196 
BIOLOGY: A. J. LOTKA 
Proc. N. A. S. 
penditures as to procure for himself a maximum of pleasure. So, for 
example, if the choice lies between two commodities Ci and C 2 (which may, 
in particular, be certain forms of energy) he will purchase quantities 
qi and q 2 , respectively, such that, if his total pleasure derived from the 
purchase is ft, then 
bfi , , m A _ . 1A 
5^ + 55** = ° CO 
where dq h dq 2 are small, arbitrary increments in the quantities of the 
commodities Ci, C 2 purchased. If pi, p 2 are the prices upon the open 
market, say, per unit quantity, of commodities &, C 2 , respectively, then 
evidently the corresponding increment in expenditure is pidqi + p2dq 2 . 
But the sum of money to be spent is fixed. We must have, therefore, 
pi dq x + p 2 dq 2 = 0 (2) 
It follows, then, from (1) and (2), that the individual will so apportion 
his purchases, that 
dqi I dg 2 p2 K 
If the commodities Ci, C 2 are "necessities of life," whose influence upon 
the life of the species is to increase r, the proportional rate of increase of 
the species, then, evidently, the interests of the species demand that the 
purchases be so apportioned as to make r a maximum, and thus, by similar 
reasoning, to make 
dqi I dg 2 p2 
If we regard the sense of values as a device for attaining, as nearly as 
may be, the adjustment (4), then we see that a perfect sense of values would 
make 
b£ / cK2 = br / Sr_ . 
bqi I hq 2 bq t / bq 2 
So that, in a community of organisms endowed with a sense of values thus 
perfectly adjusted, the marginal utilities ^ (and hence the prices on 
an open market) would be proportional to the partial derivatives ^- . In 
practise this proportionality will not be actually reached; but it repre- 
sents the limiting state towards which a race must tend to evolve. For, 
a race having tastes radically at variance with the exigencies of race 
propagation (measured by the rate of increase r), could not long survive, 
as pointed out years ago by Herbert Spencer. 4 
It is this tendency to approximate (perhaps somewhat remotely) to the 
adjustment (5), which gives rise to fairly definite economic interconversion 
factors of different forms of energy, as purchased upon the market, and 
applied to specific uses. There is no need to invoke a specific "economic 
