Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Answer:
To calculate the Price Elasticity of Supply (PES), we use the following formula:
\[
\text{PES} = \frac{\%\text{ change in quantity supplied}}{\%\text{ change in price}}
\]
### Step 1: Calculate the Percentage Change in Quantity Supplied
The initial quantity supplied (\( Q_1 \)) is 5000 units, and the new quantity supplied (\( Q_2 \)) is 7000 units.
\[
\%\text{ change in quantity supplied} = \frac{Q_2 - Q_1}{Q_1} \times 100
\]
\[
\%\text{ change in quantity supplied} = \frac{7000 - 5000}{5000} \times 100 = \frac{2000}{5000} \times 100 = 40\%
\]
### Step 2: Calculate the Percentage Change in Price
The initial price (\( P_1 \)) is $4, and the new price (\( P_2 \)) is $5.
\[
\%\text{ change in price} = \frac{P_2 - P_1}{P_1} \times 100
\]
\[
\%\text{ change in price} = \frac{5 - 4}{4} \times 100 = \frac{1}{4} \times 100 = 25\%
\]
### Step 3: Calculate PES
\[
\text{PES} = \frac{40\%}{25\%} = 1.6
\]
So, the Price Elasticity of Supply (PES) is 1.6.
### (b) By what percentage will supply extend if the price rose by a given percentage?
We need to determine the percentage change in supply (\(\Delta Q\%\)) given a percentage change in price (\(\Delta P\%\)) and using the PES calculated above.
Using the formula:
\[
\Delta Q\% = \text{PES} \times \Delta P\%
\]
Assuming a general percentage increase in price (\(\Delta P\%\)), the formula will be:
\[
\Delta Q\% = 1.6 \times \Delta P\%
\]
For example, if the price increases by 10%, the change in supply will be:
\[
\Delta Q\% = 1.6 \times 10\% = 16\%
\]
Therefore, the supply will extend by 16% if the price rises by 10%.
In general, the supply will extend by \( 1.6 \times \Delta P\% \) for any given percentage change in price.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.