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Math Help - demand and supply

  1. #1
    Member princess_anna57's Avatar
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    Post demand and supply

    Demand and supply for a commodity are given by

    qd = 18 - 2p and qs = -10 + 5p (1 - t)

    respectively where t is a tax levied on each unit sold (to be paid by the producer).

    a) Draw the supply and demand curves on the same diagram when t = 0

    b) Find the equilibrium quantity sold when t = 0

    c) Find the equilibrium quantity sold when t = 0.32 (i.e a tax rate of 32%).

    d) Derive a functional relationship between p and t in equilibrium.
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  2. #2
    Senior Member tukeywilliams's Avatar
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    Green is quantity supplied, red is quantity demanded for  t = 0 .

    For (b) set  qd = qp or  18-2p = 5p-10, p = 4 . So  t = 0, \ p = 4 .

    For (c) set  18-2p = -10 + 3.4p . So  t = 0.32, \ p = 5.\overline{185} .

    For (d) use (b) and (c) to try and find a functional relationship between  p and  t (i.e. is it a linear equation  y = ax+b , a quadratic  y = ax^2 + bx +c etc.).
    Attached Thumbnails Attached Thumbnails demand and supply-untitled.jpg  
    Last edited by tukeywilliams; July 29th 2007 at 09:17 PM.
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  3. #3
    Member princess_anna57's Avatar
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    Linear?
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  4. #4
    Member princess_anna57's Avatar
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    So is that all I'll need to write? That the functional relationship is linear?
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  5. #5
    Senior Member tukeywilliams's Avatar
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    Actually I think its quadratic now that I have plotted a few more points. We have to be careful about overfitting/ extrapolating data.

     t = 0, \ p = 4

     t = 1, \ p = 14

     t = 2, p \approx - 9.4

    So the functional form is  p = at^2 + bt + c where  a,b,c are constants.
    Attached Thumbnails Attached Thumbnails demand and supply-untitled.jpg  
    Last edited by tukeywilliams; July 29th 2007 at 10:32 PM.
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  6. #6
    Member princess_anna57's Avatar
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    hmm... interesting.
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