# Thread: Market equilibrium

1. ## 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...

2. Originally Posted by kcwillia377
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?

3. ## Sorry!

The demand function is:

pq=100+20q

4. $\displaystyle pq = 100 + 20q$

$\displaystyle 2p - q = 50$, 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?

### what is market equilibriummar

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