Tendency of the rate of profit to fall

The tendency of the rate of profit to fall (TRPF) is a hypothesis in economics and political economy, most famously expounded by Karl Marx in chapter 13 of Capital, Volume III. Economists as diverse as Adam Smith, John Stuart Mill, David Ricardo and Stanley Jevons referred explicitly to the TRPF as an empirical phenomenon that demanded further theoretical explanation, yet they each differed as to the reasons why the TRPF should necessarily occur.

In his 1857 Grundrisse manuscript, Marx called the TRPF "the most important law of political economy" and sought to give a causal explanation for it in terms of his theory of capital accumulation. In Capital, Volume III, Marx described the TRPF as "the mystery around which the whole of political economy since Adam Smith revolves" and in a letter he called his own TRPF theory "one of the greatest triumphs" over all previous economics. The tendency is already foreshadowed in chapter 25 of Capital, Volume I (on the "general law of capital accumulation"), but in Part 3 of the draft manuscript of Marx's Capital, Volume III, edited posthumously for publication by Friedrich Engels, an extensive analysis is provided.

Geoffrey Hodgson stated that the theory of the TRPF "has been regarded, by most Marxists, as the backbone of revolutionary Marxism. According to this view, its refutation or removal would lead to reformism in theory and practice". Stephen Cullenberg stated that the TRPF "remains one of the most important and highly debated issues of all of economics" because it raises "the fundamental question of whether, as capitalism grows, this very process of growth will undermine its conditions of existence and thereby engender periodic or secular crises".

Marx regarded the TRPF as proof that capitalist production could not be an everlasting form of production since in the end the profit principle itself would suffer a breakdown. However, because Marx never published any finished manuscript on the TRPF himself, because the tendency is hard to prove or disprove theoretically and because it is hard to test and measure the rate of profit, Marx's TRPF theory has been a topic of global controversy for more than a century.

Adam Smith, David Ricardo and Karl Marx

Smith 
In Adam Smith's TRPF theory, the falling tendency results from the growth of capital  which is accompanied by increased competition. The growth of capital stock itself would drive down the average rate of profit.

Ricardo 
Mistakenly interpreting Adam Smith's falling rate of profit theory to be that increased competition drives down the average rate of profit, David Ricardo argued that competition could only level out differences in profit rates on investments in production, but not lower the general profit rate (the grand-average profit rate) as a whole. Apart from a few exceptional cases, Ricardo claimed, the average rate of profit could only fall if wages rose.

Marx 
In Capital, Karl Marx criticized Ricardo's idea. Marx argued that, instead, the tendency of the rate of profit to fall is "an expression peculiar to the capitalist mode of production of the progressive development of the social productivity of labor". Marx never denied that profits could contingently fall for all kinds of reasons, but he thought there was also a structural reason for the TRPF, regardless of conjunctural market fluctuations.

Marx argued that technological innovation enabled more efficient means of production. Physical productivity would increase as a result, i.e. a greater output (of use values, i.e., physical output) would be produced, per unit of capital invested. Simultaneously, however, technological innovations would replace people with machinery, and the organic composition of capital would decrease. Assuming only labor can produce new additional value, this greater physical output would embody a gradually decreasing value and surplus value, relative to the value of production capital invested. In response, the average rate of industrial profit would therefore tend to decline in the longer term.

It declined in the long run, Marx argued, paradoxically not because productivity decreased, but instead because it increased, with the aid of a bigger investment in equipment and materials. Rosa Luxemburg stated in her 1899 pamphlet Social Reform or Revolution? that:

The central idea that Marx had, was that overall technological progress has a long-term "labor-saving bias", and that the overall long-term effect of saving labor time in producing commodities with the aid of more and more machinery had to be a falling rate of profit on production capital, quite regardless of market fluctuations or financial constructions.

Counteracting tendencies 
Marx regarded this as a general tendency in the development of the capitalist mode of production. But it was only a tendency, because there are also "counteracting factors" operating which had to be studied as well. The counteracting factors were factors that would normally raise the rate of profit. In his draft manuscript edited by Friedrich Engels (Marx did not publish it himself), Marx cited six of them:
 More intense exploitation of labor (raising the rate of exploitation of workers).
 Reduction of wages below the value of labor power (the immiseration thesis).
 Cheapening the elements of constant capital by various means.
 The growth of a relative surplus population (the reserve army of labor) which remained unemployed.
 Foreign trade reducing the cost of industrial inputs and consumer goods.
 The increase in the use of share capital by joint-stock companies, which devolves part of the costs of using capital in production on others.

Nevertheless, Marx thought the countervailing tendencies ultimately could not prevent the average rate of profit in industries from falling; the tendency was intrinsic to the capitalist mode of production. In the end, none of the conceivable counteracting factors could stem the tendency toward falling profits from production. The capitalist system would age like any other system, and would be able only to compensate for its age, before it left the stage of history for good.

Other influences 
There could obviously also be several other factors involved in profitability which Marx did not discuss in detail, including:
 Reductions in the turnover time of industrial capital generally (and especially fixed capital investment).
 Accelerated depreciation and faster throughput.
 The level of price inflation for different types of goods and services.
 Taxes, levies, subsidies and credit policies of governments, interest and rent costs.
 Capital investment into areas of (previously) non-capitalist production, where a lower organic composition of capital prevailed.
 Military wars or military spending causing capital assets to be inoperative or destroyed, or spurring war production (see permanent arms economy).
 Demographic factors.
 Advances in technology and technological revolutions which rapidly reduce input costs.
 Particularly in the era of globalization, the national and international freight rate (shipping, trucking, railfreight, airfreight).
 Substituted natural resource inputs, or marginal increased cost of non-substituted natural resource inputs.
 Consolidation of mature industries into an oligarchy of survivors. Mature industries do not attract new capital because of low returns. Mature companies with large amounts of capital invested and brand recognition can also try to block new competitors in their markets. See also secular stagnation theory.
 The use of credit instruments to reduce capital costs for new production.

The scholarly controversy about the TRPF among Marxists and non-Marxists has continued for a hundred years. There exist nowadays several thousands of academic publications on the TRPF worldwide. However, no book is available which provides an exposition of all the different arguments that have been made. Professor Michael C. Howard  stated that "The connection between profit and economic theory is an intimate one. (...) However, a generally accepted theory of profit has not emerged at any stage in the history of economics... theoretical controversies remain intense."

Main criticism of Marx 
Marx's interpretation of the TRPF was controversial and has been criticized in three main ways.

Productivity 
By raising productivity, labor-saving technologies can increase the average industrial rate of profit rather than lowering it, insofar as fewer workers can produce vastly more output at a lower cost, enabling more sales in less time. Ladislaus von Bortkiewicz stated: "Marx’s own proof of his law of the falling rate of profit errs principally in disregarding the mathematical relationship between the productivity of labour and the rate of surplus value." Jürgen Habermas argued in 1973–74 that the TRPF might have existed in 19th century liberal capitalism, but no longer existed in late capitalism, because of the expansion of "reflexive labor" ("labor applied to itself with the aim of increasing the productivity of labor"). Michael Heinrich has also argued that Marx did not adequately demonstrate that the rate of profit would fall when increases in productivity are taken into account.

Contingency 
How exactly the average industrial rate of profit will evolve, is either uncertain and unpredictable, or it is historically contingent; it all depends on the specific configuration of costs, sales and profit margins obtainable in fluctuating markets with given technologies. This "indeterminacy" criticism revolves around the idea that technological change could have many different and contradictory effects. It could reduce costs, or it could increase unemployment; it could be labor saving, or it could be capital saving. Therefore, so the argument goes, it is impossible to infer definitely a theoretical principle that a falling rate of profit must always and inevitably result from an increase in productivity.

Perhaps the law of the tendency of the rate of profit to fall might be true in an abstract model, based on certain assumptions, but in reality no substantive, long-run empirical predictions can be made. In addition, profitability itself can be influenced by an enormous array of different factors, going far beyond those which Marx specified. So there are tendencies and counter-tendencies operating simultaneously, and no particular empirical result necessarily and always follows from them.

Labor theory of value 
Steve Keen argues that since the labor theory of value is wrong, then this obviates the bulk of the critique. Keen observes that the TRPF was based on the idea that only labor can create new value (following the labor theory of value), and that there was a tendency over time for ratio of capital to labor (in value terms) to rise. However, if surplus can be produced by all production inputs, then there is no reason why an increase in the ratio of capital to labor inputs should cause the overall rate of surplus to decline.

20th century Marxist controversies 
The 20th century Marxist controversies about the TRPF focused on five issues:
The relevance of the TRPF for understanding and explaining capitalist economic crises.
The role of profitability tendencies in the final collapse of capitalism.
The political significance of the TRPF for the policy of workers' parties.
The theoretical consistency of the TRPF argument.
The data about empirical profitability trends in the long term.
In addition, philosophers and economists also discussed the sense in which the TRPF could be considered an economic "law", since it seemed unclear how a necessary tendency could be "necessary" or inevitable, if it was only a tendency, in combination with other tendencies. It was not so easy, to model a situation in which a developmental tendency would, after some time, win through despite a variety of counteracting forces that would ordinarily reduce or cancel out the tendency.

Breakdown controversy 
The first big scientific debate about Marx's economic theory, starting in the 1890s, was the so-called "breakdown controversy", in which the tendency toward falling profitability played an important role.

Eduard Bernstein 
The debate began to heat up when the veteran German socialist leader Eduard Bernstein claimed that it was wrong to think that "the end was nigh" or that capitalism would collapse through a catastrophic breakdown. He aimed to show with facts and figures that Marx's analysis of the tendencies of capitalism had turned out to be partly wrong. Bernstein believed that Marx's theory therefore had to be revised (this was known as the "revisionist" position). In response, numerous "orthodox" Marxist critics tried to prove that capitalism was necessarily doomed, at least in the long term. This controversy about the fate of the capitalist system still continues.

Henryk Grossman and Vladimir Lenin 
From the late 1920s and 1930s onward, classical revolutionary orthodox Marxists like Henryk Grossmann, Louis C. Fraina (alias Lewis Corey) and Paul Mattick  argued that at a certain point, the falling rate of profit stops the total mass of profit in the economy from growing altogether, or at least from growing fast enough. This results in a crisis of over-accumulation (or a shortage of surplus value), a drop in new productive investment, and an increase in unemployment, which brakes or stops market expansion. In turn, that leads to a wave of takeovers and mergers to restore profitable production, plus a higher intensity of labor exploitation. In the end, however, after a lot of cycles, capitalism collapses.

This interpretation contrasted with V.I. Lenin’s idea that in the crises of bourgeois society "there is no such thing as an absolutely hopeless situation", since the bourgeoisie can – in principle – always find a way out, even if it takes a war to get there. Lenin regarded the abolition of capitalism as a conscious political act, not as a spontaneous result of the breakdown of the economy. In 1931, two years after publishing his breakdown theory, Grossman qualified his idea more, emphasizing that he did not believe that capitalism had to collapse "by itself" or "automatically"; the objective law of breakdown had to be combined with the subjective factor of the class struggle.

Other theories 
Other orthodox Marxists or economists inspired by Marx (including Karl Kautsky, Mikhail Tugan-Baranovsky, Nikolai Bukharin, Rudolf Hilferding, Rosa Luxemburg, Vladimir Lenin, Otto Bauer, Fritz Sternberg, Natalia Moszkowska, Oskar Lange, Michał Kalecki, Paul Sweezy, Kei Shibata, Kozo Uno, Nobuo Okishio and Makoto Itoh) provided alternative crisis theories, focusing variously on the anarchy of capitalist production, sectoral disproportions, underconsumption and realization problems, labor-shortage and population pressures, credit insufficiency, excess capital, state policy, productivity and wages squeezing profits.

According to Professor Costas Lapavitsas, "both Hilferding and Lenin – indeed most of the leading Marxists of their time – treated crises as complex and multifaceted phenomena that could not be reduced to a simple theory of the rate of profit to fall. The notion that the normal state of capitalist production is to malfunction due to a persistently excessive organic composition of capital, or even due to falling 'surplus' absorption, would have been alien to classical Marxists." Implicitly or explicitly, it was argued by these Marxist economists that economic crises, although they are a fairly regular occurrence in the last two centuries of capitalist development, do not all have exactly the same causes. There are all sorts of things that can go wrong with capitalism, throwing the markets out of kilter.

Howard & King claim that the TRPF was mostly "neglected" in Marxist theoretical discussions during the 1920s. Callinicos & Choonera claim that the TRPF actually played a "marginal" role in much of the whole history of Marxist economics, even although it was the truly revolutionary core of Marx's teaching. During the British general strike of 1926, for example, there was no evidence of English discussion about the TRPF.

In the non-English Marxist literature, however, the TRPF did get plenty of attention, except that the TRPF was never seen as the "be all and end all" of crisis theory. For the continental thinkers, the trend in profitability was linked with many different economic variables and circumstances. The issue then was about the real interconnection of all these variables together (the Totalité or Zusammenhang), and not simply about whether the profit rate was up or down.

When Henryk Grossman published his famous 1929 breakdown theory, he intended to correct faults in the 1920s theoretical debates about the dynamics of capitalist growth - as discussed in the writings of Karl Marx, Nikolai Bukharin, Otto Bauer, Rosa Luxemburg, Fritz Sternberg and many others. "Unlike Marx's diagrams, Bauer's diagram includes the rising organic composition of capital, a falling rate of profit, a rising mass of profit, and the faster development of Department I – the department that produces the means of production – relative to Department II – the branch that produces the means of personal consumption."

Mono's vs. multi's 
Some Marxists sought the cause of capitalist crises in only one specific factor as the "root of the evil", e.g. over-accumulation, underconsumption, the anarchy of production, population pressures, class conflict, falling profits, state policy etc. Others tried to integrate different contributing causes in one theory. In modern Marxism, some mono-causal Marxist theorists (the "mono's") still attribute crises to one single factor (principally, the TRPF). Others (the "multi's") have argued for a multi-causal approach in which a distinction is drawn between the "triggers" of the crisis, its deeper underlying causes, and the concrete manifestation of crises.

Transformation problem 

The Marxian controversy about the so-called transformation problem began in earnest after the publication of Friedrich Engels's 1894 preface and 1895 supplement to his edition of Marx's third volume of Capital. In Capital, Volume III, Marx dropped his simplifying assumption that commodities are sold at their value, in favour of a theory of competitive market prices,  regulated by production prices which diverged from product-values (the so-called "transformation of commodity values into prices of production"). Yet he supplied no convincing proof or evidence, that production prices were themselves shaped and determined by product-values.

Allegedly Marx failed to prove, how the leveling out of different rates of profit through competition toward a general, average profit rate could be logically reconciled with the determination of product-values by labour-time. Marx assumed in his simple numerical examples, that the aggregate profit volume was allocated to production capitals according to a uniform profit rate, but that assumption happened to run into conflict with other assumptions in his theory. If the inconsistency could not be resolved, then the validity of a labour theory of product-values as such was put into question. Five scholarly positions emerged subsequently in the West:

Marx's transformation problem is a real and unsolvable problem (e.g. Ian Steedman).
It is a real but solvable problem (e.g. Gérard Duménil).
A pseudo-problem was created, through false interpretations of Marx, which gets in the way of consistently developing Marx's idea (e.g. Andrew Kliman).
There is no transformation problem, and there never was one, if Marx is simply understood literally, in his own terms (e.g. Fred Moseley).
There is a transformation problem (Marx did overlook some quantitative implications), but econometrically it is not very significant compared to the overall close fit between the classical theory of value and the economic data (e.g. Anwar Shaikh). The controversy about the problem was vastly bigger, than the size of the problem warranted. The mathematical insight here is, that all classical theories of value – whether Smithian, Ricardian, Millsian, Marxian or Sraffian etc. – necessarily involve a transformation problem, since they all assume that the prices for products diverge from, and oscillate around, some underlying production value or "natural" price, while profits proportional to capital size, and unequal capital compositions in different enterprises and sectors, are being assumed at the same time. 
Those socialist economists who thought that the transformation problem was a real but unsolvable problem, usually abandoned Marx's value theory, as well as his theory of the TRPF. With the other four interpretations, economists might or might not reject Marx's TRPF theory. There might also be some overlap in the five positions (e.g. when scholars thought there were both pseudo-issues and some real problems). Marxists often disagree among themselves about what the transformation problem is about, and what its implications are.

Classical debate 
Engels realized very well, that there were unsolved issues in Marx's theory of value and capital, and he had previously invited other economists to help solve them. Already before Capital, Volume III was first published, Mikhail Tugan-Baranovsky, German socialists like Conrad Schmidt and various Italian authors were critically assessing the implications of Marx's theory. But Engels himself died in 1895.

Subsequently, Eugen Böhm von Bawerk and his critic Ladislaus Bortkiewicz (himself influenced by Vladimir Karpovich Dmitriev) claimed that Marx's argument about the distribution of profits from newly produced surplus value is mathematically faulty. This gave rise to a lengthy academic controversy. Critics claimed that Marx failed to reconcile the law of value with the reality of the distribution of capital and profits, a problem that had already preoccupied David Ricardo – who himself inherited the problem from Adam Smith, yet failed to solve it.

