Expenditure function; utility
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 <math>u</math> that describes preferences over L commodities, the expenditure function
- <math>e(p, u^*) : \textbf R^L_+ \times \textbf R
\rightarrow \textbf R</math>
says what amount of money is needed to achieve a utility <math>u^*</math> if prices are set by <math>p</math>.
This function is defined by
- <math>e(p, u^*) = \min_{x \in \geq(u^*)} p \cdot x</math>
where
- <math>\geq(u^*) = \{x \in \textbf R^L_+ : u(x) \geq u^*\}</math>
is the set of all packages that give utility at least as good as <math>u^*</math>.
See also
- Expenditure minimization problem
- Hicksian demand function
- Utility maximization problem
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