27 Macro- and Microeconomic Substitution Rules
The general substitution results from the principle relation
.
Where we have seen in
connection with the derivation of the law of Gossen
after the k-th consumer choice
, we can now
formulate the most general context of substitution:
(27.1)
Because of the enormous diversity of economic
products59, ie 
, the last term
provides the case of a particulate product decision for only one product
(27.2)
from which we get a zero contribution,
since the removal of the k-th product makes no
appreciable change in the total. The relation (26.2) is exactly the deciding
factor as to whether the treatment of a system as macroeconmical
(open system) or a microeconomical problem (closed
system) is necessary or possible. The economic balance 
should disappear
for microeconomical problems. So "systemically
important" treatment is necessary, however, if this residue is
significantly different from zero. Of "systemic importance" we can
talk about when the changes of the k-products of a company leaving a
residue
, which
approximates the rate of change of GDP's:
(27.3 a)
Conversely, according to (27.1), we can write also:
(27.3 b)
and so after changing the elements
(27.3 c)
Because then always a relevance to the overall economy is given. One can thus express (26.3 c) in words:
Systemic importance is given if the total economic loss, given by the change of the trade of product k minus the change in GDP growth, is greater-equal to the damage caused by the change in trade of the product k for the producers themselve.
The amount of dY/dt has relatively high levels by 10% at the start of a national economy and then will decreases continuously down to 0 or even will become negative. We can therefore say, that over time more and more producers get relevant to the system, because of the harm reduction effect -dY/dt in (26.3 c) will decrease.
In this
context, the effect of financial products is particularly interesting. Derivative
financial products and the so-called bank's own business are characterized by
the fact that money is traded essentially in exchange for money or other
monetary products. For a closer look, we also split up the capital side to the
products of commercial banks (loans to domestic non-banks) and the products of
the investment banks (banking own transactions)
:
(27.4)
with
. These
financial
products are themselves merchandise and you can write it thus:
(27.5)
or
With 
and 
(27.6).
We now see the fundamental
problem of the banks own business: Since this increases
with time alsoincreases. As a
result, more and more financial products that come in
substitution-competition with products of the real economy. In addition, the
profits of these products have to come from the remaining capital stock of the
real economy, which gets relatively smaller and smaller over time as with 
.
This can be illustrated by considering the quantity equation. For this purpose
we differentiate now in respect to the 
trade
(ie the k-th financial
product of the number of m ) of such a
financial product:
and thus applies:
and reintegrated to:
With 
per definition. (27.7)
The net interest income of the k-th financial product is
(27.8)
which will be withdrawn from the real economy available capital stock. All financial derivatives results in the overall balance of
(27.9).
This means expressed in words:
Capital investment of commercial banks minus net interest income in investment banking = capital available for real GDP goods trade .