Expenditure Function

In microeconomics, a consumer's expenditure function describes how much money a consumer needs to be happy. That is, given a utility function and prices, it says how much wealth the consumer would need to reach a desired utility level. 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^*.

See also

 

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