Leontief utilities

In economics, especially in consumer theory, a Leontief utility function is a function of the form: $${\displaystyle u(x_{1},\ldots ,x_{m})=\min \left\{{\frac {x_{1}}{w_{1}}},\ldots ,{\frac {x_{m}}{w_{m}}}\right\}.}$$ where:

• ${\displaystyle m}$ is the number of different goods in the economy.
• ${\displaystyle x_{i}}$ (for ${\displaystyle i\in 1,\dots ,m}$) is the amount of good ${\displaystyle i}$ in the bundle.
• ${\displaystyle w_{i}}$ (for ${\displaystyle i\in 1,\dots ,m}$) is the weight of good ${\displaystyle i}$ for the consumer.

This form of utility function was first conceptualized by Wassily Leontief.