Fundamentals of Business Economics and Management · Theory of Demand and Supply

Elasticity of Demand: Formulas, Types and Numericals

Updated 10 October 2026 · Fact-checked

Elasticity of demand measures how much the quantity demanded changes when price, income or the price of a related good changes. Price elasticity = % change in quantity demanded ÷ % change in price. Find both percentage changes, divide, ignore the sign for price elasticity, and compare the value with 1.

Understand Elasticity of Demand

The law of demand tells you the direction: when price rises, quantity demanded falls. It does not tell you by how much. Elasticity of demand gives the size of that response.

There are three main kinds. Price elasticity links quantity demanded to the good's own price. Income elasticity links quantity demanded to the consumer's income. Cross elasticity links the quantity demanded of one good to the price of another good.

Price elasticity has five types. If the value is greater than 1, demand is elastic: quantity changes proportionately more than price. If it is less than 1, demand is inelastic. If it equals 1, demand is unitary elastic. If it is 0, demand is perfectly inelastic (a vertical line). If it is infinite, demand is perfectly elastic (a horizontal line). Necessities like salt usually have inelastic demand. Luxuries and goods with many substitutes, like a particular brand of biscuits, tend to be elastic.

Income elasticity tells the type of good. Positive means a normal good. Negative means an inferior good. A normal good with a value above 1 is a luxury. Cross elasticity tells the relation between goods. Positive means substitutes (tea and coffee). Negative means complements (cars and petrol). Zero means unrelated goods.

Elasticity matters in practice. A firm decides whether a price cut will raise its revenue. The government decides which goods to tax. Farmers know that a bumper crop with inelastic demand can lower total income.

Key formulas to remember

Price elasticity of demand (percentage method): Ed = (% change in quantity demanded) ÷ (% change in price) = (ΔQ ÷ Q) ÷ (ΔP ÷ P); Q and P are the original values. The value is negative for normal goods, but exam answers usually use the absolute value.
Arc (mid-point) elasticity: Ed = (ΔQ ÷ ΔP) × ((P1 + P2) ÷ (Q1 + Q2)); Use when the question asks for elasticity between two points and says average or mid-point.
Point elasticity: Ed = (dQ ÷ dP) × (P ÷ Q); For a linear demand curve, dQ ÷ dP is the slope coefficient of Q on P.
Total outlay (expenditure) method: Price up, outlay down: Ed > 1. Price up, outlay up: Ed < 1. Outlay unchanged: Ed = 1; Outlay = P × Q. Reverse the logic for a price fall: price down and outlay up means Ed > 1.
Income elasticity of demand: Ey = (% change in quantity demanded) ÷ (% change in income); Positive: normal good. Negative: inferior good. Above 1: luxury. Between 0 and 1: necessity.
Cross elasticity of demand: Exy = (% change in quantity of X) ÷ (% change in price of Y); Positive: substitutes. Negative: complements. Zero: unrelated.

How to solve Elasticity of Demand questions

Use this order for any numerical or conceptual question on elasticity.

1Identify which elasticity is asked: price, income or cross. Look at what changes (own price, income, or another good's price).
2Write down the original and new values of quantity and of the changing variable.
3Calculate the change (new minus old) for each. Keep the sign.
4Convert each change to a percentage of the original value, unless the question asks for the mid-point method.
5Divide the percentage change in quantity by the percentage change in the other variable.
6Interpret: for price elasticity compare the absolute value with 1; for income and cross elasticity read the sign.
7Check the answer against the options. A sign or a type that does not match the story in the question is a warning.

Quickest way: Fraction shortcut for elasticity

When to use it: Use for numericals with simple numbers where both changes are easy percentages.

Write ΔQ ÷ Q and ΔP ÷ P as simple fractions or round percentages.
Divide one by the other directly, without computing decimals.
Compare with 1 to name the type of price elasticity.
For sign-only questions, skip the calculation: the sign of the answer decides substitute or complement, normal or inferior.
If the question gives total outlay before and after, use the outlay test and avoid calculation altogether.

