Marx on Geometric Change (1. The Rate of Profit)

Screenshot from 2018-01-23 13-54-50

While… productive power increases in a geometric, the extension of markets proceeds at best in an arithmetic ratio. —Engels, preface to the 1886 English edition of Capital Vol. 1

Change and Progress

Theories of ‘accelerating change’ are mostly commonly associated with a particular strain of techno-utopian thought, concentrated primarily on the libertarian—and perhaps at this point, postlibertarianside of the politico-economic spectrum. The fabled law proposed by Gordon Moore, the co-founder of the Fairchild Semiconductor company and later CEO of Intel, is exemplary in this regard. In its earlier form, unveiled first in a 1965 paper bearing the cumbersome title of “Cramming More Components Onto Integrated Circuits”, and updated a decade later with “Progress in Digital Integrated Electronics”, the law suggests that the average speed of processors, the source of a computer’s processing power, would double every time years. While it would become something of self-fulfilling prophecy, with the eighteen month-to-two year time horizon becoming targets that the industry strove to hit, its recognition triggered a veritable cascading of other exponential trends: the falling movement of information technology pricing; Keck’s Law and Butter’s Law of Photonics, both of which concern the amount of capable of moving through fiber optic cables; the Carlson Curve, which concerns biotechnologies like gene sequencing; so on and so forth.

In the hands of futurists such as Ray Kurzweil and Hans Moravec, the sort of auto-magnifying trend that underscores Moore’s Law becomes identified as a condition of technological development as such—if not the general condition for any and all evolutionary processes, of which technological development becomes only a particular iteration. For Kurzweil, it is the “law of accelerating returns”; integrating Moore’s Law with W. Brian Arthur’s insights into the phenomenon of increasing returns and lock-in effects (which arose, incidentally, through studies of nascent tech industries in the 1980s), this forms the basis of what constitutes something of an eschatology. “[T]echnology, particularly the pace of technological change”, he writes, “and has been doing so since the advent of technology, indeed since the advent of evolution on Earth”—adding then that this culminates at the Singularity, the imminent situation in which this rate of change becomes “so rapid and profound it represents a rupture in the fabric of human history”. Similarly, Marovec extrapolates from these trends a host of near-unimaginable technological advances.

Despite the cutting-edge character of these sorts of theories, their fundamental core—that science and technology has an accelerative character, graspable as exponential or geometrical progression—is not in itself new. In 1904, the American history Henry Adams proposed a “law of acceleration”, which if properly elucidated could serve as a silver key for unlocking the inner motion of “all history, terrestrial or cosmic, mechanical or intellectual”. Adams would elaborate further on this law in his 1909 work The Degradation of Democratic Dogmawhere he argued that not only were developments in science and technology unfolding in an exponential rate, but that they also unfold in series of phases (e.g. the “mechanical phase”, the “electrical phase”, and the “ethereal phase”) tending towards the “control of cosmic forces on a cosmic scale”.

A very similar line of thinking appears in R. Buckminster Fuller’s notion of “ephemeralization”, which made its first appearance in his 1938 book Nine Chains to the Moon. It too is a theory of exponential change; inspired by the great acceleration of industrial productive power set-off by Henry Ford’s introduction of the assembly line, Fuller’s ephemeralization offered an understanding of efficiency as the situation in which output increases while input decreases—a tendency not towards ever-bigger, more concentrated production or the small-scale alternative that is so often reactively posited as the alternative, but the progressive honing of the ability to do more with less. As he wrote in his later work Critical Path (1981), “[e]phemeralization trends toward an ultimate doing of everything with nothing at all, which is a trend of the omniweighable physical to be mastered by the omniweightless metaphysics of intellect”.

A whole series of different components serve as the intersecting lines that give rise to these various articulations of accelerating change. There is, of course, the interrelated forces of scientific development and technological evolution that have progressively diffused over, above, and below the thin surface of the our terrestrial sphere, penetrated deep into every pore of society. On another level, there is the mathematical history of exponent or geometrical processes, which curiously appears as having always bore a striking relationship to economics: in an interesting history of ‘exponential law’, Lorenzo Curtis cites several Babylonian cuneiform tablets, dating back to around 2000 B.C., that pose questions around the moving value of precious metals in relation to annual interest rates; while the tablets fall short of discovering exponential law proper due to an inability to develop a mechanism for dealing with continuous rates of change, the tablets clearly usher in this direction (and serve as an interesting addendum to Sohn-Rethel’s argument that abstract thought itself is ultimately downstream from the social emergence of money). Fast forward to 1826 and we find Thomas Malthus, in An Essay on the Principle of Population, locking geometrical change into political economy via his (in)famous formula: “Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio”.

