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Mathematical investigations in the theory of value and prices / by Irving Fisher
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28

Irving Fisher Mathematical investigations

present memoir, however, attention is confined to those features ofproduction which are strictly analogous to consumption. (See Ap-pendix II, § 8.)

§ 6 .

ONE COMMODITYMANY CONSUMERS.

Let fig. 4 represent the utility cisterns for all individuals I, II,III, IV,... N, in the market and let utility be measured in money

4.

as before, the marginal utility of money being considered constant(say 1 util.).

The water in the connecting tubes (represented by oblique shad-ing) does not stand for commodity.

The water will seek its own level. This is exactly what happensin ihe economic world and may be stated in the theorem: A givenamount of commodity to be consumed by a market during a givenperiod will be so distributed among the individuals that the marginalutilities measured in money will be equal. Furthermore the margi-nal utility thus determined will be the price.

This follows, for there can be but one price, and each individualwill make his marginal utility equal to it, as shown in § 4.

If the stopper,* S, be pressed, more liquid (commodity) flows intothe cisterns, there is an inevitable change in level and the price de-creases. When it cheapens to 2, II begins to indulge. It is for thefirst timewithin his reach.

It is to be noted that from the standpoint of a single individualthe existence of the general price level is an unalterable fact and theamount which he consumes is accommodated to it, just as the gen-eral water level in several hundred cisterns may be said to determine

* A rubber compression ball would be used in practice. Throughout the de-scriptions, the mechanisms are those simplest to delineate and in many casesnot those which might be actually employed.