Expenditure function

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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