8a
We find then that
( ft - ¿f ) ( q - q 0
(6)
This equation yields an implicit determination of the
quantities produced, given the capitalists''outlay and
the price-cost relations in the various production lines.
It is thus an implicit multiplier equation.
We now introduce the vectors production capacity q*
( q K. q* ) and utilisation u ( u ^ 1 ) .
/W
For each product separately, i.e. for each element of the
vector q we have the definition
u q* = q and (7)
u q* ■ q Oujm. fnivoJi, -yi/friwt- frv* UaMiAi
and therefore
(9)
identically for each element of the vector,i.e.for eachproduct,
We can now substitute this in (6):
( u - u Q ) q* = ( q - q Q )
{ fi - T ) ( u - u ) q* = I ^ C.
' do)
Here (u-u Q )q* is one vector, not a vector product.
Let us now divide both sides of (10) by Y* = /3 q*,
the capacity of the total economy in terms of money value.
The vector product on the left hand side of (10) now
consists of additive terms of the form
/5(1 - ~ ) ( u - u q ) q* / I*
in which we can replace q*/Y* by y*, the share
of the respective products' capacity in the total capacity
of the economy.