Is min(1/2,x,x²) quasi-linear and why isn't it concave?

[newphysist]

Hi,

I have two questions.

(1) I am trying to understand how the following function is quasi-linear:

f = min(1/2,x,x^2)

For it to be quasi linear it has to be quasi convex and quasi concave at same time.

(2) I think the reason the above function is not concave is cause on a certain interval (0,1) f = x^2 which is convex. Am I correct in my reasoning?

Thanks guys

 

[Vargo]

What is the domain of your function?

 

[newphysist]

Real numbers R

 

[haruspex]

(1) I am trying to understand how the following function is quasi-linear:

f = min(1/2,x,x^2)

For it to be quasi linear it has to be quasi convex and quasi concave at same time.

Yes. Which it is.

(2) I think the reason the above function is not concave is cause on a certain interval (0,1) f = x^2 which is convex. Am I correct in my reasoning?

Yes, though it would be more accurate to observe that on (0, 1/√2) it is not concave. (min{.5, x/2, x} would have been concave.)

 

[Vargo]

This function is monotonic. And every monotonic function is quasilinear.