# [OPE-L:445] Infinite Interest rates

Alan Freeman (100042.617@compuserve.com)
Tue, 7 Nov 1995 14:27:28 -0800

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Re: interest rates and the price of money

In the discussion between Gil and Paul on the rate of
interest a rather important point seems to have been
overlooked.

Both Paul and Gil have assumed that price is a continuous
function of time. In this case, prices cannot 'suddenly'
rise in a step function so that at one point, let us say,
corn costs \$2 a bushel and at another point \$4 a bushel.
On this basis one can always make a comparison between
the price of corn at one point in time and the price of
corn at another and derive a finite magnitude and,
provided also the variations of price with time are
differentiable, this magnitude will tend to a definite
limit as the period of time becomes smaller.

To take the simplest case, if the price of corn is rising
at the 'rate' of 1000er year, ( that is, the transition
from \$2 to \$4 takes one year and goes up in equal
increments in every time period).

Consider first the movement over a whole year. We can say
by comparing January 1 1993 with January 1994:

(a) that the price of corn at the end of a year is twice
as much as at the beginning

(b) that the ratio of the two is as 2:1

(c) or, that the rate of 'corn interest' is 100%: i.e. if
nothing else was changing in price, the same amount of
corn would be in some sense 100 0.000000e+00ss valuable at the end
of a year; if used as a form of money, for example, it
would purchase half as many goods; if we considered its
power to purchase the past labour of society it would
(probably) purchase half as many goods, etc.

(d) or, that the 'price' of 1994 measured in 1993 corn is
2 (1 unit of 1993 corn purchase 2 units of 1994 corn) so
that in a rational and accurate futures market, one could
go to the market in 1993 and buy 1994 financial
instruments denominated in corn with face value C2 and
buy them for C1, just as one can now buy a bond, a bill
of sale or a futures contract denominated \$1 for 50 cents
because the interest on it is discounted. Or, to put it
the other way round, the interest rate is the inverted
expression of the expected price change - [here we are
dealing with a pure commodities market and not
considering instruments which also yield a regular
payment such as a dividend, i.e. we are considering the

Because of the continuous nature of the change in price,
however, we could also go to the market on July 1st and
buy 2 units of corn for \$3. That means that

(a) the price of corn after 6 months is 50% more than at
the beginning

(b) the ratio of the two is as 1.5:1

(c) the rate of 'corn interest' is *still* 100%: January
corn is 50% more 'valuable' than July corn but since the
period of time is only six months, we can say that the
price of corn is rising at 1000er year just as before,
or that its value is falling at the same rate, which is
the same thing.

(d) or, that the 'price' of July corn measured in January
corn is 1.5 (1 units of January corn purchase 1.5 units
of 1994 corn) so that in a rational and accurate futures
market, one could go to the market in January and buy
July financial instruments denominated in corn and worth
C1.5 and buy them for C1.

Looking at statements (c) in both cases we see that the
rate of 'interest' is always 100% because, no matter that
the time period becomes smaller, the rate of interest
measured on an annual basis is the same. The dimension of
time appears in both numerator and denominator when the
relation is expression in the form of interest, instead
of the form of a price.

This I take to be the substance of the dispute between
Paul and Gil. This could be a misreading.

However, there is no reason for the price of corn to rise
at a uniform rate and in general it does not. Prices,
unlike quantities, change discontinuously. They do not
rise steadily over time but in jumps. At one point the
price of corn is \$2 and in the next instant it is \$3, at
the moment the decision to change the price is made.
Indeed, in an information society this becomes more
pronounced, as changes in price are now made available on
the dealing screens within 30 seconds.

In this case, if one reduces the time interval over which
the 'own interest' in the above sense of any given
commodity is calculated,

(a) the rate of interest is not independent of the time
interval

(b) if the time interval contains the point at which a
step increase in price takes place, as the length of this
interval is decreased, the interest rate tends to
infinity. This is not the same infinity which I take Paul
refers to what happens when the time interval becomes
infinitely long. It refers to what happens when the time
interval becomes infinitely short.

