752

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

From (110-10), (122-1) and (123-5) we have

© Li'l
(123-8) | £ = T (0) db = y. [Fer (ng) df
0 Jo

Thus developing (123-8) as a Taylor series

ow [ 2 3 - i ,
(123-9) / | Or due [poas=1. / | Ly
“0 2! 3! o L 21

bz 8
2

+. [a(@y dé

Thus from (112-1)

(123-10)

‘oo ge 2 8
sou t fPTa8 84 Jos
Ce vA 2 31!

and finally

(123-11)

Yeo 0 - [7
T—7 — + =; vo 4
74, #1 (e** — T — 7’6)p(6)d6

Thus necessarily

(123-12) 0 s— To _
L— (1-Pp) Ye

for 1-o0>o0

Whatever the function ¢(8) this inequality is very important
for empirical analysis.

11] Allais - pag. 56