Price Elasticity of Demand and Supply: Question 1

Worked solution

Step 1: Recall the PED formula

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

Step 2: Substitute the given percentage changes

The price rises, so the percentage change in price is $+10\%$. The quantity demanded falls, so the percentage change in quantity demanded is $-30\%$.

$PED = \frac{-30}{10} = -3.0$

Step 3: Interpret the value

The negative sign is expected: it simply reflects the normal, inverse relationship between price and quantity demanded (when one rises, the other falls). Since the size of PED, ignoring the sign, is $3.0$, and $3.0 > 1$, demand for front-row concert tickets is price elastic. Quantity demanded is more responsive, proportionately, than the change in price.

Step 4: Rule out the other options

• Option B ($-0.33$) comes from inverting the formula, dividing the percentage change in price by the percentage change in quantity demanded instead of the other way round.
• Option C ($3.0$) drops the negative sign, losing the information that price and quantity demanded moved in opposite directions.
• Option D ($0.33$) makes both errors at once, inverting the ratio and dropping the sign.

Final answer

$PED = \boxed{-3.0}$, option A. Demand for front-row concert tickets is price elastic.