The Problem of Capital Intensity
Josef
Steindl
AL00659056
TTTIV.
THE PROBLEM OF CAPITAL INTENSITY
Chapter III of Small and Big
Business.Economic Problems of the
Size of Firms.Oxford 1945.
Entirely re-written 1988..
1. In a comparison of small and big firms the question also arises
whether they differ as far as their capital-output ratio is
concerned. Apart from the "morphological" question of the
characteristics of firms of different size there exists also the
different but somehow related question how a growing firm will
change and, in the present context, how it will use its
accumulating capital: To what extent it will use it to produce the
same output with more capital and to what extent for just
expanding capacity. This second aspect of the problem leads us to
consider the capital-output ratio in a much more general context,
including the question of its historical change.
ivvv&a<c ( l
!? u&n
1 VVv
We are not oversupplied with data on capacity or capital. I tried
to use the U.S. Statistics of Income for corporations which give
capital assets and sales ( Table 1 ).There seems to be a strong
increase in capital-sales ratios in various industries in the
highest size classes, and more generally in all industries in the
lowest size classes.The crux of these data is the vertical
integration of the big concerns. In fact it is only too easy to
see that the strong increase in the capital-sales ratio in the
highest size classes of corporations occurs in the pulp and paper
industry where the large concerns own forests, in the iron and
metal industries where they own mines, and in the chemical and
allied products industries where they own oil wells etc and means
of transport like tankers. In the other industry groups the
increase in the highest size classes is either absent or small.
On the other hand there is a very general increase in the capital-
sales ratio in the lowest size classes. This can be explained very
easily by the fairly general consideration that small firms lack
funds and therefore prefer hiring or leasing to ownership wherever
it is feasible. Thus with increasing size, from the smallest size
class to the medium ones hiring and leasing is replaced by
ownership of buildings, shops,plant, premises,means of transport
e t c .
This has practically the same effect as a decrease in
proportionate indebtedness. In fact, hiring or leasing means
borrowing capital in natura instead of incurring debt in order to
buy the equipment in question. . In the form of a rent the small
firm pays the equivalent of interest and annuity on borrowed money
and in so far as the equipment in question is necessary to the
running of the enterprise the firms profits are precharged in the
same way as they are when they have borrowed money. The practice
of avoiding ownership has therefore nothing to do with the
capital-output ratio which is a matter of technology but is rather
pertinent to the topic of the following essay on the financial
structure of firms.
As far as production technique as such is concerned statistics of
the above type can give us little help and we have to turn to
other sources such as engineering data to get at least a tentative
answer. The evidence,in fact,tends to show that the capital-output
ratio often decreases with increasing size of the production
rfj < r>
unit.To be more precise,the capital investment required for a
given capacity decreases with increasing capacity ( Weintraub
1939; Bain 1956; Haldi and Whitcomb 1967; Pratton 1971 ). This is
largely the consequence of some of the same principles which are
responsible for large scale economies: The dimensional scale
effect which implies that the surface increases less than the
volume with increasing size of a container. This gives rise to the
two-third rule: If the surface of the container is linked to the
cost and the volume to the capacity, then, since the first rises
with the square and the second with the cube of the dimension, the
cost will rise with a factor of 2/3 of a proportionate increase in
the capacity. For the firm which uses the container the rule will
be relevant, for example, for the fuel requirements; these are the
current or ordinary large scale economies. In the production of
the container the above considerations will be important for the
cost of a larger or smaller capacity. Another consideration
concerns the whole trend of technology which is typified by the
conveyor belt (mechanisation): The unremitting continuity of the
process not only saves labour but it at the same time also
increases the output of a given equipment.
2. It should be of considerable interest to analyse the relations
between capital-output ratio,profit rate, profit margin and
technology. To sharpen these concepts somewhat we shall talk of a
capital-capacity ratio,and consider a profit margin at full
capacity use. The idea is that we should distinguish between the
economies of scale and those savings which automatically arise
owing to the presence of fixed cost from a fuller utilisation of
an existing equipment. In other words we should distinguish
economies of scale and economies of utilisation. Again, we should
distinguish the changes in the capital-output ratio which arise
technology. To sharpen these concepts somewhat we shall talk of a
capital-capacity ratio,and consider a profit margin at full
capacity use. The idea is that we should distinguish between the
economies of scale and those savings which automatically arise
owing to the presence of fixed cost from a fuller utilisation of
an existing equipment. In other words we should distinguish
economies of scale and economies of utilisation. Again, we should
distinguish the changes in the capital-output ratio which arise
merely from varying utilisation of an existing equipment and
infrastructure and the changes in the capital-capacity ratio.
