I think many thanks are due to Bruce and Fred for supplying
examples as a focus for discussion that are couched in
sequential terms. I want to think more carefully about
Bruce's example before replying.
I also want to think more carefully about Fred's because
though an immediate answer leaps to mind, the way he puts it
sounds quite intuitively reasonable and I want to think
about where this intuitiveness comes from.
I think it is very important, whenever discussing value
equations, to distinguish between coefficients and
aggregates. Actually, this relates to a fundamental point
Marx makes, that the commodity is the contradictory unity of
use-value and exchange-value. Both its use-value and its
exchange-value aspect have to be considered at all times,
and if the eye drops from the ball sufficiently that this
unity is forgotten at any point, we get a failure of
comprehension. I think the apparent reasonableness of Fred's
example arises because it does not clearly distinguish
between the value which workers add per unit of use-value,
and the value they add in the whole of a sector.
In Fred's equation
p(2) = ap(0) + VA(1)
the left hand side refers to the price of a unit of output.
VA must therefore refer to the value added per unit of
output.
But if labour is becoming more productive, then indeed, the
value added per unit will decline. This, even though the
total value added may rise, stay constant, or bob around
like a yoyo. Yes, the value added per unit of output will
decline as a result of technical change. Surely an
improvement in the productivity of labour means that less
labour is needed to make the same thing.
To enquire about the total labour value added we should
multiply by the scale of output to get the more correct,
because more complete, aggregate value equation:
p(2)X = Ap(0) + VA(1)
where X is the output of this process, A is now the total
inputs instead of a coefficient, and VA now correctly stands
for total value added.
But there is no guarantee that because the unit cost of
material inputs A is reduced, the total value of output will
decrease since the capitalists might easily react by
increasing the volume of output and so consuming more A.
Conversely, since the productivity of labour has risen, if
they do not decrease the scale of output, then they will need
less labour to produce it.
They will therefore sack workers, and this is why VA(2) is
less than VA(1) - because there are less workers, not
because they add less value per worker.
Alan