Okishio's theorem is a theorem formulated by Japanese economist Nobuo Okishio. It has had a major impact on debates about Marx's theory of value. Intuitively, it can be understood as saying that if one capitalist raises his profits by introducing a new technique that cuts his costs, the collective or general rate of profit in society – for all capitalists – goes up.
For this reason the theorem, first proposed in 1961, excited great interest and controversy because, according to Okishio, it contradicts Marx's law of the tendency of the rate of profit to fall. Marx had claimed that the new general rate of profit, after a new technique has spread throughout the branch where it has been introduced, would be lower than before. In modern words, the capitalists would be caught in a rationality trap or prisoner's dilemma: that which is rational from the point of view of a single capitalist, turns out to be irrational for the system as a whole, for the collective of all capitalists. This result was widely understood, including by Marx himself, as establishing that capitalism contained inherent limits to its own success. Okishio's theorem was therefore received in the West as establishing that Marx's proof of this fundamental result was inconsistent.
More precisely, the theorem says that the general rate of profit in the economy as a whole will be higher if a new technique of production is introduced in which, at the prices prevailing at the time that the change is introduced, the unit cost of output in one industry is less than the pre-change unit cost. The theorem, as Okishio (1961:88) points out, does not apply to non-basic branches of industry.
The proof of the theorem may be most easily understood as an application of the Perron–Frobenius theorem. This latter theorem comes from a branch of linear algebra known as the theory of nonnegative matrices. A good source text for the basic theory is Seneta (1973). The statement of Okishio's theorem, and the controversies surrounding it, may however be understood intuitively without reference to, or in-depth knowledge of, the Perron–Frobenius theorem or the general theory of nonnegative matrices.
The argument of Nobuo Okishio, a Japanese economist, is based on a Sraffa-model. The economy consists of two departments I and II, where I is the investments goods department (means of production) and II is the consumption goods department, where the consumption goods for workers are produced. The coefficients of production tell, how much of the several inputs is necessary to produce one unit of output of a given commodity ("production of commodities by means of commodities"). In the model below two outputs exist , the quantity of investment goods, and , the quantity of consumption goods.
The coefficients of production are defined as:
The worker receives a wage at a certain wage rate w (per unit of labour), which is defined by a certain quantity of consumption goods.
This table describes the economy:
|Investment goods used||Consumption goods used||Output|
This is equivalent to the following equations:
In department I expenses for investment goods or for constant capital are:
In Department II expenses for constant capital are:
and for variable capital:
(The constant and variable capital of the economy as a whole is a weighted sum of these capitals of the two departments. See below for the relative magnitudes of the two departments which serve as weights for summing up constant and variable capitals.)
Now the following assumptions are made:
Okishio, following some Marxist tradition, assumes a constant real wage rate equal to the value of labour power, that is the wage rate must allow to buy a basket of consumption goods necessary for workers to reproduce their labour power. So, in this example it is assumed that workers get two pieces of consumption goods per hour of labour in order to reproduce their labour power.
A technique of production is defined according to Sraffa by its coefficients of production. For a technique, for example, might be numerically specified by the following coefficients of production:
From this an equilibrium growth path can be computed. The price for the investment goods is computed as (not shown here): , and the profit rate is: . The equilibrium system of equations then is:
A single firm of department I is supposed to use the same technique of production as the department as a whole. So, the technique of production of this firm is described by the following:
Now this firm introduces technical progress by introducing a technique, in which less working hours are needed to produce one unit of output, the respective production coefficient is reduced, say, by half from to . This already increases the technical composition of capital, because to produce one unit of output (investment goods) only half as much of working hours are needed, while as much as before of investment goods are needed. In addition to this, it is assumed that the labour saving technique goes hand in hand with a higher productive consumption of investment goods, so that the respective production coefficient is increased from, say, to .
This firm, after having adopted the new technique of production is now described by the following equation, keeping in mind that at first prices and the wage rate remain the same as long as only this one firm has changed its technique of production:
So this firm has increased its rate of profit from to . This accords with Marx's argument that firms introduce new techniques only if this raises the rate of profit.
Marx expected, however, that if the new technique will have spread through the whole branch, that if it has been adopted by the other firms of the branch, the new equilibrium rate of profit not only for the pioneering firm will be again somewhat lower, but for the branch and the economy as a whole. The traditional reasoning is that only "living labour" can produce value, whereas constant capital, the expenses for investment goods, do not create value. The value of constant capital is only transferred to the final products. Because the new technique is labour-saving on the one hand, outlays for investment goods have been increased on the other, the rate of profit must finally be lower.
