The formula for the price elasticity of supply (PES) is:

$PES = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}}$

Step 1: Calculate the percentage change in quantity supplied

The quantity supplied increased from 350 to 380. The percentage change in quantity supplied is calculated as:

$\%\ \text{change in quantity supplied} = \frac{\text{New Quantity} - \text{Old Quantity}}{\text{Old Quantity}} \times 100$

$\%\ \text{change in quantity supplied} = \frac{380 - 350}{350} \times 100 = \frac{30}{350} \times 100 \approx 8.57\%$

Step 2: Calculate the percentage change in price

The price increased by 30%, so:

$\%\ \text{change in price} = 30\%$

Step 3: Calculate the price elasticity of supply

Now, using the PES formula:

$PES = \frac{8.57\%}{30\%} \approx 0.29$

Thus, the price elasticity of supply for pencils is 0.29 (rounded to two decimals).

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What factors affect the elasticity of supply for goods in a competitive market?
2. How does the time period affect the price elasticity of supply?
3. What would happen to elasticity if the increase in quantity supplied was larger?
4. How do we interpret a price elasticity of supply less than 1?
5. Can elasticity of supply ever be negative?

Tip: Inelastic supply means quantity supplied is relatively unresponsive to price changes.