As Curtis points out, the term “exponent” derives from the French exposant, which was also used for “index”. In his history, Curtis makes the point that successive multiplication series were expressed formulaicly , beginning with Rene Descartes’ La Geometrie (an appendix to his 1637 Discourse on Method) as right superscript index—though perhaps we can make a more generalized point regarding this relation: the exponential curve in development serving as an index of the more abstract notion of progress, the other line that courses through discourses around accelerating change. The ideal of progress too is baked into the foundations of political economy; it was Adam Smith, after all, who proposed a progression across four stages of development. Smith begins with ‘hunting societies’ that, via the introduction of animal domestication, advanced into the ‘age of shepherds’. This, in turn, laid the groundwork for agricultural societies—and these societies, by generating a high degree of independence for various economic actors and a compounding surplus of goods, tend inexorably towards the epoch of commerce. Smith’s theory is a stadialism, in which society and culture pass through a series of fixed stages. If Meghnad Desai is correct, Marx’s own writings bore the imprint of this thread running through the Scottish Enlightenment: from Smith’s four stages of hunting, shepherd, agricultural and commercial societies to Marx’s fivefold progression through primitive communism, slave societies, feudal societies, capitalism and socialism.

It has often been remarked that Marx abandoned stadialism towards the end of his life, exemplified by his turn to anthropological studies and the revolutionary questions surrounding the Russian agricultural commune. This thesis has been laid to waste, however, by Raya Dunayevskaya (in Rosa Luxemburg, Women’s Liberation, and Marx’s Theory of Revolution) and Kevin Anderson (in Marx at the Margins: On Nationalism, Ethnicity, and Non-Western Societies), both of whom demonstrate quite clearly that while Marx’s early writings did indeed contain elements of stadialism, this progressively fell away in the period between the period that birthed Communist Manifesto and the early prepatory work on what would become Capital—in other words, decades prior to the anthropological turn, which appears here as the summit of this long-burning theoretical development.

This is further indicative of Marx’s complex and oppositional stance towards the very ideology of progress, at least in the presentation of a smooth, linear movement that dictates historical development. Such a movement ultimately cashes itself out in an positivistic understanding of science; consider, for example, Auguste Comte, who under the influence of Henri Saint-Simon (whose followers, the Saint-Simonians, were among the utopian socialists attacked by Marx and Engels) and Anne Roberts Jacques Turgot (a French physiocrat whose ideas freely circulated with those gesticulating in the Scottish Enlightenment, and who shared with Smith the four-stepped model of history) developed a stadialist law of scientific development. “The Law of Progress”, as he described it, holds that human intellectual development is the motor of historical development, which unfolds through the evolution of science. Each science passes through three stages: a theological stage, in which the laws governing nature are attributed to the divine; the metaphysical stage, which replaces divinity with the philosophical articulation of abstract essences, and the positive stage, in which science itself unmoors philosophy through the proper explications of natural laws as they are in themselves. The positivist approach would not only help lay the ideological justifications for the technocratic threading running through progressivist managerialism to “End of Ideology” liberalism to “End of History” neoliberalism, but also influenced theorists of accelerating change like Henry Adams, who clearly aligned the universal triumph of positivism with the apex moment of transhistorically-occurring exponentiating techno-scientific development.

