# [OPE-L:7493] determination of unique rate of profit?

From: Fred B. Moseley (fmoseley@mtholyoke.edu)
Date: Mon Aug 05 2002 - 13:48:17 EDT

```I am back from several weeks of travel, and finally have the time to think
about and respond to Gils several recent posts (especially 7398 and
7399) on whether the rate of profit is uniquely determined by the
technical conditions of production and the wage rate.  Gil, thanks very
much for your very interesting "thought experiment".  It has been
thought-provoking indeed.    Sorry for my delay in responding.

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.  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).  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), 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.

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

First of all, this equation assumes that gold is produced by capitalist
firms.  But most of the gold produced until around 1900 was not produced
by capitalist firms, but instead by self-employed "gold-diggers".  The
great increases in gold production in the 1850s and then again in the
1890s were mostly produced by self-employed producers in California and
is a capitalist industry was not true before the 20th century.  Things
changed in the 20th century.  After the easily extractable gold was
exhausted, deeper mines had to be dug and heavy machinery utilized, which
led to the dominance of capitalist firms.  And S. Africa became the main
source of gold.

In the pre-20th century case of gold not produced by capitalist firms, the
rate of profit is equalized among the (n-1) capitalist industries,
producing non-monetary commodities.  Therefore, the system of equations
expressing the equalization of the rate of profit should consist of only
these (n-1) equations, with no equation for the gold industry (such as
your accounting equation).  This system of (n-1) equations has
(n+1) unknowns - the (n-1) prices, the wage rate, and the rate of
profit.  In this system, taking the wage rate as given does not uniquely
determine the rate of profit.  These (n-1) equations  and the wage rate
are consistent with an infinite number of rates of profit, which could be
determined outside this system of equations, as in Marxs theory.  And, if
the rate of profit is also taken as given, along with the wage rate, then
this system is not overdetermined, but rather determinant of the
(n-1) absolute prices.

Secondly, your accounting equation assumes that money is a commodity,
which has not been the case since 1975.  In the current period of fiat
money, there is no industry that produces the money commodity, and no
industry whose commodity-product does not have a price.  Thus there is no
equation for the money commodity that does not have a price, like your
accounting equation.  Instead, all n industries have a price, and all n
equations have a price variable.  Thus the system of equations now
consists of n equations in (n+2) unknowns  the n price variables, the wage
rate, and the rate of profit.  Again, taking the wage rate as given does
not uniquely determine the rate of profit.  The given technical conditions
and wage rate are consistent with an infinite number of rates of
profit.  And, if the rate of profit is also taken as given, along with the
wage rate, then this system is not overdetermined, but rather determinant
of the n absolute prices.

Therefore, your accounting equation for the gold industry is not valid
before 1900 and after 1975.  At best, it is valid only for the 75 year
period of capitalistically produced gold as the money commodity, and I am
not sure it is valid for this period either.  In this case, your equation
assumes that the capitalist gold industry participates in the equalization
of the profit rate, just like all other capitalist industries.  But I am
not sure that this is true.  At the very least, the adjustment process
through which the rate of profit in the gold industry might be equalized
to the average rate of profit is fundamentally different from the usual
adjustment process in all other industries.

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.

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
REDUCTION IN THE PRICE OF ALL OTHER COMMODITIES, 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,
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).

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?

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.  The main cause of variations in the
supply of gold from hoards is changes in the purchasing power of gold,
caused by changes in the prices of all other commodities.  The rate of
profit plays no role in hoarding and dishoarding, since gold is not being
produced.  In the case just discussed, of a below average rate of profit
in the gold industry, it seems possible that a partial adjustment to equal
rates of profit, which reduces the prices of all other commodities, would
induce some dishoarding, and thus would offset the reduction in the supply
of gold currently produced, which would inhibit the further adjustment to
equal rates of profit in the gold industry.

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.

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 would appreciate any references on the gold industry, and especially on
the issue of the equalization of the profit rate in the gold industry
during the gold standard period.

Gil (and others), I look forward to your response and to more of this
productive discussion.  I am up in Maine and have access to email only 2
or 3 times a week, so my response rate will probably be slow.