A local electronics store recently increased the price of a portable speaker it sells from $15

Question

to $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?(1 point)
Responses

The demand for the portable speaker is unit elastic.
The demand for the portable speaker is unit elastic.

The demand for the portable speaker is perfectly inelastic.
The demand for the portable speaker is perfectly inelastic.

The demand for the portable speaker is price elastic.
The demand for the portable speaker is price elastic.

The demand for the portable speaker is price inelastic.

Answer 1

To determine the price elasticity of demand (PED) for the portable speaker, we can use the formula:

\[ \text{Price Elasticity of Demand (PED)} = \frac{%\ \text{change in quantity demanded}}{%\ \text{change in price}} \]

1. Calculate the change in quantity demanded:

   • Initial quantity demanded = 100 units
   • New quantity demanded = 70 units
   • Change in quantity demanded = 70 - 100 = -30 units
   • Percentage change in quantity demanded = \(\frac{-30}{100} \times 100 = -30%\)

2. Calculate the change in price:

   • Initial price = $15
   • New price = $18
   • Change in price = 18 - 15 = 3 dollars
   • Percentage change in price = \(\frac{3}{15} \times 100 = 20%\)

3. Calculate the price elasticity of demand: \[ PED = \frac{-30%}{20%} = -1.5 \]

Since the absolute value of the price elasticity of demand (1.5) is greater than 1, we can conclude that the demand for the portable speaker is price elastic.

Therefore, the correct response is:

The demand for the portable speaker is price elastic.