550 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2§ 
As x'P! is proportional to x°P°, we find that the technical 
change does not affect the distribution of labour. 
3. Let us now examine effects of a technological change of 
the labour-saving type. Suppose an increase in F, gives rise 
to an increase in b;; and a decrease in a, other parameters 
remaining unchanged. We assume that the constant returns 
to scale prevail before and after the technical invention. 
Taking account of the fact that b,; and a,; are functions of 
F, fulfilling (2) and remembering the definition of G,, we obtain, 
by differentiating (10) and solving, 
(41 
dlogv _ 1 
dE = = (I —a—0b) M, 
where M; is a column vector such that its i-th component ms, is 
, i I +7 , d by; 
(42) m=+ + log | (4, HT) / (Moi 0.) “ZF. 
and all other components are zero. We have db,;/dF,>0 by 
the definition of the technical change of the labour-saving type. 
I+r 
But (by, rd) /(a,v;) many be greater or less than unity. As was 
k 
shown in Section 2, v, increases when 7 increases. This to- 
. . . I+ . ee 
gether with 1>d, implies that (b,; SF )/(@ojV;) is à diminish- 
k 
ing function of r; it may take a value less than unity when 7 
is large, but greater than unity when small. 
When wm. is positive, we have from (41) 
dcr ov 
gu °° 
9| Morishima - pag. 22