I

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

and, using relation (117-14) we deduce

(117-16)

1 3R
E R

/ 5 (8,i)e'®do

©(8,i) de

TTT

In fact, in relation (117-15), the prices of the different factor
inputs are equal to the exponentials ¢®. The function A(:))
characterises the distribution of factor inputs. But, while ¢(0)
is of course a function of 7 it has not been differentiated with :,
since in the expression (117-16) the Sp play an analogous
role to the 8Y in relation (117-10), and since in this relation
the y are regarded as constant (*).
Thus the relation (114-16) also enables the expression for
the differential of real income to be deduced from the differential
 of the characteristic function, and we have in particular

(117-27,

(8,i)e'’de

(7

0.2)d 0

() Of course this does not mean that i is independent of time. In general
 7 should be considered as a function of time.
(?) These various formulae were first given in 1947 in mv studv Economy
 and Interest (1047), DD. I86-1RK

11] Allais - pag. 48