i
expansion for the firm is an enlargement of capacity without any
increase in the capital-capacity ratio at all.
Indeed, if the capital capacity ratio is increased and cost
reductions are thereby achieved,the profit margin will have to
increase. If investment is going to be increased further on the
same principles the point will sooner or later be reached where
the profit margin has risen to a size which makes condition (3)
invalid; the profit rate will then decrease.
For the purpose of interpreting the simple piece of algebra
presented further above two points have to be considered.
First:We shall assume that equal proportionate cost reductions
require the same effort in terms of learning. This assumption is
clearly relevant for the following statement: A given percentage
cost reduction (same effort) will have a stronger proportionate
effect on the profit margin (mark up) if the latter is small than
if it is large. This implies that the profit rate will also be
proportionately more increased in the first case than in the
second.
This may be explained in a rather intuitive way as follows:
Imagine that the profit margin is very small, nearly nil. A
certain proportionate reduction in cost,say by 10 p.c. will raise
the profit margin from a very small quantity to nearly 10 p.c.,
i.e. by a very high percentage, assymptotically infinite. On the
other hand if the profit margin is so large that the cost are a
negligible proportion of the value added then a reduction of cost
by 10 p.c. will leave the profit margin practically unchanged, its
percentage increase will be assymptotically zero. Between these
extremes of profit margin nearly zero and cost nearly zero there
is the whole range of finite positive profit margins. Their
percentage increase in consequence of a reduction of cost by 10
p.c. will continuously decline from nearly infinite to nearly zero
as the initial profit margin increases. Thus starting from a small
profit margin we have a good chance of doubling it by a certain
percentage cost reduction but with a considerably larger profit
margin the same percentage cost reduction will yield only a much
smaller proportionate increase in the margin.The conclusion is
that high mark ups ,given a certain profit rate, will discourage
more capital using methods of production.
Second:e are assuming that there is a certain targeted profit
rate, at least as a minimum, so that investments which yield less
are not carried out. To justify this assumption we can point in
the first place to the market rate of interest which is the
minimum an investment must yield to be satisfactory. In practice
the target will probably be higher if only on account of risk and
the standard will be set by the profit rate which can generally be
earned in the economy by investments similar with regard to volume
and risk to the investment considered. A monopolist (or
oligopolist) need not be satisfied with that either. But the idea
of a minimum standard of the profit rate will probably be relevant
for him,too.
3. The conceptual apparatus embodied in (3) was established in the
first place to analyse the problem of declining profit rate in the
case of an increasing firm which can realise economies of scale on
condition that it apply more capital intensive methods. The same
analytical apparatus can, however, also be applied to quite a
different case:Imagine that in the course of time new technical
methods emerge which are more capital intensive and permit a
reduction in cost ( the question of scale is disregarded in this
context). We may then simply replace the argument z (capacity) in