Alan's corn rate of interest
----------------------------
(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.
Paul
----
I would have thought the conclusion was the opposite. If
corns price doubles a ton of corn at the end of the year
with purchase twice as many other goods not half as many.
Alan
----
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.
Paul
----
Under your assumptions about the rate of 'corn interest'
the price in july should be the square root of $8.
Alan
----
(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
to be talking about, unless I misread what he says, which
refers to what happens when the time interval becomes
infinitely long. It refers to what happens when the time
interval becomes infinitely short.
Paul
----
No this is not what I meant. I was saying that since the
rate of interest is a parameterised function of time, substitution
enables one to derive an infinite number of ratios from it,
and it is thus dimensionally different from the ratios derived
from it.
Alan
----
constraint. A price change is in effect instant. There is
no time constraint which dictates that it must happen in
a finite interval.
Paul
----
It is not instant, but it can certainly be orders of magnitude
faster than production changes in certain specialised markets.
In other less speculative markets it is in practice bounded by
the rate of change of production technology.