SEMAINE D'ETUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC

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 substitution
 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 industry
 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 industry
 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