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.
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.
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.
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.
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.
Paul C