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$Let$ the utility function defined to be :

$$U(x,y)=-x^2-y^2$$

I believe they are convex, the set which is preferred to a specific indifference curve is convex, but the answer sheet says that it is concave? What is the reason behind this? Or is the answer sheet just wrong?

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closed as off-topic by Giskard, ml0105, Kitsune Cavalry, BKay, EnergyNumbers Nov 8 '16 at 18:54

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not meet the standards for homework questions as spelled out in the relevant meta posts. For more information, see our policy on homework question and the general FAQ." – Giskard, ml0105, Kitsune Cavalry, BKay, EnergyNumbers

  • $\begingroup$ Here we are talking about convexity of the indifference curves $\endgroup$ – Xenidia Nov 2 '16 at 19:17
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The utility function is concave, but the preference that the function represents is convex. It seems you're confusing between the convexity of two different objects.

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