30 



Irving Fisher — Mathematical investigations 



AGGREGATE COMMODITY. 



Let C, fig. 4, be the average curve* of all the individual curves, I, 

 II, III, . . . . N, and let the new cistern have a thickness equal to the 

 sum of the thicknesses of the individual cisterns. Then as much water 

 will be in the aggregate cistern as in all the others.* The water in 

 the aggregate cistern may be regarded as a repetition of the con- 

 tents of the individual cisterns. It represents no new commodity. 



In cistern C it is almost too evident to require mention that an in- 

 creased supply of this commodity (indicated by pressing the stopper) 

 reduces the price while a diminished supply increases it. This fact 

 is all that is usually exhibited in " demand curves " such as of 

 Fleeming Jenkin.f 



§9. 



Fig. 5 and completely analogous explanations apply to production 

 cisterns. 



5. 



* Formed as follows : Select pfs. of like price ou the individual curves, that is, 

 pts. of like ordinates (as i/i, t/2, Vs, ■ . . Vn) and using the same ordinate for the 

 new ordinate, take the average of their abscissas for the new abscissa and make 

 the thickness of the new cistern equal to the sum of the thicknesses of all the in- 

 dividual cisterns. Then if in such a cistern liquid be allowed to flow to the 

 level of the individual cisterns the amount of liquid contained in it will equal 

 all that contained in the individual cisterns. For e^ddently the free surface of 

 the water in the large cistern equals in area the total free surfaces in the small, 

 and as such equality of horizontal infinitesimal layers or laminae holds true at 

 all successive levels, it holds true of the sums of the layers. 



f The Graphic Representation of Supjjly and Demand. Grant's recess studies, 

 p. 151. 



