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 ]
- Expenditure minimization problem
- Hicksian demand function
- Slutsky equation
- Utility maximization problem
References [ edit ]
- ^ Varian, Hal (1992). Microeconomic Analysis (Third ed.). New York: Norton. ISBN 0-393-95735-7.
- Mas-Colell, Andreu; Whinston, Michael D.; Green, Jerry R. (2007). Microeconomic Theory. pp. 59–60. ISBN 0-19-510268-1.
- Mathis, Stephen A.; Koscianski, Janet (2002). Microeconomic Theory: An Integrated Approach. Upper Saddle River: Prentice Hall. pp. 132–133. ISBN 0-13-011418-9.
- Varian, Hal R. (1984). Microeconomic Analysis (Second ed.). New York: W. W. Norton. pp. 121–123. ISBN 0-393-95282-7.