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Price Elasticity of Demand and Supply: Question 10

Syllabus 2.6

Structured 10 marks

A public bus company cuts the single-journey fare on a quiet rural route from $3.00 to $2.40 to try to attract more passengers. As a result, the number of passenger journeys on the route rises from 1200 to 1260 per day.

(a) Calculate the percentage change in the fare and the percentage change in the number of passenger journeys. [2]

(b) Calculate the price elasticity of demand (PED) for journeys on this route, showing your working, and state whether demand is price elastic, price inelastic or unitary. [3]

(c) Calculate the bus company's total daily revenue from this route before and after the fare cut. [2]

(d) Using your answers to (b) and (c), explain why the fare cut caused total revenue to fall, and state what this suggests the bus company should do instead if its main aim is to increase revenue from this route. [3]

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Worked solution

Part (a): Percentage changes in the fare and passenger journeys

Percentage change in the fare, using the original fare of $3.00 as the base: %ΔP=2.40−3.003.00×100=−0.603.00×100=−20%\%\Delta P = \frac{2.40-3.00}{3.00}\times100 = \frac{-0.60}{3.00}\times100 = -20\%

Percentage change in the number of passenger journeys, using the original number of 1200 as the base: %ΔQd=1260−12001200×100=+5%\%\Delta Q_d = \frac{1260-1200}{1200}\times100 = +5\%

Part (b): Calculating and classifying PED

PED=%ΔQd%ΔP=5−20=−0.25PED = \frac{\%\Delta Q_d}{\%\Delta P} = \frac{5}{-20} = -0.25

Ignoring the sign, the size of PED is 0.250.25. Since 0.25<10.25 < 1, demand for journeys on this route is price inelastic: the percentage rise in passenger journeys (5%) is proportionately much smaller than the percentage fall in the fare (20%).

Part (c): Total revenue before and after the fare cut

Total revenue is the fare multiplied by the number of passenger journeys.

Before the fare cut: 3.00×1200=36003.00 \times 1200 = 3600 which is $3,600 per day.

After the fare cut: 2.40×1260=30242.40 \times 1260 = 3024 which is $3,024 per day.

Part (d): Why revenue fell, and what the company should do instead

Total revenue fell, from $3,600 to $3,024, when the bus company cut the fare. This is exactly what the theory of price elasticity of demand predicts, because demand for journeys on this route is price inelastic: the percentage rise in passenger journeys (5%) is much smaller than the percentage fall in the fare (20%). The extra revenue that would come from more passengers travelling is far outweighed by the lower fare now charged on every journey, including the 1200 journeys that would have happened anyway, so total revenue falls overall.

This has an important implication for the bus company. Since demand on this route is price inelastic, cutting the fare was the wrong strategy if the company’s main aim is to increase revenue: a fare cut on inelastic demand reduces revenue, as shown here. If the company instead raised the fare, the percentage fall in passenger journeys would be smaller than the percentage rise in the fare, because demand is inelastic, so total revenue would rise. Raising the fare might not suit every objective the company has (for example, it could reduce access to the service for some passengers) but in terms of maximising revenue from this specific route, raising the fare, not cutting it, is the more effective strategy.

Final answers

  • (a) %ΔP=−20%\%\Delta P = -20\%, %ΔQd=+5%\%\Delta Q_d = +5\%
  • (b) PED=−0.25PED = -0.25. Demand is price inelastic
  • (c) Total daily revenue was $3,600 before the fare cut and $3,024 after the fare cut
  • (d) Because demand is price inelastic, the fare cut reduced total revenue; raising the fare instead would be expected to increase revenue from this route