+4 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2é& 
where pis the greatest integer that multiplied by s and sub- 
tracted from ¢ leaves a positive remainder (8), the movements 
through time of the demand coefficients may be written as (?) 
‘V.q) a. (D=a. (t-0e®. 1=1,2, ... (n-1), 
where each 7; is an f; function of the technical coefficients and 
now also of (£-0). In order not to complicate the notation 
excessively, this functional dependence is not explicitly written 
in (V.4), nor will it be written hereafter, but it must always 
be taken as understood. 
Of course, the same notation in terms of 8 can be used also 
in formulations (V.1) and (V.2), and this will be done, in the 
following analysis, any time it is required by reasons of sym- 
metry. 
2. A few restrictions 
First of all, it may be useful to impose a few restrictions on 
the coefficients of our system. These restrictions do not imply 
anything new and in fact have always been implicit in our pre- 
vious analysis. We only make them explicit now for the sake 
of rigour. The reason for these restrictions is that our mathem- 
atical terms are very general and their generality needs to be 
limited to the range in which it has economic sense. 
(?) As explained in footnote (1), demand coefficients represent average 
per-capita consumption. No discussion is carried out here about possible 
complications arising from a changing distribution of income among indi- 
viduals or from a changing composition of the population as regards sex 
and age. Evidently, the simplest way of interpreting our analysis is to 
suppose that both these features remain invariant in time. However, even 
if they should change, their changes can be neither quick nor big. In any 
case, they would not affect the conclusions of the following analysis because 
their effect would simply be to anticipate or postpone turning points. 
without altering the nature of the trends through time 
10] Pasinetti - pag. 74