On the Law of the Tendency of the Rate of Profit tofall, and its discontents

drustvenaanaliza.blogspot.be /2015/03/on-law-of-tendency-of-rate-of-profit-to.html

Sašo Furlan

Introduction

Amongst the major classical political economists of the late 18th and early 19th century, the notion that theaverage rate of profit has a tendency to decline on the long term was widely accepted and considered as anevident fact. Bourgeois economists, such as Adam Smith, David Ricardo and John Stuart Mill, treated it as anempirically confirmed and therefore indisputable law that is of utmost importance for the political economy. Butalthough they were in agreement when it came to the simple task of asserting the existence of the law, theydeparted when it came to a much harder task of theoretically grasping and articulating this law. When theystruggled to explain the structural causes of the decline in the average rate of profit they offered variousdiverging and dubious explanations that were far from evident and clear. When Marx first dealt with the law ofthe tendency of the rate of profit to fall (LTRPF) in his 1857-1858 Manuscripts (Grundrisse), he could thus stressthe following: “This is in every respect the most important law of modern political economy, and the mostessential for understanding the most difficult relations. (…) It is a law which, despite its simplicity, has neverbefore been grasped and, even less, consciously articulated« (Marx 1973, p. 675).

In the Grundrisse, and the third Volume of Capital, Marx developed his own, rather sophisticated, demonstrationof the LTRPF. And ever since his account was laid out it remained a highly controversial and continuouslydisputed subject, especially among Marxist scholars. Some of them have praised Marx’s account of “the law”,considering it as a final and irrefutable solution of a riddle that occupied political economists for more than acentury, and used it as a foundation of Marx’s theory of crisis. Yet others have criticized it and denounced it asirrelevant in regards to his theory of crisis. It was the supposed intertwined connection between the LTRPF andMarx’s theory of crisis that made the discussions around this law so polemical and contentious. Since theproponents of LTRPF saw it as the ultimate argument for why the inherent systemic dynamics of growth incapitalism undermines its very conditions, and consequentially leads to periodic crises that necessitate therevolutionary overthrow of capitalism, the opponents of the law were often viewed as some sort of heretics orrevisionists whose denouncement of the law also discredits its profound revolutionary political implications.Anyhow, after more than a century of heated debates amongst Marxist scholars, there is still no generalagreement about the validity of Marx’s proof of the LTRPF, as well as no consensus on the question of theimplications of this law for a theory of crisis and political strategy. Hence, it seems as if the tradition of thecontroversies about the LTRPF still weighs like a nightmare on the brains of contemporary Marxists.

The preparatory chapter, which is dedicated to a preliminary clarification of the quantitative aspect of thecategories, by means of which the LTFRP can be grasped, will be followed by a chapter dedicated to anillustration of Marx’s account of LTRPF in the third volume of Capital. The proceeding chapters will depict themost far reaching controversies over LTFRP amongst Marxist and other economic scholars in the 20th and 21stcentury. Special attention will be dedicated to Michael Heinrich’s critique of Marx’s elaboration of the LTRPF.The political implications of the LTFRP and the disputes revolving around it will be dealt with in the last chapter.

Preliminary clarifications

Before we get to the exposition of the LTRPF we will have to make a detour, since a few preliminaryclarifications are needed. We will start with the quantitative depiction of the value of the commodity (C), which isproduced in the capitalist mode of production (see Marx 1999, p. 16). Marx outlines it in the following formula:

C = c + v + s

Constant capital (c) is the portion of value laid out in means of production, such as machines and raw materialsthat are used in the capitalist process of production, whereas variable capital (v) stands for the portion of valuethat is used to pay workers’ wages, and therefore equals the value of labour power. These two components ofcapital play qualitatively different roles in the determination of the value of the commodity. Namely, the means ofproduction do not create any new value in the process of production, but only transfer their value or a portion oftheir value to the final product. Labour power, however, does not transfer its value to the final product, but rathercreates new value in the process of production. Particularly, labour power creates a new amount of value whichis needed to cover the costs of its reproduction, and an additional amount of value which is called surplus value(see Marx 2010, p.139-46). So, if the value of the means of production constitutes one portion of value of thecommodity by means of the transfer of value, which equals c, labour power constitutes the other portion of valueof the commodity by means of the creation of new value, which equals v + s. Workers therefore produce thewhole value added, but only receive a part of this newly created value in wages. This implies that during theprocess of production workers are exploited, since they are only paid with wages that equal the value ofvariable capital, even though they also produce surplus value.

In view of the fact that, in the capitalist mode of production, only labour power or living labour produces value aswell as surplus value, the valorisation of capital rests solely on the component of variable capital. The rate of thevalorisation of capital is thus a certain ratio of surplus value to variable capital, which is called the rate of surplusvalue (see Marx 2010, p. 147-151). It can be formulated as follows:

r(s) = s/v

The concept of the rate of surplus value is of great relevance from the standpoint of theory, since it, amongother things, designates the rate of exploitation. Yet from the standpoint of the individual capitalist it is practicallyirrelevant. A capitalist does not perceive any difference between constant and variable capital as far as their rolein the creation of value is concerned. He is rather interested in the yield on total capital advanced. At the start ofthe production process, the capitalist is mostly interested in the sum of money that designates how much thecommodities which are needed for production will cost him. The crucial quantity for the individual capitalist istherefore the cost price (see Marx 1999, p. 16-17), which is formulated by Marx as:

Cp = c + v

But when the commodities are produced and about to be sold, he is mostly interested in the sum of moneyagainst which these commodities will be sold. He is thus interested in the surplus of money over the initial costprice, i.e. the difference between the sale price of commodities and the cost price. This difference, which is ofutmost importance for the capitalist, is called profit.

