The Falling Tendency of the Rate of Profit - An Elementary Computer Algorithm
1. PREFACE
This is a revised version of a paper presented by the author to the 3rd Congress of the Portuguese Informatics Association in Lisbon, as transcribed into English in November 1988.
The paper considers the conventional mathematical argument presented by mainstream economists that takes profit maximisation as the fundamental premise of the behaviour of business firms in a free competitive market. Based on that assumption and leaving aside issues such as the so-called transformation problem, the argument presented here is valid irrespective of its expression in "labour values" or "prices of production".
The original version of this paper went into some mathematical details which are now deemed to be unnecessary for our purposes and emphasised the specific and crucial role played by the then emerging information technologies on the overall process of economic growth and development, as well as productivity gains and the short term growth of profitability. The paper also drew attention to the analytical role of then emerging computer based modelling techniques, in demonstrating the long-term behaviour of the rate of profit.
The paper was also prepared as a possible analytical response to then prevailing critical views about the possible negative impact upon overall employment levels of the then expanding computer applications. Particularly in some traditional service areas then characterised by high levels of (white collar) labour intensity, such as banking and insurance.
At the time of its original writing, the author was not aware of the Okishio Theorem and the premises of that theorem relating to the effects of any improved technologies on the overall rate of profit. The conclusions on this paper are that, even though Okishio is obviously right in the short term, it turns out to be wrong in the medium to long term. The time span involved in proving Marx right and Okishio wrong, depends solely on the rhythm of accumulation and the rhythm of technical evolution (the productivity factor). In an implied manner it considers that criticisms of he Okishio Theorem that look into the valuation procedures adopted (namely issues such as “replacement costs” versus “original costs” of production) are beside the point.
The algorithm is described in logical terms suited for translation into any computer language, such as Fortran, RPG or PL/1, and was derived from - and represents an extension of - a numerical example presented by Ronald Meek in a short essay titled "The Falling Tendency of the Rate of Profit" and published both in his book "Ideology, Economics and Other Essays" (1967) and in a collection of readings ("Economics of Marx") edited by Howard and King and published in 1976 by Pelican. It seems that Meek was not able to prove beyond any reasonable doubt the law of the falling rate of profit and that according to his own words "this problem cries out for a mathematical treatment which this author is not qualified to do". A computer model enables the simulation of the dynamics inherent to the process of capitalist accumulation, which dynamics are not easily captured using analytical tools of a static nature.
2. THE CONVENTIONAL ARGUMENT
2.1 Introduction
In this paper we shall attempt to discuss, in a manner that one hopes turns out to be short, precise and concise, on the one side, the relationship between new technologies (and in particular the new technologies of information processing) and, on the other side, the orthodox or mainstream economic theory. We consider in particular, but in very general terms, the overall problem of economic development in the sense both economic growth and structural transformation of the economic system, in the strict sense.
One such discussion will contemplate two different perspectives: On the one hand, we consider the particular case of the new technologies of information and communication (N.T.I.C.’s) as a factor, or rather as an instrument, participating in the economic system, much like any other new technologies whose introduction contributes to the overall improvement of economic productivity.
On the other hand, we consider these new information technologies as possible tools of research that enable a better study of the behaviour of the economic system.
2.2 The N.T.I.C.’s as an «Intervening Factor»
Regarding the first perspective above, we are told by orthodox or neo-liberal economics theory, that the introduction of any new techniques or technologies in the economic system, although it could cause short-term disturbances in the structure of the production system, namely in what concerns the employment level, this introduction will always end-up creating more employment and an enlarged demand for goods and services, and therefore the global growth of the system.
This is supposedly what has happened with the Arkwright and Crompton machines in the textile industries at the end of XVIII century, it is supposedly what should happen with computer equipment, goods and services and other hardware and software related to these N.T.I.C.’s
The basic or fundamental argument behind this reasoning is the assumption that the jobs, actual or potential, that are “lost” in the areas or sectors of activity of the economic system where these N.T.I.C.’s are introduced, will end-up being more than compensated for, in other sectors, upstream, downstream or otherwise, where brand new jobs and activities will have to be created also for the production and servicing of these new machines, pieces of equipment, goods and complementary services. In any case, it would seem that these possible short-term disequilibria and disturbances, do not fall under the realm of economic theory, belonging rather to the wider and allegedly less rigorous realm of the social sciences (in the strict sense) and the political practice of social engineering.
And indeed, or in any case, over the last two centuries, history has shown that many have been the structural changes introduced into the economic system, by the development and introduction of many and diversified new technologies and, “in the long run”, we have not had a reduction in the absolute and global number of jobs. Quite the contrary.
On the other hand, when proposing or defending the introduction of any new technologies, one has seen the argument of productivity systematically being put forward. The idea is that, if one increases the productivity, one also increases the production per capita and therefore one increases the overall wealth to be distributed and shared by all.
There is also implied in here the argument that, since the economic system “necessarily” has to be a competitive market oriented system, one also has o take into consideration and alleged “law of the survival of the fittest”. The so-called “economic Darwinism” essentially means that only those sectors or business firms with the highest productivities will survive. Thereby minimising the overall waste of resources in the system.
Under this perspective it is the usual thing to point to the N.T.I.’s as representative and crucial instrumental factors in the struggle for national, sectoral and entrepreneurial competitiveness.
