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, re- 
mains 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 flow- 
input — labour — and one stock quantity—capital. The coeffi- 
cients 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