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where A’ is the transpose 
vector of net outputs, then 
x 
if we use 
vv to denote the 
(IV. 10) 
J 
on premultiplying (IV. 9) by q. The elements of y are now ti. 
be related to the labour and capital inputs they require. 
In our original exposition [7] (where, incidentally, we did 
not distinguish between q and y), we proposed to relate outputs 
to primary inputs by a modified form of the CoBB-DoUGLAS 
function. This modification, proposed by PITCHFORD in [31] 
and by ARROW and others in [1], is designed to generalise 
the CoB-DoucLas function so that the elasticity of substitu- 
tion between labour and capital, though still a constant, need 
no longer be numerically equal to one. This type of function 
can be written in the form 
(IV. 1... 
y. 
— Lt 
0 {. Vs 
+ 
where the suffix s denotes the s’th element of each vector. 
Thus y, denotes the net output of industry s, and /, and k, 
denote respectively the inputs of labour and capital into in- 
dustry s. The three parameters a, b, and c, can be given an 
economic connotation: a, is associated with the efficiency with 
which labour and capital are used in industry s; b, is associated 
with the shares of labour and capital in the net output of in- 
dustry s; and c, is associated with the substitution of labour 
and capital in industry s. The elasticity of substitution between 
labour and capital in industry s is equal to (1 +c,)7", and so, 
as c,>o (IV.11), approaches the simple form of the CoBB- 
DoucLAS function. 
1] Stone - pag. 45