018 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

When K grows from zero to infinity, A grows from 3/4 to 1,
so that

(515-16)

3/4

In all cases it can be seen that a sufficiently rapid decline
in the w,_; will result in a value of A relatively near to 1.
From this, it may be deduced that in this case the properties
 of the model will not differ greatly from those of the exponential
 model.

Case in which the w__, vanish bevond a Certain Rank

516. Now examine the case in which the »,_, vanish beyond
a certain rank and assume that

516-1)
w, 4 =0

for

n>b+l

a) Case in which all w__, are of the same order of magnitude

Assume firstly that all w,_, are of the same order of magnitude,
 for example, that they are all equal.
Then from relation (512-14)

(516-2)

—

pi ple]
ES

2 vad J

(22)

'11] Allais - pag. 222