Let us assume, the new technique spreads through all of department I. Computing the new equilibrium rate of growth and the new price gives under the assumption that a new general rate of profit is established:
If the new technique is generally adopted inside department I, the new equilibrium general rate of profit is somewhat lower than the profit rate, the pioneering firm had at the beginning (), but it is still higher than the old prevailing general rate of profit: larger than .
Nobuo Okishio proved this generally, which can be interpreted as a refutation of Marx's law of the tendency of the rate of profit to fall. This proof has also been confirmed, if the model is extended to include not only circulating capital but also fixed capital. Mechanisation, defined as increased inputs of machinery per unit of output combined with the same or reduced amount of labour-input, necessarily lowers the maximum rate of profit.
1) Some Marxists simply dropped the law of the tendency of the rate of profit to fall, claiming that there are enough other reasons to criticise capitalism, that the tendency for crises can be established without the law, so that it is not an essential feature of Marx's economic theory.
Others would say that the law helps to explain the recurrent cycle of crises, but cannot be used as a tool to explain the long term developments of the capitalist economy.
2) Others argued that Marx's law holds if one assumes a constant ‘’wage share’’ instead of a constant real wage ‘’rate’’. Then, the prisoner's dilemma works like this: The first firm to introduce technical progress by increasing its outlay for constant capital achieves an extra profit. But as soon as this new technique has spread through the branch and all firms have increased their outlays for constant capital also, workers adjust wages in proportion to the higher productivity of labour. The outlays for constant capital having increased, wages having been increased now also, this means that for all firms the rate of profit is lower.
However, Marx did not know the law of a constant wage share. Mathematically the rate of profit could always be stabilised by decreasing the wage share. In our example, for instance, the rise of the rate of profit goes hand in hand with a decrease of the wage share from to , see computations below. However, a reduction in the wage share is not possible in neoclassical models due to the assumption that wages equal the marginal product of labour.
3) A third response is to reject the whole framework of the Sraffa-models, especially the comparative static method. In a capitalist economy entrepreneurs do not wait until the economy has reached a new equilibrium path but the introduction of new production techniques is an ongoing process. Marx's law could be valid if an ever-larger portion of production is invested per working place instead of in new additional working places. Such an ongoing process cannot be described by the comparative static method of the Sraffa models.
According to Alfred Müller the Okishio theorem could be true, if there was a coordination amongst capitalists for the whole economy, a centrally planned capitalist economy, which is a Contradictio in adjecto. In a capitalist economy, in which means of production are private property, economy-wide planning is not possible. The individual capitalists follow their individual interests and do not cooperate to achieve a general high rate of growth or rate of profit.
Up to now it was sufficient to describe only monetary variables. In order to expand the analysis to compute for instance the value of constant capital c, variable capital v und surplus value (or profit) s for the economy as whole or to compute the ratios between these magnitudes like rate of surplus value s/v or value composition of capital, it is necessary to know the relative size of one department with respect to the other. If both departments I (investment goods) and II (consumption goods) are to grow continuously in equilibrium there must be a certain proportion of size between these two departments. This proportion can be found by modelling continuous growth on the physical (or material) level in opposition to the monetary level.
In the equations above a general, for all branches, equal rate of profit was computed given
whereby a price had to be arbitrarily determined as numéraire. In this case the price for the consumption good was set equal to 1 (numéraire) and the price for the investment good was then computed. Thus, in money terms, the conditions for steady growth were established.
To establish this steady growth also in terms of the material level, the following must hold:
Thus, an additional magnitude K must be determined, which describes the relative size of the two branches I and II whereby I has a weight of 1 and department II has the weight of K.
If it is assumed that total profits are used for investment in order to produce more in the next period of production on the given technical level, then the rate of profit r is equal to the rate of growth g.
In the first numerical example with rate of profit we have:
The weight of department II is .
For the second numerical example with rate of profit we get:
Now, the weight of department II is . The rates of growth g are equal to the rates of profit r, respectively.
For the two numerical examples, respectively, in the first equation on the left hand side is the input of and in the second equation on the left hand side is the amount of input of . On the right hand side of the first equations of the two numerical examples, respectively, is the output of one unit of and in the second equation of each example is the output of K units of .
The input of multiplied by the price gives the monetary value of constant capital c. Multiplication of input with the set price gives the monetary value of variable capital v. One unit of output and K units of output multiplied by their prices and respectively gives total sales of the economy c + v + s.
Subtracting from total sales the value of constant capital plus variable capital (c + v) gives profits s.
