Re: A corrected footnote

["William B. Ryan" <william_b_ryan@xxxxxxxxxxx>]

----------from Trond Andresen------------
http://csf.colorado.edu/mail/pkt/dec98/0176.html

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Footnote: The danger of perpetuities
==========================

If a certain share of a capitalist's expenditure is on the condition
that it shall yield a future stream of dividends, and these in the next
round are not spent but financially reinvested in the same proportion,
etc., then simple maths indicate that for certain parameter values the
aggregate of all financial assets (mirrored by corresponding debts) will
grow exponentially. (In the following we consider stocks on a par with
consols, i.e. as implying a permanent claim to a future income stream):

Let -

aggregate net non-money financial assets (debt) = A(t) [$]
initial aggregate assets at t = 0 is A(0) = A0
average interest (dividend) rate = i [% / year]
the propensity to save out of financial income = s [ ]
average loan repayment rate (incl. perpetuities) = d [% / year]

Then accumulation will occur following the simplest
possible linear homogeneous differential equation there is:

dA/dt = ( -d + s (i +d) ) A(t) (1)

or, with the net asset growth factor defined as

g = -d + s (i +d) , (2)

dA/dt = g A(t) (3)

which has the solution

A(t) = A0 exp(gt) (4)

A(t) will grow, and we have asset/debt polarization, if g > 0.
In other words, this can be avoided with g <= 0. This condition may be
reformulated in three equivalent ways,

s <= d / (i+d) (5)

or (1-s) >= i / (i+d) (6)

or is <= (1-s) d (7)

For low nominal interest rates, savings rates, short average repayment
time (= 1/d) on loans - the system will not experience growing debt
burdens.

Note especially, following (7), that a relative increase in s has a
stronger impact towards polarizaton than a corresponding increase in the
interest rate i.

Tron Andresen

-----------------------------------------------------
-----------------------------------------------------
--------------in reply-------------------------------

>>>For low nominal interest rates, savings rates, short average
repayment time (= 1/d) on loans - the system will not experience growing
debt burdens.<<<

I think I follow this argument, but I'm not sure.  I believe what you
are talking about is compound interest or its equivalent.  Aren't you
saying that if wealth in general grows fast enough it will grow faster
than the wealth that accumulates through interest compounding, so there
would be no burdensome polarization?  Isn't that Berglund's argument?

Incidentally, during the 1920s, the phenomenon of round after round of
financial reinvestment was discussed by Douglas in *Credit-Power and
Democracy* and elsewhere in terms of it being a corollary to the A + B
theorem.

Bill Ryan: http://www.geocities.com/CapitolHill/Senate/7018

-------------from John Tyler------------
(personal e-mail)

>>>It is not exactly a theory, there are two very strong mathemtical
arguments that the traditional formula for compound interest is wrong.
This would affect practically every calculation in finance.  In
particular, it would bring into the question the theory of perfect
financial markets.  If market participants do not know the correct
formula to use in valuing securities, how could the market be perfect?
This is an argument with many, very serious implications.

By the way, I have heard of social credit, but I had no idea it was
still alive...<<<

John Tyler: j_tyler@xxxxxxxxxxx



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