2.3 The mathematical argument
We follow here the line of reasoning of the conventional argument, as was presented – at least in the 1980’s - in corporate sales schools around the world and then presumed to be representative of received wisdom in the field of sales and marketing of new technologies.
Using a relatively elementary mathematical language, the argument thus put forward, in favour of the introduction of any new technologies, by their conventional or mainstream proponents, would go on to a relatively common sense conclusion that given any particular general price level, one has to reduce "unit labour costs" (or ULC) in order to grow the margin of profit.
This overall line of argument is then resumed to the equation:
Labour Costs
Margin = 1 – ——————————
Volume of Production
On the other hand, following the same line of reasoning, the profit rate is then expressed by the formula:
P x Q – W x L – dK
R = ———————————
K
Or, in plain English, the rate of profit is equal to the volume of production minus labour costs minus depreciation of machinery, divided by the invested capital.
Volume of Production – Labour Costs – Depreciation
R = ————————————————————————
Invested Capital
It is from this reasoning that the general statement "it is the Unit Labour Cost that determines the competitiveness of a product in the export market” is supposed to result.
This “Unit Labour Cost” is made up of two basic components: First, the basic salary (or W) and second, the productivity (or Q / L) as expressed by a ratio between the quantity of goods produced and the quantity of labour used in that production.
On the assumption that we are reasoning in terms of equivalent quality and on the premise that one does not want to reduce the general salary level, one has to conclude that the only way to reduce ULC, so that we can grow M, is by growing the productivity, Q/L. It should not be necessary to point out that we do not want to reduce the general salary level, not only because that would run against the basic logical argument, in an economics analytical framework, but also because in real life that could turn out to entail not only serious “transaction costs”, at the macro level, but it would also mean a need for, and a diversion into, other disciplines of the social sciences.
Assuming that the depreciation rate on the used machinery is constant, it then becomes necessary to investigate the remaining variable in the equation above: the ratio between invested capital and production volume.
2. If one wants to grow the rate of profit by growing the productivity, then it is obvious that at constant prices and for the same quality, one has to grow the quantity more than one grows the capital invested in machinery. This is presumed to be precisely the overall objective of the whole process of automation across the whole of the production system.
Coming now back to the “Unit Labour Cost” concept (or ULC), which expresses the relationships between quantity produced, salaries earned and time units of work, one can easily conclude that any improvement in the quantity produced, while wages and time units of work remain constant, can only come from an improvement in the ratio Q/L. In other words, it corresponds to a reduction in ULC by means of an improvement in Q/L, and that is exactly what one is looking for.
2.4 The problems with this mathematical argument
The line of argument outlined above does not need to b referenced as it results, directly or indirectly from the so-called “reference texts” or “text books” and is, indeed, part o non-classified material and documentation used for training purposes in large multinational corporations, as well as in state-owned or other public enterprises and business oriented institutions.
When presenting their defence or theoretical justification, of the undoubtedly positive role of the N.T.I.C.’s in relation with the productivity growth, the conventional, main stream, economists seem to forget, or to bypass a few, not at all negligible, points which we try to outline next. While we are at it we could try to explain some of the reasons that might account for this apparent “forgetfulness”.
In the first place, we have perhaps a too constrained or narrow perspective of their universe of study, of the kind “to study the trees but ignore the forest”. Philosophers of science would talk here of the problems of methodological individualism
In the second place, we have perhaps some inability to separate the political level of analysis from he economic level of analysis. To separate the “social scientist” from the “social engineer”.
Thirdly, perhaps some inability to apply to the economic universe the systems approach that seems to prevail in the disciplines of Information Theory, Ecology or simply in Biology.
Finally, and most importantly, perhaps some inability to consider the economic system as a closed planetary system without any extra planetary outlets…
In other words, or in a bit more detail, the following points do not seem to enter the conventional wisdom in mainstream economics:
1. No company or industrial sector, on the on hand, nor any country, on the other, constitutes an island of socio-economic isolation. This means that any decision taken by any company anywhere in this planet of ours, will end up having reflexes and consequences in the activities and decisions of other companies, in other sectors, in other countries. Such an elementary and simple truth, worthy of Monsieur de La Palice has, however, some fundamental consequences, at least on a theoretical level, on economic sciences or “economics”.
2. In any case, from the previous point it results that the sum of individual efforts, undertaken by each and every company, searching for the maximization of R, must necessarily lead to the fact that the system as a whole must be in a permanent and indefinite movement of expansion. Even if not necessarily in a restricted sense of quantitative “geographic” or “demographic” expansion, as seemed to be the fear of the members of the Club of Rome.
3. On the other hand, so that everything goes well, in the best of all possible worlds, it is necessary that the actual profits, which are generated from that profit rate R, which one wants maximised and, if at all possible, growing (…), are themselves distributed and/or re-invested in a way such that it ensures the effectiveness of demand at every next stage of the endless economic cycle. And yet, in the 1980’s it already had been about 50 years since Keynes had pushed the concept of effective demand onto the stage of economic thinking. Not to mention the role of the leisure class as discussed by Thorstein Veblen or the role of state bureaucracies on the consumption side of the equation, as discussed by John Kenneth Galbraith.
