Download Department of Economic History, Stockholm University

Department of Economic History
Stockholm University
The process of
capital accumulation
Paper presented 010427 at higher seminar
by
Rodney Edvinsson
Department of Economic History, Stockholm University
1
- Content 1. Introduction
2. Theoretical Background
3. Towards a theoretical synthesis
4. Operationalisation
2
1. Introduction
1.1. Purpose
The purpose of my project Long Term Determinants of Economic Growth, Crisis and
Transformation, which will result in a licentiate treatise and a PhD dissertation, is to focus on
the significance of macroeconomic variables behind the economic growth, crisis and
transformation in Sweden. A totality picture is searched for, where different theories and
different variables are contrasted against each other and tested on the empirical data. More
specifically my PhD-thesis has a three-fold purpose:
1)
The study is not purely empirical. I have also theoretical ambitions with my research.
I intend to develop and refine a model of the long-term development of capitalism in
general, based on Marxist theory, while using Sweden as a case study to both test
different hypotheses and to generate new theoretical insights. For this purpose I
contrast different Marxist traditions against each other, and these traditions against
non-Marxian models. Many insights of, above all, neoclassic growth models have not
been taken account of by Marxists, and there is a need to incorporate them into
Marxism, by reinterpreting their results in Marxian categories. This is a vacuum I am
trying to fill. Hence the theoretical part also has a comparative feature.
2) The part where my model is operationalised into indicators, that are adequate to make
use of the rich statistical material that exist at present, plays a fundamental part in my
study, and is in itself an separate investigation, which has feed-back effects on both
theory and the interpretation of the material itself. The concepts and methods behind
the statistical material at my disposal are quite eclectic, and have to be reinterpreted
and transformed to suit any theoretical perspective.
The empirical part of my study is to investigate the specific capitalist development in
Sweden between 1850 and 2000. Here is the purpose of both investigating the short-term
business cycle fluctuations and long-term alternation between periods of different growth
patterns, and to grasp the link between the two latter. The material I am using consists of
statistics over national account from Statistics Sweden and earlier economic-historical
research that have constructed longer time series, as the Historical National Accounts of
Sweden. I also use aggregate statistics over companies from Statistics Sweden. In spite of the
rich material that exist there hasn’t been done much empirical research on the history of
Sweden’s business-cycles and long-term growth, and here I think my study can make
important contributions independent of the marxian perspective I am applying and
developing.
I want to emphasize that all three purposes have an important place in my PhD-thesis. The
part on operationalisation shouldn’t be underestimated, as this step in the research has serious
repercussions on the other parts of the investigation, and as I am not using any clear ready
manual on how to proceed, which thus mean new insights have to be generated.
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In my licentiate treatise I concentrate on part 1 and 2, where the empirical result more
illustrate the theory and method I am using. The empirical part has a more prominent place in
my PhD-thesis.
In this paper I present preliminary versions on the chapters on past theoretical
contributions, the theoretical synthesis I am trying to construct and how I intend to
operationalise the model and the concepts I am using. I have, however, done quite a lot of
empirical research already, and the chapters in this paper are based on much of the insight I
have got from such a direct confrontation with the statistical material. My next paper will be
of more empirical character. I have earlier, in my outline for my PhD-thesis, discussed at
higher seminar in May 2000, already presented some preliminary empirical results concerning
fluctuations in the GDP of Sweden between 1850 and 2000.
1.2. Theoretical and methodological perspective
My study is based on Marxian theory, method and categorisation. I choose this perspective
because I think Marxism is the most adequate to understand capitalism as a totality of social
relations in its historically transient movement and as rooted in the material conditions of
human life.
Stating this I don’t want to devaluate the contributions of other perspectives in explaining
capitalist growth, crises and transformations. Mainstream neo-classical economics has
constructed, from a technical-mathematical point of view, more advanced growth models and
taken up aspects of capitalist accumulation not dealt much by Marxian economists, as for
instance the role of knowledge. Schumpeterians have made important contributions by
emphasizing the role of innovation and the process of firm births and deaths. Etc.
Neither is Marxian economics monolithic. Many of the controversies in mainstream
economics are also reflected by tensions between different Marxian schools. For instance, the
friction between demand- and supply-side economics has its Marxian equivalent.
Choosing a specific Marxian perspective I don’t think it is a good research strategy to just
work on the bases of one perspective and ignore other. It is important to contrast mutually
exclusive theories against each other, in order to at least theoretically make it possible to
falsify specific hypotheses. To only suggest one theory brings forth the risk of formulate this
theory in a tautological manner, implying that everything in the empirical material can be
arranged in a way that will confirm this theory. For a researcher it is important to state under
what conditions his or her theory can be said to be verified, and under what conditions it can
be said to be falsified, and an alternative theory to be verified. Of course, no theory will ever
be falsified and verified in an absolute manner. Even if this should be obvious it is too often
the case that the researcher only considers one favourite theory, and “forgets” to consider the
alternatives in a satisfactory manner.
Saying that I am trying to avoid an eclectic method, of taking bits from mutually exclusive
perspectives in an incoherent way. Instead I strive to “marxify” the contributions of other
perspectives, by reinterpreting them in Marxian categories. Where, for instance, neoclassical
economics is the strongest, on constructing mathematical models that uncover interesting
aspects of economic life under capitalism, it is also the weakest, through its lack of a social
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and historical interpretation of the concepts it is using and the quantitative relations it is
deducting, which precisely is the strongest attribute of Marxian economics.
Mainstream positivistic economics have a quite unproblematic view on the relation between
theory and reality, between the model and its object matter, thus displaying a kind of
rationalism and naïve realism at the same time. On the one rationalistic extreme there are the
model builders that don’t care much about the empirical, as they tend to equate the models
with the reality itself. On the other naïve realistic extreme are the statisticians who in an
eclectic way are trying to draw general conclusions from the surface phenomena in economic
life, hence forgetting the crucial role of coherent theory and concepts in understanding our
world.
Marxian economics is trying to abridge the cleavage between theory/model and the
empirical by using a dialectical method, where knowledge about reality is seen as a mediated
and not absolute.
Marxists are distinguishing between the essence and the appearance. 1 To work out the
essence of a phenomena is to investigate the totality of this phenomena, both in a synchronic
and diachronic sense - its material roots, its historical appearance and decline, its driving
forces, its inner structure and composition, its contradictory nature, its main relations to other
phenomena, etc. But essence doesn’t appear to human beings in a direct way. Appearance is
only a temporary and one-sided disclosure of essence. To understand essence a theoretical and
conceptual filtration is necessary of the empirical. On the other hand, the knowledge of
reality, and thus also essence, can only be achieved through its different appearances. Pure
contemplation or model building, without confrontation with the empirical, will not reveal
essence. Consequently, mediation between essence and appearance is necessary, in spite of
the partly divergent relationship between the two.
The dialectical method is a route to grasp the reality by a series of conceptualisations and
models, and thus never state to have arrived at a completely conclusive result. The method is
by its own assumptions self-critical. It presupposes the imperfect and limited nature of every
concept used and every statement, including its own.
In my thesis I apply some of the concepts of Marxian economics – labour value, surplus
product, organic composition of capital, etc. I also strive to take into account the limited and
elusive nature of these concepts, and when necessary differentiate a rougher notion into two
or more distinct, though related, concepts, in this way approaching the object under study
more closely. Nevertheless, such a differentiation also has a price, being too detailed
description, making it more difficult to see the forest as a whole for all the trees. Thus I don’t
abandon the simpler, cruder, undifferentiated concepts and models altogether, because they
still serve the purpose of getting a more total picture, of being the glue that holds together the
more complex construction.
The purpose of my study is to grasp the essence of economic growth, crises and
transformation under capitalism. The driving force is capital accumulation. Other aspects –
consumption behaviour, technology, institutional change, etc – are of course important, but
1
Se for instance McBride, 1977: p. 38 and 68, and Nicolaus, 1993: p18 ff.
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they have to be viewed in their connection to capital accumulation. To understand a totality it
is necessary to identify primary and secondary aspects of the whole. This may seem
subjective. Nevertheless, to identify an essence is partly subjective and dependent on the
purpose of the research. For instance, for a demographic study the essence of history would
probably be changes in the population, and related phenomena, and not capital accumulation.
This does not mean I advocate a post-modern standpoint; being more explicit about the
subjective assumptions made can precisely increase objectivity.
I try to grasp the essence of capital accumulation by studying a concrete case of the process
– long term economic growth, crises and transformation in Sweden – in this way also
contribute to understand the former. This also poses a limitation, because only a study of
international capitalism should provide a true understanding of capital accumulation.
The dialectic between essence and appearance is especially important when it comes to
operationalise a conceptual system. This I find problematic, but also challenging. In this
respect there are two risks that I try to avoid: empiricism, an a-theoretical, eclectic adaptation
to appearance of taking things as they appear to be and not questioning the definitions used
behind the empirical material, and of rationalism, of emphasising the essence in such a degree
as to not see that theory in the last instance must be confronted with empirical material and
that this confrontation also will change the understanding of essence.
A common criticism directed specifically against Marxian economists is the complicated
nature between its theoretical concepts and their existence as manifested appearances, i.e. the
so-called transformation problem. But the transformation problem arises in any scientific
research, because the theoretical concepts never have a direct correspondence in empirical
material, something that is called out validity. Thus, why direct a criticism specifically against
Marxism that constitutes a general problem for all quantitative social sciences?
One criticism against neoclassic economics is generally directed against its use of
mathematical models. I don’t share the criticism. I think mathematical models, both
deterministic and statistical, are necessary in understanding economic phenomena. Models
can have two purposes, a heuristic purpose to underline the essential traits of reality, and
hence raise understanding, or a more empirical purpose, to describe and to test concrete
reality. The problem with much neoclassic research is not mathematical modelling in itself,
but that the models tend to meet neither of these two purposes: the assumptions they make are
difficult to interpret, too technically derived, and they are, to a certain extent, too simple and
too rigid to be used in studying and be tested on empirical reality.
In my view of a quantitative model the interpretation of the concepts that are used must be
an important part of this model. Two models that consist of exactly the same equations, and
use the same definitions, are not identical if they interpret their results in different ways.
The empirical material is not very well suited for application of my the concepts I am using,
not least because the different definitions are quite eclectically derived, and has also changed
several times, so that there is not even a conceptual consistency over time. The quality of the
empirical material is particularly poor, both in theoretical and empirical sense, especially for
earlier times.
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To investigate the causal relations between the different series prevalent statistical methods
are used, as correlation and time series analysis. I also construct my own (or partly my own)
statistical models that are more adequately suited to the specific questions I am posing. In
deciding significance levels I also have to use simulations. As far as possible I try to calculate
the theoretical values for the critical area of the test statistics, but this is not always easily
done, because statistical models often imply very complicated calculations and sometimes
don’t even allow direct calculations of theoretical values. The poor reliability and validity of
the material affects, and increase in an unknowable way, the confidence interval of the
statistical tests I am using.
In my research I attempt to falsify or verify different hypotheses at reasonable significance
levels. There is, however, a clear danger with this method. If you, for instance, set the
significance level at five percent and randomly investigate 20 mutually independent cases
there will be a 64 percent chance that the H0-hypothesis will be rejected for at least one of
these cases if the H0-hypothesis is true for all of them.2 There is two ways to come around this
trouble: to lower the significance level (if in my example the significance level for each
individual case is lowered to 0.26 percent there will be a five percent chance that the H0hypothesis will be rejected for at least one of the cases) or to have clearly motivated
hypotheses before the testing is conducted. In my research I use both these research strategies,
although the borderline between them is somewhat diffuse.
According to some authors (the popperian tradition) verification is not possible and only
falsification is so. In my view this is a wrong idea. For instance, when I falsify hypothesis “A”
I will at the same time verify hypothesis “not-A”. I also disagree with both postmodernists,
for whom no verification or falsification is possible, and positivists, for whom verification and
falsification is 100 percent sure (“only positive knowledge is meaningful”). Both verifications
and falsifications are possible to make, but these will always be relative, and could turn out to
be wrong in the future.
The outer validity problem, concerning the direct relationship between essence and
appearance, I partly solve by using indicators, which roughly correspondent to the concepts I
am using. Many of the common statistical methods, as for example factor and spectral
analysis, are rather difficult to interpret. In my study I try to understand and interpret the
mathematical construction of the methods I use, so as to base all derived quantitative relations
on the qualitative characteristics of the material. The reliability problem I am trying to
overcome through using different sources measuring about the same phenomena, and thus
investigating if the same result could be achieved.
The problem of inner validity permeates the whole treatise. The purpose of my study is not
strictly empirical, where theory is applied on the material in a mechanical way. On the
contrary I have also theoretical ambitions with my research. This combination of theoretical
and empirical endeavour is partly an attempt to contribute in abridging the present gap
between a-theoretical empirical-historical research and a-historical theoretical-mathematical
economics. There has all the time being a feedback from the confrontation with the empirical
2
See Blom, 1998, p. 141 ff for a discussion of this problem.
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on the theory and the conceptual constructions themselves, thus also revealing inner validity
weaknesses in the first naïve theoretical formulation, in a process named as a “hermeneutic
circle” (or rather “hermeneutic spiral”, because you never come back to the same point).
2. Theoretical Background
In this chapter I contrast the different Marxian models against the one advocated by nonMarxian, mainly mainstream, economics. In the next chapter I try to find the kernel in
Marxian economics concerning the process of capital accumulation to construct a model that
is applied on empirical material in later chapters.
I have found that the crucial difference between Marxian and mainstream economics
doesn’t always lie in the empirical statements, but mainly in the language used, which affects
the interpretation. Many empirical statements, as for example if crises mainly are cause by to
low consumption or because of supply-side factors, the difference within Marxian
respectively bourgeois economics can be greater than the difference between the two. I have,
however, found that the different statements of bourgeois economics, expressed in
mathematical terms, can be “translated” into Marxian economics, and vice versa. In this
chapter I am trying to make such a translation concerning growth and crisis theories, when I
formulate a theoretical synthesis.
What unite Marxists are many of the concepts used, dismissed by (almost) all modern
bourgeois economists, especially the category of labour value.
2.1. Fundamental categories of Marxian economics
In volume I of Capital Marx formulates his distinctive labour theory of value.3 There he
begins the analysis by explaining the distinction between use and exchange value, which he
overtook from earlier thinkers (with roots as far as to Aristotle). The exchange value of a
commodity is a function of the social necessary labour time it takes to produce it, including
raw materials and the tear and wear of the machines. But labour-values become a reality only
by use or consumption. Thus new technology, assuming labour time in society being constant,
contributes to increasing the amount of use values, but not to the amount of exchange or
labour value. This is the foundation of all further Marxian analysis, concerning exploitation,
accumulation of capital, crisis, long-term decline of capitalism, etc.
