Question

Which formula is used for this question, point income elasticity or arc income elasticity?

B. Calculate the income elasticity of demand for a consumer who increases the consumption of commodity X from 100 units to 300 units per year when the income of the consumer increases from $16,000 to $20,000 per year. Is commodity X normal or inferior? Necessity or luxury?

Answer 1

Here, Y1 = 16,000      Q1 = 100

          Y2 =20,000       Q2 = 300

Arc income elasticity will give better result

IED = ∆Q/∆Y *( Y1 + Y2) / (Q1 + Q2)

       = (Q2 - Q1) / (Y2 - Y1) * ( Y1 + Y2) / (Q1 + Q2)

       = (300 - 100) / (20,000 - 16,000) * (16,000 + 20,000) / (100 + 300)

       = (200 / 4,000) * (36,000 / 400)

        = 7,200,000 / 1,600,000

        = 4.5

Since IED is positive, commodity X is a normal good.

Since IED is greater than 1, commodity X is a luxury good.