Now the value composition of capital c/v, the rate of surplus value s/v, and the "wage share" v/(s + v) can be computed.
With the first example the wage share is and with the second example . The rates of surplus value are, respectively, 0.706 and 1.389. The value composition of capital c/v is in the first example 6,34 and in the second 12.49. According to the formula
for the two numerical examples rates of profit can be computed, giving and , respectively. These are the same rates of profit as were computed directly in monetary terms.
The problem with these examples is that they are based on comparative statics. The comparison is between different economies each on an equilibrium growth path. Models of dis-equilibrium lead to other results. If capitalists raise the technical composition of capital because thereby the rate of profit is raised, this might lead to an ongoing process in which the economy has not enough time to reach a new equlibrium growth path. There is a continuing process of increasing the technical composition of capital to the detriment of job creation resulting at least on the labour market in stagnation. The law of the tendency of the rate of profit to fall nowadays usually is interpreted in terms of disequilibrium analysis, not the least in reaction to the Okishio critique.
Between 1999 and 2004, David Laibman, a Marxist economist, published at least nine pieces dealing with the Temporal single-system interpretation (TSSI) of Marx's value theory. His ""The Okishio Theorem and Its Critics" was the first published response to the temporalist critique of Okishio's theorem. The theorem was widely thought to have disproved Karl Marx's law of the tendential fall in the rate of profit, but proponents of the TSSI claim that the Okishio theorem is false and that their work refutes it. Laibman argued that the theorem is true and that TSSI research does not refute it.
In his lead paper in a symposium carried in Research in Political Economy in 1999, Laibman's key argument was that the falling rate of profit exhibited in Kliman (1996) depended crucially on the paper's assumption that there is fixed capital which lasts forever. Laibman claimed that if there is any depreciation or premature scrapping of old, less productive, fixed capital: (1) productivity will increase, which will cause the temporally determined value rate of profit to rise; (2) this value rate of profit will therefore "converge toward" Okishio's material rate of profit; and thus (3) this value rate "is governed by" the material rate of profit.
These and other arguments were answered in Alan Freeman and Andrew Kliman's (2000) lead paper in a second symposium, published the following year in the same journal. In his response, Laibman chose not to defend claims (1) through (3). He instead put forward a "Temporal-Value Profit-Rate Tracking Theorem" that he described as "propos[ing] that [the temporally determined value rate of profit] must eventually follow the trend of [Okishio's material rate of profit]"  The "Tracking Theorem" states, in part: "If the material rate [of profit] rises to an asymptote, the value rate either falls to an asymptote, or first falls and then rises to an asymptote permanently below the material rate" Kliman argues that this statement "contradicts claims (1) through (3) as well as Laibman's characterization of the 'Tracking Theorem.' If the physical [i.e. material] rate of profit rises forever, while the value rate of profit falls forever, the value rate is certainly not following the trend of the physical [i.e. material] rate, not even eventually." 
In the same paper, Laibman claimed that Okishio's theorem was true, even though the path of the temporally determined value rate of profit can diverge forever from the path of Okishio's material rate of profit. He wrote, "If a viable technical change is made, and the real wage rate is constant, the new MATERIAL rate of profit must be higher than the old one. That is all that Okishio, or Roemer, or Foley, or I, or anyone else has ever claimed!"  In other words, proponents of the Okishio theorem have always been talking about how the rate of profit would behave only in the case in which input and output prices happened to be equal. Kliman and Freeman suggested that this statement of Laibman's was simply "an effort to absolve the physicalist tradition of error." Okishio's theorem, they argued, has always been understood as a disproof of Marx's law of the tendential fall in the rate of profit, and Marx's law does not pertain to an imaginary special case in which input and output prices happen for some reason to be equal.
