SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 
where E denotes an operator which advances by one year the 
variable to which it is applied, so that Ee denotes next year’s 
consumption vector; I denotes the unit matrix; and y denotes 
a diagonal matrix of the growth rates of the components oi 
consumption. 
It has been shown in [7] [43] that on these assumptions 
(IV. 4) 
U 
5 KI y5 
4! 
This is the relationship we need. It has been shown in _«/ _ 
that the infinite sum in (IV. 4) will converge provided that the 
largest element of » does not exceed the smallest latent roof 
of K(I- A)-!. This problem is also discussed in [17]. 
If the components of consumption are assumed tc grow 
linearly rather than exponentially, then (IV. 3) is replaced by 
(IV. 5) 
i.e = (I+ 07) 
and (IV. 4) is replaced uy 
(IV. 6) 
v=K(l- A) ‘we 
which is simply the first term of (IV. 4). 
It has been shown in [7] that (IV. 4) is capable of two 
generalization. First, if technology, as summarised in A and 
K, is changing in a known way, the expression corresponding 
to (IV. 4) can be derived. Second, if allowance is made for 
different investment lags, then (IV. 2) must be rewritten. To 
do this we need information about the work that must be done 
on investment goods in the successive years of their construc- 
tion. If we have this information, then, again, we can rewrite 
(IV. 4) in an appropriate way. The information is important 
1] Stone - pag. 43