412 lotka: objective standard of value 



is the additional pleasure^ derived from the consumption per 

 unit of time of a small increment drrii of the commodity Ai, and 

 if co'i dfi is the additional pleasure (negative in this case, i.e., 

 pain) derived from the concomitant production per unit of time 

 of a small increment dji of fatigue per unit of time incurred in the 

 corresponding increment dL-, of labor per unit of time, then the 

 total additional pleasure d 9, derived from the production and 

 consumption per unit of time of the increments dmi, dm 2 .... of 

 commodities Ai, A2 . . . is given by 



d Q = CO 1 dm 1 + CO 2 dvi 2 + . . . 



+ Co'id/i + C0'2d/2 + . . . (1) 



Case 1 . We shall consider first the simple case in which coi is a 

 function of rrii only, C02 of m^ only, etc.; i.e. the pleasure of pro- 

 duction and consumption of any one commodity depends only 

 on the amount of that particular commodity produced and con- 

 sumed per unit of time, and is independent of the production and 

 consumption of other commodities. In that case we can write^ 



CO, = CO2 



dwi dm2 



, dfi , dfi 



CO 1 = CO 2 



(2) 



and 



d/, d/2 



do. = ~ pi dLi-\- p-, dL-i-\- 



'drrii dmo 



■ dfi , ,^ , dfi / 77- , 

 d/, d/2 



(3) 



The condition for a maximum of the total pleasure fi is evi- 

 dently that the right hand member of (3) shall vanish for all 

 arbitrary values of dLi, dL^ . . . . , or 



* wi is the marginal ophelimity of commodity Aj. (Pareto, Manuel d'Economie 

 Politique, 556. 1909.) 



' The function fi defined by equations (2) and (3) measures total ophelimity. 

 (Pareto, loc. cit.) 



