in the theory of value and prices. 



33 



This follows because if the individual should vary his consumption 

 from such a distribution, by expending an extra dollar on A he 

 would divert that amount from another article or articles, say B. 

 Then the level in the A cistern would be higher than in the B, which 

 interpreted, is the dollar spent on A had less utility than if it had 

 been devoted to B. 



If the stopper be pressed, i. e. if the individual had had a larger 

 income, the valuation of the last dollar's worth of each commodity 

 decreases, or the marginal utility of money decreases. If it becomes 

 at the maximum marginal utility of B he begins to spend on B. As 

 it is in the figure he " cannot afford it." 



The amount spent on any particular commodity depends on the 

 general water level, i. e. the valuation of a dollar, while reversely 

 the valuation of money depends on the total amount to be spent on 

 all commodities. 



Three conditions suffice to make the distribution determinate : 

 (1) that due to the forms of the cisterns, (2) the condition that the 

 total income equals a specified amount, (3) uniformity of marginal 

 utility (per dollar's worth) of each commodity. 



4. 



ANALYTICAL. 



Let A, B, C, . . . M be the (unknown) quantities of various com- 



modities consumed by I, and 



cm 



clTJ 



,,.... ^ their (unknown) mar- 

 ginal utilities. Let p^, p^, . . , p^ be their (known) prices. 

 Then the above three conditions become : 



(1) 



(2) 



(The unit of commodity is the dollar'' s worth.) 



\ A^„ + B/>4 



+ 



Trans. Conn. Acad., Vol. TX. 





cW 

 (IM. 



= F(M) 



y 



m equations. 

 2m unknowns. 



Mp^ = K j- 



1 equation. 



no new unknowns. 



July, 1892. 



