192 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
-- CASE OF A CONSTANT RATE OF GROWTH 
OF PRIMARY INCOME 
Hypothesis (c): Constant ç 
230. It is impossible to obtain simple expressions for o(t, 0) 
and Ro) in the more general case where ç is a function of t, 
and it does not appear that invariance of p, or its equivalent, 
invariance of the function af, 6), can be deduced solely from 
hypotheses (a) and (b) (*) (3. 
Thus we are led to pose the constancy of p and therefore 
of 1 as a new hypothesis. 
The Functions (t, 8) and Ra(t, 
231. If the supplementary hypothesis is made that the rate 
of growth p(#) is constant, i.e. that the process considered is 
a quasi-stationary process with a constant rate of growth of 
primary income, the functions l(t, 8) and Ro (2) can be spe- 
cified. 
(Y) § 210 and 211. 
(?) Nevertheless it may not be impossible to show that a constant value 
of p is a necessary consequence of the general hypotheses made in my 
Cambridge paper, from which I deduced the asymptotic property of inva- 
riance of i(t)—p(#), and hypothesis (b). This point still requires further 
slucidation. Up to now. it has not been possible +0 make this demonstration. 
it] Allais - pag. 96