Another refinement needs to be made,too. Instead of gross value of
output we shall use the concept of value added when we define
capacity,that is, we shall talk of capacity in terms of value
addegl; and in defining the profit margin we shall, instead of
relating cost to output value consider the cost net of raw
materials and other goods bought from outside the firm in relation
to the value added. In this way different degrees of vertical
integration will not, in principle, disturb the comparison between
firms because a firm with raw material supplies integrated will
not only have more capital but also a correspondingly greater
value added and a greater profit.
Let us now try to define the relations in terms of algebra. Let c
be the cost exclusive of raw materials at full capacity use,and v
the capacity output in terms of value added. The ratio of the two
will be a function of the size z of the firm (measured in terms of
real capacity -a quantity!):
e Coil /tflur oi fctf
2 OOj^JtuXiv^ OidyLvdl Aom* wHuJL odjeUcb
* Affe rf it* V/vv.
2- f aß?
(1)
which
will be
in terms
c/v = F(z).
If we assume that large scale economies outweigh the cost
firms have to occur in order to obtain a larger market F
a decreasing function of z. The profit margin will be
1 - c/v = 1 - F(z) or 1/F - 1 if we measure the margin
of cost (mark up); it will thus be, on the conditions just stated,
an increasing function of z. From this it does not necessarily
follow that the rate of profit will be an increasing function of
the size of the firm, if the increasing size by any chance
involves a greater capital intensity. We ask now for the
conditions under which the larger firm will be superior also in
terms of the profit rate.
Let the ratio of capital to capacity be a function of the size of
the firm i.e.of capacity z:
I /v = (p* (z) ( 2)
As we have seen above this function may well be decreasing; but
the interesting case which we are going to analyse arises when it
is increasing.
The rate of profit can be defined as follows:
el = v - c;
e J ( z ) = 1 - F ( z ) •
e=( 1 - F
If the rate of profit is to be increasing,constant or decreasing
with size its derivative with respect to size z must be
positive,zero or negative:
de/dz /e = - Fy/(1-F) - ^ 0.
The condition for a constant or increasing profit rate will thus
be
4.
- F/F ( 1/F - 1 ). (3)
The condition (3) involves three magnitudes: The proportionate
increase in the capital-capacity ratio <j$ /^? , the proportionate
decrease in the cost to value added ratio VjfF, and the profit
margin as a percentage of cost, 1/F - 1 (the mark up). In words
the condition (3) says: If an increase in the size of the firm
involves a certain proportionate increase in the capital-capacity
ratio then this must not be larger than the proportionate decrease
in the cost-value ratio, divided by the mark up, if the rate of
profit is to be prevented from falling. Thus if the increase of
the firm is associated with more *’capitalistic** methods of
production their adoption will be limited not only by the possible
proportionate cost saving achieved but also by the size of the
mark up from which we start.
Now it will be appreciated that usually firms have more than one
way of expanding by investment.They can avoid more capital
intensive methods altogether if only by continuing to use the same
techniques on a larger scale.In many cases they will, however,
find superior new techniques which enable them to expand their
size without increasing the capital-capacity ratio at all. Neo-
classical theory, in the contrary, can conceive of additional
investment only in the form of using more capital intensive,more
’’capitalistic" methods of production. The reason for this is
probably that they assume,tacitly or openly, full employment. If
we are not constrained by this assumption we can easily see from
the above analysis that there are powerful impediments against
increasing the capita1-capacity ratio and that the natural way of
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
the functions F and &) by t (time), where t may be conceived as
operational time.so that it really measures the pace of technical
progress.We deal now instead of with scale effects and firm size
with the historical development of technical methods and of
capital accumulation i.e. with the declining rate of profit as it
was conceived by Karl Marx. The conditions established in equation
) fully apply to^ this case, too, __ __________________ ^
TWe alTe^Tnyw—foFced , however , to elaborate, our simple concepts a
little further. The ratio of cost to value added is in reality the
resultant of two very different forces: Product per man, a concept
pertaining to the "real"sphere,and the wage price ratio, dr "real
wa'ge" , a concept which belongs to the price sphere. We can ^put
this in the simplest form if we choose to adjust our definitions
for\this purpose: Let us exclude depreciation from the valueV
resultant of two very different forces: Product per man, a concept
pertaining to the "real"sphere,and the wage price ratio, or "real
wage", a concept which belongs to the price sphere. We can put
this in the simplest form if we choose to adjust our definitions
for this purpose: Let us exclude depreciation from the value
added,treating it like a raw material, so that value added
consists only of wages and net profits. We can then define
c/v = m/z . w/p. (5)
Here m is the employment so that z/m denotes product per man; w is
the wage and p the price, w/p may be called the "real wage"; more
precisely it is the real wage in terms of the products of labour.
