# 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 $\min(u_1,\dots,u_m)$. – Herr K. Nov 29 '15 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? – ChinG Nov 29 '15 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. – Erel Segal-Halevi Dec 1 '15 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. – Maarten Punt Apr 5 at 18:44