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Non-convexity (economics)
In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer extremes to in-between values) and convex budget sets and on producers with convex production sets; for convex models, the predicted economic behavior is well understood. When convexity assumptions are violated, then many of the good properties of competitive markets need not hold: Thus, non-convexity is associated with market failures, where supply and demand differ or where market equilibria can be inefficient. Non-convex economies are studied with nonsmooth analysis, which is a generalization of convex analysis. Demand with many consumers If a preference set is ''non-convex'', then some prices determine a budget-line that supports two ''separate'' optimal-baskets. For example, we can imagine that, for zoos, a lion costs as much as an eagle, and further that a zoo's budget suffice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C Subcategories
C, or c, is the third letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''cee'' (pronounced ), plural ''cees''. History "C" comes from the same letter as "G". The Semites named it gimel. The sign is possibly adapted from an Egyptian hieroglyph for a staff sling, which may have been the meaning of the name ''gimel''. Another possibility is that it depicted a camel, the Semitic name for which was ''gamal''. Barry B. Powell, a specialist in the history of writing, states "It is hard to imagine how gimel = "camel" can be derived from the picture of a camel (it may show his hump, or his head and neck!)". In the Etruscan language, plosive consonants had no contrastive voicing, so the Greek ' Γ' (Gamma) was adopted into the Etruscan alphabet to represent . Already in the Western Greek alphabet, Gamma first took a '' form in Early Etruscan, then '' in Classi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epigraph (literature)
In literature, an epigraph is a phrase, quotation, or poem that is set at the beginning of a document, monograph or section thereof. The epigraph may serve as a preface to the work; as a summary; as a counter-example; or as a link from the work to a wider literary canon, with the purpose of either inviting comparison or enlisting a conventional context. A book may have an overall epigraphy that is part of the front matter, or one for each chapter. Examples * As the epigraph to '' The Sum of All Fears'', Tom Clancy quotes Winston Churchill in the context of thermonuclear war:Why, you may take the most gallant sailor, the most intrepid airman or the most audacious soldier, put them at a table together – what do you get? The sum of their fears. * The long quotation from Dante's ''Inferno'' that prefaces T. S. Eliot's "The Love Song of J. Alfred Prufrock" is part of a speech by one of the damned in Dante's Hell. * The epigraph to E. L. Doctorow's ''Ragtime'' quotes Scott Joplin' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Economics
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity. Mathematics allows economists to form meaningful, testable propositions about wide-ranging and complex subjects which could less easily be expressed informally. Further, the language of mathematics allows economists to make specific, positive claims about controversial or contentious subjects that would be impossible without mathematics. Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microeconomics
Microeconomics is a branch of mainstream economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics focuses on the study of individual markets, sectors, or industries as opposed to the national economy as whole, which is studied in macroeconomics. One goal of microeconomics is to analyze the market mechanisms that establish relative prices among goods and services and allocate limited resources among alternative uses. Microeconomics shows conditions under which free markets lead to desirable allocations. It also analyzes market failure, where markets fail to produce efficient results. While microeconomics focuses on firms and individuals, macroeconomics focuses on the sum total of economic activity, dealing with the issues of growth, inflation, and unemployment and with national policies relating to these issues. Microeconomics also deal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Aumann
Robert John Aumann (Hebrew name: , Yisrael Aumann; born June 8, 1930) is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel. He also holds a visiting position at Stony Brook University, and is one of the founding members of the Stony Brook Center for Game Theory. Aumann received the Nobel Memorial Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game theory analysis. He shared the prize with Thomas Schelling. Early years Aumann was born in Frankfurt am Main, Germany, and fled to the United States with his family in 1938, two weeks before the Kristallnacht pogrom. He attended the Rabbi Jacob Joseph School, a yeshiva high school in New York City. Academic career Aumann graduated from the City College of New York in 1950 with a B.Sc. in mathematics. He received his M.Sc. in 1952, and his Ph.D. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Shubik
