Exercise 9 You are a supplier of peanuts. Your research department estimates that the price elasticity of demand for peanuts is 2.5 . By what percentage will quantity demanded rise if you lower price from \( \$ 4 \) to \( \$ 2 \) ?

To calculate the percentage change in quantity demanded based on the price elasticity of demand, we can use the formula: \[ \text{Percentage Change in Quantity Demanded} = \text{Price Elasticity of Demand} \times \text{Percentage Change in Price} \] First, we need to calculate the percentage change in price. The initial price is \( P_1 = 4 \) and the new price is \( P_2 = 2 \). The percentage change in price can be calculated as follows: \[ \text{Percentage Change in Price} = \frac{P_2 - P_1}{P_1} \times 100 \] Substituting the values: \[ \text{Percentage Change in Price} = \frac{2 - 4}{4} \times 100 = \frac{-2}{4} \times 100 = -50\% \] Now, we can use the price elasticity of demand, which is given as \( 2.5 \): \[ \text{Percentage Change in Quantity Demanded} = 2.5 \times (-50\%) \] Calculating this gives: \[ \text{Percentage Change in Quantity Demanded} = -125\% \] Since the quantity demanded cannot decrease by more than 100%, this indicates that the quantity demanded will increase significantly due to the price drop. However, since we are looking for the increase in quantity demanded, we interpret the absolute value: \[ \text{Percentage Increase in Quantity Demanded} = 125\% \] Thus, the quantity demanded will rise by **125%** if you lower the price from \( \$4 \) to \( \$2 \).