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 Das Kapital, Volume 3. It was generally accepted in the 19th century. Economists as diverse as Adam Smith, John Stuart Mill, and Stanley Jevons noticed a long-run empirical trend for the internal rate of return on capital invested to produce industrial products to decline, and Marx called this tendency "the most important law of political economy" and sought to give a causal explanation for it, in terms of his labour theory of value.
Adam Smith's 1776 comment on the rate of profit
"Profit is so very fluctuating that the person who carries on a particular trade cannot always tell you himself what is the average of his annual profit. It is affected not only by every variation of price in the commodities which he deals in, but by the good or bad fortune both of his rivals and of his customers, and by a thousand other accidents to which goods when carried either by sea or by land, or even when stored in a warehouse, are liable. It varies, therefore, not only from year to year, but from day to day, and almost from hour to hour. To ascertain what is the average profit of all the different trades carried on in a great kingdom must be much more difficult; and to judge of what it may have been formerly, or in remote periods of time, with any degree of precision, must be altogether impossible. But though it may be impossible to determine, with any degree of precision, what are or were the average profits of stock, either in the present or in ancient times, some notion may be formed of them from the interest of money. It may be laid down as a maxim, that wherever a great deal can be made by the use of money, a great deal will commonly be given for the use of it; and that wherever little can be made by it, less will commonly be given for it. According, therefore, as the usual market rate of interest varies in any country, we may be assured that the ordinary profits of stock must vary with it, must sink as it sinks, and rise as it rises. The progress of interest, therefore, may lead us to form some notion of the progress of profit." (The Wealth of Nations, chapter IX)
Marx argued that increased investment in constant capital (fixed capital (factories, machines, buildings), raw materials) relative to variable capital (labor) reduced the margin of surplus labor time relative to the total capital invested (constant capital plus variable capital). According to Marx, surplus labor time is the source of surplus value. Now the rate of profit equals surplus value divided by total capital, so the fall in surplus labor time relative to capital results in a fall in the rate of profit for newly produced commodities.
Even as investment in constant capital increases productivity (i.e. the margin of surplus labor relative to regular labor, and thus of surplus value relative to variable capital), it reduces the rate of profit (i.e. the ratio of surplus value relative to total capital). The capitalist then responds by investing more in raising productivity or expanding the scale of production, which in turn reduces profits per unit further after a while, and so on and so forth, in a vicious cycle of diminishing returns.
This is, then, the general tendency in capitalism, but it is only a tendency, because there are also "counteracting factors" operating which had to be studied also. In his draft manuscript (he did not publish it himself), Marx cited six of them:
- more intense exploitation of labour (raising the rate of exploitation);
- reduction of wages below the value of labour power (commonly referred to as the "immiseration thesis");
- cheapening the elements of constant capital by various means;
- the growth and utilization of a relative surplus population (the reserve army of labour);
- foreign trade reducing the cost of industrial inputs and consumer goods; and
- the increase in share capital, which devolves part of the costs of using capital on others.
But there could obviously also be several other factors involved which Marx did not discuss in detail, including:
- reductions in the turnover time of industrial capital generally (e.g., an increase, driven by technology or management, in the productivity of fixed capital investment);
- accelerated depreciation and faster throughput;
- the level of price inflation for different types of goods and services;
- capital investment into 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
- consolidation of mature industries into an oligarchy of survivors. Mature industries do not attract new capital because of low returns. Also, mature companies with large amounts of capital invested and brand recognition create barriers to entry against new competitors. See also secular stagnation theory.
Some of these "countervailing factors" can only temporarily postpone the fall of the rate of profit. Wages, for instance, cannot fall below zero, the turnover period of capital also cannot fall below zero, and so on.
The controversy about the TRPF nowadays concentrates on whether the cheapening of elements of constant capital could indefinitely counteract the TRPF, and what effect increased productivity has on the rate of profit on production capital.
