37

in the theory of value and prices.

whence, since the marginal utility of money to I is the same in eachcase,

dJJ dUc?A, ‘ dB,

dU

tfM,

= P« : lh

Pn,

Since this is true for every individual and the prices to all individ-uals are the same, we may write:

dU

dV

d U

— dA,

dBf

' ' ‘ dM,

dU

dU

dU

~ dA a

dBf

' ' ' rfM,

d\J

dU

dXJ

' rfB. ’ • '

- - ' dM„

These equations express in the most general way the theory ofmarginal utilities in relation to prices. This theory is not, as some-times stated, “ the marginal utilities to the same individual of allarticles are equal,” much less is it “ the marginal utilities of the samearticle to all consumers are equal,” but: The margined utilities ofall articles consumed by a given individual are proportional to themarginal utilities of the same series of articles for each other con-sumer, and this uniform continuous ratio is the scale of prices ofthose articles.

The idea of equality is inadequate and must be replaced by theidea of proportionality. The problem which confronts the individ-ual must be figured as to so adjust his consumption of all commodi-ties that the utilities of the last pound, yard, gallon, etc., shall hearthe ratio which he finds their prices do, while the market as a wholemust cause such prices to emerge as will enable each individual tosolve this problem and at the same time just take off the supply.

§ 4 -

This notion of a ratio is introduced into the following more com-plicated mechanism (fig. 8). Fig. 9 (an elevation of fig. 8) showsthe various cisterns of various commodities for the individual I.The ordinates represent marginal utility per unit of commodity.It corresponds to fig. 6, except that in the latter the utility is perdollar’s worth of commodity. The tops of the cisterns are no longerat the same level. The cisterns are now to float like boats in a