Supply and Demand

Question

HI All-

 

I'm having a  little trouble with my economics class.  Supply and demand are not making sense to me and I need a little help with the following question:

 

Find the equilibrium quantity and price for the commodity whose supply and demand functions are given.  Supply p=q^2+30q Demand p=-2q^2+10q+8500

 

If any one could help with this I'd appreciate it.  Would you also explain how you got the answer as my textbook is not easy to understand.

 

Thanks!

Answer 1

Supply = Demand 

p=q^2+30q =p=-2q^2+10q+8500

q^2+30q = -2q^2+10q+8500

3 q^2 + 20 q - 8500 = 0

(3 q +170) (q - 50) = 0

3 q +170 = 0    q - 50 = 0

q1 = -170/3 (quantity can't be negative number, so it doesn't fit the requirement) 

q2 = 50

 

Plug q2 = 50 into p=q^2+30q:

p = 50^2 + 30(50) = 2500 + 1500 = 4000