4. Finally, it is necessary that the mass of the unemployed and/or dis-employed originated as a result of the introduction of any new technologies, namely the N.T.I.’s, in any company or sector, be “sucked in” or absorbed by other companies and/or sectors, up-stream, down-stream or side-stream, but within the system.
Let’s say that to “push out of the system” all those “unemployed” or “dis-employed” (including those that come afresh into the market place looking for a job and for whom there I no fresh “net positive” jobs creation), would be tantamount to “theoretical cheating” and a by-pass of the system’s own intrinsic logic. In short, it means that a system which has always been closed (although with “room for expansion”) and whose last geographical frontiers have been reached about a century ago, is still being regarded as an open system. And yet, ecologists have been ringing the bell for quite some time now.
3.0 THE INTRODUCTION OF NEW TECHONOLOGIES AND AN OLD POLEMIC
3.1 Introduction
Until now we have been presenting, albeit and necessarily in a very short manner, what might be termed as the "official position of the 'ideological' subsystem, that participates in the more economic global system at the level of interpretation and explanation of its functioning. This more or less "official" position is the one usually presented in seminars, conferences, meetings and reports of all kinds of institutions one would consider as part of the "establishment". These explanations are also presented, at least occasionally, in order to assuage fears of a deepening in the structural level of unemployment and eventual social crisis, as these fears are some time expressed by some of the institutional members that participate in our economic system.
On a more "down to earth" plane, one could also say that it is not the computers, nor the robots, that are causing de current growth in unemployment, at least when the issue is considered on a world-wide basis (not just in a few major countries…). As one clear-cut historical example, we could draw attention to the 1930's, when there were no computers, nor any robots, and yet unemployment levels in most industrialized countries reached proportions beyond our current worst fears. But, if the introduction of new technologies had nothing to do with the Great Depression, which were then the causes of that crisis and what have new technologies of information and the development of computer models of economic reality, got to do with that analysis?
For a more comprehensive understanding of the occurrence of periodic crisis, within the historically recorded functioning of the capitalist system, we have to change perspective and look upon capitalism as a whole systemic unity, whose behaviour seems to be determined by a specific and peculiar set of rules in a permanent and continuous process of iterations and their consequences, within a secular process of accumulation with a set of permanent feedback mechanisms.
Of those basic rules of the system, the most fundamental one seems to be the permanent need to accumulate and reinvest, in order to get more capital to get more profit, to invest anew and still get more capital, in a never ending spiral of transformation of the planet and its resources.
In that never ending search for more capital and profits, competition in a set of free and tendentially non regulated markets, seems to make it mandatory that the basic motive and incentive for business enterprises of all kinds, is profit maximization. We draw the attention of readers to the fact that in some of the literature on business management and business economics, the argument has been put forward that in our modern day and age, profit maximization is no longer the true motive determining business behaviour. Other motives have been advanced as being more relevant, such as “market share”, “sales maximization”, “total company worth”, “the prestige and welfare of executive management”. The question of management versus shareholders interests has been extensively discussed and some of these discussions have turned into classics. In any case, it is possible, in a logical and consequent manner, to reduce most of these other objectives and motivational factors to the ultimate motive of profit maximization. Be it on a short-term basis, or on a longer-term basis.
So, all in all, what we are talking about here is the fundamental motive that explains the regular functioning of the capitalist system: profit and profit maximization. In that context it becomes crucial to understand the systemic behaviour of that particular variable within the system: the rate of profit.
The question of a falling tendency of the rate of profit is, of course, as old as the history of the discipline of Political Economy, and all the classical authors tried to explain why that was so. Karl Marx considered it the most fundamental law of the whole of Political Economy. We may add here that this falling tendency of the rate of profit is to the realm of human societies as the law of gravity is to the world of stars and their planets. General relativity not withstanding… And yet quite a number of authors, including scholars and students of Marx and Ricardo, argue that there is no such tendency. Some go as far as stating that we are yet to observe such a tendency in the first place. Others argue that, on the contrary, there is a growing tendency of the rate of profit.
Amongst those we assert the existence of such a tendency we might classify them into two broad categories: the externalists (such as Ricardo) who argue that the falling tendency of the rate of profit is just another expression of the general law of “diminishing returns”, and the internalists (such a Marx) who argue that the FTRT is the ultimate expression of the inner contradictions of the system’s own logic. And then there are those that point out the apparent indeterminacy of behaviour that is inherent to the combined behaviour of the various factors and variables involved, namely the evolution of constant and variable capitals and the organic composition of capital.
Okishio, for example, seems to assume and argue that, with the introduction of new and more efficient new technologies, the rate of profit must simply go up, not down. The idea that it might go up, and then flatten and finally, later on, declining, does no seem to merit research and discussion. As to those scholars that claim that there has been no actually recorded falling tendency, and those other scholars who have been trying to identify and compute it through research of available reports and statistics, one is reminded of the reasoning used by Adam Smith who merely used the evolution of the interest rate, as a proxy indicator for the behaviour of the profit rate. In any case, that falling tendency may express itself through other observable effects and that is precisely what a dynamic approach may allow us to do.
Other important results and consequences to the functioning of the system as whole and its inner logic arising from the wide spread of the new information and communications technologies comes from its impact upon the “price subsystem”, as a “transport system” that conveys relevant economic information to all participants of the system. It could be argued that, in any case, the issue of asymmetry of information access has just gained a new twist and sophistication. A detailed discussion of that particular impact of the N.T.I.C.’s is way beyond the purpose of this paper.
