where: This form of utility function was first conceptualized by Wassily Leontief.
Leontief utility functions represent complementary goods.
For example: A consumer with a Leontief utility function has the following properties: Since Leontief utilities are not strictly convex, they do not satisfy the requirements of the Arrow–Debreu model for existence of a competitive equilibrium.
There are restricted families of Leontief economies that do have a competitive equilibrium.
[3] This has several implications: Moreover, the Leontief market exchange problem does not have a fully polynomial-time approximation scheme, unless PPAD ⊆ P.[4] On the other hand, there are algorithms for finding an approximate equilibrium for some special Leontief economies.