In Karl Marx's critique of political economy and subsequent Marxian analyses, the capitalist mode of production refers to the systems of organizing production and distribution within capitalist societies. Private money-making in various forms (renting, banking, merchant trade, production for profit and so on) preceded the development of the capitalist mode of production as such. The capitalist mode of production proper, based on wage-labour and private ownership of the means of production and on industrial technology, began to grow rapidly in Western Europe from the Industrial Revolution, later extending to most of the world.The capitalist mode of production is characterized by private ownership of the means of production, extraction of surplus value by the owning class for the purpose of capital accumulation, wage-based labour and—at least as far as commodities are concerned—being market-based.Criticisms of Marxism
Criticisms of Marxism have come from various political ideologies and academic disciplines. These include general criticisms that there is a lack of internal consistency, criticisms related to historical materialism, that it is a type of historical determinism, concerns about suppression of individual rights, the implementation of communism and economic criticisms that there is a distortion or absence of price signals and reduced incentives. In addition, empirical and epistemological concerns are raised.Exchange value
In political economy and especially Marxian economics, exchange value (German: Tauschwert) refers to one of four major attributes of a commodity, i.e., an item or service produced for, and sold on the market. The other three aspects are use value, economic value, and price. Thus, a commodity has:
a value (note the link is to a non-Marxian definition of value);
a use value (or utility);
an exchange value;
a price (it could be an actual selling price or an imputed ideal price).These four concepts have a very long history in human thought, from Aristotle to David Ricardo, becoming ever more clearly distinguished as the development of commercial trade progressed but have largely disappeared as four distinct concepts in modern economics. This entry focuses on Marx's summation of the results of economic thought about exchange-value.Exploitation of labour
Exploitation of labour (or labor) is the act of treating one's workers unfairly for one's own benefit. It is a social relationship based on an asymmetry in a power relationship between workers and their employers. When speaking about exploitation, there is a direct affiliation with consumption in social theory and traditionally this would label exploitation as unfairly taking advantage of another person because of his or her inferior position, giving the exploiter the power.
Karl Marx, who is considered the most classical and influential theorist of exploitation, did not share the same traditional account of exploitation. Marx's theory explicitly rejects the moral framing characteristic of the notion of exploitation and restricts the concept to the field of labour relations. In analyzing exploitation, many political economists are often stuck between the explanation of the exploitation of labour given by Marx and Adam Smith. .labours are exploited to the possible extent.Index of contemporary philosophy articles
This is a list of articles in contemporary philosophy.
1926 in philosophy
1962 in philosophy
A New Philosophy of Society: Assemblage Theory and Social Complexity
A New Refutation of Time
A. C. Grayling
Abstract labour and concrete labour
Accumulation by dispossession
Against His-Story, Against Leviathan
Alain de Benoist
Alan Ross Anderson
Alan Stout (philosopher)
Alfred I. Tauber
Alfred Jules Ayer
Alfred Jules Émile Fouillée
Alfred North Whitehead
Anarchism and anarcho-capitalism
Anarchism and Friedrich Nietzsche
Anarchism in Israel
Anarchism in Russia
Anarchism in Spain
Anarchism in Sweden
Anarchism in the United States
Anarchism in Turkey
Anarchism: A Documentary History of Libertarian Ideas
Anarcho-capitalism and minarchism
André Malet (philosopher)
Anti-Semite and Jew
Antonio Caso Andrade
Asiatic mode of production
Association for Logic, Language and Information
Australasian Journal of Philosophy
Bas van Fraassen
Base and superstructure
Being and Nothingness
Being in itself
Bernard Bosanquet (philosopher)
Bertrand de Jouvenel
Between Past and Future
Black swan theory
Bob Hale (philosopher)
Bracha L. Ettinger
C. D. Broad
C. S. Lewis
C. Stephen Evans
Capital, Volume I
Capitalist mode of production
Carl Gustav Hempel
Charles Morris, Baron Morris of Grasmere
Charles Parsons (philosopher)
Charles Taylor (philosopher)
Chicago school (mathematical analysis)
Clarence Irving Lewis
Consumption of fixed capital
Contemporary Political Theory
Contingency, irony, and solidarity
Contrast theory of meaning
Contributions to Philosophy (From Enowning)
Criticism of capitalism
Criticism of postmodernism
Criticisms of electoralism
Critique of Cynical Reason
Critique of Dialectical Reason
Critiques of Slavoj Žižek
Curt John Ducasse
Das Argument (journal)
David Braine (philosopher)
David Kellogg Lewis
David Oswald Thomas
David Pearce (philosopher)
David S. Oderberg
David Wong (philosopher)
Degenerated workers' state
Deleuze and Guattari
Democracy in Marxism
Dewitt H. Parker
Differential and Absolute Ground Rent
Doctrine of internal relations
Donald Davidson (philosopher)
Eric Higgs (philosopher)
Ernesto Garzón Valdés
Ethical problems using children in clinical trials
F. C. S. Schiller
F. H. Bradley
Fact, Fiction, and Forecast
Faux frais of production
Fi Zilal al-Qur'an
Form of life (philosophy)
Frank R. Wallace
Fred Miller (philosopher)
Frederick C. Beiser
From Bakunin to Lacan
Future Primitive and Other Essays
G. E. M. Anscombe
Geoffrey Hunter (logician)
George Dickie (philosopher)
George Edward Moore
George H. Smith
Gödel's ontological proof
Gordon Park Baker
Hao Wang (academic)
Harald K. Schjelderup
Helene von Druskowitz
History and Future of Justice
History of the Church–Turing thesis
Howison Lectures in Philosophy
Humana.Mente – Journal of Philosophical Studies
I Heart Huckabees
I. A. Richards
Ideal observer theory
In Defense of Anarchism
Indeterminacy of translation
International Association for Philosophy of Law and Social Philosophy
International Journal of Žižek Studies
International Philosophical Quarterly
Introduction to Mathematical Philosophy
Is God Dead?