Marx was already aware of this theoretical problem when he wrote The Poverty of Philosophy (1847). It gets a mention again in the Grundrisse (1858). At the end of chapter 1 of his A Contribution to the Critique of Political Economy (1859), he referred to it, and announced his intention to solve it. In Theories of Surplus Value (1862-1863), he discusses the problem very clearly. His first attempt at a solution occurs in a letter to Engels, dated 2 August 1862. In Capital, Volume I (1867) he noted that "many intermediate terms" were still needed in his progressing narrative, to arrive at the answer. Engels suggested, that Marx had indeed solved the problem in the posthumously published Capital, Volume III, but critics alleged Marx never delivered a credible or definitive solution.

Specifically, critics claimed that Marx failed to prove that average labour requirements are the real regulator of product-prices within capitalist production, since Marx failed to demonstrate what exactly the causal or quantitative connection was between the two. As a corollary, Marx's theory of the TRPF was undermined as well, since it was based on a necessary long-term evolution of value-proportions between the composition of production capital and the yield of production capital.

Ricardianism 
According to the classical Ricardian economists, solving the transformation problem was an essential prerequisite for a credible theory of prices – a theory that would genuinely explain the relationship between the different variables determining prices, and the effects of changes in those variables. The theory of economic value was the foundation for the theory of prices, because prices could not be understood and explained without assumptions about economic value. Somehow, the labour theory of the substance of product-value had to be reconciled with observed patterns in the distribution of profits and prices. Hence, a version of the transformation problem already existed in Ricardian economics, before it existed in Marxian economics, and, according to Marx, Ricardo's inability to solve it, directly contributed to the break-up of the Ricardian school, and to the demise of the labour theory of value.

Marx's claim all along was, that Smith and Ricardo could not solve the problem, because they fudged the correct definition of very basic concepts and categories in political economy. Marx implied, that if things were correctly conceptualized, then the pieces of the puzzle could be fitted together in a logically sound way. The subsequent debate then centered on whether Marx had really solved a fundamental problem of the classical labour theory of value which Ricardian economics had failed to solve, so far, or whether there was an alternative (Ricardian) solution preferable to Marx's. Prof. Anwar Shaikh states that, among economists, this issue divided supporters of the labor theory of product-value for more than one century.

What made the 20th century debate especially complicated and confusing, was that Ricardo's theory and Marx's theory were often mixed up with each other. It was often unclear or controversial, what the exact differences between them were, and how that mattered. In criticizing and reworking Ricardian theory, Marx had kept some of its ideas, but also altered the whole theoretical frame of reference, creating a new social and economic ontology. Some Marxian professors, like Makoto Itoh,  Michael Heinrich, Ernesto Screpanti, Tony Smith and Chris Arthur, aim to re-edit Marx's dialectical transformation argument, in order to cleanse it from all "Ricardian residues" – the suggestion being, that Marx himself had never completely freed himself from Ricardian concepts in the economic manuscripts which he did not publish himself.

Wassily Leontief and Paul Sweezy 
The German transformation controversy, insofar as it concerned the reproduction of capital, helped to inspire Wassily Leontief's matrix system of input–output economics which later made it possible to obtain measures of the Marxian rate of profit (see below). In Berlin, Ladislaus Bortkiewicz co-supervised the young Leontief's doctoral studies together with Werner Sombart.

Leontief's father, a professor in economics, studied Marxism and did a Phd on the condition of the working class in Russia. Leontief himself studied Marxism as undergraduate, but claimed later that he had been interested in Marx only as a "classical economist"; he took a dim view of Marx's mathematical ability and of the labour theory of value. Leontief was primarily interested in applied economics and testable hypotheses. His personal experience as a student with Cheka persecution made Leontief wary of Marxism, whatever his appreciation of Marx.

The transformation problem nevertheless remained a relatively obscure academic dispute, until Paul Sweezy drew attention to it in his widely read 1942 book The Theory of Capitalist Development. The Bortkiewicz-Sweezy interpretation of Marx was very influential in the second half of the 20th century, in Marxist, neo-Ricardian and Post-Keynesian circles. From the 1970s, the academic debate broadened to the more general issue of what exactly is the relationship between values and prices, and how that should be conceptualized.

Marx's theory 
In Capital, Volume I, Marx analyzed how the capitalist enterprise buys materials and labour-power (inputs) to produce commodities sold for profit (outputs). At that stage he was not concerned much with price fluctuations or market volatility (except for the price of labour hired). In chapter 9 of Capital, Volume III, he notes that he had previously assumed that, to the purchasing capitalist, the value of a commodity bought was the same as its cost-price. In reality, he argued, this cost-price is itself a market price based on a production price (a cost-price + a profit) of the supplying capitalist producer: the input purchasing price of one capitalist is the output selling price of another capitalist. So the acquisition cost-price of inputs itself corresponded to both a value and a surplus value, and the market prices of inputs might diverge from the labor-value of inputs.  Hence, said Marx, if the cost-price of a newly produced output is assumed to be equal to the labor-value of the inputs used up in producing it, "it is always possible to go wrong" in the calculation of the output production price (because input acquisition prices and input labor-values could diverge, given that the inputs could be bought above or below their value, and given that after purchase their inventory value could change, during the production process).

In drafting a simple model of profit distributions, Marx straightforwardly equated – for the sake of argument – the total cost-price of society's new gross output with the total production capital advanced to produce it, abstracting from many intervening variables such as capital depreciation and turnovers. Marx furthermore assumed, that at the point where a new output had been produced, its cost-price in the bookkeeping (a sum of money-capital representing materials costs, wage costs and operating costs) was a given, unchangeable datum, and he considered that price-value discrepancies of inputs bought were irrelevant to his analysis, since it was the value of this new output (and not the capital advanced) that was being related to a general price level and a general profitability level in the markets where the output was sold.

The cost-price of the new output was not based on a hypothetical "labor-value" of inputs, but based on what the producers actually paid for the inputs that were used up to create their outputs. Using various inputs, a new output was produced. This new output had a value, but precisely how much of that value would be realized as revenue, was difficult to know in advance. The difference between the selling price and the cost price of the new output sold, was the surplus value realized as profit by the producer of that output, and the argument was, that this profit would normally (assuming ordinary competition) tend to gravitate to an amount reflecting the average profit rate on capital. The question was about how the profit volume included in the total value product would be distributed among the producing enterprises.

If businesses could not reach a baseline profitability, they would be driven out of business sooner or later, or they would be taken over by another business and restructured, so that they did become sufficiently profitable. Inversely, if businesses overcharged for their commodities to obtain more profit, fewer people would buy them, and they would suffer decline as well. So output could normally be sold only within a fairly narrow range of prices, acceptable to both buyers and sellers. Marx then examined what the division of the total newly produced surplus value would be, among producing enterprises with varying capital compositions, on the hypothetical assumption of a uniform profit rate established by free competition.

Under Marxism–Leninism and Sraffianism, the "uniform rate of profits" was often taken as the literal truth. Marx himself knew very well though that a uniform profit rate (a "general profit rate", e.g. a 10% net profit on all production capital) did not truly exist in the real world, except as a tendency in the competitive process, as a norm for acceptable returns, or as a statistical average. If it is accepted that "perfect competition" does not exist in the real world, then a "uniform rate of profit" also cannot exist in the real world – both are just idealizations used to understand some implications of a model.

Marx wanted to examine the share-out of newly produced surplus value in its simplest and purest forms, abstracting from all kinds of variability of circumstances that would make his own calculation extraordinarily complex (see further prices of production). The formation of a normal rate of profit on capital invested, common to most producers, defined the basic parameters of competition, and thereby it defined the main developmental dynamic of the capitalist production system.

Ladislaus Bortkiewicz 
The theoretical problem that nevertheless remained in Marx's story, according to Ladislaus Bortkiewicz and other Ricardian theorists like Mühlpfordt, Dmitriev and Charasoff, was how the input and output results of interacting sectors of industry could be modeled in aggregate, so that total product values and total production prices would exactly match up in aggregate, and so that the price-value divergences at the micro-level would all cancel out at the macro-level.

For Bortkiewicz, this redistribution was a purely mathematical problem, a matter of correct formalization. The equality of total production prices and total values (Bortkiewicz talks about "price units" and "value units", with a "system of prices", and a "system of values") could be understood to mean, that they were both equal to a given quantity of gold, or a given quantity of labor hours, or a given quantity of an assumed standard commodity (where value = price). A perfectly consolidated result was required, as a proof that production prices represented merely and only a quantitative redistribution of product-values.

In turn, that Marxian quantitative proof would, in Bortkiewicz's interpretation, confirm logically that there was a determinate relationship between product-values and product-prices, since every value quantity would always map to a price quantity and, in aggregate, every positive price-value deviation would always be balanced out exactly by a proportional negative price-value deviation. Marx's system of categories for describing the accumulation of capital from production, and his theory of the levelling out of differences in rates of profit, would be validated as logically sound, and as meeting a standard of scientific rigour.

The relevant point here was, that price-value divergences occurred both with regard to inputs to production and with regard to outputs; but Marx himself had ignored the input price-value divergences in his simple quantitative illustrations of the distribution of profit. Since outputs become inputs and inputs become outputs, critics alleged that unless input values are transformed in the calculation as well, the absurd mathematical effect in the model is, that capitalist producers selling a good obtain a sale price that differs from the price paid by capitalist producers buying the same good.

Five ideas 
In a static three-sector model, it proved mathematically difficult to join up five ideas. These five ideas were:
 1. All production capitals attract the same profit rates, so that profits are distributed in proportion to the size of the capitals (the so-called "uniform profits" assumption).
 2. Production units or sectors each have a different organic composition of capital.
 3. The sum of production prices is equal to the sum of product values.
 4. The total profit-money distributed to production units is equal to the total surplus value produced.
 5. The rate of profit in price terms, is equal to the rate of profit in value terms.

The input-output equations could be made to work, only if additional assumptions were made. But even in a dynamic model, it can be shown mathematically that assumptions (1), (3) and (4) have a crippling effect on the plausibility of longterm quantitative results obtained with the model. However, what ought to be concluded from this modelling exercise, still remains very much in dispute (is the theory wrong, are the concepts and assumptions wrong, is the interpretation of the concepts wrong, is there a big difference between the model and the real world, etc.).

The algebra of the classical transformation problem is rather simple; the real difficulty is about whether the economic relationships involved are adequately conceptualized, and how we could know that. Both Marx and von Bortkiewicz actually admitted or implied themselves that assumptions (1), (3), (4) and (5) cannot be true in the real world, but this was never recognized in the 20th century literature. It casts doubt on the importance or relevance of the classical transformation problem (in particular because it largely disregards the social ontology of values and prices, as well as the techniques to measure product-values in the real world).

In 1950, Cambridge economist Joan Robinson dismissed the transformation problem as "just a toy", arguing that "the whole argument is condemned to circularity from birth, because the values which have to be 'transformed into prices' are arrived at in the first instance by transforming prices into values."

Redundancy of value 
Bortkiewicz's analysis nevertheless raised the very important question of what the point of Marx's value theory is. Is there is any real difference between Marx's "values" and theoretical prices? If there is no real difference, neo-Ricardians argued, then Marx's value theory is redundant; one could then just as well make all the same sorts of arguments in price terms. In Sraffa's alternative theory, production prices can be calculated straightforwardly from physical quantities, the technical coefficients of production and the real wage, without any reference to the labour-value of inputs and outputs.

The advantage of this approach seemed to be, that:
There exists no "transformation problem" of converting values into prices through a quantitative adjustment anymore.
The whole awkward issue of the exploitation of labour is circumvented.
Value theory can be replaced with equilibrium theory to explain prices, since "value" then simply stood for "equilibrium prices" (such as the Smithian or Ricardian "natural prices").
A system of equilibrium prices could be formulated for the critical variables involved in production, to explain price relationships.

At the same time, Marx's theory of the formation of a general rate of profit, and his theory of the TRPF, would no longer be valid. This trend of thought is exactly what happened in leftwing economics, during the second half of the 20th century (see below), although a minority of Marxists – inspired by Isaak Illich Rubin and Roman Rosdolsky – continued to defend Marx's theory of the forms of value (somewhat confusingly, however, many value-form theorists also reject Marx's own value theory, or modify it according to their own taste).

In classical Ricardian economics, the theory of economic value still played an important role, but in neo-Ricardian economics there exists only a theory of prices; the role of "value" is reduced to that of an aggregation principle for price magnitudes, but value not a real determinant of the rate of profit.

Value theory as add-on 
However, there are also Marxists who think that value-theory is still a useful "add-on" to ordinary neo-Ricardian or post-Keynesian price theory, because value-theory penetrates through the "appearances" of commodity fetishism to the "essence" of exploitation as the source of profit. According to this interpretation, price-relationships express the observable (but deceptive) surface appearance of what happens in the economy, while value relationships express the unobservable essence of what happens. Rob Bryer stated that "The majority of Marxists today argue defensively that [Marx] did not intend [his theory of value] to explain prices and rate of return on capital, but gave us only a qualitative theory of capitalist exploitation". Paul Burkett for example claims that "Marx’s primary purpose in Capital ... was not to theorize market prices, but to dig beneath market appearances 'to reveal the economic law of motion of modern society".

In this interpretation, there is no necessary connection between price-relationships and value-relationships, quantitative or otherwise, because the value theory models and the price theory models exist at qualitatively different levels of abstraction (although, in principle, both refer to the same reality). It then follows quite logically, that value theory cannot offer any substantive explanation of price movements (including empirical profits), whether in theory or in reality and that price theory is a completely separate area of concern.

Five main objections are made to the "add-on" approach.

Metaphysics 
With the add-on approach, the theory of value as such becomes an untestable, metaphysical theory: value is a mysterious, hidden entity, that can never be observed in any way, let alone measured, only intuited by pure theory among academic Marxist initiates (or divined by the Central Committee).

Marx himself stated in his manuscript that his analysis of the configurations of capital aimed to "approach step by step the form in which they appear on the surface of society... in competition, and in the everyday consciousness of the agents of production themselves". Evidently Marx then did intend to show the connections of labour-values with the observable price relationships, although he did not write a detailed analysis of the competition process himself. This task was only taken up later by Marxian economists (including Samezō Kuruma, Anwar Shaikh, Willi Semmler and Lefteris Tsoulfidis).

If, as Marx argued in Capital, Volume III, pricing and product-values influence each other, through successive adjustments, his value theory in fact makes no sense at all without reference to prices. It would be like saying, that to understand the economic value of a commodity, its price can be disregarded. Marx claimed no such thing – he merely started off by assuming, for argument's sake, that the price and value of commodities produced were the same. This initial simplifying assumption seemed reasonable enough, since competition would constrain the margins of value/price deviations for the distribution of most commodities – the deviations would ordinarily not be very large (ordinarily, vastly overvalued or undervalued goods could not be sold in a competitive market). Econometric research done from the 1980s onward suggests that this is true.

Eclecticism 
An integral, consistent economic theory becomes impossible with the add-on approach, since market prices, product-values and social relations are always in different baskets. This theoretical eclecticism results in low explanatory power, and low predictive power – there exist multiple different theories and concepts at once, which all can interrelate/combine in all kinds of possible and ad hoc configurations, like a kaleidoscope, and therefore "explain" and "predict" everything and nothing.

When the results of the eclectic analysis appear implausible, the kaleidoscope is twisted slightly, to highlight the perfect geometry of yet another (though similar) "pattern". It means, that there is no clear idea about what the anomalies facing the theories should be attributed to (because they could be all kinds of things), and that no firm conclusions can be drawn from experience (all that happens, is that one theoretical preference is replaced with another flavour, that jells better with the concerns of the day).

Essences 
The add-on approach misunderstands Marx's concepts of value, value-form and price-form, and falsifies the meaning of Marx's distinction between "essence" and "appearance".

According to Marx himself, the "essence" is not some kind of esoteric, mystical "unobservable" kernel. Indeed, he says himself that the essence of the matter is "comprehensible to the popular mind" ["der ordinären Vorstellung geläufig sind"] – it is just that the "real interconnection" of phenomena, the "real story" about how it works, is usually clouded by all kinds of peripheral aspects, irrelevancies, biases, one-sided representations, and distractions. Market phenomena can appear other than they are, and their real significance may not be immediately obvious (beyond occasional glimpses, the essence of the matter becomes perfectly clear, only at particular "crunch" moments, or when the researcher has actually done the real work to dig it out, and put it in context).

If there existed a "world of essences" which were never observable in any way, and always "hidden", it would be impossible to do any science, to find out what the essences are. It would be impossible to get at any essence, ever – analogous to a court of justice which examined case after case, but could never reach any certainty at all about whether any crime was committed or not. That is obviously not what Marx argues. Hegel never argued that either; Hegel's philosophical "doctrine of the essence" is not at all about "esoteric, mysterious hidden mechanisms". Instead, it explains in detail, how "first, essence shines within itself, or is reflection; second, it appears; third, it reveals itself."