Quote from Marx on the Tendency of the rate of profit to fall
The progressive tendency of the general rate of profit to fall is, therefore, just an expression peculiar to the capitalist mode of production of the progressive development of the social productivity of labour. This does not mean to say that the rate of profit may not fall temporarily for other reasons. But proceeding from the nature of the capitalist mode of production, it is thereby proved a logical necessity that in its development the general average rate of surplus-value must express itself in a falling general rate of profit. Since the mass of the employed living labour is continually on the decline as compared to the mass of materialised labour set in motion by it, i.e., to the productively consumed means of production, it follows that the portion of living labour, unpaid and congealed in surplus-value, must also be continually on the decrease compared to the amount of value represented by the invested total capital. Since the ratio of the mass of surplus-value to the value of the invested total capital forms the rate of profit, this rate must constantly fall. (Karl Marx, Capital, vol. 3, chapter 13) 
Later Marxist interpretation
Henryk Grossmann and Paul Mattick argued that mass long-term unemployment prevalent in the 19th and early 20th centuries was the result of the long-term effect of labor-saving technological innovations. At a certain point, they argued, the falling rate of profit stops the total mass of profit in the economy from growing altogether, or at least from growing at a sufficient rate. This results in a crisis of over-accumulation (or a shortage of surplus-value), and consequently a drop in new productive investment, causing an increase in unemployment. This, in turn, leads to a wave of takeovers and mergers to restore profitable production. In Capitalism versus Planet Earth, Fawzi Ibrahim argues that while profits can be maintained and in fact grow as rates of profit fall provided capital investment increases by the same or a larger proportion than the fall in the rate of profit, down the line, as capital accumulation reaches the high levels witnessed in advanced economies of the west, a ‘tipping point’ is reached when the additional capital investment necessary to offset a fall in the rate of profit becomes prohibitingly large, profits begin to tumble and capital enters a ‘critical zone’ ushering in an economic crisis qualitatively different from those of the past. 
However, nearly a century ago, economists such as Eugen von Böhm-Bawerk and Ladislaus Bortkiewicz found Marx's argument mathematically faulty. This gave rise to a controversy about the so-called transformation problem. Marx himself pointed out the need to find a general rule to transform the "values" of commodities into the "competitive prices" of the marketplace in chapter 9 of the draft of Volume 3 of Capital, where he also tried to solve it. The essential difficulty was this: given that profit ("surplus value") was derived from direct labour inputs, and that the amount of direct labour input varied widely between commodities, how to explain the tendency towards a uniform rate profit on production capital invested?
This has important implications for Marx's theory of labour exploitation and economic dynamics, namely that there is no inevitability of decline in the rate of profit from capital accumulation.
In the 20th century, many Marxists have moved away from Marx's labour theory of value and tried to provide alternative crisis theories in the Marxian tradition, focusing variously on the chaos of capitalist production, sectoral disproportions, under-consumption, labor-shortage and population pressures, credit insufficiency, and wages squeezing profits. Some theories attribute crises to one single factor (such as the TRPF), while others argue 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.
Marxist economist Chris Harman has advanced a reading of Marx that sees economic crisis as the main effective countervailing factor, but which places limits on its effectiveness as the capitalist system ages and units of capital become larger and more interlinked.
Against the allegations of internal inconsistency, proponents of the Temporal single-system interpretation (TSSI) such as economics professor Andrew Kliman maintain that the evidence presented by von Böhm-Bawerk, Bortkiewicz, Okishio and others are invalid refutations of the logic in Marx's argument. Kliman argues in Reclaiming Marx's Capital (2007) that the famous logical deficiencies arise not from a plausible reading of Marx but from the critics' interpretations and alterations ("corrections") of Marx, interpretations and alterations that are inspired by bourgeois general equilibrium theory. Once Capital is interpreted as temporal (as opposed to simultanist) and single-system (that values and prices are not worlds apart) the transformation problem disappears and the theory of the tendency of the profit rate can no longer be dismissed on logical grounds.
Marx’s interpretation has been the source of intense controversy, and has been criticized in different main ways:
- Firstly, it is argued that, by raising productivity, labour-saving technologies increase the average industrial rate of profit.
- Secondly, how exactly the average rate of industrial profit will evolve is uncertain and unpredictable.
- Thirdly, the labor theory of value has largely been rejected since the advent of Marginalism due to its incongruity with observed economic behavior. As Marx's economic critiques are systematically dependent on his version of the labor theory of value, rejection of this premise obviates the bulk of the critique. Marginal utility theory predicts that a high rate of profit as compared to other goods attracts further investment, but each additional unit of production will generally tend to be of less utility (and therefore less value) to the market, causing the overall rate of profit to fall absent any technological innovation increasing productivity. The commodity in question will lose its appeal to investors, who will then invest in other, newer lines of production offering higher returns.
The Japanese economist Nobuo Okishio (see Okishio's theorem) famously argued, "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 (Okishio, 1961, p. 92). 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 fall, only 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 rate of profit can only be brought about by rising wages.)
