# Market equilibrium

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

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