A local electronic store recently increased the price of a portable speaker it sells from $15-$18. The owner of the store noticed that the store went from selling 100 units a month to 70 speakers a month. Which of the following choices correctly describes the price elasticity of demand for the portable speaker?
The price elasticity of demand for the portable speaker can be determined by comparing the percentage change in quantity demanded to the percentage change in price.
Percentage change in quantity demanded = ((New quantity - Original quantity) / Original quantity) * 100
Percentage change in price = ((New price - Original price) / Original price) * 100
For this scenario:
Original quantity = 100 units
New quantity = 70 units
Original price = $15
New price = $18
Percentage change in quantity demanded = ((70 - 100) / 100) * 100 = -30%
Percentage change in price = ((18 - 15) / 15) * 100 = 20%
To determine the price elasticity of demand, we divide the percentage change in quantity demanded by the percentage change in price:
Price elasticity of demand = (-30% / 20%)
Price elasticity of demand = -1.5
Since the price elasticity of demand is negative, indicating an inverse relationship between price and quantity demanded, and the magnitude is greater than 1 (in absolute value), we can conclude that the demand for the portable speaker is elastic. Thus, the correct choice is "Elastic."