Income Elasticity of Demand Formula

Income Elasticity of Demand Formula (Table of Contents)

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What is the Income Elasticity of Demand Formula?

The term “income elasticity” shows how the demand for certain good changes with the change in consumer’s real income. In other words, it is a measure of the responsiveness of the demand for the good to changes in real income. The formula for income elasticity of demand can be derived by dividing the percentage change in quantity demanded of the good (∆D/D) by the percentage change in real income of the consumer who buys it (∆I/I). Mathematically, it is represented as,

Income Elasticity of Demand = Percentage Change in Quantity Demanded (∆D/D) / Percentage Change in Income (∆I/I)

However, the formula for income elasticity of demand can be further expanded as,

Income Elasticity of Demand = (D₁ – D₀) / (D₁ + D₀) / (I₁ – I₀) / (I₁ + I₀)

where,

D₀ = Initial Quantity Demanded
D₁ = Final Quantity Demanded
I₀ = Initial Real Income
I₁ = Final Real Income

Examples of Income Elasticity of Demand Formula (With Excel Template)

Let’s take an example to understand the calculation of Income Elasticity of Demand in a better manner.

You can download this Income Elasticity of Demand Formula Excel Template here – Income Elasticity of Demand Formula Excel Template

Income Elasticity of Demand Formula – Example #1

Let us take the example of some exotic cuisine. Let us assume that recently the average income level has gone up by 75% that resulted in extra money which eventually resulted in an increase in consumption of exotic cuisines by 25%. Calculate the income elasticity of demand based on the given information.

Solution:

Income Elasticity of Demand is calculated using the formula given below

Income Elasticity of Demand =Percentage Change in Quantity Demanded (∆D/D) / Percentage Change in Income (∆I/I)

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Income Elasticity of Demand = 25% / 75%
Income Elasticity of Demand = 0.33

Therefore, the income elasticity of demand for the exotic cuisine is 0.33, i.e. it is a normal good.

Income Elasticity of Demand Formula – Example #2

Let us take the example of cheap garments. The weekly demand for cheap garments went down from 4,000 pieces to 2,500 pieces as the level of real income in the economy increased from $75 per day to $125 per day. The reason is the shift in preference due to the availability of extra money on the back of increased income level. Calculate the income elasticity of demand based on the given information.

Solution:

Income Elasticity of Demand is calculated using the formula given below

Income Elasticity of Demand = (D₁ – D₀) / (D₁ + D₀) / (I₁ – I₀) / (I₁ + I₀)

Income Elasticity of Demand = [(2,500 – 4,000) / (2,500 + 4,000) ] / [($125 – $75) / ($125 + $75)]
Income Elasticity of Demand = -0.92

Therefore, the income elasticity of demand for cheap garments is -0.92, i.e. it is an inferior good.

Explanation

The formula for income elasticity of demand can be derived by using the following steps:

Step 1: Firstly, determine the initial real income and the quantity demanded at that income level that are denoted by I₀ and D₀ respectively. Similarly, determine the final real income and demand denoted by I₁ and D₁ respectively.

Step 2: Next, calculate the change in quantity demanded by subtracting the initial quantity from the final quantity. Now, the percentage change in quantity demanded is calculated by dividing the change in quantity demanded by the average of the final and initial quantities i.e. 2 * (D₁ – D₀) / (D₁ + D₀).

Step 3: Next, calculate the change in real income by subtracting the initial income from the final income. Now, the percentage change in real income is calculated by dividing the change in real income by the average of the final and initial incomes i.e. 2 * (I₁ – I₀) / (I₁ + I₀).

Step 4: Finally, the formula for income elasticity of demand can be derived by dividing the percentage change in quantity demanded of the good (step 2) by the percentage change in real income of the consumer who buys it (step 3) as shown below.

Income Elasticity of Demand = (D₁ – D₀) / (D₁ + D₀) / (I₁ – I₀) / (I₁ + I₀),

Relevance and Uses of Income Elasticity of Demand Formula

It is important to understand the concept of income elasticity of demand because it helps businesses to predict the impact of economic cycles on their product sales. Based on the value of the income elasticity of demand, businesses categorize goods into two broad categories – normal goods and inferior goods.

Normal goods exhibit the value of income elasticity of demand of more than zero which indicates that the quantity demanded of normal goods increases with the increase in the level of income. Necessity goods are the type of normal goods whose value of income elasticity of demand lies in the rage of zero and one and belong to the group of products and services that are bought regardless of the changes in income levels. On the other hand, luxury goods are the type of normal goods that have a value of income elasticity of demand of greater than one.

Inferior goods exhibit the value of income elasticity of demand of less than zero which indicates that the quantity demanded of inferior goods decreases with the increase in the level of income because of consumer preference shifts from cheaper products and services to better ones.