Profit is a form of realization of surplus value; it is surplus value that is realized as the yield on total capitaladvanced (c + v). But note that as soon as surplus value is realized in the form of profit, its own source becomesconcealed. We have stressed that surplus value originates in the exploitation of labour power in the process ofproduction. However, when profit is realized, this fact becomes veiled. The return on capital is considered, bythe capitalist, as the yield on the whole capital advanced , i.e. the yield on c and v. This is why it seems as ifsurplus value does not originate from a specific part of capital, from variable capital, but from constant andvariable capital equally. The actual conditions of the creation of surplus value are thus mystified in its realizationin the form of profit (see Heinrich 2012, p. 143-144). From the point of view of the capitalist, the rate ofvalorisation of capital is not the ratio between surplus value and variable capital but the ratio between surplusvalue and the whole capital advanced. This rate of valorisation is outlined in the formula of the rate of profit(Marx 1999, p. 27):

r(p) = s / (v + c)

Every time capital is advanced, the capitalist is, of course, interested in the highest possible rate of profit. Thebasic way in which the rate of profit can – under otherwise constant conditions – be raised, is by an increase inthe rate of surplus value. This can be done in two different ways, either by the increase in the production ofabsolute surplus value or by the increase in the production of relative surplus value . The increase of theproduction of absolute surplus value is achieved by lengthening surplus labour time (i.e. the time in whichworkers produce surplus value), which is achieved by the method of lengthening the workday. On the otherhand, the increase of relative surplus value is achieved by an increase in the productivity of labour. The most

important mechanism for increasing the productivity of labour in the capitalist mode of production is the use of(heavy) machinery. When the productivity of labour, in the branches that produce the means of subsistence or inthe branches that produce inputs for those branches, increases due to introduction of labour saving technology,the value of the means of subsistence decreases. Since the value of labour power is determined by the value ofthe means of subsistence, by the value necessary for the reproduction of labour power, the value of labourpower also decreases. Socially necessary labour time for the production of commodities therefore falls, andalthough the workday does not increase, surplus labour time relative to necessary labour time increases (seeMarx 2010, p. 354-361). It has to be stressed that in the context of the capitalist mode of production, theproduction of surplus value in general or of relative surplus value in particular, is for an individual capitalist, anecessity. Should a certain capitalist lack far behind in productivity increases relative to his competitors, hewould soon lose his market share, and in turn go out of business.

We have shown how an increase in the rate of surplus value can - under otherwise constant conditions - affectthe rate of profit. The rate of profit, however, does not fluctuate only due to changes in the rate of surplus value.Capitals which produce with the same rate of surplus value can have different rates of profit. This is becausedifferent capitals can have different compositions of capital. According to Marx the composition of capital shouldbe understood in a two-fold sense. On the side of value it is determined by the proportion in which it is dividedinto constant capital and variable capital, whereas on the side of the material it is determined by the relationbetween the mass of the means of production employed and the mass of labour necessary to employ them(Marx 1999, p. 428). The composition of capital on the side of value is value composition of capital ; it is a ratioof constant to variable capital in value terms:

Vcc = c / v

The composition of capital on the side of material is the ratio of the mass of means of production to the mass oflabour employed. This ratio is the technical composition of capital . Value composition of capital and technicalcomposition of capital are in a certain correlation. Marx expresses this correlation with the concept of organiccomposition of capital, which is the value composition insofar as it is determined with the technical compositionof capital. Organic composition of capital can therefore be mathematically portrayed in the same way as valuecomposition of capital:

Occ = c / v

Yet, the organic composition of capital only varies as a consequence of changes in the technical composition ofcapital, but it does not reflect changes in value of variable and constant capital that might occur due to otherreasons.

We have said that different capitals with equal rates of surplus value can have different rates of profit.Particularly, capital with a low organic composition of capital will realise a higher rate of profit then capital with ahigh organic composition of capital. This can be illustrated by a numerical example:

I) Occ = c/v = 40/60 ; r(s) = s/v = 100% ; r(p) = s/(c+v) = 60/(40+60) = 60%

II) Occ = c/v = 60/40 ; r (s) = s/v = 100% ; r(p) = s/(c+v) = 40/(40+60) = 40% We can see from the equations that – in otherwise constant conditions – the higher the organic composition ofcapital, the lower the rate of profit, and vice versa.

Following this conclusion, we are immediately faced with a problem, because, in reality, capitalists tend to realizea certain unified rate of return on their capital advanced, which seems to be totally independent of organiccompositions of their capitals. Marx explains why this is so (see Marx 1999, p. 118-133). Following the thesisthat the sole interest of an individual capitalist is the maximization of profit, the capitalist recognizes that, if somebranches offer lower rates of profit than others, then he will pull out his capital from these branches and invest itin branches with higher rates of profit. The rates of profit in different branches will thus tend to converge,because capital will flee from the branches with low rates of profit to branches with high rates of profit.Equalization of the various rates of profit will, according to Marx, at least in the context of free movement ofcapital, take place automatically by the mechanism of competition. Namely, if capital is withdrawn from thebranches with low rates of profit, the supply of commodities in these branches will shrink. Consequentially, theprices of commodities will rise, and, in turn, cause the rates of profit in these branches to rise again. On theother hand, if the branches with high rates of profit are witnessing an influx of capital, this will cause the supply

of the commodities in these branches to rise. Their prices will therefore fall and automatically cause the rate ofprofit to also fall. That is why the mechanism of competition will produce a tendency for the rates of profit inbranches with different organic compositions of capital to equalize. Rates of profit of different capitals will thusequalize into a general or average rate of profit .

