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Understanding QuasiLinearity

by newphysist
Tags: quasi linear
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newphysist
#1
Nov13-12, 06:39 PM
P: 12
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
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Vargo
#2
Nov13-12, 06:56 PM
P: 350
What is the domain of your function?
newphysist
#3
Nov13-12, 06:58 PM
P: 12
Real numbers R

haruspex
#4
Nov13-12, 07:22 PM
Homework
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Thanks
P: 9,783
Understanding QuasiLinearity

Quote Quote by newphysist View Post
(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
#5
Nov14-12, 08:59 AM
P: 350
This function is monotonic. And every monotonic function is quasilinear.


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