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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Constant elasticity of substitution ： ウィキペディア英語版 Constant elasticity of substitution Constant elasticity of substitution (CES), in economics, is a property of some production functions and utility functions. Specifically, it arises in a particular type of aggregator function which combines two or more types of consumption, or two or more types of productive inputs into an aggregate quantity. This aggregator function exhibits constant elasticity of substitution. ==CES production function== The CES production function is a neoclassical production function that displays constant elasticity of substitution. In other words, the production technology has a constant percentage change in factor (e.g. labour and capital) proportions due to a percentage change in marginal rate of technical substitution. The two factor (capital, labor) CES production function introduced by Solow, and later made popular by Arrow, Chenery, Minhas, and Solow is: :$Q\; =\; F\; \backslash cdot\; \backslash left(a\; \backslash cdot\; K^r+(1-a)\; \backslash cdot\; L^r\backslash right)^\}$ where * $Q$ = Quantity of output * $F$ = Factor productivity * $a$ = Share parameter * $K$, $L$ = Quantities of primary production factors (Capital and Labor) * $r$ = $\}$ * $s$ = $\}$ = Elasticity of substitution. As its name suggests, the CES production function exhibits constant elasticity of substitution between capital and labor. Leontief, linear and Cobb–Douglas functions are special cases of the CES production function. That is, * If $r=1$ we have a linear or perfect substitutes function; * If $r$ approaches zero in the limit, we get the Cobb–Douglas production function; * If $r$ approaches negative infinity we get the Leontief or perfect complements production function. The general form of the CES production function, with ''n'' inputs, is:〔http://www.econ.ucsb.edu/~tedb/Courses/GraduateTheoryUCSB/elasticity%20of%20substitutionrevised.tex.pdf〕 :$Q\; =\; F\; \backslash cdot\; \backslash left(a\_X\_^\backslash \; \backslash right)^\}$ where * $Q$ = Quantity of output * $F$ = Factor productivity * $a\_$ = Share parameter of input i, $\backslash sum\_^n\; a\_\; =\; 1$ * $X\_i$ = Quantities of factors of production (i = 1,2...n) * $s=\backslash frac$ = Elasticity of substitution. Extending the CES (Solow) form to accommodate multiple factors of production creates some problems, however. There is no completely general way to do this. Uzawa showed the only possible n-factor production functions (n>2) with constant partial elasticities of substitution require either that all elasticities between pairs of factors be identical, or if any differ, these all must equal each other and all remaining elasticities must be unity. This is true for any production function. This means the use of the CES form for more than 2 factors will generally mean that there is not constant elasticity of substitution among all factors. Nested CES functions are commonly found in partial equilibrium and general equilibrium models. Different nests (levels) allow for the introduction of the appropriate elasticity of substitution. 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「Constant elasticity of substitution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.