20 Irving Fisher — Mathematical investigations 



the price to be the same, so that the last pound she then buys has 

 the same utilit^T^ as the last pound she previously bought. She may 

 buy fifteen pounds. A fortnight later only five, all depending on 

 her plans for using it. The whole yearly purchase may be 250 lbs. 

 and we may write : 



ut. (10th lb.) Jan. 1 = ut. (15th lb.) Jan. 15. 



= ut. ( 5th lb.) Jan. 30. 

 =: etc. 

 = ut. (250th lb.) for whole year. 



Thus : The marginal utility of a certain quantity of a Gommodity 



for a given period (say a year) is defined to he the marginal utility 



of that commodity on all occasions during that year at ichich it is 



bought or consumed, the sum of the individual purchases being the 



given yearly purchase and consumption. 



§ 10- 



In the hypothetical case the marginal utility of 250 pounds per 

 year equalled the marginal utility of LO cts. In the same manner 

 we maj'- practically estimate the marginal utility of 200 pounds by 

 supposing the price to be such that our housewife would buy 200 

 pounds. Thus a number of alternative suppositions are made for 

 the same period. By means of these a utility curve can be con- 

 structed, one of the coordinates of which is the yearly consumption 

 of sugar. To do this statistically is of course quite a different and 

 mtore difficult though by no means hopeless proceeding. 



Curves of this nature are the only ones to be here considered. 

 But it is clear that there also exist utility curves for each time of 

 purchase.* These would differ both from the " yearly " curve as 

 well as from each other. 



§11. 



To meet a possible objection it must be pointed out that the use 

 of a " yearly " utility curve assumes no nice calculation on the part 

 of the individual as to his future income and receipts. He may even 

 be and generally is totally ignorant of the number of pounds of 

 butter he consumes per year. He creejDS along from purchase to 

 purchase and only at these individual acts does he estimate his needs 

 and his abilities. Yet if he always completes his purchase with the 

 same estimate of marginal utility as measured against other com- 



* They would be the curves of Fleeming Jenkin : Graphic Eepresentation of 

 Supply and Demand. Grant's Recess Studies, p. 151, Edinburgh, 1870. 