Unobservables 
The observable/unobservable distinction being drawn by the add-on approach is simply false – while some prices are observable, others are not (since they are inferred or derived magnitudes, or purely theoretical idealizations), and some prices are a mixture of both actual and assumed magnitudes (combining observations and extrapolations in the same calculation). The naive concept of prices as an "observable surface phenomenon" fails utterly once we understand more about what prices mean (see value-form and real prices and ideal prices).

Unfortunately, Marxist philosophers speculatively invented a "secret world" of "hidden causal mechanisms" beyond "surface appearances", instead of investigating the real world, to understand what the "mechanisms" actually are. In the absence of verification, theorizing spins off in all kinds of directions without any attempt at proofs – because it lacks an empirical, objective explanandum, it becomes unclear what the explanatory purpose of theorizing activity actually is. It could be just a theory about theories, or theory for the sake of theory.

The result is either a postmodern skepticism/timidity about the possibility to know anything, a conspiracy theory, or else an arrogant faith in the power of pure theory to divine the truth about society, through transcendental intuition (without thorough study of the relevant facts). None of these approaches is particularly helpful for scientific research.

Abstractionism 
Talk about "levels of abstraction" by the add-on crowd is vacuous, unless the exact limits of application of the abstractions can be specified clearly. Without such specification, nothing can be tested or substantively contested (logically or empirically). It just remains loose philosophical talk, sophistry or petitio principii, uncommitted to any particular consequence.

Theorizing about capital and labour, Marx certainly engaged in abstraction, but not willy-nilly in some speculative sense. Instead, he critically sifted through what political economists, businessmen, statesmen, factory inspectors, journalists and workers had actually said and done, to develop a new theory that would be rigorous, consistent and durable. He did not make any great claims to originality, and carefully footnoted "who said it first". The theory ended up going far beyond immediate experience, but it was rooted in the stubborn facts of experience, and returned to those facts all the time. It had to explain the observable facts, and also explain why their meaning was construed in specific ways. That was Marx's "science". If Marxists want to cling sentimentally to "value theory" regardless of facts and logic, this cannot be called a "science" - it has more in common with a new age religion.

Okishio's theorem 

The Japanese economist Nobuo Okishio famously argued in 1961, "if the newly introduced technique satisfies the cost criterion [i.e. if it reduces unit costs, given current prices] and the rate of real wage remains constant", then the rate of profit must increase.

Assuming constant real wages, technical change would lower the production cost per unit, thereby raising the innovator's rate of profit. The price of output would fall, and this would cause the other capitalists' costs to fall also. The new (equilibrium) rate of profit would therefore have to rise. By implication, the rate of profit could in that case only fall, if real wages rose in response to higher productivity, squeezing profits.

This theory is sometimes called neo-Ricardian, because David Ricardo also claimed that a fall in the average rate of profit could ordinarily be brought about only by rising wages (one other scenario could be, that foreign competition would drive down the local market prices for outputs, causing falling profits).

At first sight, Okishio's argument makes sense. After all, why would capitalists invest in more efficient production on a larger scale, unless they thought their profits would increase? Orthodox Marxists have responded to this argument in various different ways.

Criticism 
The absence of fixed capital in Okishio's model is rather crucial, because:
fixed capital is usually the largest part of the physical capital outlay.
lowering unit costs long-term typically requires additional fixed investment.
the increase in productivity which new fixed capital makes possible, typically goes along with wage rises.
it is primarily the growth of fixed capital which, in Marx's theory, lowers the profit rate in the long term.

John E. Roemer therefore modified Okishio's model, to include the effect of fixed capital. He concluded though that:

It is also possible to construct an alternative Okishio-type model, in which the rising cost of land rents (or property rents) lowers the industrial rate of profit.

Cycle or long run 
One dispute which has never been finally resolved is whether the TRPF should be interpreted as a cyclical tendency, or as a secular long run trend. Geert Reuten from the University of Amsterdam has argued that there is evidence that Marx originally believed in a long run secular tendency, but that, later on, he changed his position to a cyclical tendency. In contrast to this view, Anwar Shaikh from the New School in New York City argued that Marx meant the TRPF as a secular long run trend; a cyclical tendency and a long-run tendency could also be combined in one theory, where a series of cycles shows a gradual fall in the average rate of profit, although there is an upturn in each cycle.

Following Michael Heinrich, David Harvey criticized Engels's editing of Capital, Volume III, and emphasized in a conference text that Engels himself inserted the sentence "In practice, however, the rate of profit will fall in the long run, as we have already seen." The suggestion is, that in the text preceding Engels's inserted sentence, Marx himself had never said anything about such a long-run falling tendency.

Harvey's view contrasts with Marx's preceding text, in which Marx says that as the capitalist mode of production advances, its general rate of profit must steadily decline, "since the mass of living labour applied continuously declines in relation to the mass of objectified labor [i.e. means of production] that it sets in motion." However, Michael Heinrich argues that Marx in his old age paid no attention anymore to the falling tendency, suggesting it was no longer important to him.

First empirical tests 
In the 1870s, Marx certainly wanted to test his theory of economic crises and profit-making econometrically, but adequate macroeconomic statistical data and mathematical tools did not exist to do so. Such scientific resources began to exist only half a century later.

In 1894, Friedrich Engels did mention the research of the émigré socialist Georg Christian Stiebeling, who compared profit, income, capital and output data in the U.S. census reports of 1870 and 1880, but Engels claimed that Stiebeling explained the results "in a completely false way" (Stiebeling's defence against Engels's criticism included two open letters submitted to the New Yorker Volkszeitung and Die Neue Zeit). Stiebeling's analysis represented "almost certainly the first systematic use of statistical sources in Marxian value theory."

Although Eugen Varga and the young Charles Bettelheim; already studied the topic, and Josef Steindl began to tackle the problem in his 1952 book, the first major empirical analysis of long-term trends in profitability inspired by Marx was a 1957 study by Joseph Gillman. This study, reviewed by Ronald L. Meek and H. D. Dickinson, was extensively criticized by Shane Mage in 1963. Mage's work provided the first sophisticated disaggregate analysis of official national accounts data performed by a Marxist scholar.

Long waves 
Starting off with pioneering work by Ernest Mandel from 1964, various attempts have been made to link the long waves of capitalist development to long-term fluctuations in average profitability. By "long waves" Mandel did not mean "long cycles".

Mandel vs. Grossman 
Mandel's influential Phd thesis Late Capitalism (in German 1972, English version 1975) was a critical response to Henryk Grossman's theory. Like Henryk Grossman, Mandel was convinced of the centrality of profitability in the trajectory of capitalist development, but Mandel (following Rosdolsky's critique of Rosa Luxemburg's theory) did not believe that Marx's reproduction models could be used to create a theory of capitalist crises.

In Grossman's profitability model, there was only a series of business cycles and, sometime after the 34th cycle, a general breakdown of capitalism, because insufficient surplus value was being generated. Leaving aside the issue of the validity of Grossman's model, his picture of capitalist development did not explain historical phases of faster and slower economic growth lasting about 25 years or so. After World War 2, a long boom occurred, instead of a deepening capitalist crisis which many Marxists had expected. That was what Mandel wanted to explain (Mandel's and Grossman's growth models both ignore the accumulation of non-productive capital assets and profits not arising from new surplus-value).

Rowthorn vs. Mandel 
Mandel's interpretation was strongly criticized by Robert Rowthorn. Although Mandel's profit theory was enormously more complex than Grossman's profit theory, this complexity itself became problematic: there were so many interacting "semi-autonomous variables" in Mandel's theory, that observable empirical trends could be attributed to any number of interacting variables; this meant that no particular result necessarily followed from the theory, and that the explanans (that which explains) became confused with the explanandum (that which has to be explained).

Thus, "It is never clear, for example, whether Mandel considers capitalism has an inherent tendency toward overproduction which periodically expresses itself in a falling rate of profit, or whether overproduction itself is caused by a falling rate of profit."

Mandel replied to such criticisms in his 1978 essay "Marxism and the crisis", where he argued this dichotomy does not make sense, because it is based on a false social ontology. Overproduction and overaccumulation were, he argued, inseparable phenomena, and surplus value could not be realized as profit income unless output was sold; consequently the average rate of profit and the rate of market expansion mutually determined each other.

Shaikh vs. Mandel 
Anwar Shaikh argued that Mandel got it wrong, because Mandel saw "evidence of a rise-and-fall in the actual rate of profit causing the long upturn and downturn". According to Shaikh, Mandel's interpretation mixed up the rate of profit with the mass of profit, and ignored the impact of changes in capacity utilization on the rate of profit. Instead, Shaikh argued that "...in Marx's theory of the falling rate of profit, the transition between long-wave phases is correlated with the movements of mass of profit, and not with that of the rate of profit (as in Mandel)". Mandel replied, that Shaikh's own data series showed that an upturn in the average rate of profit occurred at the start of the long boom, in addition to the fall in the average rate of profit toward the end of the boom.

Profits and crises I 
Mandel maintained that falling profits were only one factor in the recurrent sequence from boom to slump. Being a Marxist socialist, he argued that the basic reason why capitalist crises occurred is that capitalism is a system of production run by competing producers, based on private property. In this system, "what is rational from the standpoint of the system as a whole is not rational from the standpoint of each great firm taken separately, and vice versa." According to Mandel, that also explained why bourgeois macroeconomics and microeconomics contained quite different principles and concepts of economic behaviour (in contrast to Marx's economics, where macro and micro share the same concepts).

Thus, in every branch of economic activity, capitalist business could never escape from recurrent problems of overinvestment and underinvestment, which periodically culminated in general crises. Following György Lukács, Mandel portrays capitalist rationality as a "contradictory combination of partial rationality and overall irrationality." It is not that competing businessmen are "irrational", far from it, but that their own "instrumental rationality" and "value rationality" (in a Weberian sense) differ from the functional logic of capitalism as a market system, and, therefore, the two run into serious conflicts at times – leading to crises. Simply put, markets and government policy can work in your favour, but they can also work against you. In a private enterprise system based on competition, when things get to the crunch, it becomes impossible to reconcile self-interest with the general interest, even with mediation by the state. Then there are winners and losers, on a very large scale. During the boom, most people can make some gains, even if the gains are unequal. In a real crisis, the gains of some are at the expense of others - competition intensifies, and often becomes brutal.

In a 1985 article, reprinted as an appendix in the last French edition of Late Capitalism, Mandel tried to defend his interpretation against accusations of vulgar eclecticism. His final view was that "...under capitalism, the fluctuations of the average rate of profit are in a sense the seismograph of what happens in the system as a whole... that formula just refers back to the sum-total of partially independent variables, whose interplay causes the fluctuations of the average rate of profit". The analytical challenge was to verify this interplay empirically, to understand why the long-term ups and downs in the average profit rate occurred.

Underproduction 
In the modern epoch of financialization, the main criticism of Mandel's idea is that over-accumulation can combine with underproduction, if it is safer (or more profitable) to invest in solidly insured non-productive assets (financial assets, stockpiles and real estate). Thus, much less is actually produced than could be produced.

Martin Wolf stated: "the world economy has been generating more savings than businesses wish to use, even at very low interest rates." Joseph Stiglitz similarly argued that from the 1990s onward, banks lent more and more money to investors who mainly did not use it to create new business producing things, but to speculate in already existing assets for capital gain, thereby pushing up asset and property prices.

The general claim made here is that, in the real world (and outside bourgeois propaganda rhetorics), modern Western-style capitalism is not anything like a "risk-taking" capitalism. It is more like a political economy of insurance capitalism, where state insurance, the private insurance industry, the hedging industry, the funds management industry and the burgeoning derivatives markets rake in trillions of dollars per year, just to protect people and assets against all significant risks and losses. Bourgeois sociologists like Ulrich Beck and Anthony Giddens began to refer to the concept of the risk society in a deregulated investor capitalism, where there is big money in talking about risks. The nervous anxiety about risk, critics argue, vastly exceeded the actual risks.

In the underproduction critique, the only real "risk-takers" left in the brave new Western world of "risk-free accumulation" are (1) the workers, peasants and poor people who have to do long hours of hard, hazardous and/or dirty work for a living, for a low wage, often with meagre or non-existent pensions, insurance and healthcare, (2) sundry people who reject or fall outside the rules of the insurance system, or who are connected with criminality, (3) people who do adventure sports and the like.

Although the global insurance apparatus has grown huge, so far there exists no general Marxian theory of risk insurance and its effect on the average rate of profit. It is obvious though, that if one can insure capital against losses at a fairly small cost, the gains may outweigh the costs considerably, raising business certainty, market confidence and profit yields across time – a likely reason why the volume of derivative contracts has continued to grow strongly. However, this point has been disputed after the 2007–2009 financial crash, since the very financial products that were intended to secure capital and profits, ended up creating more insecurity for the global majority (food, housing, jobs, incomes, savings and pensions).

Secular trend 
In defense of the theory that the organic composition of capital does rise in the long term (lowering the average rate of profit), Mandel claimed that there does not exist any branch of industry where wages are a growing proportion of total production costs, as a secular trend. The real trend is the other way: toward semi-automation and full automation which lowers total labor costs in the total capital outlay.

Critics of that idea point to low-wage countries like China, where the long run trend is for average real wages to rise. For example, the Chinese Communist Party aims to double Chinese workers' wages by 2020. Zhang Yu and Zhao Feng provide some relevant data. Minqi Li has compared average profit rates for China, Japan and the USA. Dr. Bin Yu, a member of the Academy of Marxism at the Chinese Academy of Social Sciences (the highest scientific authority on Marxism in China), affirms that the TRPF theory is correct, and that the data prove it. Hao Qi found that profitability in the PRC fell after 2008.

Monopoly profits 
Rosa Luxemburg already stated in her 1899 pamphlet Social Reform or Revolution? that:

In the course of the 20th century, this idea became widely accepted among Marxists - it was taken over e.g. by Nikolai Bukharin,  Rudolf Hilferding and Henryk Grossman. For example, Grossman wrote in his Breakdown book that:

Inspired by Josef Steindl and Baran's earlier work, Paul Baran and Paul Sweezy postulated in their 1966 work Monopoly Capital that there existed a "law of increasing surplus" which counteracted the TRPF within a capitalism that had fundamentally changed. Just after the book was published, the average industrial rate of profit in most advanced capitalist countries began to fall, and continued to fall substantially for about 5–7 years.

The official orthodox Marxist–Leninist theory of state monopoly capitalism ("stamocap") similarly suggested that in the 20th century epoch of the "general crisis of capitalism", the state, its public funds and imperialist exploitation acted as the guarantor and promoter of stable monopoly profits by corporations – counteracting the TRPF. The general thrust of monopoly theories is that profitability does not fall, because the ordinary laws of capitalist market competition are overruled by (1) state intervention, (2) corporate monopolization of resources and markets, and (3) colonial superprofits.

However, Ben Fine and Laurence Harris combined the TRPF with state monopoly capitalism theory at a higher level of abstraction: "[The TRPF] is not a law which predicts actual falls in the rate of profit (in value or price terms)". At an even higher level of abstraction, Michael A.Lebowitz postulated "the inner tendency of Capital to become one". Anwar Shaikh however recently made the case that monopoly capital has never truly existed, since normally speaking business cannot totally monopolize a market, or evade competition altogether; as a logical corollary, business cannot evade the TRPF. Shaikh rejects the idea that bigger enterprises necessarily have higher profit rates than smaller ones.

Also inspired by Josef Steindl's analysis, Ernest Mandel argued (after Rudolf Hilferding) that if corporations monopolizing product markets can evade price competition to a considerable extent, they can also evade the general tendency for differences in profit rates to level out through competition (in the direction of an average rate). Even if monopoly profit rates fell, they would usually remain higher than the profit rates of small and medium-sized firms. The monopolists could raise their prices only within certain limits, beyond which they would attract competitors (including other monopolists) able to supply alternative products at a lower price. Nevertheless, in reality, there existed not one, but two kinds of "average profit rates" in capitalist production: a higher one for corporations in the monopolized sectors of product markets, and a lower one for smaller firms in the non-monopolized sectors. Together with the anarcho-communist Daniel Guérin, Mandel published a survey of economic concentration in the United States.

Post-war boom 
In the 1970s, there were two main debates about profitability among the Western New Left Marxists, one empirical, the other theoretical.

Profit squeeze 
The empirical debate concerned the causes of the break-up of the long postwar boom. Orthodox Marxists like David Yaffe, for example, argued that the cause was the TRPF, while other Marxists (and non-Marxists) argued for a "profit squeeze" theory.

According to the profit squeeze theory, profits fell essentially because, in the course of the long boom, demand for labour grew more and more, so that unemployment reduced to a very low level. This allowed workers to pick and choose their jobs, meaning that employers had to pay extra to attract and keep their staff. The increased labor costs therefore "squeezed" profits. This could be sustained for some time, while markets were still growing, but at the expense of accelerating price inflation. As their input prices and costs increased, business owners raised their own output prices, which fed the inflationary spiral. In the 1970s, employers began to scale back their investments in production, and there was enormous political pressure on the state to curb wage increases and reduce price inflation, bringing the long post-war boom to an end.

