Price elasticity of demand: definition and calculation

G3 Economics - syllabus K343, 2027

What this lesson teaches

  • I can define price elasticity of demand (PED).

    Syllabus K343, 2.6.1. Definition of PED

  • I can calculate PED, say what the value means, and draw demand curves with different elasticities.

    Syllabus K343, 2.6.2. Calculation of PED: calculation of PED using the formula; interpretation of the significance of the PED value: perfectly inelastic, inelastic, unitary, elastic, perfectly elastic; drawing and interpretation of demand curve diagrams to show different PED

Make a guess

A cinema cuts its ticket price by 25% and sells 50% more tickets. Is demand for its tickets elastic or inelastic?

  1. Inelastic: a 25% cut is a big change.
  2. You cannot tell without the dollar prices.
  3. Elastic: quantity changed by more than price.
Show the answer

Elastic: quantity changed by more than price.

PED = 50 / -25 = -2. Ignore the sign: 2 is above 1, so demand is price elastic.

PED measures how strongly quantity demanded responds to a change in price.

Price elasticity of demand (PED) measures how responsive quantity demanded is to a change in the good's own price.

PED = percentage change in quantity demanded / percentage change in price. A percentage change is the change divided by the original value, times 100.

PED is negative because price and quantity demanded move in opposite directions. Economists often ignore the minus sign when comparing values, but keep it in a calculation answer.

Always use the original values as the base. Work out each percentage change first, then divide. Check the sign: a price rise with a fall in quantity gives a negative answer.

PED
Responsiveness of quantity demanded to a change in price.
Formula
PED = % change in quantity demanded / % change in price.
Sign
Usually negative, because price and quantity demanded move in opposite directions.

Worked example: Calculating PED step by step

Suppose a cinema cuts ticket prices from $12 to $9. Weekly tickets sold rise from 2,000 to 3,000.

  1. Change in price = 9 - 12 = -3. Percentage change = -3 / 12 x 100 = -25%.
  2. Change in quantity = 3,000 - 2,000 = 1,000. Percentage change = 1,000 / 2,000 x 100 = 50%.
  3. PED = 50% / -25% = -2.
  4. Interpret: the value is greater than 1 (ignoring the sign), so demand is price elastic.

Try it step by step

Problem 1

A hawker raises the price of a plate of chicken rice from $4.00 to $4.40. Daily plates sold fall from 300 to 285.

Show the working
  1. Percentage change in price: Change = 4.40 - 4.00 = 0.40. Percentage change = 0.40 / 4.00 x 100 = +10%
  2. Percentage change in quantity demanded: Change = 285 - 300 = -15. Percentage change = -15 / 300 x 100 = -5%
  3. PED: PED = -5 / 10 = -0.5. Ignoring the sign, 0.5 is below 1, so demand is inelastic.

Problem 2

A bookshop cuts the price of a comic from $5.00 to $4.00. Weekly sales rise from 200 to 300.

Show the working
  1. Percentage change in price: Change = 4.00 - 5.00 = -1.00. Percentage change = -1.00 / 5.00 x 100 = -20%
  2. Percentage change in quantity demanded: Change = 300 - 200 = 100. Percentage change = 100 / 200 x 100 = +50%
  3. PED: PED = 50 / -20 = -2.5. Ignoring the sign, 2.5 is above 1, so demand is elastic.

Problem 3

A bubble tea shop raises its price from $3.00 to $3.60. Daily cups sold fall from 500 to 400.

Show the working
  1. Percentage change in price: Change = 3.60 - 3.00 = 0.60. Percentage change = 0.60 / 3.00 x 100 = +20%
  2. Percentage change in quantity demanded: Change = 400 - 500 = -100. Percentage change = -100 / 500 x 100 = -20%
  3. PED: PED = -20 / 20 = -1. Ignoring the sign, exactly 1, so demand is unitary.

Watch out for this

PED = change in price / change in quantity.

It is the other way round, and it uses percentage changes: percentage change in quantity demanded divided by percentage change in price.

Check your understanding

Price rises from $10 to $12 and quantity demanded falls from 500 to 450. What is the PED?

  1. -0.1
  2. -2
  3. -0.5
Show the answer

-0.5

Right. Quantity falls 10% (50 / 500) and price rises 20% (2 / 10). -10% / 20% = -0.5.

Check your understanding

The price of a good falls by 10% and quantity demanded rises by 25%. What is the price elasticity of demand?

  1. -0.4
  2. -15
  3. -2.5
  4. -35
Show the answer

-2.5

Right. PED = % change in quantity / % change in price = 25 / -10 = -2.5.

The Wise Otter

Getting your study space ready