But, this same mechanism will, in the eyes of an individual capitalist, also additionally conceal the fact thatsurplus value originates from labour, since it will solidify the illusion that surplus value is but a rate of return onthe whole capital advanced. Under the conditions of equalizing rates of profit, each individual capitalist receivesan average rate of profit no matter how big the ratio of variable to constant capital in his capital advanced(Heinrich 2012, p. 147). Average profit can be mathematically depicted as:

p(a) = (c + v) x r(pa) With the quantity of average profit at hand we can also calculate what Marx calls the price of production, whichis a sum of cost price and average profit:

p(p) = c + v + p(a)

Note that the price of production is basically a sale price of a commodity by means of which a capitalist realisesan average rate of profit.

We stressed that production of relative surplus value, which is achieved by increases in the productivity oflabour by means of the introduction of labour saving technology, is, for an individual capitalist, a necessity.However, the capitalists do not increase productivity by the introduction of machines for its own sake, but ratherfor the sake of extra-profits. Extra-profit is defined as profit above the average profit (Marx 1999, p. 33). Anindividual capitalist can realize an extra profit if he reduces his costs of production below the social average.Hence, the capitalist will introduce machinery only if a boost in productivity will lower his cost price and henceraise his rate of profit. We can illustrate this with a simple numerical example. Suppose that in a branch thatproduces cars, all commodities, i.e. cars of all companies are sold at the uniform price of production, which isdenoted as: p(p) = c + v + p(a) = 100 + 100 + 50 = 250

Note that the average profit equals 50. Now let’s assume that in one of the car companies a new labour savingtechnology is introduced, and that, by means of this technology, labour productivity increases substantially.Should the productivity increase for 100%, the time that is needed for the production of a car would be cut inhalf. This means that the capitalist would now be able to produce the same car with 50% less variable capital. Ifwe assume that c would increase for 10 units his new cost price would be:

c(p) = c + v = 110 + 50 = 160

We can see that the cost price for the car selling capitalist has shrunk for 40 units: from 200 to 160. But we havesaid that all commodities in the branch are sold according to the uniform price of production. Should ourcapitalist sell the car for the cost of production, his new profit would be:

p = p(p) – c(p) = 250 – 160 = 90

The capitalist will thus realize an average profit of 50 and an additional extra-profit of 40. The labour savinginnovation and the corresponding productivity boost in the car factory in question will of course lead to theincrease of the output. However, this increase of the output, i.e. the magnitude of cars produced, is worthnothing for the capitalist, if it is not accompanied by a corresponding increase in the demand for his cars. Theusual way to take care of this problem, for the individual capitalist, is to lower the prices of his commodities. It isevident that the discussed capitalist can sell the cars below the price of production by which the cars are sold byhis competitors, and still realize an extra-profit. For example, he can sell the cars at the price of 240, and stillrealize a substantial amount of extra profit.

p = p(n) – c(p) = 240 – 160 = 80

In these conditions the capitalist will realize an average profit of 50 and an extra profit of 30.

However, the capitalist’s decision to lower the prices of commodities is not without consequences for his fellowcapitalist competitors. Insofar as their cars become relatively dearer in comparison with the cars of the“innovative capitalist”, they start to lose their market share. They will thus be structurally compelled by the ironlaws of competition to follow the paths of the innovative capitalist and increase the productivity of labour in orderto bring down their cost price. In this fashion capitalist competition tends to generalize the productivity boostsand cost reductions. Conceding that the productivity hike is generalized throughout the whole branch, the extra-profit of the aforementioned capitalist disappears (see Marx 2010, p. 218-221; Heinrich 2012, p. 106-108). In asmuch as the cost price now sinks for all the capitalists, the advantage for the capitalist that initiated the increasein productivity ceases to exist.

Marx’s exposition of LTRPF

In the third volume of Capital, Marx tried to illustrate that the average rate of profit has a tendency to decline,which originates in the peculiar nature of the capitalist mode of production itself1 . Marx did not argue that therate of profit in capitalism is subjected to a certain straightforward decline no matter the circumstances. Marxwas of course aware that a rising average rate of profit may very well be the case. He considered variouscountervailing factors that can either postpone the fall or result in a temporary rise in the rate of profit.Particularly, in Capital volume 3 Marx discussed several so called countertendencies of the LTRPF , such asreduction of wages below the value of labour power, cheapening of the factors of constant capital by variousmeans, reduction of the costs of industrial inputs and consumer goods by means of foreign trade, the increasein share capital, which devolves part of the costs for the usage of capital to others, etc. (see Marx 1999, p. 159-164) Marx did not at any point deny that these countertendencies may very well result in a rise of the rate ofprofit. However, he did argue that these countertendencies are of temporary nature. From the standpoint of theinherent dynamics of the capitalist mode of production they are but contingencies. Hence, in his exposition ofthe LTRPF Marx’s intention was to prove that independent of such contingent factors of temporary nature, therate of profit has a tendency to fall due to the inherent dynamics of the capitalist mode of production.

