Transformation Problem
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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 a tendency toward an average rate of profit on all capital invested among industries, if such a tendency (as predicted by Marx and Ricardo) exists? Marx's theory Marx defines value as the number of hours of labor socially necessary to produce a commodity. This includes two elements: First, it i ...
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Karl Marx
Karl Heinrich Marx (; 5 May 1818 – 14 March 1883) was a German philosopher, economist, historian, sociologist, political theorist, journalist, critic of political economy, and socialist revolutionary. His best-known titles are the 1848 pamphlet ''The Communist Manifesto'' and the four-volume (1867–1883). Marx's political and philosophical thought had enormous influence on subsequent intellectual, economic, and political history. His name has been used as an adjective, a noun, and a school of social theory. Born in Trier, Germany, Marx studied law and philosophy at the universities of Bonn and Berlin. He married German theatre critic and political activist Jenny von Westphalen in 1843. Due to his political publications, Marx became stateless and lived in exile with his wife and children in London for decades, where he continued to develop his thought in collaboration with German philosopher Friedrich Engels and publish his writings, researching in the British Mus ...
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Commodity
In economics, a commodity is an economic good, usually a resource, that has full or substantial fungibility: that is, the market treats instances of the good as equivalent or nearly so with no regard to who produced them. The price of a commodity good is typically determined as a function of its market as a whole: well-established physical commodities have actively traded spot and derivative markets. The wide availability of commodities typically leads to smaller profit margins and diminishes the importance of factors (such as brand name) other than price. Most commodities are raw materials, basic resources, agricultural, or mining products, such as iron ore, sugar, or grains like rice and wheat. Commodities can also be mass-produced unspecialized products such as chemical substance, chemicals and computer memory. Popular commodities include Petroleum, crude oil, Maize, corn, and gold. Other definitions of commodity include something useful or valued and an alternative ter ...
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Piero Sraffa
Piero Sraffa (5 August 1898 – 3 September 1983) was an influential Italian economist who served as lecturer of economics at the University of Cambridge. His book ''Production of Commodities by Means of Commodities'' is taken as founding the neo-Ricardian school of economics. Early life Sraffa was born in Turin, Italy, to Angelo Sraffa (1865–1937) and Irma Sraffa (née Tivoli) (1873–1949), a wealthy Italian Jewish couple. His father was a professor in commercial law and later dean at the Bocconi University in Milan. Despite being raised as a practising Jew, Sraffa later became an agnostic. Due to his father's activity, the young Piero followed him during his academic wanderings (University of Parma, University of Milan and University of Turin), where he met Antonio Gramsci (leader of Communist Party of Italy). They became close friends, partly due to their shared political views. Sraffa was also in contact with Filippo Turati, perhaps the most important leader of the Ita ...
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Wassily Leontief
Wassily Wassilyevich Leontief (russian: Васи́лий Васи́льевич Лео́нтьев; August 5, 1905 – February 5, 1999), was a Soviet-American economist known for his research on input–output analysis and how changes in one economic sector may affect other sectors. Leontief won the Nobel Memorial Prize in Economic Sciences in 1973, and four of his doctoral students have also been awarded the prize (Paul Samuelson 1970, Robert Solow 1987, Vernon L. Smith 2002, Thomas Schelling 2005). Biography Early life Wassily Leontief was born on August 5, 1905, in Munich, Germany, the son of Wassily W. Leontief (professor of Economics) and Zlata (German spelling ''Slata''; later Evgenia) Leontief (née Becker). Wassily Leontief Sr. belonged to a family of Russian old-believer merchants living in St. Petersburg since 1741. Evgenia (Genya) Becker belonged to a wealthy Jewish family from Odessa. At 15 in 1921, Wassily Jr. entered University of Leningrad in present-day St. P ...
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Ladislaus Bortkiewicz
Ladislaus Josephovich Bortkiewicz (Russian Владислав Иосифович Борткевич, German ''Ladislaus von Bortkiewicz'' or ''Ladislaus von Bortkewitsch'') (7 August 1868 – 15 July 1931) was a Russian economist and statistician of Polish ancestry. He wrote a book showing how the Poisson distribution, a discrete probability distribution, can be useful in applied statistics, and he made contributions to mathematical economics. He lived most of his professional life in Germany, where he taught at Strassburg University (Privatdozent, 1895–1897) and Berlin University (1901–1931). Life and work Władysław Bortkiewicz was born in Saint Petersburg, Imperial Russia, to two ethnic Polish parents: Józef Bortkiewicz and Helena Bortkiewicz (née Rokicka). His father was a Polish nobleman who served in the Russian Imperial Army. Władysław graduated from the Law Faculty in 1890. In 1898 he published a book about the Poisson distribution, titled ''The Law of Small ...
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Makoto Itoh
is a Japanese economist and is considered internationally to be one of the most important scholars of Karl Marx Karl Heinrich Marx (; 5 May 1818 – 14 March 1883) was a German philosopher, economist, historian, sociologist, political theorist, journalist, critic of political economy, and socialist revolutionary. His best-known titles are the 1848 ...'s Theory of value (economics), theory of value. He teaches at Kokugakuin University, Tokyo, and is professor emeritus of the University of Tokyo. He belongs to the school of economic thought founded by Kozo Uno and is one of the few Japanese Marxian economics, Marxian economists who has published widely in English-language journals such as Science & Society, Monthly Review, Capital & Class, New Left Review and Ampo. He has published 24 books, of which 6 are in English, and 5 are translated and published in Chinese. Books in English * ''Value and Crisis'' (1980). * ''The Basic Theory of Capitalism'' (1987) * ''The world e ...
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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 charges of inconsistency 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 ...
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Ernest Mandel
Ernest Ezra Mandel (; also known by various pseudonyms such as Ernest Germain, Pierre Gousset, Henri Vallin, Walter (5 April 1923 – 20 July 1995), was a Belgian Marxian economist, Trotskyist activist and theorist, and Holocaust survivor. He fought in the underground resistance against the Nazis during the occupation of Belgium. Life Born in Frankfurt, Mandel was recruited to the Belgian section of the international Trotskyist movement, the Fourth International, in his youth in Antwerp. His parents, Henri and Rosa Mandel, were Jewish emigres from Poland, the former a member of Rosa Luxemburg's and Karl Liebknecht's Spartacist League. The beginning of Mandel's period at university was interrupted when the German occupying forces closed the university. During World War II, while still a teenager, he joined the Belgian Trotskyist organisation alongside Abraham Leon and Martin Monath. He twice escaped after being arrested in the course of resistance activities, and survived imp ...
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Simultaneous Linear Equations
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, :\begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in the three variables . A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by the ordered triple :(x,y,z)=(1,-2,-2), since it makes all three equations valid. The word "system" indicates that the equations are to be considered collectively, rather than individually. In mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject which is used in most parts of modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A syste ...
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Competitive Equilibrium
Competitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium introduced by Kenneth Arrow and Gérard Debreu in 1951 appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices. Competitive markets are an ideal standard by which other market structures are evaluated. Definitions A competitive equilibrium (CE) consists of two elements: * A price function P. It takes as argument a vector representing a bundle of commodities, and returns a positive real number that represents its price. Usually the price function is linear - it is represented as a vector of prices, a price for each commodity type. * An allocation ...
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