in the theory of value and prices.

99

second by p a and since the first members will become identical wehave a common continuous equation:

dJJ

cZU (HJ

dA x tfB,

tfU — <?U

( 3 )

dm t ' dm i '

that is, the marginal utilities of all commodities to all consumers areequal when the unit of utility is the marginal utility of money andthe unit of commodity the dollar’s worth. Hence the total utilityin whole market thus measured is a maximum.*

However it may justly be objected that the marginal utility ofmoney to one person is not equatable to that of another, that is thatit is unfair to use the unit of utility for the poor man the high mar-ginal utility of his small income and add the small number of suchlarge units in a poor man’s gain to the corresponding rich man’s gainin which the unit of measure is small and the number of units large.

If we suppose by some mysterious knowledge an exact equiv-alence of utilities were possible between different individuals (seePart II, Ch. IY, §2) and by some equally mysterious device ofsocialism we could without changing the aggregate commodities altertheir distribution so as to make the whole market utility a maximumour condition would be

This could be brought about by a change in the relative incomes,taking from the rich and giving to the poor until

_ d\Jdm , dm,

- = etc.

which applied to equation (3) will evidently afford the required (4),

or by breaking down the condition of uniformity of price and mak-

ing each man’s price inversely as his marginal utility of money,which applied to (3) will evidently yield (4).

To interpret equation 4 in the mechanism we may alter the posi-tion of the stoppers in fig. 8 until the ordinates in each front andback row are equal. (This will not be when “ incomes are equallydivided ” nor when “ gains ” are equal, for persons differ in theirpower of enjoyment, and it would still be true that those whose

* Cf. Auspitz und Lieben, p. 23 and 435.