In response to Andrew's OPE-L:5221:
I think you're raising some very pertinent questions in this post. My
specific comments follow your points:
>Duncan: "I took the value of labor power, w*, as given, and defined it as wm
>where m is the reciprocal of the MELT, in my definition, then we have,
>writing
>X for the vector of gross output, so that (I-A)X is the vector of net
>product,
>lX the total living labor, and P(I-A)X the value added:
>
>w = w* (P(I-A)X)/lX
>
>This equation determines w, and it is clear that changing w will change the
>profit rate. Since the vector X includes both wage and luxury goods, in
>general the surplus value exploited in the luxury sector will influence the
>rate of profit, as Marx says."
>
(Andrew remarks:)
>I agree that *if* one takes w* as determined exogenously, production
>conditions in luxuries will influence the profit rate even given simultaneous
>determination, in the special case in which all workers are paid the value of
>their labor-power.
>
>As I noted in a previous post, however, "How one defines the value of
>labor-power is totally irrelevant to the issue at hand. First, because it is
>irrelevant whether workers are paid the full value of their labor-power or
>more or less. To replicate Marx's result, one must do so in the general
>case,
>not just in a special case." I don't have Duncan's 1982 RRPE article with
>me,
>but I do have _Understanding Capital_ (UC). It notes on p. 36 that "There
>might be circumstances in which actual wages differed from what we would view
>as their normal level." On p. 43 it states that w* is the "*average* wage
>multiplied by the value of money" (my emphasis). On p. 49, it states that w*
>"depends on ... the *average* standard of living of workers" (my emphasis).
>There are a couple of other passages which also note that wages don't always
>conform to the value of labor-power. Thus, the question arises: when w does
>not equal w*/m, do luxury-producing sectors influence the general profit
>rate,
>according to this version of the New Interpretation? I may as well add a
>related question: in the general case, in which profit rates are unequal, do
>luxury-producing sectors influence the general profit rate, according to this
>version of the New Interpretation?
As I said in my EEA paper, I'm not sure I'm completely happy with the UC
conception of the value of labor-power, not because I want to go back to
the labor embodied in workers' consumption, but because Marx's conception
of the value of labor-power has an ex ante aspect to it that my ex post
definition doesn't catch. (There was some discussion of this point on the
list a few months ago.)
However, the conception of surplus value in UC would always include the
surplus value generated in luxury sectors, since it equals the non-wage
share in value added, which includes luxury production. The idea was
precisely to define an aggregate surplus value that would be distributed
over various sectors by prices (perhaps, but not necessarily to equalize
profit rates), but in such a way that the total surplus value is conserved,
and proportional to the unpaid labor time.
Andrew continues:
>
>Though this is a different matter, I do not happen to agree with the
>theory of
>wage determination implicit in the above. Unless w* is given because it
>drops
>down from the sky, what seems to ground this theory is a sort of
>post-Keynesian story in which the wage share of NNP (which is what w* is)
>determined by a macro bargain -- "class struggle." What is more relevant to
>the issue at hand is whether this is consistent with Marx's theory and
>therefore whether it can be invoked in order to claim that one is replicating
>Marx's result. I don't think so, but any attempt to demonstrate that through
>textual evidence will just end up with two different interpretations of the
>text, so there's no use arguing the point.
Since UC tends to be ex post, it is largely agnostic on the ex ante
determination of the level of wages. Again, a few weeks ago we started a
discussion of the determination of the level of wages and the wage share. I
took w* as given in my reply to you because it seemed to me that was the
"ground rule" of the transformation problem in the abstract. In fact I
suppose the value of labor-power in the UC sense is determined
conjuncturally by the intersection of a whole bunch of concrete
determinations. What makes me somewhat uncomfortable is my feeling that
there is a longer-run conception of workers' standard of living that plays
a real role in the system and is not just the ex post outcome period by
period.
