The 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 average income.
- Calculate the percentage change in quantity demanded and income using the changes and averages.
- Compute the income elasticity by dividing the percentage change in quantity demanded by the percentage change in income.
- Analyze the signs of the changes to determine if the goods are normal or inferior.
For example, consider caviar with an initial quantity demanded of $9,000 and an increase 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: ($9,000 + $11,000) / 2 = $10,000
- Average income: ($9.50 + $10.50) / 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 luxury normal good, meaning that as income increases, the demand for caviar increases even more significantly.
In contrast, if the income elasticity had been less than 1 but still positive, it would indicate a normal good that is a necessity. A negative income elasticity would suggest that the good is inferior, where demand decreases as income rises.
Understanding these distinctions is essential for businesses and economists as they analyze consumer behavior and market trends in response to changes in income.