416 lotka: objective standard of value 



Definition. Relative to a given species, those are the true or 

 objective values Vi, V2 . . .of commodities Ai A2 . . . , the 

 adoption of which by the species would make the adjustment of 

 feelings to actions perfect, or, in other words, would make the rate 

 of increase of the species, under existing conditions, a maximum. 



This definition now enables us to obtain directly a mathematical 

 expression for the '' objective values" of a set of commodities. 

 For if, as before, the representative individual has the choice of 

 distributing his energies in the production of commodities A,, A2 

 . . . , and if r is the rate of increase per head and per unit of 

 time, of the species, the distribution of labor leading to a maximum 

 rate of increase of the species is given by 



^^ + ^_<'/LldL.+ j^*5L+^i4|dL,+ . . . .=0(11)' 

 dwi] dL, d/i dLj ) i dm2 dLo d/2 dLo) 



for all arbitrary values of dLi dLz .... 

 But if we denote by 



Vi = /cooi = /v .,Yo=ko)2 = k -, . . . . (12) 



^m^ bnii 



the true values in exchange of commodities Ai, A2 . . . , that is 

 to say, those which would prevail if the individuals had a perfect 

 sense of values; and if we similarly denote by 



y\=kZ:\ = k~,Y".=k^'2 = k^, .... (13) 



the true values (in exchange) of fatigue Ji, fi . . . , then by our 

 definition of "true value," the same distribution as defined by 

 (11) must also be given by 



^'l""+^-<^:^i|rfi,+ |-^*^ + AS * bL.,+ . . .=dQ = U(14) 

 dm, dLy dfi dL^ J ( dm^ dLz d/2 dL^ ) 



for all arbitrary values of dLi, dL^, etc., equation (14) being 

 simply a special case of equations (3) and (4) . 



dr . dr . 



^ It is here assumed that ^;— is a function of mi only, c — a function of mz 



Onii Oniz 



only, etc. The more general case where this is not the case will be considered later. 



