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Fundamentals of Business Economics and Management · The Fundamentals of Economics

Elasticity of Demand and Supply: Formulas and Numericals

Updated 10 October 2026 · Fact-checked

Elasticity measures how much quantity demanded or supplied responds to a change in price, income or the price of another good. Calculate it as the percentage change in quantity divided by the percentage change in the cause. Then read the value: above 1 is elastic, below 1 is inelastic, and exactly 1 is unitary.

Understand Elasticity of Demand and Supply

Demand and supply tell you the direction of a change. If price rises, demand usually falls. Elasticity tells you the size of that change. It is a pure number, because it compares percentage changes, so units like rupees or kilograms cancel out.

Price elasticity of demand (PED) shows how sensitive quantity demanded is to the price of the good itself. Because demand normally falls when price rises, the raw value is negative. In exams you usually quote the absolute value (ignore the sign) unless the question asks otherwise.

PED has five types. Perfectly elastic (Ed = ∞): a tiny price rise drops demand to zero. Elastic (Ed > 1): quantity changes by a bigger percentage than price. Unitary (Ed = 1): both change by the same percentage. Inelastic (Ed < 1): quantity changes by a smaller percentage than price. Perfectly inelastic (Ed = 0): quantity does not change at all.

Income elasticity of demand (YED) measures the response of quantity demanded to a change in consumer income. A positive value means a normal good. Above 1 it is a luxury; between 0 and 1 it is a necessity. A negative value means an inferior good. Cross elasticity (XED) measures the response of demand for good X to a change in the price of good Y. Positive means substitutes (tea and coffee), negative means complements (cars and petrol), zero means unrelated goods.

Price elasticity is higher when a good has close substitutes, is a luxury, takes a large share of income, has a long time to adjust, or has many uses. It is lower for necessities, habit-forming goods and goods with no substitutes. Elasticity of supply (Es) measures how quantity supplied responds to price. It is usually positive and is higher when producers can raise output easily, stock can be stored, and more time is available.

Key formulas to remember

Price elasticity of demand (percentage method)
Ed = (% change in quantity demanded) ÷ (% change in price)
Usually quoted as an absolute value. % change in quantity = (ΔQ ÷ original Q) × 100.
Price elasticity (original-value form)
Ed = (ΔQ ÷ Q) ÷ (ΔP ÷ P) = (ΔQ ÷ ΔP) × (P ÷ Q)
Use the original (old) price and quantity unless the question says to use the average.
Arc (midpoint) elasticity
Ed = (ΔQ ÷ ΔP) × [(P1 + P2) ÷ (Q1 + Q2)]
Use when the question asks for elasticity between two points or the average method. It gives the same value in either direction.
Point elasticity on a straight-line demand curve
Ed = lower segment ÷ upper segment (of the demand line, measured from the point)
At the midpoint of the demand line Ed = 1. At points above the midpoint Ed > 1, and at points below the midpoint Ed < 1.
Total expenditure method
Price up and total expenditure down: Ed > 1. Price up and expenditure unchanged: Ed = 1. Price up and expenditure up: Ed < 1. Price down and total expenditure up: Ed > 1. Price down and expenditure unchanged: Ed = 1. Price down and expenditure down: Ed < 1.
Expenditure moves opposite to price when demand is elastic, and with price when inelastic. The rule works the same for a price rise or a price fall.
Income elasticity of demand
YED = (% change in quantity demanded) ÷ (% change in income)
Positive: normal good. Negative: inferior good. Above 1: luxury.
Cross elasticity of demand
XED = (% change in quantity of X) ÷ (% change in price of Y)
Positive: substitutes. Negative: complements. Zero: unrelated.
Elasticity of supply
Es = (% change in quantity supplied) ÷ (% change in price)
Above 1 is elastic supply, below 1 is inelastic, equal to 1 is unitary.

How to solve Elasticity of Demand and Supply questions

Use this order for any elasticity question, numerical or theory.

  1. 1Identify which elasticity is asked: price, income, cross or supply. This decides which change goes in the denominator.
  2. 2Write down the old and new values of quantity and of the cause (price, income or other good's price).
  3. 3Find the changes: ΔQ = new Q − old Q, and the same for price or income.
  4. 4Convert to percentage changes using the old value as base, unless the question says average or midpoint.
  5. 5Divide the percentage change in quantity by the percentage change in the cause.
  6. 6Read the sign and size. For price elasticity, drop the sign and compare with 1. For income and cross elasticity, the sign tells the type of good.
  7. 7Match your result to the option, and check it makes economic sense (for example, a necessity should not show a very high elasticity).

