<p>Quasi-concave utility functions represent convex preferences. But that preferences are convex means that the weakly-better sets are convex, it is not about the convexity of any function.</p>

CC BY-SA 3.0
2018-01-05T12:11:11.977Z
2018-01-05T12:11:11.977Z
Michael Greinecker
<p>Why is the bliss point utility function convex even though it has concave portions to it ?</p>

<p>According to Nicholson and Snyder (authors of Microeconomic theory - Basic principles and extensions) a function has diminishing MRS and is convex only if it is quasi-concave. Accordingly, I checked quasi concavity for the bliss point utility function $U (x, y) = 12x + 16y –x^2 – y^2$, and it showed that the function is quasi concave throughout. This means that the function should be convex throughout, but that is not the case here. </p>

CC BY-SA 3.0
2018-01-05T05:50:42.650Z
@denesp Where are you for this one?
EconJohn
CC BY-SA 3.0
2018-01-05T11:16:48.910Z
@EconJohn One does not get notifications if tagged in a question where one has no posts. I am also unsure what you mean? I am not the single arbiter of truth.
Giskard
CC BY-SA 3.0
2018-01-05T21:17:27.297Z
@denesp whoops, Didn't know that. In the past you seemed to be knowledgeable on bliss points i.e. https://economics.stackexchange.com/questions/13782/utility-function-used-to-indicate-bliss-point
EconJohn
<microeconomics><utility><consumer-theory>
Bliss point utility doubt
Meera Unni
# Bliss point utility doubt

(Asked by: username_0 on 2018-01-05)

Why is the bliss point utility function convex even though it has concave portions to it ?

According to Nicholson and Snyder (authors of Microeconomic theory - Basic principles and extensions) a function has diminishing MRS and is convex only if it is quasi-concave. Accordingly, I checked quasi concavity for the bliss point utility function $U (x, y) = 12x + 16y –x^2 – y^2$, and it showed that the function is quasi concave throughout. This means that the function should be convex throughout, but that is not the case here.

**Tags:** microeconomics, utility, consumer-theory
> **Comments:**
> **username_1**: @denesp Where are you for this one?  
> **username_2**: @EconJohn One does not get notifications if tagged in a question where one has no posts. I am also unsure what you mean? I am not the single arbiter of truth.  
> **username_1**: @denesp whoops, Didn't know that. In the past you seemed to be knowledgeable on bliss points i.e. https://economics.stackexchange.com/questions/13782/utility-function-used-to-indicate-bliss-point  

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## 1 answers

### Answer by username_3 on 2018-01-05. Score: 4 | Accepted answer

Quasi-concave utility functions represent convex preferences. But that preferences are convex means that the weakly-better sets are convex, it is not about the convexity of any function.


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