Orthodox Marxists however argued that the main cause of falling profits was the rising organic composition of capital, and not wage rises. On this view, the falling average rate of profit on production capital in the end "choked off" the growth of the total mass of profit, leading to a stagnation of business investment and rising unemployment.

Yaffe became quite famous. In a 1980s satire about the British far Left, John Sullivan stated that Yaffe had done "sterling work on the velocity of the falling rate of profit, and has almost got it down to the nearest foot per second." Yaffe claimed that "It is precisely the crisis of profitability that makes a growing state expenditure necessary." This idea was strongly criticized by Ian Gough.

Neo-Ricardianism 
The theoretical New Left debate in the 1970s was a clash  between orthodox Marxists believing in a labor theory of value and neo-Ricardian socialists inspired by Piero Sraffa. The neo-Ricardian socialists, basing themselves on the ideas of Maurice Dobb, Ronald L. Meek, Michio Morishima, and Ian Steedman, believed that Sraffa's models had made Marx's value theory redundant, and that Marx's TRPF theory was mathematically incoherent once it was rigorously modeled. Sraffa's theory was not incompatible with some kind of labor theory of value as such, as several neo-Ricardians emphasized, but it was incompatible with Marx's TRPF. This debate still continues.

The overall Marxist criticism of the neo-Ricardian socialists was, that they treated Marx as if he was a Sraffian. But, they claimed, Marx wasn't a Sraffian, because Marx's concepts were really quite different. The Sraffians believed, that if Marx's theory cannot be restated in a mathematically consistent and measurable way, it has no scientific validity. Since the Marxists allegedly failed to formalize Marx's theory in a convincing way, the Sraffians dropped it, although they might still have socialist sympathies (Sraffa himself admired Marx, and was an avid collector of Marx memorabilia).

Anwar Shaikh among others replied, that regrettably the mathematical formalizations offered by neo-Ricardian theorists to interpret Marx's idea were really more a sleight-of-hand, since, in the process of modelling, highly questionable assumptions were introduced which had nothing to do with Marx. Moreover, one could also use the same mathematical techniques with different assumptions, to compute results that were quite consistent with Marx's theory. On his website, Andrew Kliman adopted the motto: "I ain't going to work on Piero's farm no more."

International Socialists and British Socialist Workers Party interpretation 
In the 1990s, a leader of the British Socialist Workers Party, Chris Harman, advanced a reading of Marx that sees economic crisis as the main effective countervailing factor to the TRPF, but which places limits on its effectiveness as the capitalist system ages and units of capital become larger and more interlinked. However, David Harvey mentions that in the Grundrisse, "Marx lists a variety of other factors that can stabilize the rate of profit 'other than by crises'." Since the 1970s, the International Socialists have staged a theoretical struggle against underconsumptionism, regarded as a reformist ideology, and reaffirmed the TRPF as the true revolutionary theory.

Empirical studies 
Since the theoretical disputes failed to clinch the argument, more scholars raised the question of whether the theory of the falling rate of profit corresponded to the facts. They wanted to "count the horse's teeth" empirically, to shed light on the issue.

In the United States, pioneering empirical research on the average rate of profit was published from 1979 onward by Edward N. Wolff and Thomas Weisskopf, followed by Anwar Shaikh. After some articles, Fred Moseley also published a booklength analysis of the falling rate of profit. Wolff and Moseley together edited an international study.

In the 1980s, the Italian scholar Angelo Reati, who worked for the European Commission in Brussels and who tried to combine Marxian, neo-Ricardian and Post-Keynesian approaches, analyzed industrial profitability data for Italy, the UK, France, and Germany. This resulted in a series of papers, and a book in French. Gérard Duménil, Mark Glick and José Rangeĺ studied the empirical tendency of the rate of profit to fall in the United States using a variety of sources.

An important econometric work, Measuring the Wealth of Nations, was published by Anwar Shaikh and Ertuğrul Ahmet Tonak in 1994. This work sought to reaggregate the components of official gross output measures and capital stocks rigorously, to approximate Marxian categories, using some new techniques, including input-output measures of direct and indirect labor, and capacity utilization adjustments. Shaikh and Tonak argued that the falling rate of profit is not a short-term trend of the business cycle, but a long-term historical trend. According to their calculations, the Marxian rate of profit on production capital fell throughout most of the long boom of 1947–1973, despite an enormous expansion of the volume (mass) of profit.

The celebrated New Left historian Robert Brenner from California has also attempted to provide an explanation of the postwar boom and its aftermath in terms of profitability trends. Brenner's interpretation was heavily criticized by Anwar Shaikh, who argued that it is not really credible from an econometric or theoretical point of view. According to Shaikh, Brenner had an inflated view of American factories, to the point where Brenner believed that the profitability of US manufacturing determined the destiny of the whole world economy. In reality, US factory production wasn't that big.

A lot of detailed work on long run profit trends was done by the French Marxist researchers Gerard Duménil and Dominique Lévy.

In Britain, the Oxford group around Andrew Glyn used mainly OECD-based profitability data to analyze longterm trends.

Prof. Lefteris Tsoulfidis, based at the University of Macedonia, has participated in a lot of sophisticated empirical research on profitability.

This type of research was replicated by Marxian scholars in many other countries around the world, who often introduced their own technical refinements in the data sets.

Theoretical works 
In the course of the 1990s, many leftist academics lost interest in Sraffian economics. Although he had written a few articles and edited the collected works of David Ricardo, Sraffa had authored only one book himself, a neo-Ricardian analysis about the distribution of value-added from production among workers and capitalists (Sraffa calls net value-added the "surplus"). While Sraffa had provided an alternative to the problematic labor theory of value of the orthodox Marxists, while undermining the marginalist theory of capital, Sraffa's book provided no answers to many important contemporary macroeconomic issues. It was not designed for that purpose. For example, "The Sraffa system, like many stationary-state general equilibrium models, contains no good which, uniquely, possesses all the important features of money."

Michał Kalecki 
Instead, many Marxists and leftists became more focused on the political economy of Michał Kalecki, who tried to combine Marxian and Keynesian economics in a more realistic way, without relying on any labor theory of value. Kalecki also believed in a cyclical tendency for profits to fall, but more as a result of the changing balance of power between the working class and the capitalist class, or changes in capital intensity.

Stephen Cullenberg 
In 1994, Stephen Cullenberg published a book on the falling rate of profit which reviewed the whole controversy to date (with special attention to Okishio's Theorem).

Temporal single-system interpretation 

Reviving and developing ideas first mooted in the 1980s, proponents of the temporal single-system interpretation (TSSI) such as Andrew Kliman, Alan Freeman, Paolo Giussani and Guglielmo Carchedi have argued from the 1990s onward that the arguments by von Böhm-Bawerk, Bortkiewicz, and Okishio do not refute Marx's case.

Kliman argues in Reclaiming Marx's Capital (2007) that the apparent inconsistency of Marx's case arises out of a misreading of Marx through the prism of general equilibrium theory and double-entry accounting.

Once the operations of capitalist production are interpreted as "temporal and sequential" (as opposed to a "simultaneist" model where inputs and outputs are valued simultaneously, so that total input and total output valuations are always exactly equal) and "single-system" (where values and prices always co-exist, and are co-dependent, not separate systems), it is argued that the transformation problem disappears, and that the TRPF can no longer be dismissed on logical grounds.

Criticism of TSSI 
The modern TSSI approach has been criticized by other Marxist and neo-Ricardian scholars including Gérard Duménil, Duncan K. Foley, Michel Husson, David Laibman, Dominique Lévy, Simon Mohun, Gary Mongiovi, Ernesto Screpanti, Ajit Sinha, and Roberto Veneziani.

The TSSI's rival school is called "The New Solution" or "New Interpretation" school which was founded in the early 1980s by Alain Lipietz, Duncan Foley and Gérard Duménil. The main idea of these critics is, that if equilibrium is let go of, then capitalism is an unpredictable chaos, and no coherent theory of prices or profits is possible anymore.

Equilibrium concepts 
The reply of TSSI sympathizers is, basically, that the concept of equilibrium itself is confused with (1) the concept of continual (and haphazard) market adjustment, and (2) the concept of socio-economic stability. This happens because, tacitly, “the market” is conflated with “the economy” and with “society as a whole”. Supply and demand may continually adjust to each other without ever being in equilibrium, other than momentary coincidences, and the lack of a perfect match between supply and demand does not necessarily prevent social stability, as long as enough workers turn up for work each working day to produce more capital.

Capitalist equilibrium means "business as usual" for capitalists, and "back to work" for workers. But "business as usual" does not mean market balance. Disequilibrium is precisely the life of the market, and equilibrium is the life that the market observably doesn't have. There is always some branch of activity in a capitalist economy which is experiencing a crisis, but whether the crisis will spread or not, will depend on the conjuncture and on how different business entities are linked to each other.

Marx himself had never argued that capitalist society is "held together" or "balanced out" by the market; instead, what held society together was the relations of production, i.e. the mutual dependencies arising out of the necessity to produce and reproduce human life co-operatively, within the framework of a system of property rights enforced by the state. Thus, a consistent Marxian theory of prices and profits is claimed to be possible, without assuming that the market, the economy or the society spontaneously gravitate to an "equilibrium state" of economic harmony through the "price mechanism". In this view, the idea of equilibrium is itself poorly conceptualized by economists, and given a magical, arcane power which it does not really have, once we understand the conjuror's trick.

Riccardo Bellofiore 
In 1997, the Italian Marxian economist Riccardo Bellofiore released an edited volume of essays by leading Marxist scholars on Capital, Volume III which reappraised Marx's text in the light of the previous criticisms. Bellofiore also helped to revive interest in the profit theories of Hyman Minsky, which briefly became popular again in the 2007–2009 crisis. The crisis was called a "Minsky moment".

Debt and profitability 
Increasingly leading Marxist and semi-Marxist scholars began to focus on the importance of debt-driven accumulation for the average rate of profit. In the 1980s and 1990s, governments forced interest rates and inflation rates down to a very low level, and began to deregulate capital markets. They expected that new business investment would take off, and that unemployment problems would disappear.

To an extent that was true, in the shorter term – although real wages did not increase much anymore. The long-term structural effect was skyrocketing private debt. People borrowed more and more cheap money, either to finance consumption, or reinvest it for extra profit in financial assets, corporate takeovers, stockpiles and real estate. That was often easier, more profitable and less risky, than investing in new production. People could live now, and pay later, with the option of withdrawing their capital at pretty short notice.

The average debt-load per capita and per household grew strongly. Financial profits mostly grew faster than industrial profits, across the whole world. So, more and more generic profit income took the form of interest, rents and capital gains. David Harvey stated that "the connection between profit of enterprise and the interest rate is now very strong". These trends led to a new academic discourse about "financialization".

In the short term, the economic results of leveraged accumulation were financial “bubbles”, that burst after a while (overvalued assets are suddenly devalued in a downturn, often prompting recessions or depressions). In poorer countries, the financial crashes were often linked to currency and exchange-rate crises (when the local currency was devalued, repayments of debts denominated in foreign currencies could no longer be made – see e.g. Latin American debt crisis, Mexican peso crisis, 1997 Asian financial crisis). For the period 1970–2011, IMF researchers identified 147 systemic banking crises in the world, 211 currency crises and 55 sovereign debt crises.
The long-term consequence is, that the total private debt of countries (and sometimes also public debt) grows faster than the total income that has to pay off the debt (countries tend to become "debt zombies"). To make up the shortfall, "somebody" has to pay, sooner or later. That increases socio-economic inequality globally, because the people who pay, are those who can least avoid paying (they cannot escape from paying tax and from the effects of budget cuts, they cannot contract new debt, to pay off old debt etc.).
The more debt there is in the business world, the more financial pressure exists, to increase yield in any way possible, to be able to keep paying off liabilities, stakeholders and other claimants. It is no longer just that a healthy profit rate is desirable, but that reaching a certain profit rate becomes a mandatory requirement, to pay creditors.
It became possible, within the framework of tax law, for an increasing number of companies to be formed that generated plenty of income, although technically (in accounting terms) they operated at a loss.
This situation reaches its limit at some point, when it takes very little to cause (1) serious cash-flow problems, (2) very large asset sell-offs, (3) a freeze of investment activity and (4) a sharp drop in market confidence and sales. It creates the permanent risk of large credit defaults, banking crises and financial panics, which can trigger a severe global slump. The slump goes global, because all the world's financial markets (stocks, securities, currency, investment capital, real estate, derivatives etc.) are interconnected. If, for example, U.S. stock market activity plunges, stock markets around the world all react within a day (or, in some cases, within a matter of hours).

21st century Marxist controversies 
Globalization and financialization have changed the way capitalism operates in the 21st century, and that has raised new points for debate about the rate of profit which had been overlooked, or regarded as less significant, in the 20th century. According to the orthodox Marxist economist Costas Lapavitsas, financial profit is distinct from normal capitalist profit. Nasser Saber states that "Finance is a specialized branch of economics precisely because the movement of securities prices is separate from (albeit not unrelated to) the dynamics of the physical capital." By 2007, the US financial sector was said to be generating more than 40% of US corporate profits.

Production capital/total capital 
One issue concerns the relationship between the real economy (producing goods and services) and the financial economy (trading assets). Peculiarly, most workers work in the real economy, yet the financial sector has gained enormous economic and political power. Some argue, like Marx did, that the tendency of the rate of profit to fall applies only to the sphere of the capitalist industrial production of commodities, not to the whole capitalist economy. Thus, it is argued, it is eminently possible that while industrial profitability stagnates, average profitability in activities external to the sphere of industrial production increases.

Financialization 
In fact, Michael Hudson claims that in the United States, only about a quarter of workers' gross wages is spent on the direct purchase of actual goods and services. All the rest is spent on the payment of rents and mortgages, retirement schemes and insurance, loans and interest, and various taxes. Costas Lapavitsas adds to this insight that not just household liabilities, but also household assets have to be looked at: the richest 20% of the world's workers have substantial deposits and savings invested with banks and retirement funds, so that, on both sides of the ledger, they become fully dependent on finance capital. Since labor incomes rose strongly in rich countries along with population growth in the second half of the 20th century, very large savings became available in retirement funds, representing an additional source of capital invested for profit worldwide and increasing the economic power of the finance industry.

In 2008, the world's total tradeable financial assets (stocks, debt securities and bank deposits) were estimated at $178 trillion, more than three times the value of what the whole world produces in a year. In June 2017, the world's total public and private debt was estimated at US$217 trillion, again more than three times the value of what the whole world produces in a year. If one assumes a grand-average net profit rate of 5% on this global debt, the profit made from global debt is roughly equal in value to the GDP of China. This has created a world in industrialized countries that is very different from the orthodox classical revolutionary Marxist analysis of the commodity, where workers simply exchange their commodity labor power for a wage to buy a bundle of consumable commodities with.

The accounting category of "gross output" suggests the production of things but, in reality, the major part of it nowadays refers to the value of "services" which often maintain, distribute or increase holdings of already existing assets, local or imported. This is especially true of developed capitalist economies. Investment in production is, according to Marx, one mode of capital accumulation, but not the only one. Accumulating capital could be as simple as buying currency and subsequently selling it at a higher exchange rate (which happens on a grand scale nowadays – see: Foreign exchange market). Thus, even if the growth rate of industrial production slows or stagnates, asset and property sales may boom. Within certain limits, the income generated by an asset boom may indeed stimulate additional demand in particular sectors, until the boom collapses.

Factory focus 
In advanced capitalist societies such as the United States, the stock of constant capital applied in private sector productive activities represents only about 20–30% of the value of the total physical capital stock, and perhaps 10–12% of total capital assets owned, and therefore it is unlikely that a fall in the industrial rate of profit could by itself explain economic crises. Marxists ignored this reality, because they tacitly assumed in their economic model that the economy consists just of factories, and that Marx's analysis of the capitalist mode of production was a complete analysis of the whole economy, which is not true.
The famous Marxist scholar David Harvey claims that "Money, land, real estate and plant and equipment that are not being used productively are not capital".
In his original 2001 Phd thesis in economics, the leading Dutch Marxist Robert Went borrows an idea from Christian Palloix, and transplants the categories of Capital, Volume II summarily to the whole world economy. Went claims that there exist only three circuits of capital (commodity capital, money capital and production capital), even although, according to Marx himself, these circuits refer only to the capitalist mode of production.
In Japan, Kozo Uno equated Marx's theory of the capitalist mode of production with the theory of capitalist society.
Murray Bookchin states that "Marxism’s economic insights belonged to an era of emerging factory capitalism in the nineteenth century."

Marxists also assumed that earnings from production must be either spent on consumption or reinvested in production, but that is in reality not the case.  Modern financial capitalism has put into question traditional models of causal chains in the economy. The main reason for that is, that there now exists a large amount of capital in rich countries that is not invested in production, yet strongly influences the developmental pattern of production and consumption.

