lotka: objective standard of value 



417 



Now equations (11) and (14) are satisfied by the same values 

 of TTii, 7712, . . . , /i, /2, . . . , provided that 



dr 



drill 



Pi 



dr 

 dm2 



Pi 



dr , dr , 



P 1 = — P 2 = 



F&)^p. 

 orrii 



F (n) ^ p. 



= -F(n)^p\=-F(Q)^p', = . . . 



5/l C)/2 



where F (fi) is an arbitrary function of 12. 



We may conveniently select for the function F the form 



(15) 



(16) 



F (fi) = constant 

 Then we have by (12), (13), (15), (16) 



dr dr 



1 



(17) 



Vi : Vo : . . . : V ] V 2 



drrii drrii 



dr 



dr 



(18) 



or 



1 r dr 1 , dr 



Vi = k ; — , V2 = k 



drrii 



dnii 



v\ = k 



, dr 



(19) 



where A;' is an arbitrary constant which appears wherever we are 

 dealing with values in exchange, and the signification of which is 

 that the choice of one commodity as standard of reference always 

 remains arbitrary. In the present case it will be most convenient 

 to fix the value of the constant k' arbitrarily by putting 



k' = 1 



(20) 



The value of the constant k which appears in equations (12) 

 and (13) depends on the units employed in measuring marginal 

 ophelimities. It will be simplest to measure these directly by 

 the corresponding values in exchange, in which case we have 



k = 1 



(21) 



We have then for the "true" values in exchange and for the 

 corresponding "ideal" ophelimities (i.e. those attached to the 



