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Calculate the price elasticity of demand given initial and final prices and quantities.

Economics

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Answer

B) 0.22\text{B) 0.22}

Step-by-step solution

5 steps
  1. Identify the initial and final prices and quantities.

    Initial Price (P1P_1) = N20
    Final Price (P2P_2) = N80
    Initial Quantity (Q1Q_1) = 300 units
    Final Quantity (Q2Q_2) = 500 units

  2. Use the point elasticity of demand formula.

    The formula for point elasticity of demand is:

    Ed=Q2−Q1Q1P2−P1P1E_d = \frac{\frac{Q_2 - Q_1}{Q_1}}{\frac{P_2 - P_1}{P_1}}
  3. Calculate the change in quantity and change in price.

    Change in quantity (ΔQ\Delta Q) = Q2−Q1=500−300=200Q_2 - Q_1 = 500 - 300 = 200 units
    Change in price (ΔP\Delta P) = P2−P1=80−20=60P_2 - P_1 = 80 - 20 = 60 N

  4. Substitute these values into the elasticity formula.

    Ed=2003006020E_d = \frac{\frac{200}{300}}{\frac{60}{20}} Ed=233E_d = \frac{\frac{2}{3}}{3} Ed=23×13E_d = \frac{2}{3} \times \frac{1}{3} Ed=29E_d = \frac{2}{9}
  5. Convert the fraction to a decimal and compare with the options.

    Ed≈0.2222...E_d \approx 0.2222...

    This value is approximately 0.22.

    The final answer is B) 0.22\text{B) 0.22}.

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