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Math Help - Algebra problem!

  1. #1
    Junior Member
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    Feb 2011
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    Algebra problem!



    I'm working from a book called Mathematics for Economics and Finance (Martin Anthony and Norman Biggs) I have a problem with one of their damn examples on supply and demand.

    the supply set is S={(p,q)|q=bp-a} and D={(p,q)|q=c-dp}

    when an excise tax is imposed i need to find the equilibrium quantity ()

    this is found by finding the equilibrium price ()

    So I solve simultaneously and get:



    which is in the book. Now I need to find qT which the book states is found by:



    I can't figure out how the hell these people managed to get bc-ad as the numerator for the first term, Can someone tell me how they got this!?
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  2. #2
    Member
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    q^T = c - d\left(\dfrac{c+a}{b+d} + \dfrac{bT}{b+d}\right)

    = c - \dfrac{dc+da}{b+d} - \dfrac{bdT}{b + d}

    = \dfrac{bc + dc}{b + d} - \dfrac{dc+da}{b+d} - \dfrac{bdT}{b + d}

    = \dfrac{bc + dc - dc - da}{b + d} - \dfrac{bdT}{b + d}

    = \dfrac{bc - da}{b + d} - \dfrac{bdT}{b + d}
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  3. #3
    MHF Contributor

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    This problem was also posted in the "algebra and prealgebra" section.
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