1. **Stating the problem:** We have a demand schedule for motel rooms with prices, quantities demanded, total revenue, and percentage changes in price and quantity. We need to verify if the percentage changes are correct using the midpoint method. 2. **Formula for midpoint method:** The percentage change in price or quantity between two points is calculated as: $$\% \text{ change} = \frac{\text{New value} - \text{Old value}}{\frac{\text{New value} + \text{Old value}}{2}} \times 100$$ 3. **Check % change in price and quantity between each pair of points:** - Between $20$ and $40$: - Price change: $$\frac{40 - 20}{(40 + 20)/2} \times 100 = \frac{20}{30} \times 100 = 66.7\%$$ (Given: 100%, so incorrect) - Quantity change: $$\frac{20 - 24}{(20 + 24)/2} \times 100 = \frac{-4}{22} \times 100 = -18.18\%$$ (Given: 16.7%, incorrect sign and value) - Between $40$ and $60$: - Price change: $$\frac{60 - 40}{(60 + 40)/2} \times 100 = \frac{20}{50} \times 100 = 40\%$$ (Given: 50%, incorrect) - Quantity change: $$\frac{16 - 20}{(16 + 20)/2} \times 100 = \frac{-4}{18} \times 100 = -22.22\%$$ (Given: 20%, incorrect sign and value) - Between $60$ and $80$: - Price change: $$\frac{80 - 60}{(80 + 60)/2} \times 100 = \frac{20}{70} \times 100 = 28.57\%$$ (Given: 33.3%, close but slightly off) - Quantity change: $$\frac{12 - 16}{(12 + 16)/2} \times 100 = \frac{-4}{14} \times 100 = -28.57\%$$ (Given: 33.3%, incorrect sign and value) - Between $80$ and $100$: - Price change: $$\frac{100 - 80}{(100 + 80)/2} \times 100 = \frac{20}{90} \times 100 = 22.22\%$$ (Given: 25%, close but slightly off) - Quantity change: $$\frac{8 - 12}{(8 + 12)/2} \times 100 = \frac{-4}{10} \times 100 = -40\%$$ (Given: 50%, incorrect sign and value) - Between $100$ and $120$: - Price change: $$\frac{120 - 100}{(120 + 100)/2} \times 100 = \frac{20}{110} \times 100 = 18.18\%$$ (Given: 20%, close but slightly off) - Quantity change: $$\frac{4 - 8}{(4 + 8)/2} \times 100 = \frac{-4}{6} \times 100 = -66.67\%$$ (No given value to compare) 4. **Conclusion:** - The percentage changes in price and quantity given in the table are mostly incorrect in value and sign. - The midpoint method always yields symmetric percentage changes with correct signs (negative for decreases). - Your answers in the boxes are not correct based on the midpoint method calculations. 5. **Recommendation:** - Recalculate all percentage changes using the midpoint formula shown. - Remember that quantity decreases should show negative percentage changes. **Final note:** The total revenue values are correct as $\text{Price} \times \text{Quantity}$. **Summary:** Your percentage change answers are not correct according to the midpoint method.