This is not a hypothetical or marginal case but
corresponds to what actually happens. In the last big
European devaluation, for example, following traditional
theory based on the principles which Gil outlines, the
Swedish government attempted to maintain the exchange
rate of the Krone for the DMark by raising the interest
rate on the Krone. If the rate of change of this exchange
rate was bounded above, then this would have been a
rational procedure. There would have to be an interest
rate at some point, no matter how high, at which this
interest rate exceeded the (expected) rate of devaluation
of the Krone and at this point speculators would have
stopped selling Krone, taken their earnings, and sold off
their DMarks to buy Krone at this extraordinarily
profitable rate of interest.

What happened was that the rate of interest on the Krone
rose to a ceiling of 500%. At this point the Swedish
monetary authorities concluded that there was (their
words) "no rate of interest at which the market would
accept Krone".

The reason for this is not hard to see. In the case of
the production of use values, the rate at which new use
values can appear on the market is determined by the
constraints of production. Use values cannot appear out
of nowhere. They have to be fabricated or, in the case of
services, provided, and this takes time. This time of
production is in my view one of the fundamental reasons
why equilibrium representations of the market do not
work.

In the case of price changes however there is no such
constraint. A price change is in effect instant. There is
no time constraint which dictates that it must happen in
a finite interval.

A second but distinct point, which I think we should
discuss, is the following:

What is the status of transfers of commodities between
capitals or 'circulation' in the pure sense (abstracting
from price movements)? This is in principle also
instantaneous. However, in an exchange of commodities
there is no transfer of values. This I believe is one of
the 'axioms' of any sound value theory; value is what is
conserved in exchange at any given set of prices, not
only in the sense that the total value is conserved, but
in the sense that the value in the hands of each party to
the exchange is preserved. I think it can be shown that
logical contradiction arises whenever there is an
assumption which amounts to arguing that the exchange of
commodities results *either* in the creation of new value
*or* in a transfer of value.

If one accepts this, then it follows that new value can
only be created in production, a giant step forward in
clarity. From then we can proceed to discuss what actual
component of the productive process is responsible for
the creation of new value, and we will find that if we
identify any agent other than labour (e.e 'capital') , we
are led back into contradiction because we are driven to
conclude that value can be created independently of
production.

That is, production *is* the expenditure of labour, and
that is why the magnitude of labour is the most
appropriate measure of the magnitude of value.

So in that case, when does the transfer of value take
place? In my view, at the point when the change in price
takes place. If I have commodities whose value prior to a
change in prices is \$10 per unit, and you have
commodities whose value similarly is \$10 per unit, and we
exchange my commodities for your commodities, then there
is clearly an exchange of equals and no value has been
transferred. I had \$10 (times the quantity exchanged) in
value before, and so did you; I have value \$10 (times the
quantity exchanged) after, and so do you.

Now suppose that the price of my commodities sinks to \$5
and the price of yours rises to \$15. This price is now
different from the value of the commodity. One (false)
way of looking at what happens is this: clearly if we
trade in a ratio given by these prices I have to supply
three units to each one of yours. Therefore, for each one
of these units you acquire \$10, \$30 in all, but give up
only 1 or \$10 worth of value. You have apparently gained
\$20.

However, the loss of value did not take place at the time
we traded but at the time when the price changed. The
moment that my commodities fell in price from \$10 to \$5,
I lost \$5 for each unit of that commodity in my
possession and similarly you gained \$5 for each unit in
your possession. This is quite regardless of what we
actually trade. It is a transfer of value effected by the
price system, not by the act of trade.

with Ricardo for not recognising that 'commodities are
dispute it might be useful to return to the text of Marx
on this question.

Value theory in my opinion has to recognise the
fundamentally different character of transfers of value
effected by a change in price, transfers of value
effected by a movement of commodities or titles to a
commodity, and transfers of value effected by production.
This is why, in my opinion, the first act of abstraction
in establishing the foundation of a system of value is to
distinguish clearly between production and circulation.

Paul Cockshott [OPE-L:364] Contrast between interest and
the value form
Paul Cockshott [OPE-L:363] Re: Chaion Lee's Short
Question
Gil Skillman [OPE-L:366] Re: Chaion Lee's Short Question
Paul Cockshott[OPE-L:367] Re: Contrast between interest
and the value form
Duncan Foley [OPE-L:372] Re: Contrast between interest
and the value form
Gil Skillman [OPE-L:373] Re: Chaion Lee's Short Question
Gil Skillman [OPE-L:383] Re: Contrast between interest
and the value form

Alan Freeman