Suppose the supply and demand for a certain videotape are given by: supply: p=1/3q^2; demand: p=-1/3q^2+48
and?
To find the equilibrium price and quantity, we need to set the supply equal to the demand and solve for q.
Step 1: Set the supply equal to the demand:
1/3q^2 = -1/3q^2 + 48
Step 2: Combine like terms:
2/3q^2 = 48
Step 3: Multiply both sides by 3/2 to isolate q:
q^2 = 72
Step 4: Take the square root of both sides:
q = √72
Step 5: Simplify the square root:
q = √(36 * 2)
q = 6√2
Now that we have the value of q, we can substitute it back into either the supply or demand equation to find the equilibrium price.
Let's use the demand equation:
p = -1/3(6√2)^2 + 48
p = -1/3(36 * 2) + 48
p = -12 + 48
p = 36
Therefore, the equilibrium quantity (q) is 6√2 and the equilibrium price (p) is 36.