in the theory of value and prices. 19 



(7) The name utility-value of a commodity may he given to the 

 product of the quantity of that commodity by its marginal utility or 



d^l 

 dx 



X 



The name is suggested from money-value which is quantity of 

 commodity times its price. (Cf. § 3). 



(8) The GAIN or consumer's rent is total utility minus utility value. 

 That is : 



«/o 



(Tain = / -^- ax •— X . -^ 

 dx ax 



It is the actual total utility diminished by that total utility which 

 the commoditj^ would have if it were all rated at the same degree of 

 utility as the last or least useful increment. 



It is to be observed that total utility and gain are not experiences 

 in tim,e but the sum of increments of utility suhstitutionally succes- 

 sive. The individual is to assign the marginal utility for the 90th 

 loaf on the hypothesis that he were consuming 90 loaves per year, and 

 then abandoning this supposition to substitute successively the hy- 

 pothesis of 91 loves, 92, 93, etc., all for the same year. That is, a 

 number of mutually exclusive hypotheses for the same period are 

 thought of. 



§9. 



The preceding definitions have been expressed relative to a par- 

 ticular instant of time. This was because in actual life purchases 

 are made by separate instantaneous acts. But the important com- 

 modity-magnitudes in economics are " tons per year," " yards per 

 day," etc., bought, sold, produced, consumed. In order to make our 

 definitions applicable to such quantities the element of time must be 

 introduced. Hence the following supposition : 



During the given period of time (that is, the period for which 

 commodity-magnitudes are considered) the marginal utility to a 

 given individual of a given commodity is the same at all histants at 

 which he buys or consumes it or sells or produces it. 



This involves supposing that prices do not vary, for prices (as we 

 shall see) are proportional to marginal utilities. 



A housewife buys (say) 10 lbs. of sugar at 10 cts. per pound. As 

 she closes the bargain she roughly estimates that the last or tenth 

 pound is about worth its price. She did not stop at five pounds for 

 she wanted a sixth more than the 10 cts. it cost her. She may not 

 buy sugar again for a fortnight. When she does, we shall suppose 



