I need an example of a

  • Convex, non-monotonic preference

  • Non-convex, monotonic preference

I figured that an example of non-convex, monotonic utility preference could be $U(x,y)=x^2+y^2$. For convex, non-monotonic preference, I cannot think of a standard example. As far as my understanding goes, lexicographic preferences are convex, but I don't think these are non monotonic. Please help me figure out the examples so that I can conceptually understand monotonicity and convexity.

  • 1
    $\begingroup$ $-(x-1)^2 -(y-1)^2$ is an example of convex, non- monotonic preference $\endgroup$ – Amit Jun 16 '19 at 9:01
  • $\begingroup$ @Amit Thank You! $\endgroup$ – S.Rana Jun 16 '19 at 12:46
  • $\begingroup$ @Amit Also post answers you think are correct as answers. $\endgroup$ – Giskard Jun 16 '19 at 13:51
  • 1
    $\begingroup$ It's an example of an utility function that represents convex, non-monotonic preferences, actually. $\endgroup$ – Pedro Cavalcante Jun 16 '19 at 20:31

$u_1(x, y) = -(x-1)^2 - (y-1)^2$

$u_2(x, y) = -|x-1| - |y-1|$

are examples of utility functions that are concave, and therefore represent the preferences that are convex. Also, these preferences are not monotonic.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.