Jack Russell Weinstein
James E. Faulconer
James Franklin (philosopher)
James G. Lennox
James Griffin (philosopher)
James M. Edie
Jason Walter Brown
Joel J. Kupperman
John Corcoran (logician)
John Foster (philosopher)
John Greco (philosopher)
John L. Pollock
John N. Gray
John P. Burgess
John von Neumann
José Ortega y Gasset
Joseph de Torre
Joseph Henry Woodger
Joseph J. Spengler
Journal of Aesthetics and Art Criticism
Journal of Applied Non-Classical Logics
Journal of Logic, Language and Information
Journal of Philosophical Logic
Juan Manuel Guillén
Karen J. Warren
Krishna Chandra Bhattacharya
L'existentialisme est un humanisme
Lacan at the Scene
Law of accumulation
Law of value
Leo Mikhailovich Lopatin
Les jeux sont faits
Lewis White Beck
Lila: An Inquiry into Morals
Linguistics and Philosophy
List of contributors to Marxist theory
Logic of information
Luitzen Egbertus Jan Brouwer
Lwow-Warsaw School of Logic
Mark de Bretton Platts
Martin Hollis (philosopher)
Marx W. Wartofsky
Maurice De Wulf
Michael Tye (philosopher)
Michel Foucault bibliography
Milan Damnjanović (philosopher)
Mohandas Karamchand Gandhi
Muhammad Husayn Tabatabaei
Myth of Progress
Narhar Ambadas Kurundkar
Nassim Nicholas Taleb
Nationalism and Culture
New Libertarian Manifesto
New Times (politics)
Nietzsche and Philosophy
Nina Karin Monsen
Norwood Russell Hanson
Notes on "Camp"
Now and After
Objet petit a
Oets Kolk Bouwsma
Olavo de Carvalho
On Contradiction (Mao Zedong)
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Organic composition of capital
Original proof of Gödel's completeness theorem
Orlando J. Smith
Outline of anarchism
Oxford Literary Review
P. F. Strawson
Paul de Man
Paul R. Patton
Periyar E. V. Ramasamy
Permanent war economy
Peter Stillman (academic)
Philosophical interpretation of classical physics
Philosophical Investigations (journal)
Philosophy and Phenomenological Research
Philosophy and Real Politics
Philosophy and Social Hope
Philosophy and the Mirror of Nature
Philosophy in a New Key
Philosophy of artificial intelligence
Philosophy of dialogue
Philosophy of engineering
Philosophy of information
Philosophy of technology
Pirsig's metaphysics of Quality
Plato and a Platypus Walk Into a Bar
Postmodern social construction of nature
Postmodernism, or, the Cultural Logic of Late Capitalism
Prices of production
Psychoanalysis and Religion
R. G. Collingwood
Ralph Johnson (philosopher)
Ralph Tyler Flewelling
Rate of profit
Received view of theories
Religion & Ethics Newsweekly
Religious interpretations of the Big Bang theory
Richard A. Macksey
Richard von Mises
Robert Rowland Smith
Ruth Barcan Marcus
Samuel Maximilian Rieser
Sathya Sai Baba
Search for a Method
Semantic view of theories
Simple commodity production
Six Myths about the Good Life
Sketch for a Theory of the Emotions
Social conflict theory
Socially necessary labour time
South Park and Philosophy: You Know, I Learned Something Today
State monopoly capitalism
Stephen David Ross
Subject of labor
Syed Ali Abbas Jallapuri
Temporal single-system interpretation
Tendency of the rate of profit to fall
The Absence of the Book
The Birth of the Clinic
The Bounds of Sense
The Case for God
The Imaginary (Sartre)
The Logic of Scientific Discovery
The Myth of Sisyphus
The Philosophical Forum
The Royal Way
The Seminars of Jacques Lacan
The Sublime Object of Ideology
The Transcendence of the Ego
Thierry de Duve
Thomas Samuel Kuhn
Three Worlds Theory
Toronto School of communication theory
Two Dogmas of Empiricism
Valentin Ferdinandovich Asmus
Varadaraja V. Raman
Vincent F. Hendricks
W. D. Ross
Walter Terence Stace
What Is Literature?
