Results 1 to 3 of 3

Math Help - Cobb-Douglas Function: Inverse function and marginal cost

  1. #1
    Newbie
    Joined
    Mar 2013
    From
    Oslo
    Posts
    4

    Cobb-Douglas Function: Inverse function and marginal cost

    Ok, so I wonder wether or not I have done this correctly:
    It would be of great help to me.

    I have the Cobb-Douglas function x=An^e
    Were x is produced quantum and n is the input labour.

    First question: Is the inverse function n=(x/A)^{1/e} ? and does that equal: n=(1/A^{1/e})(x^{1/e}) ?

    So the cost function then, were w is the price of labour: wn = (w/A^{1/e})(x^{1/e})

    Second Question: Is the derivative of the inverse function (if Ive done correctly on the first question):

    (w/eA^{1/e})(x^{(1/e)-1})
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,651
    Thanks
    602

    Re: Cobb-Douglas Function: Inverse function and marginal cost

    Hey EconNor.

    As a general rule, we find the inverse function (if it exists) by swapping the independent and dependent variable and re-solving for an expression of the new independent variable in terms of the dependent variable. In other words,

    y = f(x) [Original function] Swapping gives us
    x' = f(y').
    Now re-arrange to get
    y' = g(x') and g is our inverse function.

    In your example y = x and x = n. Doing the above gives us:

    n = Ax^e
    (n/A)^(1/e) = x so our inverse function is

    x^(-1)(n) = (n/A)^(1/e) just as you predicted.

    For the second we use the normal power rule which gives:

    d/dn[(n/A)^(1/e)]
    = (1/A)^(1/e) * (1/e) * n^(1/e - 1)

    Where did you get your w from?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2013
    From
    Oslo
    Posts
    4

    Re: Cobb-Douglas Function: Inverse function and marginal cost

    Ok, thank you.

    Oh, the w is just for the cost function.... w = wage n=Hours of labour ... so the cost function is wn.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cobb-Douglas Function - Help obtaining k*
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: October 9th 2012, 12:20 AM
  2. Concavity of Cobb-Douglas production function
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: June 16th 2012, 02:16 AM
  3. Replies: 3
    Last Post: August 16th 2010, 03:16 AM
  4. Cobb-Douglas production function
    Posted in the Business Math Forum
    Replies: 0
    Last Post: October 11th 2008, 11:37 PM
  5. Cobb-Douglas Production function help
    Posted in the Business Math Forum
    Replies: 0
    Last Post: May 3rd 2008, 02:52 PM

Search Tags


/mathhelpforum @mathhelpforum