20 Rule of Thumb: the Economic half-life Time
Already in the measured values for the
investment banking industry a certain half-life can be seen. So we ask
ourselves what such dynamic effects are a result of and whether there is a way
to estimate such times, at least roughly. Thus we consider the following highly
simplified model of a closed economy: An economy has the economic performance
given to a start
time. Whereas a lot of money
is delivered.is slightly
larger than, so that all
things can be paid for with money in circulation
,
as well as a general reserve asset
can
be accumulated:
(20.1)
With the growth of the economy now is growing the capital stock. Thus we can write
(20.2)
It is considered that
arises more money with the economic growth41
, and the
inflation rate
becomes effective
and, finally, the deposits with the banks earn
of interest. We compute, as always, on an annual basis
, therefore the
time factor
is the number of
years. We are now following the question: At what juncture
is the capital
stock greater than the sum of tradable goods? So mathematically, the
inequality:
(20.3) ?
Now, the relative share of capital stock at all levels of the economy, goods and assets, results from the ratio of capital stock to total national wealth
(20.4)
and to reduce the fracture results in
(20.5).
This gives a dimensionless
value that is called the "significance number" of capital in an
economy. When this value gets greater than 0.5 = 50%, so there will be a
transition, after which the meaning of production falls behind the financial
sector . This equation can now be easily resolved to the critical time 
, as in the case of equality holds
(20.6)
and thus after a short algebra we get
(20.7).
As is
, one can also
see that the critical time
goes
to infinite for
or
, which
corresponds to a stable system. Typical values for the savings rate and
interest rate are about 10% and 5% in the FRG. This gives a critical time of
years.
For moderate values, about 7% and 3%, the corresponding time is
years,
which is already more than
two generations. The critical time of a monetary economy depends so much on the
return on investment: With every percentage point it drops considerably.
Somewhat less strongly is the influence of the savings rate. With only 1% for
each
and, the critical
time is more than 400 years. An increase in interest rates to 10% results in a
lifetime of only a few decades. An increase in the savings rate alone to 10%
reduced but this time not much, it is then still almost 300 years. At moderate
values ofandthe critical
period is therefore from
years.
The rule of thumb for the
critical period can be reduced to a simple rule because of the shallow curve of
the natural logarithm. Asand
are significantly
smaller than one and commute to values of about 5%=0.05, one can roughly
approximate:
and
(20.8).
So that we can remember as a "raw rule of thumb" for the average lifetimes of capital driven economies:
(20.9).
With average interest rate on all assets of about 5%, we obtain for example
years (20.10)
magnitude as for the estimation of the saturation level.