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Logarithmic elasticities

  1. Sep 19, 2011 #1
    1. The problem statement, all variables and given/known data
    Find an expression (in terms of x and y) for the elasticity of y wrt x:
    ln(y) = 10 + 0.9x - 0.6x^2


    2. Relevant equations
    ln(y) = 10 + 0.9x - 0.6x^2


    3. The attempt at a solution
    I first tried the normal way of doing elasticities:

    ElxY = (x/y)*y'(x) which I got to:

    [x / 10 + 0.9x - 0.6x^2] * (0.9 - 1.2x) --> 0.9x - 1.2x^2 / (10 + 0.9x -0.6x^2)

    Furthermore, the log stated on the left-hand side is somewhat worrying me so I also tried the logarithmic rule in relation to elasticities:
    ElxY = dlnY/dlnX but I got a really wierd answer when I started to differentiate wrt x.

    Could someone just point me in the right direction so that I could have an attempt at the problem? I would very much appriciate any help I can get!

    EDIT: If that one is too complex to explain I also have a simpler version which is similar:
    lny=ax + bx
    ElxY = (x/ax + bx) * a + bx ---> ax / ax = 1.
    However, the same problem happens here with regards to the lny, which I assume makes my answer incorrect.
     
    Last edited: Sep 19, 2011
  2. jcsd
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