To calculate the Price Elasticity of Supply (PES), we use the following formula:

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

Where: $\% \text{ change in quantity supplied} = \frac{Q_2 - Q_1}{Q_1} \times 100$ $\% \text{ change in price} = \frac{P_2 - P_1}{P_1} \times 100$

Here, the initial price $P_1$ is $45, the new price $P_2$ is $55, the initial quantity supplied $Q_1$ is 20 units, and the new quantity supplied $Q_2$ is 30 units.

Now, let's calculate each component.

Step 1: Calculate the percentage change in quantity supplied

$\% \text{ change in quantity supplied} = \frac{30 - 20}{20} \times 100 = \frac{10}{20} \times 100 = 50\%$

Step 2: Calculate the percentage change in price

$\% \text{ change in price} = \frac{55 - 45}{45} \times 100 = \frac{10}{45} \times 100 \approx 22.22\%$

Step 3: Calculate the Price Elasticity of Supply

$PES = \frac{50\%}{22.22\%} = \frac{50}{22.22} \approx 2.25$

Conclusion:

The Price Elasticity of Supply is approximately 2.25, so the correct answer is:

9/4 = 2.25

Let me know if you'd like further clarification on any part of the calculation!

---

Here are some related questions you might find interesting:

1. How would the Price Elasticity of Supply change if the price change were smaller (e.g., from $45 to $50)?
2. What would happen to the supply curve if the elasticity of supply was 0?
3. How does the time frame (short-term vs. long-term) affect the elasticity of supply?
4. How does the availability of substitute goods affect the price elasticity of supply?
5. How does the concept of price elasticity of supply differ from price elasticity of demand?

Tip: When calculating percentage changes, always remember to subtract the initial value from the new value, and divide by the initial value to get an accurate percentage.