Working my way through Alan's posts. I'd like to apologize to other
list members for the volume of argumentation; from my own experience
I realize this can be overwhelming. For what it's worth, as far as I
can tell the argument is steadily progressing, and the implications for
understanding Marx's account are fundamental.
In preview, I don't believe that "agreement 1" between Alan and I
entails the additional agreements he suggests.
Alan writes:
> Agreement 1
> ===========
> ===========================================================
> "Marx does not take the case of price-value equivalence as an
> assumption in Volume I"
> ===========================================================
Let me reaffirm and qualify this: clearly Marx could not have
*assumed* price-value equivalence as of Chapter 5, since there he
explicitly considers the case of price-value disproportionalities, a
case which would not exist if the assumption held.
However, he ends Ch. 5 with the [I argue invalid] conclusion that any
setting in which surplus value is appropriated is isomorphic to a
case which includes price-value equivalence; thus unless told
explicitly otherwise I believe that subsequent to Ch. 5 he bases
explanations on this case; otherwise we must assume, implausibly,
that he ignores his own result at the conclusion of Ch. 5. To put it
another way, according to this result, anything said in Volume I
subsequent to Ch. 5 must be presumed to hold under the condition of
price-value equivalence, unless otherwise stated.
Alan continues:
> Digression from agreement 1
> ===========================
[...]
> To use the language of speculative philosophy, the assumption
> of price-value equivalence is not a necessary precondition of
> Marx's derivation of the value and price categories of Volume
> I. It is not 'posited' by this derivation. You don't have to
> assume it, to draw the conclusions. Therefore, the conclusions
> are not based on it.
Subject to one caveat: by Marx's isomorphism argument in Ch. 5,
any conclusion about the nature or process of capitalist exploitation
must be statable under the assumption of price-value equivalence.
Alan continues:
> What I'd now like to do is draw a conclusion or two from
> agreement 1 and see they shed more light on differences.
> Starting with:
> Corollary 1 of agreement 1
> ===========================
> Any argument which does define value on the assumption of price-
> value equivalence may be interesting, but isn't Marx's.
>
> Also, both myself and Gil disagree with any such argument.
> Other options are open; for example one may say that though
> Marx didn't reason from price-value equivalence, he should
> have, and that he can only be made consistent by introducing
> this extra, additional assumption. This is one possible
> interpretation of Sweezy's intervention.
>
> We take, I think, what I shall call the strong anti-price-value-
> equivalence position: we both agree Marx didn't base his
> argument upon it....
That is, subject to the caveat given above. Marx *quite explicitly*
says that any account of capitalist exploitation must be replicable
in terms of price-value equivalence.
> Supplementary remark to corollary 1
> ===================================
>
> An example of such an argument is to be found on page 16 of
> John Roemer's "Analytical Foundations of Marxian Theory" where
> the content of Morishima-Okishio's 'Fundamental Marxian
> Theorem' is explained:
>
> ====================================================
> The rate of exploitation is defined in terms of the labor time
> embodied in the subsistence bundle. The vector of labor values
> is lambda [henceforce transliterated as v - AF], a 1 X n
> vector, where
>
> v = vA + L (1)
>
> ====================================================
>
> This argument depends on the assumption which, we both agree, is
> both wrong and not Marx's.
I disagree with this entirely; indeed, I think it is a complete _non
sequitur_. *No* statement about the connection between prices and
values is implied in defining values in this way (simply because no
statement is being made in this definition about prices at all!).
Furthermore, expression (1) seems like a straightforward
interpretation of Marx's notion that as values commodities are
"congealed labour time." That this includes both direct and indirect
labor, as (1) suggests, is affirmed by Marx when he writes " The
labour-time required for the production of the cotton, the raw
material of the yarn, is part of the labour necessary to produce the
yarn, and is therefore contained in the yarn. The same applies to
the labour embodied in the spindle..." [I, p. 294, Penguin]
> The usual justification for this equation, henceforth equation (1)
> is the following:
>
> (i)
> Values are defined, in volume I, as the prices which goods
> would sell for, if they exchanged at values;
Not only is this not part of the "usual justification", it is
circular: its logical structure is "A is defined as B if B is
equivalent to A" --that leaves us where we started.
