in the theory of value and prices.

29

the amount in any particular cistern. But, e >r the system as awhole, the price level is a consequence of the amount of commoditymarketed. What appears as cause in relation to effect to an indi-vidual is effect in relation to cause for the whole market.

The quantities of commodity and the marginal utilities mutuallylimit and adjust themselves, subject to three conditions, (1) that dueto the forms of cisterns, (2) that due to the total amount of commod-ity marketed, (3) uniformity of price, or of marginal utility.

§ 7 .

*

ANALYTICAL.

The algebraic interpretation of the preceding mechanism or of theeconomic phenomena themselves is as follows :

Let A,, A 3 , A s , . . . A n be the (as yet unknown) quantities of thecommodity consumed by I, II, III, . . . N. LetdU d\J d\J

rfA,’ rfA,’-’ dA n

be their (unknown) marginal utilities. Then the three conditionsmentioned in § 6 become :

0 )

( 2 )

(The unit of utility (util.) is that of the marginal dollar.)

r cHidA

dU m

=F.(A.)

£='■<*■> J

n equations.

2 n unknowns.

\ A + A +A +.... + A n =.K i 1 e( l uation -( 1 3 3 n (no new unknowns.

(Unit of utility is that of marginal dollar.)

j dU _ dU_d\J _ _dU ) n — 1 independent equationsK) \dA~dA~dA~ -tfAj'

no new unknowns.

Hence the number of equations is :

n +1 + (n— l)z=2n

and of unknowns :

2n + 0 + 0=2n.

Therefore the numbers of equations and unknowns are equal andall quantities and utilities are determinate.