Price Elasticity of Demand and Supply: Question 9

Worked solution

Step 1: Recall the PED formula

$PED = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}$

Step 2: Calculate the percentage change in price

Using the original price of $8 as the base: $\%\Delta P = \frac{10-8}{8}\times100 = +25\%$

Step 3: Calculate the percentage change in quantity demanded

Using the original quantity of 800 as the base: $\%\Delta Q_d = \frac{600-800}{800}\times100 = -25\%$

Step 4: Apply the PED formula

$PED = \frac{-25}{25} = -1.0$

Step 5: Interpret the value

The percentage fall in quantity demanded (25%) is exactly equal, in size, to the percentage rise in price (25%). Since the size of PED is exactly $1.0$, demand for cinema tickets is neither price elastic nor price inelastic, but unitary: quantity demanded changes by exactly the same proportion as price.

Step 6: Rule out the other options

• Option B ($+1.0$) drops the negative sign.
• Option C ($-1.25$) comes from using the new price ($10), instead of the original price ($8), as the base for the percentage change in price.
• Option D ($0$) comes from subtracting the two percentages ($25-25$) instead of dividing one by the other.

Final answer

$PED = \boxed{-1.0}$, option A. Demand for cinema tickets at this price is unitary in elasticity.