Question

Suppose the average income of a consumer decrease from R18 000 to R12 000. As a result, the quantity of product A demanded by the consumer increases from 200 units to 280 units. Use the ARC formula to calculate and classify the income the elasticity of demand for product A.

Answer 1

Solution:

Arc Income elasticity of demand = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; Income}$

Q₁ = 200

Q₂ = 280

Y₁ = 18,000

Y₂ = 12,000

Arc Ed = $\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 }\div \frac{I_{2} -I_{1}}{(I_{2}+I_{1})/2 }$

Arc Ed = $\frac{80}{240}\div \frac{-6,000}{15,000} = \frac{0.33}{-0.4} = -0.83$

Arc Income elasticity of demand = -0.83

Arc Income elasticity of demand for product A is negative which means that product A is an inferior good since quantity demanded increases with a decrease in income.