[OPE-L:4069] Re: Re: Re: Re: e: m in Marxs theory

From: Gil Skillman (gskillman@MAIL.WESLEYAN.EDU)
Date: Thu Oct 12 2000 - 15:13:04 EDT

In reply to some comments I made in an exchange with Duncan on the
analytical relevance of the LTV, Rakesh writes

>Gil, as I understand it, it is indeed true that the neo Ricardian 
>approach purports to explain (or determine) both the average rate of 
>profit and relative prices while Marx can only explain the formation 
>of the general rate of profit, as I have argued in my last reply to 
>  But the neo Ricardian approach has no relevance outside the 
>non-existent context of output unit prices not equalling input unit 
>prices--a solution can only be had if one of the n equations is 
>removed by setting input prices to output prices; otherwise there 
>would be an unknown other than a distributive variable, right?
>  That is, it is a logical solution to no-thing (except perhaps an an 
>internal critique of another no-thing--general equilibrium). Marx's 
>theory however does lay out the value theoretic determinants of the 
>average rate of profit without the simultaneist stricture which John 
>E called into question long ago. So on grounds of generality and 
>relevance it's no contest despite the absence of a real price theory 
>in Marx's value theory.

I agree about the possible indeterminacy in the Sraffian system when input
and output prices diverge, Rakesh, but I don't think this observation
affects my point here, which is:  if your theory gives you a story about
wage *rates*, as Marx's does, then it is more direct to go directly from
wage rate to profit rate, rather than the indirect route suggested by
Duncan's ratio product. Otherwise, I don't see how my story is any more or
less affected by the possibility of input/output price divergence than is

Illustration:  Suppose the average wage rate w is determined, say at the
subsistence level.  Then if p(t) is the vector of current commodity prices,
p(t-1) is the vector of prices from the preceding period, A is the unit
input requirement matrix, X is the vector of gross outputs, I is the
identity matrix,and L is the vector of unit labor inputs, the profit rate
can be written directly as

(1)     r  =   [p(t)I -p(t-1)A -wL]X / p(t-1)A, 

that is, total profits relative to the dollar value of capital.  [I'm
evaluating the capital stock at "old" prices for the sake of argument, but
I'll have some questions about this procedure below.]  Except for the
possibility of divergent input/output prices, which at least is not
*logically* alien to the Sraffian system, the indicated terms are all
perfectly recognizable Sraffian entities.

Marx's theoretical analysis of the profit rate in Capital Volume III is
based on dividing top and bottom of this ratio by the value of labor power
(presumably determined at the wage rate in t-1, but that's not central to
the point here) to yield

(2)       	{[p(t)I -p(t-1)A -wL]X / wLX}
             r =     ________________________ ,

                      {[p(t-1)A/wLX }
that is, the average rate of surplus value divided by the average
composition of capital.  Note that no direct reference to wage or profit
shares or capital productivity (Duncan's preferred theoretical categories)
is made, and you still have to know old and new prices. 

Finally, Duncan's ratio product requires that you take the data in (1),
divide and multiply by dollar value of the net product vector Y = (I-A)X,
and rearrange to get

(3)                    {[p(t)I -p(t-1)A]X / p(t-1)AX}  *  {[p(t)I -p(t-1)A
-wL]X / [p(t)I -p(t-1)A]X ,

that is, average productivity of aggregate capital (in monetary terms)
times the profit share of net product.  Notice this requires exactly the
same data as (1), but requires you to jump through more hoops to derive the
profit rate. Thus, if the divergence of input and output commodity prices
somehow creates a problem for the more direct approach I suggest, it
necessarily creates *at least* as much of a problem for the determination
of Duncan's ratio product....

....Unless, of course, it can somehow be argued that specifically *labor
value-theoretic* analysis uniquely generates statements about trends in
profit shares and capital productivity (which I dispute), *and* that these
predictions are determinate *even in the face of the input/output price
divergences you've introduced**--which I also seriously doubt, but I'm open
to a proof.      
Now, specifically on the possibility of these divergences:  I think that
this possibility creates *much* more of a theoretical problem for labor
value theory, which as you've noted doesn't offer grounds for a theory of
relative price determination, particularly across time, and a more
neoclassical approach, which does.  For example, consider two cases :
first, if the causes of dynamic price changes are known ahead of time, then
when can under plausible conditions generate an equilibrium dynamic price
path, and the indeterminacy you raise is eliminated.  For example, if the
path of technical innovation is known in advance, a corresponding dynamic
price path can be determined, and the basis of your objection is eliminated.

Put more generally, there are plausible theoretical bases for eliminating
the analytical indeterminacy you highlight, but these bases are necessarily
alien to a labor theory of value, so if this issue matters, I think it
supports my critique rather than injuring it. 

Alternatively, if dynamic price adjustments are due to shocks which cannot
be fully anticipated, then just about anything goes, and it is implausible
at best that a consideration of labor value-theoretic entities will
(uniquely) enable one to close the system, in which case my critique again
remains intact.

Finally, in expressions (1) - (3) above I've evaluated the value of capital
at their old ("input" period) rather than new ("output" period) prices in
keeping with standard practice, but a labor value theory provides no
grounds one way or other for determining if this is correct.  Who says that
capitalists don't ignore sunk costs and evaluate the profit rate solely at
"new" prices, as neoclassical analysis would suggest?  How does value
theory let one decide this?  Notice that if they do the latter, the
indeterminacy you've raised again goes away.

