328

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2

Any hope of doing this is illusory, since it has been shown
hat whatever the function 3(8), for small values of à and © we
have

(331-2)

0 ~ ry,

(1)

In practise, the rates à and p are quite small and it is therefore
 practically certain that the order of magnitude of the
value of © should be about the same as yc. But if this concordance
 does occur in fact, it only shows that the reasoning
based on the composition of the working population is correct;
in no way does it demonstrate the validity of the model proposed.
 This demonstration would only be possible if the determination
 of the function ¢(8), and therefore of ©, from the
composition of the working population, could be done accurately
 enough for the difference yc- © itself to be determined
sufficiently precisely. As has already been noted, this is an
undertaking which appears to be impossible, at least in the
present state of knowledge (?).

The Influence of the Function [3(0)

332. It is interesting to examine what the results which
correspond to the exponential model become when a non-expoaential
 expression is used for B(6).
Appendix I contains a study of the case in which the quite
acceptable hypothesis is postulated that B(8)e*® can be repre-(")

 Relation (227-6).

For i=-n=0, we have
mn

3) § 312 to 314.

‘111 Allais - pag. 132