[OPE-L:367] Re: Contrast between interest and the value form

Gilbert Skillman (gskillman@mail.wesleyan.edu)
Sun, 29 Oct 1995 15:51:25 -0800

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> This is further to the discussion, primarily with Gil
> on the utility of talking of markets in loan capital.
>
> >> an exchange
> >> ratio between x and y, is dimension y/x, whereas a rate of exchange
> >> between dollars today and dollars tommorow is a dimensionless number.
>
> >> But a second objection is that a rate of interest is not, as a I
> >> argued in a previous post, a ratio, but an exponential operator
> >> over time. As such it defines an infinity of such 'exchange ratios'.
>
> >I don't see this. The "exponential operator" only emerges by
> >allowing length of time periods to approach zero; in real world
> >divisions the relevant expression is P(0)(1+r)*t, where t, number of
> >time periods, is the exponent, and r is as I've expressed it. In any
> >case, the fact that it would have this *additional* property in the
> >special case of infinitesimal time periods doesn't negate its
> >*original* interpretation as shorthand for a price ratio.
>
> I dont see that time being differentiable has anything to do with
> it. Of course any practical calculation of interest compounds it
> at fixed time intervals, but the form of the function remains
> exponential. There exists no linear, or even polynomial function,
> that can constitute the LUB of a compounding debt. Thus an interest
> rate can never be represented by ratio - even a dimensionless one.

Sorry, Paul, I thought you meant that the interest rate entered the
exponent itself, as in the case of the expression for instantaneous
compounding.

But since this is not what what you mean, I don't see how you reach
your conclusion. I don't see how granting that the limit as t approaches infinity
of P(0)(1+r)**t is infinite implies that r cannot be expressed as a
ratio. Indeed it can be, as can be seen by anyone who lends money
for one period (or enters into a one-period futures contract, see
below).

> It is also important when discussing interest in general to abstract
> from inflation, and consider interest in terms of a currency of constant
> value. When we do this, the distinction between dollars today and
> dollars tommorrow vanishes.

No it doesn't, as any bank officer will confirm. It's just that the
distinction does not include a price-inflation component.

> The problem with brining in futures markets to establish that interest
> is a price, is that the argument works both ways. One could equally
> argue that commodity futures constitute not commodities but forms of
> debt and are thus special cases of interest, rather than interest being
> a special case of commodity exchange.

Fair enough, but it seems also fair to say that traders would
recognize a distinction between pork-bellies-today and
pork-bellies-tomorrow even in the absence of inflation.

> I agree with Gil that the dimensional congruence of interest and
> profit do not prove that they have a common social origin, but they
> sure as hell suggest it.

Perhaps a common social origin is suggested, but not necessarily the
origin Paul suggests. Cf. Marx's historical discussion of
"pre-capitalist" merchant's profit and of usurers' capital.

> Whilst Marx did not prove that there was a law of conservation of
> value in commodity exchange, he certainly asserted it. The acceptance
> of his assertion depends either on ones view of the evidence, or
> alternatively one may view it as being true by definition.

If value is defined as Marx does in Vol I, Chapter I, conservation of
value is tautologically true, since exchange is not production. I
don't know what "evidence" Paul is speaking of here.

Gil Skillman