The question is how far these two forces, product per man and real
wage, are dependent on each other. In the context of our argument
productivity increases in consequence of an investment activity
which involves a change in the technique. ( The point of view is
basically different from the neoclassical theory where real wages
play an active role in shaping production technique,the real wage
being in turn determined by the need to get the labour market
cleared). This productivity increase will change our c/v ratio,
but how far can the "real wage" modify this effect?
We have already taken account of the possibility of such an effect
further above when we discussed the case of the firm which
outgrows other firms and therefore has to capture a larger share
of the total market in order to gain the larger size: It has to
overcome the barrier of imperfect competition by increasing the
"real wage" and this will partly counteract the effect of
increased productivity on c/v.
But what about the other case, the development of technology in
the course of history,where we ask how capital intensity develops
in the course of time as a consequence of the introduction of new
techniques? We have to consider this problem by steps.lt is true
that over time an increase in the productivity will tend to lead
to higher real wages.But this can not be considered in the first
step of the analysis when the investor has to decide whether the
use of the new technology will yield him a satisfactory rate of
profit.Here we have, however, the possible necessity for the
innovator to increase his market in view of the scale of his
investment.The situation will therefore be similar to that
encountered in the comparison of firm sizes. We shall assume here
again that the sacrifice needed to overcome the barriers of
imperfect competition is more than outweighed by the gain due to
the new technology. To simplify the following analysis we shall
assume that the reduction in the price-wage ratio needed to
capture the required market is taken account of already in the
initial values of p and w from which we start. In this way we
shall be able to assume constant real wage in the analysis of the
first step of our problem. What happens after the new method is
introduced - after the first step- is another story which we are
going to deal with later. For the present we assume constant real
wages. The changes in the cost-value ratio c/v will then depend
only on the change in output per man. In the same way as we did
with the ratio c/v we can also separate the capital coefficient
I/v into a real and a price element:
I/v = I/z . p’/p .
It will be useful at this point to introduce a new measure, the
capital to cost ratio I/c. This will depend on the real capital
per man I’/m and on the ratio of investment goods prices to wages
in the investment goods industry w': )?'
I/c=I,/m.p’/w’ (6)
The difference between capital per man (capital intensity) and the
capital-output ratio has played a role in the history of
doctrines. Marx did not fully appreciate the importance and
consequences of the distinction also he was evidently aware of it.
The concept of a capital-cost ratio has been introduced above
because it is related to capital per man, as equation (6)
shows.Since we assume wages and prices to be given at this stage
of the argument, capital per man and the capital-cost ratio will
move in step.
Now it is easy to see that the link between the capital per man
and the capital-output ratio is the output per man. A similar
relation can be established for the concepts which we have
introduced. Denoting the capital-cost ratio by = I/c we have
^ = I/v = I/c . c/v = jQ. F
By differentiation we obtain
9
output ratio the
F/F.
as a condition for
following relation
an
increase
in
(7)
the capital-
That is, if the capital-cost ratio increases more quickly than the
cost-value ratio declines then the capital-output ratio will
increase. Seeing that we have assumed constant price-wage
relations this also implies that if capital per man increases more
quickly than product per man then the capital-output ratio will
increase.
That capital per man has historically increased seems to be true.
If this growth had not been matched by a corresponding growth of
output per man the capita1-output ratio would have had to
increase,but most of the empirical evidence as we have already
7
said does not seem to confirm this ( Kuznets 1962 ).
We may now arrive at something similar to condition (8) on a more
traditional path. Let us assume, for sheer analytical simplicity,
a log linear production function of the following form:
ln 1/F = a lnJ2 • O)
This is, assuming prices and wages constant, equivalent to a log
linear relation between output per man and capital per man.
If we differentiate the relation (9) we find that condition (8)
will be fulfilled according to whether a ^1; a=l corresponds to
the case of Harrod neutrality, a 1 is respectively the case of
diminishing or increasing returns. The case of decreasing returns
does not seem to be the rule in our economy whether we compare
firms of different size or the historical growth of capital
intensity; this is illustrated by the experience or the two-third
rule. It is quite possible, however, that this case of decreasing
returns of capital intensification exists potentially, i.e. it
might be experienced if the tendency to use more capital per man
were "forced" beyond the limit at which it usually has stopped.