Detailing the full Marxist critique of positivism is far beyond the scope of this present set of scribblings, so it is suffice to say while Marx did indeed share certain commonalities with the nascent perspective, his position on science and technology emphasized their relation to the wider social ensemble in which they were developed. In this schema, science often lagged behind technological development that in turn produced it, while also bearing the mark of that social ensemble. Consider his comments on Descartes in a footnote to chapter 15 of Capital Volume 1, that by “defining animals as mere machines, [Descates] saw with eyes of the manufacturing period”, or the famous description of Darwin as having reflected the attitudes of British political economists in his study of the natural sciences. And yet, at the same time, there is a side of technology that unfixes these assumptions (without, however, falling into positivism) as indicated in another footnote to Capital Volume 1, chapter 15:

Technology discloses man’s mode of dealing with Nature, the process of production by which he sustains his life, and thereby also lays bare the mode of formation of his social relations, and of the mental conceptions that flow from them. Every history of religion, even, that fails to take account of this material basis, is uncritical. It is, in reality, much easier to discover by analysis the earthly core of the misty creations of religion, than, conversely, it is, to develop from the actual relations of life the corresponding celestialised forms of those relations. The latter method is the only materialistic, and therefore the only scientific one. The weak points in the abstract materialism of natural science, a materialism that excludes history and its process, are at once evident from the abstract and ideological conceptions of its spokesmen, whenever they venture beyond the bounds of their own speciality.

There is thus something of a notion of progress at work here, but it no longer resembles the organic and linear progression messily sketched above—a natural compliment of Marx’s own break with the stadialist account of history that the ideology of progress is wedded to. This would seem to shake the latter theorists of accelerating change at their very core, precisely by injecting contingency and a decidedly non-linear understanding of progress into their baseline assumptions, which ultimately depend on deterministic accounts of history. It is interesting to find, then, that Marx himself discovers within the movement of capitalist development a cascading accelerative change in the technical side of production, which he interprets precisely through the frame of exponential or geometrical growth. This sense of geometric change doesn’t conform precisely to the those of later theorists. It complicates the picture, denying the smoothness of the upward-curving trendline—a corrective that is apt and immediately relevant in the current time, when techno-scientific explosions and singularitarian moments have failed to materialized and the specter that haunts the world is not one of unlimited progress, but a profound and seemingly-unending stagnation.

Explosion and Crisis

Marx only makes a scattered handful of references to ‘geometrical progression’ in his work, with the bulk of these to be found in the Grundrisse and Capital Volume 3. There are three points in which he takes up the language: in his critique of Malthus, in the explication of the tendency of the rate of profit to fall, and in his discussion of interest-bearing capital. In the separate discussions around Malthus and interest-bearing capital, his comments with regards to geometrical trends is negative, while in the context of the rate of profit and its tendency to fall, he affirms an account of exponential change—albeit with conditions. I’m going to avoid the critique of Malthus (best leave this to future blog posts!) and relegate the discussion around interest-bearing capital to a follow-up post to this one. This leaves the relationship between geometrical change and the rate of profit to be drawn out in full here.

First, a few words about the rate of profit and its fall. Marx was not the first to have recognized the tendency for the rate of profit to fall, with important precursors to his work having been identified by Adam Smith and David Ricardo. As Philip Mirowski describes, “[t]he classical long-period conception of the rate of profit was a quantum which was a center of gravity towards which subsets of the economy were constantly moving”. In Ricardo’s reading of Smith, the possibility for the rate of profit to fall emerged from increased competition. Simply put, the greater the competitive pressures of the market, the more the amount of profit capable of being realized on the basis of a given commodity decreased downwards, tending towards the very cost that was required to produce this commodity. It’s worth pointing out that Ricardo’s reading of Smith has been contested; in an illuminating essay, Francisco Verdera has suggested that Smith’s understanding of the falling rate of profit was a more direct precursor of Marx’s own, which emphasizes the centrality of developments in productivity.

At any rate, Marx accepted Ricardo’s reading of Smith, though he categorically rejected Ricardo’s own suggestion, against Smith, that increases in wages drove down the rate of profit. In making this proposition, Ricardo made the tendency of the rate of profit something that is ultimately contingent and bound to employee/employer relations, while Marx understood the tendency as one of the inner laws of motion governing capitalism. Similarly, Marx utilized a distinction between capital as such or capital in general and competition, which corresponded respectively to the production of surplus value (surplus value being, of course, the ultimate source of profit) and the distribution of surplus value, in which surplus value was distributed across the various branches of industry in accordance to the movement of the market (I’ve written a little bit on this distinction elsewhere). Because capital in general took primacy over competition—in other words, the sphere of production, as opposed to the sphere of circulation, as the source of capitalist determination—Smith’s market-based theory (or Ricardo’s reading of Smith’s theory that Marx took up) of the tendency of the rate of profit to fall likewise could not hold.

