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converted them into demands for industrial products and for
each product have calculated the growth rate which would
accompany a given growth rate in consumption as a whole.
The first relationship we have to consider connects this inform-
ation with the investment demands of industry. We can ignore
replacement demands since, until we improve our production
functions, these depend, as I have said, on past investment
and on the fixed life-spans assumed for different assets. We
need therefore a relationship connecting consumption demands.
and their rates of growth with industrial extensions.
To obtain this relationship, we first write the basic flow
equation for products in the form
(IV. 1)
q=Ag+v+e
where q, v and e denote respectively vectors of output, in-
dustrial investment and consumption, and where A denotes a
current input-output coefficient matrix. Equation (IV. 1) states
that output is divided between intermediate demands, Ag, and
final demands, (v+e); and that final demands are divided
between investment demands v, and consumption demands, e.
Second, we write the relationship between investment de-
mands and the growth of output from one year to the next in
the form
(IV. 2)
v=KAg
where Ag denotes the excess of next year’s output over this
year’s output and K denotes a capital input-output coefficient
matrix.
Finally, we consider the case in which the components of
consumption are to grow exponentially. This can be expressed
in the form
IV. 3)
Ee= (I+7)e
I] Stone - pag. 42