What Is Your Dangerous Idea?
Why I Am Not a Christian
Willard Van Orman Quine
Willem B. Drees
William Craig (philosopher)
William Irwin Thompson
William James Lectures
William L. Rowe
William McNeill (philosopher)
William W. Tait
Władysław Mieczysław Kozłowski
Word and Object
Zen and the Art of Motorcycle Maintenance
Zollikon SeminarsMarxian class theory
Marxian class theory asserts that an individual’s position within a class hierarchy is determined by their role in the production process, and argues that political and ideological consciousness is determined by class position. A class is those who share common economic interests, are conscious of those interests, and engage in collective action which advances those interests. Within Marxian class theory, the structure of the production process forms the basis of class construction.
To Marx, a class is a group with intrinsic tendencies and interests that differ from those of other groups within society, the basis of a fundamental antagonism between such groups. For example, it is in the laborer's best interest to maximize wages and benefits and in the capitalist's best interest to maximize profit at the expense of such, leading to a contradiction within the capitalist system, even if the laborers and capitalists themselves are unaware of the clash of interests.
Marxian class theory has been open to a range of alternate positions, most notably from scholars such as E. P. Thompson and Mario Tronti. Both Thompson and Tronti suggest class consciousness within the production process precedes the formation of productive relationships. In this sense, Marxian class theory often relates to discussion over pre-existing class struggles.Marxian economics
Marxian economics, or the Marxian school of economics, is a heterodox school of economic thought. Its foundations can be traced back to the critique of classical political economy in the research by Karl Marx and Friedrich Engels. Marxian economics comprises several different theories and includes multiple schools of thought, which are sometimes opposed to each other, and in many cases Marxian analysis is used to complement or supplement other economic approaches. Because one does not necessarily have to be politically Marxist to be economically Marxian, the two adjectives coexist in usage rather than being synonymous. They share a semantic field while also allowing connotative and denotative differences.
Marxian economics concerns itself variously with the analysis of crisis in capitalism, the role and distribution of the surplus product and surplus value in various types of economic systems, the nature and origin of economic value, the impact of class and class struggle on economic and political processes, and the process of economic evolution.
Marxian economics, particularly in academia, is distinguished from Marxism as a political ideology as well as the normative aspects of Marxist thought, with the view that Marx's original approach to understanding economics and economic development is intellectually independent from Marx's own advocacy of revolutionary socialism. Marxian economists do not lean entirely upon the works of Marx and other widely known Marxists, but draw from a range of Marxist and non-Marxist sources.Although the Marxian school is considered heterodox, ideas that have come out of Marxian economics have contributed to mainstream understanding of the global economy. Certain concepts developed in Marxian economics, especially those related to capital accumulation and the business cycle, have been fitted for use in capitalist systems (for instance, Joseph Schumpeter's notion of creative destruction).
Marx's magnum opus on political economy was Das Kapital (Capital: A Critique of Political Economy) in three volumes, of which only the first volume was published in his lifetime (1867); the others were published by Friedrich Engels from Marx's notes. One of Marx's early works, Critique of Political Economy, was mostly incorporated into Das Kapital, especially the beginning of volume 1. Marx's notes made in preparation for writing Das Kapital were published in 1939 under the title Grundrisse.Neo-Ricardianism
The neo-Ricardian school is an economic school
that derives from the close reading and interpretation of David Ricardo by Piero Sraffa, and from Sraffa's critique of neo-classical economics as presented in his The Production of Commodities by Means of Commodities, and further developed by the neo-Ricardians in the course of the Cambridge capital controversy. It particularly disputes neo-classical theory of income distribution.
Prominent neo-Ricardians are usually held to include Pierangelo Garegnani, Krishna Bharadwaj, Luigi Pasinetti, Joan Robinson, John Eatwell, Fernando Vianello, Murray Milgate, Ian Steedman, Heinz D. Kurz, Neri Salvadori, Bertram Schefold, Fabio Petri, Massimo Pivetti, Franklin Serrano, Fabio Ravagnani, Roberto Ciccone, Sergio Parrinello, Alessandro Roncaglia, Maurice Dobb, Gilbert Abraham-Frois, Theodore Mariolis and Giorgio Gilibert.
