Leontief utilities
In economics, especially in consumer theory, a Leontief utility function is a function of the form: formula_1 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.