Economic and Business Environment · Basics of Demand and Supply and Forms of Market Competition

Elasticity of Demand: Price, Income and Cross Elasticity

Updated 11 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 the percentage changes, divide, ignore the minus sign for price elasticity, and compare the result 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 the response. It is a ratio of two percentage changes, so it has no units.

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

For price elasticity, demand is elastic if the value is greater than 1, inelastic if it is less than 1, and unitary elastic if it equals 1. The extremes are perfectly elastic (infinite; a tiny price rise reduces demand to zero) and perfectly inelastic (zero; quantity does not change at all). Necessities such as salt tend to be inelastic. Luxuries and goods with many substitutes tend to be elastic.

Income elasticity is positive for normal goods and negative for inferior goods. If it is above 1, the good is a luxury: demand rises faster than income. Cross elasticity is positive for substitutes (tea and coffee) and negative for complements (cars and petrol). It is near zero for unrelated goods.

The main ways to measure price elasticity are the percentage (proportionate) method, the total expenditure method and the point method on a straight-line demand curve. The arc method is used for a stretch between two points.

Key rules to remember

Price elasticity of demand (Ed): Ed = (% change in quantity demanded) ÷ (% change in price); Ignore the negative sign when comparing with 1. % change = (change ÷ original) × 100.
Price elasticity (direct form): Ed = (ΔQ ÷ Q) ÷ (ΔP ÷ P) = (ΔQ ÷ ΔP) × (P ÷ Q); P and Q are the original values. ΔQ and ΔP are the changes.
Income elasticity (Ey): Ey = (% change in quantity demanded) ÷ (% change in income); Positive: normal good. Negative: inferior good. Greater than 1: luxury.
Cross elasticity (Exy): Exy = (% change in quantity demanded of X) ÷ (% change in price of Y); Positive: substitutes. Negative: complements. Zero: unrelated.
Point elasticity on a straight-line demand curve: Ed = lower segment ÷ upper segment of the curve at that point; Equals 1 at the midpoint, above 1 in the upper half, below 1 in the lower half.
Total expenditure method: Total expenditure = Price × Quantity demanded; Price falls and expenditure rises: Ed > 1. Expenditure unchanged: Ed = 1. Expenditure falls: Ed < 1.

How to solve Elasticity of Demand questions

Use this method for any numerical or theory question on elasticity.

1Identify which elasticity is asked: price, income or cross. Note which variable changes and which quantity responds.
2Write down the original and new values of price (or income) and quantity.
3Find the change: new value minus original value. Keep the sign.
4Convert to percentage change using the original value: (change ÷ original) × 100.
5Divide the % change in quantity by the % change in the cause variable.
6Read the result. For price, drop the sign and compare with 1. For income and cross, keep the sign and interpret it.
7State the conclusion in words (elastic, inferior good, substitutes) and write the formula at the top for method marks.

Quickest way: Shortcut with the direct formula

When to use it: Use when numbers are given as units and rupees and the question asks for a single elasticity value.

Compute ΔQ ÷ Q and ΔP ÷ P as fractions. No need to multiply by 100, since it cancels.
Divide the first fraction by the second.
Check the sign: price elasticity is normally negative, so quote the absolute value.
For a quick type check, use total expenditure: compare P × Q before and after.

Common mistakes in Elasticity of Demand

Using the new value instead of the original value as the base for percentage change.
Students divide by whichever number is nearer.
Fix: Always divide the change by the original (starting) price, income or quantity unless the question asks for the arc method.
Comparing a negative price elasticity with 1 without removing the sign.
The law of demand makes the ratio negative, and students forget this.
Fix: Take the absolute value for price elasticity before deciding elastic or inelastic.
Inverting the ratio and dividing price change by quantity change.
Mixing up cause and effect.
Fix: Quantity response goes on top, cause (price, income) goes at the bottom.
Treating a negative income elasticity as an error.
Students assume elasticity must be positive.
Fix: A negative income elasticity is valid. It means an inferior good.
Saying substitutes have negative cross elasticity.
Confusion between substitutes and complements.
Fix: Substitutes: price of Y rises, demand for X rises, so positive. Complements: negative.
Thinking a flat demand curve is perfectly inelastic.
Mixing slope with elasticity.
Fix: A horizontal curve is perfectly elastic. A vertical curve is perfectly inelastic.

Worked examples

Example 1

The price of a notebook rises from ₹40 to ₹50 and the quantity demanded falls from 200 to 130. Calculate the price elasticity of demand and state whether demand is elastic or inelastic.

Show the solution

Change in quantity = 130 − 200 = −70. % change in quantity = (−70 ÷ 200) × 100 = −35%.
Change in price = 50 − 40 = 10. % change in price = (10 ÷ 40) × 100 = 25%.
Ed = −35 ÷ 25 = −1.4.
Absolute value = 1.4, which is greater than 1, so demand is elastic.
Check with total expenditure: before = 40 × 200 = ₹8,000; after = 50 × 130 = ₹6,500. Price rose and expenditure fell, which confirms Ed > 1.

Answer: Ed = 1.4 (in absolute terms), so demand is elastic.

Example 2

When the monthly income of Ravi rises from ₹20,000 to ₹25,000, his demand for packaged juice rises from 10 to 12 bottles. His demand for loose tea falls from 8 kg to 6 kg. When the price of coffee rises by 10%, demand for tea rises by 5%. Find the income elasticity for juice and for tea, and the cross elasticity of tea with respect to coffee. Interpret each.

Show the solution

Income change = (25,000 − 20,000) ÷ 20,000 × 100 = 25%.
Juice: % change in quantity = (12 − 10) ÷ 10 × 100 = 20%. Ey = 20 ÷ 25 = 0.8. Positive and less than 1: a normal good, a necessity-type good.
Tea: % change in quantity = (6 − 8) ÷ 8 × 100 = −25%. Ey = −25 ÷ 25 = −1. Negative: an inferior good.
Cross elasticity = 5 ÷ 10 = 0.5. Positive: tea and coffee are substitutes.

Answer: Juice: Ey = 0.8 (normal good). Tea: Ey = −1 (inferior good). Cross elasticity of tea with coffee = 0.5 (substitutes).

Exam tips

Write the formula first. Even if arithmetic slips, you earn method marks.
For theory questions, give each type with a one-line definition, formula, classification by value and an Indian example such as salt, petrol or tea and coffee.
Learn the five degrees of price elasticity with their values and curve shapes. They are a favourite short-note topic.
Always state the interpretation in words after the number. Examiners look for it.
Draw a small neat diagram of the demand curve when asked for perfectly elastic or inelastic demand, and label the axes P and Q.

Practice questions from Basics of Demand and Supply and Forms of Market Competition

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?

Ed = % change in quantity demanded ÷ % change in price. You can also write it as (ΔQ ÷ ΔP) × (P ÷ Q). Use the original price and quantity as the base.

What is the difference between income elasticity and cross elasticity?

Income elasticity shows how demand for a good responds to a change in consumer income. Cross elasticity shows how demand for one good responds to a change in the price of another good. The first sign tells normal or inferior; the second tells substitute or complement.

Can price elasticity of demand be negative?

Yes. Because price and quantity move in opposite directions, the ratio is usually negative. For classification you take the absolute value and compare it with 1.

Which goods have inelastic demand?

Necessities with few substitutes, such as salt, medicines and basic food grains, usually have inelastic demand. Goods that take a small share of income also tend to be inelastic.