886 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2K

umptions would no longer be acceptable if the population
declined to a point where sectors experiencing increasing returns
 became dominant (1).

The General Case

421. These results are completely independent of the hypotheses
 concerning the function 3(8) providing that the assumption
 be made that y is constant, at least as a first approximation.

In fact, it has been shown that for any quasi-stationary
process with steady growth. we have

(421-1) I dR 1 dc.
4 RU C7

&

so that from relation (110-1) We have

(421-2)

Ra=(1-0oy)R

whence for k=1 and at least as a first approximation (*)

(421-3)

R =(1 —0 Y)R

!) ALLAIS (1963): Some Analytic and Applied Aspects of the Theory
capital.
(*) Relations (123-2) and (132-2)
(3) Relation (229-2).

:1] Allais - pag. 190