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Irving Fishei—Mathematical investigations

§8.

AGGREGATE COMMODITY.

Let C, fig. 4, be the average curve* of all the individual curves^ I,II, III, .... N f and let the new cistern have a thickness equal to thesum of the thicknesses of the individual cisterns. Then as much waterwill be in the aggregate cistern as in all the others.* The water inthe aggregate cistern may he 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 factis all that is usually exhibited in “demand curves” such as ofFleeming Jenkin. f

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Fig. 5 and completely analogous explanations apply to productioncisterns.

5.

* Formed as follows : Select pts. of like price on the individual curves, that is.pts. of like ordinates (as y,, yi, y*, . . . y„) and using the same ordinate for thenew ordinate, take the average of their abscissas for the new abscissa and makethe 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 thelevel of the individual cisterns the amount of liquid contained in it will equalall that contained in the individual cisterns. For evidently the free surface ofthe 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 atall successive levels, it holds true of the sums of the layers.

f The Graphic Representation of Supply and Demand. Grant’s recess studies,p. 151.