Marx’s most mature version of the theory, which is found imbedded implicitly in the Grundrisse but only made explicit, in its full terminological might, in the three volumes of Capital, revolves around what he calls the organic composition of capital. The organic composition of capital is the ratio of constant capital to variable capital, with constant capital marking the value of machinery, raw materials, and other non-human inputs into the production process, while variable capital concerns the investments in wagesThese are the requirements for the production of commodities, which are then sold on the market; for the capitalist, the goal is recuperate these investment outlays (the ‘recovery’ of constant and variable capital), plus an excess above them—surplus value, realized as profit. The rate of profit, then, is the ratio of profit—at the level of the totality of the capitalist system—to the total capital. Expressed as a formula, this p’=s/(c+v), where p’ is the rate of profit, s is surplus value, c is constant capital and v is variable capital.

At this level, this seems all very straightforward. The problem arises, however, when we consider the ultimate origins of surplus value. Surplus value may be realized via competition in the sphere of circulation, but it is produced in the sphere of production. The English rendering is a little obsfucating in this regard: surplus value is translated from the German word mehrwert, meaning “value-added”. For Marx, surplus value arises in the first instance from the excess above their necessary-labor time, which is to say the actual value of their labor. The amount of this excess is, in turn, a question of the level of productivity that governs the dynamics of the industrial process, which brings Marx to the tendency of the organic composition to rise. Over time, capital must ever-increase the level of productivity, which leads to a higher rate of investment in constant capital over variable capital. A corresponding increase in the excess beyond necessary-labor time occurs—a situation in which the number of commodities produced climbs ever higher, though each commodity reflects less value. Extrapolated across the totality of capitalism, the falling amounts of value translates into a falling rate of profit, which is easily obscured by, on the one hand, a growing mass of profits held by certain capitals, and on the other by a generalized condition of overproduction. Capital thus simultaneously puts into motion an upswing of efficiency and productivity and a contradictory fault-line that courses through the whole of the system, in which this upswing clashes with the very foundation of the system. Marx’s enthusiasm for this discovery radiates through the following passage, found in the Grundrisse: 

This is in every respect the most important law of modern political economy, and the most essential for understanding the most difficult relations. It is the most important law from the historical standpoint. It is a law which, despite its simplicity, has never before been grasped and, even less, consciously articulated.

It is precisely at this point that Marx brings the language of geometrical progression into play, as a theory not of external techno-economic innovation, but as the internal trans-innovation tendency to increase the productivity of labor through predominantly technical means:

Every increase in the mass of capital employed can increase the productive force not only at an arithmetical but at a geometrical rate; although it can increase profit at the same time—as increase of productive force—only at a much lower rate. The influence of the increase of capital on the increase of productive force is thus infinitely greater than that of the increase of the productive force on the growth of capital.

In the thought experiment that gives rise to this suggestion, the “mass of capital” alludes to both of what would become known as constant and variable capital, that is, the organic composition. In keeping with general investment trends, both are increasing, though constant capital is increasing at a rate much higher than that of variable capital. Thus we have the possibility of a rising rate of profit, but the rate of productivity itself runs far ahead it. Insights like these are perhaps the source of the suggestion made by Engels, quoted at the outset of this post, that productive power increases at a geometrical or exponential rate, in contrast to the arithmetical rate that the market increases. The wording of course is vague and difficult to quantify (how exactly would market increases be measured arithmetically in a way that can be compared with exponentiating productivity?), but what is telling is the way that it maps across the distinction between the sphere of production and the sphere of circulation: with the former developing at a much higher rate than the latter, we arrive back at this problem bracing capital, the specter of overproduction (and at the limit, the absolute crisis of overproduction).

