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Need a concave function

  1. Jun 22, 2011 #1
    I need a concave function in 2 variables X and Y for some modelling i'm doing.

    For 0<x<1 and 0<y<1, the function needs to satisfy the following:

    f(x,y) < 0 for x<0.5 and/or y<0.5
    f(x,y) = 0 for x=0.5 and y=0.5
    f(x,y) > 0 for x>0.5 and y>0.5

    MUST be concave.. i.e. second order partials wrt X and Y must both be < 0.

    My maths was never that good and I can't seem to make any progress here.. can anyone help out? Thanks
  2. jcsd
  3. Jun 22, 2011 #2

    I like Serena

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    Homework Helper

    Hi johnd17! Welcome to PF! :smile:

    What about:
    [tex]f(x,y) = \ln(x + \frac 1 2) + \ln(y + \frac 1 2)[/tex]
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