456 lotka: objective standard of value 



civilized community spends a certain amount of labor and money 

 on sanitary measures, the function of which is to keep the param- 

 eters Xi, Xj . . . , say the death rates from diseases Si, Si, at 

 certain values Xj, Xj . . . Equation (3) for the distribution of 

 labor in different pursuits is in point of fact incomplete in that it 

 takes account only of labor spent in the production of material 

 commodities measurable in units of mass. To complete it we 

 must add to the right hand member a number of terms of the form 



Equation (3) thus amplified by (31) is now in a form which 

 covers in general all activities of a given species. For this reason 

 it is of value in the treatment of the general theory of the struggle 

 for survival, or in other words, the ''evolution" in a system com- 

 prising a number of different species of organisms. It is not pro- 

 posed to enter here into detail as regards this phase of the subject. 



Case II. Lastly it remains for us to consider the general case, 

 when coi is not a function of 77ii alone, as we assumed above, but 

 when 



0)1 = coi {nil, W22 . . .), C02 = 0)2 {nil, mi . . .), (32) 



In other words, we now regard the marginal ophelimity of com- 

 modity Ai as depending not only on the rate of consumption of 

 A\, but also on that of the remaining commodities. In this case 

 the total pleasure derived from the production and consumption of 

 the increments dnii, dmi ... of commodities ^i, ^2 ... in 

 general depends, not only on mi, m2 . . . , but also on the "path, " 

 i.e. on the order in which the several commodities are produced 

 and consumed. 



We can here still write 



dfi = (o)i pi + oj'i p'l ) dLi + . . . 



but we cannot simply put, as before. 



In fact, the value of the partial differential coefficient is in 



dm, 



