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Understanding QuasiLinearity

  1. Nov 13, 2012 #1
    Hi,

    I have two questions.

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

    Code (Text):

    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
     
  2. jcsd
  3. Nov 13, 2012 #2
    What is the domain of your function?
     
  4. Nov 13, 2012 #3
    Real numbers R
     
  5. Nov 13, 2012 #4

    haruspex

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    Yes. Which it is.
    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.)
     
  6. Nov 14, 2012 #5
    This function is monotonic. And every monotonic function is quasilinear.
     
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