Please excuse the lack of an immediate response to all Gil's
points; I want to work my way carefully through the discussion
so far before responding in what I hope will be a more rounded
way.
I have two or three preliminary questions to deal with meanwhile
on which I will post separately.
The first concerns the supposed 'dimensional incompatibility'
between price and value.
In OPE 960 dated 6/2/96 Gil says
"Putting aside for the moment that L() insofar as the entity
is commonly understood, is measured in units of labour time,
and p(), insofar as the entity is commony understood, is
measured in money unts..."
I'd rather we didn't put this aside for very long, because it
is the source of much confusion. The idea of a 'dimensional
incompatibility' between price and value has been floating
around for a while [I first found it in Abraham-Froix and
Berrebi; does any OPE member know of an early mention?] and I
think we need to clarify it to avoid unnecessary confusion.
Other OPE members may also have a view on this; I find quite
often that dialogues of the deaf can arise if two people are
discussing the same equation using different units.
Marx, in Chapter I of Volume I, explains that both price and
value have two measures:
(a) the intrinsic measure, labour time
(b) the extrinsic measure, money
There are many citations relating to this which I can provide
if this idea is disputed but I won't give them here to avoid
clogging up this post.
Thus in the disputed Chapter V discussion of wine whose value
is $40 and corn whose value is $50, we may represent this equally
in either money or labour.
If the value of money is 1 hour per dollar or, which is the
same thing, if the monetary expression of labour is 1 dollar per
hour, then the wine has a value of 40 hours and the corn a value of
50 hours. If on the other hand the value of money is 2 hours
per dollar then the value of the wine is 80 hours, and so on.
But exactly the same applies to price. If the price of the wine
is $45, and the value of money is 1 hour per dollar, then the
price of the wine is also 45 hours.
This is precisely the reason that, even though because of a
monetary inflation, or what Marx terms a 'general rise in all
nominal prices', the price of the wine may be $45, or $45*2, or
$45*3 as Gil says, nevertheless its price when represented in
terms of the intrinsic measure is always 45 hours, which is how
the equality of total price and total value holds: the wine's
value in hours is 40, the corn's value in hours is 50, and the
price of each in hours is 45 and this is true independent of
the money price; it abstracts from monetary inflation.
The equality of prices and values flows, among other things,
from the fact that the value expressed in hours is a magnitude
independent of exchange relations and therefore cannot be
altered by the circumstances of exchange.
We can always express any money price as the product of two
completely independent factors; the intrinsic measure of the
value 'commanded in exchange' by a commodity (a magnitude
expressed in labour hours), multiplied by the monetary
expression of labour itself (a ratio, measured in dollars per
hour) to obtain the extrinsic measure of price (a magnitude
expressed in dollars). It follows that we can break down any
*change* in money price into the sum of two components: the
difference between the two intrinsic measures of price, plus a
factor due to the change in the value of money.
It follows that, since value in money terms is no other than a
special price, we can always express a price-value difference
as the sum of an intrinsically-measured difference and a factor
due to the change in the value of money.
I will return to this important point later because it relates
directly to Marx's definition of the value of money which, I
agree is not unproblematic, but on the other hand is clearly
and extensively theorised by Marx and is, in a certain sense,
his most distinctive economic contribution; his theory of money
remains not only totally distinct from any other I know of, but
empirically far more accurate and - I think - the real key to
his understanding of what capitalism really is. I think I will
be able to show that this is both consistent and clear.
For now, note that every value can be measured either in money
or labour-time, and *also* every price can be measured either
in money or labour-time.
It is of course absurd to measure one in money and the other in
labour-time, and Marx never does this.
These are two different scales for measuring the same thing,
arising from the fact that the commodity participates in two
distinct equivalence relations. Relation 1, labour time,
concerns the circumstances of its production. Relation 2, money
price, concerns the circumstances of its exchange.
This is, it seems to me, not an invention of Marx but very
common in science. For example if I ask you 'how much beer is
there in this glass' you can answer in two ways: you may either
say 'a pint' or 'twenty ounces'. Neither answer is wrong; and
the relation between the two measures is an important
scientific ratio, density.
Of course if we ran a pub in which the customers asked for four
whiskies, and we gave them two glasses plus two grammes of
whisky and said 'that makes four', we would get into trouble.
If we gave them two glasses plus two Kilogrammes, they would
get into trouble. Either way, we get trouble.
In the same way if we say 'here are three hours of labour plus
two dollars of value, that makes five units of value' then I
quite agree, we will come up with an absurdity.
