Answer: The equilibrium point is where; Quantity supplied = 100 and Quantity demanded = 100
Step-by-step explanation: The equilibrium point on a demand and supply graph is the point at which demand equals supply. Better put, it is the point where the demand curve intersects the supply curve.
The supply function is given as
S(q) = (q + 6)^2
The demand function is given as
D(q) = 1000/(q + 6)
The equilibrium point therefore would be derived as
(q + 6)^2 = 1000/(q + 6)
Cross multiply and you have
(q + 6)^2 x (q + 6) = 1000
(q + 6 )^3 = 1000
Add the cube root sign to both sides of the equation
q + 6 = 10
Subtract 6 from both sides of the equation
q = 4
Therefore when q = 4, supply would be
S(q) = (4 + 6)^2
S(q) = 10^2
S(q) = 100
Also when q = 4, demand would be
D(q) = 1000/(4 + 6)
D(q) = 1000/10
D(q) = 100
Hence at the point of equilibrium the quantity demanded and quantity supplied would be 100 units.