3.2 The Falling Tendency of the Rate of Profit
Let us then consider, from the convention Marxian perspective, the main actors in this film of real life, permanently in motion, which is the functioning of the capitalist economic system, of which we are all part and parcel. We shall basically consider the same or equivalent concepts as those used above – in the conventional mainstream approach – and then try to consider their respective interactions as we set the system model in motion.
In the literature that discusses these matters one can find all kinds of arguments and criticisms as to the exact meanings each scholar attributes to each specific term. Some of the concepts are under permanent scrutiny and some authors also go into the details of what exactly Marx is supposed to have written and what was it that he actually meant by this or that term or expression.
Unfortunately this is not the time or place to go into such convoluted discussions and one only hopes that, at the very least, some of the concepts and analytical categories used in this paper, can be looked upon as proxies of similar concepts used elsewhere even if with slightly different meanings.
In any case, any reader who is familiar with the conventional Marxian presentation is free to skip directly into some basic comments bellow.
Having said that, let the following definitions stand:
c = The value of capital invested in physical equipment, machines, tools, buildings, energy and other material infrastructures. In the abstract, this should reflect the totality of material resources available anywhere in the global system.
v = The value of capital invested in human resources, labour, technical know-how, management expertise. Also in the abstract, this should reflect the totality of human resources available anywhere in the global system.
C = The global or total sum of invested capital and, therefore the sum of c + v.
s = The value of economic surplus, it is a portion of conventional “value added” and, for all practical purposes may be considered as corresponding to “M = profit margin” in the previous line of argument.
K = Index of capital intensity. To use the Marxian terminology, this is the “organic composition of capital", and shows the relative proportions of ‘c’ and ‘v’ in the value of total investment.
e = Rate or productivity index. For all practical purposes it is the equivalent of the same concept as used in the previous line of argument. Marxians, however, give it the cursed name of “rate of exploitation”. It is the result of a division of 's' by 'v'
r = Profit rate or rate of return on investment.
After some well known algebraic transformations we come to the conclusion that the overall "rate of profit is equal to rate of exploitation divided by the organic composition of capital plus one".
Or, in formal algebraic language:
3.2 Some basic comments
This last equation that states that "rate of profit is equal to rate of exploitation divided by the organic composition of capital plus one" may seem pretty straightforward and yet it has caused quite a number of polemical discussions because of its complex nature. We write here “complex nature” as used in systems theory, in the sense that you cannot touch upon one single element of its constitution without affecting the behaviour of the other elements.
The basic comments one has to make about this equation are then the following:
1. The very first comment has to do with the methodology adopted and its verbal expression. On the one hand we consistently argue that the behaviour analysis of the capitalist system has to be done on a global scale and considering the system as a single, worldwide entity. As if the capitalist system was made up of one gigantic business enterprise. And yet, on the other hand, we are continuously referring to the decisions and constraints of individual firms. There is no contradiction here, as the decisions of every one and all of the business firms in the system must also be absorbed somewhere else in the system. In order to obtain a comprehensive understating of the system we do have to permanently joggle (so to speak) between a "top down" and a "bottom up" approach.
2. According to the previous line of argument, i.e., according to main stream economics, what one wants and is predicated for the system as a whole, is to achieve on a continuous basis the relative or percent improvement of R, in order to ensure the competitiveness of a company or the economic sector, or a country or region, whatever that may be. At the very least, the idea is to keep R on par with your competitors. No sales maximization, just profit maximization.
3. In order to improve or increase R it is necessary to increase e (the productivity factor) proportionately more than the term K + 1. In other words, it is necessary that the improvements or gains in productivity be proportionately greater than the increases in investment, either through better or more efficient machines, or through better-trained human resources. Indeed, to invest in better performing machines, more advanced technologies and in more specialized training of human resources, just so that "everything remains the same" does not seem to be exactly a very attractive proposition for most pragmatic and down-to-earth company managers of this world of ours. And yet, competitive markets tend to ensure that the relative position of most companies does indeed "remain just the same".
Again, this so simple conclusion seems to be worthy of our Monsieur de La Palice.
4. It should be noted however, that it is theoretically and technically possible to increase R as well as K + 1, be it in a equi-proportional manner, be it in a manner in which R grows more than the increases in K + 1.
As a matter of fact it should be noted that when businesses try to increase K + 1, it is with the specific and ultimate goal of trying to increase R. On the other hand, there is also the line of argument that states that investments in new and more advanced machines and equipment, in general, do not necessarily correspond to increases in K since these larger or increased investments in more sophisticated equipment are compensated for by larger investment expenses in more qualified personnel. Also, with more advanced and/or improved fabrication techniques, so the argument goes, machines and other material equipments also tend to become themselves cheaper and cheaper. In fact, when we consider all those possibilities, both the numerator e and the denominator K +1, may seem to tend to "infinity".
It is exactly the fact of all these existing possibilities that has been at the origin of the polemic and controversial issue, above referred to, and that has been used by all those that claim and discard Marx's alleged error in postulating the "law of the falling tendency of the rate of profit".
