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Elasticity of Demand Methods and Numericals ISC Class 12

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EconomicsISC Class 12 · Elasticity of Demand

Measuring Elasticity of Demand: Percentage, Total Expenditure and Geometric Methods with Numericals

Updated 17 October 2026 · Fact-checked

Price elasticity of demand (Ed) measures how strongly quantity demanded responds to a change in price: Ed = (percentage change in quantity demanded) / (percentage change in price), taken without the sign. Ed greater than 1 is elastic, equal to 1 unitary, less than 1 inelastic. ISC requires three methods (percentage, total expenditure, geometric) and numericals on the percentage method only.

On a straight-line demand curve, Ed at a point is the lower segment divided by the upper segment, so it falls from infinity to 0 and equals 1 at the midpoint.

Illustration drawn for QuestionBuddy.

Understand Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods

1. Meaning and degrees. Elasticity of demand is the degree of responsiveness of quantity demanded to a change in one of its determinants. Price elasticity relates quantity demanded to the price of the good itself. Its degrees are:

  • Perfectly elastic (Ed = infinity): a horizontal demand curve; at one price any quantity is bought, none above it.
  • Elastic (Ed > 1): the percentage change in quantity is larger than the percentage change in price; flatter curve.
  • Unitary (Ed = 1): the two percentage changes are equal (rectangular hyperbola).
  • Inelastic (Ed < 1): quantity changes proportionately less than price; steeper curve.
  • Perfectly inelastic (Ed = 0): a vertical demand curve; quantity does not change whatever the price.

2. Percentage (proportionate) method. Ed = (percentage change in Q) / (percentage change in P) = (change in Q / original Q) divided by (change in P / original P). Equivalent form: Ed = (change in Q / change in P) x (original P / original Q). Ignore the minus sign (the demand curve slopes downward) unless the question asks for the sign. *This is the only method on which ISC numericals are required.*

3. Total expenditure (outlay) method. Compare total expenditure (price x quantity) before and after a price change:

  • Price falls and total expenditure rises (or price rises and it falls): Ed > 1.
  • Total expenditure unchanged: Ed = 1.
  • Price falls and total expenditure falls (or price rises and it rises): Ed < 1.

The signs of price change and expenditure change are opposite for elastic demand and the same for inelastic demand.

4. Geometric (point) method. On a straight-line demand curve, the elasticity at any point equals the ratio of the lower segment to the upper segment of the line at that point: Ed = lower segment / upper segment (the lower segment being the part from the point to the quantity axis). Consequences:

  • At the midpoint of the line Ed = 1.
  • At any point above the midpoint (nearer the price axis) Ed > 1.
  • At any point below the midpoint Ed < 1.
  • At the price-axis intercept Ed = infinity; at the quantity-axis intercept Ed = 0.

So a single straight line has all degrees of elasticity at different points.

5. Income and cross elasticity (to be explained, no numericals required).

  • Income elasticity of demand Ey = percentage change in quantity demanded / percentage change in income. Positive for normal goods (above 1 for luxuries, below 1 for necessities); negative for inferior goods.
  • Cross elasticity Exy = percentage change in quantity demanded of x / percentage change in the price of y. Positive for substitutes, negative for complements, zero for unrelated goods.

6. Factors affecting price elasticity. Availability of substitutes (more substitutes, more elastic), nature of the good (necessity or luxury), proportion of income spent, time period (longer period, more elastic), number of uses, habits and the level of price.

Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods: key facts

Percentage method
Ed = (change in Q / Q) / (change in P / P) = (change in Q / change in P) x (P / Q)
Total expenditure
TE = P x Q; compare TE before and after the price change
Geometric method
Ed = lower segment / upper segment (straight-line demand curve)
Income elasticity
Ey = % change in Q / % change in income
Cross elasticity
Exy = % change in Qx / % change in Py

How to answer Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods questions

Elasticity numericals are short but need careful bases: always use the original price and quantity as the denominator.

  1. 1Write the change in price (new minus old) and the change in quantity.
  2. 2Convert each change into a percentage of its original value.
  3. 3Divide percentage change in quantity by percentage change in price; drop the sign.
  4. 4Classify: more than 1 elastic, 1 unitary, less than 1 inelastic.
  5. 5If the total expenditure method is asked, compute P x Q before and after and read the rule.
  6. 6For the geometric method, find the quantity at the point and use lower segment divided by upper segment.

Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods in real life

The idea, met in an everyday situation. Answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Fare change on a local train

Suppose a city suburban train raises its monthly pass price from Rs 400 to Rs 440 and the number of pass holders drops from 1,000 to 970 because many travellers have no other quick option.

Find the price elasticity of demand and say what the fare rise does to the railway's collection.

Try it first, then show the solutionSolution
  1. Percentage change in price = 40/400 = 10%.
  2. Percentage change in quantity = 30/1,000 = 3%.
  3. Ed = 3/10 = 0.3 (inelastic).
  4. Collection before = 400 x 1,000 = Rs 4,00,000; after = 440 x 970 = Rs 4,26,800.