The neoclassic marginalist theory, the other theory that try to give a material basis to the
price, confuses cause and effect, by saying that the price of the product is determined by
marginal utility; while the opposite is true, the marginal utility is determined by the price, and
price still has to be explained. This is so because price determines how much individuals
consume one product which in its turn determine the marginal utility, as it falls the more the
individual consumes of the product.
3
Marx, 1965: pp. 35 ff.
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The labour theory of value is the foundation for Marx theory of exploitation. The
extraordinary attribute of labour power, in contrast to other commodities, is that the use value
of labour power, when the capitalist consumes it (i.e. puts it in the production process), is
generally higher than its exchange value. Marx illustrates this by showing that one part of the
day the worker works for himself/herself and the other part works for the capitalist.
Later Marx makes the distinction between constant capital (c), variable capital (v) and
surplus value (s).4 The invested capital can be divided between constant capital – raw
materials, the wear and tear of machines and buildings, etc (though not-produced
commodities, as land, is generally not included in this category) – and variable capital, the
expenses on wages. The constant capital doesn’t contribute to any new labour value, but only
transfer its old labour value to the new product. But the variable capital not only transfers its
old value, but also creates new value, i.e. surplus value.
The rate of exploitation (e) is a relation between variable capital and surplus value,
algebraically: e = s/v. The rate of profit (p) is a relation between surplus value and total
invested capital, algebraically: p = s/(c+v). These two relations imply that the rate of profit is
always lower than (or, in the exceptional case when no constant capital is used, equal to) the
rate of exploitation.
Marx also introduces the concept organic composition of capital (org), which is the relation
between constant to variable capital, algebraically: org = c/v. 5 The profit ratio can then be
seen as a function of both the organic composition of capital and the rate of exploitation,
algebraically:
p = s/(c+v) = (s/v)/((c+v)/v) = e/(org+1)
(1)
Partial differentiation gives:
∂p/∂e = 1/(org+1) > 0;
(2)
and:
∂p/∂org = –e/(org+1)2 < 0
(3)
(2) means that the profit rate always increases, holding organic composition constant, when
the rate of exploitation increases. (3) means that the profit ratio always decreases, holding rate
of exploitation constant, when the organic composition increases.
Like many classic economists Marx also makes a distinction between productive and
unproductive labour, which has created a debate amongst later Marxists about what labour
contributes to production and surplus value. Marx has in fact two concepts of productive
labour, labour that is materially necessary (creates use value in general), and labour that
creates material surplus value for capitalists (is useful for capital), i.e. increases material
4
5
Marx, 1965: pp. 199 ff.
Marx, 1965: p. 612 and Marx, 1966: pp 145 ff
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capital.6 Commercial workers are unproductive in both senses, as they materially contribute to
production, but just circulate existing products, and as they don’t produce and surplus value
for the capitalist class as a whole, though they create profit for the individual capitalist, that is
just part of the surplus value created in the productive sector. Self-employed and workers in
state hospitals can be materially productive, though they are not productive for capital as they
don’t create any profits. Productive labour for capital does not only involves physical
production, but also so-called “productive services”, i.e. services that creates a use value and
can be sold for profit.7
In volume II and III of Capital Marx further elaborates his theory of labour value. In reality
there isn’t any mechanical relationship between price and labour value; the determination is of
a mediated nature. The analysis becomes ever more complicated when the model is made to
approach closer and closer to the reality, in a series of approximations. Marx makes clear that
the turnover time of capital also is a determinant the profit ratio, and so is the ratio between
fixed and circulating capital.8 Marx also claims that the price of non-produced commodities,
like land, often doesn’t reflect any material labour value content.
To simplify the model Marx and most other authors make the assumption that all of the
invested capital is consumed in the production process, that the turnover time of all inputs is
one year and that the circulating costs are zero. In reality, as for example the empirical
material that I use, e.g. fixed capital is not immediately consumed in the production process,
the turnover time of inputs is often shorter or longer than one year and different for different
inputs, and circulation is a big cost. Marx develops these points further in volume II of
Capital. The capital stock (K) can for example be calculated as capital consumed during one
year (c+v) times the average turnover-time (T) of this capital expressed in years: K= (c+v)T.
In the turnover-time we would also include both the time capital is used in the production
process and the average time when the capital exists in the form of commodity capital. Kmaterial
would thus symbolise the material capital stock. If we also include the capital existing as
money capital, Kmoney, we would obtain the total capital stock, Ktotal. The profit ratio
calculated as s/(c+v) is thus different from profit ratio calculated as s/K.
In volume II of Capital Marx defines Department I as the economic sector where the means
of productions are produced and Department II as the sector where the consumption goods of
both workers and capitalists are produced.9
Constant
Variable
Surplus
capital
capital
value
Dep. I 400
100
100
Dep.
200
50
50
Total
value
600
300
p
s/(v+c)
0.2
0.2
900
0.2
=
k= c/v
4
4
II
Total
600
150
150
4
6
See Cohen, 1991: p. 33.
Marx, 1993: pp. 305 and 306, and Marx, 1967: pp 134 ff.
8
Marx, 1967: pp. 156 ff.
9
Marx, 1967: pp. 399 ff.
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10
Table 1: Example of a division of the economy into two departments under assumption of
simple reproduction. The figures are both in labour values and prices.
Table 1 exemplifies Marx division of the economy into two departments under assumption
of simple reproduction. Simple reproduction means that the capitalists don’t accumulate, that
they don’t expand the production process, as opposed to expanded reproduction where part of
the profit/surplus value is invested in new constant and variable capital. Simple reproduction
demands that vI+sI equals cII, which it does in table 1 (100+100 equals 200); i.e. that the
consumption of the workers and capitalists in department I, what they buy from department II,
must equal the constant capital in department II, the amount of raw materials, machines, etc
that department II buys from department I (the workers and capitalists in department II don’t
buy any consumption goods from department I).
Under conditions of expanded reproduction this assumption does not necessarily holds.
Then capitalists in both departments don’t consume the whole surplus value, and spend a part
of it on buying investment goods from department I, which necessitates an expansion of
department I at the expense of department II and a formation of a wage fund for the extra
workers for the next, expanded, production cycle.
In the example of table 1 the organic composition is equal in both departments, which
means that the profit ratio is 20 percent in both departments and that no transfer of surplus
value between the two departments occur. von Bortkiewicz made the point that this is an
unrealistic assumption, and that the organic composition of capital generally will be different
in different sectors of the economy. Also Marx was conscious that his examples were built on
this unrealistic assumption, but didn’t apply this to his reproduction scheme.
In volume III of Capital Marx introduced the important concepts of cost and production
price.10 The different organic compositions of different capitals imply that the competitive
production prices of a commodity systematically deviate from their labour values. This is a
consequence of the equalisation of the profit rate between different capitals, assuming
competitive conditions.
If for example the economy consists of two capitals, assuming the rate of exploitation to be
100 percent, capital 1 with cost price 90 labour units (l.u.) in constant capital and 10 l.u. in
variable capital and capital 2 with cost price 10 l.u. in constant capital and 90 l.u. in variable
capital this would mean that capital 1 is producing commodities worth 110 l.u. and capital 2
commodities worth 190 l.u. But if capital 1 sells its commodities at its labour value it only
makes a profit at 10 percent while capital 2 would make a profit at 90 percent. An equal profit
would demand that both capitalists sell their commodities at a price of 150 l.u., which would
mean that both capitals make a profit at a ratio of 50 percent. The profits of the individual
capitals would be equal to the surplus value only under assumption of an equal organic
composition of capital. (There should be pointed out that the production price is not the same
10
Marx, 1966: pp 142ff.
11
as actual price or market price, because in reality the profit ratio will not be the same in all
industries).
Through such an equalisation of the profit rate Marx claims there is a transfer of value from
the more labour intensive capital 2 to capital 1. In other words, capital 1 appropriates not only
the surplus value of its own workers but also part of the surplus value produced by the
workers of capital 2. To the individual capitalist this would appear as if the amount of
constant capital contribute as much as the amount of variable capital to his/her profit. But
Marxists don’t view capitalism in this individualistic manner; they see capitalism at an
aggregate level. How the capitalists distribute the surplus value among themselves is a
secondary (though not unimportant) issue.
Let us now assume different organic composition in the two above-mentioned departments.
The analysis becomes more complicated than before, because the transfer of value between
the departments also means that the prices of inputs will deviate from labour values, which
leads to a second approximation that further changes the prices of inputs, and so on. But such
a transfer also means that the price of the product of Department I must be higher than its
labour value, if the organic composition of capital is higher in Department I than in II. If the
organic composition would be lower in Department I than in Department II, a quite unrealistic
situation, an opposite situation would occur: total price would be lower than total labour
value, and the aggregate profit ratio would be higher in price terms than in labour values.
This all means that one of the invariance conditions that Marx suggests, i.e. that total prices
and total labour values equals on the aggregate level, though not necessary on an individual
level, only holds in the special case when the organic composition of capital is the same in the
different departments or if the profit ratio is zero. If we divide Department II into a
Department II, goods consumed by workers, and a Department III (“luxury industry”), goods
consumed by capitalists, under the condition of different organic composition of the capital in
Department II and Department III industries, total surplus value calculated in prices and in
labour values also deviate from each other (the same amount of money buys more labour
value if it is spent on wage goods than on “luxury goods”).11
Thus Marx’ claim that in aggregate prices and labour values are equal can only be true (by
construction) of one of the aggregate variables (total production, total net production or total
surplus value). In my view its most correct to set the labour value and price of net product
equal, because it best corresponds to the spirit of the theory of labour value that only the
labour of the workers contribute to the value of the produced commodities, a method I apply
in this study. Total production encompasses both present and past labour, but the labour of the
past is often viewed as less valued than present labour if productivity increases. Neither is it
especially interesting how much concrete labour time the profit mass as product bought
encompasses, as the same profit mass can be spend in different ways, but how much abstract
social labour time it encompasses.
Of course there is problems with Marx labour theory of value, but this theory should be
seen as a heuristic model that tries to grasp the essence of capitalism, and as every other
11
See Howard and King, 1992: pp. 227 ff for a further discussion.
12
model is not a perfect representation of reality. For instance the problem of deflating GDP is
much more dubious and complicated than transforming labour values into prices, and then the
GDP-concept still have the disadvantage that nobody really knows what it stands for, while
labour values are much more graspable. Nor is even such simple economic concept as price
unproblematic. Prices never exist unequivocally, as prices vary between different regions and
sellers, etc.
2.2. Long-term trends in capitalist development
Marx doesn’t write so much about the long-term development of capitalism. He doesn’t
formulate a breakdown theory of capitalism, though he suggests that the alternative in the
long run would be socialism or barbarism. But he points out some long-term tendencies of the
system: growing concentration of capital, proletarisation of the petit-bourgeoisie, penetration
of capitalism to the whole globe which would destroy pre-capitalist modes of production, the
development of the credit system, the growing importance of share-holding, increasing
organic composition of capital and decreasing profit rates, etc.
Marx scheme of extended capital accumulation form the basis of his theory of a Tendency
for the Rate of Profit to Fall (TRPF). The accumulation of capital both implies that more
workers are employed by capital and that the amount of capital per labour, or the organic
composition of capital (org = c/v), increases, which in its turn boosts productivity. This is so
because higher productivity involves more dead labour (constant capital) replacing workers.
Holding the rate of exploitation (e = s/v) constant (∆e = 0) its consequence is a fall in the rate
of profit (s/(v+c)), algebraically (where t symbolise time):
pt+∆t = e/((orgt+∆org)+1) < e/(orgt+1) = pt
(4)
Marx doesn’t clam the profit ratio falls mechanically as capitalism develops, but in a
mediated and contradictory way. That is why he calls this fall a tendency and not a law, a
tendency that is constantly contradicted by a set of counteracting forces that partly emanates
from the tendency itself. The two most important of the counteracting forces are the
following:
• A falling rate of profit will force the capitalists to try to increase the rate of exploitation,
and thus increase the profit ratio. This is also helped by the higher productivity, which means
that wage goods could be cheapened and hence the wages lowered in labour value without
being lowered in the amount of goods they can by. There is, though, a limit for this
counteracting tendency, which is the total amount of surplus labour that can be sucked out
from the workers. Marx made clear that the profit ratio in the long run would fall even if
workers wouldn’t be paid anything (“living on air”).
• An increase in the productivity, due to higher organic composition of capital, also leads to
a cheapening (in labour values) of the commodities that constitute constant capital. This
implies that while the technical composition of capital, the physical relation between
machines/raw materials and workers, increases it is not necessary so that the (labour) value
composition of capital must increase (or at least not necessary increase with the same rate).
13
Marx thinks that in the long run the value composition of capital also will increase, but it is
unclear exactly for what reasons.
Tugan-Baranovsky claims that the rise in the rate of exploitation, a consequence of constant
real wages and increasing productivity, theoretically can be sufficient to offset any putative
increase in the organic composition of capital. If the organic composition of capital increases
org
by ∆org, it’s enough for the rate of exploitation to increase 1 
times to offset any
org t  1
decrease in the profit rate, algebraically, after also using (1):

org 
 (org t  org  1) =
pt+∆t = et+∆t/(orgt+∆t+1) = e t 1 
 org t  1 
 org t  1  org 
 (org t  org  1) = et/(orgt+1) = pt
= e t 
org t  1


(5)
This is partly a consequence of how Marx expresses the organic composition of capital
mathematically, which I think is problematic for several reasons. A better expression would,
in my view, be the capital/output-ratio or, in Marxian terminology, the dead labour/living
labour-ratio, c/(s+v), where the labour value of whole net product (instead of only the wages
of the workers) is divided by the value of constant capital.
The inverse of Ω, (s+v)/c, is the maximum rate of profit, i.e. what the profit rate would be
if the wages would be zero and the workers would live on air. 12 When Ω approaches infinity
the maximum profit rate, and so also the profit rate, approaches zero, and this can’t be offset
by any increase in the rate of exploitation. In fact even when the profit is equal to the
maximum rate of profit while the rate of exploitation increases to infinity the profit rate must
fall in this case.
Ω is also preferable for theoretical reasons. If for example real wages fall by half, holding
everything else constant, this would mean that the organic composition would double
(c/(v/2) = 2*c/v), but Ω would be the same as before. The increase of the organic composition
of capital would in this case reflect an increase in the rate of exploitation, but Ω would be the
same. Therefore Ω better reflects the technical relations better than org.
Rosdolsky claims there are two factors that Marx recognizes will ensure that the organic
composition will increase over time. First, while each machine decreases in value, the
production process becomes more complex as a whole system of machines replaces the few
machines previously employed in production. Second, the amount of raw materials used
increase greatly as workers become more productive. It’s a strong argument, but still these are
not necessary phenomena of increased productivity. It’s thinkable that the labour value of raw
materials and the whole system of machines will fall enough to offset an increase in the
technical composition of capital.