This is where some additional comments and considerations are in order or come into play. We will consider only two basic points: the systemic nature of the capitalist system and the indeterminacy character of the mathematical equation that expresses the "law of the falling tendency of the rate of profit". Along the way we refer to a possible analytical error of Marx which may have contributed to the polemic.
A. The vast majority of economists seem to consider that the economic system is an "open system". Basically this is because they use, either implicitly or explicitly, the terms of reference of Stafford Beer (1969), whereby any socio-economic system is considered to be a probabilistic hyper complex system, and so, by definition, an open system. It should also be noted that while a closed system is characterized by a reversible kinetic equilibrium1, an open system is characterized by its indeterminacy towards a stationary state dynamically irreversible. We find here, a reformulation of some of the ideas of the classics of Political Economy whereby the world economy would tend to a stationary state. From this perspective the world economy or the world system would indeed have to be considered to be an open system.
However, we also have to look into this matter, of the system being "open" or "closed", not only from the perspective of its internal complexity - the criteria most commonly used - but also, and in this case most specially, from the point of view of "transactions with the external arena" (to use here the terminology usually associated with the world-system school.
Whereas from the point of view of "national accounts" each and every one of the "national economies" is obviously an "open system", when we aggregate the sum total of all the "national" economies, it seems obvious that we end up with one single "closed system".
La Palice or not, this simple fact has significant implications for the understanding of the system's historical behaviour. We simply cannot ignore the planetary dimension of the system and its global integration. In other words, the economic system whose behaviour one wants to analyse, has definite geographic and demographic frontiers, which even if sometimes they are not very clear, they are certainly very objective and concrete.
As stated before, we have then to consider the not at all negligible point above referred to, which is the need for the system to be in a permanent and indefinite state of expansion. At this stage it should be noted, even though in an incidental manner, that we are touching here upon one fundamental issue that opposed Marx to the "classical economists" of his time. That issue consists in the fact that those economists postulated the inherent and natural stability of the economic system, as they knew it, whereas Marx postulated its inherent instability precisely as a result of falling tendency of the rate of profit.
But, if the modern controversy has been (and continues to be) possible, such is also due to the fact that those economists that discard the "law of the falling tendency of the rate of profit", do so by using or referring to the possibility that is inherent to the system when growing or in expansion of growing R more than the growth of K + 1. That also means that the introduction of any new technologies is beneficial to the growth of the profit rate.
At the same time, these same economists seem to discard yet another not at all negligible point, already referred to above: the new values which have been generated from an improved R, must most certainly be distributed and eventually re-invested in the next stage of the economic cycle. When they are not consumed in conspicuous style by the leisure class, nor invested in new reproductive opportunities, some of those "new values" tend to vanish and dissipate themselves in the thin air of international speculative finance.
B. Turning now to the indeterminacy character of the mathematical equation that expresses the "law of the falling tendency of the rate of profit", the following comment seems to be pertinent. As indicated before, it seems that it is possible, both technically and theoretically, to have both the numerator and the denominator of our equation moving in the same direction and in equi-proportional manner. As formulated by some economists with whom this matter has been discussed, both the numerator and the denominator tend to infinity and therefore the equation itself is indeterminate. When this matter is presented to engineers or plain mathematicians, the almost automatic response is, "it's just a matter of raising the indeterminacy".
Also, and still in this same line of reasoning, even though it is a fact that both members of the equation may tend to infinity, it has now been well over a century since the German mathematician Georg Cantor has demonstrated the existence of different infinities and that, therefore, some infinities are larger than other infinities. In any case, the important issue here is not so much the fact that both members of the equation may tend to infinity, but the fact that both tend to infinity at different rates of progression.
This is exactly the crucial dynamic character of the system's complexity which is captured by the formula R = e / K + 1.
3.3 A very brief reference to History
If we now jump from the somewhat abstract concepts of "closed" versus "open" systems and onto the more visible realm of History, one could argue that all the various pre-capitalist systems could act and be considered as "open systems", but only in the sense that apparently they could expand indefinitely from their starting borders. And indeed, the most dynamic of these historical system did in fact expand until they would encounter other, more or less, equally expanding systems… When this happened quite often they clashed and wars ensued until one or more of those weaker systems were integrated into the more powerful ones. Human societies being what they are, as a result of some of these wars a new vacuum was created out of the war destructions. In this respect, and considering the more recent wars that have plagued mankind, one could then also argue that these wars of destruction have had the added effect of bringing the system frontiers back to a stage from where it could re-start again in a renewed expansionary movement.
This all means that, since the economic system has now reached a stage of global integration on a planetary scale, we can no longer begin our analysis of its behaviour from the theoretical principle, even if unconscious that we are dealing with a system capable of indefinite extension. Perhaps in a somewhat remote future we shall be able to expand into, and trade with, other planets. But that is no longer positive analysis of our currently existing socio-economic system.
