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Math Help - Market equilibrium

  1. #1
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    Exclamation Market equilibrium

    The supply function is 2p-q=50.
    Demand function is pq=100=20q.

    What are the price and quantity of market equilibrium?

    I can't figure this out. I think you have to isolate "p" and set the two equations equal to each other...but I can't solve it...
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  2. #2
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    Quote Originally Posted by kcwillia377 View Post
    The supply function is 2p-q=50.
    Demand function is pq=100=20q.

    What are the price and quantity of market equilibrium?

    I can't figure this out. I think you have to isolate "p" and set the two equations equal to each other...but I can't solve it...

    please clarify the demand function ... is one of those equal signs a (+) sign?
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  3. #3
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    Sorry!

    The demand function is:

    pq=100+20q
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  4. #4
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    pq = 100 + 20q

    2p - q = 50, solve for q ... q = 2p-50

    substitute (2p-50) for q in the first equation ...

    p(2p-50) = 100 + 20(2p-50)

    solve for p ...

    2p^2 - 50p = 100 + 40p - 1000

    2p^2 - 90p + 900 = 0

    p^2 - 45p + 450 = 0

    (p - 15)(p - 30) = 0

    if p = 15, q = -20

    if  p = 30, q = 10

    now, which set of solutions is valid?
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