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 ${\displaystyle u}$ that describes preferences over n commodities, the expenditure function

says what amount of money is needed to achieve a utility ${\displaystyle u^{*}}$ if the n prices are given by the price vector ${\displaystyle p}$. This function is defined by

where

is the set of all bundles that give utility at least as good as ${\displaystyle u^{*}}$.

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