Measurement of Income Elasticity of Demand

Measurement of Income Elasticity of Demand

a) The Point Method:

1. \(E_y = \cfrac{\Delta Q}{\Delta Y} \times \cfrac{Y}{Q}\) (for a demand schedule)
2. \(E_y = \cfrac{\delta Q}{\delta Y} \times \cfrac{Y}{Q}\) (for a demand function with one independent variable)
3. \(E_y = \cfrac{\partial Q}{\partial Y} \times \cfrac{Y}{Q}\) (for a demand function with two or more independent variables including consumer income).

b) The Arc Method:

\(E_y = \cfrac{\Delta Q}{\Delta Y} \times \cfrac{Y_1 + Y_2}{Q_1 + Q_2}\)

Example:

Consider the following demand schedule for a good.

	Period 1	Period 2
Income (₦)	50,000	70,000
Demand	200	250

You are required to calculate for the good:

a) Point income elasticity of demand and interpret your result.
b) Arc income elasticity of demand and interpret your result.

Solution:

a) Point income elasticity of demand

\(E_y = \cfrac{\Delta Q}{\Delta Y} \times \cfrac{Y}{Q}\)

Where:
\(\Delta Q = 250 - 200 = 50\)
\(\Delta Y = ₦70,000 - ₦50,000 = ₦20,000\)
\(Y = ₦50,000 (Y_1)\)
\(Q = 200 (Q_1)\)

\(E_y = \cfrac{50}{20,000} \times \cfrac{50,000}{200}\)
\(= 0.63\)

Therefore, the good has an inelastic demand and is normal.

b) Arc income elasticity of demand

\(E_y = \cfrac{\Delta Q}{\Delta Y} \times \cfrac{Y_1 + Y_2}{Q_1 + Q_2}\)
\(= \cfrac{250 - 200}{70,000 - 50,000} \times \cfrac{50,000 + 70,000}{200 + 250}\)
\(= \cfrac{50}{20,000} \times \cfrac{120,000}{450}\)
\(= 0.67\)

Therefore, the good has an inelastic demand and is normal.

Note: The results from the different methods may be slightly different but not enough to change the interpretation.