in the theory of value and prices. 



53 



The condition that the incomes are given is: 



The utility functions (the cistern-forms) are: 



n equations. 



m new unknowns 



(prices). 





The principle of proportion is: 



dJJ 

 dM^ 



d\J 



' ^M =^(^^^-> 



'sr^w '^ 



c^U 



c?M 



l-=F(M.) 



m?i equations. 



^2^ new 



unknowns 



(marg. ut.). 



dV 



dJJ 



dV 



dJJ 



"\ 



dA^ 



' ^B, 



cTC . • • 



' ' dM^~ 





dJJ 



dV 





dU 





'dA, 



■ dB\ 





' ' c?M, ~ 



• : Pn. 



dV 



dJJ 

 dB„- 



.... 



dJJ 



71 (in — 1) 



independent 



equations. 



no new 

 unknowns. 



Total number of equations : ni + 7i + 7i) n + 7i {in— I) =z 2'mn + 7n 

 " " unknowns ^7^?? -|- m + ^^?^ + = 27nn-\-7n 



Therefore all magnitudes are determinate and the number of these 

 magnitudes as well as the number of the equations is twice the num- 

 ber of commodities times the number of individuals j^lus the num- 

 ber of commodities. 



The valuation of money for each individual can be found from 

 the equations: 



dV 



IF == ^^, (Ch. IV, § 2.) 

 d)n^ p. 



dJl 



dm^ 



=. etc. 