In the equation you give in OPE-L:960, namely
V = [p(t)A(t) + L(t+1) x(t+1)]
all quantities must be in the same unit, viz either dollars, or
hours.
However, if we use dollars instead of hours, there is an
additional problem to deal with if the value of money has
changed between [t] and [t+1]; we must make a correction for
inflation. That is, we must distinguish between current prices
and historic prices, just as the National Income Accounts do.
Otherwise, we will find that enormous profits can be made
without producing anything, as follows: suppose the value of
money halves between 1990 and 1991. Then, if I buy a bar of
iron in 1990 for $100, and merely hoard it, then in 1991 the
same bar of iron will be worth $200 and I have a money profit
of $100 by doing nothing.
I know I've asked this before but I can't resist doing it
again: under these circumstances, do you consider that new
value has been created?
And do you really think it is wholly unreasonable, circular
or without foundation, to claim that no new value has been
created?
And isn't it rather useful to have a theoretical basis on
which to make this distinction clear?
A much more serious problem, therefore, than the supposed
incompatibility between hours and dollars, is the very real
incompatibility between 1990 dollars and 1991 dollars which you
seem to ignore. These appear to be the same scale of
measurement but are not, and we cannot just add 1990 dollars to
1991 dollars when discussing production; in production we must
reduce all magnitudes to a single, common measure.
Marx explains this, in 'towards a critique of Political
Economy' using the very revealing phrase that money is a
'dynamic' standard of value. On occasions he uses the
phraseology that labour-time is the measure of value, but money
is the standard of price. But he makes it clear that labour-
time also serves as the measure of price, and money as the
standard of value, since 'price is but the monetary expression
of value.'
In calculating the effects of either production or exchange, a
complication therefore arises if we are using money, because we
must account mathematically for any change in the value of
money with the addition of an extra term to the equation you
have given. Marx generally avoids going into this in detail by
stating that he assumes the value of money to be constant. This
is the ruling assumption in Volume III for example(a
'purifying' assumption that is often glossed over) However, the
appropriate correction can be consistently expressed
mathematically, and I will endeavour to show this.
But the simplest and most general way to resolve this is to
reduce all magnitudes to a common measure by expressing them in
the intrinsic measure of value, labour hours. This is the
simplest way to interpret the equation you supply. Therefore,
everything in this equation should be given in hours.
Then we can analyse the effects of production independent of
monetary effects.
Or, a proper correction term should be added for any change in
the value of money during the course of production. One of the
problems with Post-Keynesian/Kaleckian dynamics is that it does
not separate out this correction term, allowing producers to
impose an arbitrarily high markup.
I don't ask you to accept all this, which prefigures a fuller
explanation I have not yet supplied, but I think it reasonable
to ask whether you accept that there are indeed two measures of
value and that in any value equation, all magnitudes must be
given in the same units - either all in hours, or all in money.
Alan
Mathematical Appendix
=====================
Let M be money price, m be the monetary expression of labour,
and P be price in hours. For simplicity magnitudes in upper
case are not 'unit' prices but the total price of the given (x
units) quantity of a commodity (eg 'wine sells for $50' translates
as M = $50). Consider a change in price. Using D for 'delta' or
'the change in' we have:
M = mP
M + DM = (m+Dm)(P+DP)
= mP + mDP + (P+DP)Dm
DM = mP + mDP + (P+DP)Dm - M
= mP + mDP + (P+DP)Dm - mP
= mDP + (P+DP)Dm
using M' for the new money price (M + DM) and P' for the new
labour-hour price (P + DP) we get
DM = m(P' - P) + P'dm
Finally in the special case where P is the value of the
commodity we get
DM = (Price-Value difference in money terms)
= m*(Price-Value difference in hours) + (Price in hours)*dm
When we sum these two quantities over the whole of exchange, we
find that Sigma(DM), the total difference between the monetary
expression of price, and the monetary expression of value, is equal
to
m*(Total price-value difference in hours)
+ (Total Price in hours)*dm
that is, a breakdown of price-value difference in money terms
into two distinct components, one representing the underlying
price-value difference expressed in hours, and the other
representing the effects of monetary inflation or deflation.
Abstracting from changes in the value of money, as Marx does
after establishing that a general rise in all nominal prices
cannot give rise to an increment in value, leaves the value of
money constant (dm=0) so that the second term is zero and the
whole expression reduces to
m*(Total price-value difference in hours)
which, Marx's argument shows, is zero; though I agree aspects
of this remain to be 'proven', which I will try to do later.
Alan