586 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
each commodity, so that (II.6) say that production of each 
commodity exclusively depends on demand. If there were no 
demand, there would be no production. On the other hand, 
each of the coefficients (a, a, ... a, ,_;) expresses the labour 
imput in each physical unit of output, so that (II.7) say that 
the price of each commodity is directly proportional to the 
quantity of labour required to produce it. In other words, 
prices, in this simple case, are explained by a pure labour 
theory of value. 
3. À necessary condition for full employment 
Condition (II.5) will recur time and again in the subsequent 
analysis and we may well investigate its economic meaning 
immediately. 
From a mathematical point of view, the fulfilment of (II.5) 
is a necessary condition for each of the systems (II.3) and 
IT.4) to have positive solutions. However, non-fulfilment does 
not imply no solution. The coefficient matrix of (II.3)-(II.4) 
has a particular form (all its entries are zeros, except on the 
last row, on the last column, and along the diagonal), which 
means that the solutions of the systems can be derived directly, 
without substitution, from the first (7 — I) equations of (II.3) 
and from the first (n- I) equations of (II.4) respectively. 
Therefore, relative prices and relative quantities are determined 
independently of condition (II.5), whose binding restrictions fall 
entirely on the last equation of each of the two systems. Let us 
n—l 
see what this means. Suppose, for example, that > a,; 4, CI. 
i=1 
This inequality implies two things. In the context of system 
(IL.4) it implies (3) that Za, P,<P,, namely that average per- 
() From now on, for shortness sake, the limits of the summations will 
be omitted. In other words, all summations that will appear in our analysis 
have to be interpreted as running from 1 to (n—1), unless otherwise specified. 
10] 
Pasinetti - pag. 16