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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.