To keep posts to manageable length, I'll respond to your other points in a
separate post.

>>Second, Marx's *value* analysis leads one uniquely to think about trends in
>>capital productivity only with respect to his value-based story about
>>*biased* technical change, not about trends in capital productivity *per
>>se*.  One can find dynamic stories about increased (labor and) capital
>>productivity through innovation, without the detour into the concern about
>>biased technical change, in Smith, Ricardo, Malthus, and Mill, just to name
>>a few.  So maybe it's because Marxists had these other stories in the back
>>of their minds that they were led to thinking about capital productivity,
>>without particular reference to the specific factor biases that *Marx* is
>>led by his value theory to focus on.  Can it be shown otherwise?
>Gil, I don't think you find Marx's main point anywhere else. He 
>argues that profit is appropriated in terms of an average rate or so 
>called mark up on the basis of the average cost price in any given 
>industry, not in terms of the value actually produced. Therefore, it 
>is possible that one could lower his cost price vis-a-vis competitors 
>while producing less value relative to the money investment and still 
>gain an extra profit. This will make no sense unless we rigorously 
>differentiate between profit and surplus value.
>That is, Marx's argument (capital 3, p. 270) is that the most 
>effective and available (though not only) way to reduce cost price is 
>through technological innovation by which paid labor is reduced per 
>unit more than machine, raw material, depreciation, etc costs are 
>increased thereby (this of course does not mean unit values are 
>necessarily  falling because as a result of a rising rate of 
>exploitation, surplus value per unit could be rising and thus 
>neutralizing the decline in c+v per unit, v falling more than c is 
>rising as a result of the effort to reduce cost price).
>While unbeknowst to the entrepreneur this may have the effect of 
>draining the system as a whole of the value substance and thereby 
>exerting downward pressure on the profit rate, it will give an 
>immediate advantage to an innovator who will still claim the average 
>profit rate--which for all practical purposes will be unaffected by 
>his single innovation--on the basis of the average cost price in the 
>industry, not his own reduced cost price. He stands to make extra 
>profit even as he drains the system as a whole of the value substance.
>The most effective way to secure profit will thus appear, in apparent 
>violation of the labor theory of value, to be the saving of labor and 
>the greater (relative) use of fixed capital.
>The way Marx thinks this paradox works can only be explained on the 
>basis of his theory of value. Of course even accepting marx's value 
>theory, one can still argue that the innovations will become inputs 
>in other industries and as such will lower costs and raise profits 
>But this is a separate question, and the Okishio like arguments which 
>van Parijs describe depends on the methodology of comparative 
>statics, no?
>>  >>1)  The notion that that commodity prices are somehow "regulated,"
>>>>"rationalized (i.e. rendered non-"imaginary")" or at least in some
>>>>meaningful sense undergirded by corresponding labor values, measured by
>>  >>socially necessary labor time, a notion that Marx twists himself into
>>>>logical knots to defend under conditions of pure competition in V.III,
>>>>Chapter 10.  A corollary of this is his attempt to establish the aggregate
>>>>"transformation" identities in Ch. 9.
>>>Where does Marx "emphasize" this?
>>Here is a partial count:  Volume I (references are to page numbers in the
>>Penguin edition): 156, 168, 182, 188, 196, 269 (footnote, where he makes
>>the point emphatically because he needs it to justify his inference about
>>the salience of price-value equivalence at the end of Ch. 5), 476; Volume
>>III, throughout chapter 10, 478 (where he contrasts the determination of
>>the interest rate with the determination of typical commodity prices),
>>774-775, 1020; Grundrisse, 136-138;  and Marx's famous letter to Kugelmann.
>No, no! once the assumptions are dropped, what Marx is saying is that 
>changes in relative prices over time can be accounted for on useful 
>approximation by changes in the values of commodities. Allin says 
>this is the position of Ricardo for whom then value was an inherently 
>temporal and dynamic category, not reducible merely to exchange 
>ratios as some, like Bailey, would have it today. Marx is not saying 
>price is directly determined by value.
>>And last but not least, let's not forget the final point of my post:  the
>>basic raison d'etre for a Marxist theory of profit rate determination, such
>>as suggested by your macro identity, is as a component of a theory of
>>capitalist crisis. **But since the labor theory of value is
>>constitutionally incapable of distinguishing returns to "opportunity costs"
>>from "economic rents," it is constitutionally incapable of explaining why a
>>given fall in the profit rate (so long as it remains [even infinitesimally]
>>positive) would create a crisis.**  This seems like sufficient reason in
>>itself to question the relevance of value theory to the analytical project
>>your identity suggests.
>Again, I am not following you. But the falling rate of profit is not 
>what engenders capitalist crisis! Where did you get this idea--this 
>has been clarified since Grossmann, as Steindl recognizes.
>  It is the lack of surplus value as a mass for all the surviving 
>capitalists to meet the accumulation they have to undertake to beat 
>off intensified competition at a late stage of accumulation.
>The shortage then leads to widespread bankruptcies, credit 
>retraction, unemployment, underconsumption problems.
>Yours, Rakesh

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