3.4 The construction of our rudimentary model
Coming now back to the issue of the relationship between, on the one hand, new technologies in general and informatics in particular, and on the other hand, the fundamentals of economic theory, and considering the role of informatics as an instrument of analysis to study the potential behaviour of an economic system, in this case a system that is motivated and determined by the rules of competition and driven by the profit motive, what we have done has been the development of an elementary computer model reflecting the relationships between the various variables in the system and expressed by the fundamental equation:
We took into consideration the famous counter tendencies as discussed by Marx, namely the intensification of labour processes and specifically the extension of the working day in terms of "socially surplus work". The issue of reducing the relative level of workers salaries has also been considered but, from an inner logic of the system, the relative size of exploitation (derived from surplus work or from lower salaries) is reduced to a difference in the time span for the "law" to manifest itself. The same comment could be applied to a third counter tendency, that of extended usage of machinery that technological evolution may have rendered obsolete. As to the search for cheaper raw materials in foreign markets, as well as the role of these same foreign markets in terms of potential outlets for surplus production, these "counter tendencies" would only be relevant in an open system environment, but not when one considers the issue from a closed system perspective.
We have also taken into account the following factors:
1. Volume of employment, in the sense of "employable population" or the number of "working people" which can be hired with the available capital funds, expressed in v and which are in search of profitable applications.
2. Useful working hours, or simply the number of hours of daily work of that same "population". This can be assumed as constant. One might consider and increasing or decreasing number of daily working hours per "employee", but that would simply create a logical diversion in the model, without altering the fundamental conclusion.
3. The percentage of surplus that flows back into the system in each following cycle, both for investment in physical capital and in the hiring of human resources. Obviously enough, the remainder surplus is supposedly spent in (conspicuous…) consumption by the entities that receive it. In the example shown in this paper, we have used a feedback rate of 5%, of which…
In this example we have departed slightly from Ronald Meek's essay (1976). We believe that the use of computer models is the obvious solution to that author's statement that, if memory serves, "this problem cries out for a mathematical treatment that this author is not qualified to do".
Until now we have failed to find a similar or more effective approach to the solution of this problem.
4. The Model Results
|
Ratios |
Amounts |
Number workers |
Ratios |
|||||
C |
c |
v |
K |
c |
v |
s |
e |
R % |
|
12,000 |
1.00 |
5.00 |
0.20 |
2,000 |
10,000 |
10,000 |
2,000 |
1.00 |
83.33 |
13,000 |
1.10 |
4.94 |
0.24 |
2,536 |
10,465 |
12,585 |
2,305 |
1.29 |
96.81 |
14,259 |
1.21 |
4.12 |
0.29 |
3,237 |
11,021 |
15,729 |
2,675 |
1.43 |
110.31 |
15,832 |
1.33 |
3.74 |
0.36 |
4,154 |
11,680 |
19,550 |
3,123 |
1.67 |
123.48 |
17,787 |
1.44 |
3.40 |
0.43 |
5,344 |
12,444 |
24,156 |
3,660 |
1.94 |
135.81 |
20,203 |
1.60 |
3.09 |
0.52 |
6,893 |
13,312 |
29,768 |
4,309 |
2.24 |
147.34 |
23,180 |
1.76 |
2.80 |
0.63 |
8,946 |
14,232 |
36,598 |
5,080 |
2.57 |
157.89 |
26,840 |
1.90 |
2.54 |
0.76 |
11,588 |
15,250 |
44,790 |
6,004 |
2.94 |
166.98 |
31,319 |
2.12 |
2.30 |
0.92 |
15,022 |
16,298 |
54,562 |
7,080 |
3.35 |
174.21 |
36,775 |
2.33 |
2.09 |
1.11 |
19,386 |
17,309 |
65,811 |
8,325 |
3.78 |
178.96 |
43,356 |
2.56 |
1.93 |
1.39 |
24,886 |
18,470 |
78,740 |
9,721 |
4.26 |
181.61 |
51,230 |
2.81 |
1.72 |
1.63 |
31,778 |
19,451 |
93,639 |
11,909 |
4.81 |
182.78 |
60,594 |
3.09 |
1.54 |
1.98 |
40,266 |
20,328 |
109,982 |
13,031 |
5.41 |
181.51 |
71,592 |
3.39 |
1.41 |
2.40 |
50,562 |
21,030 |
128,120 |
14,916 |
6.09 |
178.96 |
84,404 |
3.72 |
1.28 |
2.91 |
62,797 |
21,608 |
147,202 |
16,881 |
6.81 |
174.40 |
99,124 |
4.09 |
1.16 |
3.53 |
77,223 |
21,902 |
166,908 |
18,881 |
7.62 |
168.38 |
115,815 |
4.49 |
1.05 |
4.28 |
93,863 |
21,950 |
187,100 |
20,905 |
8.52 |
161.55 |
134,525 |
4.93 |
0.95 |
5.19 |
112,789 |
21,734 |
207,046 |
22,870 |
9.53 |
153.91 |
155,230 |
5.42 |
0.86 |
6.30 |
133,972 |
21,257 |
225,923 |
24,718 |
10.63 |
145.54 |
177,822 |
5.96 |
0.78 |
7.64 |
157,243 |
20,579 |
243,251 |
26,383 |
11.82 |
136.79 |
202,147 |
6.55 |
0.70 |
9.36 |
182,627 |
19,517 |
259,303 |
27,882 |
13.29 |
128.27 |
228,077 |
7.20 |
0.63 |
11.43 |
209,729 |
18,351 |
272,939 |
29,129 |
14.87 |
119.67 |
255,371 |
7.92 |
0.57 |
13.89 |
238,226 |
17,145 |
283,645 |
30,079 |
16.54 |
111.07 |
283,736 |
8.71 |
0.51 |
17.08 |
268,042 |
15,695 |
292,045 |
30,774 |
18.61 |
102.93 |
312,941 |
9.58 |
0.46 |
20.83 |
298,599 |
14,338 |
297,352 |
31,169 |
20.74 |
95.02 |
342,676 |
10.53 |
0.41 |
25.68 |
329,831 |
12,842 |
300,388 |
31,323 |
23.39 |
87.66 |
372,715 |
11.58 |
0.37 |
31.30 |
361,180 |
11,540 |
300,360 |
31,190 |
26.03 |
80.59 |
402,751 |
12.73 |
0.33 |
38.58 |
392,580 |
10,177 |
298,213 |
30,839 |
29.30 |
74.04 |
432,572 |
14.00 |
0.30 |
46.07 |
423,500 |
9,075 |
293,425 |
30,250 |
32.00 |
67.83 |
461,915 |
15.40 |
0.27 |
57.04 |
453,961 |
7,959 |
286,821 |
29,478 |
36.04 |
62.09 |
490,597 |
16.94 |
0.24 |
70.59 |
483,739 |
6,853 |
278,707 |
28,556 |
40.67 |
56.81 |
518,468 |
18.63 |
0.21 |
88.72 |
512,698 |
5,799 |
269,421 |
27,520 |
46.62 |
51.96 |
Notes on the table
C = Total Social Capital, represents the total productive capacity in existence. In a general sense it is the global aggregate of current productive capital and the sum total of our common material, scientific and technological heritage.
