Question
Suppose the price elasticity of supply for jackets is 3 . After a price increase, quantity supplied increased by \( 30 \% \). What was the percentage change in price that caused this change in quantity supplied? The percent change in price was .... If appicable, round your answer to iwodecimal places.
Ask by Wood Allan. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The percentage change in price was 10%.
Solution
To find the percentage change in price that caused the change in quantity supplied, we can use the formula for price elasticity of supply (PES):
\[
PES = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}
\]
Given:
- \( PES = 3 \)
- Percentage Change in Quantity Supplied = \( 30\% \)
We can rearrange the formula to solve for the percentage change in price:
\[
\text{Percentage Change in Price} = \frac{\text{Percentage Change in Quantity Supplied}}{PES}
\]
Now, substituting the known values:
\[
\text{Percentage Change in Price} = \frac{30\%}{3}
\]
Calculating this gives:
\[
\text{Percentage Change in Price} = 10\%
\]
Thus, the percentage change in price that caused the change in quantity supplied was \( 10\% \).
If applicable, rounding to two decimal places, the answer remains \( 10.00\% \).
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Simplify this solution Extra Insights
To find the percentage change in price using the price elasticity of supply formula, we use the formula: \[ \text{Price Elasticity of Supply (E)} = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}} \] Given that the price elasticity of supply is 3 and the percentage change in quantity supplied is 30%, we can set up the equation: \[ 3 = \frac{30\%}{\text{Percentage Change in Price}} \] Now, rearranging to find the percentage change in price, we have: \[ \text{Percentage Change in Price} = \frac{30\%}{3} = 10\% \] So, the percent change in price was **10.00**.
