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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 Elasticity of substitution ： ウィキペディア英語版 Elasticity of substitution Elasticity of substitution is the elasticity of the ratio of two inputs to a production (or utility) function with respect to the ratio of their marginal products (or utilities). It measures the curvature of an isoquant and thus, the substitutability between inputs (or goods), i.e. how easy it is to substitute one input (or good) for the other.〔Technically speaking, curvature and elasticity are unrelated, but isoquants with different elasticities take on different shapes that might appear to differ in a general sense of curvature (see )〕 In the modern period, John Hicks is considered to have formally introduced this concept in 1932, however he had, by his own admission, introduced the inverse of the elasticity of substitution, or the elasticity of complementarity. The credit then, also by Hicks' own admission, should go to Joan Robinson. ==Mathematical definition== Let the utility over consumption be given by $U(c\_1,c\_2)$. Then the elasticity of substitution is: :$E\_\; =\backslash frac$ =\frac)} =\frac})}}} =\frac}} where $MRS$ is the marginal rate of substitution. The last equality presents $MRS\_\; =\; p\_1/p\_2$ which is a relationship from the first order condition for a consumer utility maximization problem in Arrow-Debreu interior equilibrium. Intuitively we are looking at how a consumer's relative choices over consumption items change as their relative prices change. Note also that $E\_\; =\; E\_$: :$E\_\; =\backslash frac)\}$ =\frac)\right)} =\frac)} = E_ An equivalent characterization of the elasticity of substitution is:〔Given that: :$\backslash \; \backslash frac\; =\; d\backslash log\; (x\_2/x\_1)\; =\; d\backslash log\; x\_2\; -\; d\backslash log\; x\_1\; =\; -\; (d\backslash log\; x\_1\; -\; d\backslash log\; x\_2)\; =\; -\; d\backslash log\; (x\_1/x\_2)\; =\; -\; \backslash frac$ an equivalent way to define the elasticity of substitution is: :$\backslash \; \backslash sigma\; =-\backslash frac\backslash frac=-\backslash frac$.〕 :$E\_\; =\backslash frac$ =-\frac =-\frac)} =-\frac})}}} =-\frac}} In discrete-time models, the elasticity of substitution of consumption in periods $t$ and $t+1$ is known as elasticity of intertemporal substitution. Similarly, if the production function is $f(x\_1,x\_2)$ then the elasticity of substitution is: :$\backslash sigma\_\; =\backslash frac/\backslash frac)\}$ =\frac}/\frac)}/\frac}} =-\frac}/\frac)}/\frac}} where $MRTS$ is the marginal rate of technical substitution. The inverse of elasticity of substitution is elasticity of complementarity. 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「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.