Total assets 
In Capital, Volume I, Marx analyzed the direct production process of capital: the activities which create new commodities sold for profit. But when he analyzes the circulation and reproduction of capital in the second volume, he begins to develop the category of society's total capital. Initially, he refers rather loosely to gesellschaftliches  Kapital (social capital), Gesellschaftskapital (society's capital), and gesellschaftliches  Gesamtkapital (society's aggregate capital) as interchangeable terms. In the third volume, the concept of the total capital of society is developed further, as it becomes apparent that there exist all kinds of capital funds and assets in society which are not directly related to production.

Marx never completed his story with an analysis of the credit system as a whole, the real estate market, international trade, civil society and public finance; his work was very much unfinished. Yet in a mature, developed capitalist society, such as it exists a century and a half after Marx's studies, it is typical that more capital assets exist outside private capitalist production than are invested inside it (excluding "human capital", a concept which Marx rejected). That is the end result of centuries of capital accumulation, mechanization, state-building, and restructuring business operations.

More empirical studies 
A new development in the early 21st century was the attempt to compute the trend in a "world rate of profit" by Minqi Li and other Chinese researchers. Michael Roberts subsequently tabled his own "world rate of profit" trend estimates in 2012, arguing that the data supports the TRPF. Roberts claims that the United Kingdom experienced a secular decline of the average rate of profit on capital since 1855, confirming Marx's hypothesis.

In 2007, John Bradford reassessed the theory of the TRPF, and computed the trends for US manufacturing and non-financials for 1930 to 2005.

Basu et al. (2012) reported evidence of a falling U.S. profit rate at about 0.3% a year on average for 1948–2007.

Basu et al. (2013) noted there is no "general theory" of capitalist crisis, and that the correct measurement and true economic role of profitability are still disputed.

In a 2014 Swedish thesis, Kalogerakos applies multivariate cointegration analysis to U.S. manufacturing data 1948–2011, to analyze the relationships between the profit rate, capital intensity, real wages, labour productivity and the unemployment rate. A secular declining trend in the rate of profit was not confirmed.

Elveren and Hsu (2015) report that some scholars argue for a secular long-run TRPF, others argue against it, and still others say that no secular trend exists either way. They examined the effect of military expenditure on profit rates in 1963–2008 for 24 OECD countries, and found a positive effect throughout the period, but also negative impacts after 1980. There are differences in impact between arms-exporting countries and non-exporting countries.

For Germany, Thomas Weiß (2015) reported that the average profit rate fell after 1959, and stabilized from 1982 at a level similar to that in the 19th century. He reports that all German enterprises together now invest 60% of their capital in financial assets, as against 40% in 1970.

Ivan Trofimov (2017) finds diverse patterns in profit rates in different groups of developed countries, suggesting that a universal law governing profit rates is unlikely, and that just one hypothesis cannot explain all the data.

Resende (2018) found no systematic evidence for a falling tendency in the U.S. rate of profit.

So far, there does not exist any study yet, which collates and compares all the analyses of empirical profitability trends that have been done internationally.

Profit statistics 
Much more is known nowadays about the trends in empirical measures of profitability. Hence, the econometric discussions are becoming more technical, focusing more on the validity of the underlying concepts, and on issues of data quality and the reliability of measures.

P/C ratio 
Simon Mohun states that the rate of profit is "most easily measured as the proportion of net output not returned as wages to the aggregate fixed capital stock" and that it is this rate of profit that is "generally used in empirical work". If the growth of the gross profit component of value-added (P) is statistically compared with the growth of the estimated fixed capital stock plus inventory holdings (C), it is certainly true that almost all measures will show that the ratio P/C does drop over time. The real value of the physical capital stock appears to grow faster in real terms than the real value of the operating surplus associated with that physical stock, in the long run.

The same effect persists even when various different depreciation techniques are used. The data trend is analogous to a rising tendency of the capital coefficient (referring to the capital/output ratio), where in the course of time more and more capital is required to obtain each additional increase in output. The profit rate rises again, only after a major crisis or a war which destroys a sufficiently large amount of capital value, raises the rate of surplus value, and clears the way for new production techniques.

Business profit 
However, it is a simple accounting error to think, that:
the gross profit share of value-added is equal to true business profit,
constant capital invested in physical assets (fixed equipment and inventories) represents the only capital that an enterprise owns, other than a fund to pay wages.
profits from product sales are the only net income the corporation has.
Almost any corporate account can show that such hypotheses are false.

If an enterprise borrows or leases capital for production, rather than investing its own equity, this affects the total cost of enterprise capital that is tied up at any particular time. How the profitability of capital is accounted for, depends very much on who owns the capital, as distinct from who borrows it, or who uses it. So the rate of profit concept which Marx uses in his theoretical analysis of capitalist production (i.e. S/(C+V)) differs from the actual business concept of the rate of profit, because it disregards all sorts of financial and ownership issues, and because it concerns only part of the total circuit of capital. Marx's concept expresses the relationship between the value of labour payments, physical capital costs, and the value of surplus labour, which is not the same as the financial profitability of a company (although the two are related).

While orthodox classical revolutionary Marxist academics are convinced that the statistical data show that profitability is falling, businessmen can often happily see their profits grow anyway, and they have more real money in the bank. In theory they should have less money, but in practice they have more. That is because financial relationships between quantities of money (financial flows defined using a currency unit) can vary from the value proportions that exist between products or physical assets (defined in terms of the MELT, i.e. the monetary equivalent of labor time). A simple example of this is share repurchase.

Value added 
If there is a significant drop in overall profitability, this will very likely also be reflected in data about the profit included in value-added, but that is only a rough indicator of the trend – the data quality may not be very great. Official statistics include in value-added only the netted value of new production (the net output); if a business makes money simply from selling an asset it has, or from asset appreciation, this is not normally considered "value-added", but property income.  If that was not the case, then any kind of business income (or just about any kind of income) would represent value-added. It does not.

The original designers of gross product accounts (such as Simon Kuznets, Colin Clark, Edward Fulton Denison and Richard Stone) aimed precisely to exclude any capital gains (or other income from asset transactions and revaluations) from their measure of gross output, just like transfer payments. They wanted a reliable standard measure that would indicate changes in the value of the net new addition to wealth per year or per quarter: roughly, the total sales revenue from production less intermediate costs, or, the value of total outputs produced less the value of goods and services used up to produce them, or, the sum of factor incomes directly generated by production. The original meaning of the statistical measure "capital formation" was the real increase in the physical capital stock.

The issue then is, how exactly the grossing and netting must be done to obtain the value of total output, or the net addition to the value of the total capital stock, and it is done in a different way than business itself would do it (to eliminate non-production income/expenditure, ensure uniform valuation, and remove double counting; from the point of view of national accounts, in fact real credits can become theoretical debits, and real debits can become theoretical credits).

Econometric issues 
Normally, true gross profit is larger than the profit component of value-added shown in official statistics, because true profit typically contains net property income, part of corporate officer's earnings and part of the depreciation write-off. The logical possibility exists that although the profit rate can indeed fall, if aggregate profit is measured only as the profit component of value-added, in reality it does not fall, or not as much, for various reasons. Sixteen aspects could be mentioned, the typical result of which is that the growth of the profit volume is underestimated, and that the growth of the capital stock is exaggerated. The data effect is, that the overall profit rate seems to fall, although in reality it does not fall, or not nearly as much.

Property income 
Organizations increasingly make money from trading in already existing assets which are not used by them to produce any new products and services with. Put differently, an increasing share of total generic profit income consists of net interest, net taxes, net capital gains, fees and royalties and rents.

This can happen because a lot of non-productive assets have been accumulated that are available for trade; second-hand physical assets, financial assets and properties are being traded; all sorts of things are traded internationally, taking advantage of currency and cost differentials; assets are being held via all kinds of special financial constructions to extract profit, etc. And, an increasing amount of interest payments, rents and capital gains have been excluded from operating surplus because, by statistical definition, they are not classified as production expenditure at all (i.e. they are not counted as value-added).

Post-Keynesian researchers such as Wynne Godley and Marc Lavoie therefore tried to devise more adequate measures of the real financial profitability of companies. If a lot of capital is borrowed at a cost which is lower than the income obtained from reinvesting it in assets that appreciate in value, then a lot of profit income is earnt which has nothing directly to do with creating new product value, and therefore is in principle not counted as value-added. Instead, existing wealth is transferred from one set of owners to another.

Write-offs 
Generous depreciation write-off provisions or depletion allowances are in reality pure profit, or are at least partly a de facto profit component. The government may give tax incentives, provide guaranteed minimum prices, various economic subsidies etc.

The statistical concept of "economic depreciation" (consumption of fixed capital) diverges considerably from actual depreciation – economic depreciation is only an imputation, and is not directly derived from real gross revenue.

If the total actual write-off is larger than economic depreciation, for example because of tax incentives for new fixed investment, it is likely that a component of profit income is being ignored in the statistical measure (there exists no other way to verify what the value of total net output is, than adding together the various components of factor income/expenditure).

Fixed assets 
Nobody knows for sure what the true value of the total physical capital stock is, because all statistical estimates of that value involve theoretical extrapolations, with a margin of error which remains unknown unless very detailed and comprehensive surveys are done. What a fixed asset is worth becomes apparent only upon sale, yet even then assets may be sold above or below their true value – an important reason why statisticians adjust depreciation rates retrospectively and use price deflators.

Even where detailed information is available, however, assessments of what an asset is worth still depend on the valuation criteria used. Those criteria often differ from the actual criteria used by business, since they must conform to a standard statistical definition for measurement comparisons.

Transfer costs 
When government statisticians compile gross fixed capital formation (GFCF) figures, they usually add in "ownership transfer costs" (fees, taxes, charges, insurance costs, installation costs etc.) associated with the acquisition of a fixed asset put in place. In the United States, these costs represent around 1% of GDP, or around 4.5% of total fixed investment.

This inclusion may be perfectly valid for the purpose of a realistic gross investment measure, but when GFCF data is subsequently used to extrapolate the value of fixed capital stocks using the PIM (the perpetual inventory method), it includes elements which are, strictly speaking, not part of the value of fixed assets themselves. It appears "as if" ownership transfer costs are incurred and depreciated each year in the lifetime of fixed assets, since the value of these costs is carried forward in the perpetual inventory (unless a special adjustment is made). This has the effect of raising the fixed capital stock estimate above true value, cumulatively.

Scrap value 
The British researchers Richard Harris & Stephen Drinkwater also highlighted the problem that the PIM does not account for premature scrapping (meaning that fixed assets are got rid of, well before they are totally depreciated). The reason is that a constant depreciation rate (based on average asset lives) is applied for the stock; a discrepancy therefore arises between depreciated value and scrap value (often statisticians also fail to track what happens to fixed assets that are got rid of, and therefore the assets can be counted twice in the same year).

The mathematical problem is that, given a constant depreciation rate, the effect of overstated stock values in the data will increase cumulatively across a series of years, unless a special adjustment is made. Thus, Harris & Drinkwater's 2000 study of fixed capital in British manufacturing 1970–1993 (23 years) found that, if the effect of capital scrapping which occurs due to plant closures is ignored from the 1969 benchmark onward, then this will lead to a 1993 capital stock estimate for plant and machinery which is 44% larger, than it would be when an appropriate adjustment is made for premature asset disposals.

Another depreciation measurement problem is the accelerating replacement of fixed assets, particularly of computer systems, affecting estimated asset lives and therefore average depreciation rates. These two factors alone could, according to a 1997 OECD paper, make a difference of 10% to the estimate of the annual capital stock for some UK industries.

Dutch and French statisticians suggested that if capital scrapping is ignored, capital stock results obtained with the PIM could be up to 20% larger than they probably are. New Zealand statisticians acknowledge explicitly that "PIMs may typically overstate the gross capital stock because of a failure to account for changing cyclical or accelerating rates of retirements".

Although he is not a Marxist, Thomas Piketty usefully discusses many problems with the PIM. Unlike orthodox classical revolutionary Marxist academics, Piketty and Zucman did not use the PIM method to get a measure of the capital stock, but instead used book values and corporate equity at market value.

Profit sharing 

Remuneration packages for corporate officers, including stock options and profit-sharing, have been included under "compensation of employees" as a labor cost, rather than being included in gross profit. This fact is particularly important in the United States, because the incomes of corporate officers are often very large.

The idea of supersized CEO pay has been disputed by the American Enterprise Institute who claim that the "average" CEO pay, according to BLS statistics, is more like US$220,000; only "a handful" would earn more than that. 
It is certainly true, as indicated by BLS data, that many CEO's do not earn supersized salaries.
Statistically, however, the value of median CEO pay which BLS cites, is just six and a half percentage points below the mean amount, suggesting there's "more than a handful" involved here.
The BLS numbers include only gross salary earned, for ordinary employee hours worked by CEO's (in total, around US$46 billion a year), and not the total income CEO's have in their position (as indicated by IRS and household survey data), including profits and capital gains. 
The BLS measure excludes all overtime, severance pay, non-production bonuses, supplementary benefits and training grants. 
The AEI's own numbers refer only to grand averages of normal, pre-tax work salary, and abstract from all disparities in the real distribution of net personal incomes.

Land sales 
Profit income from ordinary land sales is excluded from official value-added, since land is not considered to be a "produced asset". (see gross fixed capital formation). Included in capital formation is only the value of certain land improvements which are excluded from investments in building & construction (land clearing, land reclamation, land drainage, irrigation works, flood barriers, contouring, creation of wells and watering holes etc.).

So if a business makes money from land sales, the profit is in principle not counted in output measures because nothing is being  "produced" (except possibly the "factor income" of supplied services). Official fixed capital aggregates exclude the value of land, and no very reliable official estimates exist for the value of land, because of problems with credibly valuing land in a standard way for measurement purposes. If the world market prices for primary products rise, profit rates on land sales and commercial land values will increase; even if the number of land sales stays constant, the profit on land sales will increase.

Mary Taylor states that "What is new all around the world... is that huge financial investors and huge agro-industries began to create join ventures to invest in land as a financial asset on its own. That had never happened before. .. buying cheap land, waiting for the price to climb, and then selling it with "profit" (the conceptual term would be "financial rent")". Yet, reliable data on the profits from land transactions are very scarce – partly because they are conceptually excluded from the statistical definition of value-added and capital formation, and partly because even if the value of land sales is known, it is difficult to ascertain what exactly the net profit on those sales would have been (after purchase and before sale, the landowner may have maintenance costs, improvement costs and taxes to pay, as well as revenue from the use of the land).

Asset valuation 

All sorts of differences occur in asset and stock valuation practices used by business (historic cost, current replacement value, current sale value etc.) affecting fair value and GAAP-based accounting (among many other issues, if the profitability of a capital asset falls, the market value of the capital asset itself will fall as well, in response – irrespective of whether it is a physical asset or a financial asset, and irrespective of its acquisition cost; this reduces the fall of the profit rate).

The valuations made are themselves influenced by the way price inflation is actually calculated using price indexes. Jochen Hartwig found that the divergence in growth rates of real GDP between the U.S. and the EU since 1997 "can be explained almost entirely in terms of changes to deflation methods that have been introduced in the U.S. after 1997, but not – or only to a very limited extent – in Europe". See further real prices and ideal prices.

Tax dodging 
Tax-dodging techniques of various kinds, reducing reported profit income and the reported value of sales, altering cashflows or exaggerating costs (legal constructions, creative accounting techniques, offshoring, tax havens etc. - see Tax evasion, Tax avoidance and Tax noncompliance). If tax data are used as a basis for statistical estimates, the reported amounts only reflect legal (fiscal) requirements and may well differ from the real situation. In 2012, a G20 meeting set up the Base Erosion and Profit Shifting (BEPS) project to combat global tax evasion, under the auspices of the OECD.

In July 2018, Thomas Tørsløv, Ludvig Wier and Gabriel Zucman tabled their working paper "The missing profits of nations", which computes empirical estimates to show how "profit shifting" reduces official profit figures. A comprehensive data appendix and slide show is included (see further The Hidden Wealth of Nations). Zucman et al. estimate that "close to 40%" of the profits of multinational corporations are shifted to tax havens. Ludvig Wier & Hayley Reynolds said in December 2018 that the OECD's official estimate of profit shifting is likely to be "dramatically underestimated".

Financial techniques 
The use of (1) credit instruments, (2) capital insurance (derivatives) to protect capital value, and (3) various legal constructions that split out the ownership, control, financing, management and use of capital. This allows the costs, sales and profits to be arranged in ways more favourable to the enterprise or corporate group – often using various different business entities located in different countries.

Statistical accuracy 
Statistical inclusions and exclusions, and survey accuracy problems can cause true profit to be underestimated. The biggest sources of error, at base level, are (1) improper revenue recognition, and (2) overstating assets (or capitalization of expenses). In principle, in the gross product account, only those profits are counted, which are considered to represent value-added.