That would mean that the neo-classical economists which postulated
such a law of diminishing returns were quite right in so far as
they talked about a possibility but wrong in so far as this
possibility seems to have had little practical relevance.
The implication of this is, as (8) shows,that the capital-capacity
ratio does not increase either with firm size or as a function of
time and technical progress,and the available data do not seem to
contradict this conclusion.
As we have seen further above an increasing capital-capacity ratio
would ,in our simple steady state growth model, sooner or later
invalidate the condition (3) because it would necessitate an
increased profit margin which would make the adoption of capital
using methods less and less likely.
Is it not natural that techniques which lead to such results are
not applied by those business men who survive the struggle for
existence? I would be inclined to answer in the affirmative and
the conclusion would then be that the simple relations embodied in
equations (3) and (4) and the arguments put forward above in
connection with it offer an explanation for the apparent fact that
entrepreneurs do not "force" capital intensification, that the
capital-output ratio did not rise historically, in other words
capital using processes are in general avoided and entrepreneurs
with funds to invest prefer "horizontal" expansion to a purely
"vertical"one and apply capital intensive techniques not before
they have been developped in such a way as to guarantee sufficient
cost savings to keep them out of the range of diminishing returns.
4.So far the analysis has proceeded on the assumption of constant
real wages but this is only the first step of the argument
concerning the historical evolution of the capita1-output ratio.In
the next stage the real wage rises as a result of the efforts of
labour to capture a share of the increased prosperity due to the
enlarged output per man. We have to assume that this adjustment
takes some time because if it were immediate it would leave no
gain for the innovator, and in so far as he could anticipate such
an outcome it would eliminate any incentive to innovate.
When it finally takes place the increase in real wage can take the
form either of a decline in prices or of an increase in money
wages. The effect on c/v = F will in both cases be the same.What
will be the effect on I/v? So far we have taken I as given which
really implies that we have left the whole department producing
capital goods outside of our system which in this way really
represented only the consumption goods department. Extending the
analysis now to the capital goods sector we can see that I/v will
have to increase as a consequence of the rise in real wages. If
money wages increase this will affect also the capital goods
sector; the prices there will be marked up and I will increase.
If, in the alternative case, the prices in the consumption goods
sector decrease this will depress v and in this way again lead to
an increase of I/v.
Thus the rate of profit in the consumption goods sector will
decline for two reasons: The profit margin will decline and the
capital-output ratio will increase:
e = (1 - F )j$
If the real wage ( w/p ) increases just so much as to compensate
for the decline in real cost ( m/z ) we are back in the situation
from which we started, as far as the cost-value ratio (c/v = F) is
concerned: In fact, the increase in "real wage", as we have seen,
will increase the capital-output ratio; this could be avoided only
if the "real cost" of the production of capital goods has been
reduced to a corresponding extent by technical progress in this
sector.
Even that,however, would not be sufficient to restore the profit
rate to its former level if the capital-capacity ratio had been
increased in the process of technical change in the consumption
goods department. In fact, it will be realised that a policy of
constant"efficiency wage”, that is, of compensating reductions in
"real cost" by corresponding increases in real wages is not
compatible with an increase in the capital-capacity ratio. But
we have hardly heard of that problem in the decades of full
employment when something like efficiency wage policy was often
practiced, and this seems to confirm the opinion expressed further
above that an increase in the capital-capacity ratio can hardly
have played a role in that time.
If technical progress in the capital goods sector has not kept
pace with its advance in the consumption goods department there
will be a fall in the rate of profit in the latter department, and
a brake on investment. This will produce a structural crisis in
the capital goods industries. Sooner or later this will enforce a
process of cheapening capital goods by introducing new more
efficient types of equipment as a condition for the survival of
this industry. In this way the process of innovating by investment
can be set in motion again in the consumption goods industries.
Thus there seems to be a race between cheapening of output (or of
labour) and the cheapening of equipment so that neither gets too
far ahead of the other which again tends to explain why the
capital-capacity ratio has not risen historically and why it does
not rise with the size of the firm.
THE DISPERSION OF EXPECTATIONS IN A SPECULATIVE MARKET.
It may be assumed with some plausibility that the participants in
a speculative market - for example a market for bonds or for
foreign exchange - have different expectations with regard to the
future price, or the direction in which prices are going to
change.
Contrary to some opinions this diversity of expectations is a
condition for the attainment and maintenance of equilibrium in
these markets. ; it must be fulfilled in order to assure that an
additional offer coming from outside will find buyers or that an
additional demand coming from outside will will find sellers. A
further condition is that there must be a generally accepted idea
of a normal price level to which prices ultimately tend to return.
