Irrationality of calling interest the price of money
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It is irrational to call interest the price of money
not because of any dependence on the labour theory of
value, but on the purely formal terms in which the
universal equivalent form is analysed in chap 1 vol 1.
It relates to the mathematical type or dimensionality
of price. In type theoretic terms, prices are operators
that map between two types of numbers, where the first
is a type used to measure physical quantities of
commodities - what Marx calls a use value, and the
other is a type used to measure quantities of money.
Let P be the price of commodity x
Let q be a quantity of commodity x
then the effect of functionally applying P to q,
P(q) is of type m, where m is the money type.
Thus we have for all P, P:( x -> m)
where x is some commodity measure.
In contrast a rate of interst is an operator that
takes as its argument a time interval and yields
a real number, thus
for all R, R:( time -> real )
This is why it is irrational to call interest a price
of money. It would be marginally less irrational to
call it a price of time, but this is still wrong,
since it maps time onto the real numbers.
In order to get anything like a price of money one
needs another ternary function, let us call it
INTEREST_DUE which has the type
INTEREST_DUE: (m, ( time->real ), time -> m)
that is to say a function that takes the following
parameters
1. A quantity of money
2. A function from time to the reals
3. A period of time
If we Curry this function by partially applying it
to the second and 3rd parameters we can get towards
a price of money.
Let ContractGen:( R:(time->real),T:time ->(m->m) )=
INTEREST_DUE( , R, T)
That is to say, ContractGen is an operator which when
parameterised with a rate of interest and a time
interval yields an operator from money to money,
i.e., it yields a price of money.
Note that this argument is purely at the typetheoretic
level. It depends neither upon the concept of the
law of value, nor upon the specific form of the
price and interest rate operators. By specific form
I mean the fact that price is a linear operator
whereas the rate of interest is an exponential one.
The fact that the rate of interest and the rate
of profit are both exponential operators over
time, serves to indicate their similarity, but
it does not of course prove which one determines
the existence of the other.
The apparattus needed to formulate this argument
was perphaps poorly developed in Marx's time, though
the dimensional calculus of Newton and Babbages
work on the calculus of functions might have
provided a way of formalising it. In the absence
of adequate tools from mathematical logic, Marx
did a heroic task at formalising value theory in
vol 1 chap 1. The work of 20th century logicians
like Russel, Church, Martin-Lof etc provides us
with much clearer concepts to deal with it.