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At this price determine and interpret the price elasticity of demand.

Economics

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Answer

-0.67

Step-by-step solution

4 steps

  1. Identify the initial and final price and quantity demanded.

    The initial price is P1=20P_1 = 20.
    The final price is P2=25P_2 = 25.
    The initial quantity demanded is QD1=120QD_1 = 120.
    The final quantity demanded is QD2=100QD_2 = 100.

  2. Calculate the change in quantity demanded (ΔQD\Delta QD) and the change in price (ΔP\Delta P).

    ΔQD=QD2−QD1=100−120=−20\Delta QD = QD_2 - QD_1 = 100 - 120 = -20 ΔP=P2−P1=25−20=5\Delta P = P_2 - P_1 = 25 - 20 = 5

  3. Apply the point price elasticity of demand formula.

    The formula for point price elasticity of demand (PED) is:

    PED=ΔQDΔP×P1QD1PED = \frac{\Delta QD}{\Delta P} \times \frac{P_1}{QD_1}

    Substitute the values:

    PED=−205×20120PED = \frac{-20}{5} \times \frac{20}{120} PED=−4×16PED = -4 \times \frac{1}{6} PED=−46PED = -\frac{4}{6} PED=−23PED = -\frac{2}{3} PED≈−0.67PED \approx -0.67

    The absolute value of the price elasticity of demand is ∣−0.67∣=0.67|-0.67| = 0.67.

  4. Interpret the price elasticity of demand.

    Since the absolute value of the price elasticity of demand is 0.67, which is less than 1 (∣PED∣<1|PED| < 1), the demand is inelastic. This means that the percentage change in quantity demanded is less than the percentage change in price. For example, a 1% increase in price leads to a 0.67% decrease in quantity demanded.

    The price elasticity of demand is −0.67\boxed{-0.67}.
    The demand is inelastic.

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