This peculiar dynamics of the capitalist mode of production rests on the production of relative surplus value. Wehave shown that the production of relative surplus value depends on technical innovation, in other words, on theadoption of labour saving technologies. An obvious result of constant adoption of new and ever more efficientmeans of production is the displacement of human labour from the process of production. Herein lays the cruxof Marx’s argument. Since profit crucially depends on the production of surplus value, which rests on surpluslabour, performed solely by living labour in the process of production, the displacement of living labour withmachines will – in otherwise constant conditions – result in a fall in the rate of profit. It is obvious that increasesin productivity, by means of displacing living labour by machines, necessitates a rise in the organic compositionof capital. Now let’s see how the rise in organic composition of capital affects the rate of profit. The generalformula of the rate of profit is:

r(p) = s / (c + v)

If we divide the numerator and the denominator with v, we get the following formula:

r(p) = (s/v) / (c/v + 1)

Note that the denominator of the equation now expresses the organic composition of capital, and the numeratorindicates the rate of surplus value. Following this equation it is easy to show that the rise in the organiccomposition of capital, a result of the adoption of labour saving technologies, will – in otherwise constantconditions – necessitate a fall of the rate of profit.

I) r(p) = 2 / (1 + 1) = 1 = 100%

II) r(p) = 2/ (3 + 1) = 0,5 = 50%

We can see that the rise in the organic composition of capital from 100% (1) to 300% (3) results in a fall in therate of profit from 100% to 50%.

Nonetheless, Marx was well aware that this is not enough to prove the LTRPF. We mentioned that theproduction of relative surplus value is achieved by decreasing the value of the means of production whichtranslates in to sinking value of labour power which is equal to the value of variable capital. This means that the

factors that necessitate a rise in the organic composition of capital also necessitate a rise in the rate of surplusvalue. Since the rate of surplus value is depicted as s/v, it is evident that the fall in the value of labour power (v)will result in a rise of the rate of surplus value. Taking this effect into account, the proof for the fall in the rate ofprofit becomes much more difficult, because we can now easily imagine how the adoption of labour savingtechnologies results ether in a fall or in a rise of the rate of profit. A simple numerical example should suffice:

I) r(p) = 2/ (1 + 1) = 1 = 100%

II) r(p) = 3/(3 +1) = 0,75 = 75%

III) r(p) = 5/ (3 + 1) = 1,25 = 125%

We can see that the rate of profit can either fall, as is the case in the second equation where the rate of surplusvalue increases from 200% (2) to 300% (3), or rise, as is the case in the third equation where the rate of surplusvalue increases from 200% (2) to 500% (5) . Thus and thus, it becomes clear that the LTRPF cannot be simplydeduced from the fact of the rising organic composition of capital. For the proof to be logically valid, anothercondition has to be fulfilled. It has to be proved that the rise of the organic composition of capital will on the longterm compensate for the rise in the rate of surplus value. Namely, it has to be shown that the organiccomposition of capital will tend to rise faster or to a higher degree then the rate of surplus value (Heinrich 2012,p. 151-152). Marx provided one argument for why this would be the case. He argued that, as opposed to the riseof the organic composition of capital, the level of the increase in the rate of surplus value is limited, since the risein the mass of surplus value has definite limits that cannot be surpassed (Marx 1999, p. 272). This argumentcan again be depicted with a numerical example. We presuppose that 100 workers are employed in a certainfactory. Each of them performs 5 hours of daily surplus labour, which produces surplus value. The sum of dailyhours of surplus labour performed is thus:

h(s) = 100 x 5 = 500h

Let’s now assume that, due to the adoption of labour saving technology, the amount of living labour employedreduces substantially: from 100 to 10. Consequentially, it becomes evident that, no matter what, 10 workers arenot able to produce as much surplus labour (500h) as the aforementioned 100 workers, even if we assume thatall of the 10 workers are performing 24 hours of surplus labour a day:

h(s) = 10 x 24 = 240h

It becomes clear that the rise in the mass of surplus value has unsurpassable limits. If this is so, then the rise inthe rate of surplus value also has definite limits, because sooner or later, the displacement of workers will leadto a fall of the numerator in the equation of the rate of surplus value (s/v). According to Marx, the rise in theorganic composition of capital, on the long term, cannot be compensated by a rise in the rate of surplus value toa higher degree. Thus, on the long term, the rate of profit will – under otherwise constant conditions –necessarily fall. On these grounds Marx concluded:

“The progressive tendency of the general rate of profit to fall is, therefore, just an expositionpeculiar to the capitalist mode of production of the progressive development of the socialproductivity of labour. This does not mean to say that the rate of profit may not fall temporarily forother reasons. But proceeding from the nature of the capitalist mode of production, it is therebyproved the logical necessity that in its development the general average rate of surplus-valuemust express itself in a falling general rate of profit. Since the mass of the employed living labouris continually on the decline as compared to the mass of materialised labour set in motion by it,i.e., to the productively consumed means of production, it follows that the portion of living labour,unpaid and congealed in surplus-value, must also be continually on the decrease compared tothe amount of value represented by the invested total capital. Since the ratio of the mass ofsurplus-value to the value of the invested total capital forms the rate of profit, this rate mustconstantly fall.” (Marx 2010, p. 146)

