[OPE-L:2420] Re: commodity money in Marx's theory

Paul Cockshott (wpc@cs.strath.ac.uk)
Thu, 30 May 1996 02:28:24 -0700

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>I think that Marxist theory could accomodate pre and post 1971 events. My
>point is a theoretical one: is not a money commodity system simply a
>limiting case of extended barter? is not in the nature of money to be a
>final means of payment precisely excluding barter and mere bilateral
>credit? is not money commodity something which must be capistically
>produced, and hence financed?
Clearly not, in that commodity monies are very ancient, long
ante-dating the rise of capitalism. Even within capitalist societies,
there is no requirement that the gold they used for money had been
capitalistically produced - it could have been looted from
earlier civilisations or produced under conditions of slavery.

>I would here revert the argument which goes
>from money commodity to valueless money. I would rather side with
>Schumpeter, saying that logically the credit money is prior to the money
>commodity, though historically the process *may* go on in the other
>direction - BTW, there are a lot of studies who question even this.

Paul C
I think that you are onto something here, but that your use of the
term debt to mark what you mean is perhaps mistaken.
Given the logic of the set of exchange relations existing in
a developed market, the set of sets of isovalent commodity bundles
is fully orderd and isomorphic to the real number line.
One can treat commodity bundle space as a metric space with
the metric function

d= |x(a1 - a2) + y(b1 -b2) + .... | (1)

where d is the distance between two points [a1, b1, ...]
[a2, b2, ...] in commodity bundle space, where
ai, bi stand for amounts of the ath, bth, etc commodities.
and x,y,... are a set of constants defined by the exchange
ratios of the commodities.

If we take the position of an agent having zero of all
commodities to be the origin in commodity bundle space,
then we can define the worth of any agent, in terms
of their distance from the origin, by substituting
zeros for the a1, b1 etc in the formula above. We then
get a formula for worth w as

w = |xa + yb + .... | (2)

This imposes an ordering on the bundles of commodities which
is isomorphic to the real number line.

It is this isomorphism that is the underlying logical basis
of a unit of account. It does not, however, immediately
imply the existence of debt, since a series of transactions
can be carried out between agents with positive balances
of all commodites using one of the commodities as an

The logical possibility of debt arises from a topological
peculiarity of euclidean 1 space - that the points on the
unit circle are disconnected. Consider the unit circle
in a metric space defined by some origin p. It consisits
of all points of distance 1 from p.

In Euclidean 2 space, the unit circle is topologically
continuous, one can move from one point on the circumference
to any other by an infinite set of intermediate points.
In Euclidean 1 space on the other hand, the unit circle
is the finite set {-1, 1}, which are not continuously
deformable into one another. Since the underlying metric
of commodity exchange imposes a topology on commodity space
that is isomorphic to 1 space, the unit circle defined
by all points with w=1 in equation (2) must be discontinuous.
In fact (2) defines a pair of parallel hyper planes on either
side of the origin.

One hyper-plane intersects the axes at positive and the other
at negative positions. We label agents on the first plane
net creditors and the others net debtors. The first plane is
familiar as the 'budget line' of neo-classical economics.

This creates the logical possibility of debtors, but that
is all. The logic of commodity exchange actually excludes
anyone becoming a net debtor. Any a movement that an agent
engages in by commodity exchange leaves them on the same
hyper-plane as they started out on. It does however leave
the loogical possibility of an equivalent exchange taking place
whereby an agent exchanges a negative amount of one
commodity for a positive amount of another.

But here we have the problem that there are no negative
natural numbers. There can be no negative quantities of real
commodities, you can not have -10 tons of barley in your
store. Negative numbers are un-natural and can only exist
within symbolic manipulation systems.

This raises the issue of the technology of calculation. So
long as this is done via calculi in the original sense or by coins,
reckoning tables or abacuses, you can not have negative numbers.
To get them you need written number systems, debt thus requires
the technology of written records.

Logically therefore commodity money is prior to debt, since the
latter involves the symbolic virtualisation of one or more
axes of commodity space. It is these symbolic or virtual axes
that consitute modern money. But they have to be symbolic before
credit can exist. Virtualisation is the precondition for credit.

Paul Cockshott