394 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - ”R 
For the maximum value Rg, of the real national income con- 
sumed 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 expan- 
sions 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