8t) 



Irv ing Fisher — Mathematical investigations 



The total work done by a particle in The total disutility suffered by an indi- 



moving from the origin to a given po- 

 sition is the integral of the resisting 

 forces along all space axes (resisting 

 forces are those directed toward the | 

 origin) multiplied by the distances j 

 moved along those axes. i 



The " total energy " (the work done 

 upon the particle) may be defined as 

 the like integral with respect to im- 

 pelling forces. 



The net energy of the particle may be 

 defined as the " total energy" less the 

 "total work." 



vidual in assuming a given position in 

 the "economic world " is the integral 

 of the marg. disut. along all commod. 

 axes (marg. disut. are directed to- 

 ward the origin) multiplied by the 

 distances moved along those axes. 



The total utility enjoyed by the individ- 

 ual is the like integral with respect 

 to marg. utilities. 



The net ut. or gain of the individual is 

 the "total utility" less the "total 

 disutility." 



Equilibrium will be where net energy Equilibrium will be where gain is max- 

 is maximum ; or equilibrium will be imum ; or equilibrium will be where 

 where the impel, and resist, forces the marg. ut. and marg. disiit. along 

 along each axis will be equal. ; each axis will be equal. 



(If " total energy " be subtracted from \ (If "total ut." be subtracted from 

 "total work" instead of vice versa j "total disut." instead of vice versa f 

 the difference is ^"potential'''' and is | the difference may be called ^^ loss^'' 

 minimum). and is minimum). 



CHAPTER IV. 



UTILITY AS A aUANTITY. 



In Part I, Chap. I, Utility was defined with reference to a single 

 individual. In order to study prices and distribution it is not neces- 

 sary to give any meaning to the ratio of two men's utilities. Jevons 

 apparently did not observe this. Auspitz und Lieben did. So did 

 George Darwin.* 



§ ^• 



It would doubtless be of service in ethical investigations and pos- 

 sibly in certain economic problems to determine how to compare the 

 utilities 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 resj^ects show to each other their sat- 



The Theory of Exchange Yalue, Fortnightly Review, new series, xvii, 243, 



