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Irving Fisher—Mathematical investigations
The total work done by a particle in 'moving from the origin to a given po- isition is the integral of the resisting :forces along all space axes (resistingforces are those directed toward theorigin) multiplied by the distancesmoved along those axes.
The “ total energy ” (the work done ,upon the particle) may be defined as 'the like integral with respect to im- jpelting forces. |
The net energy of the particle may bedefined as the “ total energy” less the“total work.”
Equilibrium will be where net energy Iis maximum; or equilibrium will be 'where the impel, and resist, forces Ialong each axis will be equal. |
(If “ total energy ” be subtracted from“total work” instead of vice versathe difference is “ potential ” and isminimum).
The total disutility suffered by an indi-vidual in assuming a given position inthe ‘ ‘economic world ” is the integralof the marg. disut. along all commod.axes (marg. disut. are directed to-ward the origin) multiplied by thedistances moved along those axes.
The total utility enjoyed by the individ-ual is the like integral with respectto marg. utilities.
The net ut. or gain of the individual isthe “ total utility ” less the “totaldisutility. ”
Equilibrium will be where gain is max-imum ; or equilibrium will be wherethe marg. ut. and marg. disut. alongeach axis will be equal.
(If “total ut.” be subtracted from“total disut.” instead of vice versathe difference may be called “loss”and is minimum).
CHAPTER IV.
UTILITY AS A QUANTITY.
In Part I, Chap. I, Utility was defined with reference to a singleindividual. In order to study prices and distribution it is not neces-sary to give any meaning to the ratio of two men’s utilities. Jevonsapparently did not observe this. Auspitz und Lieben did. So didGeorge Darwin.*
It would doubtless be of service in ethical investigations and pos-sibly in certain economic problems to determine how to compare theutilities of two individuals. It is not incumbent on us to do this.When it is done the comparison will doubtless be by objective stand-ards. If persons alike in most respects show to each other their sat-
* The Theory of Exchange Value.
Fortnightly Review, new series, xvii, 243.