Hicksian demand function

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In microeconomics, a consumer's Hicksian demand function h(p,u), also called the compensated demand function, gives the cheapest bundle under a price level p for which the consumer derives a utility level of at least u. The function is named after John Hicks.

Hicksian demand functions are often convenient for mathematical manipulation because they don't require income or wealth to be represented. However, Marshallian demand functions of the form x(p,w) that describe demand given prices p and income w are easier to observe directly. The two are trivially related by

where e(p,u) is the expenditure function (the function that gives the minimum wealth required to get to a given utility level), and by

where v(p,w) is the indirect utility function (which gives the utility level of having a given wealth under a fixed price regime). Their derivatives are more fundamentally related by the Slutsky equation.

The Hicksian demand function is intimately related to the expenditure function. If the consumer's utility function u(x) is locally nonsatiated and strictly convex, then

[edit] See also

• Marshallian demand function
• Convex preferences
• Expenditure minimization problem