what is the equilibrium price and quantity?

Question

Demand equation: p=840-12q

supply equation: p=7q²+2q

Answer 1

Equilibrium point is where demand equals supply

therefore

840-12q=7q^2+2q...bring like terms to form equation

7q^2+2q+12q-840=0

7q^2+14q-840=0...divide all by common factor, 7

q^2+2q-120=0

(q+12)(q-10)

q=-12, q=10

 

Quantity =10

 

using 10 as quantity...

substitute to find price

p=7(10)^2+2(10)=$720

p=840-12(10)=840-120=$720