Determine an interpret the price elasticity for a price change from 40 to 60.

Question

ScanSolve AI Tutor · Accepted Answer

To determine and interpret the price elasticity of demand, we will use the midpoint formula.

Identify the initial and final prices and quantities.
Given:
Initial Price ( $P_1$ ) = $40 Initial Quantity Demanded ($ QD_1 $) = 920 Final Price ($ P_2 $) =$ 60 Final Quantity Demanded ( $QD_2$ ) = 880
State the formula for price elasticity of demand (midpoint method).
$PED = \frac{\frac{QD_2 - QD_1}{(QD_1 + QD_2)/2}}{\frac{P_2 - P_1}{(P_1 + P_2)/2}}$
Calculate the percentage change in quantity demanded.
$\Delta QD = QD_2 - QD_1 = 880 - 920 = -40$ $\text{Average } QD = \frac{920 + 880}{2} = \frac{1800}{2} = 900$ $\% \Delta QD = \frac{-40}{900} = -\frac{4}{90} = -\frac{2}{45} \approx -0.0444$
Calculate the percentage change in price.
$\Delta P = P_2 - P_1 = 60 - 40 = 20$ $\text{Average } P = \frac{40 + 60}{2} = \frac{100}{2} = 50$ $\% \Delta P = \frac{20}{50} = \frac{2}{5} = 0.4$
Calculate the price elasticity of demand.
$PED = \frac{-\frac{2}{45}}{\frac{2}{5}} = -\frac{2}{45} \times \frac{5}{2} = -\frac{10}{90} = -\frac{1}{9}$ $PED \approx -0.111$
Interpret the result.
The price elasticity of demand is approximately $-0.111$ . Since the absolute value of PED ( $|-0.111| = 0.111$ ) is less than 1, the demand is inelastic. This means that the quantity demanded is not very responsive to changes in price. Specifically, a 1% increase in price leads to approximately a 0.111% decrease in quantity demanded.

The price elasticity of demand is $\boxed{-0.111}$ .
The demand is inelastic.

Answer