Answer: Ed = 0.3, so demand is inelastic and the collection rises from Rs 4,00,000 to Rs 4,26,800 even though the number of passengers falls.

Memory hook: Few substitutes, so riders keep coming.

Tricks to remember Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods

Short memory aids. Say each one aloud once, then use it on a question the same day.

  • Expenditure moves with price means inelastic

    If price and total expenditure move in the SAME direction, demand is inelastic; in OPPOSITE directions, elastic.

    Use it when: Total expenditure method questions.

  • Lower over upper

    Geometric method: Lower segment goes on top, Upper segment at the bottom (L over U).

    Use it when: Straight-line demand curve.

  • Original base

    Percentage always uses the OLD value in the denominator.

    Use it when: Avoid the commonest numerical slip.

Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Reading the degree · 1 mark · MCQBoard level

A 10 per cent rise in the price of a good reduces the quantity demanded by 20 per cent. The price elasticity of demand is:
(a) 0.5
(b) 2
(c) 10
(d) 200

Try it first, then show the solutionSolution
  1. Ed = 20/10 = 2, so demand is elastic.

Answer: (b) 2

Example 2: Percentage method · 3 marks · Short answerBoard level

At a price of Rs 40 a household buys 60 kg of a pulse in a month; when the price rises to Rs 50 it buys 54 kg. Calculate the price elasticity of demand by the percentage method and name the degree. (3 marks)

Try it first, then show the solutionSolution
  1. Change in price = 50 - 40 = Rs 10; percentage change = 10/40 x 100 = 25%.
  2. Change in quantity = 54 - 60 = -6 kg; percentage change = -6/60 x 100 = -10%.
  3. Ed = 10/25 = 0.4 (sign ignored).

Answer: Ed = 0.4, less than 1: demand is inelastic.

Example 3: Total expenditure method · 4 marks · Short answerHarder board level

The price of a good falls from Rs 10 to Rs 8. (a) The quantity demanded rises from 50 to 55 units. (b) In another situation it rises from 50 to 75 units. Using the total expenditure method, state the nature of elasticity in each, and verify with the percentage method. (4 marks)

Try it first, then show the solutionSolution
  1. (a) TE before = 10 x 50 = Rs 500; after = 8 x 55 = Rs 440. Price fell and TE fell: same direction, so Ed < 1.
  2. Check: %change in Q = 5/50 = 10%; %change in P = 2/10 = 20%; Ed = 10/20 = 0.5 < 1.
  3. (b) TE after = 8 x 75 = Rs 600 > Rs 500: price fell, TE rose, so Ed > 1.
  4. Check: %change in Q = 25/50 = 50%; Ed = 50/20 = 2.5 > 1.

Answer: (a) Ed = 0.5, inelastic; (b) Ed = 2.5, elastic; both methods agree.

Example 4: Geometric method · 4 marks · Short answerHarder board level

A straight-line demand curve meets the price axis at Rs 100 and the quantity axis at 50 units. Find the elasticity at the price of Rs 60 by the geometric method. Then state the elasticity at Rs 50 and at Rs 20. (4 marks)

Try it first, then show the solutionSolution
  1. The demand line is P = 100 - 2Q, so at P = 60, Q = 20 units.
  2. Lower segment (point to quantity axis) corresponds to 50 - 20 = 30 units; upper segment (point to price axis) corresponds to 20 units. Ed = 30/20 = 1.5 (also P/(100 - P) = 60/40 = 1.5).
  3. At Rs 50 (the midpoint, Q = 25): Ed = 25/25 = 1.
  4. At Rs 20 (Q = 40): Ed = (50 - 40)/40 = 10/40 = 0.25 (also 20/80).

Answer: Ed = 1.5 at Rs 60 (elastic, above the midpoint), 1 at Rs 50 (midpoint) and 0.25 at Rs 20 (inelastic, below the midpoint).

Example 5: Revenue decision using elasticity · 4 marks · Short answerHOTS / competency

A seller's product has Ed = 0.6, and another seller's product has Ed = 2. Each seller raises price by 10 per cent. Using the quantity changes implied by the elasticities, find the effect on each seller's total revenue and advise the sellers. (4 marks)

Try it first, then show the solutionSolution
  1. Seller A: fall in quantity = 0.6 x 10 = 6%. New revenue = 1.10 x 0.94 = 1.034 of the old: it rises by about 3.4%.
  2. Seller B: fall in quantity = 2 x 10 = 20%. New revenue = 1.10 x 0.80 = 0.88 of the old: it falls by 12%.
  3. A price rise helps the seller whose demand is inelastic; it hurts the seller whose demand is elastic.

Answer: Seller A's revenue rises by about 3.4% and Seller B's falls by 12%. Seller A may raise price; Seller B should avoid it (a price cut would raise B's revenue).

Where students lose marks in Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods

The slips examiners see most often, and what to write instead.

  • Mistake: Using the new value as the base

    Dividing the change by the later price or quantity.

    Wrong working

    %change in P = 5/25 = 20%.

    Right working

    %change in P = 5/20 = 25%.

    Do this: Original value is always the denominator.

    Usually costs: 1-2 marks.

