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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
Hence we have from (45) 
46) 
a: 
dr 
> 0. 
In words, a biased technical improvement which a substitution 
of by; for a, accompanied increases the ratio of the value of 
output of industry % to that of industry i. It is also seen 
from (40) and (46) that the amount of labour used by industry 
k is increased in comparison with the amount employed by 
industry 1. 
4. A similar argument may be applied to examine effects 
of a technological change of the capital-saving type. Suppose 
a substitution between a,; and b,; in favour of a,; accompanies 
an increase in F;. Differentiating (10), we obtain (41) and (42), 
dby; . : — — 
where 7F 1s now negative. Let r be the value of # which 
makes m;=0. We shall arrive at the following final results: 
(47) 
(48) 
d log v, dlog f; 
JF. < 77 SO 
a, 
— -_-<O0. 
a= 
1f 
#C 
ld 
(47) states that when industry ? makes a technical improvement 
which saves the capital good k, and is greater than r, then 
the prices of all goods (in terms of labour) will diminish, and 
that of 7 will do so by the largest percentage. (48) implies that 
‘9] Morishima - pag. 26