Suppose the price of a ticket to a Billie Eilish concert is
69 and the quantity demanded decreased to 9,300, what is the price elasticity of demand for a Billie Eilish concert ticket
The Correct Answer and Explanation is:
Correct Answer:
To calculate the price elasticity of demand (PED), the following formula is used:Price Elasticity of Demand (PED)=% change in quantity demanded% change in price\text{Price Elasticity of Demand (PED)} = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}}Price Elasticity of Demand (PED)=% change in price% change in quantity demanded
However, the problem only provides a new price and new quantity demanded without the original values. Therefore, one of the following must be true:
- The original price or quantity demanded is missing
- More information is needed to compute elasticity accurately
Assuming a hypothetical scenario:
Suppose the original price was $60 and the original quantity demanded was 10,000 tickets. The new price is $69, and the new quantity demanded is 9,300.
Step 1: Calculate the percentage change in quantity demanded
% change in quantity=9300−1000010000×100=−70010000×100=−7%\%\ \text{change in quantity} = \frac{9300 – 10000}{10000} \times 100 = \frac{-700}{10000} \times 100 = -7\%% change in quantity=100009300−10000×100=10000−700×100=−7%
Step 2: Calculate the percentage change in price
% change in price=69−6060×100=960×100=15%\%\ \text{change in price} = \frac{69 – 60}{60} \times 100 = \frac{9}{60} \times 100 = 15\%% change in price=6069−60×100=609×100=15%
Step 3: Calculate PED
PED=−7%15%=−0.47\text{PED} = \frac{-7\%}{15\%} = -0.47PED=15%−7%=−0.47
Result: -0.47 (usually expressed as 0.47 in absolute value)
Explanation:
The price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its price. A PED value of 0.47 indicates that the demand is inelastic, meaning the quantity demanded changes less proportionally than the price does. This often occurs for goods that are considered necessities, have few substitutes, or are tied to strong consumer preferences—such as tickets to a favorite artist’s concert.
When demand is inelastic, raising the price leads to a relatively small drop in quantity demanded, potentially increasing total revenue. Conversely, lowering the price would not boost sales enough to compensate for the lower price, possibly decreasing total revenue.