> There may be another justification for it, but I haven't seen it.
See above.
> But we have just agreed that the goods which make up constant
> capital (here, vA) cannot be assumed to be purchased at their values.
No we haven't. The definition of constant capital in value terms is
logically independent of the question of whether commodities exchange
at their respective values. We have thus not made a judgment one way
or another on this question.
> But in that case, the usual justification for equation (1) has just
> vanished.
I don't see how this conclusion possibly follows.
Moreover, suppose another justification exists. This would require,
> in Volume I, that inputs transmit to the product a quantity
> of value different from the value of the money paid for them.
No, again these issues are entirely separate. The first has to do
with the quantitative expression of value, as in equation (1). The
second has to do with the independent question of the value of
commodities and "the value of the money paid for them."
> By what mechanism is this achieved?
>
> We find nothing in Marx which suggests such a mechanism. As far
> as Marx is concerned, the value of constant capital is represented,
> for the capitalist, by the value of the money with which the
> capitalist must part in order to obtain this constant capital.
I don't see how this follows.
> The universal assumption that, in Volume I, goods exchange at
> their values, has allowed the academic world to ignore this issue
> - the so-called 'transformation of inputs' - until Volume III. But
> once agreement 1 is reached, the issue must be addressed where it
> belongs, and where Marx in fact 'solved' it (I place the word
> "solved" in quotes, because there is in fact nothing to solve)
> - in Volume I.
>
> Corollary 2 of agreement 1
> ==========================
>
> If goods do not sell for their values, the money paid by the
> capitalist is no longer necessarily equal to the value of the
> elements of constant capital. The standard justification for
> equation (1) therefore ceases to exist.
Since I don't agree with Alan's representation of the "standard
justification", I don't agree that this corollary has been
established.
Fast forward....
> A contradiction has opened out, which John has signalled in the
> discussion with Fred: is the value transmitted to the product
> by the elements of constant capital equal to their value, or
> their price? And if it is not equal to their price, where does
> the difference go?
>
> We have to make a choice, which the traditional interpretation
> neatly avoids: is the value transmitted to the product by
> constant capital equal to the labour embodied in it, or the
> labour its elements represent in the process of circulation?
>
> The implications of this choice are genuinely 'Fundamental'.
>
> If the capitalists can add value to their product which is
> different than the value of the money they part with, there
> are indeed sources of value other than living labour. If you
> stick with equation (1), Marx's 'second equality' is not in general
> true.
For what it's worth, I think that this is true: Marx's "second
equality" is inconsistent with his Volume I definition of value. One
can repair this inconsistency, perhaps in the manner of
Kliman-Freeman-McGlone et al, or perhaps via the less draconian
approach of Foley-Lipietz-Dumenil; and perhaps there is good reason
to do so; but that's a separate issue.
The importance of this is not some scholastic reverence
> for the texts; it is the real 'Fundamental Marxian' proposition
> which is that *only living labour creates value*.
But that is the issue that remains to be determined.
> Moreover, if Marx did not assume value-price equivalence in
> Volume I, but nevertheless assumed equation (1), then Volume I
> is full of many unpardonable lapses, for again and again he
> refers to the 'price' of the goods making up constant capital
> as the basis for the formation of value: for example in the
> very passage which Fred cites in support of reproduction
> valuation, from p317 but also see the eye-opening discussion
> on p969, both Volume I Penguin/International edition.
