If Sam the Pizzaiolo lowers the price of their pizzas from \( \$ 6 \) to \( \$ 5 \) and finds that sales increase from 400 to 600 pizzas per week, then the demand for Sam's pizzas in this range is: a. elastic. b. Inferior. c. Inelastic.

To determine the elasticity of demand for Sam's pizzas, we'll calculate the **price elasticity of demand (E)** using the **midpoint (arc elasticity) formula**. This method provides a more accurate measure when there's a significant change in price and quantity. **Given:** - Initial Price (\( P_1 \)) = \$6 - Final Price (\( P_2 \)) = \$5 - Initial Quantity (\( Q_1 \)) = 400 pizzas - Final Quantity (\( Q_2 \)) = 600 pizzas **Step 1: Calculate the Percentage Change in Quantity (\( \Delta Q / Q_{avg} \))** \[ \Delta Q = Q_2 - Q_1 = 600 - 400 = 200 \text{ pizzas} \] \[ Q_{avg} = \frac{Q_1 + Q_2}{2} = \frac{400 + 600}{2} = 500 \text{ pizzas} \] \[ \Delta Q / Q_{avg} = \frac{200}{500} = 0.4 \text{ or } 40\% \] **Step 2: Calculate the Percentage Change in Price (\( \Delta P / P_{avg} \))** \[ \Delta P = P_2 - P_1 = 5 - 6 = -1 \text{ dollar} \] \[ P_{avg} = \frac{P_1 + P_2}{2} = \frac{6 + 5}{2} = 5.5 \text{ dollars} \] \[ \Delta P / P_{avg} = \frac{-1}{5.5} \approx -0.1818 \text{ or } -18.18\% \] **Step 3: Calculate Elasticity (E)** \[ E = \frac{\Delta Q / Q_{avg}}{\Delta P / P_{avg}} = \frac{0.4}{-0.1818} \approx -2.2 \] **Interpretation:** - The absolute value of elasticity (\( |E| = 2.2 \)) is greater than 1. - **Elastic Demand**: Consumers are relatively responsive to price changes. **Conclusion:** The demand for Sam's pizzas in this price range is **elastic**. **Answer:** a. elastic.