Expenditure Minimization Problem
From Wikipedia, the free encyclopedia.
In
microeconomics, the
Expenditure Minimization Problem is the
dual problem to the
Utility Maximization Problem:
how much money do I need to be happy?. This question comes in two parts. Given a consumer's
utility function, prices, and a utility target,
Expenditure function
Formally, the
expenditure function is defined as follows. Suppose the consumer has a utility function
u defined on
L commodities. Then the consumer's expenditure function gives the amount of money required to buy a package of commodities at given prices
p that give utility greater than
u * ,
-
where
-
is the set of all packages that give utility at least as good as
u * .
Hicksian demand correspondence
Secondly, the
Hicksian demand correspondence h(p,u * ) is defined as the cheapest package that gives the desired utility. It can be defined in terms of the expenditure function with the
Marshallian demand correspondence
- h(p,u * ) = x(p,e(p,u * )).
If the Marshallian demand correspondence
x(p,w) is a function (i.e. always gives a unique answer), then
h(p,u * ) is also called the
Hicksian demand function.