Expenditure function

Expenditure function

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^*) : extbf R^L_+ imes extbf R ightarrow extbf 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 extbf R^L_+ : u(x) geq u^*}

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

ee also

* Expenditure minimization problem
* Hicksian demand function
* Utility maximization problem


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