362

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -

28

Values of @ for y,=3.5 and i—p=4%

“a

D

3.5
3.5
3.5
5
5
3.5

0.05 | 0.10 | 0.14 | 0.25

3-5
3-50
*.48
?,42
:-22
2,37

3-5
3-50
2.48
2.39
13
III

3-5
3-51
2.48
- 30
oO

3-5
3.52
2.50
= 42

Bi

0.5 | 0.75 ,

3.5
1.56
56
221
51
3.44

3.5
3.59
2.62
2.64
2.66
3.66

3-5
3.63
3.68
3.72
3.74
1.77

Le

3)

6

Yc (f—p)—ow
(1—w)(—p)

le __ _ ©
—w (1—w)(i—g)

whence

4)

0 < 0 .

I —

Yo (à — Ç)

b) yeli—p) < vw < 1.
T tends to zero and from (536-1), we have
0 — 7 —
9 PTIT ,T
I — (I —p)

5)
so that

I I—w i — p)l
((—p)L I—Yl—P) ©
Here, © can tend to any value according to the value of w.
For en=1 we have

(i-This
 is the same limit as for ©.

7)

=

T

GLI 1e =o

c) w= Yc(i—p).
Here T again tends to zero and relation (536-2) gives
8) AewT
Thus ®, tends to zero.

i1] Allais - pag. 266