A brief history of the LTRPF controversy

We have mentioned that as soon as Marx’s account of the LTRPF was put forth, it became a highly controversialand exceedingly disputed topic. We will depict the most important controversies around Marx’s LTRPF in the20th century2. The first decidedly influential critique of the LTRPF was elaborated by Ladislav Bortkiewitz in his1907 article Value and Price in the Marxian System . Bortkiewitz argued that Marx’s pivotal flaw lies in hisconflation of price calculations with value calculations when considering the dynamics of technical innovationthat supposedly lead to an inevitable fall in the rate of profit (Bortkiewitz 1952, p. 12). According to Bortkiewitz,Marx wrongly alleged that the capitalists adopted new techniques of production in order to increase themagnitude of products, which in turn lowers the values of wage goods (means of consumption) and capitalgoods (means of production). Yet, Bortkiewitz’s argument was that capitalists only introduce new techniques ofproduction if they will contribute to lowering the costs of production denominated in prices, and therefore resultin the rise of the rate of profit, which is also denominated in prices. Following these assumptions, Bortkiewitzused a linear model of prices of production to illustrate that, if labour saving technologies are adopted, a newrate of profit is established, which could not be lower than the rate of profit before technical change (Cullenberg1992, p. 46-47). Bortkiewitz concluded that the inherent dynamics of capitalist production, based on technicalchange, does not result in the decline in the rate of profit. In several aspects Bortkiewitz anticipated many othercritiques of Marx’s that appeared more than fifty years later, amongst which that of Nobuo Okishio was the mostfar reaching.

Another important critique of Marx’s account of the LTRPF in the early 20th century came from Mikhail Tugan-Baranowsky. If Bortkiewitz was to be remembered for his arguments against Marx’s LTRPF, Baranowsky was tobe recalled for his influential rejection of the LTRPF as a basis for a theory of crisis. Baranowsky was a memberof the so called school of “legal Marxists” in Russia. This group criticized the “underconsumptionist” theories ofcrises, which held that capitalist crises originate from the lack of purchasing power of the working class, as wellas the theories that, following the LTRPF, argued that crises were a result of the contradictions inherent in thedynamics of capitalist production. In contrast to these theories Baranowsky reasoned that crises are a result ofthe anarchic nature of competition. Baranowsky’s argument was that crises in capitalism occur as a result of thelack of coordination between capitalists, which constantly cause disproportionalities between different branchesof production (Millios and Soutiropoluos, p. 6-10). Such an account, however, implies that, crises, resulting fromthe chaotic character of competition, can be prevented by state interventions, which would effectively inhibit thedisproportionalities between different branches of production. In future debates on the LTRPF Baranowsky’saccount was vastly controversial, since it implied that the crisis ridden dynamics of capitalism can be avoidedwith reformist strategies of state interventionism.

For some of the Marxian proponents of the LTRPF, accounts such as Baranowsky’s were often fiercelycontested precisely due to their political implications. For authors such as Henryk Grossman denunciations ofthe LTFRP were equal to the denigration of the historical imperative of socialism. In his 1929 work Law of theAccumulation and Breakdown Grossman argued that Marx’s LTRPF amounts to the law of imminent breakdownof capitalism, which is “the fundamental law that governs and supports the whole of Marx’s thought” (Grossman2005), and tried to demonstrate that reformist strategies are futile attempts to eliminate the crisis riddendynamics of capitalism. He interpreted the LTRPF as a law with profound revolutionary implications, anddenounced the theories of disproportionality or underconsomptionism as theories with reformist politicalimplications. Grossman was the first broadly known Marxian scholar who ascribed to the LTRPF such a vastpolitical relevance.

Two significant critiques of the LTRPF were published in 1941, one in The Theory of capitalist development byPaul Sweezy, and the other in An Essay on Marxian Economics by Joan Robinson. Sweezy and Robinson,however, did not challenge the LTRPF as a basis for a theory of crisis or political strategy, but rather argued thatthe infamous LTRPF is logically inconsistent. Sweezy and Robinson insisted that the long term trend of the rateof profit is indetermined. Their argument was twofold. First, they challenged Marx’s view that the adoption oflabour saving technologies will necessarily increase the organic composition of capital. According to Sweezyand Robinson, mechanisation can, on the contrary, also result in a decline of the organic composition of capital.They argued that the productivity increases in the branches that produce capital goods (means of production)will cause the unit values of the means of production to decrease. That is why, they claimed rather convincingly,it is easy to imagine that the rise in the technical composition of capital can result not in the rise but in the fall ofthe organic composition of capital. That is to say, the productivity increases in branches producing capital goodsmay very well result in the cheapening of the elements of constant capital in value terms, and thus overwhelmthe increases in the mass of constant capital. Consequentially, the devalorisation of the units of constant capitalcan overpower the increase in the technical composition of capital and in turn cause the rate of profit to rise.

Second, they emphasised that the effects of the adoption of labour saving technologies and the subsequentincrease in the productivity of labour will also affect the branches producing wage goods (means ofsubsistence). Particularly, the unit values of wage goods will fall, and in turn lower the value of variable capital,and thus cause the rate of surplus value to rise. According to Sweezy and Robinson, the effect of the increase ofthe rate of surplus value could theoretically very well surpass the effects of the rising organic composition ofcapital, and, again, result in the rising rate of profit. Thus, Sweezy and Robinson claimed, that there is no apriori reason to assert that the rate of profit will on the long term necessarily fall (Cullenberg 1992, p. 47-48).