Qualitative change 
The problem with long-run time series for price aggregates is, that they often disregard many qualitative changes in the components of those aggregates, or, it is assumed that these qualitative changes have no real quantitative significance for comparative purposes. A variable is thought to stay qualitatively the same across time, when in reality it does not remain the same.

Michael Perelman shows that the content and economic meaning of capital aggregates can change considerably even within one decade or so. For example, the changing stratification of physical capital assets in the total capital stock, in terms of their age, exerts an independent influence on the productivity and profitability of enterprises.
Stephen Cullenberg says that "profit is typically modeled as a homogeneous concept across time and space" – it is wrongly assumed that "changes in the amount of the rate of profit will uniformly impact all firms and decision-makers in the economy", disregarding different institutional frameworks, tax laws, accounting protocols and time horizons.
Anwar Shaikh showed, that even if a capital holding in industry stays constant from time t onward, it can in principle generate more profit at t+1, exclusively because the capacity utilization rate rises. During the upturns, higher capacity utilization raises profit rates even higher (more sales in less time, for the same capital holding), and during downturns, lower utilization depresses profits on capital extra (capital tied up in plant & equipment is used less, or is idle more often). To understand the real long-run trend in average profit per unit of production capital (and what causes that trend), the historical data series for that profit rate therefore ought to be adjusted for changes in the capacity utilization rate across time (for which Shaikh constructed special indexes).

Data quality 
In general, the orthodox revolutionary classical Marxist data constructs, based on value-added statistics and the PIM method, lack the scientific accuracy and reliability required to prove whether very long-run trends in profitability are up or down. This is due mainly to important changes occurring across time in:
tax regimes;
accounting rules;
survey, classification and estimation procedures;
technological innovation, social relations and the division of labour;
commercial practices and the legal structure of companies/institutions;
price indexation and price deflation methods.
As economic historians and statisticians know, it is very difficult, or even impossible, to construct fully consistent series for price variables across 100 or 150 years – at most, the series can reveal some likely trends, up or down, or give an indication of the broad proportions involved.

So at best, the data offer an accurate indicator of short-term trends (5–7 years). For example, no economist on record has ever denied that between 1967 and 1973 the average rate of profit fell in the OECD area, but there has been dispute about how much it fell, and why.

Michael Perelman concluded that "Although empirical work is undeniably important, we should be more modest in the way we regard it. Quantitative analysis should drop any pretense of exactness".

Multiple rates 
Empirical Marxists have rarely analyzed the differences between true business profit and statistical profit figures, but the empirical arguments about profitability among empirical Marxists have to deal with five ideas: 

These five ideas turn out to be discrete variables, but the profit rate will go up or down, depending on the choice of measure. Stephen Cullenberg states "as any business person knows, there is no single uniform definition of profit, but rather an array of measures of returns on investment (ROI), profit rates, and so on." Andrew Kliman states in his book The Failure of Capitalist Production that "I believe that there are many different legitimate ways of measuring rates of profit, and that none serves as an all-purpose measure. The most relevant rate of profit to consider always depends upon the particular question being addressed." This pluralist approach provides plenty possibilities for all kinds of different interpretations of all kinds of profit rates, depending on what the question is thought to be, to which a profit rate is supposed to be the answer. To figure out what is going on, a great variety of measures need to be collated and compared (which is also what business analysts do).

Archaic accounting 
The traditional hurdles in interpreting the statistical rate of profit were mainly that: 
About half of all adults in advanced capitalist societies like Britain only have numeracy skills at the level of an 11-year-old child.
Most academics and journalists criticizing GDP have no idea what it means, how it is measured, what the theory and history behind it is, and what it is good for (if people want to replace the GDP measure with something else, they ought to know at least what they are replacing).
Among economic researchers "there is a worldwide illiteracy in national accounting."

The additional problem today is that, because the structure of modern capitalism is now different from half a century ago, a macroeconomics based on the traditional national accounting concepts can no longer credibly represent economic activity. Although the financial industry now dominates capital flows in the world economy, US government statisticians admit frankly that "Unfortunately, the finance sector is one of the more poorly measured sectors in national accounts".

Radical economists point out, that a considerable portion of incomes and expenditures is not captured by the GDP concept, because it falls outside the defined production boundary, while incomes/expenditures within the production boundary are allocated to categories which are substantially misleading.

Not only are GDP data frequently revised after first publication, but the popular idea that GDP equals "the whole economy" is a fallacy. It is a fallacy, not just because intermediate items, transfers and net factor income from abroad are excluded, but also because more domestic assets, incomes, transfers and spending exist beyond the defined "production" boundary for Gross Output (including, importantly, activities of government, financial institutions/companies, and households).

A gross product account for a nation (in which GDP is an entry) is an account of factor incomes and factor expenditures generated by production. It is not (as Thomas Piketty highlighted) an account of the total capital assets of a nation, that shows what happens with those assets, nor an account of the distribution of all the nation's incomes. When journalists equate GDP with "the whole economy", this is not only false; it also hides half of what is going on.

The more that the national accounts system has been revised across fifty years, and the more that economic theory and practice have changed, the less meaningful the main national accounts aggregates have become in capturing what is happening in reality. Analysts end up doing a lot of detailed disaggregate research to figure out what is going on, because the official main national accounts aggregates don't tell them what they want to know (more detailed data is increasingly available, because official statisticians make available digital data warehouses, enabling datamining).

Wealth creation 
The 2008 revision of the UNSNA standard system of national accounts tries to realign the system more with the modern realities of capital finance, but in the process, the original intention of the accounts to measure "physical" changes in wealth is, in some respects, superseded.

Intangibles 
Noting the falling rate of profit and low capital formation in both Japan and Korea, scholars like Hyunbae Chun and Tsutomu Miyagawa say that "Economists increasingly stress the importance of investment in intangibles such as human and knowledge capital as a way to stimulate economic growth."

According to OECD data for the year 2000, cited by the World Bank, physical capital represents only one-quarter of the capital stock of rich countries, and all the rest is "intangible capital". Yet UNSNA national accounts were originally never designed to measure the "intangible capital."

The closest we can get to the intangibles are the flow of funds tables, measures of human capital, intellectual capital, household capital and social capital (including network capital), and measures of the potential value of natural resources. Except for goodwill, the intangibles are usually off-balance sheet items. They are usually imputations or inferred magnitudes which do not refer to any real financial stocks and flows ("money in the bank"), although they might take into account real costs. There is no standard convention for measuring them (which explains why there are mostly no official standard estimates).

For example, a restaurant may generate good profits, because of its location, and therefore its location has an "intangible value" which attracts a steady stream of customers – but we cannot really identify objectively and exactly how much of its value and earnings are due exclusively to its location. All we can say is, that investors will pay a higher than average price for the restaurant, because of expected future earnings. The investors are interested in the "intangible" factor, because they can convert it into extra "tangible" profits (which Marx calls Extramehrwert or surplus-profits). It became a popular theme in the booming era of the dot-com bubble and academics postulated a new economy which generated spectacular profits from intangibles. The idea of intangible wealth persists in financialization theory, where any kind of resource (tangible or intangible) can in principle be capitalized as a tradeable asset, and leveraged for profit.

When the value of intangible assets is calculated to be much larger than the ordinary physical and financial assets we own, we might argue that "we are richer than we think we are", but that also calls into question the validity of conventional statistics of wealth. Other things remaining equal, the bigger a nation's capital is calculated to be, the lower its rate of profit will be (unless some "intangible profits" are factored in). An additional complication arises, when we venture into the region of intangibles: their measures can overlap with each other (for example, human capital contains intellectual capital, or social capital contains household capital). The boundaries between different kinds of intangibles could actually turn out to be quite fuzzy.

Physicalism 
The contemporary concept of "wealth creation" is substantially different from the concept that was entertained in the mid-20th century, also because who exactly and legally "owns" the wealth, often becomes a secondary issue in business. An asset may be held which generates profit income, but it could be a borrowed asset via-via, or an asset of which the value be difficult to define (see also dot-com bubble). This can create new problems for statisticians seeking to estimate real additions to wealth.

Orthodox Marxists such as Andrew Kliman have decried a "physicalist" interpretation of value along Sraffian lines, but their own interpretation of profit was (arguably) "physicalist" because, basing themselves on value-added statistics, they tacitly permitted only the existence of profits that appear out of a physical increase in the stock of goods and services newly produced. Profit income from asset transactions was largely disregarded.

However, Kliman et al. (2014) compared the profits of US financial and non-financial corporations, using national accounts data, in order to argue that it is not financialization which has depressed productive investment, but that instead the real cause is the falling profit rate of non-financial corporations. A rival argument is presented by Mejorado & Roman. According to Bezreh & Goldstein (2013), the US financial sector did squeeze the profit share of the non-financial corporations.

The validity of econometric techniques used by Marxists to estimate labour-values and Marxian profit rates remains in dispute.

Unproductive labor 
Some claim that for Marx, commercial trade and asset speculation were unproductive sectors, in which no new value can be created. Therefore, they argue, all income of these sectors represents a deduction from the new value created in the productive sectors of the economy. Booms in unproductive sectors may temporarily act as a countervailing factor to the TRPF, but not in the long run.

Fred Moseley's theory 
Professor Fred Moseley argues that in the United States the grand-average rate of profit on production capital is lower than it was in the first decades after World War II, in part because of a rising share of unproductive labor in the total workforce, raising aggregate costs. This is a reason of its own for a falling average rate of profit. It suggested that, if the unproductive labor was "weeded out", then the profit rate would rise.

How the distinction between productive and unproductive labor is drawn obviously has a big mathematical effect on the estimated total profit rate on production, if unproductive labor costs are excluded from the total variable capital outlay, and included in the part of total net output which represents total surplus value produced. If the proportion of unproductive labor increases, paradoxically the total surplus value will then also increase, with the effect of raising the rate of profit.

Prof. Moseley resolves this paradoxical effect by distinguishing between primary and secondary income distributions, and between gross and net surplus value. In his account, first the total net value-added is produced by the productive workers, and then the gross wages of the unproductive workers are deducted from the gross surplus value; in that interpretation, it follows that the larger the wage-bill of unproductive workers is, the lower the netted surplus value will be. Chris Harman noted large quantitative differences in the estimates of unproductive labor by different orthodox Marxists. Moseley's calculations and his definition of unproductive labor have been criticized by other Marxists.

Objections 
The main objections discussed about the productive/unproductive distinction (usually denoted as "PUPL") are conceptual and empirical.

Conceptual issues 
The main conceptual objection is, that the distinctions between productive and unproductive labor offered by various Marxists are essentially arbitrary, and without a genuine, scientifically sound foundation. In a complex division of labor, specialist productive work relies on a network of indispensable managerial, facilitary and technical support services, without which it could not take place at all.

It is merely that, during a capitalist boom, when plenty finance is available, there are many more opportunities to "diversify" and expand the division of labour, with all kinds of new and interesting job titles - adding extra workers, to take on tasks, that the regular staff no longer want to touch themselves. Especially (but not only) during the economic slump, the division of labour is restructured by managers, so that fewer employees get to do more work, more precisely focused on the "core business" (reducing the "employee fat" of the business, that grew in the preceding era).

Marx himself never said that managerial functions were wholly "unproductive", but rather that they combined productive and unproductive tasks. He pointed out that there were continually disputes about whether labour was productive or not, depending on who could make money from it – and that in turn depended on how the accounting was done as well as on property rights. Whether workers physically and directly produce something tangible or not, they are all necessary, or at least most of them are (as Marx acknowledges with his concept of the "collective worker" or, in German, Gesamtarbeiter). It is therefore impossible to attribute the creation of new value only to workers who directly produce a tangible product.

Marxists often assume in their social accounts that the total payment of unproductive labor is made from a redistribution of part of the current surplus value produced by productive labor, but there is no proof of that assumption whatsoever, and indeed some Marxists have argued that the "overhead expense" of unproductive labor represents an outlay of circulating constant capital. David Ramsay Steele has defended the productive economic role of financial markets.

Empirical issues 
The main empirical objection is that there exists no accurate way to separate out productive and unproductive labor in official statistics (and the value each represents), even if the conceptual distinction could be validly defined. The main reasons are the following;
The concept of "productive labor performed" is not equivalent to "productive worker".
Productive work may create goods and services which cannot be profitably sold.
The same worker may perform tasks which are classified as partly productive and partly unproductive.
How the product of various services (or the role of services in production) should be defined remains controversial.
When statisticians allocate producer's occupations and outputs to a classification scheme, their defining criterion is the "main activity" of producers, disregarding their ancillary activities. Thus, already the base data represent an abstraction from reality.
For some Marxist theorists, these issues are not so weighty because, they argue, in the vast majority of cases it is quite clear and obvious whether labour is "productive labour" or not; the controversial cases represent only a residual number in the total. For other Marxists, things are more complicated, because Marx says that the same work can be either productive or unproductive, depending on whether or not surplus-value (producer's profit) can be extracted from it. The "services economy" is an under-researched topic among Marxian theorists.

Business practice 
A businessman looks at the deployment of labor in a different way, but faces a similar analytical problem. All labor produces something, but it does not necessarily help to create profit for one reason or another. What interests a businessman in a financial sense, is the cost of labor which directly creates the product or service that generates profit, versus the cost of labor that is effectively only a necessary overhead expense for his own business. The general aim is, to maximize productive labor in this sense, and minimize unproductive costs. That is the efficiency principle that guides the development of the division of labor organizationally.

For example, tasks that are not part of the "core business" are outsourced to other companies, if there is a cost/profit advantage or efficiency gain. Modern factories are often not "stand alone" operations, but highly specialized plants linked to a whole web of non-manufacturing companies that supply various products and services – things which, in the old days, used to be produced "in-house". Statistically, it might then look like the manufacturing sector and its profit have shrunk, but in reality, the factories produce even more goods, supported by many companies in other sectors (see also vertical disintegration and dynamic manufacturing network). Profit receipts may only appear in the accounts of a subsidiary or parent company that handles the sales contracts.

Ideally speaking, everything the employee does would directly contribute to profit for the enterprise (but in reality it usually doesn't). If employers paid piece wages then, in theory, they would incur costs, "only if" their employees created new value for them. Marx believed that piece wages – whether paid on an individual or team basis – were, in the long term, the most favorable form of remuneration for capitalist labor-exploitation, although he recognized that often workers earning piece-wages could initially earn more than workers on time-wages.

The trouble though is, that this productive/unproductive distinction is not easily made in practice, given changes in the market, in social-organizational efficiency, and in production techniques, and it does not necessarily have anything to do with whether a worker produces something tangible or not. What looks like an efficiency gain from "weeding out" seemingly unproductive activity may in fact not be an efficiency gain in total, or it may be very difficult to prove that it is. If fewer workers are made to do more work, intensifying labor, then accidents, illness or errors may increase.

Commodification 

In the real world, technical efficiency and financial efficiency are not necessarily the same thing at all. Hence there is continual debate in management theory about these issues, with few "general" answers being available, since much depends on the specific organizational technique of enterprises.

The only "general" managerial answer there is, is to recast the accounting for every detailed activity that workers perform as a statistically observable input-output relationship which results in a "product", even if the "product" is no real product at all, but some kind of service or performance result. By describing a labor-service or a task performance as a product, it seems identifiably productive, although substantively it may not create any new product. It enables the creation of data about the production, distribution and consumption of the product that creates profit.

In Marxist theory, this is called the "commodification of services": each specific service is accounted for as a specific alienable product with a certain price tag, and managed accordingly. Eventually, the commodified service is turned into a vendible commodity, just as people are replaced by machines. Many services which used to be performed by trained staff are replaced by mass-produced things, because that is more profitable and cheaper to buy. For example, a teacher is replaced with an instruction video.

Divisions of labour 
What orthodox Marxists traditionally tried to do, is to create concepts for a very precise standard classification schema of occupations and output-defined industrial activities, which splits the working class into productive and unproductive employees. This schematic approach to the issue was strongly influenced by the official orthodox Marxist–Leninist Material Product System (MPS) in the Soviet Union, Eastern Europe, China, Cuba and Vietnam. The MPS national accounts divide economic activity into a productive sector where tangible physical goods are produced, an unproductive sector creating services, and households. Another influence was Piero Sraffa's revival of the classical distinction between the production of "basic" and "non-basic" goods.

What Marx himself was concerned with was something else: the evolutionary tendencies of the capitalist division of labor, from the first urban workshops in medieval times, to large joint-stock companies employing thousands of workers in different countries. Since the division of labor changes when new technologies and forms of organization are introduced, the definition of what is "productive" labor must change as well. "Modern manufacturing no longer thinks in terms of white or blue collar — the workers it needs now are 'new-collar'".

Although Marx assumed that the basic institutional set-up of capitalist production remained the same (with respect to property rights and trading circuits) he never assumed that its specific organisational forms would stay the same. Methods of organisation had evolved, and were repeatedly changed as new inventions and techniques became available. 21st century managers are not just concerned with the design of work-tasks, like Frederick Winslow Taylor was, but with the design of the total organizational environment within which workers function.

