To calculate the price elasticity of supply (PES), we use the midpoint formula. The formula for price elasticity of supply is:

$\text{PES} = \frac{\left( \frac{\Delta Q}{Q_{\text{avg}}} \right)}{\left( \frac{\Delta P}{P_{\text{avg}}} \right)}$

where:

• $\Delta Q$ is the change in quantity supplied,
• $\Delta P$ is the change in price,
• $Q_{\text{avg}}$ is the average of the initial and final quantities,
• $P_{\text{avg}}$ is the average of the initial and final prices.

Step 1: Identify the data

• Initial price ($P_1$) = $8,000 per ton
• Final price ($P_2$) = $6,000 per ton
• Initial quantity supplied ($Q_1$) = 16,000 thousand tons
• Final quantity supplied ($Q_2$) = 15,500 thousand tons

Step 2: Calculate changes in price and quantity

• $\Delta P = P_2 - P_1 = 6,000 - 8,000 = -2,000$
• $\Delta Q = Q_2 - Q_1 = 15,500 - 16,000 = -500$

Step 3: Calculate the average price and average quantity

• $P_{\text{avg}} = \frac{P_1 + P_2}{2} = \frac{8,000 + 6,000}{2} = 7,000$
• $Q_{\text{avg}} = \frac{Q_1 + Q_2}{2} = \frac{16,000 + 15,500}{2} = 15,750$

Step 4: Plug values into the midpoint formula

$\text{PES} = \frac{\left( \frac{-500}{15,750} \right)}{\left( \frac{-2,000}{7,000} \right)}$ $\text{PES} = \frac{-0.0317}{-0.2857} = 0.1111$

Step 5: Round to two decimal places

The price elasticity of supply is approximately 0.11.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What does a price elasticity of supply less than 1 imply about the resource's supply elasticity?
2. How would the elasticity change if the quantity supplied had decreased by 1,000 thousand tons instead of 500?
3. How does the midpoint formula differ from the basic elasticity formula?
4. What happens to the elasticity if the price changes more drastically?
5. Why is elasticity important in understanding market behavior?

Tip: Price elasticity of supply measures how responsive the quantity supplied is to a change in price. Elasticities less than 1 are considered inelastic.