Common mistakes in Elasticity of Demand

Dividing by the new value instead of the original value when finding percentage change.
Students rush and use the last number in the question.
Fix: Always take the original (first) value as the base, unless the question says mid-point.
Confusing elasticity with the slope of the demand curve.
Both involve ΔQ and ΔP, and a flatter curve looks more elastic.
Fix: Remember elasticity uses percentages and the ratio P ÷ Q, so it changes along a straight-line curve, while slope does not.
Treating a value of 0.5 as elastic and 2 as inelastic.
Students reverse the comparison with 1.
Fix: Greater than 1 is elastic, less than 1 is inelastic. Quantity moves more than price when elastic.
Mixing up perfectly elastic and perfectly inelastic demand.
The words sound similar and the curve shapes are easy to swap.
Fix: Perfectly inelastic: Ed = 0, vertical line, quantity does not change. Perfectly elastic: Ed = ∞, horizontal line.
Ignoring the sign in income and cross elasticity.
Students are used to dropping the sign in price elasticity.
Fix: Keep the sign here. It carries the meaning: negative income elasticity means inferior good, negative cross elasticity means complements.
Using the outlay test the wrong way round.
Students memorise the result for a price rise and apply it to a price fall.
Fix: Ask what happened to price and to outlay. If they move in opposite directions, demand is elastic. If they move in the same direction, it is inelastic.

Worked examples

Example 1

When the price of a notebook falls from ₹50 to ₹40, the quantity demanded rises from 100 to 140. Find the price elasticity of demand and state its type.

Show the solution

ΔQ = 140 − 100 = 40. Percentage change in quantity = 40 ÷ 100 × 100 = 40%.
ΔP = 40 − 50 = −10. Percentage change in price = −10 ÷ 50 × 100 = −20%.
Ed = 40 ÷ (−20) = −2.
Absolute value = 2, which is greater than 1.

Answer: Ed = 2 (in absolute value). Demand is elastic.

Example 2

Rahul's monthly income rises from ₹20,000 to ₹25,000. His purchase of packaged juice falls from 10 litres to 8 litres. Find the income elasticity and say what kind of good juice is for him.

Show the solution

Percentage change in income = (25,000 − 20,000) ÷ 20,000 × 100 = 25%.
Percentage change in quantity = (8 − 10) ÷ 10 × 100 = −20%.
Ey = −20 ÷ 25 = −0.8.
The value is negative, so quantity falls as income rises.

Answer: Ey = −0.8. Packaged juice is an inferior good for Rahul.

Exam tips

Read the question stem first to see which elasticity is asked. Options often include the same number under different names.
For type-identification MCQs, memorise the five types with their values (0, less than 1, 1, more than 1, ∞) and curve shapes.
For sign-based questions, eliminate options using the sign alone before calculating.
In numericals, use the original value as the base unless the question says mid-point or average.
Time is tight, so do the simple-number numericals by fractions and avoid long decimals.

Practice questions from Theory of Demand and Supply

Elasticity of Demand in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Elasticity of Demand: frequently asked questions

What is the formula for price elasticity of demand?

Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. In symbols, Ed = (ΔQ ÷ Q) ÷ (ΔP ÷ P). For normal goods the value is negative, but exams usually ask you to compare its absolute value with 1.

What is the difference between price elasticity and cross elasticity of demand?

Price elasticity measures how demand for a good responds to a change in its own price. Cross elasticity measures how demand for one good responds to a change in the price of a different good. Cross elasticity also shows whether goods are substitutes (positive) or complements (negative).

How do I calculate income elasticity of demand?

Find the percentage change in quantity demanded and the percentage change in income, then divide the first by the second. A positive result means a normal good and a negative result means an inferior good. A value above 1 marks a luxury.

What are the types of price elasticity of demand?

There are five: perfectly elastic (Ed = ∞), elastic (Ed > 1), unitary elastic (Ed = 1), inelastic (Ed < 1) and perfectly inelastic (Ed = 0). Each has a typical curve shape and real-life example, and exams ask you to match them.