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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 that describes preferences over n commodities, the expenditure function

says what amount of money is needed to achieve a utility if the n prices are given by the price vector . This function is defined by

where

is the set of all bundles that give utility at least as good as .

Expressed equivalently, the individual minimizes expenditure subject to the minimal utility constraint that giving optimal quantities to consume of the various goods as as function of and the prices; then the expenditure function is

Expenditure and indirect utility [ edit ]

The expenditure function is the inverse of the indirect utility function when the prices are kept constant. I.e, for every price vector and income level :[1]:106

See also [ edit ]

References [ edit ]

  1. ^ Varian, Hal (1992). Microeconomic Analysis (Third ed.). New York: Norton. ISBN 0-393-95735-7.
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