This normal price will be a range of prices rather than one single
price. Though the estimate of this range of prices may not be
uniform either,it is much more uniform than the earlier mentioned
price expectations: It must have some basis in objective facts.
Thus in the case of a manufactured good there may be some general
information about the range of costs. In the case of an exchange
rate there is - or at least there used to be - an idea about
purchasing power parity or relative cost, although in our times
this has obviously become more and more an obscure and irrelevant
quantity. In the case of the long term rate of interest there used
to be a historical experience that it rarely goes outside a
certain range,but again this "basis in fact" has become more and
more shaky in view of the violent fluctuations of modern capital
markets.The undermining of concepts of normalcy in certain markets
has been accompanied by great instability, so that it does not
contradict but rather tends to confirm the rule that generally
accepted ideas of a standard of normalcy are necessary in order to
maintain more or less stable markets.
The different expectations of participants in a market could be
ordered in the form of a frequency distribution (see figure 1 ).It
will be the distribution of expectations in a market according to
expected price. In the case of a market in long term bonds let us
assume in the first instance that each of the participants has the
same amount of financial resources which he can either invest in
bonds or hold as cash ( or treasury bills ). We can draw a
cumulative distribution function showing the number of people who
expect a price equal to or lower than p, say B(p).These people
will hold money if the ruling price is p, while all the others,
(1 - B(p)), will hold bonds. If now a buyer from outside the
market (let us say from abroad) enters the market with the
intention of buying a certain amount B of bonds then he will
have to offer a higher than the ruling price. The new price p’
will be just high enough to turn a sufficient number of bulls into
bears so as to satisfy the additional demand of the outside
buyer.The underlying assumption is that the people who expected
prices between p and p’ are now, when the price has become
p*,still sticking to their belief that prices will not maintain
themselves at the new level but go back to the old level again. In
other words the underlying beliefs are conservative. This, it
appears is a condition for stability. If instead of the implied
negative feedback of price movements on expectations ( which acts
like a controller ) there is a positive feedback then the price
movement whether up or down would never come to a halt.
The above argument was based on the extremely restrictive
assumption that every member of the population of participants has
the same amount of financial resources. If we drop this assumption
we may at the same time also drop the implicit assumption that
every participant expects one and only one definite price. This
is,in fact, rather artificial. In reality he probably considers
several alternative prices and perhaps attributes greater or
lesser probability to one or the other alternative. If this
variety of expectations has any practical consequence it will mean
that he divides his resources according to the prices"on which he
speculates”, acting as a bull in relation to one part and as a
bear in relation to the other, the proportions depending on the
probability he attributes to the various expectations. In fact the
participant may be regarded as a divided personality consisting of
various parts each of which holds the same amount of wealth (a
standard unit which may be determined by the minimum unit which
can be traded).Again these expectations of the various
"subpersonalities” may be ordered statistically and combined with
the orderings of the other participants. In probabilistic terms
this will mean a convolution of the various frequency
distributions of the individual expectations. The resulting total
frequency distribution for all participants together will show
just how much funds are associated with each expected price. This
is a cumulative frequency distribution as before but without the
restrictive assumption of equal resources for each participant.The
shift from bull to bear or vice versa may now take place within
the resources of one and the same person or it may take place
between persons.
The distribution function just described may now be used to define
and measure uncertainty. The measure of uncertainty in the group
of participants in a market is given by the variance of the price
expectations . This cannot be observed directly but it will show
itself through the strength of the price response which a certain
additional offer or demand from outside (an exogenous
disturbance)will produce. If expectations are closely concentrated
a small change in the price will shift a large volume of financial
resources from bull to bear or the other way round. If they are
spread out widely a large change in price will be necessary in
order to shift a modest amount of resources. It has to be noted,
however, that the strength of reaction will also depend on whether
the price initially is in the middle of the distribution (near the
mode) or nearer to one of the tails.
The peculiarity of the above definition of uncertainty is that it
does not apply to an individual but to a group. Instead of being
psychological it is a social concept.
The above analysis can also be seen as an alternative to
traditional concepts of supply and demand. Instead of two
different functions relating the same two variables we have only
one function. The supply (offer) and the demand are exogenous
quantities. The ticklish point in the analysis is the
identification and definition of "exogenous”. We have assumed
implicitly that the amount of bonds is given and invariable. The
new entrant into the market who brings in a new demand or a new
supply must therefore indirectly find the necessary adjustment in
the quantity of the no-bonds, that is money, which is assumed to
adjust automatically in Kaldorian fashion.