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Additive utility

Concept in economics

Wikipedia contributorsAdapted for Fathomly · View authors
1 min read
Source updated April 18, 2026

In economics, additive utility is a cardinal utility function with the sigma additivity property.

Additive utility
Au(A)
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apple5
hat7
apple and hat12

Additivity (also called linearity or modularity) means that "the whole is equal to the sum of its parts." That is, the utility of a set of items is the sum of the utilities of each item separately. Let S be a finite set of items. A cardinal utility function u:2^{S}\to \mathbb {R}, where 2^{S} is the power set of S, is additive if for any A,B\subseteq S,

u(A)+u(B)=u(A\cup B)+u(A\cap B).

It follows that for any A\subseteq S,

u(A)=u(\emptyset )+\sum _{x\in A}{\big (}u(\{x\})-u(\emptyset ){\big )}.

An additive utility function is characteristic of independent goods. For example, an apple and a hat are considered independent: the utility a person receives from having an apple is the same whether or not he has a hat, and vice versa. A typical utility function for this case is given at the right.

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