# Quasiconcavity of a function

1. Jun 19, 2012

### Alesak

My teacher is telling me that the below function is quasiconcave, but I think it is not.

1. The problem statement, all variables and given/known data
Show that u(c, l) = 20 000 c + c2+ l is or is not quasiconcave, in the first quadrant. c>=0 and l>=0.

2. Relevant equations
From wikipedia:

3. The attempt at a solution
I've rewriten it, for some level curve, as l = M + 10000 + (c+100)2, so it looks like a circle. Since the function u is increasing in both arguments, the upper level set looks like the outside of the circle, which is not convex, therefore the function is not quasiconcave. Correct? We are talking here only about the first quadrant.

2. Jun 25, 2012

### ougoah

I don't think it is quasiconcave in the first quadrant. The level curves I get are parabolas, not circles, but in any case, the upper level sets in the first quadrant are shapes that curve around like a parabola and are not convex. Have you talked to your teacher again about this?

3. Jul 4, 2012

### Ray Vickson

It is a conVEX function on the whole space -∞ < c < ∞, -∞ < I < ∞. Thus, it is quasiconVEX (because a convex function is automatically quasiconvex as well).

RGV