12
See for instance Cullenberg, 1994: p. 46.
14
Another trend in the long-term development of capitalism is the process of concentration
and centralisation, which in the end leads to monopoly capital. Marx differentiates between
two distinct processes, the process of increasing concentration through the normal route of
accumulation, and through competition and credit, which he calls centralisation.
Accumulation is a quite slow process of concentration, not least because there is also a
tendency of splitting-off of new capitals. It is the centralisation of capital - through destruction
or buy-up of weaker capitalists or through mergers, helped by the credit system - that really
speeds up the process.13
The different theories of imperialism, which came after Marx, purport that the different
economic tendencies in capitalism – monopolisation, the growth of the international markets,
the expansion of capitalism beyond the national borders, the rise of finance and share
capitalism, etc – gives rise to a new stage in capitalist development, the imperialist epoch.
When the monopoly capital has conquered the national markets it turns its eyes to the abroad,
especially the colonial and semi-colonial part of the world. The economic expansionism forms
the basis for political imperialism. The Marxian theories of imperialism are therefore
intimately connected to the theories of capitalist crises, where imperialism is seen as a way to
postpone the final death of capitalism by conquering new markets for further expansion. But
imperialism also means that the barbaric alternative to socialism starts to make its way, of
which world war is the clearest example.14
2.3 Marxian crisis theory
Marxian economics points to the contradictory nature of capitalism to explain its recurrent
crises. This can be contrasted to mainstream economics arguing that capitalism, or the market,
is fundamentally harmonious (always tending towards an optimal equilibrium), and that
different crises happen only due to exogenous factors (government interventions,
technological shocks, bad institutional arrangements, etc) or some unfortunate circumstances
(oil price rises, inadequate information, etc).
Marx didn’t develop any clear and coherent crisis theory though makes several suggestions
about the causes of capitalist crises. The focus of his writing in Capital has been to generally
understand how the capitalist system works. Many of the suggestions that Marx makes about
the causes of capitalist crises partly contradict each other if posed against each other. These
suggestions have later also formed the basis for competing schools of Marxian crisis theories.
It is important to distinguish between different types of crises. Amongst Marxists the
discussion generally concerns three different types15:
1) the more short-run crises connected to the usual business cycle;
2) crises that can last for a decade or longer involving stagnation or lower than average
growth rate; and
3) the final crises of capitalism, implying a breakdown of the system.
13
Dictionary of Marxist Thought, 1991: p. 76.
Kemp, 1972: pp. 9 ff.
15
Dictionary of Marxist Thought, 1991: p. 162.
14
15
A very important discussion amongst Marxian economists has been about the relation
between these three.
Writers, as Tugan-Baranovsky and Otto Bauer, argues that Marx scheme of extended
reproduction is fully compatible with a forever-expanding capitalism. According to such a
view it can’t be proven mathematically that capitalism must collapse. Though the system is
crisis-prone, it will always find a way out if it is not abolished.
Other Marxian economists, such as Rosa Luxemburg, Henryk Grossmann, Paul Sweezy
and Ernst Mandel, despite the difference between them when it comes to locating the causal
mechanism, argue that these three levels are intimately linked to each other, where each crisis
should be viewed as a memento mori (reminder of death) for capitalism.16 Thus a theory of
capitalist crisis must also be a theory of the breakdown of capitalism. Of course each crisis
doesn’t immediately lead to a breakdown of capitalism, because of the counteracting forces,
which partly such crisis initiates, and which create new room for capitalist expansion. But
expansion can’t continue forever, and each crisis is a reminder of the limits for capitalist
expansion in the very long run.
Sweezy differentiates between two types of crises, (1) those resulting from the tendency of
the rate of profit to decline and (2) those emanating from the difficulties in the realisation of
surplus value. Each of these headings, in turn, contains two distinct crisis theories, making
four theories of crises all in all. Underconsumptionism and disproportionality form the basis
for crises arising from realisation problems. Overaccumulation theory and the theory of the
Tendency for the Rate of Profit to Fall (TRPF) due to an increase in the organic composition
of capital form the basis of theories of a falling rate of profit.17 Other causes, as for example
credit squeeze, have, in the Marxian tradition, generally been subordinated to one of these
four.
The underconsumtionists claim that the crisis of capitalism is caused by the fact that
workers underconsume in society, which means that the capitalists can’t sell all the goods that
are produced and a realisation crisis turn up. The crisis is solved by destruction of the
overproduced goods and the upswing can begin again, or is not solved and the system
collapses.
The underconsumptionist theory have been criticised from a number of different
approaches, both Marxian and non-Marxian. Tugan-Baranovsky for example means, in a
polemic against the Russian populists who claimed that capitalism had no future in Russia
because of its underconsumptionist tendency, that consumption demand has no privileged role
in the operation of capitalism. Capitalism is precisely the system of accumulation, where part
of the surplus is accumulated, at the expense of present consumption, to expand the level of
production and so to increase the profit mass of capitalists at the next reproduction cycle.
The disproportionality theories suggest that capitalist crisis is caused by the anarchistic and
unplanned nature of capitalism, by the lack of coordination between capitalists. Sometimes
too much is produced of machines, and sometimes to little is produced of other goods. The
16
17
Sweezy, 1970: p.189.
Howard and King, 1992: pp. 11ff.
16
disequilibria lead to a crisis, but in the end a new equilibrium is established. There is therefore
no unsolvable crisis of capitalism.
Tugan-Baranovsky is one of the better-known earlier representatives of the
disproportionality theory. He describes the root problem of the malfunction of capitalism as
the lack of institutions that will ensure proportionality. He sees underconsumption as an
example of disproportionality, but doesn’t point out underconsumption as the main
disproportionality. But these disproportionalities won’t lead to any permanent stagnation.
There are always forces operating in a capitalist economy that will ensure an upswing.18
Theories of a falling rate of profit have not only been the domain of Marxian discourse. In
fact many of the classical economists were very concerned by this issue. For Adam Smith it is
the sphere of circulation where the reason for a fall in profits is to be found. As the economy
developes, the stock of capital employed expands as far as the extent of the market allows,
which creates fierce competition and a fall in the profit rate. Ricardo instead seeks the cause
of this fall in the sphere of production; it is a consequence of the decreasing labour
productivity of agriculture labour, which in the long run leads to increased rents and wages,
hencefore squeezing profits. Also neoclassical economics contains a king of theory of a
declining rate of profit.19
Overaccumulation theory asserts that as capitalism develops there is an accumulation of too
much capital. A fierce competition between the capitalists develops, which leads to a profit
squeeze because of lower prices and higher real wages. The lower profit rate makes the
capitalists less eager to produce and invest, and a crisis develops. The theory is almost
identical to the one formulated by Adam Smith. In Marxian terms the overaccumulation
theory can be seen as a theory of a decreasing rate of exploitation (though in my theoretical
model I view overaccumulation in a broader sense also encompassing TRPF due to increased
capital/output-ratio, see below). It is the combination of higher wages and lower profits that
leads to a decreased rate of exploitation.
Both the overacculumation theory and the theory of TRPF emphasise the lowering of the
profit ratio as the main cause of crisis. But the causes these two theories claim to explain this
fall is of qualitative different natures. The theory of TRPF doesn’t depend on the rate of
exploitation, and implies that the profit rate in the long run will fall regardless of the level of
the rate of exploitation.
Marx formulates his theory of the Tendency for the Rate of Profit to Fall (TRPF) first in
Grundrisse and developed it further in the third volume of Capital.20 His theory is clearly of a
different nature than the earlier ones. He agrees with Ricardo that such a theory should focus
18
The disproportionality theories do not, however, in itself logically exclude the breakdown theory of
capitalism. If, for instance, we assume the age of capitalism being exponentially distributed having a probability
of two percent that it collapses during a randomly chosen ten years long period due to “extreme
disproportionality” (devastating war or environment destruction, a sudden fall of GDP that the economy can’t
heal itself from, etc), then the probability that capitalism will not reach 350 years will be 50 percent and the
probability that it will become 5000 years or older will only be 0.005 percent. For any system to have a chance
of reaching infinite lifetime it has to constantly decrease its probability to collapse.
19
Cullenberg, 1994: pp. 3ff.
20
Marx, 1966: pp 211ff.
17
on the sphere of production, not on the sphere of circulation as the case with Adam Smith’s
theory. But Marx also criticises Ricardo that he “flees from economics to seek refuge in
organic chemistry”21. Marx claims, instead, that the rate of profit falls not because labour
becomes less productive but rather because it becomes more productive, an example where
the development of the productive forces comes into contradiction to the existing social
production relation.
Henryk Grossmann’s is probably the first who tries to investigate what kind of implications
an increasing organic composition can have in the long run, which is the basis both for his
breakdown- and crisis-theory. In Grossman’s model constant capital is assumed to grow at 10
percent and variable capital at 5 percent per period. This model implies that an ever-greater
portion of the surplus value must be accumulated. This is so because of the faster growth of
constant capital than variable capital, in turn a consequence of a rising organic composition of
capital. Sooner or later capitalism must break down, because accumulation stops when the
consumption of capitalists start to be negative as accumulation becomes larger than the
surplus value. Grossmann suggests several countertendencies to this model, e.g. wages cuts
and export of capital. But the main tendency will eventually make its way through. The exact
date of breaking point depends, though, on the initial conditions. Grossmann expected there to
be a series of crises, followed by a “final crisis” when the counteracting tendencies cease to
operate.22
However, if constant and variable capitals grow at the same rate this doesn’t happen, and
only imply a constant organic composition of capital. A model can, however, easily be
constructed in which (1) the constant capital will grow faster than variable capital, thus
implying a rising organic composition of capital, but in which (2) the difference between
these two growth rates will fall asymptomatically to zero over infinite time. In such a model
accumulation will never exceed surplus or newly added value, but the organic composition
will rise to infinity over infinite number of periods. An organic composition of capital that
goes towards infinity does not logically imply the breakdown of capitalism, if the profit rate is
allowed to approach zero (but stay positive and thus give an incentive for continued
production). This clearly shows that capitalism doesn’t necessarily collapse in the way
Grossmann thinks.
2.4. Neoclassic growth theories
Mainstream growth models are mostly neoclassic in their construction, and assume perfect
competition, perfect information, no externalities, and so on. They are highly technical and
mathematical, but the price is often assumptions and conclusions that are difficult to interpret,
and a loss of realism and of historical and social content. The conclusions of these models are
therefore similar: in the long run the economy follows a stable deterministic growth path with
the same growth rate year after year. They are unable to explain endogenously, from within
21
22
Marx, 1993: p. 754.
See Grossmann, 1992.
18
the economic system, downturns, breakdowns or a slow-down of economic growth in the long
run.
The main differences between various neoclassic models is about which variables behind
the output level are to be explained from within the model, i.e. endogenously, and which
variables are to be viewed as determined from without the model, i.e. explained exogenously.
It is important to underline that the difference between exogenity and endogenity is decided in
relation to the model (itself a subjective construct), and is not necessary viewed as an
objective property of reality itself, i.e. for instance as endogenous and exogenous to the
economic system.
The main variables that these models take into account, in determining output Y(t), are:
population, N(t), capital, K(t), labour, L(t), technical level, A(t) and (gross) saving rate, s(t).
Population is assumed to grow at rate n(t), technological level at rate g(t) and capital to
depreciate at rate δ(t). Output, Y(t), is gross output, in which the depreciation of capital,
δ(t)K(t), is included. Net output would, on the other hand, be defined as Y(t) - δ(t)K(t). The
growth rate of capital is a function of these variables. If we assume that the (gross) investment
ratio equals the (gross) saving ratio, then:
K' (t)
sY(t)
sY(t) - δ(t)K(t)
=
=
 δ(t)
K(t)
K(t)
K(t)
(6)
The Solow growth model is the simplest model, which therefore is the basic reference point
for the other (neoclassic) growth models. It takes population, technical level and the saving
rate as exogenously determined (with n, g and δ being constant), only capital and labour are
determined endogenously. This is why the Solow model is labelled as an exogenous growth
model, while in endogenous growth models saving rate and/or technical level are determined
endogenously.
In the Solow growth model the production function takes the form23:
Y(t) = F(K(t), A(t)L(t))
(7)
AL is referred to as effective labour, a category that is quite difficult to interpret. Most
authors read A as knowledge or technical level, and (2) means that A affects output by
augmenting labour. An alternative formula could be Y = F(AK, L), which would imply that A
is capital-augmenting, but such a formula is more difficult to interpret.
One example of (7), which also is the most commonly used one, is the Cobb-Douglasfunction, where output is a weighted geometric average of capital stock and effective labour,
with weights α and 1-α:
(7) is assumed to satisfy the Inada conditions: (i) limK/AL → 0∂Y/∂K = ∞, i.e. that the marginal product of capital
approaches infinity when capital per effective labour, AL, approaches zero; and (ii) lim K/AL → ∞∂Y/∂K = 0, i.e.
that the marginal product of capital approaches zero when capital per effective labour approaches infinity. It is
also assumed that the production function has constant returns to scale in its two arguments, capital and effective
labour, i.e. that F(cK, cAL) = cF(K, AL).
23
19
Y = Kα(AL)1-α ; 0 < α < 1
(8)
In the Solow model there is always full employment. In the long run the economy follow a
"balanced growth path", with output and capital stock growing at a constant and equal rate. In
this situation total investment, sY, equals break-even investment, (n + g + δ)K, i.e. the amount
of investment that keep the capital/output-ratio, K/Y, at a constant level and thus only keep up
with growth in population, technical development and depreciation of capital. When K(t)/Y(t)
is constant, Y(t) and K(t) must grow at the same rate. This follows from the following logical
chain24:
(K(t  Δt) - K(t))
K(t)/Y(t) = c
and

K(t+∆t)/Y(t+∆) = c
(Y(t  Δt) - Y(t))
Δt = c
(together
with
Δt
K(t)/Y(t) = c)  K(t)/Y(t) = K’(t)/Y’(t)  Y’(t)/Y(t) = K’(t)/K(t)
(9)
Algebraically :
K(t+∆) = K(t) + sY(t)∆t – δK(t)∆t
K' (t)
sY(t)  δK(t)
s
=
=
– δ.
K(t)
K(t)
K(t)
Y(t)

K(t+∆) - K(t) = [sY(t) – δK(t)]∆t

(10)
The last means that if s, δ and K/Y are constant then the growth rate of capital stock is also
constant, and the same as the growth rate of output (because K/Y is constant, see deduction of
(4) above).