Intuitively, 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 typically responded to this argument in the following basic ways (there are, of course, numerous other arguments, involving more or less complex mathematical models):
- Capitalists operating in a competitive environment may not have any choice about investing in new technologies, to keep or expand their market share, even if doing so raises the pressure for all of them to spend an ever larger share of their income on newest technology, thereby reducing the available surplus to finance expansion of employment.
- It may be that in the heyday of a technological breakthrough, profits do indeed initially increase, but as the new technologies are widely applied by all enterprises, the overall end result is that average rate of return on capital falls for all of them. (This, however neglecting #4, is exactly what Okishio's equilibrium model seeks to refute.)
- A slight reduction in profit rates on capital invested due to more expensive productive equipment may not seem such a problem to business anyhow, if it is compensated by an increase in profit volume (profit margins) through increased sales and market shares. The yield on capital might decline somewhat in percentage terms, while total net income from capital employed increases.
- Arguments such as Okishio's are based on a fundamental misunderstanding of the TRPF and of basic aspects of Marxian economics such as a confusion of rate of profit with surplus value and wage as an expense from the capitalist with wage as a non exploited value added to production. Marx himself acknowledged that productivity increases even as the rate of profit decreases, and that these two tendencies necessarily go hand in hand. However, the decrease in production cost per unit brought about by investment in constant capital translates not to an increase in the rate of profit, but rather to an increase in surplus value: it increases the surplus labor time relative to variable capital. But meanwhile, the constant capital has expanded relative to variable capital (as a result of the capitalist's investment in productivity), meaning that surplus value, even though it has expanded relative to variable capital, shrinks relative to total capital. Since the rate of profit is defined as ( being surplus value and being total capital, i.e., constant capital plus variable capital), the rate of profit therefore tends to fall.
Responses 1 and 2 can be interpreted as a prisoner's dilemma in which the capitalists are caught.
Okishio argues in terms of a comparative static analysis. His starting point is an equilibrium growth path of an economy with a given technique. In a given branch of industry, a technical improvement is introduced (in a way similar to what Marx described) and then the new equilibrium growth path is established under the assumption that the new better technique is generally adopted by the capitalists of that branch. The result is that even under Marx's assumptions about technical progress, the new equilibrium growth path goes along with a higher rate of profit. However, if one drops the assumption that a capitalist economy moves from one equilibrium to another, Okishio's results no longer hold.
The "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 labour saving, or it could be capital saving. Therefore, the argument goes, it is impossible to infer definitely that a falling rate of profit must 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 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 follows from them.
In terms of mainstream economics
Typically, economic growth is described in the usual growth models (e.g., the Solow-Swan growth model) in terms of equilibrium ("steady state"), that is, input per worker and output per worker grow at the same rate. This means that 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 labor theory of value, this means that the value composition of capital does not rise, and the constant rate of growth of employment also indicates, in terms of the labor theory of value, that there is no reason for the rate of profit to decline.
In this framework, followers of a tendency of the rate of profit to decline assume that input per worker is increased by capitalists at a larger rate than output per worker, because
1) either, overcapacities might be built to fend off competition;
2) or, this leads, as an incentive for capitalists, to a larger percentage increase of output per worker than input per worker has been increased beforehand. This results in an alternate movement in which 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 input per worker before. The rate of growth of employment declines in such a scenario.
Some argue, with Marx, that the TRPF applies only to the sphere of capitalist production. Thus, it is argued, it is eminently possible that while industrial profitability declines, average profitability in activities external to real production (for example, commercial trade, capital gains and asset speculation) increases. Investment in production is one mode of capital accumulation, but not the only one. Thus, even if the growth rate of production stagnates, asset sales may boom. In advanced capitalist societies such as the United States, 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 profit could by itself explain economic crises.
Others claim that for Marx, commercial trade and asset speculation were unproductive sectors, in which no value can be created. Therefore, they argue, all income of these sectors is a deduction on the 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. On the contrary, Fred Moseley argues, in the United States the rate of profit is lower than it was in the decades after World War II, because of a rising share of unproductive labor with respect to productive labor. This is a reason of its own for a falling general rate of profit in distinction to the TRPF. Yet both Moseley's calculations and his definition of unproductive labor have been criticised by other Marxists.
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- Marginal utility
- Crisis theory
- Crises (economic)
- Economic stagnation
- Profit (accounting)
- Rate of profit
- Profit margin
- Internal rate of return
- Return on capital
- Capital accumulation
- Diminishing returns
- Marx, Karl, Capital, vol. 3, edited by Frederick Engels. New York: International Publishers, 1967 (orig. ed. 1894). Chapter 2, "The Rate of Profit", and chapter 13, "The Law as Such".
