in the theory of value and prices. 



29 



the amount in any particular cistern. But, for the system as a 

 whole, the price level is a consequence of the amount of commodity 

 marketed. What appears as cause in relation to effect to an indi- 

 vidual is effect in relation to cause for the whole market. 



The quantities of commodity and the marginal utilities mutually 

 limit and adjust themselves, subject to three conditions, (1) that due 

 to the forms of cisterns, (2) that due to the total amount of commod- 

 ity marketed, (3) uniformity of price, or of marginal utility. 



ANALYTICAL. 



The algebraic interpretation of the preceding mechanism or of the 

 economic phenomena themselves is as follows : 



Let Aj, Aj, A3, . . . A„ be the (as yet unknown) quantities of the 

 commodity consumed by I, II, III, . . . IST. Let 



c?A/ dA^' ' dA, 



be their (unknown) marginal utilities. Then the three conditions 

 mentioned in § 6 become : 



(The unit of utility (util.) is that of the marginal dollar.) 



(1) 



r cfu 



dA^ 



d\J 



< dA. 





V 



S=^-(^") 



n equations. 

 2 n unknowns. 



(2) 



(3) 



1 2 ' 3 ' ' n I nn 11 PAW nnl 



no new unknowns. 



(Unit of utility is that of marginal dollar.) 



cW dJJ dV 



dJJ ) ?i — 1 independent equations 

 ^^ j no new unknowns. 



<^Aj dA^ dA^ 



Hence the number of equations is : 



n-\-l-i-{n—\)=27i 

 and of unknowns : 



271 + -\- 0=z27i. 



Therefore the numbers of equations and unknowns are equal and 

 all quantities and utilities are determinate. 



