 4, etc. are connected with rods RRH, whichin turn are connected by vertical pins with the rear walls of thecisterns. A motion of one of these rods causes all back compart-ments in that row to expand or shrink in unison. The pivots 3, 4,etc. are so situated on these rods that if the levers F34, etc. shouldassume a right-and-left position along the dotted line FF, the backcompartment of every cistern would be completely closed. HenceR3 equals the thickness of each back compartment in the A vow,R4 the corresponding thickness in the B row and so on.

By the similar triangles FR3 and F34 in fig. 10 , it is clear thatthe lines R3 and R4, and consequently the rear thickness in the Aand B rows are proportional to the distances of the A and B rodsR and R from the float F. But we have just seen that the ordinatesof IA and IB are proportional to these same distances. Hence thethicknesses of the back compartments of the cisterns are propor-tional to the ordinates of those cisterns, that is to marginal utilities.Hence we are free to call the thickness of each back compartment,the money* price of the commodity to which that cistern relates.

* Money is here used solely as a measure of value. It is not one of the com-modities in the market. The high or low price of commodities in terms ofthis money is dependent entirely on the amount of it at which we agree to ratethe yearly consumption of the market, that is the amount of liquid originally inthe hack cisterns. We are so accustomed to' regard money as the medium ofexchange and therefore as a commodity that we may not observe that it is per-fectly possible to have a measure of value which is not a commodity at all. Thuswe might agree to call the consumption of the United States for a year $10,000,-000,000, and this agreement would immediately fix a measure of value, though thenew dollar need have no equality to the gold or silver dollar. It would be easyto translate between such an arbitrary standard and-any commodity standard.Thus if statistics showed that the consumption measured in gold dollars was$12,000,000,000, the agreed standard is at 120 compared with gold and by meansof this factor we can reduce the prices of all commodities. In the mechanismthe aggregate amount of liquid in the back cisterns corresponds to the $10,000,000,000. If we take it so and if the amount of liquid in the I row is given at$1,000, this means that (in whatever standard) the consumption of I is one-ten"millionth in value the aggregate consumption.