Temporarily an increased saving ratio (s + ∆s) can speed up the growth rate of output and
capital stock. But as the capital/output-ratio rises an increasing proportion of output needs to
be invested to equip the increasing labour force, to keep up with technical development and to
compensate for depreciation, to the point where the additional saving is devoted entirely to
maintaining the higher capital/output-ratio. In the opposite case a decreased saving ratio (s ∆s) slows down the growth rate of output and capital stock. But as the capital/output-ratio
decreases a decreasing proportion of output is invested to keep up with increasing labour
force, technical development and depreciation of capital, which slows down further decreases
in capital/output-ratio, until this ratio attain a unchanging, though lower, level. In both cases
24
Normally the deductions is based on capital/effective labour-ratio, K/AL, while I have preferred to formulate
them in terms of capital/output-ratio, K/Y, because in my view K/Y is easier to understand than the more nonintuitive K/AL.
20
the economy returns to the balanced growth path in the long run, though on different
capital/output-levels.25
25
Algebraically the last points can be shown as followed. Actual investment minus break-even-investment,
sY(t) - (n + g + δ)K(t), is the change of capital beside that part that goes into upholding the old capital/outputratio. The derivative of capital/output-ratio will thus be:
sY(t) - (n  g  δ K(t)
∂(K(t)/Y(t))/∂t = lim∆t → 0
Y(t  Δt)
Δt
Δt
= s - (n + g + δ)
K(t)
(11)
Y(t)
(11) shows that when actual investment equals break-even-investment, the capital/output-ratio doesn’t change
and the economy is on a balanced growth path:
sY(t) = (n + g + δ)K(t)
 ∂(K(t)/Y(t))/∂t = s - (n + g + δ)
K(t)
=0
(12)
Y(t)
s
(12) also shows that on the balanced growth path capital/output-ratio equals
.
ngδ
On the other hand when the saving rate rise, thus making the economy to leave the balanced growth path, actual
investment becomes larger than break-even-investment, which makes the capital/output-ratio to grow, because
its derivative becomes positive:
(s + ∆s)Y(t) > (n + g + δ)K(t)
 ∂(K(t)/Y(t))/∂t = (s + ∆s) - (n + g + δ)
K(t)
>0
(13)
Y(t)
(13) shows that when the capital/output-ratio starts to grow its derivative decreases, and approaches zero when
(s  s)
K
approaches
(as t approaches infinity). Thus the economy approaches a new balanced growth
Y
ngδ
path, though with a higher capital/output-ratio than at the old path.
In the opposite case, when the economy leaves the old balanced growth path through a decrease in the saving
ratio, actual investment becomes smaller than break-even-investment, which makes the capital/output ratio to
decrease, because its derivative becomes negative:
(s - ∆s)Y(t) < (n + g + δ)K(t)
 ∂(K(t)/Y(t))/∂t = (s - ∆s) - (n + g + δ)
K(t)
<0
(14)
Y(t)
(14) shows that when the capital/output-ratio starts to decrease its derivative increases, and approaches zero
(s  s)
K
when
approaches
(as t approaches infinity). Thus the economy approaches a new balanced
Y
ngδ
growth path, though with a lower capital/output-ratio than at the old path.
In all three cases, of (12), (13) and (14), the economy approaches a balanced growth path in the long run, which
was to be proved. Of course if the saving ratio would fluctuate over time the economy doesn’t approach any
specific balanced growth path, but the assumption of the Solow growth model is precisely of a constant saving
ratio, and a change in the saving ratio is viewed as an occasional event. It can also be showed that the growth
rate of output and capital stock on the balanced growth rate is independent of the saving ratio, and equals
population growth rate plus growth rate of knowledge, which means that increased or decreased saving ratio only
has a temporary effect on the growth rate:
21
One important further development of the Solow model is the construction of models that
take the saving rate as endogenous. These models, therefore, are micro-founded, and make
assumption about households behavior in terms of consumption and saving, which depend on,
apart from the production function, the discount rate, how households value future
consumption relative to current consumption, and the utility function (which normally
assumes a decreasing marginal utility). The interest rate is determined from within the
models, but population growth (n) and technological development (g) are determined
exogenously as in the Solow model. Under assumption of optimisation of welfare, and the
budget constraints, the saving rate turns out to be constant, and the economy converges to a
balanced growth path as in the Solow model.
The two most important models are the Ramsey-Cass-Koopmans model, where households
are supposed to have an infinite horizon, and the Diamond over-lapping generation model,
which assumes a turnover in population. In the former the assumption is made of a fixed
number of infinitely-lived households, whose size have a growth rate of n, while in the latter
new individuals are continually being born, and old individuals are continually dying.
The major difference between the balanced growth path of the Ramsey-Cass-Koopmans
and Diamond models involves welfare. Because the individuals in Diamond model have a
finite horizon the equilibrium need not to be Pareto-efficient (i.e. a situation where nobody
can be better off without anybody else being worse off). This can arise when the number of
persons in the younger generation is larger than in the older generation, and the optimization
hits the older generation, while in the long run every generation would be better off if a
transfer would be made from each young person to the older generation.
Or to draw this reasoning to the extreme; of course the younger generation would be better
off if it kills the older generation, that doesn’t work. But if every younger generation do this
every generation will also loose, because the younger generation will become the next old
one. This situation doesn’t arise in the Ramsey-Cass-Koopmans model because of the infinite
horizon of households.
In the most recent theoretical development the importance of knowledge and educations has
been underlined, something that clearly reflects broad processes in the modern economy, with
a decline of industry and a rise of information technology (“the new economy”).
One type of models emphasise the importance of accumulation of knowledge. The
economy is divided into two sectors, a goods-producing sector where output is produced and a
Research & Development sector where additions to the stock of knowledge (∆A) are made.
Thus the growth rate, g(t), of A will vary with how large the latter sector is. The quantity
produced at time t is, under the assumption of a Cobb-Douglas production function:
Y(t) = [(1-aK)K(t)]α[A(t)(1-aL)L(t)]1-α
Y' (t)
=
Y(t)
= (n + g + δ)
K' (t)
=
K(t)
K(t) Y(t)
sY(t)  δK(t)
K(t)
-δ=n+g
= s
Y(t)
;0<α<1
(16)
- δ = [because s = (n + g + δ)
K(t)
K(t)
, see (12)] =
Y(t)
(15)
Y(t) K(t)
22
aK and aL symbolize the amount of K(t) and L(t) respectively that is directed towards
production of new ideas, which lowers the present output but also increases A(t). Under the
assumption of generalized Cobb-Douglas production the change in A(t) is determined by:
A’(t) = B[(aK)K(t)]β[aLL(t)]γA(t)θ; B > 0, β ≥ 0, γ < 0
(17)
B is a shift parameter. In addition, the production function of knowledge is not assumed to
have contant returns to scale to capital and labour, which allows for the possibility of both
diminishing and increasing returns in R&D.
Depending on the level of investment in R&D the growth rate of output and capital can be
speeded up or slowed downed, but the assumption of optimization behaviour of households
allows a balanced growth path. The existence of the latter depends on the values of β and θ.
Different values will have different effects on gA(t), the growth rate of capital, and on gA(t),
the growth rate of knowledge. If β + θ < 1, implying diminishing returns in R&D, the
economy converges to a balanced growth path, if the saving rate is assumed to converge to
some constant level, as in the Solow model. If β + θ > 1, implying increasing returns in R&D,
the growth rates of both A and K, and hence the growth rate of output, increase continually.
But when β + θ = 1 and if the population growth is zero, the long-run growth rate of output is
non-accelerating, but temporary increases in the saving rate and in the population size
increases the long-term growth rate.
That population size affects the level of growth can be seen as a consequence of the fact
that more knowledge can be produced if population is larger and because knowledge is a nonrival good in contrast to, for instance, capital.
One interesting model of knowledge accumulation is known as the learning-by-doing
model. The central idea is here that as individuals produce goods they come up with new
ways of improving the production process. The simplest case is when learning occurs as a
side effect of production of new capital, and when:
A(t) = BK(t)ф; B > 0, ф > 0
(18)
Substituting (18) into (8) yields:
Y(t) = B1-α K(t)ф+α-фαL(t)1-α
(19)
One interesting case of (19) is when ф = 1 and n = 0. Then Y(t) = B1-αL(t)1-αK(t) and
K’(t)/K(t) = sB1-αL(t)1-α. Hence the long-run growth of K(t) is endogenous and depends on the
saving ratio and population size, which also means that output grows at the same rate since it
is proportional to capital stock.
There is an important distinction to be made between abstract knowledge, which is a nonrival good, and so-called human capital, that consists of the abilities, skills and knowledge of
particular workers and that, like conventional economic goods, is rival and excludable
23
(though knowledge could also be excludable, but is less likely to be so). An example of a
model of human capital is:
Y = K(t)αH(t)β(AL)1-α- β
; α < 0, β < 0, α + β < 1
(20)
H(t) is the stock of human capital, and plays a similar role as K(t). sK denotes the fraction of
output devoted to physical accumulation and sH the fraction of output devoted to human
accumulation, and both of these categories could be assumed to depreciate with certain rates.
As in the Solow model the economy in the long-run reaches a balanced growth path, on which
physical capital stock, human capital stock and output grow at the same and constant growth
rate, n + g (where both n and g are determined exogenously).
One obvious problem with the neoclassic growth models is the assumptions of perfect
competition, no externalities, etc. These are quite unrealistic assumptions, and not even the
most laissez-fair economy will conform to those. The Harrod-Domar growth model, which
assumes fixed capital/output-ratio and fixed saving rate, allows for endogenously generated
unemployment and slump, but such models have been compromised amongst present growth
theoreticians. Also the possibility of a slow-down in growth rate in the long run, due to
decelerating technical development or to limited natural resources, or break-down of the
system from within, are not popular study objects.
2.5. Non-marxian business cycle theories
The Real Business Cycle Theory sees economic fluctuations as a result of real economic
shocks, mainly variations in the rate of technical progress and government purchases. This
can be contrasted to traditional Keynesian theories that attribute economic fluctuations to a
combination of real shocks, monetary shocks, and the dynamics resulting from time lags in
economic decision-making.26
The real business cycle theory takes it starting point in the Walrasian model – that is a
model of perfect competition without any externalities, asymmetric information, missing
markets, or other imperfections. The theory especially underlines, in contrast to Keynesian
models, that nominal disturbances don’t have any real effect on the economy. The agents
immediately adjust themselves to any such nominal disturbance, which hence eliminate its
possible real effects.
Technology is subject to random shocks. Thus ln[A(t)] = #A + gt + A*(t), where #A is a
constant and A*(t) reflects the effects of the shock. A*(t) is assumed to follow a first-orderautoregressive process, i.e. A*(t) = AA*(t-1) + (A,t), where –1 < A < 1. (A,t) are whitenoise disturbances, a series of mean-zero shocks that are uncorrelated with each other. A
describe how much of the previous period’s disturbance affects the next period. As A<1 it
means that the effect of a technical shock gradually disappears over time.
26
See for instance Roemer, 1996.
24
Government purchases are described in a similar manner as technical shocks, where
ln[G(t)] = #G + (n + g)t + G*(t), and G*(t) = GG*(t-1) + (G,t), where –1 < G < 1.
How the economy reacts to positive or negative shocks is a complicated function of the
mentioned parameters. In the normal case improved technology raises current wages relative
to expected future wages, which acts to raise labour supply, thus increasing the output. An
increase in government purchases tends to cause private consumption to fall and labour
supply to rise because of the negative wealth effects, hence slightly to increase output. The
opposite happens when negative shocks occur. Because technical level and government
purchases in the long run fluctuate around and follows a deterministic trend, the effects of a
shock eventually approach zero.
The theory could maybe explain some smaller fluctuations, but to, for instance, explain the
Great Depression of 1930s it would have to claim that there was a large technical regress. The
theory also shares the problem of the other growth theories of being stuck to the mysterious
variable A, which rather should be interpreted as a residual component than as technical level
or knowledge.
It is also problematic to define the business cycle as co-movement of deviations from trend
in macroeconomic variables (the usual definition, in contrast, looks at the growth figures).
Such standpoint sees the trend as the natural motion of the economy, and deviations from this
trend as only temporary aberrations. It also means that a phase of quick growth will be viewed
as part of a ”downturn” if output is to be found below the trend, and a phase of negative
growth as part of an ”upturn” if output is located above the trend, something that should be
considered as a somewhat peculiar description of economic fluctuations.
In Schumpeter’s theory of the business cycle the permanent presence of equilibrium is
questioned. According to him equilibrium is a static concept. The nature of innovation, which
introduces something new to the economy and changes the production function, is precisely
its unpredictability. The entrepreneurs are the one that generate innovations, driven by the
super-profits of being the first one out, and hence disturb the initial “neighbourhood of
equilibrium”. Imitators later follow these first entrepreneurs, and the process initially creates a
booming economy. But innovation also means a “creative destruction” of the old firms, and
the boom is followed by a downturn, which can be particularly sever if the initial creative
destruction becomes purely destructive as a consequence of cumulative forces. Thus the
economic development have a cyclical form, where the length of the cycles can vary
depending on how large part of economy the “cluster of innovations” affect, from a few years
to long cycles of 60 years.
There are some interesting similarities between Real Business Cycle Theory and
Schumpeter’s theory of entrepreneurial innovation. Both share the view of seeing new
technical disturbances as constituting the most important factor behind economic fluctuations.
In Schumpeter’s theory the function of the entrepreneur is to introduce new innovations,
which disturb the earlier equilibrium, and bring economic growth.
There are, however, several differences between these two approaches. Schumpeter
advocates the belief that in equilibrium no technical progress is made, and that entrepreneurial
innovations come in, and hence create, regular cycles. In contrast Real Business Cycle Theory
25
doesn’t allow for any disequilibria, sees smooth and constant technical progress as part of the
equilibrium trend, and claims that any disturbances comes from without the economic system,
which also do not have any permanent effects because the economy finally returns to its trend.
The Keynesian view on capitalist economy is that it has a capacity to remain for a long
period in a short-term equilibrium involving a significantly lower output than would be
consistent with full employment. The economy is assumed to be, to a large extent, demanddetermined, and the level of output can be affected by nominal factors, as money supply,
nominal interest rate, inflation, etc, and hence monetary or fiscal policy. Keynesian models
make quite simple assumption about the behaviour of economic agents, which make these
models quite robust to the details of microeconomic environment.
The multiplier- accelerator model plays a crucial role in explaining how output is affected
by demand. The multiplier implies that an initial unit of extra spending on domestic goods
raises output more than the extra unit, as the extra spending creates incomes for suppliers,
who in turn spend part of it, and so on. The multiplier effect finally dies out, because parts of
the extra incomes are saved and not spent (the multiplier is less then one). The accelerator is
an result of the fact that firms invest more when output increases, as the extra output demands
more capital (the capital/output-ratio still decreases because the accelerator normally is less
then one). These two, the multiplier and the accelerator, interact and tend to reinforce each
other.
