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

Initially, 8,000 roses were sold at $1, and 30,000 roses were sold at $2.

$\%\ \text{change in quantity} = \frac{30,000 - 8,000}{8,000} \times 100 = \frac{22,000}{8,000} \times 100 = 275\%$

Step 2: Calculate the percentage change in price

The price increased from $1 to $2.

$\%\ \text{change in price} = \frac{2 - 1}{1} \times 100 = 100\%$

Step 3: Calculate the price elasticity of supply

$\text{PES} = \frac{275\%}{100\%} = 2.75$

So, the price elasticity of supply is 2.75.

Would you like further details on this or have any additional questions?

Here are 5 questions that extend the discussion:

1. How does a price elasticity of supply greater than 1 affect the market?
2. What would happen if the supply of roses were inelastic instead?
3. Can the price elasticity of demand be calculated from the given data?
4. What factors could cause the supply curve for roses to shift?
5. How would a constant demand curve alter the elasticity calculation?

Tip: A supply elasticity greater than 1 indicates that producers are very responsive to price changes, increasing supply significantly when prices rise.