Income Elasticity of Demand
This is a measure that shows the response of consumers in the quantity they demand as a result of changes in their income. In other words, it is the percentage change in the quantity demanded resulting from a given percentage change in income. It is calculated as the percentage change in quantity demanded divided by the percentage change in income.
Income Elasticity of Demand and Different Types of Goods
Normal Goods
Most goods are normal, which means that the quantity demanded and income move in the same direction. In other words, as income increases, the quantity demanded also increases. For this reason, normal goods have a positive income elasticity of demand.
Inferior Goods
Some goods are inferior, meaning that an increase in income reduces the quantity demanded of the good. Since in this case, income and quantity demanded move in opposite directions, inferior goods have negative income elasticities. A classic example is the demand for public transportation services: as income increases, people tend to buy private vehicles.
Essential Goods
The income elasticity of demand varies greatly between different goods. Essential goods tend to have low income elasticities because consumers make an economic effort to acquire them even when their income is low.
There is a law called Engel's Law, named after the 19th-century statistician who discovered it. It states that as a family’s income increases, the proportion of income spent on food decreases, even when the total or absolute expenditure on food has increased. In other words, the income elasticity of demand for food is less than 1.
Luxury Goods
The opposite occurs with luxury goods, which tend to have high income elasticities of demand. This is because consumers easily adjust their consumption of these goods when their income changes. In other words, they quickly forgo luxury goods when their income decreases, meaning that luxury goods have an income elasticity greater than 1.
How is Income Elasticity of Demand Calculated?
Income elasticity of demand is defined as:
\[ E_{d, income} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in income}} \]
The change in quantity demanded (\(\Delta Q\)) and the change in income (\(\Delta Y\)) are calculated as the difference between initial and final values. That is:
- \(\Delta Q = Q_{\text{final}} - Q_{\text{initial}}\), where \(Q_{\text{initial}}\) is the initial quantity demanded, and \(Q_{\text{final}}\) is the quantity demanded after the change.
- \(\Delta Y = Y_{\text{final}} - Y_{\text{initial}}\), where \(Y_{\text{initial}}\) is the income before the change, and \(Y_{\text{final}}\) is the income after the change.
We can then express the income elasticity of demand in terms of percentage changes in quantity demanded and income as follows:
\[ E_{d, income} = \frac{\frac{\Delta Q}{Q}}{\frac{\Delta Y}{Y}} \]
Next, we multiply both sides of the equation by \(\frac{Y}{\Delta Y}\) to isolate \(E_{d, income}\):
Multiplying:
\[ E_{d, income} \cdot \frac{\Delta Y}{Y} = \frac{\Delta Q}{Q} \]
Now, rearranging the equation to solve for \(E_{d, income}\):
\[ E_{d, income} = \frac{\Delta Q}{Q} \cdot \frac{Y}{\Delta Y} \]
Where:
- \(\Delta Q\) = change in quantity demanded
- \(\Delta Y\) = change in income
- \(Y\) = initial income
- \(Q\) = initial quantity demanded
This form is useful for calculating income elasticity of demand using data on changes in quantities and income.
When the quantity demanded increases as a result of income increases, the income elasticity of demand is positive. If the quantity does not change, the income elasticity is zero. If the quantity demanded decreases with income increases, the income elasticity is negative.
Example of Calculating Income Elasticity of Demand
Let’s see a specific example to calculate income elasticity of demand.
Suppose that:
- Initial quantity demanded (\(Q\)): 100 units
- Final quantity demanded (\(Q_f\)): 80 units
- Change in quantity demanded (\(\Delta Q\)): \(\Delta Q = Q_f - Q = 80 - 100 = -20\) units
- Initial income (\(Y\)): 200 monetary units
- Final income (\(Y_f\)): 150 monetary units
- Change in income (\(\Delta Y\)): \(\Delta Y = Y_f - Y = 150 - 200 = -50\) monetary units
Substituting these values into the formula:
\[ E_{d, income} = \frac{\Delta Q}{Q} \cdot \frac{Y}{\Delta Y} \]
Substituting the values:
\[ E_{d, income} = \frac{-20}{100} \cdot \frac{200}{-50} \]
Calculating each part:
- \(\frac{-20}{100} = -0.2\)
- \(\frac{200}{-50} = -4\)
Now, multiply both results:
\[ E_{d, income} = -0.2 \cdot -4 = 0.8 \]
Therefore, the income elasticity of demand is 0.8, indicating that the quantity demanded increases by 0.8% for every 1% increase in income, in absolute terms.