**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 performancegiven to a start time. Whereas a lot of moneyis delivered.is slightly larger than, so that all things can be paid for with money in circulation, as well as a general reserve assetcan 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 growth^{41}, and the
inflation ratebecomes effective
and, finally, the deposits with the banks earnof interest. We compute, as always, on an annual basis, therefore the
time factoris the number of
years. We are now following the question: At what junctureis 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 timegoes to infinite foror , 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 eachand, 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.