The school partially overlaps with post-Keynesian and neo-Marxian economics.Nobuo Okishio
Nobuo Okishio (置塩 信雄, January 2, 1927 – November 13, 2003) was a Japanese Marxian economist and emeritus professor of Kobe University. In 1979, he was elected President of the Japan Association of Economics and Econometrics, which is now called Japanese Economic Association.
Okishio studied mathematical economics under Kazuo Mizutani. In 1950 he graduated from Kobe University and later taught there. He soon began to doubt the premises and results of modern economics, and decided to search for alternatives by studying Marxian economics.
Okishio worked to clarify the logic of Karl Marx’s economic system, offering formal and mathematical proofs for many Marxian theorems. For example, in 1955, he gave the world's first proof of the “Marxian fundamental theorem”, as it was later named by Michio Morishima, which is the theory that the exploitation of surplus labor is the necessary condition for the existence of positive profit. Concerning Marx’s Falling Rate of Profit, Okishio considered that his famous theorem would not deny it.Okishio wrote many papers covering various important fields in modern and Marxian economics, for example value and price, accumulation theory, critical analysis of Keynesian economics, trade cycle theory and on the long run tendency of capitalistic economy. They were published in over twenty books and two hundred papers, almost all in Japanese. About thirty of his published papers have been translated in English, and much of these materials are collected in the book (Nobuo Okishio, Michael Kruger and Peter Flaschel, 1993).Organic composition of capital
The organic composition of capital (OCC) is a concept created by Karl Marx in his critique of political economy and used in Marxian economics as a theoretical alternative to neo-classical concepts of factors of production, production functions, capital productivity and capital-output ratios. It is normally defined as the ratio of constant capital (capital invested in plant, equipment and materials) to variable capital (sum total of wages). The concept does not apply to all capital assets, only to capital invested in production (i.e. production capital). The neoclassical concept most similar to the increasing organic composition of capital is capital deepening.
Marx first referred to the idea in 1847
and discussed it in detail in Capital Vol. 1, chapter 25 ("The General law of Capitalist Accumulation"). In Capital Vol. 3 Marx demonstrates that the organic composition of capital decisively influences industrial profitability.
According to Marx, the OCC expresses the specific form which the capitalist mode of production gives to the relationship between means of production and labor power, determining the productivity of labor and the creation of a surplus product. This relationship has both technical and social aspects, reflecting the fact that simultaneously consumable use values and commercial exchange-values are being produced.
Marx calls this capital composition "organic", because it refers to the relationship between "living" and "dead" (or inert) elements in a capital investment. The "living element" is employed labour actively at work. The "dead" parts are the tools, materials and equipment worked with, which are the results of past labour (sometimes referred to as "dead labour").
Marx argues that a rising organic composition of capital is a necessary effect of capital accumulation and competition in the sphere of production, at least in the long term. This means that the share of constant capital in the total capital outlay increases, and that labor input per product unit declines.Overaccumulation
Overaccumulation is one of the potential causes of the crisis of capital accumulation. A crisis of capital occurs due to what Karl Marx refers to as the internal contradictions inherent in the capitalist system which result in the reconfiguration of production. The contradiction in this situation is realized because of the condition of capitalism that requires the accumulation of capital through the continual reinvestment of surplus value.
Accumulation can reach a point where the reinvestment of capital no longer produces returns. When a market becomes flooded with capital, a massive devaluation occurs. This over-accumulation is a condition that occurs when surpluses of devalued capital and labor exist side by side with seemingly no way to bring them together. The inability to procure adequate value stems from a lack of demand.
