0

I am given the following two functions, and I am to figure out if they are concave.

Utility Function_1

Utility Function_2

I used the formula for determining if it is concave or convex. If my calculations are correct, this function is convex in certain cases and concave in certain different cases. My question is, then is this function both concave and convex? On the other hand, if it is strictly convex in a specific case is the function becomes convex because strictly convex dominates?

Thanks for the help guys

CheeseBurger
  • 101
  • No, these are discontinuous piecewise functions. – CheeseBurger Oct 13 '19 at 21:11
  • I added the tag because it was referring to piecewise-continuity not necessarily function being piecewise continuous. I thought it could be related to concavity or the convexity of the function, but in any case, I removed the tag not to cause any misconception I apologize if I caused any. – CheeseBurger Oct 13 '19 at 21:17
  • a function can be neither convex nor concave ($f(x) = \sin(x)$ for example), but for either label you do first need continuity. – Y. S. Oct 14 '19 at 08:19

1 Answers1

0

This function is neither concave or convex. As a side note, you do not need continuity for a function to be concave or convex.

CheeseBurger
  • 101