Soon after the publication of their critique of the LTRPF, Sweezy’s and Robinson’s account was contested.Amongst the most influential challengers of their reasoning were Roman Rosdolsky and Ronald Meek. AgainstSweezy’s and Robinsons argument for the possibility of devalorisation of the capital goods to outstrip theincrease in the technical composition of capital, Rosdolsky in Kyklos (1956) presented a substantial amount ofempirical evidence, which implied that the mass of capital goods has risen to such an extent that nodevalorisation of capital goods can counteract it. Similarly, Meek in his article in Science and Society (1960)demonstrated, by means of plentiful numerical demonstrations, that the scenario where productivity increasesresulting from introduction of labour saving technologies result in the fall in the organic composition off capital,and in turn cause the rate of profit to rise, is highly unlikely. Both Rosdolsky and Meek also tackled the secondSweezy’s and Robinson’s argument that the rise in the rate of surplus value might overpower the rise in theorganic composition of capital. They claimed that Marx has already anticipated such counterarguments andsufficiently rejected them, by showing that, as opposed to the rise in organic composition of capital, the rise inthe rate of surplus value has definite limits, since the growth of the mass of surplus value is limited, because ofthe 24 hour limit of the workday (Ibid, p. 48).

The last amongst the most influential critiques of Marx’s LTRPF in the 20th century was that of Nobuo Okishio,portrayed in his article Technical Change and the Rate of Profit from 1961. In line with Bortkiewitz, Okishioargued that Marx was wrong in depicting the rate of profit as aggregate surplus value divided by the sum ofconstant and variable capital (s/(c+v)). According to Okishio, Marx should have used a depiction of the generalrate of profit in accordance with the linear price of production model, used by Bortkiewitz and other Ricardinanand Sraffian economists. Moreover, Okishio argued that Marx was wrong in presupposing that capitalists wouldadopt labour saving technologies in order to increase the productivity of labour. Okishio contended thatcapitalists do not introduce new technology in order to upturn the productivity of labour as such, but ratherintroduce it only if they result in the reduction of the costs of production. (Ibid, p. 49) By means of a linear price ofproduction model Okishio demonstrated that the adoption of labour saving technologies, which actually result inthe lowering of the price of production for the capitalist adopting this technology, can only result in the rise in hisrate of profit, and subsequently in a formation of the new general rate of profit, which cannot be lower than theone in the previous period (Nakatani 1993, p. 3). Okishio’s account served as a basis for further critiques of Marx’s LTRPF, developed by scholars such as JohnRoemer, Michio Morishima and Takesh Nakatani, yet it also became a subject of vehement critique by Marxistauthors such as John Weeks, Anwar Shaikh, Alan Freeman and Andrew Kliman. They have offered severalarguments against Okishio, which cannot be depicted here. For the purposes of this article, it is enough tostress that they have credibly shown that critiques of LTRPF such as Bortkiewitz’s and Okishio’s suffer fromserious methodological defects. Particularly, the critiques of LTRPF by Bortkiewicz, Okishio and their followers,are based on the presupposition of perfect competition, characteristic of neoclassical economics. Theirrefutations of the LTFRP are thus demonstrated by means of linear price of production models, which areconsistent with Ricardian and Sraffian general equilibrium models, but are in fact light years away from thepresuppositions of Marx’s own depiction of the LTRPF. Moreover, the methodology used in linear price ofproduction models is strictly individualistic, since the criteria for the adoption of new technologies are deducedfrom the considerations of the rationality of the individual capitalist in question. Such methodology, again,diverges substantially from Marx’s depiction, where the dynamics of technological change is considered to bean effect of the impersonal dynamics of capitalist accumulation and competition. That is why Bortkiewitz andOkishio fail to demonstrate the internal inconsistency of the LTRPF, since their refutation of the LTRPF is basedon an imposition, upon Marx, of the methodological assumptions which are external to his mode of presentationof the LTRPF. It could be argued that the only aforementioned critique of the LTRPF that actually tackles Marx’s demonstrationon its own terms, and thus fulfils the criteria of immanent critique of the logic of Marx’s elaboration of the LTRPFis that of Sweezy and Robinson. Namely, Sweezy and Robinson accept Marx’s account of the dynamics ofcapitalist production that facilitates the increases of the technical composition of capital, and try to show that thissame dynamic can result in outcomes, which are opposed to what Marx has envisaged on the basis of thisdynamic. The first argument of their critique, portraying the possibility of the fall in the unit values of constant

capital, which can outdo the effects of the rising mass of constant capital, and thus cause the rate of profit torise, is hard to contest. We have seen that it was challenged by Meek and Rosdolsky, who claimed thatSweezy’s and Robinson’s argument is empirically incorrect. However, as Michael Heinrich has argued, theLTRPF can neither be substantiated nor refuted on the basis of empirical evidence:

“The ‘law’ claims that a fall in the rate of profit results in the long-term from the capitalist mode ofdevelopment of the forces of production. If the rate of profit has fallen in the past, this does notconstitute a proof – since the law purports to apply to future development, and the mere fact of afall in the rate of profit in the past says nothing about the future. If the rate of profit has risen in thepast, then this is also not a refutation, since the law does not require a permanent fall, but rathermerely a ‘tendential’ fall, which can still occur in the future. Even if the law cannot be empiricallyverified, the argumentative conclusiveness of Marx’s reasoning can be discussed.” (Heinrich2013)

That is why we can assert that only the second argument made by Meek and Rosdolsky against Sweezy andRobinson fulfils the criteria of immanent logical critique, which could show that Marx’s LTRPF is logicallyincoherent. In this case, Rosdolsky’s and Meek’s refutation of Sweezy’s and Robinson’s argument that wecannot a priori conclude that the rate of profit will fall on the long term, since there is no reason to presupposethat the rise in organic composition of capital will outstrip the rise in the rate of surplus value, can be consideredlogically sound, because Sweezy and Robinson do not take into account Marx’s clearly and irrefutablydemonstrated proof that the rise in the magnitude of surplus value has limits, due to the definite limit of theworkday (24 hours). Provoked with this simple counterargument made by Rosdolsky and Meek, Sweezy’s andRobinsons argument proves to be insufficient. However, as we will see, Sweezy’s and Robinson’s claim thatthere is no reason to believe that the rise in the organic composition of capital will necessarily outstrip the rise inthe rate of surplus value, and therefore necessitate the fall of the rate of profit, can nevertheless be validated iftheir account is substantiated with an additional argument, which can defend their claim against critiques suchas Rosdolsky’s and Meek’s.

