Here's a question.
My reading of Marx is that if the working day is extended,
this creates more value and ceteris paribus more profit for
the capitalist.
But, in the equation systems of Fred and Bruce, as far as I
can see, the rate of profit is independent of the length of
the working day.
For, let variable capital be V. The profit equation can be
written:
pX = (pA+V)(1+r)
where X = output
A = inputs
p = price
r = rate of profit.
This seems to be to give a magnitude of r that is independent
of the length of the working day, unless V is a function of
the length of the working day, and I see no reason to suppose
that it is.
In that case, how can the capitalists gain anything from
increasing the working day?
In a sequential presentation this problem does not arise since
p(t)A is given at time t. Letting Q stand for the value of
total output we have
Q(t+1) = p(t)A + L(t)
which clearly will be bigger, the larger is L. Hence total
profit, given by
Q(t+1)-V
will be bigger and so will the profit rate, for a given p(t)A.
This seems to me to be quite a substantial problem for the
simultaneous interpretation.
Alan