But I think there is a legitimate alternative explanation for such
"lapses". As I've mentioned before, Marx considered price-value
equivalence as the "pure" case of commodity exchange, and his Ch. 5
isomorphism result seems to back up this judgment; thus Marx may have
felt (legitimately, if only his Ch. 5 argument were valid) that
nothing of significance was lost in referring without discrimination
to prices and values in the context Alan mentions.
> Thus once price-value equivalence is dropped, very little basis
> remains for equation (1).
As argued above, I don't see how this possibly follows; thus neither
does the claim
> Therefore some *other* equation defining value must be sought,
> which makes no reliance on price-value equivalence.
> Supplementary remarks to Corollary 2
> ====================================
>
> I make this point for three reasons:
>
> (i)
> to test the real extent of the agreement. If others in the
> debate (not just Gil) are happy to sacrifice equation (1)
This is putting words in my mouth on the basis of an at best
problematic argument. I'm not "happy" to sacrifice equation (1).
then
> I think we really are in new territory and I'm very happy. If
> not, then I suspect we will have to come back and ask why the
> equation has to be defended: what is so 'special' about it that
> we can't do without it?
Because it seems to implement what Marx says in VI Ch. 1, which does
not depend on any assumption one way or the other about price value
equivalence.
> (iii)
> if agreement 1 holds then - as remark (i) argues - we lose
> the entire traditional explanation of what Marx means by value;
> which means we have to discuss what goes in its place. We can't
> just leave an empty hole. I take a lot of what Gil says to be
> making this point, though this could be a misreading.
>
> My gut feeling is that Gil thinks nothing goes in its place;
> that Marx has no real argument, so that the whole house of
> cards falls down, once the assumption of exchange at values
> goes. Hence the importance (to him) of re-establishing Marx's
> main qualitative conclusions by other means.
Rather: I'm willing to grant that for some purposes labor values can
serve as a basis for a theory of exploitation. Doing so does not
alter the fact that, as I understand it, (1) Marx's isomorphism
result in Ch. 5 is invalid, and at least as standardly interpreted,
is inconsistent with his historical argument; (2) Marx nowhere
asserts that total prices equal total values, and if he did the
assertion is either true only by definition or in general wrong.
Fast forward: [...] Alan continues:
> Theorem 1: Equality of value and price sums in Volume I
> =======================================================
>
> The precondition for further progress is, I believe, to thrash
> out the substance of disagreements around an almost throwaway
> remark of Gil's in OPE:861, which I already picked up on but I
> want to repeat, because it is one of those remarks which makes
> you realise that, just when you think you are talking the same
> language, you are really just using the same words. This is:
[I assure you it wasn't a throwaway remark. I've been making the same
remark since the URPE summer conference, among others.]
> ===============================================================
> "In anticipation, I note that the passage [on p263-AF] does not
> suggest--nor could it validly suggest in general--that the sum
> of values is equal to the sum of commodity prices."
> ===============================================================
>
> I just don't understand the basis for this remark.
>
> As I said in my quick response:
>
> ===============================================================
> The wine and the corn must have the same price, in order to
> exchange. So the wine costs L45 and the corn L45. The wine has
> a price of L45 and a value of L40, the corn has a price of L45
> and a value of L50.
>
> Total value = L40 + L50 = L90 Total price = L45 + L45 = L90
>
> What's the problem?
> ===============================================================
>
> Well, what *is* the problem? To me, it is obvious that's what
> Marx meant, and there's the numbers which prove it.
And as I said in an earlier post, they "prove it" only because Alan
*assumes* the exact money prices necessary to yield the result. No
such money prices are asserted in the passage by Marx Alan refers to.
The "equality" falls to the ground if the common money
price is any level but $45.
I say this
> not to diss the objections without considering them but
> because, if we can establish why this solution is *not*
> considered acceptable - nay obvious - we might just clarify the
> semantic and ontological issues at stake.
