# A term for utility functions based on the max operator

What is a standard term for utility functions of the type:

$$u(x_1,\dots,x_m) = \max(\frac{x_1}{w_1},\dots,\frac{x_m}{w_m})$$

where $x_i$ is the amount of commodity type $i$, and $w_i$ is a constant weight?

This is similar to Leontief utilities, only with max instead of min.

What term describes the type of goods with such a utility function? Initially I thought they were called "perfect substitutes", but now I see that this term is used for linear utility functions.

• Perhaps anti-Rawlsian? :) since the Rawlsian social welfare function is of the form $\min(u_1,\dots,u_m)$. Commented Nov 29, 2015 at 19:29
• Cant you transform this into a Leontieff? i.e. shouldn't this representation be equivalent to a min over the negative x's? Commented Nov 29, 2015 at 21:17
• @ChinG probably yes, but what is the meaning of negative quantities? I don't think such function has the properties of Leontief utility. For example, with Leontief utilities, the products are complementaries, and with the maximum utility function. they are not. Commented Dec 1, 2015 at 10:53

• +1 although I disagree with the lotto player statement, at least in the context of this utility function. The $w_i$ could represent a weight according to probabilities. Commented Apr 5, 2019 at 18:44