quasi concavity/quasi convexity.

[lucy]

Consider the production function: Q = max {K, L}
Which of the following is true about Q?
a) Q is both quasi-convex and quasi-concave
b) Q is quasi-convex and not quasi-concave
c) Q is quasi-concave and not quasi-convex
d) Q is neither quasi-convex nor quasi-concave

[Dreyfus]

Q is only quasiconvex because its lower contour/level set is a convex set.

[lucy]

isn't the upper contour set also convex, since the funcction is a cube. Also Q=max{k,l} is a concave function and aren't concave functions quasi concave too?

[bear]

I think its both quasi concave and quasi concave.

[lucy]

But the answer is option b. I don't know how.

[Dreyfus]

Hi Lucy, just plot the level curves for this function with some constant c = max{L,K}. On plotting you will find that the level curves are mirror image of inverse L shaped curves and the convex set is the lower level set not the upper level set.
And also Since L and K are linear functions thus they are both convex and concave functions but Q(L,K)=max(L,K) is a "Convex function" not "Concave function"!

[Cermank]

Isn't the max function concave??

[Dreyfus]

[hs]

hey drefus bro ur help needed in other post of pareto optimality
pls chek