>
> The construction which led to the prices above is perfectly
> general. Given any arbitrary set of values and any arbitrary
> set of exchanges we can always ascertain a unique set of prices
> which effect these exchanges, corresponding to which is a set
> of gains and losses of values - 'value transfers' which sum to
> zero. Each good has a perfectly distinct value and a perfectly
> distinct price, in general not the same as its value, and the
> value lost or gained by the owner of any commodity bundle is
> equal to the sum of the value-price differences of each item in
> the bundle. Over the capitalist class as a whole, the net gain
> or loss of value is zero.
But that's a vastly different statement. It's one thing to say that
the sum of prices necessarily equals the sum of values, and quite another to
say that "we can always ascertain a unique set of prices" which ensure
this result. Of course we can--but *nothing* in the logic of
exchange guarantees that these will be the prices that obtain. In
general they will not be. That is the fallacy in Alan's argument.
Consider: a subset of the prices which *may* obtain are those which
ensure a Walrasian exchange equilibrium. Even normalizing the value
of one commodity--say the money commodity--to one, these prices (and
thus their weighted sum) can be varied arbitrarily by varying a
parameter which affects the excess demand functions. But since, as
Alan affirms above, values, and thus the sum of values, are
determined independently, it will *not* be the case that the
aggregate in terms of money prices equals the aggregate in terms of
values--except by accident. This is true even given we control for
inflation by normalizing the price of the money commodity.
Now, if Alan's equality cannot be guaranteed in the special
consistency case of Walrasian equilibrium, then nothing whatsoever
guarantees this aggregate equality in any non-equilibrium set of
prices.
> As Paul and I both put it, value is conserved in exchange.
Yes, within a given metric. This, I believe, is the sense of marx's
argument. It does not imply that aggregates are equated across
metrics, i.e. values and money prices, whether or not values are
expressed in money terms.
> Moreover we can always express any price magnitude, and any
> value magnitude, either in money or in hours of socially
> necessary abstract labour.
Perhaps, but it does not follow that in aggregate these are the
*same* magnitudes.
> The only complication arises if there is a general inflation or
> deflation of all money prices, that is, if the value of money
> falls or rises. This also is dealt with by Marx in Chapter 5,
> on p263, I think quite clearly. We have to reduce the sum of
> values, calculated prior to monetary inflation, and the sum of
> prices, calculated after monetary inflation, to a common unit.
> We can no more compare two monetary sums expressed in a
> different monetary unit, than the macroeconomists can compare
> production in 1990 and in 1980 and argue that the economy has
> grown 200% because prices have doubled. Or, as Marx puts it,
> you can no more create value by inflating money, than by
> expressing prices in silver instead of gold.
As shown, my argument above abstracts from inflationary effects.
> It could be that he feels cheated; that Marx's construction or
> my figures express a tautology.
> Don't knock tautology: every theorem in the first order
> predicate calculus is formally speaking a tautology, and there
> are a lot of them about, some of them quite hard to prove.
>Such as Fermat's last theorem.
There is an important difference between a deductive tautology, such
as Fermat's last theorem, and a definitional tautology, where one
achieves one's conclusion by assuming that conclusion, as Alan did
above with his numerical example. Furthermore, there is no textual
evidence that Marx does this, since the passage Alan originally cited
does not refer to money prices (understood as distinct from values)
at all.
> If what is required is a proof I'm happy to give one but I
> suspect that this isn't what's at issue. I think almost anyone
> could construct this proof *if* they follow the line of
> argument. The underlying problem is that something, and I don't
> know what, leads Gil to reject this entire way of arguing. So
> what is it? Show us the arithmetical error in the figures given
> for the example chosen, construct another example where this
> equality, which I think really *is* a 'Fundamental Marxian
> Equality' breaks down, or tell us the logical fallacy involved
OK: Alan gets his result, and except by accident can *only*
guarantee his result, by assuming it. To translate this definitional
tautology into an analytical claim is a pretty big fallacy.
Furthermore, I don't believe Marx commits it.
In solidarity, Gil