Additive utility


In economics, additive utility is a cardinal utility function with the sigma additivity property.
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apple5
hat7
apple and hat12

Additivity 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 be a finite set of items. A cardinal utility function, where is the power set of, is additive if for any,
It follows that for any,
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.