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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.

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  • $\begingroup$ @denesp Where are you for this one? $\endgroup$
    – EconJohn ♦
    Commented Jan 5, 2018 at 5:50
  • $\begingroup$ @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. $\endgroup$
    – Giskard
    Commented Jan 5, 2018 at 11:16
  • $\begingroup$ @denesp whoops, Didn't know that. In the past you seemed to be knowledgeable on bliss points i.e. economics.stackexchange.com/questions/13782/… $\endgroup$
    – EconJohn ♦
    Commented Jan 5, 2018 at 21:17

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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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