5642 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
These coefficients, however, cannot be taken as exogenously 
given. How they are determined will be discussed in section 4. 
At time zero, since the system is in equilibrium, all demand 
coefficients considered together are such as to require the full 
utilization both of the labour force and of the existing pro- 
ductive capacity. 
B. Movements through time. — As time goes on, the fol- 
lowing movements take place: 
a) population increases at a steady percentage rate g, 
so that 
(V.I) 
X,#)=X,(0) e¥ ; 
b) productivity changes at a particular percentage rate of 
change in each sector. It will be assumed that these rates of 
change (p;) are different from one sector to another but that 
they are steady through time in each sector. This means that 
(V.2) a(t) =a,;(0) € 
at ; (2) =a, (0) eo 
1=T. 2, ... (n-1). 
Most p;'s and Pr, 8 (j=1, 2, ... n- 1) are positive, but a few 
of them (referring to those sectors where the exhaustion of 
natural resources is particularly heavy) might be negative: 
c) per-capita demand changes at a particular percentage 
rate of change for each commodity. We shall denote these rates 
of changes as r, ({=1, 2, ... n-1). The r;s are not constant 
over time; they change as a result of a very complex process, 
as has been explained in the previous chapter. The #,’s as such 
are not exogenous magnitudes. in our analvsis. What has been 
10] Pasinetti - pag. 72