Suppose that when the price of premium jeans rose from \( \$ 114 \) to \( \$ 188 \), the quantity demanded decreased from 58 to 35 . Using the midpoint formula, what is the of the price elasticity of demand? Include a negative sign if applicable, and round your answer to two decimal places.

To calculate the price elasticity of demand (PED) using the midpoint formula, we can apply the following formula: \[ \text{PED} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}} \] 1. **Calculate the change in quantity and price:** - Change in Quantity = \( Q_2 - Q_1 = 35 - 58 = -23 \) - Change in Price = \( P_2 - P_1 = 188 - 114 = 74 \) 2. **Average Quantity and Price:** - Average Quantity = \( \frac{Q_1 + Q_2}{2} = \frac{58 + 35}{2} = 46.5 \) - Average Price = \( \frac{P_1 + P_2}{2} = \frac{114 + 188}{2} = 151 \) 3. **Calculate the percentage changes:** - Percentage Change in Quantity = \( \frac{-23}{46.5} \approx -0.4957 \) - Percentage Change in Price = \( \frac{74}{151} \approx 0.4901 \) 4. **Plug these values into the formula for PED:** \[ \text{PED} = \frac{-0.4957}{0.4901} \approx -1.01 \] So, the price elasticity of demand is approximately **-1.01** (rounded to two decimal places).