Paul writes #2403
"I believe that any theory that assumes an equalised profit
rate is unrealistic, but, given that you are trying to give
an interpretation of Marx's price of production theory, you
are forced, along with the Sraffians to accept this."
Fred writes #2021
"My argument is: the transformation process involves: (1) the
equalization of profit rates (2) that happens through the
transformation of values into prices of production."
You must admit it would seem quite hard on the face of these
two positions to satisfy both of you. But I'll do my best.
I agree it is completely unrealistic to assume that profit
rates actually equalise (or, which is the same thing, that
goods actually sell for their prices of production).
I also happen to think Marx rejects this unrealistic assumption.
At the outset he describes the general rate of profit as 'an
ideal average, an average that does not really exist.' (p173
L/W-Progress edition CIII) Moreover the very existence of the
category of surplus-profit means that even if sectoral rates
were to equalise, there still could not be a generally equal
profit rate because within each sector, individual capitals
will receive very high individual profit rates.
I don't know if this is a wise discussion to pursue as it could
veer into scholasticism. But since your case is based on the
assertion that Marx 'forces' us to assume equalisation, I couldn't
avoid some reference to it.
So let me start from the following question: why consider equal
profit rate solutions at all?
If we could start from scratch, with no pre-existing body of
theory to contend with, I don't think there is any practical
or theoretical reason to consider equal profit rate solutions
at all. I think they are a complete waste of space, especially
now we have the modern and precise concept of an attractor to
express what people often try to say - and fail - using the
concept of stationary state.
But there are two reasons why it is useful and often necessary
to present equal-profit-rate solutions:
1) As a fully general theory, we also hope to explain special cases,
which includes the case of profit rate equalisation. Since this is
important in the literature if not the real world, in order to
measure our own theory against the predictions of other theories,
I think we do need to study what happens to our model under their
assumptions.I think this is a necessary scientific activity. If
our solutions were not valid or consistent for equalised profit
rates, they would not be fully general. So it's part of the legitimate
process of testing them.
2) As Fred's response shows, if we didn't exhibit equal-profit-
rate solutions 900f the marxists (not to mention 1000f
Marx's enemies) would say we haven't solved the problem as Marx
posed it.
We could always, of course, explain that this is not actually
the problem as Marx posed it, and every now and again we try
to do that. But this has little impact on these discussions because
most people have already made up their mind how Marx poses it
and my general experience is that this is an unshakeable faith.
Indeed the general tendency is to regard anything Marx actually
said as immaterial.
Thus it is not Marx, but the marxists, who force us to consider
equal profit rate solutions. I would be only too happy to throw
the whole damn thing into the same dustbin of history that
Bortkiewicz dragged it out of in 1905. The problem is that we
live in a world of equal-profit-rate junkies, so we can't avoid
offering illustrations dealing with this case.
Nevertheless I think it *is* possible to do two useful things
(1)to avoid building equalisation into the foundations of the
theory. My view is that a fully general theory cannot
assume equalisation. I think it is a wrong theoretical
method to construct foundational concepts which incorporate
special case assumptions.
[For the same reasons I think a fully general theory
cannot incorporate into its definition of value, the
assumption that goods sell at values]
(2)to consider special cases once the general theory is
established. Thus a fully general theory of motion cannot
assume a fixed frame of reference. However, it can
*include* the case of a fixed frame of reference and even
provide a complete theory of this special case.
In the same way, a general economic theory can include the
situation where profit rates do equalise as a special case.
Indeed, otherwise it is not fully general.
I therefore don't think there is such a big problem with
exhibiting special-case solutions where the profit rate does
equalise (or even where prices are constant) provided it is
made clear this is only a special case and provided one makes
no proofs that rely on the special case assumptions.
The difficulty is, that because of the way that neoclassical
theory, and the standard treatment of Marx, has gotten everyone
thinking, the minute you produce such a special case
illustration, everyone thinks it's a model. This is very hard
to avoid.
The crux of the matter for me is this: what is the basis of the
proof? Does the proof require the special-case assumptions?
If you look carefully at the proofs of the claims that, for
example, the two equalities are satisfied or the price rate of
profit falls, you will find them to be independent of the
assumption of equal profit rates. These proofs can be repeated
or reconstructed without this assumption. My own proofs - in
Marx and Non-Equilibrium Economics - make no reference to this
assumption and explicitly deny it: because like you I don't
think it's true, though unlike you, I don't think Marx said it
was.
I look at it this way: we exhibit solutions where the profit
rate does not equalise and can follow any law of motion you
please, or no law at all, or a stochastic law; whatever you
want, you can do. Anyone can.
All anyone has to do, to 'become' temporal, is drop all the
simplifying assumptions except labour values. What's correct,
I think, is what's left when you've done that.
Alan