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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 Roy's identity ： ウィキペディア英語版 Roy's identity Roy's identity (named for French economist René Roy) is a major result in microeconomics having applications in consumer choice and the theory of the firm. The lemma relates the ordinary (Marshallian) demand function to the derivatives of the indirect utility function. Specifically, where $V(P,Y)$ is the indirect utility function, then the Marshallian demand function for good $i$ can be calculated as: :$x\_^=-\backslash frac\}\}\}$ where $P$ is the price vector of goods and $Y$ is income. == Derivation of Roy's identity == Roy's identity reformulates Shephard's lemma in order to get a Marshallian demand function for an individual and a good ($i$) from some indirect utility function. The first step is to consider the trivial identity obtained by substituting the expenditure function for wealth or income $Y$ in the indirect utility function $V\; (P,\; Y)$, at a utility of $u$: :$V\; (\; P,\; e(P,\; u))\; =\; u$ This says that the indirect utility function evaluated in such a way that minimizes the cost for achieving a certain utility given a set of prices (a vector $p$) is equal to that utility when evaluated at those prices. Taking the derivative of both sides of this equation with respect to the price of a single good $p\_i$ (with the utility level held constant) gives: :$\backslash frac\; \backslash frac\; +\; \backslash frac\; =\; 0$. Rearranging gives the desired result: :$-\backslash frac\}\}=\backslash frac=h\_i(P,\; u)=x\_i(P,\; e(P,u))$ with the second-to-last equality following from Shephard's lemma and the last equality from a basic property of Hicksian demand. 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「Roy's identity」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.