Expenditure function; function is:

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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