Heinrich’s critique of the LTRPF

Meek, Rosdolsky and, so it seems, Marx himself, thought the proof that the rise in the mass of surplus value hasa definite limit, was sufficient to prove, on logical grounds, the LTRPF. As we have already demonstrated, Marxwas indeed right to point out that when the number of workers falls beyond a certain limit, the amount of surplusvalue produced also necessarily decreases. We have verified this with a numerical example including thereduction of the number of workers from 100 to 10. Nonetheless, Heinrich persuasively argues that this is notenough to prove the LTRPF3. Heinrich starts by repeating Sweezy’s and Robinson’s argument that it isimpossible to prove that the rise in the rate of surplus value cannot outdo the rise in the organic composition ofcapital. But, as opposed to Sweezy and Robinson, Heinrich develops a supplementary argument that takes intoaccount the important claim, first stressed by Marx and repeated by Meek and Rosdolsky, that the rise in themass of surplus value has a limit, which cannot be surpassed.

According to Heinrich, the declining mass of surplus value indicates a certain fall in the rate of profit only whenwe presuppose that the mass of total capital that is needed for the production of this surplus value does notdecline, but at least remains constant (Heinrich 2012, p. 153). This thesis can be demonstrated with a numericalexample, which depicts the effects of rising organic composition of capital, and the decline in the mass of surplusvalue on the rate of profit:

I) s / (c + v) = 50 / (50 + 50) = 0,5 = 50%

II) s / (c + v) = 40 / (60 +40) = 0,4 = 40%

III) s / (c + v) = 40 / (60 + 10) = 0,57 = 57%

We can see that only in the second case, where there is a slight rise of the organic composition of capital and afall in the mass of surplus value, the profit rate declined, whereas in the third case the rate of profit increased

despite the fact that the mass of surplus value has declined and despite the fact that the organic composition ofcapital has increased substantially:

I) c / v = 50 / 50 = 100%

III) c / v = 60 / 10 = 600%

In the third case, the rate of profit has increased because the mass of total capital advanced has dropped from100 to 70. The profit rate has fallen only in the second case in which the value of the total capital advancedremained constant (100). This is precisely why the necessity of the fall of the mass of surplus value does notalso automatically dictate the fall in the rate of profit (see Heinrich 2012, p. 153). If we now return to our exampleof the reduction of the number of workers, we can clearly see why such a reduction is insufficient to indicate acertain fall in the rate of profit. Should the number of workers be reduced from 100 to 10, this would mean thatthe value of variable capital would fall to 1/10 of its previous value. Keeping the general formula of the rate ofprofit in mind (s / (c + v)), it is evident that this would result in a substantial fall of the denominator, which couldvery well cause the rate of profit to rise. Moreover, the displacement of workers by introduction of labour savingtechnology also implies the reduction of the value of means of subsistence that determine the value of labourpower. Along these lines, the effect would be a reduction of the value of labour power, which automaticallytranslates into a further decline in the variable capital. This means that variable capital that employs 10 workerswill shrink to even less than 1/10 of the value of variable capital that employs 100 workers (see Ibid, p. 152-153).

In these conditions the proof that the rate of profit will fall is only possible if we can also prove that the constantcapital will increase by at least the same amount by which the variable capital has been reduced (Ibid, p. 153).Only then can we exclude the possibility of a falling mass of the whole capital advanced and consequentiallyprove that the fall in the rate of profit is certain. However, on such a general level, this simply cannot be proven,since we cannot possibly know if the increase in productivity was implemented with a substantial or just a minorincrease in the value of constant capital. Heinrich outlines this dubiousness as follows:

“If constant capital does not increase strongly enough to compensate the reduction of variablecapital, then the total capital advanced declines. In this case, we have a declining mass of surplusvalue and declining capital. Whether the rate of profit falls depends upon what falls quicker, themass of surplus value or the advanced capital. If the mass of surplus value falls quicker than theadvanced capital, then the rate of profit declines; if the advanced capital declines quicker than thesurplus value, then the rate of profit increases despite the reduction in the mass of surplus value.”(Ibid, p. 153)

Hence, the conclusion would be that departing from that dynamics of the capitalist development we cannotassume in advance that there is a law of the tendency of the rate of profit to fall. The rate of profit of coursemight fall due to this dynamics – this possibility cannot be excluded – but it might very well rise due to this samedynamics. Its long term course cannot be determined in advance.