c = Constant capital or the sum total of fixed capital and circulating capital of a material nature.
v = Variable capital or the sum total of human resources available to work, with their know-how. It really is immaterial, for the final purposes and conclusions of this model, if this "variable capital" is expressed as "physical basket of subsistence goods" of "money-capital" available to hire and pay those available human resources.
K = The ratio between constant capital and variable capital, also known as "organic composition of capital". A common proxy indicator is "capital intensity".
s = Surplus product or the sum total of whatever is produced in excess of a simple total social reproduction scenario. In short, the economic surplus that results from sales proceedings minus the amount of investments made. When appropriated by the non-working owners of capital, it originates a certain level of "rate of exploitation".
e = The rate of exploitation of non-owners of capital. The ratio between surplus product and the reproduction needs of the aggregate of workers. A common proxy indicator would be a coefficient of labour productivity.
R = The rate of profit.
On this particular iteration we have used a rate of feedback of 10%. In other words, 10% of the total surplus produced in the system goes back to accumulation in an enlarged reproduction schema.
It was also considered that this would have a positive impact of 10% on both "labour" and "capital" productivity growth.
General comments
1. The column "workers" represents either the number of workers, or the number of workers/hours required and employed by the system at its regular working level and at an average wage. This is historically determined and its price (and deviations from intrinsic "value") is subject to the interplay of "supply" and "demand" in the labour markets.
2. The permanent growth of c versus v is naturally due to the permanent competitive pressure for productivity gains, through machinery, irrespective of decreasing costs of new machinery. It also means a global decrease in the relative proportion of "socially necessary labour".
3. The first fact to be noticed in the model results, is that R, the rate of profit starts by growing (as foreseen by Okishio…) and goes on growing for a period of 11 cycles. After that it flattens out and starts to decrease (as foreseen by Marx…)
4. The second thing to be noticed is that the number of workers required and usable to the system (on its production side, not on the consumers' demand side…) grows from an initial number of 2.000 and goes up to a number of 31,323, for a period of about 25 years, after which it starts to generate unemployment.
5. The third thing to be noticed is that the value or "real amount" of capital that is available to hire and pay the required and usable workers, grows from its initial amount of 10,000 units up to 21,950 units (for a period of 16 cycles) and then starts to decrease. This should be contrasted with the permanent growth of the value (or "real amount") of c, the capital allocated to material equipment.
Some general considerations
1. One could easily be tempted to dismiss this whole exercise as "these are just numbers produced by a computer program which was programmed to produce them in the first place…" However, the same could be said of any computer modelling of socio-economic reality. What is really at stake here is the validity of the relationships supposedly represented by the equation above. In that case, if those relationships expressed in that fundamental equation hold true, what this rudimentary model shows are general tendencies of a non regulated market system.
The institutional members of the system are bound to try and improve their competitiveness, and by doing so they have to try and improve their respective coefficients of productivity. This they cannot do without increasing the intensity of e and K.
This model only pretends to show tendencies. Economics is, first of all and foremost, a social and historical science which deals with the a specific facet of the behaviour of rational human beings and groups. The fact that birds, butterflies and aeroplanes do fly, does not negate the presence and action of the force of gravity. This means that although these tendencies are present in the economic system, it is not at all impossible, on the contrary (!) to counteract these tendencies. The issue then becomes one of how and when do leading institutional members perceive and realize, even if only empirically, what is happening and what do they do about that.
It is our contention that this model could be adapted and then "easily" applied to explain historical phenomena such as mass migrations, wars of destruction, reconstruction booms, stagnations and depressions. Indeed, the model could be adjusted (in its parameters) to "coincide" with the long waves of Kondratieff, and thereby confirming Mendel's perception of a relationship between the law of the falling tendency of the rate of profit and the long waves of economic activity.
