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