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What is income elasticity of demand? The table below shows the various incomes and demand for different commodities.

Economics

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2 (a) What is income elasticity of demand?
Income elasticity of demand (YED) measures the responsiveness of the quantity demanded for a good or service to a change in consumers' income. It indicates how much the demand for a product changes as income changes.

2 (b) Calculate the income elasticity between:
The formula for income elasticity of demand (YED) using the midpoint method is:

YED=Q2−Q1(Q1+Q2)/2Y2−Y1(Y1+Y2)/2=Q2−Q1Q1+Q2×Y1+Y2Y2−Y1YED = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{Y_2 - Y_1}{(Y_1 + Y_2)/2}} = \frac{Q_2 - Q_1}{Q_1 + Q_2} \times \frac{Y_1 + Y_2}{Y_2 - Y_1}

b) (i) A and B

  1. Identify initial and final values for income and quantity demanded.

    For A: Y1=20,000Y_1 = 20,000, Q1=120Q_1 = 120
    For B: Y2=36,000Y_2 = 36,000, Q2=96Q_2 = 96

  2. Substitute the values into the YED formula.

    YEDAB=96−120120+96×20000+3600036000−20000YED_{AB} = \frac{96 - 120}{120 + 96} \times \frac{20000 + 36000}{36000 - 20000} YEDAB=−24216×5600016000YED_{AB} = \frac{-24}{216} \times \frac{56000}{16000} YEDAB=−19×72YED_{AB} = -\frac{1}{9} \times \frac{7}{2} YEDAB=−718≈−0.3889YED_{AB} = -\frac{7}{18} \approx -0.3889

    The income elasticity between A and B is −0.39\boxed{-0.39}.

    b) (ii) C and D

  3. Identify initial and final values for income and quantity demanded.

    For C: Y1=40,000Y_1 = 40,000, Q1=160Q_1 = 160
    For D: Y2=44,000Y_2 = 44,000, Q2=200Q_2 = 200

  4. Substitute the values into the YED formula.

    YEDCD=200−160160+200×40000+4400044000−40000YED_{CD} = \frac{200 - 160}{160 + 200} \times \frac{40000 + 44000}{44000 - 40000} YEDCD=40360×840004000YED_{CD} = \frac{40}{360} \times \frac{84000}{4000} YEDCD=19×21YED_{CD} = \frac{1}{9} \times 21 YEDCD=219=73≈2.3333YED_{CD} = \frac{21}{9} = \frac{7}{3} \approx 2.3333

    The income elasticity between C and D is 2.33\boxed{2.33}.

    b) (iii) E and F

  5. Identify initial and final values for income and quantity demanded.

    For E: Y1=45,000Y_1 = 45,000, Q1=240Q_1 = 240
    For F: Y2=47,000Y_2 = 47,000, Q2=252Q_2 = 252

  6. Substitute the values into the YED formula.

    YEDEF=252−240240+252×45000+4700047000−45000YED_{EF} = \frac{252 - 240}{240 + 252} \times \frac{45000 + 47000}{47000 - 45000} YEDEF=12492×920002000YED_{EF} = \frac{12}{492} \times \frac{92000}{2000} YEDEF=141×46YED_{EF} = \frac{1}{41} \times 46 YEDEF=4641≈1.1220YED_{EF} = \frac{46}{41} \approx 1.1220

    The income elasticity between E and F is 1.12\boxed{1.12}.

    c) What kind of good is [the commodity]?
    For the range A to B, the income elasticity of demand is negative (approximately −0.39-0.39), indicating that the good is an inferior good at lower income levels. For the ranges C to D (approximately 2.33) and E to F (approximately 1.12), the income elasticity of demand is positive and greater than 1, indicating that the good is a luxury good at higher income levels. Therefore, this commodity exhibits characteristics of both an inferior good at lower income levels and a luxury good at higher income levels.

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