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9708 · 2.2

Price elasticity of demand — practice questions

Practice and worked examples for 9708 Price elasticity of demand. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

Price rises from £4 to £5; quantity falls from 200 to 160. Find PED.

Show solution outline

ΔP = +25%, ΔQ = −20%

PED = (−20%)/(+25%) = −0.8 (inelastic)

TR before = £800; after = £800 — unchanged direction confirms inelastic range near unit.

Worked example 2

A cinema reduces its ticket price from $12 to $10. Consequently, weekly ticket sales increase from 500 to 700. Calculate the PED and advise the cinema on its pricing strategy.

Show solution outline
  1. Calculate Percentage Change in Price (%ΔP): Change in Price = $10 - $12 = -$2 %ΔP = (-$2 / $12) * 100 = -16.67%
  2. Calculate Percentage Change in Quantity Demanded (%ΔQd): Change in Quantity = 700 - 500 = +200 %ΔQd = (200 / 500) * 100 = +40%
  3. Calculate PED: PED = %ΔQd / %ΔP = 40% / -16.67% = -2.4
  4. Interpret the result and advise: The absolute value of PED is 2.4, which is greater than 1. This means demand is price elastic. Original Total Revenue (TR) = $12 * 500 = $6,000 New Total Revenue (TR) = $10 * 700 = $7,000 Since demand is elastic, the price reduction led to a proportionally larger increase in quantity demanded, causing total revenue to increase by $1,000. The cinema's decision to lower the price was correct for increasing revenue.

Worked example 3

Average incomes in a town rise from £30,000 to £33,000. Over the same period, demand for restaurant meals rises from 5,000 to 6,000 a month, while demand for own-brand instant noodles falls from 8,000 to 7,600 packets a month.

(a) Calculate the YED for restaurant meals and for instant noodles. (b) Classify each good.

Show solution outline

Percentage change in income: (33,000 − 30,000) ÷ 30,000 × 100 = +10%

(a) Restaurant meals %ΔQd = (6,000 − 5,000) ÷ 5,000 × 100 = +20% YED = +20% ÷ +10% = +2

Instant noodles %ΔQd = (7,600 − 8,000) ÷ 8,000 × 100 = −5% YED = −5% ÷ +10% = −0.5

(b) Classification Restaurant meals: YED = +2. Positive, so a normal good; greater than 1, so a luxury: demand grows twice as fast as income. Instant noodles: YED = −0.5. Negative, so an inferior good: as incomes rise, people buy fewer and trade up.

State the sign with the value every time. A YED written as '2' or '0.5' without its sign cannot be classified and loses the interpretation mark.

Worked example 4

The price of Coca-Cola rises from £1.00 to £1.10 a can. Weekly sales of Pepsi in the same shop rise from 2,000 to 2,300 cans. Separately, the price of a printer falls from £100 to £80 and weekly sales of its ink cartridges rise from 500 to 560.

(a) Calculate the XED of Pepsi with respect to the price of Coca-Cola. (b) Calculate the XED of ink cartridges with respect to the price of printers. (c) State the relationship between each pair of goods.

Show solution outline

(a) Pepsi and Coca-Cola %ΔP of Coca-Cola = (1.10 − 1.00) ÷ 1.00 × 100 = +10% %ΔQd of Pepsi = (2,300 − 2,000) ÷ 2,000 × 100 = +15% XED = +15% ÷ +10% = +1.5

(b) Ink cartridges and printers %ΔP of printers = (80 − 100) ÷ 100 × 100 = −20% %ΔQd of cartridges = (560 − 500) ÷ 500 × 100 = +12% XED = +12% ÷ −20% = −0.6

(c) Relationships Pepsi and Coca-Cola: XED = +1.5, positive, so substitutes; a value above 1 shows close substitutes. Ink cartridges and printers: XED = −0.6, negative, so complements: cheaper printers mean more printers in use and more cartridges bought.

Write the goods the right way round: the quantity is always good A's and the price is always good B's.

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