# Additive multiattribute nonlinear utility functions

I am interested in the cases where a decision maker possesses a multiattribute utility function ($u$) of the form:

$u(x) = \sum\limits_{i=1}^{n} u_i(x)$, with $x=(x_1, \ldots, x_m)$, and where $u_{i \in [1, n]}$ is a multiattribute nonlinear utility function.

In particular, what is their relevance in microeconomics, utility theory, and decision-making in general? Are there any examples or references?

Thanks.

• What kind of situation does such a utility function represent? It would be useful to include that kind of information to your post. Does it refer to a single person or is it some form for a social welfare function? Mathematical entities in Economics are interesting to the degree that they can be mapped to a real-world situation. It appears you are asking us about that, but it doesn't work that way. Why are you interested in such a utility function? – Alecos Papadopoulos Feb 28 '17 at 19:34
• Here are two examples of applications of non-linear multiattribute utility functions: link1, link2. – rmas Mar 3 '17 at 5:26

Utility of this form arises fairly naturally in macro and finance. If your current utility depends on lagged consumption as well as current, then you get utility of this form, $$\sum_{t=1}^\infty u(C_{t-1}, C_t),$$ where $C_t$ is time $t$ consumption. One particularly common form is $$\sum_{t=1}^\infty u(C_{t} - h C_{t-1}),$$ which is known as habit utility, since it captures (for $h > 0$) the idea that get used to a certain level of consumption, so if it drops you are very unhappy.