606 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
We shall consider in this chapter the simplest of all cases 
of dynamic change. We shall assume that, as time goes on, 
the only « exogenous » factor which is moving is population. 
This simple case has been extensively dealt with already in 
current economic literature, and the purpose of the present 
chapter is not, therefore, to obtain new results. The purpose 
is simply to evince the connections with the known growth mo- 
dels and at the same time to develop formulations which will 
be needed in the following analysis. Our assumptions may be 
listed schematically as follows: 
a) first of all, the initial conditions are such that, when our 
analysis begins, at a time defined as zero, the system is 
operating in equilibrium. There is full employment of la- 
bour and full utilization of productive capacity; 
b) as time goes on, population increases at a steady percentage 
rate g, so that 
111.1) 
X,(t)=X, (0) eë 
where ¢ denotes time, and e is the well-known base of the 
natural logarithms; 
technical conditions remain fixed over time; expansion takes 
place at constant returns to scale. In other words, all 
technical coefficients (the a,’s, the a, s and the Ts, 
i=1, 2, .... n— I) remain unchanged in time; 
1) consumers’ tastes also remain constant, which means that, if 
individuals continue to receive the same income, their con- 
sumption — i.e. all the coefficients a;,’s, ¢=1, 2, .... (n-1) 
— remain constant through time. 
>) 
These are all the assumptions that are needed, besides of 
course the convention (discussed in section 6 of the previous 
chapter) of taking the rate of profit as given. The reader may 
‘101 Pasinetti - pag. 36