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expenditure function : ウィキペディア英語版
expenditure function
In microeconomics, the expenditure function gives the minimum amount of money an individual needs to spend to achieve some level of utility, given a utility function and the prices of the available goods.
Formally, if there is a utility function u that describes preferences over ''n '' commodities, the expenditure function
:e(p, u^
*) : \textbf R^n_+ \times \textbf R
\rightarrow \textbf R
says what amount of money is needed to achieve a utility u^
* if the ''n'' prices are given by the price vector p.
This function is defined by
:e(p, u^
*) = \min_ p \cdot x
where
:\geq(u^
*) = \
is the set of all bundles that give utility at least as good as u^
*.
Expressed equivalently, the individual minimizes expenditure x_1p_1+\dots +x_n p_n subject to the minimal utility constraint that u(x_1, \dots , x_n) \ge u^
*, giving optimal quantities to consume of the various goods as x_1^
*, \dots x_n^
* as functions of u^
* and the prices; then the expenditure function is
:e(p_1, \dots , p_n ; u^
*)=p_1 x_1^
*+\dots + p_n x_n^
*.
== See also ==

* Expenditure minimization problem
* Hicksian demand function
* Slutsky equation
* Utility maximization problem

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「expenditure function」の詳細全文を読む



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