[OPE-L:7494] Re: determination of unique rate of profit?

From: Gil Skillman (gskillman@mail.wesleyan.edu)
Date: Tue Aug 06 2002 - 19:23:16 EDT

Hey Fred, welcome (almost) back.

>First, a summary of Gil's argument as I understand it.  Gil has agreed
>with me that absolute prices should be defined as exchange-ratios with
>money, rather than pure numbers (as in Sraffas theory), from which it
>follows that the money commodity itself (e.g. gold) does not have an
>absolute price (in the above sense), because the money commodity is not
>exchanged with itself.

Not exactly.  I argued in 7398 that the difference you saw in Marx's and 
Sraffa's account was apparent but not real, since Sraffa's units-free 
prices could be directly translated into exchange-ratios with money without 
changing any substantive aspect of Sraffa's argument.  Thus I argued that 
Sraffa's use of unit-free "absolute prices" was justifiable on "Occam's 
razor" grounds--inconsistent with the categorical assertion that absolute 
prices "should be defined" as exchange ratios with money, rather than pure 
numbers.  So let me put it instead that if desired Sraffian absolute prices 
*can* be expressed, without any loss or change in his theoretical results, 
as exchange ratios with money.  As a corollary, there is no *formal* 
difference between saying that the money commodity does not have an 
absolute price and representing it as the numeraire good in a system that 
includes it as a commodity.

>   Therefore, Gil suggests that the "price of
>production" equation for the gold industry should be replaced by an
>"accounting equation", which does not have the price of gold as a variable
>(since money has no price).

Rather, there's nothing to "replace," since the issue here is only one of 
interpretation:  how does the unit of gold-value tautologically present in 
a unit of gold break down into elements of the cost of producing that unit, 
augmented by the economy-wide rate of profit?

>   The resulting system of equations consists
>of n equations ((n-1) price equations and the "accounting equation" for
>gold) and (n+1) unknowns (the (n-1) absolute prices, the wage rate, and
>the rate of profit).
>Now, if the wage rate and the rate of profit are taken as given, along
>with the technical conditions of production (as I have suggested, because
>the rate of profit is determined outside this system of equations),

The coherence of the term "because" in the previous sentence is precisely 
the point under dispute, so it might be best to avoid a phrasing, such as 
the above, that takes this conclusion as given.

>  then
>this system of equations would be overdetermined, with n equations and
>(n-1) unknowns, such that no consistent solution is possible.  If, on the
>other hand, only the wage rate is taken as given, then the rate of profit
>would be uniquely determined, contrary to my previous argument.
>Gil, I hope this summary is accurate.  Please correct, if necessary.

Mostly differences of interpretation--see above.

>I think the flaw in Gil's argument is the "accounting equation" for the
>gold industry.

Let's see.  In the first argument that follows, you take issue with my 
purely theoretical scenario on the *historical* grounds that 1) prior to 
1900 gold was typically produced by self-employed miners rather than 
capitalist firms, so that the rate of profit in the gold sector was not 
necessarily equalized with that in sectors of commodity production and 2), 
money has not been a commodity since 1975, taking the form rather of fiat 

Now, let me say up front that I realize we have to come to terms with the 
implications of fiat money, and I was going to do that next, after our 
discussion re the system with commodity money had been settled.  But 
putting that next step aside for now, I don't see how these historical 
points bear on the purely theoretical issue in question, which has to do 
with Marx's Volume III treatment of the "transformation of commodity values 
into prices of production," and your characterization of the implications 
of that analysis.  As we know, Marx's analysis of capitalism proceeded on 
the basis of given levels of abstraction rather than on the basis of 
descriptively faithful representations of that system.  And the theoretical 
analysis Marx develops in K.III, Ch. 9, so far as I can tell, assumes both 
that (1) money is in commodity rather than fiat form and (2) all 
commodities (thus also the money commodity) are produced by capitalist 
firms.  Therefore I understand his theoretical results, which you defend, 
to depend on these conditions.  The point of my scenario, of course, was to 
show that the rate of profit *could not* be coherently understood as being 
determined analytically "prior" to prices of production under the 
conditions envisioned by Marx.

With regard to the form of money assumed in his analysis, Marx first posits 
that the "value of money" is fixed (K.III, p. 142), and then considers the 
implications of allowing "the value of the money commodity" to vary (K.III, 
p. 236, 238).  Between these passages and the treatment of the 
"transformation problem" a few chapters later, Marx neither outlaws 
commodity money nor even introduces the prospect of fiat 
money.  Consequently it is presumptive that his analysis is based on money 
taking the commodity form.