- Harris, Seymour E. (1943). Postwar Economic Problems. New York, London: McGraw Hill Book Co. pp. 67–70<Chapter IV Secular Stagnation by Alvin Sweeny.>
- Ayres, Robert U. (1998). Turning Point: The end of the Growth Paradigm. London: Earthscans Publications. p. 4
- Capitalism versus Planet Earth, an Irreconcilable Conflict, Muswell Press, 2012.
- "The falling rate of profit and capitalism today" in International Socialism 115 (Summer 2007)
- For a detailed presentation of the Marxian 'Law of the Falling Rate of Profit' and its various criticisms, see Mariolis Theodore, Critical Exposition of The Marxian 'Law of the Falling Rate of Profit': Income Distribution, Capital Accumulation and Technological Change in the Long-run (in Greek), MPRA Paper, 2010.
- Marx, Capital, vol. 3, p. 216.
- Marx, Karl. Grundrisse. Translated by Martin Nicolaus. Middlesex, England: 1973 (orig. ed. 1939), p. 745. 
- A mathematical description of traditional growth models is, for example, here: * Allen, R.G.D.: Macro-Economic Theory : A Mathematical Treatment. - London, Melbourne, Toronto: Macmillan, 1968.
- Karl Marx, Das Kapital Vol. 3
- Theories Combining Keynes, Kondratieff, Marx and Smith: R. L. Norman, Jr.
- Robert Brenner, The Boom and the Bubble - the US in the World Economy. Verso London, New York 2002. (empirical data for the post WWII era)
- James H. Chan-Lee and Helen Sutch, "Profits and rates of return" (an OECD study)
- Notes on a Combined Falling Rate of Profit and Internet Crisis
- Steve Cullenberg, The Falling rate of Profit. London: Pluto, 1994. (a review of Marxist arguments)
- Gerard Duménil and Dominique Lévy, The Economics of the Profit Rate: Competition, Crises, and Historical Tendencies in Capitalism. Aldershot, England: Edward Elgar, 1993. (looks at long term empirical trends)
- Alan Freeman: Price, value and profit - a continuous, general, treatment in: Freeman, Alan und Carchedi, Guglielmo (Hrsg.) "Marx and non-equilibrium economics". Edward Elgar, Cheltenham, UK, Brookfield, US 1996 (a mathematical defense of the law)
- Joseph Gillman: The Falling Rate of Profit, London, Dennis Dobson, 1957 (the first attempt to test Marx's hypothesis empirically).
- Shane Mage, The Law of the Falling Tendency of the Rate of Profit; Its Place in the Marxian Theoretical System and Relevance to the US Economy. Phd Thesis, Columbia University, 1963. (a response to Gillman with an elaborate statistical analysis).
- Chris Harman: Explaining the Crisis - a Marxist Reappraisal. London Chicago Sydney, Bookmarks 1999. (a defense of the law)
- Daniel M. Holland (ed.) Measuring profitability and capital costs : an international study. Lexington, Mass. : Lexington Books, c1984. (another study of empirical trends).
- Alfred Kleinknecht, Ernest Mandel and Immanuel Maurice Wallerstein (eds.), New findings in long-wave research. New York, N.Y.: St. Martin's Press, 1992. (links the profitability issue to the Kondratiev waves).
- Fred Moseley, The rate of profit and economic stagnation in the United States economy. Historical Materialism, Volume 1, Number 1, 1997
- Reuben L. Norman Jr., The Internet, Creative Destruction and The Falling Rate of Profit Crisis, February 8, 2000, Paper on how the Internet might precipitate first falling rate crisis and a new 1929 Depression, 
- Nobuo Okishio, "Technical Change and the Rate of Profit", Kobe University Economic Review, 7, 1961, pp. 85–99. (the famous criticism)
- Anwar Shaikh, The Current Crisis: Causes and Implications (a Solidarity pamphlet) (a succinct modern Marxist interpretation)
- John Weeks, Capital and exploitation, chapter 8 (Princeton University Press, 1980) (careful analysis of the Marxian TRPF in terms of value theory).
- Elroy Dimson, Paul Marsh, and Mike Staunton, The Millennium Book, A century of Investment Returns (London: London Business School and ABN AMRO, 2000).
- Elroy Dimson, Paul Marsh, and Mike Staunton, Triumph of the Optimists: 101 Years of Global Investment Returns (Princeton, N.J.: Princeton University Press 2002).