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Calculate the price elasticity of demand at Point A and Point B, given P1=45, Q1=20 and P2=35, Q2=30.

Economics

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Answer

-2.25
-1.17
-1.6

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Definition:
Price elasticity of demand measures the responsiveness of the quantity demanded of a good or service to a change in its price. It indicates how much the quantity demanded changes in percentage terms for a one percent change in price.

Given data:
Point A: P1=45P_1 = 45, Q1=20Q_1 = 20
Point B: P2=35P_2 = 35, Q2=30Q_2 = 30

  1. Calculate the change in quantity and price.

    The change in quantity (ΔQ\Delta Q) is Q2−Q1=30−20=10Q_2 - Q_1 = 30 - 20 = 10.
    The change in price (ΔP\Delta P) is P2−P1=35−45=−10P_2 - P_1 = 35 - 45 = -10.
    The slope of the demand curve (ΔQΔP\frac{\Delta Q}{\Delta P}) is 10−10=−1\frac{10}{-10} = -1.

  2. Calculate the price elasticity of demand at Point A.

    The formula for point elasticity of demand is Ed=ΔQΔP×PQE_d = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}.
    Using the values at Point A (PA=45P_A = 45, QA=20Q_A = 20):

    Ed at A=−1×4520E_d \text{ at A} = -1 \times \frac{45}{20} Ed at A=−1×2.25E_d \text{ at A} = -1 \times 2.25 Ed at A=−2.25E_d \text{ at A} = \boxed{-2.25}

  3. Calculate the price elasticity of demand at Point B.

    Using the values at Point B (PB=35P_B = 35, QB=30Q_B = 30):

    Ed at B=−1×3530E_d \text{ at B} = -1 \times \frac{35}{30} Ed at B=−1×1.1666...E_d \text{ at B} = -1 \times 1.1666... Ed at B=−1.17 (rounded to two decimal places)E_d \text{ at B} = \boxed{-1.17} \text{ (rounded to two decimal places)}

  4. Calculate the price elasticity of demand between Point A and B (Arc Elasticity).

    The formula for arc elasticity of demand is:

    Ed=Q2−Q1P2−P1×P1+P2Q1+Q2E_d = \frac{Q_2 - Q_1}{P_2 - P_1} \times \frac{P_1 + P_2}{Q_1 + Q_2}

    Substitute the given values:

    Ed arc=30−2035−45×45+3520+30E_d \text{ arc} = \frac{30 - 20}{35 - 45} \times \frac{45 + 35}{20 + 30} Ed arc=10−10×8050E_d \text{ arc} = \frac{10}{-10} \times \frac{80}{50} Ed arc=−1×1.6E_d \text{ arc} = -1 \times 1.6 Ed arc=−1.6E_d \text{ arc} = \boxed{-1.6}
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