Political implications of the LTRPF

Hence, we have come to a conclusion that we cannot logically derive the LTRPF from the dynamics of capitalistdevelopment. But does this mean that we have adopted a cosy reformist political stance, and denounced theneed for the overthrow of capitalism, as the most ferocious proponents of the LTRPF would want us to believe? We have mentioned that many of them treated Marx’s LTRPF as the ultimate argument for why the inherentsystemic dynamics of growth in capitalism necessarily undermines its own conditions, and consequentiallyleads to periodic crises that necessitate the revolutionary overthrow of capitalism. Authors such as HenrykGrossman, Anwar Shaikh, John Weeks, Andrew Kliman, Michael Roberts and many others have emphasisedthat a profound political issue is at stake in the debates on the LTRPF. In the words of John Weeks: “What is atstake is whether capitalism is by its very nature stable and capable of sustained dynamism, or whether theaccumulation of capital is self-limiting.” Therefore, “the debate over the tendency for the rate of profit to fall doescorrespond to the debate over revolutionary strategy ... involved here is the debate over the possibility of a

peaceful road to socialist transformation.” (Weeks 1982, p. 76) Weeks’s argument is in line with Grossman whoasserted that to deny that there is a LTRPF is to deny that there are objective revolutionary situations. If thefalling rate of profit and hence crises are not permanent built-in features of the capitalist mode of production,then there is no objective necessity for the transcendence of capitalism.

However, to adopt a revolutionary political position that is straightforwardly deduced from an abstract law suchas the LTRPF seems farfetched, to say the least. It entails a rather mechanicistic political vision, embedded in adeterministic worldview, which, in a theleological manner, views the end of capitalism, and often also aproletarian revolution, as an inevitable occurrence – irrespective of what happens in the actual course of history.Moreover, the political position derived from the LTRPF is problematic, since it is derived from a general law,which is depicted on a level of abstraction, where no consideration of concrete historical political conditions inwhich politics is actually made, can be taken into account. Furthermore, such forthright derivations can lead torather bizarre conclusions. If we were categorically to claim that the affirmation of the LTRPF implies arevolutionary position, this would mean that not Marx, but rather the bourgeois economists such as Adam Smith,David Ricardo and even the champion of marginalist economics, William Stanley Jevons, were the ultimatetheoreticians of the revolution and implicit proponents of the overthrow of capitalism, since all of them had, eachin their own way, argued for the inexorable inevitability of the decline in the rate of profit. Considering the factthat their political attitude was far from revolutionary, establishing direct connections between LTRPF andpolitical strategy seems highly unsound. In line with Heinrich we can conclude that to criticize theories such asthe LTRPF means in no way to defend capitalism. Such critiques just aim to fighting against capitalism withoutillusions based on inconclusive or unverifiable theories.

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References:

Bortkiewitz, Ladislaus. 1952. Value and Price in the Marxian System:http://classiques.uqac.ca/classiques/Bortkiewicz_ladislaus_von/value_and_price_marxian_system/value_price_marxian_system.pdf.

Cullenberg, Stephen. 1983. The Political Economy of Marx’s Theory of the Falling Rate of Profit:Methodological Considerations: http://www.helsinki.fi/jarj/inem/methodus/pdf/v4n1/v4n1p44.pdf.

Grossman, Henryk. 2005. Law of the Accumulation and Breakdown:https://www.marxists.org/archive/grossman/1929/breakdown/index.htm.

Heinrich, Michael. 2012. An Introduction to the Three Volumes of Karl Marx's Capital. New York: MonthlyReview.

Heinrich, Michael. 2013. Crisis Theory, The Law of the Tendency of the Profit Rate to Fall, and Marx'sStudies in the 1870's: http://monthlyreview.org/2013/04/01/crisis-theory-the-law-of-the-tendency-of-the-profit-rate-to-fall-and-marxs-studies-in-the-1870s/.

Marx, Karl. 1973. [1857-1858] Grundrisse. London: Penguin Books.

Marx, Karl. 1993. Capital, Volume III:http://www.marxists.org/archive/marx/works/download/Marx_Capital_Vol_3.pdf.

Marx, Karl. 2010. Capital, Volume I: https://www.marxists.org/archive/marx/works/download/pdf/Capital-Volume-I.pdf.

Nakatani, Takesh. 2000. The Theoretical Work of Nobuo Okishio: https://www.google.si/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CB8QFjAA&url=http%3A%2F%2Fwww.iwgvt.org%2Ffiles%2Fsympnakatani-okishio.rtf&ei=2cYVVPKTAceuPOClgJgE&usg=AFQjCNEbndI8yzFGvleOyOrTlZARmd2lEg&sig2=hgd8UKsyIh_8Tm8MsoCcrA.

Millios, John and Sotiropoluos, Dimitris. 2007. Marxist Approaches to Economic Crises:http://www.iippe.org/wiki/images/b/b2/CONF_CRISIS_Milios.pdf.

Weeks, John. Equilibrium, Uneven Development, and The Tendency of the Rate of Profit to Fall: http://cnc.sagepub.com/content/6/1/62.full.pdf.

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This text was provided by the author for the conference on Critique of Political Economy held in Institute for

Philosophy and Social Sciences in Belgrade, December 2013.

1 Marx dealt with LTFRP in several writings. Our illustration, however, is limited to an examination of his accountin chapters 13 and 14 of the third volume of Capital. ↩2 What follows is a brief overview of the most influential discussions. An in-depth depiction and criticalevaluation of several complex arguments of all the authors in question is beyond the scope of this article. Theoverview follows Stephen Cullenbergs chronological synopsis of the debates on the LTRPF presented in his:The political Economy of Marx’s Theory of the Falling Rate of Profit. ↩3 Heinrich first elaborated his critique of Marx's LTRPF in his book: Die Wissenschaft vom Wert in 1990. Hiscritique was presented to the english speaking public in his An Introduction to the Tree Volumes of Karl Marx'sCapital (2012) and in his article: Crisis Theory, The Law of the Tendency of the Profit Rate to Fall, and Marx'sStudies in the 1870's published in Monthly review in 2013. ↩