92 



Irmng Fisher — Mathematical investigations 



the other two) it is only necessary to have a plane curve of appro- 

 priate form and to represent any two of the above economic magni- 

 tudes by any two geometrical magnitudes determined by the posi- 

 tion of points in the curve. 



Out of the numerous possible methods thus included, the one se- 

 lected for the preceding discussion was to represent marginal utility 

 by the Cartesian ordinate and commodity by the area included be- 

 tween the curve, the axes of coordinates, and the abscissa drawn 

 from the j)oint. 



§2. 



In order to show the connection between this system of coordi- 

 nates and those of Jevons and of Auspitz und Lieben, the following 

 scheme is presented : 





Jevons 





Auspitz & Lieben. 



The new curves. 



Commodity 



.__- = Xj 





= ^a 



z= fxdy 



Marginal ) 

 utility j 



--=2/. 





= ^^^ = tan 6 



= y 



Total ) 

 utilitj^ j 



----=fyf^ 





= Va 



- Jyxdy 



Gain 



.... =Syflx^— 



^jVj 





=zfyxdy-yfxdy 



39. 



30. 



31. 



32. 



