Income(Rs.) 200. 240. 280. 320 Quantity. 50. 80. 100. 110 Calculate the income elasticity of demands..

Economics

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here are the calculations for the income elasticity of demand for each interval:

Calculate the income elasticity of demands.

The formula for income elasticity of demand (EyE_y) is:

Ey=ΔQΔY×YQE_y = \frac{\Delta Q}{\Delta Y} \times \frac{Y}{Q}

Where:
ΔQ\Delta Q = Change in quantity demanded
ΔY\Delta Y = Change in income
YY = Original income
QQ = Original quantity demanded

1. When income increases from Rs. 200 to Rs. 240:

  1. Identify the initial and final values.

    Initial Income (Y1Y_1) = Rs. 200
    Final Income (Y2Y_2) = Rs. 240
    Initial Quantity (Q1Q_1) = 50 units
    Final Quantity (Q2Q_2) = 80 units

  2. Calculate the change in income (ΔY\Delta Y) and change in quantity (ΔQ\Delta Q).

    ΔY=Y2−Y1=240−200=40\Delta Y = Y_2 - Y_1 = 240 - 200 = 40 ΔQ=Q2−Q1=80−50=30\Delta Q = Q_2 - Q_1 = 80 - 50 = 30
  3. Apply the income elasticity of demand formula.

    Ey=ΔQΔY×Y1Q1E_y = \frac{\Delta Q}{\Delta Y} \times \frac{Y_1}{Q_1} Ey=3040×20050E_y = \frac{30}{40} \times \frac{200}{50} Ey=0.75×4E_y = 0.75 \times 4 Ey=3E_y = 3

    The income elasticity of demand is 3\boxed{3}.

    2. When income increases from Rs. 240 to Rs. 280:

  4. Identify the initial and final values.

    Initial Income (Y1Y_1) = Rs. 240
    Final Income (Y2Y_2) = Rs. 280
    Initial Quantity (Q1Q_1) = 80 units
    Final Quantity (Q2Q_2) = 100 units

  5. Calculate the change in income (ΔY\Delta Y) and change in quantity (ΔQ\Delta Q).

    ΔY=Y2−Y1=280−240=40\Delta Y = Y_2 - Y_1 = 280 - 240 = 40 ΔQ=Q2−Q1=100−80=20\Delta Q = Q_2 - Q_1 = 100 - 80 = 20
  6. Apply the income elasticity of demand formula.

    Ey=ΔQΔY×Y1Q1E_y = \frac{\Delta Q}{\Delta Y} \times \frac{Y_1}{Q_1} Ey=2040×24080E_y = \frac{20}{40} \times \frac{240}{80} Ey=0.5×3E_y = 0.5 \times 3 Ey=1.5E_y = 1.5

    The income elasticity of demand is 1.5\boxed{1.5}.

    3. When income increases from Rs. 280 to Rs. 320:

  7. Identify the initial and final values.

    Initial Income (Y1Y_1) = Rs. 280
    Final Income (Y2Y_2) = Rs. 320
    Initial Quantity (Q1Q_1) = 100 units
    Final Quantity (Q2Q_2) = 110 units

  8. Calculate the change in income (ΔY\Delta Y) and change in quantity (ΔQ\Delta Q).

    ΔY=Y2−Y1=320−280=40\Delta Y = Y_2 - Y_1 = 320 - 280 = 40 ΔQ=Q2−Q1=110−100=10\Delta Q = Q_2 - Q_1 = 110 - 100 = 10
  9. Apply the income elasticity of demand formula.

    Ey=ΔQΔY×Y1Q1E_y = \frac{\Delta Q}{\Delta Y} \times \frac{Y_1}{Q_1} Ey=1040×280100E_y = \frac{10}{40} \times \frac{280}{100} Ey=0.25×2.8E_y = 0.25 \times 2.8 Ey=0.7E_y = 0.7

    The income elasticity of demand is 0.7\boxed{0.7}.

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