But second, Marx explicitly assumes that the profit rate is equalized 
across all sectors of commodity production.  In principle this could be the 
case whether or not all production is undertaken by capitalist firms (e.g., 
even self-employed miners might care about the rate of profit they're 
earning relative to other endeavors), but in context Marx is discussing the 
process of "Capitalist Production as a Whole," meaning that he's analyzing 
a system in which all production is subsumed  under capital. Consequently, 
it would seem that the scenario I constructed is relevant to the level of 
abstraction invoked by Marx in K.IIII Chapter 9, whatever the historical 
facts of the case.

Next, you argue that

>The usual adjustment process through which the rate of profit in a given
>industry is equalized to the average rate of profit is through a CHANGE IN
>THE PRICE of the commodity produced in that industry.  If, for example,
>the rate of profit in a given industry is below the average rate of
>profit, then capital will flow out of this industry, causing a reduction
>in the supply of this commodity, which in turn causes an increase in its
>price and therefore an increase in its rate of profit toward the average
>rate of profit.

Two points here:  first, the key word in your first sentence is "usual"--as 
opposed to "necessary."  Granting that gold doesn't have an absolute price 
in Marx's sense, the adjustment won't work like this, but that doesn't 
imply that the relevant *system* of prices can't be understood as adjusting 
to achieve the equalization of profit rates.  Presumably, in the 75-year 
historical window in which you grant that both commodity money and 
capitalist production of said commodity coexisted, there was some process 
that allowed a tendency toward profit rate equalization.  But even if not, 
per the comments I made near the top of this post no special qualitative 
difficulty is introduced to the problem of price adjustment by the 
inclusion of a numeraire good.  And second, this consideration goes outside 
of Marx's concerns in K.III Ch. 9, where he is not in fact considering the 
specific mechanism of price adjustment that achieves profit rate equalization.

>However, this usual adjustment mechanism is not possible for the money
>commodity, because the money commodity has no price.  Therefore, its price
>cannot change in order to equalize the rate of profit.  Instead, if the
>rate of profit in the gold industry is lower than the average rate of
>profit, and if capital flows out of the gold industry as a result, thereby
>reducing the supply of gold, then the effect will be a proportional

(expressed in gold)

>rather than an increase
>in the price of gold (since this is not possible).  This reduction in the
>price of all other commodities increases the purchasing power of gold, and
>also increases the rate of profit in the gold industry to a small extent,

there is no basis for quantitative judments such as that indicated by your 
use of the word "small" here.  Again, no special complication in the logic 
of price adjustment is introduced by specifying a numeraire good--even if 
it is understood that the numeraire "can't" have a price.

>to the extent that the price of its inputs are reduced by the general
>decline of all prices (which is likely to be very minor).

There is simply no basis in the foregoing for the use of the term "minor" 
in this characterization.  The same *systemic* logic that allows relative 
prices to adjust to ensure profit rate equalization in an economy without 
commodity money would also be at work here.

>Now, what if the rate of profit in the gold industry is still below the
>average rate of profit:  will there be a further outflow of capital, or
>will the extra incentive of the increased purchasing power of gold be
>sufficient to stop further capital outflow, in spite of the fact that the
>rate of profit is still below the average?

Since there is no barrier to complete adjustment to ensure profit rate 
equalization, there is nothing logically problematic about this 
scenario.  Relative prices will continue to adjust until profit rates are 
equalized, assuming the prices of production equations have a solution at all.

You next argue

>A related unique aspect of the adjustment process in the gold industry is
>that part of the adjustments in the supply of gold in circulation is
>through hoarding and dishoarding.

Again, this prospect is not featured in the abstraction on which Marx bases 
his analytical results in K.III Ch. 9, and thus is not at issue 
here.  Again, Marx's analysis in that chapter has nothing to say one way or 
the other about the details of the actual process by which prices adjust to 
achieve profit rate equalization, with or without the presence of the money 

>In sum, because the adjustment process to equilibrium of supply and demand
>in the gold industry is by means of a change in the price of all other
>commodities, rather than a change in its own price, the purchasing power
>of gold seems to play a more important role in the supply of gold, and
>perhaps even a more important role than the rate of profit.

In light of my previous comments, I don't see how this follows.

>I will stop here for now, and see what Gil (and Gary and others) have to
>say about the above.  I just think that the money commodity is
>fundamentally different from all other commodities, and that we should not
>just blithely assume that the rate of profit is equalized in the gold
>industry, like in every other industry.  I want to study the actual
>workings of the gold industry during the gold money period, and also think
>some more about the theoretical issues involved.

I agree that the historical details about the gold industry are 
interesting, but I just don't see how they are relevant to the purely 
theoretical issues--in keeping with Marx's abstraction in K.III Ch. 
9--being pursued here.  Let me capsulize the foregoing arguments another 
way:  do you agree that, were we to abstract from complications associated 
with hoarding, price adjustment, non-capitalist production, and fiat money, 
then in a fully capitalist economy with commodity money, one cannot *in 
general* coherently assert that the determination of the profit rate is 
analytically prior to the determination of prices of production?


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