Suppose Anne only consumes food and clothes, and she spends 20% of her income on food

The responsiveness of percentage change in quantity demanded to a percentage change in income is known as income elasticity of demand.

Here, it is given by:

• Income elasticity of demand = Percentage change in quantity demanded of food / Percentage change in income

or

• ef = (Δ F / F) / ( Δ I / I) where
  • F = food demanded
  • I = Income
  • ΔF = change in the value of food demanded
  • Δ = change in income
  • ef = income elasticity of food

Given that the elasticity is 0.6 and 20% is spent of food, we have:

• ef = ( ΔF / I) / (1/ (F / I)
• 0.6 = ( Δ F / I) / (1 / 0.2)
• Δ F = 0.12 Δ I

Now, we know that Anne consumes ONLY food and clothes. If Anne spends 0.12 of her changed income on food, it means that she will spend 0.88 on cloth.

So, we have:

• Δ C = 0.88 Δ I
• Δ C / Δ I = 0.88

Now, elasticity of clothes is:

• ec = (Δ C / Δ I ) / (Y / Dc)

Since, 20% of the income is spend on food, the remaining 80% is spent on clothes. So, we have:

• ec = ( 1 / 0.8) / Δ C / Δ
• ec = 0.88 / 0.8
• ec = 1.1

Therefore, the income elasticity of clothes is 1.1.