When we move from the simultaneous-yet-unequal increase of constant and variable capital to the point in which variable capital investments stay stationary over time or begin to fall, the tendency of the rate of profit manifests itself proper. The exponential churn of productivity gives rise to crisis; while Marx never truly offered a comprehensive crisis theory, he remained adamant that the falling rate of profit was an integral component in their realization. In the Grundrisse, Marx begins to form a picture of crises exhibiting a rhythmic character, periodic events that explode the ebb and flow of the rate of profit. Drawing a picture that brings to mind Benjamin’s vision of history as a succession of compounding catastrophes, Marx offers us the following apocalyptic image:

…the highest development of productive power together with the greatest expansion of existing wealth will coincide with depreciation of capital, degradation of the labourer, and a most straitened exhaustion of his vital powers. These contradictions lead to explosions, cataclysms, crises, in which by momentaneous suspension of labour and annihilation of a great portion of capital the latter is violently reduced to the point where it can go on. These contradictions, of course, lead to explosions, crises, in which momentary suspension of all labour and annihilation of a great part of the capital violently lead it back to the point where it is enabled [to go on] fully employing its productive powers without committing suicide. Yet, these regularly recurring catastrophes lead to their repetition on a higher scale, and finally to its violent overthrow.

There’s a common argument that Marx’s early writings, such as the Communist Manifesto, where written under the cloud of a capitalism seeming like it was the verge of imminent collapse. There’s an immediacy to these texts, which were after all written in the context of an economic depression that rocked Europe and served as an accelerator for the class struggle. Later writings like Capital, however, are often seen as having abandoned this position, replacing the atmosphere of turbulence and violence with a more gradualistic, evolutionary understanding of capitalist development. If this schema is accurate, the Grundrisse appears as something as a halfway point: as the quote above clearly illustrates, the sense of capitalism’s catastrophic character and inevitable violent collapse is retained. But something else is emerging alongside this. The catastrophe of economic crisis might be taking on a rhythmic character that is chugging its way towards an ultimate breakdown, but they also serve to forestall its advent by “lead[ing] it [capital] back to the point where it is enabled [to go on] fully employing its productive powers without committing suicide”.

By the time Marx was working on the 1861-63 manuscripts, this picture had become more pronounced. To quote from a section titled “General Law of the Fall in the Rate of Profit”:

The whole of the Ricardian and Malthusian school is a cry of woe over the day of judgement this process would inevitably bring about, since capitalist production is the production of profit, hence loses its stimulus, the soul which animates it, with the fall in this profit. Other economists have brought forward grounds of consolation, which are not less characteristic. But apart from theory there is also the practice, the crises from  superabundance of capital or, what comes to the same, the mad adventures capital enters upon in consequence of the lowering of [the] rate of profit. Hence crises—see Fullarton—acknowledged as a necessary violent means for the cure of the plethora of capital, and the restoration of a sound rate of profit.

This is the mature understanding that would be cemented in place in the three volumes of Capital. The apocalyptic moment, in which capital hits its absolute limit, falls into the background, and what rises to the fore is a something that could neither be described as linear (the straightforward progression of the the rate of profit downwards into crisis) nor cyclical (the momentary lapse in a rate of profit brought back to stability), but something like a spiral: an overarching tendency, punctuated by rises and falls, periods of stability and crisis, that is constantly changing, constantly evolving, constantly compressing itself into higher phases of productivity that are violently assaulted by their hidden implications.

The Historical Mission and Its Discontents 

A recurring motif in Marx’s writings is an emphasis on the joint-stock company acting as  reflection not only of capital’s tendency towards mass-scale exploitation, but of the progressive element, the side that is angled towards a world beyond capital. Take the letter from Marx to Engels, dated April 2nd 1858, where Marx provides the first faint outline of the project that became Capital:

Capital falls into 4 sections. a) Capital en général (This is the substance of the first instalment) b) Competition or the interaction of many capitals. c) Credit, where capital, as against individual capitals, is shown to be a universal element. d) Share capital as the most perfected form (turning into communism) together with all its contradictions.

[for an interesting discussion of Marx’s elaborations on share capital and joint-stock companies, I recommend Judith Dellheim’s paper “‘Joint-Stock Company’ and ‘Share Capital’ as Economic Categories of Critical Political Economy”]

In the Grundrisse, the joint-stock company is connected to the tendency of the rate of profit to fall. Marx quotes the political economist Thomas Hopkins (who offered a version of a falling rate of profit close to the Ricardian interpretation of Smith): “Joint-stock companies, to accomplish great improvements, are the natural offspring of a falling rate of profit. It also induces individuals to fix their capital in the form of buildings and machinery”. Recall that for Marx the falling rate of profit proceeded from rising investments in constant capital as a means to raising the degree of labor’s productivity. From one direction, this capital-intensive nature of this drive towards intensification is carried out by those with the greatest access to investable capital, which thus tends more and more towards large-scale industry. From another direction, the elimination of the ineffectual firms on the terrain of the competitive market also reinforces this drive (this is closer to how Hopkins understood the joint-stock companies as the offspring of the falling rate of profit, as detailed in his 1834 book Great Britain for the Last Forty Years).

