Results 1 to 2 of 2

Math Help - Simple (not for me) algebra problem

  1. #1
    Junior Member
    Joined
    Feb 2011
    Posts
    66

    Simple (not for me) 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 ( q^{T})

    this is found by finding the equilibrium price ( p^{T})

    So I solve simultaneously and get:

    p^{T}=\frac{(c+a)}{(b+d)}+\frac{bT}{b+d}

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

    q^{T}=c-dp^{T}=\frac{(bc-ad)}{(b+d)}+\frac{bdT}{b+d}

    I can't figure out how the hell these people managed to get bc-ad, Can someone tell me how they got this!?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,988
    Thanks
    1128
    Okay, so you know that p^T= \frac{c+a}{b+d}+ \frac{bT}{b+d}. You also know that q= c- dp.

    So q= c- \frac{dc+ da}{b+d}- \frac{dc+da}{b+d}- \frac{bT}{b+d}
    \frac{cb+ cd}{b+d}- \frac{dc+ da}{b+d}- \frac{bdT}{b+d}

    Notice that the two "cd" and "dc" terms cancel, leaving cb- da= bc- ad. Of course, because it is subtracted, -\frac{bT}{b+d} becomes \frac{bT}{b+d}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple Algebra Problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 13th 2011, 10:52 PM
  2. Simple algebra problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: December 11th 2010, 10:06 AM
  3. simple algebra problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 19th 2008, 09:13 PM
  4. Simple algebra problem
    Posted in the Algebra Forum
    Replies: 5
    Last Post: November 15th 2007, 05:42 AM
  5. Simple Algebra Problem
    Posted in the Algebra Forum
    Replies: 6
    Last Post: May 19th 2007, 01:24 AM

Search Tags


/mathhelpforum @mathhelpforum