# Income Elasticity of Demand Calculator

Created by Tibor Pal, PhD candidate
Reviewed by Dominik Czernia, PhD candidate and Jack Bowater
Based on research by
Krugman, P.; Wells R. Economics, Fifth Edition (2017)
Last updated: Jul 10, 2022

The income elasticity of demand calculator (with steps) helps you measure the effect of changes in consumers' incomes on demand for a given good. It is measured as the ratio of the percentage change in quantity demanded to the percentage change in income.

Read further and learn the following:

• What is income elasticity of demand;
• How to find income elasticity of demand - the income elasticity of demand formula; and
• The application of income elasticity of demand.

Moreover, we present a practical example to understand the macroeconomic intuition behind the income elasticity of demand.

## What is income elasticity of demand?

As you may know, multiple factors can affect the quantity of a good demanded. Its prices, for example, measured by the price elasticity of demand, is a prominent variable that can alter demand.

Another variable that can induce such changes by shifting the demand curve is the income of consumers. More precisely, the income elasticity of demand measures how responsive the demand for a good is to changes in consumers' incomes. We will say more about the formula for calculating the income elasticity of demand in the following paragraphs.

## The income elasticity of demand of normal and inferior goods

Like the cross-price elasticity of demand between two goods, the income elasticity of demand for a good can also be positive or negative.

The sign of the income elasticity of demand reveals whether a good is normal or inferior. On the one hand, the good is normal when the demand increases when income rises. On the other hand, a good is considered inferior when demand decreases when income rises.

To sum up:

• A positive income elasticity of demand coefficient indicates that the good is a normal good: the quantity demanded at any given price increases as income increases.
• A negative income elasticity of demand coefficient indicates that the good is inferior good: the quantity demanded at any given price decreases as income increases.

Our income elasticity of demand calculator with steps shows you such a result interpretation after making the computations.

## Application of income elasticity of demand

While the income elasticity of demand for a normal good is always positive, its value contains further helpful information. Policymakers are often interested in how a particular industry will grow as consumers' income increases over time to support economic decisions promoting employment or economic growth. By determining whether the income elasticity of demand for a good is larger or less than 1, one can distinguish between income-elastic and income-inelastic goods.

The demand for a good is income-elastic if the income elasticity of demand formula for that good yields more than 1. It means that when income rises, the demand for income-elastic goods rises faster than income.
Luxury goods such as holiday houses, expensive cars and international travel are income-elastic examples.

The demand for a good is income-inelastic if the income elasticity of demand is less than 1. It suggests that when income rises, the demand for income-inelastic goods rises more slowly than income. Necessities such as food and clothes are typically income-inelastic.

## How do you calculate income elasticity of demand?

The formula for calculating income elasticity of demand is the following:

1. Find the change in quantity demanded.
2. Determine the change in income.
3. Divide the first value by the second:

Income elasticity of demand = Change in quantity demanded / Change in income

You can compute the percentage change in the quantity demanded ($x_1$) and income ($x_2$) in two different ways:

1. With the standard way of computation:

$\Delta x = (x_{i2} - x_{i1}) / x_{i1}$

1. Calculate income elasticity of demand using midpoint method:

$\Delta x = (x_{i2} - x_{i1}) / \lparen (x_{i1} + x_{i2})/2\rparen$

where:

• $\Delta x$ - Change in quantity demanded or income;
• $x_{i1}$ - Quantity demanded or income in period 1; and
• $x_{i2}$ - Quantity demanded or income in period 2.

## How to use the income elasticity of demand calculator

In the default mode of the income elasticity of demand calculator, you need to set the following two parameters to get the result for the income elasticity of demand:

• Percent change in income; and
• Percentage change in quantity.

You can also input additional numbers for periods 1 and 2 separately, and we also provide the option for choosing between the standard and the midpoint method of estimation:

• Method - by default, we use the standard approximation, but you can also calculate income elasticity of demand using the midpoint method;
• Income in period 1;
• Income in period 2;
• Quantity demanded in period 1; and
• Quantity demanded in period 2.

## How to calculate income elasticity of demand example with steps

Let's take a simple example to see how income elasticity of demand works. In the demand curve below:

• For the first period, while income was 1000, the quantity demanded was 100; and
• For the second period, when the income increased to 1200, the quantity demanded increased to 150.

So, the example of how to calculate income elasticity of demand is the following:

1. Estimate the percentage change in quantity demanded:

Change in quantity demanded = (150 - 100) / 100 = 0.05 = 50%

1. Compute the percentage change in income:

Change in income = (1200 - 1000) / 1000 = 0.02 = 20%

1. Calculate income elasticity of demand:

Income elasticity of demand = Change in quantity demanded / Change in income = 0.05 / 0.02 = 2.5

The result suggests that the income elasticity curve represents an income-inelastic normal good, such as foods or clothes.

## Income elasticity of demand example in macroeconomics

A practical way to demonstrate the relevance of the income elasticity of demand is to take a real-world example.

You may be able to envisage a picture of an American family living on a farm, but do you know what portion of the population lives on a farm in the U.S. nowadays? The figure is surprisingly low if we make a comparison over history. While in the 18th century, many Americans lived in the countryside and took part in agriculture, only about 1.3 % of the population does so in our times.

Why did this significant change happen? The income elasticity of demand gives the answer. Since food demand is typically income inelastic (its income elasticity of demand is much less than 1), as consumers' income grew, the proportion of food in a general basket of consumers' basket became smaller. Putting it on a macro scale, the falling share of income in the GDP spent on food means a lower income share earned by farmers. Moreover, the considerable technological progress in the agrarian sector triggered high competition between farmers, which depressed prices of agricultural goods, ceteris paribus, further reducing the total revenue of farmers.

To summarize, the combination of the income elasticity of demand of foodstuffs and the fast technological progress in agriculture explains the relative decline of farming in the United States.

## FAQ

### What are the factors that affect income elasticity of demand?

The main factors which affect income elasticity of demand are:

• The degree of necessity of the good;
• The level of income of consumers; and
• The rate at which the desire for the good is satisfied as consumption increases.

### What is the importance of income elasticity of demand to the government?

By estimating the income elasticity of demand, economists can distinguish industries according to their growth potential when consumer income grows over time. Such information can help policymakers decide on possible interventions in the market.

### Can the income elasticity of a good be negative?

Yes. Negative income elasticity of demand coefficient indicates that the good is an inferior good: the quantity demanded at any given price decreases as income increases because people can now afford better quality equivalents.

### What is the income elasticity of demand for luxury goods?

Luxury goods typically have a greater than one income elasticity of demand, which means that their demand increases at a greater proportional rate than income.

For example, if the demand for expensive watches increases by 22 percent when aggregate income increases by 20 percent, then watches are considered luxury goods because they have an income elasticity of demand of 1.1.

Tibor Pal, PhD candidate
Method
Standard
Income
Income in period 1
$Income in period 2$
Change in income
%
Demand
Quantity demanded in period 1
Quantity demanded in period 2
Change in quantity
%
Result
Income elasticity of demand
People also viewed…

### Car heat

The hot car calculator shows you how fast the interior of a car heats up during a summers day.

### PVIFA

The PVIFA calculator finds the present value interest factor of annuity (PVIFA for short) for your newest investment.

### Tenure

The tenure calculator helps find average years of service for employees in an organization.