Martin Shubik (1926-2018) was an American mathematical economist who specialized in game theory, defense analysis, and the theory of money and financial institutions. The latter was his main research interest and he coined the term "mathematical institutional economics" in 1959 to describe it and referred to it as his "white whale" (only considering it caught after publishing his final five books on the topic). He spent the majority of his career at Yale University, where he was heavily involved with the Cowles Foundation for Research in Economics, and launched the virtuaMuseum of Money and Financial Institutions Outside of economics, he began studying inclusion body myositis (IBM) after a 2003 diagnosis. He provided seed money to the Yale School of Public Health for thIBM Disease Registryin 2011, a survey was conducted in 2012-2013, and he is a co-author on a 2015 paper about the initial results (along with his son-in-law Seth Richards-Shubik). Personal life Martin Shubik was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lloyd Shapley
Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern. With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design." Life and career Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of astronomers Harlow Shapley and Martha Betz Shapley, both from Missouri. He attended Phillips Exeter Academy and was a student at Harvard when he was drafted in 1943. He served in the United States Army Air Corps in Chengdu, China and received the Bronze Star decoration for breaking the Soviet weather code. After the war, Shapley returned to Harvard and graduated wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tjalling Koopmans
Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was a Dutch-American mathematician and economist. He was the joint winner with Leonid Kantorovich of the 1975 Nobel Memorial Prize in Economic Sciences for his work on the theory of the optimum allocation of resources. Koopmans showed that on the basis of certain efficiency criteria, it is possible to make important deductions concerning optimum price systems. Biography Koopmans was born in 's-Graveland, Netherlands. He began his university education at the Utrecht University at seventeen, specializing in mathematics. Three years later, in 1930, he switched to theoretical physics. In 1933, he met Jan Tinbergen, the winner of the 1969 Nobel Memorial Prize in Economics, and moved to Amsterdam to study mathematical economics under him. In addition to mathematical economics, Koopmans extended his explorations to econometrics and statistics. In 1936 he graduated from Leiden University with a PhD, under the directio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael James Farrell
Michael James Farrell (9 May 1926 – 27 October 1975), was a Cambridge economist professionally known as M. J. Farrell. Academically he is remembered largely for the celebrated non-parametric measure of productive efficiency that he published in 1957. Biography Mike Farrell was born in Swindon, England, in 1926. He was the son of Richard J. Farrell, OBE, an engineer for the Crown Agents for Overseas Governments and Administrations, and Margaret E. Deane. In 1934, his family moved to Sheffield, England, and in 1936 he entered King Edward VII School, Sheffield. In 1944 he won a scholarship to New College, Oxford. He travelled to the US in 1951. While in the USA he met Margaret Bacon, later a psychologist and psychotherapist, daughter of Ernst Bacon, whom he married in 1952. He returned to Cambridge with Margaret in 1953. They had five sons. In 1957, he contracted poliomyelitis. He spent most of a year in the hospital, never recovering fully. Being an avid tennis player and â ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Journal Of Political Economy
The ''Journal of Political Economy'' is a monthly peer-reviewed academic journal published by the University of Chicago Press. Established by James Laurence Laughlin in 1892, it covers both theoretical and empirical economics. In the past, the journal published quarterly from its introduction through 1905, ten issues per volume from 1906 through 1921, and bimonthly from 1922 through 2019. The editor-in-chief is Magne Mogstad (University of Chicago). It is considered one of the top five journals in economics. Abstracting and indexing The journal is abstracted and indexed in EBSCO, ProQuest, EconLit , Research Papers in Economics, Current Contents/Social & Behavioral Sciences, and the Social Sciences Citation Index. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 9.103, ranking it 4/376 journals in the category "Economics". The journal is department-owned University of Chicago journal. Notable papers Among the most influential papers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradise Lost (1674)/Book II
''Paradise Lost'' is an epic poem in blank verse by the 17th-century English poet John Milton (1608–1674). The first version, published in 1667, consists of ten books with over ten thousand lines of verse. A second edition followed in 1674, arranged into twelve books (in the manner of Virgil's ''Aeneid'') with minor revisions throughout. It is considered to be Milton's masterpiece, and it helped solidify his reputation as one of the greatest English poets of all time. The poem concerns the biblical story of the Fall of Man: the temptation of Adam and Eve by the fallen angel Satan and their expulsion from the Garden of Eden. Composition In his introduction to the Penguin edition of ''Paradise Lost'', the Milton scholar John Leonard notes, "John Milton was nearly sixty when he published ''Paradise Lost'' in 1667. The biographer John Aubrey (1626–1697) tells us that the poem was begun in about 1658 and finished in about 1663. However, parts were almost certainly writte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
