SOLUTION: Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given. Supply: p=q^2+20q Demand: p=-2q^2+10q+5200 The equilibrium

Algebra ->  Finance -> SOLUTION: Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given. Supply: p=q^2+20q Demand: p=-2q^2+10q+5200 The equilibrium      Log On


   

Question 1154482: Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand functions are given.
Supply: p=q^2+20q Demand: p=-2q^2+10q+5200
The equilibrium quantity is q=____
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Supply:
+p=q%5E2%2B20q
Demand:
p=-2q%5E2%2B10q%2B5200
The equilibrium is when supply=demand
+q%5E2%2B20q=-2q%5E2%2B10q%2B5200
+q%5E2%2B20q%2B2q%5E2-10q-5200=0
+3q%5E2%2B10q-5200=0
+3q%5E2%2B10q-5200=0 ...factor
+3q%5E2-120q+%2B130q-5200=0
+%283q%5E2-120q%29%2B%28130q-5200%29=0
+3q%28q-40%29%2B130%28q-40%29=0
%28q+-+40%29+%283q+%2B+130%29+=+0-> we need only positive solution
so, q=40

The equilibrium quantity is q=40.