# What is income elasticity of demand?

Finds the income elasticity of demand by the midpoint method from two incomes and the quantities demanded at each, and says whether the good is normal or inferior.

- Page: https://www.acalculator.org/finance/income-elasticity-calculator
- JSON spec: https://www.acalculator.org/finance/income-elasticity-calculator.json
- Version: 43463fb850ea

## Default answer

Example with the default inputs (Starting income $40,000.00, New income $50,000.00, Starting quantity 20, New quantity 24): The income elasticity of demand is 0.8182: this is a normal good.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| i1 | Starting income | The income before the change. |
| i2 | New income | The income after the change. |
| q1 | Starting quantity | How many units buyers want at the starting income. |
| q2 | New quantity | How many units buyers want at the new income. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| elasticity | Income elasticity of demand | % change in quantity demanded ÷ % change in income (midpoint method), with its sign. |
| good | The good is | A normal good when the elasticity is positive, an inferior good when it is negative. |
| quantityChange | % change in quantity | (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) × 100. |
| incomeChange | % change in income | (I₂ − I₁) ÷ ((I₁ + I₂) ÷ 2) × 100. |

## Method

Elasticity = (% change in quantity demanded) ÷ (% change in income), where each % change = (new − old) ÷ ((new + old) ÷ 2) × 100 (the midpoint method).

## Assumptions

- The midpoint (arc) method, so going from A to B gives the same elasticity as going from B to A.
- Everything else that affects demand stays the same between the two points.
- Incomes are at least $0.01; quantities are 0 or more, not both 0.

## Worked examples

1. i1 = $40,000.00, i2 = $50,000.00, q1 = 20, q2 = 24 gives elasticity = 0.8182, good = a normal good, quantityChange = 18.18%, incomeChange = 22.22%. Source: OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (income elasticity of demand = % change in quantity demanded ÷ % change in income; normal good positive, inferior good negative), https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price (retrieved 2026-11-01); OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01).
2. i1 = $40,000.00, i2 = $50,000.00, q1 = 50, q2 = 45 gives elasticity = −0.4737, good = an inferior good, quantityChange = −10.53%. Source: OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (income elasticity of demand = % change in quantity demanded ÷ % change in income; normal good positive, inferior good negative), https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price (retrieved 2026-11-01); OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01).
3. i1 = $40,000.00, i2 = $50,000.00, q1 = 30, q2 = 30 gives elasticity = 0, good = neither: the quantity did not change. Source: OpenStax, Principles of Economics 3e, section 5.1 (midpoint method), https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply (retrieved 2026-11-01).

## FAQ

### What is the income elasticity of demand?

It measures how the quantity demanded responds to a change in income: the percent change in quantity demanded divided by the percent change in income.

### How do I calculate income elasticity of demand?

If income rises from $40,000 to $50,000 and the quantity rises from 20 to 24, the % change in quantity is 4 ÷ 22 = 18.18% and the % change in income is 10,000 ÷ 45,000 = 22.22%. The income elasticity is 18.18 ÷ 22.22 = 0.8182.

### What is a normal good?

A good with a positive income elasticity: buyers want more of it as their income rises.

### What is an inferior good?

A good with a negative income elasticity: buyers want less of it as their income rises.

### Why does this page use the midpoint method?

Each percent change is measured against the average of the two values, so a move from A to B gives the same result as a move from B to A. OpenStax defines the method in section 5.1, and this page applies it to the formula in section 5.4.

### Why is the sign kept here?

The sign separates normal goods from inferior goods, so this page does not show the result as an absolute value.

## Sources

- OpenStax, Principles of Economics 3e, section 5.4 Elasticity in Areas Other Than Price (income elasticity of demand = % change in quantity demanded ÷ % change in income; a normal good is positive, an inferior good negative). Retrieved 2026-11-01. https://openstax.org/books/principles-economics-3e/pages/5-4-elasticity-in-areas-other-than-price
- OpenStax, Principles of Economics 3e, section 5.1 Price Elasticity of Demand and Price Elasticity of Supply (the midpoint method). Retrieved 2026-11-01. https://openstax.org/books/principles-economics-3e/pages/5-1-price-elasticity-of-demand-and-price-elasticity-of-supply