Quickest way: Percentage shortcut with a sign and size check

When to use it: Use in the 50-MCQ paper when the numbers are clean and you have about a minute per question.

  1. Work out each percentage change in your head from the fraction ΔQ ÷ Q and ΔP ÷ P.
  2. Divide the two fractions directly. Skip multiplying by 100 because it cancels.
  3. For type questions, only compare with 1: bigger percentage change in quantity means elastic.
  4. For total expenditure questions, just see if expenditure moved opposite to price: if yes, elastic.
  5. For goods classification, look only at the sign: YED negative means inferior, XED positive means substitutes.

Common mistakes in Elasticity of Demand and Supply

  • Using the new price and quantity as the base instead of the old ones.

    Students divide by whichever number is nearer or larger.

    Fix: Unless the question says average or midpoint, the base is always the original value.

  • Inverting the formula by dividing the percentage change in price by that in quantity.

    The word 'price' comes first in the name, so it is placed on top.

    Fix: Quantity response always goes on top. Remember: response over cause.

  • Calling Ed = 0 perfectly elastic and Ed = ∞ perfectly inelastic.

    The words and numbers are confused.

    Fix: Zero means no response (perfectly inelastic). Infinity means unlimited response (perfectly elastic).

  • Treating a negative price elasticity as inelastic.

    Students compare −2 with 1 and see it as smaller.

    Fix: Take the absolute value first. Ed = −2 means |Ed| = 2, which is elastic.

  • Dropping the sign for income or cross elasticity.

    The habit of ignoring the sign from price elasticity carries over.

    Fix: For YED and XED the sign carries the meaning. Keep it.

  • Thinking a steeper straight-line demand curve has the same elasticity at every point.

    Slope and elasticity are confused.

    Fix: Elasticity changes along a straight line: high at the top, 1 at the midpoint, low at the bottom.

Worked examples

Example 1

When the price of a notebook falls from ₹50 to ₹40, quantity demanded rises from 100 to 130 units. Find the price elasticity of demand and state its type.

Show the solution
  1. ΔQ = 130 − 100 = 30. Percentage change in quantity = 30 ÷ 100 × 100 = 30%.
  2. ΔP = 40 − 50 = −10. Percentage change in price = −10 ÷ 50 × 100 = −20%.
  3. Ed = 30 ÷ (−20) = −1.5.
  4. Absolute value = 1.5, which is greater than 1.

Answer: Ed = 1.5 (absolute value), so demand is elastic.

Example 2

Income of a consumer rises from ₹20,000 to ₹25,000 per month. His demand for good X rises from 40 to 44 units. Find the income elasticity of demand and classify the good.

Show the solution
  1. Percentage change in income = 5,000 ÷ 20,000 × 100 = 25%.
  2. Percentage change in quantity = 4 ÷ 40 × 100 = 10%.
  3. YED = 10 ÷ 25 = 0.4.
  4. The value is positive and between 0 and 1.

Answer: YED = 0.4 (positive and between 0 and 1), so X is a normal good that is a necessity.

Exam tips

  • Read the question for the word 'average' or 'midpoint'. If it is missing, use the old values as the base.
  • Memorise the sign rules: YED negative is inferior, XED positive is substitutes, XED negative is complements.
  • Learn the five types of price elasticity with their numbers (∞, above 1, 1, below 1, 0), as direct match questions are common.
  • For the total expenditure method, remember that elastic demand means expenditure moves opposite to price.
  • There is no negative marking, so always attempt every question. Eliminate options with the wrong sign or wrong size first.

Practice questions from The Fundamentals of Economics

Elasticity of Demand and Supply 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 and Supply: frequently asked questions

What is the formula for price elasticity of demand?

Ed = percentage change in quantity demanded ÷ percentage change in price. You can also write it as (ΔQ ÷ ΔP) × (P ÷ Q). Usually you quote the absolute value.

How do I calculate income elasticity of demand?

Divide the percentage change in quantity demanded by the percentage change in income. Keep the sign. A positive result means a normal good, and a negative result means an inferior good.

What are examples of cross elasticity of demand?

Tea and coffee are substitutes, so a rise in the price of tea raises demand for coffee and XED is positive. Cars and petrol are complements, so a rise in petrol price lowers demand for cars and XED is negative.

What factors affect elasticity of demand?

The main factors are the availability of substitutes, whether the good is a necessity or luxury, the share of income spent on it, the time period, habits and the number of uses. More substitutes and a longer time make demand more elastic.