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 differen- 
tial 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 ge- 
neral 7 should be considered as a function of time. 
(?) These various formulae were first given in 1947 in mv studv Eco- 
nomy and Interest (1047), DD. I86-1RK 
11] Allais - pag. 48