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Math Help - [SOLVED] Rearranging.

  1. #1
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    [SOLVED] Rearranging.

    I have been given this equation.

     \Pi_t=\gamma\Pi_t+(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)

    And told it can be rearranged to get this.

     \Pi_t=\Pi_{t-1}-\frac{\alpha(u_t-u_n)}{(1-\gamma)}

    I don't understand how they got this. It's off my lecture slides.
    Could someone please enlighten me?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by el123 View Post
    I have been given this equation.

     \Pi_t=\gamma\Pi_t+(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)

    And told it can be rearranged to get this.

     \Pi_t=\Pi_{t-1}-\frac{\alpha(u_t-u_n)}{(1-\gamma)}

    I don't understand how they got this. It's off my lecture slides.
    Could someone please enlighten me?

    HI

    \Pi_t=\gamma\Pi_t+(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)

    \Pi_t-\gamma\Pi_t=(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)

    (1-\gamma)(\Pi_t)=(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)

    \Pi_t=\frac{(1-\gamma)\Pi_{t-1}-\alpha(u_t-u_n)}{1-\gamma}

    so it becomes

     \Pi_t=\Pi_{t-1}-\frac{\alpha(u_t-u_n)}{(1-\gamma)}
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  3. #3
    Member
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    Ahhhh! Thanks i see where i was getting confused now . Cheers!
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