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A local electronics store recently increased the price of a portable speaker it sells from $15 to $18. The owner of the store n...Question
A local electronics store recently increased the price of a portable speaker it sells from $15
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 price inelastic.
The demand for the portable speaker is price 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 unit elastic.
The demand for the portable speaker is unit elastic.
The demand for the portable speaker is perfectly inelastic.
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 price inelastic.
The demand for the portable speaker is price 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 unit elastic.
The demand for the portable speaker is unit elastic.
The demand for the portable speaker is perfectly inelastic.
Answers
GPT-4o mini
To determine the price elasticity of demand for the portable speaker, we can calculate the price elasticity of demand (PED) using the following formula:
\[
PED = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}
\]
1. **Calculate the percentage change in quantity demanded:**
- Initial quantity = 100 units
- New quantity = 70 units
- Change in quantity = 70 - 100 = -30 units
\[
\%\text{ change in quantity demanded} = \frac{-30}{100} \times 100 = -30\%
\]
2. **Calculate the percentage change in price:**
- Initial price = $15
- New price = $18
- Change in price = 18 - 15 = $3
\[
\%\text{ change in price} = \frac{3}{15} \times 100 = 20\%
\]
3. **Calculate the price elasticity of demand:**
\[
PED = \frac{-30\%}{20\%} = -1.5
\]
The absolute value of price elasticity is 1.5, which indicates that the demand for the portable speaker is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price.
Therefore, the correct response is:
**The demand for the portable speaker is price elastic.**
\[
PED = \frac{\%\text{ change in quantity demanded}}{\%\text{ change in price}}
\]
1. **Calculate the percentage change in quantity demanded:**
- Initial quantity = 100 units
- New quantity = 70 units
- Change in quantity = 70 - 100 = -30 units
\[
\%\text{ change in quantity demanded} = \frac{-30}{100} \times 100 = -30\%
\]
2. **Calculate the percentage change in price:**
- Initial price = $15
- New price = $18
- Change in price = 18 - 15 = $3
\[
\%\text{ change in price} = \frac{3}{15} \times 100 = 20\%
\]
3. **Calculate the price elasticity of demand:**
\[
PED = \frac{-30\%}{20\%} = -1.5
\]
The absolute value of price elasticity is 1.5, which indicates that the demand for the portable speaker is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price.
Therefore, the correct response is:
**The demand for the portable speaker is price elastic.**