Question

What is the formula for the income elasticity of demand?

Short answer

The formula for the income elasticity of demand (IED) is: \( IED = \frac{Percentage \: Change \: in \: Quantity \: Demanded}{Percentage \: Change \: in \: Income} = \frac{(\Delta Q / Q)}{(\Delta Y / Y)} \) Where: - IED stands for Income Elasticity of Demand - ΔQ represents the change in quantity demanded - Q refers to the initial quantity demanded - ΔY denotes the change in income - Y denotes the initial income level

Step-by-step solution

Definition of Income Elasticity of Demand

Income elasticity of demand measures the responsiveness of the quantity demanded for a good to a change in the income of the consumer. It is calculated as the percentage change in the quantity demanded divided by the percentage change in income.

Formula for Income Elasticity of Demand

The formula for calculating the income elasticity of demand (IED) is given by: \( IED = \frac{Percentage \: Change \: in \: Quantity \: Demanded}{Percentage \: Change \: in \: Income} \) We can also express IED as: \( IED = \frac{(\Delta Q / Q)}{(\Delta Y / Y)} \) Where: - IED stands for Income Elasticity of Demand - ΔQ represents the change in quantity demanded - Q refers to the initial quantity demanded - ΔY denotes the change in income - Y denotes the initial income level

Calculate Percentage Changes

To find the income elasticity of demand, we need to calculate percentage changes in quantity demanded and income. For this, we can use the formula of percentage change: Percentage Change = \( \frac{Change \: in \: Quantity}{Initial \: Quantity} × 100 \) In our context, Percentage Change in Quantity Demanded = \( \frac{\Delta Q}{Q} × 100 \) Percentage Change in Income = \( \frac{\Delta Y}{Y} × 100 \)

Simplify and Solve for IED

Once we have the percentage changes in quantity demanded and income, we can plug them into our IED formula and solve: \( IED = \frac{Percentage \: Change \: in \: Quantity \: Demanded}{Percentage \: Change \: in \: Income} = \frac{(\Delta Q / Q)}{(\Delta Y / Y)} \) By calculating the values for income and quantity changes, the income elasticity of demand can be found. This value can provide insights into the relationship between income and demand for a particular good or service.