In many ways Keynesian models seem to be more realistic than the neoclassic account of
economic fluctuations. Probably economic fluctuations arise from a number of different
causes, and Keynesian models are more open to such reality. The belief that government
could be able to eliminate capitalist crises has, though, been shattered by the experience since
the 70s.
An advantage of Real Business Cycle over Keynesian models are their more long-term
view (despite their positivism) as the former are fully specified general equilibrium models,
while the latter often make quite static assumptions about economic relations. The long-term
perspective seems to be missing amongst Keynesian, which is reflected in Keynes’ statement:
”In the long-run we are all dead”, as if the long run wouldn’t matter.
Many of the non-Marxian theories of crises, at least the endogenous models that explain
crises as something intrinsic to the capitalist system, can be subsumed in one of the above
four Marxian crisis models. There is, for instance, a linkage between the disproportionality
theory, and underconsumption as a case of it, and Keynesianism. The Keynesian multiplier
and accelerator effect have clear affinities with disproportionality. Schumpeter’s theory of
innovation and “creative destruction” could also be viewed as a theory of disproportionality
between different capitalist sectors. The classical explanation of unemployment as caused by
too high wages have some affinities with, or can even be made as special cases of, the
Marxian overaccumulation theory.
26
2.6. Patterns of long-term growth
Below follows a classification of different views on, or “ideal types” of, the patterns of longterm capitalist development.27 This classification also abstracts from the causes behind the
specific patterns and what it the best measurement of capitalist development, which thus
means that each “view” can contain very dissimilar theories that nevertheless agree on the
general pattern.
(1) According to “long-cycle”-theories, the fluctuations form a quite mechanical movement
in all the different phases, which in many ways resembles a sine curve. Similar mechanisms
that cause the long downturn also cause the long upturn. The cycle does not necessary has to
be a cycle of the absolute values but can as well be a cycle of the growth rate (so called
“growth cycles”28). If no exogenous factors would affect this movement, it could go on
forever as a perpetual motion machine.
The Soviet economist Kondratiev formulates such a theory in the beginning of the twenties,
which later inspires Schumpeter. According to Schumpeter, a long cycle last 60 years,
consisting of four phases. In Sweden one prominent advocate of this theory is Lennart
Schön.29
Mandel makes a distinction between theories of “long cycles” and theories of “long
waves”.30 According to him theories of long waves are less mechanical and less deterministic.
The difference between a cycle and a wave-motion is that a cycle automatically repeats itself
and causes a new cycle, while a wave-like movement can consist of one singular wave and
doesn’t automatically lead over to new waves. While the cycle always is a wave-likemovement, the wave-motion is not necessary a cycle. The transition between the long
upswing and the long downswing is, according to Mandel, similar to the one for the shorter
business cycle, and is caused by endogenous economic factors. The organic composition of
capital increases, the rate of exploitation decreases because of the growing strength of the
workers, etc. But for a long upswing to take place several factors have to be combined. The
working class has to be defeated and thus the rate of exploitation increased, new markets have
to be found, etc. These are clearly non-economic exogenous factors, which have to operate in
the right direction. The question whether there are any qualitative differences between longcycle and long-wave theory is of course an open question.
The long-wave/cycle-theory is criticised both by Marxists and non-Marxists. The main
criticism is that this theory tries to fit the reality into a schema, which doesn’t really fit this
reality.
“Breakdown-theories” state that capitalism during a whole epoch takes the productive
forces forward, but later is followed by a stagnating stage. The problems of capitalism
become ever greater, the downturns of the normal business cycles become ever deeper, and,
finally, the whole system collapses.
For a classification of seven “idealtypes” see my Master thesis Debatten om sk långa vågor i den kapitalistiska
utvecklingen – En jämförelse mellan Schumpeter och Mandel, submitted at the Department of Economic History,
Stockholm University, in May 1999.
28
Niemira and Klein, 1992, pp. 6ff.
29
Schön, 1993, pp. 264-291.
30
Mandel, 1995, pp. 25ff.
27
27
Rosa Luxemburg claims that capitalism can only survive if it expands to non-capitalist
markets. When these markets are saturated, and capitalism has conquered the whole world,
capitalism collapses. Henryk Grossmann tries to prove the breakdown of capitalism
mathematically, and constructs a model where the whole system will collapse in the 36th
reproduction period, though admits that the exact date of breakdown depends on the initial
conditions and some other secondary factors.31
One category could be labelled as theories of phases, stages or segments of capitalist
development.32 According to such theories there are distinct periods of low, average or aboveaverage growth in the economy and of different qualitative nature.
Kontradieff's theory is criticised in the beginning of the twenties by Trotsky, followed by
several Soviet economists. Trotsky thinks that Kontradieff mixed up the presence of periodic
cycles with distinct “historic segments”. The nature and length of these segments are
determined by exogenous conditions in which capitalism develops. But these conditions,
precisely because they are exogenous, can’t be fitted into a mechanistic model.
But how long such periods or segments last, and if periods of low growth generally are
followed by periods of high growth, are open questions, though they still imply a pattern in
the long-term development. If the model would be correct, any predictions about the future
would be difficult to make.
In my view, segment-theories are the most reasonable ones. One problem with these is,
however, that they incline towards saying everything and thus nothing, i.e. that they become
impossible to falsify because of their open character. Every other category listed here could be
described as a special case of a phase/segment-theory of development. In order to apply a
phase/segment-theory in a meaningful way it is important to make clear what hypothetical
empirical cases could falsify them.
“Steady-growth”-theories claim that left on its own, capitalism tends towards a stable and
smooth growth, which is the dominant model of neoclassic growth research, already dealt
with above. It is only unpredictable exogenous factors, the intervention of states, strong
unions, external shocks, sudden increase in the saving rate, etc, which upset this smooth
rhythm. In the long run the rate of GDP follow a "balanced growth path", with GDP and
capital stock growing at a constant and equal rate.33
According to “stochastic theories” periods of low or high growth rates can be explained by
stochastic fluctuations of the shorter business cycles. Alternatively, it could be supposed that
the average growth rates of two consecutive business cycles are positively correlated, which
implies that shorter cycles of similar growth rates tend to cluster, which mathematically can
be describe as a Markov chain. Both the “random shocks” of Real Business Cycle Theory and
disproportionality of Marxian economics have a tendency towards this ideal type. The
For an interesting discussion and critique of Luxemburg’s and Grossmann’s theories, see Howard and King
1989.
32
For example Angus Maddison uses the term “phases of growth” (Maddison, 1991, pp. 111ff.), but the term
“phase” still gives an impression that it is part of some kind of periodical movement. A number of authors have
used the term “stage of capitalist development”, but this presupposes an ordinal hierarchy between these
“stages”. Trotsky uses the term “segment”, which also is preferred by Klas Eklund in his paper Long Waves in
the Development of Capitalism? (1979: pp 6ff.).
33
Romer, 1996, p. 5ff.
31
28
question that still poses itself is how and why such a stochastic behaviour arises. These
theories are based on quite deterministic assumptions about the probability itself. The big
advantage of these theories is, however, that they should be easy to test empirically.
The sceptics will declare that it is best not to have any theory at all about the long term
development and that the researcher should concentrate his or her studies to the unique
phenomena or to the subjective assumptions of others. The counter questions, which pose
themselves here, are two: what theoretical assumptions do the sceptics base themselves on
when they dismiss general theories and under what conditions would the sceptics accept that
their viewpoint would be falsified?
3. Towards a theoretical synthesis
3.1. Introduction
My model (or models) is build on a theoretical and conceptual synthesis both of different
Marxian currents, where differences in my view often reflects emphasis on different aspects
of capitalist economy rather than always mutually exclusive propositions, and between
Marxism and some propositions of non-Marxian economics incorporated through
reinterpretation by using a Marxian language. Though I think seemingly opposed propositions
and tradition can be synthesised, such a synthesis must be built on a clear conceptual
framework. I do not wish trying achieving a “middle ground”, eclectic synthesis, where all
propositions are viewed as of equal weight.
In my model I try to ask what the essential traits are of capitalist development. My belief is
that there exist a hierarchy between different factors behind capitalist growth and crisis.
When viewing the relation between these factors and their effects I have not necessarily
interpreted this in a crude casual sense. In reality there is never a clear relation between causes
and effects. The factors that are most easy to connect with a certain effect are often the
secondary ones. The factors I emphasise are the ones that ontologically most clearly can be
connected to the general existence of capitalism.
In opposite to neoclassic I think capitalist development must primarily be studied on the
aggregate level, and also understood on this level, irreducible to a summation of individual
behaviours. In contrast to Keynesians and underconsumptionists I also think that capitalism,
its development and contradictions primarily has to be derived from how this system
organises production. Circulation and nominal prices are of course important, but they have to
be viewed as secondary to production.
Model building is precisely about this: to emphasise some, abstract from others, and then to
see how well this model fits to reality. But the model should never be confused with the
reality itself, which under no circumstances will be fully grasped in its infinite complexities.
Theory is grey, only the trees are green, to quote Goethe.
When describing different economic categories, I am using an explanation on two “levels”.
The economy should be explained both as a specific social system and as a general way of
29
organising production abstracted from the specific social circumstances that this production is
performed. Thus the different categories must be given two different explanations. Capital (at
least material) is a dialectical unity of means of production/past labour and ownership of those
in the specific capitalist setting. All societies use means of production, but only capitalism
will the latter be turned into capital. The specific social form is one solution, amongst several,
of solving a general problem, i.e. organising labour in society to create products and services.
3.2. The problem of value
In a model of capitalist growth and crises, the fundamental concepts must be capital (c),
labour (v), production (gross product c+v+s, and net product v+s) and profit (s), and the
relation between those. The profit arises through the production process, where labour is
exploited. It is profit that enables capital accumulation.
Saying this, to formulate a model of capitalist growth and crises, and then apply it on
empirical material, we have to specify how these different categories should be measured. On
this subject there are some unresolved problems in Marxian economics. In my model I
elaborate with three main concepts of value: use value, labour value and price. These can be
differentiated even further, which is done in the chapter on operationalisation.
The most important aspect with the theory of labour value is that the economy is seen as a
structure to organise the labour at the disposition of society, which makes it so fundamental to
Marxian economic theory. The price of products reflects how much social labour they
contain. It is precisely this link between price and social labour under capitalism that force the
system to allocate resources in a reasonably efficient way.
When prices deviates from labour value the difference can itself be interpreted as if it
would contain labour value, the labour value can here serve as a reference point. More
productive labour can be viewed as being a multiple of average labour; the value of nonreproducible items is set with reference to items that have a labour value; etc.
Many of the models of neoclassic economics are not completely incompatible with the
labour theory of value, if their categories can be translated into Marxian ones.
For instance, I would claim that the Solow model in some respects is more compatible with
labour theory of value than Marx reproduction scheme. This is so because the Solow model is
simpler as it only assume one department of production (only one type of product, that can
either be consumed or invested) and homogenous labour. The Marxian reproduction schemes,
on the other hand, usually assume more than one department, something that generally creates
a deviation between price of production and labour value when the organic composition of
capital is different in the different departments. Simplifications have clear advantages, but
they also abstract from the qualitative aspect of production. In reality productivity grows with
different rates in different sectors, and thus changes the relative prices between products,
while modern growth theories base themselves on one homogenous commodity.
Neoclassic models that take the saving rate as endogenously determined, especially by
considering how households value future consumption relative to current consumption, can
illuminate important aspects of how the capitalist economy functions. Of course the
assumption of most of these models of a classless society, where all households have equal
30
incomes, is opposite to how Marxists view capitalism. However, the important question here
is what function capital plays. Capital can be viewed as a kind of monopolisation, which
explains the transfer of surplus value between capitalists from more, to less capital-intensive
sector, as the more capital-intensive capitalists have monopolised a larger part of society’s
means of production than less capital-intensive capitalists. Capital can also be viewed as
representing past labour, which has been taken from past consumption to be accumulated in
order to increase present production. If society wouldn’t care about future consumption
nothing would be accumulated and all products, including the part that otherwise would go for
reinvestment, consumed today. Of course the motive for the individual capitalist is profit, not
future consumption of society, but this is the specific solution of a general problem that for
society is to allocate between present and future consumption.
When the labour value is different from prices of production it implies a situation where
production is not optimised in a situation where current consumption is prioritised before
future. But there is logic in this inadequacy. If all members of society would be indifferent
between current and future consumption, and the level of consumption in different time
periods, then profits would have to be zero and production price would equal labour value,
otherwise nobody would consume today. A higher production price than labour value in
sectors of higher organic composition of capital reflects the need of society to consume less of
such products, i.e. the price of these products are set in such a manner as if they would have a
higher labour value then they actually contain.
Depending on which measurement we use, use value, labour value or price, the answer to
the question how much capital stock and production has increased or decreased, or how large
is the profit ratio, can be different. The material content of capital or production can very well
increase, even if the amount of social labour time this capital or production represents
decreases. In price term the change in capital stock or production could be still different. The
same reasoning can be applied to the profit ratio, expressed as p’=(K+sk)/K, where K is the
change in capital stock and sk the amount of surplus value that is consumed.
The big problem is thus how to use the theory of labour value when productivity changes.
The problem is similar to that when productivity is different in different companies producing
the same product. Here Marx makes a distinction between individual and social labour value,
where the individual labour value is the actual labour it has taken to produce an item, and
abstract social labour value is how long time in average it takes to produce the item. This can
also be applied for trade, differentiating between average international and country specific
labour value.
For the time problem I introduce the two concepts of diachronic and synchronic labour
value. Synchronic labour value is the time it takes to produce a product in its own time.
Diachronic labour value is defined as how long time it takes to produce a product in time t
when the productivity would be that of time s, or an average between time t and s. Such a
comparison between time periods will thus be similar to the comparison between different
countries or different companies producing the same products.
This solves the problem with a one-sector model, but not when we have several sectors.
Productivity of different products can change differently. I therefore also make a distinction
31
between generalised and specific diachronic labour value, where specific refers to the
individual product or branch, and generalised to the economy as a whole. If we replace the
term labour value with the term price we have a similar problems acknowledged in
descriptive statistics when constructing different deflators for the economy as a whole and for
specific branches and products, which I further develop in the next chapter. Generalised
diachronic labour value is thus similar to the concept of real GDP, and the latter could be used
and interpreted as an indicator of the former.
3.3. Components of production and capital
One important issue concerns what really constitute production and capital, which have
serious repercussions when measuring these concepts. This issue is connected both to the
debate about productive and unproductive labour within Marxism, and to new growth theory
based on the concepts of knowledge and learning.