The term "overaccumulation" is also used in a neoclassical context.Perron–Frobenius theorem
In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector can be chosen to have strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical systems (subshifts of finite type); to economics (Okishio's theorem, Hawkins–Simon condition);
to demography (Leslie population age distribution model);
to social networks (DeGroot learning process), to Internet search engines and even to ranking of football
teams. The first to discuss the ordering of players within tournaments using Perron–Frobenius eigenvectors is Edmund Landau.Rate of exploitation
In Marxian economics, the rate of exploitation is the ratio of the total amount of unpaid labor done (surplus-value) to the total amount of wages paid (the value of labour power). The rate of exploitation is often also called the rate of surplus-value.Rate of profit
In economics and finance, the profit rate is the relative profitability of an investment project, a capitalist enterprise or a whole capitalist economy. It is similar to the concept of rate of return on investment.Socialization (Marxism)
In the theoretical works of Karl Marx and Friedrich Engels and subsequent Marxist writers, socialization (or the socialization of production) is the process of transforming the act of producing and distributing goods and services from a solitary to a social relationship and collective endeavor. With the development of capitalism, production becomes centralized in firms and increasingly mechanized in contrast to the pre-capitalist modes of production where the act of production was a largely solitary act performed by individuals. Socialization occurs due to centralization of capital in industries where there are increasing returns to scale and a deepening of the division of labor and the specialization in skills necessary for increasingly complex forms of production and value creation. Progressive socialization of the forces of production under capitalism eventually comes into conflict with the persistence of relations of production based on private property; this contradiction between socialized production and private appropriation of the social product forms the impetus for the socialization of property relations (socialism).In Marx's critique of political economy, as capitalism develops a contradiction emerges between the increasingly socialized act of production and the private ownership and appropriation of surplus value. Classical Marxist theory posits that this contradiction will intensify to a point where socialization of surplus value appropriation in the form of social ownership of the means of production will be necessitated, resulting in a transition from capitalism to socialism.Technological determinism
Technological determinism is a reductionist theory that assumes that a society's technology determines the development of its social structure and cultural values. Technological determinism tries to understand how technology has had an impact on human action and thought. Changes in technology are the primary source for changes in society. The term is believed to have originated from Thorstein Veblen (1857–1929), an American sociologist and economist. The most radical technological determinist in the United States in the 20th century was most likely Clarence Ayres who was a follower of Thorstein Veblen and John Dewey. William Ogburn was also known for his radical technological determinism.
The first major elaboration of a technological determinist view of socioeconomic development came from the German philosopher and economist Karl Marx, who argued that changes in technology, and specifically productive technology, are the primary influence on human social relations and organizational structure, and that social relations and cultural practices ultimately revolve around the technological and economic base of a given society. Marx's position has become embedded in contemporary society, where the idea that fast-changing technologies alter human lives is all-pervasive.
Although many authors attribute a technologically determined view of human history to Marx's insights, not all Marxists are technological determinists, and some authors question the extent to which Marx himself was a determinist. Furthermore, there are multiple forms of technological determinism.Temporal single-system interpretation
The temporal single-system interpretation (TSSI) of Karl Marx's value theory emerged in the early 1980s in response to renewed allegations that his theory was "riven with internal inconsistencies" and that it must therefore be rejected or corrected. The inconsistency allegations had been a prominent feature of Marxian economics and the debate surrounding it since the 1970s. Andrew Kliman argues that since internally inconsistent theories cannot possibly be right, the inconsistency charges serve to legitimate the suppression of Marx's critique of political economy and current-day research based upon it as well as the "correction" of Marx's inconsistencies.Proponents of the temporal-single system interpretation of Marx's value theory claim that the supposed inconsistencies are actually the result of misinterpretation; they argue that when Marx's theory is understood as "temporal" and "single-system", the internal inconsistencies disappear. In a recent survey of the debate, a proponent of the TSSI concludes that "the proofs of inconsistency are no longer defended; the entire case against Marx has been reduced to the interpretive issue".Critics of TSSI, including David Laibman (see Criticism section below), argue that Marx intended to present what they characterize as "a structurally consistent" model of value formation in a capitalist economy with competitive profit-rate equalization. They claim that Marx's formulations fail to do this, but also what they characterize as his fundamental insights can be revealed, and extended, by means of models and concepts that emerged after his time. Instead of trying to defend the consistency of Marx's original statements, non-TSSI Marxist theorists pursue what they characterize as ever-more effective versions of what they claim to be the core theory. They also claim that they believe that Marx himself would have done this.Transformation problem
In 20th-century discussions of Karl Marx's economics, the transformation problem is the problem of finding a general rule by which to transform the "values" of commodities (based on their socially necessary labour content, according to his labour theory of value) into the "competitive prices" of the marketplace. This problem was first introduced by Marx in chapter 9 of the draft of volume 3 of Capital, where he also sketched a solution. The essential difficulty was this: given that Marx derived profit, in the form of surplus value, from direct labour inputs, and that the ratio of direct labour input to capital input varied widely between commodities, how could he reconcile this with the tendency toward an average rate of profit on all capital invested?Use value
Use value (German: Gebrauchswert) or value in use is a concept in classical political economy and Marxian economics. It refers to the tangible features of a commodity (a tradeable object) which can satisfy some human requirement, want or need, or which serves a useful purpose. In Karl Marx's critique of political economy, any product has a labor-value and a use-value, and if it is traded as a commodity in markets, it additionally has an exchange value, most often expressed as a money-price.Marx acknowledges that commodities being traded also have a general utility, implied by the fact that people want them, but he argues that this by itself tells us nothing about the specific character of the economy in which they are produced and sold.