# Income Elasticity of Demand

Income elasticity of demand is the ratio of percentage change in quantity of a product demanded to percentage change in the income level of consumer. It is a measure of responsiveness of quantity demanded to changes in consumers income.

Income elasticity of demand indicates whether a product is a normal good or an inferior good. When the quantity demanded of a product increases with an increase in the level of income and decreases with decrease in level of income, we get a positive value for income elasticity of demand. A positive income elasticity of demand stands for a normal (or superior) good. When the quantity demanded of a product or service decreases in response to an increase and increases in response to decrease in the income level, the income elasticity of demand is negative and the product is an inferior good.

## Formula

$$\text{Income Elasticity of Demand}\ (\text{E} _ \text{i}) \\= \frac{\text{%\ Change in Quantity Demanded}}{\text{%\ Change in Consumers Income}}$$

Percentages are calculated using the mid-point formula, i.e. by dividing the change in quantity by average of initial and final quantities, and change in income by the average of initial and final values of income. Therefore:

$$\text{Income Elasticity of Demand}\ (\text{E} _ \text{i}) \\= \frac{\text{Q} _ \text{f} - \text{Q} _ \text{i}}{(\text{Q} _ \text{f} + \text{Q} _ \text{i}) ÷ \text{2}} ÷ \frac{\text{I} _ \text{f} - \text{I} _ \text{i}}{(\text{I} _ \text{f} + \text{I} _ \text{i}) ÷ \text{2}}$$

Where, Qf and Qi are the final and initial quantities demanded of the product, respectively; and If and Ii are the final and initial incomes of consumer, respectively.

## Examples

### Example 1

Pegasus Air operates from majority of the big air travel hubs. It offers three classes of service: economy, comfort and luxury. Jennifer Aclan is a financial analyst assisting the BoD. The economy is under recessionary pressures and consumption is declining. Jennifer has observed that more and more people are opting for economy class tickets instead of comfort class. Which class most likely has negative income elasticity of demand?

The recessionary pressures have decreased incomes on average and people are looking to save money. They are switching to low cost option i.e. economy class. The increase in quantity demanded of economy class tickets corresponding to a decrease in income level tells us that the ratio of percentage change in quantity demanded of economy class to percentage change in income level is going to be negative. Negative income elasticity of demand indicates that economy class is an inferior good.

### Example 2

Genovia has experienced exceptional growth in recent years. Its GDP per capita has increased from around $30,000 to$50,000 in last 5 years. Over the period quantity demanded of personal cars has increased from 450,000 units per year to 600,000 units. Quantity demanded of public transport, however, has declined from 10,000 buses to 7,000 buses. Calculate income elasticity of demand and tell which product is a normal good and which one is inferior.

Percentage increase in income level
= ($50,000-$30,000) ÷ {($50,000+$30,000)/2}
= 50%

Percentage increase in quantity demanded of cars
= (600,000-450,000) ÷ {(600,000+450,000)/2}
= 28.57%

Percentage increase in quantity demanded of buses
= (7,000-10,000) ÷ {(7,000+10,000)/2}
= -35.29%

Income elasticity of demand of cars
= 28.57%/50%
= 0.57

Income elasticity of demand of buses
= -35.29%/50%
= -0.71

Since cars have positive income elasticity of demand, they are normal goods (also called superior goods) while buses have negative income elasticity of demand which indicates they are inferior goods.