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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

1. The conditions for a dynamic equilibrium

According to our assumptions, when our analysis begins
(time zero), the economic system we are considering is in equilibrium
 — there is full employment and full utilization of productive
 capacity. We know already that, if this equilibrium
situation is to be kept, two types of conditions must be satisfied.
First of all, since both population and technology are changing,
 the system must continually enlarge its productive capacity
 so as to keep up both with the increasing demand and with
the increasing labour force. This means that, in each sector,
a very definite relation must be satisfied between new investment
 and the rate of change of the corresponding final demand
for consumption goods. The problem has been discussed already
 in section 2 of chapter III. By following here exactly the
same procedure. the mentioned relations emerge as

(V.8) A, ,(t)=(g+r;) a,,(t), 1=1. 2. ... (n-1)

which represent the capital accumulation conditions for keeping
 full employment over time.
After explicitly inserting the dynamic movements of demand
and of population that have been postulated, the (V.8) mav also
be written as

(V.9) a, (BO =(g+7) a,(t-0 gard

or, if we refer them to total net investment in each sector (instead
 of referring them to per-capita investment), they may also
be written as

(V.10) Xpa)=(g+7) X, (t- 0) a,(t-0) 9+"

(10] Pasinetii - pag. 78