SEMAINE D’ETUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 64y 
These relations define equilibrium investment in each single 
sector, and therefore their sum defines total equilibrium invest- 
nents in the system as a whole. As can be clearly seen, equi- 
librium investments, in physical terms, are exclusively deter 
mined by the expansion of demand. 
Yet, as we know, the actual undertaking of all these invest- 
ments only provides the required productive capacity, i.e. po- 
tential full employment. For the system to reach full employ- 
ment, a further macro-economic condition about total effective 
demand must also be satisfied. 
In mathematical terms, all this is expressed by the fact 
‘hat conditions (V.g) only come to complete the two systems 
of equations (II.g) and (II.13), by defining at any point of 
ime the series of coefficients (demand coefficients for new in- 
vestments) which was still missing. But the two systems of 
equations, thus completed, are of the linear and homogeneous 
type, and their coefficient matrix must be singular if they are 
‘o yield non-trivial solutions. This condition of singularity, 
which was expressed by (II.20) with reference to a particular 
period of time, must now be kept satisfied over time. After 
substituting (V.q) into (II.20) and after explicitly expressing 
‘he movements of the coefficients. we obtain 
V.11) 
1,,(-0) a, (1-9) eri—ed. 
+247.) apai-0) a, (1-9) erro 
Pl 
which finally represents, under our present hypotheses, the 
effective demand condition for keeping full emplovment over 
time. … 
This expression, as pointed out earlier, refers to the eco- 
aomic system as a whole. The effect of substituting into it 
sxpressions (V.q) is that now (V.11), besides stating the general 
[10] Pasinett: - pag. 79