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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