# Market equilibrium

• March 23rd 2009, 03:59 PM
kcwillia377
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...
• March 23rd 2009, 04:20 PM
skeeter
Quote:

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?
• March 23rd 2009, 04:33 PM
kcwillia377
Sorry!
The demand function is:

pq=100+20q
• March 23rd 2009, 04:48 PM
skeeter
$pq = 100 + 20q$

$2p - q = 50$, 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?