394 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - ”R

For the maximum value Rg, of the real national income consumed

 we find

(251-17) Rom = «(/) Safe —kBy0

where e is NAPIER’s constant, and o(#) and R,(f) are given. This
formula enables the influence of p on the maximum value Rom to
de studied (§ 420-421). |
The expression obtained for R,/Rg,, is very interesting since it
depends only on two unknown quantities k and ®, But it is easy
to show that the order of magnitude of k and ©, are respectively 1
and y. which is a statistical datum.
The expression for Rg, shows that of all the processes of
growth (p>o0) the most advantageous one is that for which the rate
of growth of primary income is zero.
For small values of the rates i and p it is possible to expand the
different macroeconomic’ quantities as TAYLOR series as functions of
hree constants k, 0, and A if the first terms of the TAYLOR expansions
 only are considered (§ 220, 240 and 241).
In particular

Re k 2 (7 2
251-18) RIT 78 (7— p)

5) If we assume, as is quite natural, that the elasticity 8(0) is
decreasing exponentially i.e

(250-5)

8.
ke

11] Allais - pag. 298