In Capital Volume 1, these considerations around joint-stock companies and share-capital are subsumed into the discussion of the tendencies of concentration and centralization of capital, in particular this latter form. As Bukharin put it, centralization of capital is the process of “the joining together of various individual capital units which thus form a new larger unit”—or, in the words of Marx, anticipating later theories of lock-in and increasing returns by centuries: “the attraction of capital by capital”. This attraction “always ends in the ruin of many small capitalists, whose capitals partly pass into the hands of their conquerors, and partly vanish completely”. Taking cue from Hopkins, Marx further argues that

Centralization supplements the work of accumulation by enabling industrial capitalists to extend the scale of their operations. Whether this latter result is the consequence of accumulation or centralization, whether centralization is accomplished by the violent method of annexation—where certain capitals become such preponderant centers of attraction for others that they shatter the individual cohesion of the latter and then draw the seperate fragments to themselves—or whether the fusion of a number of capitals already formed or in process of formation takes places by the smoother process of organizing joint-stock companies—the economic effect remains the same. Everywhere the increased scale of industrial establishments is the starting-pint for a more comprehensive organization of the collective labor of many people, for a broader development of their material motive forces, i.e. for the progressive transformation of isolated processes of production, carried on by customary methods, into socially combined and scientifically arranged processes of production.

From this high level overview of the capitalist totality, Marx plunges us back down again, into the circuitry which loops together these violent clashes and ongoing integration of titantic economic forces with the oscillating changes taking place within the organic composition of capital. He does not mention the geometrical change in productivity here, but he does touch on precisely what ongoing technical transformation as this pace entails: the phenomenon of accelerative change. Reiterating his comments in the Grundrisse that productivity will run ahead of capitalist accumulation, he alludes to “change in the organic composition of capital” and the “productivity of labor” developing at a “quickening rate”, and then to the “accelerated rate” in the decline of the demand for labor relative to the growing magntitudes of total capital. Soaking up capital, flinging labor from itself through mechanization and intensifying the work carried out by what remains, the entire ensemble speeds itself up:

 The intermediate pauses in which accumulation works as a simple extension of production on a given technical basis are shortened. It is not merely that an accelerated accumulation of the total capital, accelerated in a constantly growing progession, is needed to absorb an addition number of workers, or even, on account of the constant metamorphosis of old capital, to keep employed those already performing their functions. This increasing accumulation and centralization also becomes in its turn a source of new changes in the composition of capital, or in other words of an accelerated diminution of the capital’s variable component, as compared with its constant one. This accelerated relative diminution of the variable component, which accompanies the accelerated increase of the total capital and moves more rapidly than this increase, takes the inverse form at the other pole, of an apparently absolute increase in the working population, an increase which always moves more rapidly than that of the variable capital or means of employment. But in fact it is capitalist accumulation itself that constantly produces, and produces indeed in direct relation with its own energy and extent, a relatively redundant working population, i.e. a population which is superfluous to capital’s average requirements for its own valorization, and is therefore a surplus population.

The rate of profit hasn’t been brought into this picture yet, though it moves beneath these interlocking processes. It won’t be until Capital Volume 3, and most specifically the 15th chapter, that the falling rate of profit is integrated into this diagram. In many ways, it reads almost like a direct follow-up to the above passages from Volume 1, plugged together via some imperceptible hyperlink:

A fall in the rate of profit and accelerated accumulation are different expressions of the same process only in so far as both reflect the development of productiveness. Accumulation, in turn, hastens the fall of the rate of profit, inasmuch as it implies concentration of labour on a large scale, and thus a higher composition of capital. On the other hand, a fall in the rate of profit again hastens the concentration of capital and its centralisation through expropriation of minor capitalists, the few direct producers who still have anything left to be expropriated. This accelerates accumulation with regard to mass, although the rate of accumulation falls with the rate of profit.

On the other hand, the rate of self-expansion of the total capital, or the rate of profit, being the goad of capitalist production (just as self-expansion of capital is its only purpose), its fall checks the formation of new independent capitals and thus appears as a threat to the development of the capitalist production process. It breeds over-production, speculation, crises, and surplus-capital alongside surplus-population.

