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. d. unit elastic.

To determine the **price elasticity of demand** for Sam's pizzas, we'll use the **arc elasticity formula**: \[ \text{Elasticity (E)} = \frac{\frac{Q_2 - Q_1}{\frac{Q_2 + Q_1}{2}}}{\frac{P_2 - P_1}{\frac{P_2 + P_1}{2}}} \] **Given:** - Initial Price (\( P_1 \)) = \$6 - New Price (\( P_2 \)) = \$5 - Initial Quantity (\( Q_1 \)) = 400 pizzas - New Quantity (\( Q_2 \)) = 600 pizzas **Calculations:** 1. **Change in Quantity:** \[ \Delta Q = Q_2 - Q_1 = 600 - 400 = 200 \] \[ \text{Average Quantity} = \frac{Q_2 + Q_1}{2} = \frac{600 + 400}{2} = 500 \] \[ \text{Percentage Change in Quantity} = \frac{200}{500} = 0.4 \text{ or } 40\% \] 2. **Change in Price:** \[ \Delta P = P_2 - P_1 = 5 - 6 = -1 \] \[ \text{Average Price} = \frac{P_2 + P_1}{2} = \frac{5 + 6}{2} = 5.5 \] \[ \text{Percentage Change in Price} = \frac{-1}{5.5} \approx -0.1818 \text{ or } -18.18\% \] 3. **Elasticity Calculation:** \[ E = \frac{0.4}{0.1818} \approx 2.2 \] **Interpretation:** - **Elasticity (|E| = 2.2):** Since the absolute value of elasticity is greater than 1, the demand is **elastic**. This means that the percentage change in quantity demanded is greater than the percentage change in price. **Answer:** **a. elastic.**