Irving Fisher—Mathematical investigations

First of all an analysis will serve to set the two preceding discus-sions in a common point of view.

In any purchase the last infinitesimal commodity bought has autility equal to that of the money given, that is :

ut. of dA = ut. of dm

(see Ch. I, § 3.)

or :

d\J d\3 dm

dA dm ' dA

dU dXJ

or:

dA dm ' Pa

or :

where p a is the money price.

That is, the marginal utility of a commodity (per pound, yard,etc.) equals the marginal utility of money (per dollar) times theratio of exchange of money for commodity*:

This equation is fundamental. In our first discussion (one com-modity, various consumers) the marginal utility of money was sup-posed constant so that

dU

dA 00 Pa

or the marginal utility of a commodity is measured by it pri6e.

In the second discussion the other factor, the price, was supposedConstant, and:

dXJ dU

—— oc ——

-- OC -

d A dm

Or the marginal utility is measured by the valuation of money.

In the present chapter we are restricted to neither of these specialsuppositions. For the individual I, we may write

dU _ dUdA } dm 1 ' Pa5U _ rfUd B, ” dm % ‘ Pb

dX3__dA3c/M, dm l ' Pm