<p>These are sometimes known as "quasi-separable utility functions".  A recent paper that describes the theory is <a href="http://www.trembling-hand.com/wp-content/uploads/2018/01/addrep.pdf" rel="nofollow noreferrer">Quasi-Separable Utility</a> by Qin and Rommeswinkel.</p>

<p>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 $h &gt; 0$) the idea that get used to a certain level of consumption, so if it drops you are very unhappy.</p>

CC BY-SA 4.0
2018-05-25T20:54:37.270Z
2018-05-25T20:54:37.270Z
arsmath
<p>I am interested in the cases where a decision maker possesses a multiattribute utility function ($u$) of the form:</p>

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

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

<p>Thanks.</p>

CC BY-SA 3.0
2017-02-28T19:34:57.400Z
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
CC BY-SA 3.0
2017-03-03T05:26:26.263Z
Here are two examples of applications of non-linear multiattribute utility functions: [link1](https://www.researchgate.net/profile/Francisco_Andre/publication/223407542_A_non-interactive_elicitation_method_for_non-linear_multiattribute_utility_functions_Theory_and_application_to_agricultural_economics/links/55ae22b108ae98e661a4be52.pdf), [link2](http://www.upo.es/serv/bib/wps/econ0602.pdf).
rmas
<microeconomics><utility><preferences><decision-theory><expected-utility>
Additive multiattribute nonlinear utility functions
rmas
# Additive multiattribute nonlinear utility functions

(Asked by: username_0 on 2017-02-28)

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.

**Tags:** microeconomics, utility, preferences, decision-theory, expected-utility

> **Comments:**
> **username_1**: 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?  
> **username_0**: Here are two examples of applications of non-linear multiattribute utility functions: [link1](https://www.researchgate.net/profile/Francisco_Andre/publication/223407542_A_non-interactive_elicitation_method_for_non-linear_multiattribute_utility_functions_Theory_and_application_to_agricultural_economics/links/55ae22b108ae98e661a4be52.pdf), [link2](http://www.upo.es/serv/bib/wps/econ0602.pdf).  

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## 1 answers

### Answer by username_2 on 2018-05-25. Score: 1 | Accepted answer

These are sometimes known as "quasi-separable utility functions". A recent paper that describes the theory is [Quasi-Separable Utility](http://www.trembling-hand.com/wp-content/uploads/2018/01/addrep.pdf) by Qin and Rommeswinkel.

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.


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