SEMAINE D'ETUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC.

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of the coefficient matrix. This inverse matrix, or more precisely
the transpose of this inverse matrix, as shown in the previous
section, provides the link between the input-output type of
classification and the one which is needed in the present model.
This means that to pass from one classification to the other is
simply a matter of computation. The procedure, which has been
shown by (VI.3) with reference to the labour coefficients, remains
 exactly the same for the stocks of capital (or for the
series of capital-output ratios). In other words, after multiply-‘ng
 the transposed inverse matrix by the vector of the capital
stocks (or of the capital-output ratios) of each input-output
‘ndustry, we obtain the vector of the capital stocks (or of the
capital-output ratios) of each vertically integrated sector. The
‘ransposed inverted matrix appears, therefore, as the linear
operator which may be applied to a classification of labour
and capital according to the inter-industry relations, in order
to reclassify it according to a new type of vertically integrated
sectors.

In this way, each production process is reduced to one flowinput
 — labour — and one stock quantity—capital. The coefficients
 representing them do not correspond to labour or capital
employed in any particular firm or industry, since the whole
framework of intermediate relations has been consolidated; but
‘hey do represent all the labour and capital which are neces
sary to produce the commodity under consideration, in what:
ever remote corner of the economy they have been applied.
Formally, the new coefficients are, therefore, derived concepts
(derived from the consolidation of the inter-industry coefficients)
out they have a deeper economic meaning and, as will be
stressed in a moment possess more favourable characteristics
‘or a dvnamic analvsis

[10] Pasinetti - pag. 10I