The falling rate of profit (tending towards geometric progression), the acceleration of capital accumulation, the annihilation of small capitals by a great centralizing motion, progressive mechanization driving up the productivity of labor, and the tendency towards overproduction—each of these constitute chaotic iterations of a singular processes, the multifaceted curve of capitalist development. Underneath it lurks the great contradiction, the conflict between the productive maximization of surplus value and downwards pressure on value itself. For this reason, Marx writes that the “capitalist mode of production involves a tendency towards absolute development of the productive forces, regardless of the value and surplus-value it contains”—obscured beneath the gains of productivity, the deluge of commodities and the swelling mass of profit, the industrial-commercial system swings out of joint with itself.

Marx goes as far to describe the progressive side of these development—the development of productive forces, the increased centrality of science to production, and the emergence potentiality, left un-actualized, of time liberated from labor—the “historical mission” of capital. And yet, as we’ve seen, none of this proceeds in a linear fashion. The revolutionary, progressive side crashes into the regressive, as the fall of the rate of profit ultimately produces the barrier preventing the “unconditional development of the social productivity of labour”. Capital becomes the site of “a continual conflict between this its historical task and its own corresponding relations of social production”; this is not only the locus of the class struggle, but the point in which the winds of crisis begin to blow. Marx:

Alongside the development of productivity there develops a higher composition of capital, i.e., the relative decrease of the ratio of variable to constant capital.

These different influences may at one time operate predominantly side by side in space, and at another succeed each other in time. From time to time the conflict of antagonistic agencies finds vent in crises. The crises are always but momentary and forcible solutions of the existing contradictions. They are violent eruptions which for a time restore the disturbed equilibrium.


The periodical depreciation of existing capital — one of the means immanent in capitalist production to check the fall of the rate of profit and hasten accumulation of capital-value through formation of new capital — disturbs the given conditions, within which the process of circulation and reproduction of capital takes place, and is therefore accompanied by sudden stoppages and crises in the production process.


Capitalist production seeks continually to overcome these immanent barriers, but overcomes them only by means which again place these barriers in its way and on a more formidable scale.

The real barrier of capitalist production is capital itself.

The crisis serves as the means to restore the rate of profit, through the simultaneous depreciation of existing capital and the liquidation of small capitalists. Investment capital and resources are freed to expand production at a higher level, though this inexorably tends back to the falling rate of profit and, again, crisis. It appears that for Marx this too was an accelerative process, with the periods between crisis becoming shorter and and their intensity sharper—though the ambiguities and multitude of forces and countervailing forces (that is, forces that are capable of slowing or temporarily reversing the falling rate of profit, such as the opening of foreign markets, the cheapening of constant capital, etc.) triggered a cascade of debates later known as the ‘revionist controversy’. At the heart of these debates was the question as to whether or not these forces implied the collapse of capital, with the fall in the rate of profit paving way for generalized stagnation, or if the continual restoration of the rate of profit, coupled to ongoing advances in productive efficiency, was meant that capitalism wasn’t heading towards collapse, and that socialism appeared through other means.

At any rate, the problem of geometric development appears clear. Unlike early philosophers of progress, and the later theorists of accelerative change, the movement is anything but linear, smooth, and straightforward. Exponential growth is denied its perfect curve, and instead appears as proceeding in starts and fits, punctuated by catastrophe and intrinsic counter-revolution. Thus the following passage from Capital Volume 3, where this is brought into sharp relief:

The law of increased productivity of labour is not, therefore, absolutely valid for capital. So far as capital is concerned, productiveness does not increase through a saving in living labour in general, but only through a saving in the paid portion of living labour, as compared to labour expended in the past, as we have already indicated in passing in Book I (Kap. XI II, 2, 5. 409/398). [English edition: Ch. XV, 2. — Ed.] Here the capitalist mode of production is beset with another contradiction. Its historical mission is unconstrained development in geometrical progression of the productivity of human labour. It goes back on its mission whenever, as here, it checks the development of productivity. It thus demonstrates again that it is becoming senile and that it is more and more outlived.

3 thoughts on “Marx on Geometric Change (1. The Rate of Profit)

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s