Suppose the supply and demand for a certain videotape are given by:
Supply: p=1/3q^2
Demand: p=-1/3q^2+48
What is your question?
That's how the question is in the book.
142
To find the equilibrium price and quantity for the given supply and demand equations, we need to set the supply equal to the demand and solve for the quantity.
Step 1: Set the supply equal to the demand equation:
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 = (48 * 3/2)
Step 4: Simplify:
q^2 = 72
Step 5: Take the square root of both sides to solve for q:
q = √72
Step 6: Simplify:
q ≈ 8.49 (rounded to two decimal places)
Now that we have the quantity (q), we can substitute it back into either the supply or demand equation to find the equilibrium price.
Using the demand equation:
p = -1/3q^2 + 48
p = -1/3(8.49)^2 + 48
p ≈ 45.51 (rounded to two decimal places)
Therefore, the equilibrium quantity is approximately 8.49 and the equilibrium price is approximately 45.51.