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Thread: 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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    $\displaystyle pq = 100 + 20q$

    $\displaystyle 2p - q = 50$, solve for $\displaystyle q$ ... $\displaystyle q = 2p-50$

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

    $\displaystyle p(2p-50) = 100 + 20(2p-50)$

    solve for $\displaystyle p$ ...

    $\displaystyle 2p^2 - 50p = 100 + 40p - 1000$

    $\displaystyle 2p^2 - 90p + 900 = 0$

    $\displaystyle p^2 - 45p + 450 = 0$

    $\displaystyle (p - 15)(p - 30) = 0$

    if $\displaystyle p = 15$, $\displaystyle q = -20$

    if $\displaystyle p = 30$, $\displaystyle q = 10$

    now, which set of solutions is valid?
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