Income elasticity of demand is a crucial concept in understanding how the quantity demanded of a good responds to changes in consumer income. This elasticity helps categorize goods as either normal or inferior. Normal goods see an increase in demand as consumer income rises, while inferior goods experience a decrease in demand under the same conditions.
The formula for calculating income elasticity of demand is:
\[E_y = \frac{\%\ \text{Change in Quantity Demanded}}{\%\ \text{Change in Income}}\]
In this formula, the quantity demanded is always in the numerator, while income is in the denominator. To compute the percentage changes, the midpoint method is often employed, which involves several steps:
- Calculate the change in quantity demanded and income.
- Sum the initial and final quantities and incomes.
- Divide the sums by 2 to find the average quantity and income.
- Calculate the percentage change in quantity demanded and income.
- Use these percentage changes to find the income elasticity.
- Analyze the signs of the changes to determine if the goods are normal or inferior.
For example, consider a scenario where the quantity demanded of caviar increases from $9,000 to $11,000 as consumer income rises from $9.50 to $10.50. Following the steps outlined:
- Change in quantity demanded: $11,000 - $9,000 = $2,000
- Change in income: $10.50 - $9.50 = $1.00
- Average quantity demanded: (11,000 + 9,000) / 2 = 10,000
- Average income: ($10.50 + $9.50) / 2 = $10.00
- Percentage change in quantity demanded: \( \frac{2,000}{10,000} = 0.2 \) or 20%
- Percentage change in income: \( \frac{1.00}{10.00} = 0.1 \) or 10%
- Income elasticity of demand: \( \frac{0.2}{0.1} = 2 \)
Since both the quantity demanded and income increased, the income elasticity is positive. A value greater than 1 indicates that caviar is a normal good and specifically a luxury good, as the increase in quantity demanded is proportionally greater than the increase in income.
In contrast, if the income elasticity were less than 1 but still positive, the good would be classified as a necessity. A negative income elasticity indicates an inferior good, where an increase in income leads to a decrease in quantity demanded.
Understanding these distinctions is vital for businesses and economists as they analyze consumer behavior and market trends based on income changes.
