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Expenditure function - Wikipedia, the free encyclopedia

Expenditure function

From Wikipedia, the free encyclopedia

In microeconomics, the expenditure function describes the minimum amount of money an individual needs to achieve some level of utility, given a utility function and prices.

Formally, if there is a utility function u that describes preferences over L commodities, the expenditure function

e(p, u^*) : \textbf R^L_+ \times \textbf R  \rightarrow \textbf R

says what amount of money is needed to achieve a utility u * if prices are set by p. This function is defined by

e(p, u^*) = \min_{x \in \geq(u^*)} p \cdot x

where

\geq(u^*) = \{x \in \textbf R^L_+ : u(x) \geq u^*\}

is the set of all packages that give utility at least as good as u * .

[edit] See also

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