>
>I referred above to "this version of the New Interpretation" because it seems
>to me that the above differs significantly from what Duncan set out in UC:
>
>(a) On p. 36, the equation has w* on the LHS and mw on the RHS, implying
>that
>causation runs from m and w to w*, which I think is correct. The verbal
>explanation also proceeds from m and w to w*.
>
>(b) On the same page, there is also a hint of a theory that the money
>wage is
>determined by a wage bargain, not by a predetermined w*: "The wage bargain
>provides a particular capitalist's workers with only the money wage agreed on
>..."
>
>(c) On p. 43, it again seems that w* is determined by the money wage per
>unit
>of labor, not the reverse: "even after the wage bargain has been struck,
>there continues to be a conflict between worker and capitalist over the
>intensity and conditions of labor." A reasonable interpretation of this is
>that the wage bargain determines the money wage per unit of labor-power, the
>degree of exploitation in production determines the amount of labor extracted
>per unit of labor-power, these two factors together determine w, the money
>wage per unit of labor, and the latter, together with m, determines w*.
This seems pretty close to the way I thought about it when I was writing UC.
>
> (d) On pp. 55-56, there's an account of the impact of technical change on
>several things (interestingly, it says that technical change does not
>influence the amount of value a given amount of social labor produces!). It
>suggests at first that causation runs from w* to w: "the value of
>labor-power
>will determine the division of value added between wages and surplus value."
>However, the example that immediately follows reverses the causation, going
>from a falling cost of means of subsistence to a falling money wage to a fall
>in w*. This conforms to Marx's account, I think.
>
>(e) The only other references to value of labor-power in the index deal with
>the value/production price transformation. It is true that w* is held
>constant in that chapter, but so are w and m, and I do not find any
>discussion
>of whether w determines w* or the reverse. In any case, none of this is
>relevant to the issue at hand, which does not concern transformation --
>whether the w* of the "value system" is the same as the w* of the actual
>economy has no bearing on whether luxury sectors influence the profit rate of
>the actual economy.
>
>
>So I wonder if Duncan is really committed to the theory that w* is
>exogenously
>determined and prior to w, which is what is required for luxury sectors to
>influence the general profit rate given simultaneous determination of input
>and output prices.
I'm not committed to the theory that w* is exogenously determined prior to
w, but I don't agree that this is required for luxury sectors to influence
the general rate of profit, as I've tried to explain above.
>
>
>
>One more thing. I had written:
>
>"Now, partition the economy into basic sectors 1, ... m, and luxury sectors
>n1, n2, .... Workers consume none of the products of the latter sectors,
>only some or all of the products of sectors 1 through m. The aggregate
>budget constraint of the workers in sector j can thus be written as
>
>[2] wj = P1*b1j + P2*b2j + ... + Pm*bmj
>
>where bij is the total amount of good i consumed by workers of sector j, per
>unit of output j."
>
>Duncan commented: "But this amounts to assuming the workers' consumption
>bundle as fixed, which is precisely what I argued against in putting forward
>the definitions of the value of labor power and the value of money (or the
>monetary expression of labor time) in _Understanding Capital_."
>
>This does *not* assume the workers' consumption bundle is fixed, in the sense
>of the bij being given exogneously. It is simply a budget constraint. The
>bij are endogenously determined on the basis of the money wage, the prices of
>nonluxuries, and, as I noted later, preferences. Substitution in consumption
>is certainly compatible with [2].
Fair enough. But the effect of putting the b vector in the equation is to
eliminate the nonbasic sectors from the determination of the profit rate.
In this sense it doesn't seem to me that it matters whether you put it in
the A' matrix directly, as you did in your first post, or add equation [2]
afterwards: the mathematical implication, as you pointed out, is that the
basic sector equations are then sufficient to determine the profit rate
independent of the nonbasic sectors.
Duncan
Duncan K. Foley
Department of Economics
Barnard College
New York, NY 10027
(212)-854-3790
fax: (212)-854-8947
e-mail: dkf2@columbia.edu