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Math Help - Thrre sector model and a production fuction question

  1. #1
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    Exclamation Thrre sector model and a production fuction question

    hi all, i have been struggling with these problems for a couple of days and would appreciate any help?
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    Last edited by bobby87; July 26th 2007 at 01:09 PM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by bobby87 View Post
    hi all, i have been struggling with these problems for a couple of days and would appreciate any help?
    What problems?

    -Dan
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    Hi sorry dan the problems are there now
    many thanks
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    Forum Admin topsquark's Avatar
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    The first part of 2 isn't as much hard as it is long.

    Y= C + I

    So
    Y = (aY_d + b) + (cr + d)

    Y = aY_d + b + cr + d

    Then
    Y =a(Y - T) + b + cr + d

    Y = aY - aT  + b + cr + d

    Then
    Y = aY - a(tY + T^*) + b + cr + d

    Y = aY - atY - aT^* + b + cr + d

    Now
    Y - aY + atY = -aT^* + b + cr + d

    Y(1 - a + at) = -aT^* + b + cr + d

    Y = \frac{-aT^* + b + cr + d}{1 - a + at}

    Y = \frac{-aT^* + b + cr + d}{1 - a(1 - t)}

    -Dan
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    Forum Admin topsquark's Avatar
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    For the partial derivatives:
    Y = \frac{-aT^* + b + cr + d}{1 - a(1 - t)}

    \frac{\partial Y}{\partial c} = \frac{r}{1 - a(1 - t)}
    since all other terms are considered to be constant.

    Also
    \frac{\partial Y}{\partial a} = \frac{(-T^*)(1 - a(1 - t)) - (-aT^* + b + cr + d)(-(1 - t))}{(1 - a(1 - t))^2} <-- By the quotient rule

    And I'll let you clean this up yourself.

    -Dan
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