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Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. By convention, the applied methods refer to those beyond simple geometry, such as differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, and other computational methods.〔Elaborated at the JEL classification codes, Mathematical and quantitative methods JEL: C Subcategories.〕〔 (TOC. )〕 An advantage claimed for the approach is its allowing formulation of theoretical relationships with rigor, generality, and simplicity.〔Debreu, Gérard (() 2008). "mathematical economics", section II, ''The New Palgrave Dictionary of Economics'', 2nd Edition. (Abstract. ) Republished with revisions from 1986, "Theoretic Models: Mathematical Form and Economic Content", ''Econometrica'', 54(6), pp. (1259 )-1270.〕 It is argued that 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.〔Varian, Hal (1997). "What Use Is Economic Theory?" in A. D'Autume and J. Cartelier, ed., ''Is Economics Becoming a Hard Science?'', Edward Elgar. Pre-publication (PDF. ) Retrieved 2008-04-01.〕 Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.〔• As in ''Handbook of Mathematical Economics'', 1st-page chapter links: Arrow, Kenneth J., and Michael D. Intriligator, ed., (1981), v. (1 ) _____ (1982). v. (2 ) _____ (1986). v. ( 3 ) Hildenbrand, Werner, and Hugo Sonnenschein, ed. (1991). v. (4. ) • Debreu, Gérard (1983). ''Mathematical Economics: Twenty Papers of Gérard Debreu'', (Contents ). • Glaister, Stephen (1984). ''Mathematical Methods for Economists'', 3rd ed., Blackwell. (Contents. ) • Takayama, Akira (1985). ''Mathematical Economics'', 2nd ed. Cambridge. (Description ) and (Contents ). • Michael Carter (2001). ''Foundations of Mathematical Economics'', MIT Press. (Description ) and (Contents ).〕 Broad applications include: * optimization problems as to goal equilibrium, whether of a household, business firm, or policy maker * static (or equilibrium) analysis in which the economic unit (such as a household) or economic system (such as a market or the economy) is modeled as not changing * comparative statics as to a change from one equilibrium to another induced by a change in one or more factors * dynamic analysis, tracing changes in an economic system over time, for example from economic growth.〔〔Chiang, Alpha C. (1992). ''Elements of Dynamic Optimization'', Waveland. (TOC ) & Amazon.com (link ) to inside, first pp.〕 Formal economic modeling began in the 19th century with the use of differential calculus to represent and explain economic behavior, such as utility maximization, an early economic application of mathematical optimization. Economics became more mathematical as a discipline throughout the first half of the 20th century, but introduction of new and generalized techniques in the period around the Second World War, as in game theory, would greatly broaden the use of mathematical formulations in economics.〔• Debreu, Gérard (() 2008). "mathematical economics", ''The New Palgrave Dictionary of Economics'', 2nd Edition. (Abstract. ) Republished with revisions from 1986, "Theoretic Models: Mathematical Form and Economic Content", ''Econometrica'', 54(6), pp. (1259 )-1270. • von Neumann, John, and Oskar Morgenstern (1944). ''Theory of Games and Economic Behavior''. Princeton University Press.〕〔 This rapid systematizing of economics alarmed critics of the discipline as well as some noted economists. John Maynard Keynes, Robert Heilbroner, Friedrich Hayek and others have criticized the broad use of mathematical models for human behavior, arguing that some human choices are irreducible to mathematics. ==History== (詳細はGerman universities, a style of instruction emerged which dealt specifically with detailed presentation of data as it related to public administration. Gottfried Achenwall lectured in this fashion, coining the term statistics. At the same time, a small group of professors in England established a method of "reasoning by figures upon things relating to government" and referred to this practice as ''Political Arithmetick''. Sir William Petty wrote at length on issues that would later concern economists, such as taxation, Velocity of money and national income, but while his analysis was numerical, he rejected abstract mathematical methodology. Petty's use of detailed numerical data (along with John Graunt) would influence statisticians and economists for some time, even though Petty's works were largely ignored by English scholars.〔Schumpeter (1954) p. 212-215〕 The mathematization of economics began in earnest in the 19th century. Most of the economic analysis of the time was what would later be called classical economics. Subjects were discussed and dispensed with through algebraic means, but calculus was not used. More importantly, until Johann Heinrich von Thünen's ''The Isolated State'' in 1826, economists did not develop explicit and abstract models for behavior in order to apply the tools of mathematics. Thünen's model of farmland use represents the first example of marginal analysis. Thünen's work was largely theoretical, but he also mined empirical data in order to attempt to support his generalizations. In comparison to his contemporaries, Thünen built economic models and tools, rather than applying previous tools to new problems.〔Schumpeter (1954) p. 465-468〕 Meanwhile, a new cohort of scholars trained in the mathematical methods of the physical sciences gravitated to economics, advocating and applying those methods to their subject,〔Philip Mirowski, 1991. "The When, the How and the Why of Mathematical Expression in the History of Economics Analysis", ''Journal of Economic Perspectives'', 5(1) pp. (145-157. )〕 and described today as moving from geometry to mechanics.〔Weintraub, E. Roy (2008). "mathematics and economics", ''The New Palgrave Dictionary of Economics'', 2nd Edition. (Abstract ).〕 These included W.S. Jevons who presented paper on a "general mathematical theory of political economy" in 1862, providing an outline for use of the theory of marginal utility in political economy.〔Jevons, W.S. (1866). "Brief Account of a General Mathematical Theory of Political Economy", ''Journal of the Royal Statistical Society'', XXIX (June) pp. 282-87. Read in Section F of the British Association, 1862. (PDF. )〕 In 1871, he published ''The Principles of Political Economy'', declaring that the subject as science "must be mathematical simply because it deals with quantities." Jevons expected the only collection of statistics for price and quantities would permit the subject as presented to become an exact science. Others preceded and followed in expanding mathematical representations of economic problems. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「mathematical economics」の詳細全文を読む スポンサード リンク
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