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 construction.
 If we have this information, then, again, we can rewrite
(IV. 4) in an appropriate way. The information is important

1] Stone - pag. 43