Question

What is the formula for the income elasticity of demand?

Short answer

The formula for income elasticity of demand (IED) is given by: \[ IED = \frac{\%\Delta QD}{\%\Delta I} \] where \(\%\Delta QD\) represents the percentage change in quantity demanded and \(\%\Delta I\) represents the percentage change in income.

Step-by-step solution

1. Definition of Income Elasticity of Demand

Income elasticity of demand (IED) measures the change in demand for a good or service resulting from a change in consumer income. It helps to understand how much the demand for a good or service will change when consumer income changes. A positive income elasticity indicates that the demand for the good or service increases as income increases, while a negative income elasticity indicates that the demand decreases when income increases.

2. Formula for Income Elasticity of Demand

The formula for calculating income elasticity of demand is: \[ IED = \frac{\%\Delta QD}{\%\Delta I} \] where: - \(IED\) is the income elasticity of demand - \(\%\Delta QD\) is the percentage change in quantity demanded - \(\%\Delta I\) is the percentage change in income

3. Calculating percentage change in quantity demanded and income

To calculate the percentage change in quantity demanded (\(\%\Delta QD\)) and income (\(\%\Delta I\)), use the following formulas: \[ \%\Delta QD = \frac{QD_{final} - QD_{initial}}{QD_{initial}} \times 100\% \] \[ \%\Delta I = \frac{I_{final} - I_{initial}}{I_{initial}} \times 100\% \] where: - \(QD_{initial}\) is the initial quantity demanded - \(QD_{final}\) is the final quantity demanded - \(I_{initial}\) is the initial income - \(I_{final}\) is the final income

4. Calculate Income Elasticity of Demand

Plug the calculated values of percentage change in quantity demanded (\(\%\Delta QD\)) and income (\(\%\Delta I\)) into the formula for income elasticity of demand: \[ IED = \frac{\%\Delta QD}{\%\Delta I} \] Compute the result to obtain the income elasticity of demand for the good or service.