384 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
~ 
an, 
Ans 
|— 
Py 
ry 
” 
(lg) 
A 
de, 
a, 1» — 
a, 7 
0 
| 
0 
| 
J 
The (a, a, .... a, ,_,) represent technical coefficients 
of production and the (a,,, a,,, .... a,_; ,) represent demand 
coefficients of consumption. An evident property of both these 
systems is that they have the same, but transposed, matrix of 
coefficients. As they have been defined, they are nothing but 
an algebraic representation of the flows which take place in 
the economic system under examination. However, they can 
be looked at in a different way. If we consider the a;’s as pa- 
rameters, then (II.3) and (II.4) form two systems of equations, 
and we can enquire into the nature of their solutions. These 
two systems are of a particular kind — they are linear and 
homogenous. Therefore, in order that they may have non- 
trivial solutions (i.e. solutions which are not all equal to zero), 
the coefficient matrix must be singular, namely it must 
satisfy the following condition (which is the same for both 
systems) (3): 
7 … 
Ton 
An) 
gg 
A, . 
(*) For shortness, the zeros will not be explicitly written from now 
on; so that all entries of our matrices which are left blank should be 
interpreted as zeros 
10] 
Pasinetti - pag. 1.