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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 Hicksian demand function ： ウィキペディア英語版 Hicksian demand function In microeconomics, a consumer's Hicksian demand correspondence is the demand of a consumer over a bundle of goods that minimizes their expenditure while delivering a fixed level of utility. If the correspondence is actually a function, it is referred to as the Hicksian demand function, or compensated demand function. The function is named after John Hicks. Mathematically, :$h(p,\; \backslash bar)\; =\; \backslash arg\; \backslash min\_x\; \backslash sum\_i\; p\_i\; x\_i$ :$\backslash \; \backslash \; u(x)\; \backslash geq\; \backslash bar$ where ''h''(''p'',''u'') is the Hicksian demand function, or commodity bundle demanded, at price level ''p'' and utility level $\backslash bar$. Here ''p'' is a vector of prices, and ''X'' is a vector of quantities demanded so that the sum of all ''p''''i''''x''''i'', is the total expense on goods ''X''. ==Relationship to other functions== Hicksian demand functions are often convenient for mathematical manipulation because they do not require income or wealth to be represented. Additionally, the function to be minimized is linear in the $x\_i$, which gives a simpler optimization problem. However, Marshallian demand functions of the form $x(p,\; w)$ that describe demand given prices ''p'' and income $w$ are easier to observe directly. The two are trivially related by :$h(p,\; u)\; =\; x(p,\; e(p,\; u)),\; \backslash$ where $e(p,\; u)$ is the expenditure function (the function that gives the minimum wealth required to get to a given utility level), and by :$h(p,\; v(p,\; w))\; =\; x(p,\; w),\; \backslash$ where $v(p,\; w)$ is the indirect utility function (which gives the utility level of having a given wealth under a fixed price regime). Their derivatives are more fundamentally related by the Slutsky equation. Whereas Marshallian demand comes from the Utility Maximization Problem, Hicksian Demand comes from the Expenditure Minimization Problem. The two problems are mathematical duals, and hence the Duality Theorem provides a method of proving the relationships described above. The Hicksian demand function is intimately related to the expenditure function. If the consumer's utility function $u(x)$ is locally nonsatiated and strictly convex, then $h(p,\; u)\; =\; \backslash nabla\_p\; e(p,\; u).$ 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「Hicksian demand function」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.