The different parts of economy can firstly be viewed in relation to their ownership
structure. Under modern capitalism we can differentiate between the pure capitalist, petit
bourgeois, state and home/voluntary sector. The GDP concept tries to measure the three
former, but does not take into account the last one. In a study of capitalism it is actually the
pure capitalist sector that should be the object of investigation. The other sectors are of course
also important, but only in their relation to the pure capitalist sector, for example when
capitalism expands at the expense of the other sectors, mainly through elimination of small
enterprises, privatisation and turning work at home, mostly performed by women, into paid
capitalist work. We must be aware that concepts such as capital and profit only make sense
when applied to the capitalist sector. This is also recognised by Marx, when he makes a
distinction between what is productive materially and for capital (i.e. in a more socially
specific sense).
The issue concerning what constitutes materially productive respectively unproductive
labour is quite complicated. Some Marxists has argued that all labour performed for capital
should be viewed as productive, this would clearly also simplify the different calculations of
for example surplus value and profit.
How we view labour has profound repercussions on the empirical conclusions we draw. For
instance, according to Shaikh and Tonak the part of total labour that is productive has
decreased the last decades, when the industrial sector has shrunken relatively and the service
sector has increased its share, as the part of labour that is unproductive in the service sector is
roughly constant. The effect is that the rate of exploitation has increased significantly the
latest decades, as the authors also include the wages for unproductive workers in surplus
value. This is quite problematic as we then risk loosing the connection between profit and
accumulation, as capitalists clearly can’t accumulate the part that goes to unproductive labour.
Rather that saying that one of these two concepts are the “correct” one, I would prefer to
relativisise the notion, in order to arrive at a fuller understanding of the economic system. It’s
also clear that capitalism behaves as if all labour would be productive, even though materially
it is not productive. For instance commercial labour is not materially necessary, but it is
socially necessary in a capitalist society. The illusion, concerning the nature of this labour,
32
which capitalism generates, is what guides the laws of motion of this system. Commercial
labour is not productive for collective capital, but it behaves, as it would be productive for
individual capital. We could here therefore distinguish between individual and social use
value, i.e. what has use value from the standpoint of society or capital as a whole and what
has use value for an individual person or capital.
We could also use different concepts of social labour value, in one case where unproductive
labour is excluded and another where it is included. In counting productivity in the first case
we would divide production only by productive labour performed, and in the second case
divide by all labour, hence arriving at a lower productivity when unproductive labour is
included. This could also be viewed as unproductive labour having zero productivity.
We could exemplify this by imagining two countries, country A, in which zero
unproductive labour if performed, for example having no circulation costs, but otherwise
showing the same productivity in the material process of production as country B, which has
some circulation costs. We would then see that the labour done in circulation is unproductive
for the capital as a whole in country B. The extra work done in the circulation process doesn’t
enable country B to increase its wealth compared to country A. But for the individual
capitalist in country B employing and exploiting workers in the circulation process does
enable him to make a larger profit. Materially the profit he makes don’t come from the
workers in the circulation process, but from the productive workers employed by other
capitalists, who hence have to transfer a part of the surplus product to the capitalist in
circulation process.
On another extreme there is those who equals productive labour with production of physical
goods, thus excluding all services from being productive, including those that have a clear use
value. This line was prevalent in Soviet Union, but is also argued by Adam Smith. In my view
it would be clearly mistaken to call all services unproductive, but the argument that
emphasises physical production as central to capitalism is not completely pointless. As
Grossmann explains the service sector has a non-material character. The physical nature of
the commodity is however a necessary precondition of its accumulation. “Values enter the
circulation of commodities, and thereby represent an accumulation of capital, only insofar as
they acquire a materialised form.”34 It is true that as industry mechanises itself more room is
created for the expansion of the service sector. But under capitalism there is also a tendency to
mechanise this kind of reproduction work, and turning the work into production of physical
goods, i.e. industrialising it. Only by such a mechanisation can the productivity increase
significantly. A more illustrative distinction would here maybe be between production of
physical products and reproduction of human life and social relations, instead of between
industry/agriculture and the service sector.
The key role of physical production to capitalism has a relevance to the discussion around
“new economic growth theories”, which include knowledge and education in the model. For
these theories almost everything seems to be subsumed under the category of capital. But
capital is not equal to all inputs in production, neither is it a naturally existing phenomena, but
34
Grossmann, 1992: p 154.
33
a social category. Material capital is only that part of production inputs that are owned by
capitalists, and that is combined with wage labour. Neither knowledge nor human capabilities
can easily be capitalised.
Under capitalism slavery is forbidden, and the system presupposes a free labour market.
What is sold on the labour market is not the labourers, but the use of the labourers for a
temporary period of time. “Human capital” is thus not capital but a capability of labour. It’s a
rival item and owned, but not owned as capital. This is also shown by the fact that the money
a company spends in educating its employees doesn’t mean it can stop the employees to leave
the company if they choose to do that. The company-related knowledge workers have is part
of their brain and can’t be ripped off from them.
Perfect competition presupposes free flows of information, and this in itself inhibits the
transformation of specific knowledge into capital. What companies can do is to try to block
the access for others to the knowledge they are using, through patents, secrecy, etc, but this is
rather a monopolistic behaviour that contradicts the competitive nature of capitalism and can
only monopolise a small part the whole stock of human knowledge. Such monopolistic
capitalisation of knowledge will also be very limited and insecure, precisely because of the
non-rival, social nature of knowledge of not easily being restricted. The capitalisation of
monopolistic advantages is in the last instance restricted by the value of material capital, if
competition is not to be severely circumscribed.
Of course new growth theory’s account of the role of knowledge and learning is more
reasonable if we view its models as of the economy in general, as a purely material entity
abstracted from the capitalist settings. However, the process of capital accumulation is more
than a material process. It doesn’t proceed in a social vacuum. In spite of the fact that
knowledge and learning contribute to increase production, only an extremely miniscule part of
it will accumulated as capital. Everybody would for instance agree that the art of writing
significantly contribute to present production, but it would be ridiculous to put a price tag on
this ability, which however would be a precondition for it to exist as “knowledge capital” and
thus also conform to a model of capital growth.
This is the background why my study primarily look on the accumulation of material
capital, especially fixed, and also why I focus on the physical production as industry and
construction. At a later stage I will also investigate the significance of learning and abstract
knowledge on productivity, but I don’t view these categories necessary as capital, and there is
also problems with quantification that has to be solved (can we really measure knowledge and
learning?).
3.4. The process of accumulation
A normal path of growth occurs when capital (c+v) can be accumulated without any
problems. But this process presupposes a reasonably high profit ratio, a steadily increased
production and additional constant and/or variable capital. The accumulation can take
different forms, depending on e.g. unit of measurement and what concept of capital we apply.
If no accumulation takes place we have stagnation, a situation of simple reproduction; or if
capital is destroyed or devalued de-accumulation, a situation of contracted reproduction.
34
First I think it is important to differentiate between material and social accumulation of
capital. Material accumulation occurs when capital as use value, or as diachronic labour
value, increases. Social accumulation occurs, on the other hand, only when capital measured
in synchronic labour value increases. For instance, if the average ICT-capitalist’s ownership
of computers increases from 50 to 100 units his/her material wealth would have increased by
100 percent. But if the labour time to produce one computer decreases from 200 hours to 10
hours his/her social wealth decreases significantly, from 10000 hours to 1000 hours. If we
assume that a worker’s wage is equal to half the amount that he/she produces, and that the
worker saves one fourth of the wage, then a worker today could be become ICT-capitalist
after just five years, compared to 50 years before, in spite of the larger amount of material
capital it would demand.
When additional workers are employed I label the process as extensive accumulation.
When the accumulation takes the form of increased capital stock or constant capital per
employed or labour time I call it intensive accumulation. Intensive accumulation can in turn
be differentiated into two cases. Materially intensive accumulation occurs when the capital
stock per employed as use value, or as diachronic labour value, increases. Socially intensive
accumulation occurs when the capital stock per employed expressed in synchronic labour
value increases. It is the interplay between these different types of accumulation that form the
basis of my model describing capitalist growth and crisis.
Materially intensive accumulation can be interpreted as technological development, when
every employee use more machines, use more material, and produce more, etc. Such kind of
accumulation implies an increasing capital/labour-ratio, in use value-terms.
Socially intensive accumulation means that the capital/output-ratio in synchronic labour
value-terms increases. It means that the dead labour - how much labour time machines, raw
materials, etc, contain - increases in relation to labour time used for present production.
Because the inverse of capital/output-ratio is the maximum profit rate, socially intensive
accumulation also constitutes the driving force behind the Marx-formulated Tendency of the
Profit Ratio to Fall (TPRF).
Materially intensive accumulation does, however, not immediately imply socially intensive
accumulation; hence doesn’t necessary decrease the maximum rate of profit. If the labour
time of producing for example machines is constant, then an increased use of machines
automatically, ceteris paribus, means both materially and socially intensive accumulation. But
if the labour time it takes to produce machines falls at the same time, which should be the
most realistic scenario, then materially intensive accumulation is not automatically associated
with socially intensive accumulation, and can actually occur at the same time as a falling
capital/output-ratio in price or labour value-terms.
The capital/output-ratio, or the inverse of the maximum profit rate, could be said to reflect a
division of labour in society. Dead labour is the labour performed earlier in time, while living
labour is the labour performed in the present (a social relation in production between labour in
different time periods), and the capital/output-ratio is the ratio between these two. The higher
the capital/output-ratio the more advanced is the division of labour.
35
The capital/output- and the profit-ratio can be measured in two different ways: either capital
is set equal to k=c+v or to the total capital stock, K=(c+v)*T, where c stands for constant
capital, v for variable capital and T for the average turnover-time. The profit ratio can be
measured either as s/k, which sometimes is labelled as the profit margin, or as s/Kstock, which
is the actual profit rate the capitalists interested of. In the same way the capital/output can be
measured either as k/Ynet=(c+v)/(v+s) or as K/Ynet=(c+v)*T/(v+s). The relationship between
these two would hence be:
K/Ynet= k/Ynet*T
(1)
k/Ynet can be said to measure a synchronic division of labour, the relationship between the
labour time of producing constant and variable capital to the labour time represented by the
value added. This would be even clearer if we would include the surplus value into capital,
i.e. capital ex post, when the goods are sold. Ynet/(c+v+s) stands for the contribution of the
individual company to the value of the product; the inverse of this is the capital ex
post/output-ratio. If the division of labour is developed in society, and companies only add
very little to the product, then this measure of synchronic labour value is very high, which
depresses the maximum profit margin.
The K/Ynet-ratio I interpret as a measurement of diachronic division of labour, a division of
labour in time. What it symbolises is how much dead labour must be stocked in relation to
living labour in order to make production going. But a high synchronic division of labour, a
high k/Ynet-ratio, doesn’t necessarily imply a high diachronic division of labour, a high
K/Ynet-ratio, because K/Ynet-ratio also depends on the turnover-time. If the turn-over-time is
very short then this will reduce the K/Ynet-ratio. According to equation (1), if for example the
k/Ynet-ratio doubles, but the turnover-time reduces by a half, the K/Ynet-ratio is not affected. If
the turnover-time reduces by more than a half, then the K/Ynet-ratio even decreases. If the
k/Ynet-ratio is constant, then the K/Ynet-ratio is proportional to turnover-time, which illustrates
the diachronic nature of the K/Ynet-ratio.
The question that poses itself in relation to Marx theory of a Tendency for the Profit Ratio
to Fall is: does an increased diachronic division of labour entail a higher productivity? If the
answer is yes then the development of capitalism should lead to a higher K/Ynet-ratio and thus
to a lower maximum rate of profit, if we assume that capitalism follows the optimalproductivity-path in the long run (which in itself is questionable). Even if increased
diachronic division of labour in the long run leads to higher productivity, this doesn’t say that
periodically increased productivity could be accompanied by a decreased K/Ynet-ratio, as for
example when the amount of inputs or turnover-time can be reduced.
This gives a more total and social picture of the trend of the profit ratio than discussions
about how much the machines will be cheapened by an increase in productivity. It also links
the theory of a falling profit ratio due to increased capital/output-ratio to Adam Smiths theory
of a tendency for the division of labour to increase over time.
The above reasoning is fully compatible with, for instance, the Cobb-Douglas-function Y =
α
K (AL)1-α (equation (3) in 2.3.), after some conceptual reinterpretations.
36
Investments and savings in neoclassical models are similar to the rate of accumulation of
Marxian models, with some crucial differences. While net investments in mainstream
economics measure the change in the capital stock turned over after one turnover-period, K,
the amount accumulated in Marxian models measure the change in capital turned over after
one year (the part of product that represents capital outlay), i.e. the change in constant and
variable capital, k=c+v.
While K in neoclassic models stands for fixed capital, K in Marxian models stands for total
capital stock, or at least total material capital stock. The Neoclassic K is simpler, and is in this
respect better suited for modelling than Marxian K, but the Marxian K is a more realistic
reflection of the capital stock that exist in real life, and that is the basis for calculating real
profit rates. But this has mainly a quantitative effect, but should not change the qualitative
interpretations of the mathematical relations. As the Neoclassic K only includes the fixed
capital stock it is natural to talk about a depreciation rate of K, . Commodity capital, or
inventory, and money capital is not included, and both of these categories could be assumed
to have a zero depreciation rate (which in itself is questionable, because inventories can be
destroyed, and money capital can loose its value compared to commodities if the inflation rate
is high). Calculating a new depreciation rate on the total capital stock can come around this
problem.
Y in the Cobb-Douglas-function is gross output, and thus the product of both past (through
depreciation of capital) and present labour, though it is net of the part of constant capital that
is not depreciation of fixed capital. The contribution of present labour would only be the net
product, is defined as Ynet = Ygross - K, which is more in correspondence to the Marxian
model.
For simplicity, at least on the model-level, we could assume that the capital stock only
consists of fixed capital, and that constant capital only consists of the depreciation of fixed
capital, which seems to be the assumption of most Neoclassic models.
For simplicity we could also assume that n and g is both equal zero. The Cobb-Douglasfunction will hence be rewrited as:
Ynet = K(AL)1- - K
(2)
Productivity of present labour could then be defined as Ynet/L. When K(AL)1- < K, i.e.
when K/Ygross < , the net output and the productivity of present labour is negative, i.e. the
past labour that is consumed in production process is larger than present labour.
If we divide both expressions in (2) with L, and then differentiate them with respect to K,
and set ∂(Ynet/L)/∂K = 0, we will get the condition that has to be fulfilled for the productivity
of present labour to be maximized (the second derivative is negative). After some elaborations
the condition can be rewrited as K/Ynet = /[(1-)] or as K/Ygross = /. The interesting thing
with this condition is that it is also the condition when consumption is at its maximum level
amongst balanced growth paths, which neoclassic growth models label as the golden-rulepath, when both population growth and technical development equals zero. Though, by using
37
my categories a deeper understanding can be achieved of why consumption is maximized,
beneath the surface of mathematical equations. My rewriting also states that when 
approaches one to maximize productivity, K/Ynet (but not K/Ygross) has to increase
indefinitely, which would however demand the profit ratio to approach zero (though the share
of capital in gross output would approach one, because of increased depreciation of capital in
relation to output), something that is in line with Marx theory of a Tendency for the Rate of
Profit to Fall.
