SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 547 
a technical change of the class (1) would not give rise to any 
effect on the capital-labour ratio of industry ¢ (6), while that 
of the class (2) (or (3)) would increase (or decrease) the capital- 
labour ratio of industry i. We may, therefore, call technical 
changes of these three classes neutral, labour-saving, and cap- 
‘tal-saving respectively. 
It is true that we may also conceive of a technical change 
such that a substitution is made between a,; and a,;. We have 
a technical change of the material-using type if the substitution 
is in favour of a;;, and of the material-saving type if it is in 
favour of a,. To these cases the following analysis of the 
biased invention can be applied mutatis mutandis. 
2. Let us first be concerned with a technological change of 
the neutral type. Suppose F; to vary, other parameters and 
he rate of interest remaining unchanged. We have from (10) 
37) 
; 107 
[4 
J 
where d log v/dF; is a column vector with components 
d log v;/dF; (j=1, ..., n) and J; is a column vector whose i-th 
component is 1/F;,, while all other components are zero. Since 
a+b is a non-negative matrix whose row sums are less than I, 
it is shown (7) that (I- a - b)-">o and that the i-th element 
of the main diagonal of (I-a- b)-! is greater than any off- 
(®) We see from (4) that the capital labour ratio of industry i (at the 
constant prices $,°, a,° a. is 
-ki 
EX bu 9 qx 
oO 
Aoi pel Par 
() MErzrer L. A., 4 Multiple-Country Theory of Income 
journal of Political Economy », LIX (February. 1951), D. 2: 
Éransfers., 
9] 
Morishima - pag. 10