52 having Fisher — Mathematical investigations 



ates in a uniform percentage without loss or gain of commoditj^ In 

 this case the price of A will decrease while that of all other articles 

 will increase exactly alike.* The valuation of money will be re- 

 duced since the ordinate of a B cistern (sa}^) has not changed while 

 its back thickness has increased. The changes just considered may 

 be brought about if A suddenly goes out of fashion. 



Perfectly analogous changes occur if a cistern or cisterns become 

 narrower. The individual is then more keenly " sensitive " to 

 changes of quantities. This change may occur through a discovery 

 by which a little of the commodity is made to " go farther " than 

 before. 



Reverse changes occur if cisterns are broadened or deepened. 



§9. 



It is impossible to combine all the A cisterns into a single demand 

 cistern for A as was done in Ch. II or to combine all the I cisterns 

 into an income cistern as in Ch. Ill, for we can no longer overlook 

 the influence of other commodities and other individuals. The 

 analysis therefore which treats of but one commodity at a time and 

 constructs a demand curve for it is a superficial one for it does not 

 reach all the independent variables. 



§ 10. Analytical. 



Suppose there are n individuals and m commodities in our given 

 isolated market during the given period and suppose the amounts 

 of the commodities A, B, C, etc., are given K^, Kj, K„ etc., and the 

 given incomes of I, II, III, etc. are K^, K^, K^, etc. Then the con- 

 dition that the commodity-sums are given is: 



A^ + A,-f-A3+ -f-A„=K, 



B, +B,-fB3+ +B„=K, 



C, +C,+C3 + +C„=K, 



M, + M, + M3-|- +M„=K_ 



m equations. 

 mn unknowns. 



* For their mutual ratios cannot change since the ordinates to which they are 

 proportional do not. 