  • Mistake: Reversing the ratio

    Writing price over quantity change.

    Wrong working

    Ed = 25/20 = 1.25.

    Right working

    Ed = percentage change in quantity / percentage change in price = 20/25 = 0.8.

    Do this: Quantity goes on top.

    Usually costs: 2 marks.

  • Mistake: Wrong rule in the expenditure method

    Not reading the direction of TE against price.

    Wrong working

    Price falls, TE falls: demand elastic.

    Right working

    Price falls and TE falls (same direction): Ed < 1, inelastic.

    Do this: Same direction means inelastic; opposite direction means elastic.

    Usually costs: 1-2 marks.

  • Mistake: Inverting the segments in the geometric method

    Choosing upper over lower.

    Wrong working

    Ed = upper/lower = 20/30.

    Right working

    Ed = lower/upper = 30/20 = 1.5.

    Do this: Lower segment is on top.

    Usually costs: 1-2 marks.

Exam tips

  • The syllabus asks for numericals on the percentage method only; practise it until it is automatic.
  • State the degree (elastic, inelastic or unitary) after every answer.
  • Draw five small diagrams for the degrees with the axes marked (horizontal line for infinity, vertical line for zero).
  • For the geometric method, always say 'on a straight-line demand curve' and mark the midpoint M.
  • Give the formula first, then the substitution, then the answer with the word 'elastic' or 'inelastic'.

Practice questions on Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

  1. Q1 · 1 mark · MCQBoard level

    A buyer purchases the same quantity of salt whatever its price. The value of Ed is:
    (a) infinity
    (b) one
    (c) greater than one
    (d) zero

    Hint

    Quantity does not respond at all.

    Answer

    (d) zero

  2. Q2 · 3 marks · Short answerBoard level

    At Rs 80 per unit a shop sells 120 units of a gadget; after a discount to Rs 60 it sells 162 units. Calculate the price elasticity of demand and state its nature. (3 marks)

    Hint

    Both changes are percentages of the old values.

    Answer

    %change in P = 20/80 = 25%; %change in Q = 42/120 = 35%; Ed = 35/25 = 1.4 (elastic).

  3. Q3 · 4 marks · Short answerHarder board level

    The price of a good falls from Rs 12 to Rs 9 and the quantity demanded rises from 40 to 44 units. Find Ed by the percentage method and confirm the result by the total expenditure method. (4 marks)

    Hint

    Compute 12 x 40 and 9 x 44.

    Answer

    %change in P = 3/12 = 25%; %change in Q = 4/40 = 10%; Ed = 10/25 = 0.4 (inelastic). TE before = 12 x 40 = Rs 480; after = 9 x 44 = Rs 396: price and expenditure fall together, which confirms Ed < 1.

  4. Q4 · 4 marks · Short answerHarder board level

    A straight-line demand curve cuts the price axis at Rs 90 and the quantity axis at 45 units. Using the geometric method, find the elasticity at Rs 60, at Rs 45 and at Rs 30. Comment on the trend as price falls. (4 marks)

    Hint

    Find Q at each price first (P = 90 - 2Q).

    Answer

    Rs 60: Q = 15, Ed = (45 - 15)/15 = 2. Rs 45: Q = 22.5, Ed = 22.5/22.5 = 1 (midpoint). Rs 30: Q = 30, Ed = 15/30 = 0.5. As price falls along a straight line, elasticity falls from above 1 through 1 to below 1.

  5. Q5 · 3 marks · Short answerHOTS / competency

    Monthly income of a household rises from Rs 20,000 to Rs 24,000 and its purchase of a good rises from 50 to 55 units. Calculate income elasticity, classify the good, and then state what a cross elasticity of +0.4 (price of tea up 10 per cent, quantity of coffee up 4 per cent) implies. (3 marks)

    Hint

    Income elasticity below 1 for a necessity.

    Answer

    %change in income = 4,000/20,000 = 20%; %change in Q = 5/50 = 10%; Ey = 10/20 = 0.5 (positive, below 1: a normal good, a necessity). Cross elasticity = 4/10 = +0.4: positive, so tea and coffee are substitutes.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

  1. 1.Ed for a horizontal demand curve?Show answer

    Infinity (perfectly elastic).

  2. 2.Price falls, total expenditure rises: Ed?Show answer

    Greater than 1.

  3. 3.Ed at the point that cuts a linear demand curve into two equal parts?Show answer

    One.

  4. 4.Which method needs numericals for ISC?Show answer

    The percentage method.

  5. 5.Sign of cross elasticity for substitutes?Show answer

    Positive.

Measuring Elasticity of Demand: Percentage, Expenditure and Geometric Methods: frequently asked questions

What is the formula for price elasticity of demand?

Ed = percentage change in quantity demanded divided by percentage change in price.

Why do we ignore the negative sign?

The law of demand makes the sign negative, so the magnitude alone tells how elastic demand is.

How is the geometric method applied?

On a straight-line demand curve, divide the lower segment by the upper segment at the point.

What are the factors affecting elasticity?

Substitutes, nature of the good, share in income, time period and number of uses.