Major Western debates

2009/2010 debate 
In 2009–2010, a fierce debate took place about the rate of profit, among leading Marxist economists from various political organizations and tendencies in Western Europe and North America.
According to the French Marxist economist Michel Husson, there were basically four bones of contention:

how had the average rate of profit in industries evolved since the early 1980s, in the larger developed capitalist countries?
what is the theoretical status of the tendential fall in the rate of profit in Marxist analysis?
what is the nature of the capitalist crisis today?
what is the political relevance of this discussion?
However, there was very little agreement about concepts, measurement principles, and political perspectives among participants. According to some (like Michel Husson) the rate of profit had gone up again since 1980, while others (like Andrew Kliman) thought it had stayed down. All kinds of different political conclusions were being drawn from the econometric evidence.

2013 Monthly Review debate 
In 2012, Monthly Review Press published Michael Heinrich's An introduction to the three volumes of Karl Marx's Capital In this book, which was endorsed by leading Western Marxist professors as the best introduction to Marx's Capital, and which received some glowing reviews, Heinrich – who is the chief editor of the leftist flagship magazine PROKLA in Germany – argued that the rate of profit can both rise and fall. Therefore, "A long-lasting tendency for the rate of profit to fall cannot be substantiated at the general level of argumentation by Marx in Capital."

By the end of 2013, leftwing economist Michael Yates stated: "What exasperates me more and more is the certainty with which so many people pontificate [about the tendency of the rate of profit to fall]". He argued the evidence for the tendency was tenuous, and that "Marx analyzed capitalism in its "ideal average," at a high level of abstraction. This "ideal average" can serve as a guide to examining the societies in which we live... but the two are not the same, something the disciples of the "tendency of the rate of profit to fall" school do not seem to grasp."

The socialist journal Monthly Review with which Yates is associated hosted a special debate about the falling rate of profit and crisis theory, featuring Michael Heinrich, Shane Mage, Fred Moseley, Michael Roberts and Guglielmo Carchedi. Michael Heinrich argued that there is now considerable evidence that in the original draft manuscripts Marx left behind, he never proposed a crisis theory in terms of the falling rate of profit, or that if he did, he was reconsidering that theory at the end of his life. The outcome of the debate was inconclusive, since the rival Marxists could not find much agreement among themselves about what is the correct interpretation.

Marx (as he said himself) only intended to provide an analysis of the capitalist mode of production in its "ideal average". Yet the categories of modern macroeconomic statistics are also idealizations and stylized facts, even although people might often believe the macroeconomic categories exist as an objective, mind-independent reality. Furthermore, although Marx accepted James Steuart's concept of "profit upon alienation", Marx's own analysis largely disregarded profit income which did not arise directly from new production by living labor – the reason being, that Marx was concerned with the capitalist mode of production, i.e. with how capital subordinates and reshapes production to fit with capital accumulation, and all that implies for workers' lives.

2016 Michael Roberts debate 
The 2016 Historical Materialism conference featured a panel which debated about Michael Roberts' book The long recession. Roberts (this is a pseudonym of the British Marxist researcher Robert McKee) stated that:

Much of the debate also took place on the Michael Roberts blog page. In 2018, Roberts & Carchedi published a joint book, titled World in Crisis: Marxist Perspectives on Crash & Crisis, which is billed "the most comprehensive empirically-based defense of Marx’s law of profitability, as the cause of capitalist crises."

Profits and crises II 
The traditional orthodox-fundamentalist Marxist narrative is, that capitalist crises are crises of profitability: the economic disturbance is caused by the circumstance that capitalists are making insufficient profits, and not because there are insufficient goods around for everybody. Thus, the masses are impoverished amidst an abundance of wealth. That situation is bound to happen, because of the tendency of the rate of profit to fall. Once workers understand that, they can break with illusions about reforming capitalism, and prepare for revolution.

However, critics point out that this kind of interpretation is problematic. There are two main reasons:
 First, in any significant economic slump, all economic indicators of output production, market sales, investment and employment are down, not just average profitability. If for example sales are down, it is logical that profit income will be down as well, but this does not mean automatically that lower profitability causes the downturn in sales. It all depends on how exactly "macro" and "micro" trends are related. Post-Keynesian economists are apt to point out that whether people are buying or not, matters a great deal to the overall functioning of the economy, and matters a great deal to overall profitability. If, for example, a lot of market uncertainty exists about the future, people are going to buy less, and that cuts into profits. The most common fault in economic analysis is that short-term trends are confused with long-term trends, and this is often what the controversy between Marxists and Keynesians is about.
 Second, average profitability is itself determined by a huge variety of influences on costs, sales and income which are all linked together in various ways. Therefore, if the crisis is blamed on lower profitability, this either states a tautology which must be true by definition ("people are not making as much money as they used to"), or else it is substantially false – since the crisis is just as much caused by a drop in sales, output, investment, incomes and employment – which all react on each other. The observed average industrial rate of profit can fall already for a series of years, before the slump arrives; therefore, it is not really credible to attribute the cause of the slump exclusively to the fall in the rate of profit (why exactly does the slump occur in year x, rather than in year x+n or year x-n?).

An additional reason, noticed for example by Michael Hudson, is that in the rich countries, the stock of privately owned physical production capital used in industries is nowadays only a minor component of the total stock of capital assets. If, therefore, the profit rate on privately owned physical industrial capital falls a percent or two, this cannot have a very large or immediate negative effect on the whole economy. To claim that it does have such a big effect, makes no mathematical or econometric sense whatever.

Underlying causes 
Profitability may be observed to fall, along with other variables, but that says nothing about the true interrelationship of the determinants which explain why it falls. David Harvey stated: "Data that show a falling rate of profit do not necessarily confirm the existence of the specific mechanism to which Marx appealed." In fact, the orthodox classical revolutionary Marxist Paul Mattick even claimed "that the conditions both of the crisis and its solution are so complex that they cannot be empirically determined. When the crisis will break out, its extent, and its duration cannot be predicted; only that there will be a crisis can be expected with certainty." Causal chains could be traced out in all sorts of directions, using the same econometric evidence. Thus, to ascertain what independent role profitability actually plays in economic development requires a much more precise analysis than Marxists have ever provided. Marxists simply assumed the centrality of profitability in capitalist production, but they failed to prove that falling industrial profitability is the root cause of all crises, rather than (say) one of the effects that are visible in crises.

In reply to this kind of criticism, orthodox classical revolutionary Marxist academics such as Andrew Kliman, Michael Roberts and Guglielmo Carchedi admit that the crisis may not be directly caused by an insufficient mass of surplus value to valorize all the capital there is (the traditional Fraina-Grossmann-Mattick argument). After all, this is not really credible in view of the great financial crisis of 2007–2009, which arose out of a financial panic about dodgy securitized products that occurred when average business profitability was high. Rather, these Marxists argue, the historically low average profitability of industry explains why depressed conditions persist, instead of a quick recovery happening after a credit bubble pops. Thus, low industrial profitability is the "underlying factor" explaining general economic stagnation.

According to this narrative, in recent decades "economic fundamentals" were in a poor state; nothing much was done about that, except that workers were beaten down; instead, the economy was artificially pumped up with cheap credit and cheap imports, prompting a housing and spending boom; when the credit bubble popped, the economy sagged right back into its poor state. Such arguments may have some plausibility, but if they are examined in fine detail, it is clear that a whole series of different arguments are actually being made about the way that falling profitability is connected to economic slumps. In reality, therefore, it is still far from resolved what the role of profitability in crises actually is.

Aftermath 
In the aftermath of the 2007–2009 slump, corporate profits surged to new heights while real wages stagnated, but this did not lead to a full recovery of real employment, real output growth and real fixed investment. As Mohamed El-Erian predicted fairly accurately in 2009, the number of jobless in the US economy has settled at a higher level that looks like persisting in the longer term. This result is mainly attributable to long-term unemployed people being unable to find paid work again, and dropping out of the labour force – plus, more people who cannot get all the paid working hours that they want.

Bureau of Labor Statistics (BLS) data showed that between 2008 and 2014, the US labor force (those employed for one hour per week or more + officially unemployed workers) stayed basically at the same size, although the proportion of unemployment within the labor force grew; yet according to the US Census Bureau the total US population increased by a net 13 million people at the same time (about half of whom were immigrants), and, according to the BLS, the number of US adults in the economically active population who are classified as "not in the labor force" increased by a net 12 million.

It took seven years for the US economy to recover from the financial crash, but US senator Bernie Sanders has claimed that real US unemployment is twice the official figures. For Europe, Mario Draghi suggested an average increase in "structural" unemployment from 8.8% in 2008 to 10.3% by 2013. Just as in the 1970s and 1980s, the grand-average jobless rate has risen to a higher level. This creates a downward pressure on the modal average real wage, though at the top end salary packages still increase. In September 2014, Robert Reich noted that although profits were at record levels, the median US household income, adjusted for inflation, was 8% lower than in 2007.

By 2016, US median personal income had recovered again to the pre-crash level, and began to rise somewhat, but there was no spectacular "earnings growth", except for supervisory staff. There are various explanations for a growing adult population that is "not in the labour force." In 2018, there were officially 6.2 million US unemployed, but also 5.1 million "not in the labour force" who wanted a job, suggesting a real unemployment rate of 7% (one in 14 workers). Since however "employed" includes all those who work for "one hour or more per week, or more", Bernie Sanders' estimate is probably valid (not 3.9% unemployed, but 8% - around one in 12 workers). At the same time, employers complained that they could not obtain the labour they required – there were mismatches between supply and demand in the labour market.

Unequal exchange 

Unequal exchange basically means that things are persistently traded above or below their "real" value or production cost, resulting in extra profits for the beneficiaries of the trade. The losers in the trade get less for what they sell, and pay more for what they buy. This phenomenon obviously has big implications for business profitability, and for the theory of labour exploitation. Faced with low profits at home, businessmen can shift their plant to other countries, where costs are much lower and revenues are higher. Then they can import or export goods and services from there, using the internet and cheap freighting, and possibly take advantage of currency and tax differentials. In this way, foreign trade and globalization reduce the effect of the TRPF.

Capital, Volume I 
According to orthodox classical revolutionary Marxism, profits can only arise from surplus labor, and therefore, it is argued that the direct source of all capitalist profits is the exploitation of wage labor. This principle is often called the "Fundamental Marxist Theorem" by mathematical Marxists: a necessary and sufficient condition for the existence of positive profits is that surplus value is positive. It is an interpretation which certainly makes sense from the point of view of Capital, Volume I where Marx assumed, for the sake of argument and for the sake of simplicity, that the prices at which the inputs and outputs of capitalist production are traded are equal to their value. In Capital, Volume I, Marx aimed to show, that even if all commodities were fairly traded on the basis of equal exchange, exploitation could nevertheless occur within capitalist production, and that if more value did not come out of production than went into it, it would be impossible to explain economic growth. The reason was simply that workers together could produce much more value than they needed themselves to live. That was, according to Marx, exactly the reason why the owners of capital hired those workers.

Capital, Volume III 
However, the analysis of capitalist competition offered in Marx's Capital, Volume III is completely based on the principle that commodities, human labor capacity, currencies and assets (physical or financial) in reality do not trade at their value. Rather, they are constantly being traded at margins above their value and below their value, in markets where sales are constantly fluctuating. It is, as Marx explains in the first chapter of Capital, Volume III, precisely the difference between the necessary cost-prices and the possible selling prices of commodities which is critical for profit margins, and which is therefore at the epicenter of competition in product markets. Commodities could also be sold below their value, at a good profit, assuming a sufficient turnover – the classical principle of competition. Moreover, the further development of the analysis in Capital, Volume III shows that goods and assets are also being traded for profit external to the sphere of production.

Capital gain 
As soon as it is admitted that, in the real world, all economic goods can trade at prices above or below their real production-cost, it can no longer be true, that the only source of all profits is the exploitation of wage labor. The reason is, that profit income can arise simply from selling the same priced good for more than it was purchased for, resulting in a capital gain for the seller, where this capital gain can be completely unrelated (or quite disproportional) to any identifiable labor cost. Effectively, more labor can exchange for less labor, and vice versa, and in the real world, this happens – fortunately or unfortunately – all the time. That insight is the basis of the theory of unequal exchange.

Point of production 
According to unequal exchange theory, exploitation is not something that is limited only to "the point of production" of the revolutionary classical orthodox Marxists. Exploitation could occur in all sorts of ways, including at the level of international trade. In turn, that means that profit rates can be influenced by the terms of market trade, quite independently of production (as long as everybody can make gains, then even if the gains are not equal, it may attract no attention; but when incomes fall, the problem becomes manifest). Profit rates may not fall, because products are made cheaply in one part of the world, and resold somewhere else for a much higher price. The financial gain involved in the resales is not made explicit by value-added statistics, except indirectly.

Unresolved issues 
The theory of unequal exchange nevertheless remains very much contested among Marxists, because they are unsure about how it could be reconciled with the pure, correct classical revolutionary Marxist orthodoxy. There are three main issues.

Theoretical issue 
If the values and prices of goods can vary independently in all kinds of ways, then the classical revolutionary orthodox Marxist principle that total production prices are equal to total product values cannot, realistically, be true; there exists no causal mechanism by which such price-value fluctuations perfectly compensate each other in aggregate, so that total product values equal total production prices. The principle can then be true only in an abstract theoretical model, but not in reality. Yet, if that classical revolutionary orthodox core principle is not true in reality, then it seems to follow there cannot be any systematic relationship in the real world between the Marxist labor-values and the actual price-levels for products – which was precisely what critics argued during the 20th century about the insolubility of the transformation problem.

If the Marxian product values are really determinants of product-prices, is there a way to express that relationship, other than as an accounting consolidation, or as a simultaneous input-output equation? There is no consensus about that issue among mathematicians and computer scientists, although the main trend is now toward probabilistic analysis and vector algebra.

Many mathematical Marxists have abandoned Marx's analysis of the equalization of the rate of profit and Marx's concept of production prices, arguing that an analysis of input-output data can straightforwardly prove a strong, robust positive correlation between product-prices and employee hours worked. They argue, with Marx, that a uniform profit rate does not exist in reality, but against Marx that, therefore, a tendency for differences in profit rates to be levelled out by competition does not exist either. Since (they argue) the deviation of product-prices from product-values is not very great in reality, the law of value is an empirical law with predictive power. At least for output aggregates, this is quite easy to prove, since net value-added (gross labour compensation earned and paid + gross profits earned and paid, net of write-offs) is by definition strongly correlated with the total amount of labour hours worked – the wage component is larger than the profit component.  This whole analysis does not, however, refer to foreign trade.

Exploitation issue 
Reinaldo A. Carcanholo stated that "...it is no easy task for those who are convinced of the depth and reality of Marx's theory of value to accept that there is profit that is not the result of exploitation."

The theory of unequal exchange moreover talks about exploitation in the sphere of distribution, in addition to the sphere of production. This is regarded by classical revolutionary orthodox Marxists as a demonic reformist threat to the core orthodox classical revolutionary Marxist principle that exploitation occurs only at the point of production, and that capitalism cannot be made fair through fair trade or redistribution, only abolished by abolishing wage labor.

Thus, for example, Paul Cockshott and Allin Cottrell prefer a Ricardian theory of comparative advantage to explain world trade. One Marxist states that "Radicals assume unequal exchange after Ricardo and want the state to intervene to equalize exchange. Marxism critiques both these theories as limited by the level of analysis."

According to Marxist theory, exploitation is a grievance of the working class, but according to unequal exchange theory, capitalists can be just as aggrieved about exploitation, in all kinds of ways, by other competing capitalists or by the state.

Analytical issue 
Even if the existence of unequal exchange is accepted as a market reality, it is not yet clear how it mainly occurs, or what its modalities are. There have been many different theories about how unequal exchange actually works.

Advanced political economy 
In his large 2016 treatise on capitalism, Anwar Shaikh has tried to resolve some of these issues, using a distinction between "profit on production" and "profit on transfer", and a theory of international capitalist competition. Shaikh's treatise easily proves he is the most important living classical economist in the world today, but nowadays he shies away from labels like "Marxist" and "Marxian", because these labels have been corrupted, and can cause confusion, distracting from the real scientific issues.

Recently, Andrea Ricci has attempted to provide a unified theoretical framework that can incorporate all the possible forms of unequal exchange mentioned in the economics literature. Persefoni Tsaliki, Christina Paraskevopoulou and Lefteris Tsoulfidis say, that little empirical research has been done on international transfers of value. They related unequal exchange theory to the modern Marxian theory of competition, and tested it out in the case of the trade between Greece and Germany.

Pollution 
One of the first ecological Marxists, Elmar Altvater, argued that "[t]he costs of clean air and clean water belong to the capital outlays and therefore increase the amount of constant capital fixed in the production process with the effect of an increasing organic composition of capital. Hence, the profit rate will fall (of course ceteris paribus)." However, not everyone agrees with that idea.

