26 Substitution Laws
We can now calculate such a utility function. Therefore we can invest the following considerations: When a new product is introduced or an existing product is promoted with the aim of increasing trade, we can estimate the resulting effects, provided by the trading volume with a prefactor:
(26.1)
The importance of this function is as follows:
Each product has a particular significance
to
the purchaser. However, this product can be degraded up to a certain degree,
(26.2)
so that the money saved can be used for another
product. This happens from the time
on.
As a rule, the substitution of a product is not abrupt, but spread over time,
so we assume a half-life
of the
substitution of the product. Such a half-life is particularly justified when we
talk about major product groups and/or a large number of buyers. We can use our
supply and demand-function that is now written as follows:
(26.3)
where, particularly in commercial and private
environment, through profit or loss or income change also an additional source
or sink of
may be present.
(26.4)
Such a source
would
allow the purchase of new products without compromising the residual volume,
in contrast, must
automatically trigger a corrective response. Let us first examine the situation
with
as it usually56 exists in an economy. We consider
the situation when two products x and y are in competition:
(25.5)
It is the product y to be advertised and
the product or product group x should be taken ago for the necessary
cash flows57 first The
remaining groups are again equal and can be subtracted.
It is therefore
and with the
function
, holds, where
the balance must be balanced:
(26.6)
This applies
and we may write with
the
following equation:
(26.7)
The product y thus takes the trade
products shares
of x. So
applies to the temporal changes
(26.8)
and because of
these changes are either be taken from 
or 
or both to
increase or to reduce. So the question still remains, which can take place in
the event of sources or sinks Q, if fromholds:
(26.9)
Now, Q may be invested in the x or y or both:
(26.10)
If the source Q is a one-time thing
, then this does
not alter the rates of change, because constants
vanish in the differentiation. If it is a permanent process, however,
like the interest on savings, then this share does not disappear. These sources
or sinks must therefore always be incorporated economically inoror both58.
This means that interest and compound interest is to generate only when trading volumes and prices rise accordingly. The same applies to income improvement or even decreases, which act according to their sign on trading volumes and prices as well.