The problem of the concepts of gross savings and gross investment is that they do not
measure the change in capital stock, as they also include depreciation of capital or
reinvestment. More suitable is then to talk about net saving and net investment (K), or:
K = sgrossYgross - K
(3)
The net savings ratio is then defined as snet = K/Ynet, which allows for the net saving ratio
to be negative if capital stock decreases. The net saving rate can also be rewritten as the
product between rate of accumulation, the part of profit that goes to increase the capital stock,
a, and the share of net products that represents exploitation, eshare:
snet = K’/Ynet = (K’/p)*(p/Ynet) = a*eshare
(4)
This ratio has more conceptual affinity with the concept of accumulation in Marxism, as the
last try to measure the expansion of capital. The rate of growth of the capital stock is thus
calculated as:
a(t) * e share (t)
K' (t) Ynet (t)
K' (t)
= k(t) =
= snet(t)* maxp(t) =
Ynet (t) K(t)
o(t)
K(t)
(5)
From (5) we see that when the capital/output-ratio increases, and in consequence the
maximum profit ratio decreases, then, assuming a constant accumulation ratio and profit
share, the growth ratio of the capital stock must decrease. The maximum growth rate of
capital is maxp(t), which we get if we set a= eshare =1 in equation (5). The maximum growth
rate of capital must decrease with a growing capital/output-ratio, which also explains the
unrealistic scheme of Henryk Grossman as he assumes that the growth rate of capital stock is
constant.
3.5. The link between crisis, breakdown and periodisation
In my view a Marxian model of capitalist crisis should be based on the process of capital
accumulation. A crisis occurs precisely when the normal path of the process is interrupted,
and has basically the character of overaccumulation.
I agree with the writers arguing that a Marxian theory of crisis must be linked to a theory of
more long-term fluctuations and to the downfall of capitalism. The fundamental contradiction
38
of capitalism is precisely, on the one hand, the immanent tendency of the system towards
limitless geometric accumulation, and on the other hand, the physical and social barriers to
such a path. This contradiction manifests itself both in the short-term crisis, in medium-term
periods of depressed or even contracted accumulation and the long-term tendency of the
system to eat up its own possibilities for further existence and to break down.
To further elaborate this point we could assume that the material capital stock (the
argument would be different if we would consider the social capital stock) increases by one
percent per year, which should be considered as a quite modest growth compared to the latest
decennia. After 100 years the capital stock would increase by 2.7 times. After 1500 years the
capital stock would increase three million times, which immediately looks quite unrealistic.
But we can, for instance, consider a country of 100000 inhabitants, which increases to ten
billion inhabitants, and that the capital stock per inhabitant increases 30 times, and we have a
situation where the total capital stock has increased three million times (the problem today is
however that capitalism already employs billions of people).
After 18500 years the capital stock in this model would have increased by 1080 times,
which probably is roughly the number of protons and neutrons in our universe. This could be
considered a purely physical limit to capitalist expansion. If we also consider that it is not
possible to travel faster than the speed of light, and that most materia is not possible to
transform into capital, our capitalists will only grab a small fraction of these protons and
neutrons. Many natural resources will in fact be depleted within 50, 100 or 200 years with
present pace of expansion. There should also be social barriers that shorten the possible
lifetime of capitalism significantly.
Of course 18500 years sounds as a very long period. But humanity has existed much longer
than that, and will hopefully survive billions of years more. And this is about theoretically
examining the argument that capitalism is an eternal system, and that limitless expansion is
possible.
Classic economists, from Adam Smith and Ricardo to John Stuart Mill, envision a similar
limit to expansion in one form or another. They write about a “stationary state”, where
economic growth virtually falls to zero. Marx also considers a static capitalist system, simple
reproduction, but this is just a theoretical construction. In reality simple reproduction is not
possible because of the competition between capitalists. Such a “stationary state” would be
quickly broken up, as some capitalists would start to accumulate in order to take over the
market shares of the others. For such a “stationary state” to exist, either competition would
have to be completely abolished, or profits would have to fall to zero. But neither of these
conditions could exist under capitalism, and if we they would have been introduced capitalism
would in essence be turned into something else.
My point of view is that capitalism can’t survive in the long run not because it retards the
development of productive forces, but because it is a dynamic system, which is incompatible
with a “stationary state”. If we look at biological life, geometrical growth is possible only for
a quite short time period. Only forms that are compatible with a “stationary state” can survive
for a very long time, even though such a “stationary state” doesn’t necessarily imply total
stagnation, and should allow for occasional evolutionary spurts now and then. Capitalism
39
presupposes a geometric growth path for capital (thus not a biological but a social progress),
which is not possible to sustain forever, at least not at the same pace as the latest 100-150
years. The classical economists are right that a kind of “stationary state” is necessary for
humanity to survive in the very long run, though their idea that this state is compatible with
capitalism is wrong.
My argument is similar to the one Malthus uses to demonstrate the contradiction between
geometrical population growth and arithmetic increase in food production. Of course Malthus
is too pessimistic for the two or three centuries after his death, as capitalism since has
increased food production geometrically, and for the possibility of birth controls, but from a
mathematical point of view his argument is correct of showing the impossibility of geometric
growth in the very long run. If we apply his argument by considering capitalist expansion into
the space it is limited by the speed of light. The volume exploited could hence be viewed as a
sphere, i.e. as V(t)=4(dt)3/3, where t is time and td the radius. The growth rate of this volume
will be V’(t)/V(t)=4d3t2/(4(dt)3/3) = 3/t, which goes to zero when t increases, making a
constant growth rate impossible in the long run for such “space imperialism”.
I don’t, however, think it is possible to logically prove the downfall of capitalism.
Theoretically it is entirely possible for capitalism to exist eternally. We could for example
consider expansion to other dimensions, a steadily decreasing growth rate of capital (i.e.
 K' (t) 

  0 ), or a perfect cutting-edge
t    K(t) 
equilibrium that would mean an eternal permanentation of the state of simple reproduction,
but I consider these scenarios as extremely improbable in reality.
The barrier towards capitalist expansion should also be viewed as relative and not absolute.
Rather there are several barriers, both of physical and social nature. There is always possible,
though not inevitable, for capitalism to push its barriers beyond its initial point. For instance,
the existence of Stalinism in one third of the world posed a social barrier for further capitalist
expansion, but this barrier was blast asunder by the collapse of Stalinism, but this collapse
shouldn’t be viewed as inevitable.
The periodisation of capitalist development can in my view best be gripped by the concepts
of accelerated and depressed accumulation, and crisis. There is never a smooth development
of capitalism, no equilibrium growth path; the latter can at best serve the purpose of a
theoretical construction.
When capitalism finds new areas of expansion accumulation is accelerated. The new
possibilities breed optimism, which contributes in creating a situation of too fast
accumulation, that eats up the new possibilities in the long run. Competition between
capitalists also contributes to a too fast accumulation; every individual company will try to
grow faster than its possible for the economy as a whole. This creates a situation of
overaccumulation, which can be solved by outright capital destruction or devaluation, which
makes accumulation possible again. Thus crisis is a necessary component in the life of
capitalism, because it solves the problem of overaccumulation. If overaccumulation is
particularly pervasive it could usher into a longer period of depressed accumulation.
above zero non-geometrical growth where lim
40
The alternation between accelerated and depressed accumulation, and the inescapability of
overaccumulation crises, does not necessary mean that this process takes a neat cyclical form,
either of short-term or so-called long cycles. Neither is it necessary for periods to be
unequivocally classified either as phases of accelerated or depressed accumulation. Periods
could possess contradictory characteristics, without being able to say which feature is the
predominant. Periods could also overlap each other, making it difficult to unequivocally
decide when one period ends and another begins. This view allows for different alternative
periodisations depending on what aspect of the accumulation process one emphasises. I rather
view the concepts of accelerated and depressed accumulation as two “poles” in between
which the capitalist line of development proceeds, and not a rigid schemata that reality can be
reduced to.
In periodisizing capitalism we should also investigate the qualitative nature of
accumulation, and not only the quantitative issue about size and growth rate of capital stock.
It is only by considering what qualitative concrete form accumulation takes – intensive or
extensive, enabled by what institutions, domestic or imperialistic expansion, etc – that we can
answer the questions why accumulation is blocked, or how barriers to accumulation are
overcome.
3.6. Crisis
I view capitalist crisis as both a memento mori (in Sweezy’s words) and a purification process
to overcome its internal contradictions. Capitalism prolongs its life only through confronting
its own death. This is why crisis can’t be avoided, for instance by government intervention. If
capital isn’t destroyed the problems of capitalism are only prolonged, and can in the future
even lead to deeper depressive tendencies than otherwise. At present the breakdown-thesis
can’t be tested as capitalism is still living economic system. The only way to test the thesis
would be to investigate all civilisations that have existed in for example our galaxy, but this
empirical material is not at our hands.35 However, what we can analyse is the near-death
experiences that capitalism encounters in the form of crisis and depressive accumulation, and
from those draw conclusions about the long-term development possibilities.
The process of accumulation is intimately linked to the profit ratio. If we assume a constant
share of profit going to accumulation (a constant a(t)), then the growth of capital is
completely determined by the profit ratio. The profit ratio can in turn be written as
eshare(t)/o(t), which shows it is proportionality related to the rate of exploitation and inversely
related to the capital/output-ratio (see equation (5)). Hence both the theory of increased
organic composition and decreased exploitation rate are necessary to explain the crises
connected with falling profit ratio, and in this way complement each other. A reduction in the
growth rate of capital, which is the essential characteristic of depressed accumulation, is
35
An indirect evidence of the non-existence of expansionary driven advanced civilisations is the fact that no
such “space imperialists” have conquered our Solar system. If space imperialism hypothetically spreads at 1/100
of the speed of light, it should have conquest our galaxy within ten million years, which is short time compared
to the probable age of the oldest civilisations, which should be 1-2 billion years if development of intelligent life
is a common occurrence in universe.
41
accompanied by either a falling rate of exploitation and/or an increased capital/output-ratio.
Of course a falling rate of accumulation can rescue the profit ratio, in spite of a situation of
depressed accumulation, but the competition between capitalists assures that the share of
profit going to accumulation is kept on a relatively high level, at least for the long-term time
period.
The fundamental role of capitalist crisis is to restore profitability. This is done by finding
new areas for capitalist expansion, devalue or destroy existing capital and/or raise the rate of
exploitation. The latter can also be viewed as an aspect of devaluation of capital, as it means
that the social value of variable capital is reduced. When a situation of overaccumulation
happens, increased rate of exploitation can in itself not solve the problems of capitalism, as
there will still be no possibilities for accumulating the increased surplus value.
The alternative Marxian model of capitalist growth, crisis and breakdown is to focus on
production and consumption instead of the development of capital stock. But the ultimate goal
for capitalists is not production or consumption, but to increase their wealth, i.e. the capital
stock. The interesting thing is how underconsumption affects the profit ratio and accumulation
of capital. Underconsumption leads to either goods being sold at lower prices, which
decreases the rate of exploitation because the real wages increases as a consequence, or by
being stocked as inventories, which increases capital/output-ratio (as inventories are part of
the capital stock). Hence in the end underconsumption in essence is just an aspect of one or
both of the two mechanisms of a falling rate of profit.
A crisis of disproportionality can be view as partial overaccumulation, occurring only in
some capitalist sectors, while others are expanding. This we can contrast to a situation of
general overaccumulation.
3.7. “Sources” of accumulation
A problem with all the neo-classical growth models is the formulation of the production
function in terms of effective labour and contributions of labour and capital. This is very
difficult to interpret, and only creates a veil that hides what lies behind the equations.
In my view it is non-intuitive to separate the contribution of capital from technological
level and labour. Such separation reflects the atomistic and analytic method of neoclassic
economics of trying to define the organic whole by the summation of its components.
If the capital stock per labour increases, the technological level should also change. This is
partly recognized by the learning-by-doing model, but the latter model also takes it for
granted that the effect of increased capital per labour as capital could be separated from its
effect on increasing knowledge. In my view “A” should rather be seen as a residual
component that contributes to the productivity of labour. “A” could be anything from the
easiness to exploit natural resources, intensity of work, to technical level holding constant for
the amount of capital per labour.
To separate the contribution of capital and labour is also dubious because capital represents
past labour. As earlier developed a large capital/output ratio could be seen as an advanced
diachronic division of labour, which in itself should contribute to the technical level.
42
If, for instance, one unit of a commodity is produced by a work done in one hour, and the
depreciation of capital represents one-hour work in the capital producing sector, then the
value added represents one hour of labour and the total value of the commodity represents two
hours of labour. To talk about the contribution of capital as such, abstracted from its essence
as crystallized labour, partly serves an ideological purpose of legitimising the profits of
capitalists, as defining them as something ”natural”. Of course the division of the labour
process into production of capital and consumption contributes to a higher output, but this is
through contributing to the productivity of labour, as one of several causes of higher labour
productivity. Marx development of the labour theory of value is precisely about to demystify
the categories of the capitalist system, and to explain how profit arises from the exploitation
of labour.
In investigating the concrete path of accumulation I instead focus on different “sources” of
accumulation on the supply side, which are directly related to my concepts of extensive and
intensive accumulation. The capital stock can be viewed as the product of the capital/labourratio, M=K/L, which is a material relation means of production and the working person, and
total labour stock, L. The capital/labour-ratio is, in turn, the product of productivity, G=Y/L,
and the capital/output-ratio, O=K/Y.36 Equation (6) presents the relations in mathematical
terms:
K=
K
YK
L =G*O*L
L = M*L =
LY
L
(6)
Logarithmic differentiation gives:
K' (t)
G' (t) O' (t) L' (t)
M' (t) L' (t)
=
+
= m(t)+l(t) =
+
+
= g(t)+o(t)+l(t) (7)
K(t)
G(t) O(t) L(t)
M(t) L(t)
(7) shows the different “sources” of accumulation, and the relation between extensive (l(t)),
materially intensive (m(t)) and socially intensive accumulation (o(t), or “above break-eveninvestment accumulation” in neoclassical terms). Hence the growth rate of capital is the sum
of the growth rates of material capital per employee, materially intensive accumulation, and
amount of employees, extensive accumulation. The growth rate of material capital per
employee, materially intensive accumulation, is in turn the sum of the growth rates of
capital/output-ratio, socially intensive accumulation, and productivity.
If we assume that in the long-run the increases in productivity, capital/output-ratio and the
labour stock tends to zero, a not completely unrealistic assumption, then there is a limit for the
expansion of capital, and thus also for capitalism.
