306 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
to be added to a basic rate of profit. Thus system (II.12) 
becomes 
11.15) 
=} 
Un. 
+ 1 
Brat 
" T,_,) 
Anne 1 
Auk, 
a, 
Ain +++ 00 Anim (an 0 —11 ay,) i (ar, _ n=Tn1 An_1,n) - 
| =i 
p, | 
P. J 
P,, 
D 
“kp 
7 
al 
Û 
QO 
Here again we have obtained a system which is linear and 
homogenous. The coefficient matrix looks different from the 
matrix of (II.g). However — interestingly enough — the 
determinants of the two matrices are exactly the same, as can 
be easilv demonstrated (5°). The condition for non-trivial so- 
1 
(°) The determinant of the matrix of (IL.g), after substituting the T 
for the a, ; ‘s comes out as: 
€ 
D2 Wi Tin + 5 Tor Arn + 2 T Anh, Uin —_ 1 
and the determinant of the matrix of (II.13) as: 
Dani in + > (ann — TiQin) px, + 2 (= + +) in A, 
i 
This second expression clearly reduces to the first by expansion. We obtain: 
>a, a, + 2%, App + > + din Un, — DT: in App, + ST Ai A, — I, 
where, as can be seen, the last two summations cancel out. 
10] Pasinetti - pag. 26