In economics, especially in consumer theory, a Leontief utility function is a function of the form: where: This form of utility function was first conceptualized by Wassily Leontief.

Examples

Leontief utility functions represent complementary goods. For example:

Properties

A consumer with a Leontief utility function has the following properties:

Competitive equilibrium

Since Leontief utilities are not strictly convex, they do not satisfy the requirements of the Arrow–Debreu model for existence of a competitive equilibrium. Indeed, a Leontief economy is not guaranteed to have a competitive equilibrium. There are restricted families of Leontief economies that do have a competitive equilibrium. There is a reduction from the problem of finding a Nash equilibrium in a bimatrix game to the problem of finding a competitive equilibrium in a Leontief economy. This has several implications: Moreover, the Leontief market exchange problem does not have a fully polynomial-time approximation scheme, unless PPAD ⊆ P. On the other hand, there are algorithms for finding an approximate equilibrium for some special Leontief economies.

Application

Dominant resource fairness is a common rule for resource allocation in cloud computing systems, which assums that users have Leontief preferences.