Externalities 
Firstly, it all depends who has to pay for the cost, and what kind of sanctions there are for polluters. If the state pays the cost out of general taxes, the costs to individual private enterprises would be much lower compared to their gains. It may be that some businesses gain from an environmentally friendly policy, while others do not, so that they are in competition with each other. Mathematicians would point out that the costs of clean air and water are only a very small component of total capital costs, but some argue that corporations are profitable precisely because they do not pay for externalities. According to Leontief Prize winner Duncan K. Foley, the perception that curbing greenhouse gases is "costly" assumes that capitalism is "efficient" without such controls, but if externality costs exist, it means precisely that capitalism is not at all operating at its "efficiency frontier".

Anti-pollution industry 
Secondly, the anti-pollution and rubbish-recycling industries can be profitable; additional income is generated by low-wage workers cleaning up the environment after it has been fouled up by rich people. After the largest oil spill in history, the 2010 Deepwater Horizon disaster in the Gulf of Mexico, J.P. Morgan analysts concluded that the business generated by clean-up work would very likely be larger than the financial losses to tourism or fishing, resulting in a net increase in GDP. However, the Bureau of Economic Analysis stated that the economic effects of the BP oil spill were "generally embedded in the source data that underlie the estimation of GDP and the national accounts and cannot be separately identified". On 5 September 2014, a US federal court ruled that BP had been "grossly negligent" and that that BP repeatedly cut corners to boost profits.

Clean technology 
Thirdly, the new technologies may be cleaner and cheaper, rather than more expensive and more polluting. For example, in 2014, the municipal authorities in the Dutch townships of Beverwijk, Heemskerk, Uitgeest and Velsen offered residents a subsidy of up to €1,050 (US$1,300) if they traded in their old petrol-driven scooter for an electric scooter.

No consensus 
So far, there is no scholarly consensus yet about what the overall long-term effect will be of environmental pollution on the average rate of profit for industries. In some cases, if a resource is depleted (and therefore much more difficult and costly to obtain), the profit yield on producing the resource might fall, since people will only buy it up to a certain price point. In other cases, if an essential resource becomes scarce, its owners can drive up the price, and thus increase their profit rate, because demand remains strong.

Housing issue 
Economists like Odran Bonnet, Boe Thio, Michel Husson, Matthew Rognlie, and Gianni La Cava have argued that Piketty's results are largely attributable to his broad definition of capital, specifically to the growth in the value and profitability of the housing stock. Once the housing stock is excluded from capital data, they argue, Piketty's results no longer hold. Academics also dispute about how the value of the housing stock should be measured; La Cava points out, that the figures for the income from housing capital are distorted by including the imputed rental value of owner-occupied housing (that "notional" component has kept increasing as a percentage of GDP in the post-war era). Michael Hudson notes, that if industrial profits are not statistically separated from real estate profits, the overall rate of return on capital that is obtained will be  "considerably understated". Anwar Shaikh argues that Piketty's measure of capital is "an inconsistent measure of real and financial assets" and that Piketty's "hybrid definition of the rate of profits is invalid".

A couple of years before the global financial crisis, William R. White, serving with the Bank of International Settlements, made a plea for comprehensive and integrated capital stock and flow statistics (financial assets and physical capital), and for better surveys of household asset and liability valuations. He stated that:

Research by Savills in 2016  points out that, as regards the value of the housing stock, size does matter. According to their calculation, the total value of the world's "developed" real estate  was $217 trillion in 2015 (this was equal to 2.7 times global GDP, or 60% of mainstream global assets; residential property accounted for 75% of the total value of global real estate property). Yolande Barnes, head of Savills world research, stated:

Specifically, Savills estimated that the investable global real estate in 2015 amounted to $81 trillion (37%), as against $136 trillion (63%) non-investable global real estate (not in the market for investors). This compared with $55 trillion of global equities, $94 trillion outstanding global securitized debt, and the $6 trillion of all the gold that was ever mined. For 2014, the OECD estimated global private equity (the business capital stock) at US$103.5 trillion, global public equity (the government capital stock) at $69 trillion, and global land value at $72.3 trillion.

A 2017 report to the United Nations Human Rights Council criticized the commodification and financialization of a deregulated housing market, causing large-scale housing speculation for profit. It said that this trend was leading to big social problems across the world. On behalf of many of the world's large cities, the mayor of Barcelona called on the United Nations to do something to help stop real estate speculators from driving up the cost of housing. If nothing is done, then in the long term, it will be impossible to reconcile stagnant or falling real incomes for a large part of the workforce, with rising housing costs. The result would be overcrowded rental housing, squatting and homelessness on a very large scale. In turn, that would cause more crime, disease, psychological problems and aggressive behavior.

In 2017, only half of Californian householders owned their homes. One out of every three renters (roughly six million people) were paying more than half of their total income to their landlord. In Los Angeles, tenants staged a rent strike in protest against extortion.

MEGA2 
In the 20th century,  Marxists were handicapped in reading Marx's texts on the rate of profit. There were five reasons:
 Many of his texts on economics had not been published, or they were originally never intended for publication (they were drafts, notes or letters – yet they were later often quoted by academics "as if" they had exactly the same definite status as writings which Marx published himself).
 If they were published posthumously, they were initially only available in German, or French or Russian language (e.g. the Grundrisse).
 The published texts were often hard to get, censored or banned (and in Nazi Germany burned).
 If the texts were translated, the translations were often far from exact, restructured by editors, or excerpted (a good example is Theories of Surplus Value which originally existed only as an unorganized collection of drafts, subsequently edited into books).
 Most editions of Marx's works were heavily influenced by the dominant interpretations of correct Marxist–Leninist ideology in the Soviet Union, East Germany and China, which recast Marx's and Engels's thought as a complete, systematic and fully consistent philosophical categorization of human existence as a whole, added to by Vladimir Lenin, Joseph Stalin and Mao Zedong.

Ronald L. Meek concluded that in dealing with Marx, academics often abandoned scholarly standards of fact-finding, evidential support and proof, and Hal Draper referred to the disease of "Marxolalia" ("the propensity to garble Marx"). The British radical Cyril Smith even claimed in 2005 that "It would not be overstating the situation to say that, right down to the present day, the "Marxists" have been among the most direct and bitter opponents of the ideas of Karl Marx." The total effect was, that for more than a century, people were miseducated about what Marx really said and stood for; his ideas were constantly being filtered through theoretical frameworks and political intentions that were far removed from his own.

All these issues have begun to be solved only from the 1970s, with the publication of the many new volumes of the Marx-Engels-Gesamtausgabe (the so-called "MEGA2"). This gigantic, annotated historical-critical edition will make available, in a planned 114 volumes (of which 62 have been published), all existing versions of practically every scrap Marx wrote on economics, in the original language in which they were written. The official German MEGAdigital website makes parts of division 2 of MEGA2 available online. The Chinese Central Compilation and Translation Bureau (CCTB, which from 2018 falls under the new Institution for Party History and Literature Research) is using the MEGA2 as a basis for a new Chinese edition of the Marx-Engels Collected Works.

However, Gareth Stedman Jones claims that all the MEGA2 volumes up to the 1990s are still tainted by Marxism–Leninism. Many old editions are still used by scholars, because they are considered sufficiently accurate, provide useful annotations and references, and offer translations not available in the MEGA2. Also, it is much easier to cross-check citations in old texts, if the old sources are to hand.

In addition, on 11 August 2015 all the original manuscripts by Karl Marx and Friedrich Engels archived at the International Institute of Social History were at once made available digitally, online and free of charge. It has unleashed new scholarly debates about the true theoretical status of Marx's work on the falling rate of profit. Some (like Dr. Michael Heinrich) argue that the original manuscripts show, that Marx himself was really far less certain and complete in his arguments than Engels later presented him to be. Others (like Prof. Fred Moseley) argue that the original manuscripts in fact strengthen Marx's argument. Recently, Ben Fowkes has translated Marx's original (unedited) manuscripts for Capital, Volume III into English, and Fred Moseley has provided an introduction for this new authentic text. Lucia Pradella refers to "a now influential trend in MEGA² studies in pursuit of a ‘new Marx’". Raúl Rojas stated – borrowing  an idea from Otto Bauer – that  "every generation has its own Marx".

Mainstream economics

Equilibrium growth 
In neoclassical economics, economic growth is described with growth models (e.g., the Solow–Swan model) in terms of equilibrium ("steady state"). Input per worker and output per worker grow at the same rate. Therefore, capital intensity remains constant over time. At the same time, in equilibrium, the rate of growth of employment is constant over time. Translated into terms of Marx's theory of value, this means that the value composition of capital does not rise, and the constant rate of growth of employment also indicates that there is no reason for the rate of profit to decline.

In this framework, a tendency of the rate of profit to decline would mean that input per worker is increased by business managers at a larger rate than output per worker, because:
 Overcapacity is encouraged to fend off competition.
 It results in a larger percentage increase of output per worker.

Thus an alternating movement occurs, where capitalists increase input per worker at a larger percentage than output per worker has risen, which, in the next period, leads to a larger percentage increase of output per worker than that of the previous input per worker. The rate of growth of employment declines in such a scenario.

Diminishing returns 
Within the framework of the neoclassical theory of the factors of production, there does also exist a law of diminishing returns. However, this law does not directly concern profit yields, but rather the variability of output yields in response to variations in the use of the factors of production (capital, labor and land). The "returns" are not profits, but output values.

This law is linked to profitability only indirectly, insofar as profit in neoclassical theory is defined as the cost (or the price) of using capital, where capital (including land) is one of the factors of production. If, however, the value of the net output yield is defined as equal to the sum of factor incomes, as it is in national accounts, then the profit income (the "marginal product of capital") generated can be related separately to the value of capital inputs to establish the income yield of capital inputs (excluding land).

Larry Summers 
Lawrence Summers criticizes Thomas Piketty for "his rather fatalistic and certainly dismal view of capitalism".  Summers argues that Piketty falsely assumes that "the return to capital diminishes slowly" and that profits are all reinvested. He says "neither of these premises is likely correct" about America's economy today.

In 2014, for example, it was reported that the world's corporations had accumulated $7 trillion in cash reserves, with the United States at $2 trillion. In turn, a large chunk of these cash surpluses was used for stock buybacks. In mid-2018, Steven Rattner explained, that the US buybacks were "really a consequence of the vast cash reserves — $2.4 trillion and rising — held by American companies." Since 2009, US companies also piled up large debts, which funded in total circa $4.7 trillion spent on buybacks and $3.4 trillion on dividends. According to Goldman Sachs, US companies were set to authorize $1 trillion worth of stock buybacks in 2018, and Europe was also joining in the spree. Buybacks in Japan were estimated at 6 trillion yen in 2016 (=US$55.1 billion) and 5.8 trillion yen in 2017 (=US$51.7 billion). In China, the value of buybacks in the first three quarters of 2018 was estimated at US$3.5 billion.

Summers argues that:

According to Summers, the "bottom line" is the net income received by investors. If profitability is as high as it has been since 2016, while interest rates are low, Summers argues, one would expect to see vastly more business activity and investment; all the ordinary neoclassical models tell us this would be so. If that is nevertheless not happening, then, very likely, "higher profits do not reflect increased productivity of capital, but instead reflect an increase in monopoly power".

In 1975, 94 corporations accounted for half the assets of all US publicly listed corporations, and 109 corporations accounted for half of the total net income of all US publicly listed corporations. In 2015, i.e. 40 years later, 35 corporations accounted for half the assets of all US listed corporations, and 30 corporations accounted for half of the total net income of all US publicly listed corporations.
Ownership concentration has increased since the mid-1990s in more than three quarters of all US industries. Companies in industries showing the largest increases in product market concentration obtain higher profit margins, positive abnormal stock returns, and more profitable merger & acquisition deals.
The problem in interpreting and generalizing about aggregate business data these days is, that roughly half of the total business activity occurs in a world that is very different from the other half. If, for example, you calculate the "average" of a set which contains the numbers 5, 10, 100, and 105, you get the number 55, but a value of 55 is nowhere near 5, 10, 100, or 105, and therefore it does not really describe the true distribution at all. It is a so-called "meaningless average".
Other liberals such as Paul Krugman  and Joseph Stiglitz have also developed mark-up theories of monopoly power. This helped to stimulate a lot of new research on the topic. According to the Financial Times, "For more than four decades, the US and most other nations have weakened laws that held the private sector in check, and made it hard for companies to wield monopoly power. The result has been increasing concentration in many sectors of the economy… The last time economic concentration and inequality were this high was during the Gilded Age of the 19th century."
Loecker & Eeckhout (2017) studied "profit mark-ups" in the US economy.  From 1950 to 1980, mark-ups remained stable.  From 1980 to 2014, mark-ups rose from 18% to 67% above cost. They explain this result neo-classically, referring to the ability of businesses to raise the market price of their output above its marginal cost (see also markup rule). A similar study of 74 countries was published by the IMF in 2018. In Europe, market power research is also being done. The OECD organized a special discussion on market concentration in June 2018.
Martin Wolf stated in 2018 that "If the natural tendency of our economies is towards ever-rising rent extraction and inequality, with all its dire social and political results, we need to respond in a thoughtful and determined way. That is the great challenge."

If market, investment and profit trends fail to behave as the neoclassical model says they should, there is logically only one answer for those who still believe that the neoclassical model is correct: extra-economic or exogenous forces (forces external to market trade itself, such as corporate monopolies, state intervention, mass psychology, climactic factors etc.) must be interfering with the rationality, efficiency and equilibrating force of free competition in the marketplace.

Keynesianism 
Within Keynesian theory, the marginal efficiency of capital (Keynes's version of the rate of profit) is expected to fall, possibly leading to an "euthanasia of the rentier".

Empirical research 
There have been a number of non-Marxist empirical studies of the long-term trends in business profitability.

Particularly in the late 1970s and early 1980s, there were concerns among non-Marxist economists that the profit rate could be really falling.

From time to time, the research units of banks and government departments produce studies of profitability in various sectors of industry. The National Statistics Office of Britain now releases company profitability statistics every quarter, showing increasing profits. In the UK, Ernst & Young (EY) nowadays provide a Profit Warning Stress Index for quoted companies. The Share Centre publishes the Profit Watch UK Report. In the US, Yardeni Research provides a briefing on S&P 500 profit margin trends, including comparisons with NIPA data.

The American-Jewish magazine Tablet claims that :[Marx’s] essential idea, influenced by Ricardo, was that capitalism would become less and less profitable and that its downward spiral toward the abyss of deflation—lower prices, lower profits—would be followed by worldwide revolution. Instead, capitalism has become vastly more profitable".

The McKinsey Global Institute claimed in 2016 that the three decades from 1985 to 2014 were the golden years for profits from stocks and bonds, but forecasts that average profitability will be lower in the future.

In May 2018, a WSJ analyst concluded that if taxcut effects are removed from the figures, real US corporate profits were not growing anymore, notwithstanding a surge in profits on S&P listed shares. Another WSJ analyst commented, at the same date, that "With the profits data, it could take several quarters for clear trends to emerge from the tax-associated noise." From September 2018 onward, as the economic and political news worsened, the bloated US stockmarkets began to deflate, while the VIX index trebled. In November 2018, Michael Wursthorn reported that "The postcrisis boom in U.S. corporate profits may be near its peak." CNBC reported a similar story. At the end of 2018, the record gains for the year by the 500 richest people listed on the daily Bloomberg Billionaires Index had been wiped out – together, they had lost more than half a trillion dollars of net wealth.

See also 
 Crisis theory
 Financial crisis
 Internal rate of return
 Steady-state economy: the stationary state in classical economics

References

External links 

 Tendency of the rate of profit to fall wiki, audio version
 Economarx bibliography
 Anwar Shaikh, Is capitalism sustainable? video
 Anwar Shaikh, Capitalism: video Lecture # 24 – Demand, Profitability and Growth
 Anwar Shaikh complete video course in classical economics, in 30 lectures
 Marx Now: A symposium 2018 (BISR)
 Turan Subasat YouTube video: David Harvey – "A commentary on the falling rate of profit in Marx’s crisis theory". Izmir University of Economics – Workshop on "The Great Meltdown of 2008: Systemic, Conjunctural or Policy-created?" (there are more videos available in this series).
 Thomas Weiss, 2018: A comment on Anwar Shaikh’s description of the tendency of the rate of profit to fall
 Andrew Kliman interview 1 of 4 video
 Minqi Li, Capitalism with Zero Profit Rate? video
 Joseph Choonera, The rate of profit and capitalism today video
 Michael Roberts – Profits, Cycles, and Breakdown video
 Cliff Bowman, Marx's Theory of Economic Crisis video
 Law of the Tendency of the Rate of Profit to Fall video
 The Falling Rate of Profit Explained: Why Capitalism will Fail video
 Falling Rate Of Profit/"Late Stage Capitalism" DEBUNKED video
 Falling Rate of Profit & Okishio's Theorem video
 Robot Burger Flippers and the Falling Rate of Profit video
 Marxian Econ Made Easy 7: The Falling Rate of Profit video

Category:Classical economics
Category:Marxian economics