SKETCH OF A PROGRAM FOR AN ALGORITHM TO
DETERMINE THE BEHAVIOUR OF THE RATE OF PROFIT
Guilherme da Fonseca-Statter
Introductory note: This algorithm was first conceived to use input data in the format of now obsolete punched cards, with the data elements recorded in two different cards. One with the initial situation of the system and the other with the various assumptions for the rate of change in the system.
Purpose: To evaluate the behaviour of the overall Rate of Profit, prevailing in any free market economy, during a time series and in an unregulated free market environment, under certain changing circumstances, such as:
Constant or Increasing Rate of Investment
Increasing Organic Composition of Capital, this increasing rate also being susceptible of change
Variations in the increasing Rate of Surplus (or “rate of exploitation”)
Increases in Productivity, both in “capital goods” industries and “wage or consumer goods” industries
The system assumes an indefinite number of workers available to enter the labour force and a constant number of total working hours.
The system also assumes a system of constant wages, these being expressed as an number of hours or “socially required work” (an overall social weighted average) that enables the workers an average and socially acceptable level of consumption.
The program should consider and treat two different types of Input data:
A – Input data defining the situation of departure at any one point in time:
Constant capital prevailing in that society at a particular moment
Variable capital prevailing in that society at that same particular moment
Average number of hours per working day
Number of workers in that society or system
B – Input data with various assumptions for the algorithm to compute results:
Rate of accumulation or flow of capital from period N as investment into period N+1 expressed as percentage. As a matter of detail, this is to be considered as investment net of depreciation
Productivity increment into capital goods industry sectors
Productivity increment into wages goods industry sectors
Optionally:
Assumptions about the initial and changing conditions may become more complex by adding a number of constraints on the model such as:
Maximum top limit on the number of workers available in the system
Setting a limit to a demographic growth either biological (within the system) or migratory from outside the system (impossible on a world wide basis).
A rate of growth for hours worked per day per worker (even if this is historically unrealistic).
A rate of “negative growth” for hours worked per day per worker (the diminishing number of average work hours per day…) which could reflect what has been observed historically).
Notes on the computation within the model:
Print the initial situation after computing
Total capital: “Total-Capital” = “Constant-Capital” + “Variable-Capital”
Ratio of “Constant-Capital” to “Variable-Capital”, e.g. 1 / 4
Organic Composition of Capital, e.g. 0.25
Surplus Product: Number of Excess or Surplus Hours worked by the average worker over and above the socially minimum required for the society to “stand still” (that is, no accumulation), times the number of workers in the system or “Excess x Workers”.
Surplus Rate or “s / v”
Profit Rate or “s / c + v”
Skip one line (for clear presentation) and start printing detail lines resulting from computations in the model, following the data in the assumptions input data set.
In principle, one data set of input (with the various variable assumptions) should cause the printing of one page (or display one screen) with the results in a table.
Following the display (or printing out) of one page of, say, 50 years, the system should (as a matter of routine) convert the displayed table into a graphic with curves showing the evolution of each and every one the columns in the table.
Note that one set of assumptions or premises should cause the printing out of one page with results for those assumptions
Proceed with computations
Compute new “Total-Capital” by multiplying previous “Total-Capital” (or the sum of “Constant-Capital” and “Variable-Capital”) by the rate of investment. This we may call “flow-back”.
Compute new Ratios by applying to each one the related or respective productivity increments
Obtain an Index of new Capital Structure by adding the two ratios (wage industry sectors and capital industry sectors)
Divide the new “Total-Capital” by this previously obtained Index and multiply the result by each one of those ratios.
This should give the new “Constant-Capital” and the new “Variable-Capital”.
Subtract the new ratio for Variable-Capital from total average number of hours worked per day per worker.
This should give new “surplus-work” in hours per day.
Compute new number of workers that can be hired with New Variable Capital at New Daily Rate or “Variable / Daily Rate (or Minimum Hours Required) = Number of Workers”
Compute new “Surplus-Amount” by multiplying “Number-of-Workers” by “Surplus-Work”, after determining this “Surplus-Work” by subtracting necessary or “Required” work from Total (or normal) working hours, thus:
Total or normal working hours – Minimum hours required = Surplus Hours of work
Number of workers x Surplus Hours of Work = Surplus Amount
Compute new “Organic Composition of Capital” by dividing new “Constant-Capital” by “Variable-Capital”
Compute new “Rate-of-Exploitation” by dividing “Surplus-Amount” by “Total-Capital”.
Compute new “Rate-of-Profit” by dividing “Surplus-Amount” by “Total-Capital”.
Print detail line with results of computation for period N+1. Immediately afterwards, set N+1 back to N and go to the first instruction under paragraph 3.
At the end of 30 lines or periods of time (30 years, for example. It could be any number decided in advance), printout a “comments” line indicating the contents and/or description of assumptions or premises.
Go to next set of different assumptions and to a new page or scenario.
1. In a general sense, a system that is characterized by a minimum of interactions with the environment. However, when one thinks of it, there are really no closed systems in its exact definition, in the sense that there will always be some degree of minimal interaction between a system and its environment. The idea is to designate those systems whose behaviour is of a deterministic and predictable character and whose states can be repeated along an axis of time in an indefinite manner as if the law on entropy did not apply to those systems.
Guilherme da Fonseca-Statter
Ph.D. «Political Economy of Development»
ISCTE-Lisbon University Institute
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