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

Economics

ScanSolve AI Answer

Answer

-2

Step-by-step solution

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

    From the provided demand schedule:
    The initial price is P1=40P_1 = 40.
    The initial quantity demanded is QD1=40QD_1 = 40.
    The final price is P2=60P_2 = 60.
    Looking at the schedule, the quantity demanded becomes 0 at a price of 50.Foranypriceequaltoorgreaterthan50. For any price equal to or greater than 50, the quantity demanded will be 0. Therefore, for P2=60P_2 = 60, the final quantity demanded is QD2=0QD_2 = 0.

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

    ΔQD=QD2−QD1=0−40=−40\Delta QD = QD_2 - QD_1 = 0 - 40 = -40 ΔP=P2−P1=60−40=20\Delta P = P_2 - P_1 = 60 - 40 = 20
  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=−4020×4040PED = \frac{-40}{20} \times \frac{40}{40} PED=−2×1PED = -2 \times 1 PED=−2PED = -2

    The absolute value of the price elasticity of demand is ∣−2∣=2|-2| = 2.

  4. Interpret the price elasticity of demand.

    Since the absolute value of the price elasticity of demand is 2, which is greater than 1 (∣PED∣>1|PED| > 1), the demand is elastic. This means that the percentage change in quantity demanded is greater than the percentage change in price.

    The price elasticity of demand is −2\boxed{-2}.
    The demand is elastic.

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