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We consider a closed private economy, a two class model,
in which workers do not save. Let us define a vector q
of the quantities of the various commodities ( only final
products are considered, the economy is imipagined to be
integrated, so that costs consist, only of wages and salaries),
We write then for the gross national income Y and for the
wage and salary bill W the following equations:
Y = ß f q. (1)
W = $q + wj 1 . (2)
Q the price of each product, and iC its^wa|l n and salary
cost per unit are vectors. The income Y and wage bill W
are given by the inner produci/of the vectors and
are
therefore scalar. 1 is the unit vecter and w„ are the
fixed wage and salary cost.
At the break even point q Q
cost, we have therefore
ßw o f 1
From this follows that
( ß -S' /q 0 - w D i.
income equals wage and salary
(3)
(4)
The difference between equations (1) and (2) taking account
of (4) will give the profits ( a scalar );
I.
P = Y - W =
( /5 - ) ( q - q 0 )
(5)
We now make use of Kalecki's profit equation,
P = I + C
where I is the investment and C the consumption of capitalists
which we assume, for simplicity, to be independent of profits.