36
The capital/output-ratio is measured in price or labour-value terms (which in my model are assumed to be
equal). It could also be calculated in use-value-terms, but in this case it would be the same ratio, because I am
elaborating with a one-sector-model, where the unit of capital stock and output is the same (we could for
example consider production of wheat, which can both be consumed and used as input capital for further
production).
43
The expansion of capitalism presupposes areas of expansion that could be subsumed under
one of the three “sources” of accumulation in (7). This links my model to several theories of
Marxian economics – falling rate of profit due to increased organic composition of capital
and/or decreased rate of exploitation, the process of concentration/centralisation and
monopolisation, and imperialism – where I view these theories as different aspects of the
same process contained in equation (7). It also incorporate aspects of non-Marxian theories of
capitalist development, as for instance Schumpeters emphasis on the role of technological
change, which in (7) is taken account of by the variable g(t).
Extensive accumulation implies that the amount of labour for capitalist exploitation
increases. L(t), here measured as total worked hours, can be written as a function of the
different factors that influence its size, expressed in equation (8). P is the size of population. D
is the part of population in working age. W is the relation between number of workers and
population in working age (which can be larger than 1, if the number of workers not in
working age is larger than the number of non-working people in working age). H(t) is the
number of hours worked per year and per worker. C(t) is the share of the capitalist sector in
total hours worked. A(t) is the total hours worked in nationally owned capitalist firms (both in
the country and abroad) in relation to total hours worked in capitalist sector.
L(t) = P(t)*D(t)*W(t)*H(t)*C(t)*A(t)
(8)
Logarithmic differentiation gives:
L' (t)
P' (t) D' (t) W' (t) H' (t) C' (t) A' (t)
=
+
+
+
+
+
L(t)
P(t) D(t) W(t) H(t) C(t) A(t)
(9)
Demographic factors, P, D and W, have a significant effect on the possibilities for capitalist
accumulation. The size of global population is the ultimate limit for the number of people that
can be exploited, and if there exist a maximum population size for Earth this will be the limit
for extensive accumulation (of course expansion in space is another possibility). For an
individual country immigration can be an important source for accumulation over shorter or
longer period, which USA is a good example of. If the number of women in the workforce
increases sharply this also contributes to extensive accumulation, while increased average
time of education, increased unemployment and decreased pension age reduces the room for
accumulation. Increase in the working time of employees contributes to accumulation, a
phenomena Marx calls intensified absolute exploitation, while its reduction has a negative
impact on capitalist expansion.
C and A are describing the relation between capitalism and it’s surrounding. As Marx
explains capitalist expansion occurs at the expense of non-capitalist institutions. Capitalism
feeds on these institutions, in Luxemburg’s words, and when capitalism conquers the whole
society this specific expansion path is destroyed. These non-capitalist institutions are
disparate as the self employed sector, feudalism, slavery, modern public sector, domestic
labour performed within the family (if we exclude domestic labour from labour this factor
44
could also be accounted by W, which would thus be reduced), etc. When the expansion
possibilities within a country’s borders are shrinking, expansion abroad becomes more
important, through capital export, which turns capitalism imperialistic. If the unit analysed is
the whole world we can however strike out A from the equation.
Another source of expansion for individual capitalists, not taken account of by equation (9),
is also to devour or destroy other capitalists, through a process of concentration, centralisation
and monopolisation, of fusion, bankruptcy and liquidation, or in mathematical form:
Lbig business(t) = Cbig business(t)*L(t)
(10)
Cbig business(t), the share of big business in total hours worked in capitalist sector, plays here
similar role as C(t) and A(t) for capitalism in (9). When Cbig business(t) increases the room for
other (smaller) capitalists must at the same time shrink. This can also be extended in the
relation between capitalist countries. An imperialistically dominated capitalist country will
tend to own less capital abroad than foreign capital own capital in that country, meaning that
A(t) will be reduced below 1, thus turning a possible expansion path to its opposite.
The processes of concentration/monopolisation, imperialist domination, destruction of noncapitalist institutions, erosion of patriarchy, etc are, in other words, intimately related to each
other, and should be view as a whole, i.e. as aspects of extensive accumulation.
The role of productivity for capitalist expansion is a problematic issue. According to
Schumpeter innovations benefit individual capitalists, who can make an above-average profit.
But when innovations have been introduced in the whole economy, the ones who benefits are
the consumers, not the capitalists. However, because capitalists also are consumers of capital
goods, they should also benefit in material terms, as their material capital stock will increase,
even under the assumption of no extensive or socially intensive accumulation (i.e. a constant
value of capital stock in synchronic labour value-terms).
The capital stock measured as synchronic labour value doesn’t necessarily increase as a
consequence of increased productivity. Such a measurement of capital is quite relevant if we
consider the opportunity costs for capitalists. A capitalist can as an alternative invest in nonreproducible items, as land, many of which have a price that preserves or even increases
synchronic labour value (land can also in addition give a regular income when rented out).
For capitalists to in the long run stay in production, there should be possible to increase the
capital stock not only as material, but also as social value. If we calculate the capital stock in
synchronic labour-values (or the capital stock in use-value terms assuming constant
productivity rate), the growth of the capital stock is:
K' (t)
K' (t)
(social) =
(material) – g(t) = o(t)+l(t)
K(t)
K(t)
(11)
(11) shows that social accumulation is possible only by increasing the capital/output-ratio
(socially intensive accumulation) and/or through employing more workers (extensive
accumulation). The problem here is obvious. Capital/output-ratio leads to a decreasing
45
maximum profit and capital growth ratio, while extensive accumulation is limited by the size
of population.
In contrast to most other Marxists, I view the TPRF due to increased capital/output-ratio as
an aspect of overaccumulation. This is partly what Grossmann shows in his model, when the
capital/output-ratio is steadily increasing a constant growth rate, which can’t be upheld. If for
example the capital stock is worth 100 times more than output, its growth must fall below one
percent, as one percent of the capital stock represents the whole output, and the capital stock
can’t grow by more than output (in reality by less, because society still has to consume).
Grossmann is calling the situation underaccumulation, as to little is accumulated to uphold a
constant positive growth rate of capital stock, but such “underaccumulation” can be viewed as
a consequence of overaccumulation, of too much accumulation, from the point of view of
capitalim, in the past that has constributed to a too high capital stock. The only solution is a
significantly lower growth rate of capital, or even destruction of capital, i.e. a period of
depressed accumulation.
The TRPF due to increased a capital/output ratio does not necessary entail that the
capital/output-ratio will increase indefinitely, and hence the maximum profit ratio fall towards
zero. Increased capital/output-ratio is an expansion path for capitalism, but this path is limited
because o(t) can’t be increased indefinitely. What the tendency rather implies is that the
capital/output-ratio will most likely be higher in the end of a period of accelerated
accumulation than in its beginning, which thus decreases the profit ratio, and also higher in
the later stages of capitalism, so contributing to its downfall.
In the presentation above the impression is could be given that all the different areas for
capitalist expansion can be studied in their isolation, which later just are summed up. In
reality there is a significant interaction-effects. For instance, expansion abroad, can be
accompanied by a lower capital/output-ratio for the additional labour employed because of
lower technical development in the country abroad.
3.8. Components of capital stock
The concept of capital stock has more dimensions than the first impression gives.
First we have to differentiate between material capital, Kmaterial, and nominal capital,
Knominal. Material capital consists of both fixed capital and inventories. A part of variable
capital will be included in inventories, but a part of it will be left out if wages have been paid
out but the work done not yet got a materialised form.
Nominal capital consists of (1) money capital, which doesn’t give any interest; (2) finance
capital, i.e. interest-bearing papers; and what I would call (3) fictitious capital. Material,
money and finance capital constitute the substance value of a company, these are also
represented in accounting. The price at which the company will be sold will normally differ
from the substance value - because of monopoly power, of expectations of higher than
average profits in the future, the risk to start and develop companies (or capitalisation of
“founders profit” in Hilferding’s words), etc - a difference I call fictitious capital (as it does
not represent any real values, only subjective evaluations).
46
Changes in total capital stock will hence not only reflect material accumulation, but also
changes in nominal capital. If for example optimism about future profit grows, then ficticious
capital grows significantly in relation to material capital stock, which in turn decreases the
calculated profit ratio. This has a similar effect as if the material capital/output-ratio grows. In
reverse, if expectations are not fulfilled and ficticious capital disappears, the calculated profit
ratio is partly restored, which has a similar effect as if material capital would be destroyed.
The movements of ficticious capital hence exacerbate the fluctuations of profit ratio due to
changes in capital/ouput-ratio.
[In my thesis I will also write about the role of finance and money capital, and business
failures, in the process of capital accumulation, which I haven’t had time to explicate on up
till now.]
4. Operationalisation
[This is a very sketchy outline for a chapter, which will be given much more substance later. I
am also thinking about skipping this chapter altogether, and deal with operationalisation in the
empirical part of the treatise.]
My sources are primarily different publications of Statistics Sweden for the period after 1950,
and historical statistics gathered by economic historians for earlier periods. Even if most of
the data exist in printed form, most of it doesn’t exist as ready files for further processing on
computer, and thus has to be scanned or typed in.
The quality of the empirical material is often quite poor, both in theoretical and empirical
sense, especially for earlier times. The concepts used are quite eclectically derived. For some
variables and for some years no data exist at all. The theoretical conceptualisations and
interpretations are therefore as important as the data collection itself.
The sources for national account data – GDP, employment, capital stock, investment, etc are for the period after 1950 mainly publications by Statistics Sweden, and for earlier period
primarily the research done in the project Historical National Accounts (HNA) for Sweden,
conducted by the departments of economic history at Lund and at Umeå University.
Jungenfeldt (1966) has collected and constructed data on labour statistics for the period before
1950; unfortunately there are no statistics on employment for the years between 1950 and
1960.
The main for aggregate accounting data concerning Swedish companies are Enterprises
1965- for the period 1965 and onwards, and Income, Expenditure and Profits of Business
Enterprises for the period 1950 and 1964. The important variables are here the profit ratio, the
capital stock and its composition, size and turnover. This sources are most problematic, but
also the most central to the project. The definitions change every three or four years, which
complicates comparisons over longer time periods. Data for earlier periods are very scarce
and unreliable.
47
The most important variables to be operationalised for my model are the capital stock (K)
and its composition, production (Y), the mass of profit (s), employment (L) and amount
accumulated (K). From these variables I derive others, as the profit ratio, growth of capital
stock, capital/output- and material/labour- ratios, etc.
Many of the assumptions in the theoretical model are not valid when investigating concrete
empirical material, mainly because I in reality face a multi-sector reality while the model only
assumes one sector. This means for example that productivity change is different for capital
goods than for output, and individual labour values not directly proportional to prices, making
the pertinent equations looking more complicated and difficult to grasp.
Even if it would be practically possible to find a direct measurement for my theoretically
derived concepts, the data available only allows construction of indicator that only indirectly
are connected to the relevant variables. Neither can the significance of an indicator only be
judged by how well it corresponds to the theoretical variable, i.e. its validity, but also by its
availability, consistency over time and space, i.e. its reliability. In this respect gross figures
are often more reliable because of their higher consistency over time, even if net figures have
a higher validity.
Production can be measured either as or synchronic labour or as diachronic labour/material
value.
When Y is measured in synchronic labour it equals L, which either can be the amount of
employed or total hours worked. The simplest way of deriving a relation between abstract
social labour value and price or use value is simply to divide the net output in price or
material terms with total hours worked, which will show how many currency or material units
it goes on an hour labour unit. The result will be different depending on what unit of
production we choose - a country, the world market or an individual company. This is in itself
an interesting result, as it shows how different production units relate to each other in terms of
how the labour in one unit is valued to the labour of another.
One indicator of use value or diachronic labour value of production is real GDP, despite its
flaws. Aggregate GDP also encompasses production and services performed by non-capitalist
institutions, as government and self-employed. But in most circumstances there are data on
these specific sectors, which thus can be deducted.
The GDP-concept in itself is quite problematic. Real GDP-growth will be different whether
we use Laspeyre’s, Paache’s, Edgeworth’s or chain index. If relative prices would be the same
over time the deflation problem would be non-existent, but we know that especially when the
studied time period is very long relative prices change dramatically. Take a country that
during the first year produces 10 bananas and 10 apples, and during the second year produces
15 bananas and 5 apples. Have such a country experienced a positive, negative or zero growth
rate in real terms? The answer to this question depends on how we value bananas compared to
apples (i.e. the relative prices).
Net Domestic Product is, for theoretical reasons, a better measure than Gross Domestic
Product, but here we have the problem of making reasonable estimations of the capital
depreciation every year in addition to the deflator-problem.
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Measuring profit poses particular problem. Should for example taxes, depreciation and
interest rates paid and received be included or excluded? The aggregate company accounting
data provides the relevant figures, from which different measurements of profit can be
constructed. The most inclusive measurement, the pre-tax and pre-depreciation profit, is
probably the most consistent over time, but also the one that least corresponds to the
theoretical concept of profit I use in the theoretical model.
The measurement of material capital stock is similar to the measurement of production. The
price of capital stock can both be translated into synchronic and diachronic labour value. To
measure the capital stock I am using different sources. The aggregate company accounting
data is most detailed, but also most problematic. The amount of for instance machine capital
that a company declare to own is primarily an accounting, not a real, measure, derived as the
purchase price minus an ad hoc amount of depreciation over the years, which most certainly
differ from the price the company would have to pay to get a new such machine, or it would
get if it would sell the old machine. If for instance, the depreciation time is five years, the
declared value of the machine could be zero, in spite of the fact that the machine is still used
for many more years after the expiration date. The data should, though, still be related to the
real value of material capital, and changes over time should reflect changes in real values. The
national accounting data over capital stock exist from 1950 to 1995, and they are more
reliable than the aggregate accounting data, though often doesn’t differentiate between the
private and the state sector, or between small and large companies, as the accounting data
does.
Depending on which components we include in the capital stock the profit ratio will vary.
The normal conduct is to calculate the profit rate on the basis of the most inclusive concept
of capital, i.e. the price put on the company at the market. But this is quite unreliable
measurement, as the evaluation of the market can change very quickly, which the sharp
fluctuations on the stock market clearly show.
Another measurement is to exclude financial incomes and expenses from the profit mass,
and only include material and money capital in the capital stock. The measurement of profit
mass represents here only profits derived from the production created within the company,
and the capital stock only capital not related to production in other companies (i.e. shares).
Both the aggregate company and national accounting provides data for investment. By
deducting depreciation I get a measurement of accumulation. Another measurement of
accumulation is also the difference between the synchronic or diachronic labour value of
capital in one year from the value in preceding year, but this measurement should be based on
longitudinal data rather than cross-sectional.
49
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