A Fare Rise That Raises Revenue: Should the Minibus Owner Push to ₦300?
A minibus operator on the campus-to-town route raises the fare from ₦200 to ₦250 per passenger. Before the increase his fleet carried about 4,000 passengers a day and took ₦800,000. Two weeks after the increase, daily passengers settle at 3,400, and daily costs, which are almost entirely fixed (fuel contracts, drivers' wages, vehicle licences), remain at ₦520,000. The owner is delighted: revenue is up. His accountant is less sure. She points out that a tricycle union charges ₦150 for the same short trip, that two new tricycles start work at the campus gate next month, and that a second campus route will open in the same period. The owner wants a decision: push the fare to ₦300, hold at ₦250, or go back to ₦200. He also wants to know how much weight the two-week passenger figure can bear, since several buses already leave the campus full at peak times.
1. Calculate the price elasticity of demand for the fare increase using the midpoint formula, interpret it, and work out what happened to revenue and profit.
Read the worked answer
Identify the points. P₁ = ₦200, Q₁ = 4,000; P₂ = ₦250, Q₂ = 3,400.
Percentage changes (midpoint method).
- ΔQ = 3,400 − 4,000 = −600; average Q = 3,700; %ΔQ = −600 ÷ 3,700 = −16.2%.
- ΔP = 50; average P = 225; %ΔP = 50 ÷ 225 = +22.2%.
Elasticity. PED = −16.2 ÷ 22.2 = −0.73, so |PED| = 0.73 < 1: demand is price-inelastic over this range.
Why revenue rose. With inelastic demand, the percentage fall in passengers (16.2%) is smaller than the percentage rise in fare (22.2%), so total revenue increases: 4,000 × 200 = ₦800,000 becomes 3,400 × 250 = ₦850,000, a rise of 6.25%.
Profit. Costs are fixed at ₦520,000, so profit rises from ₦280,000 to ₦330,000, up ₦50,000 (17.9%). Note the profit rises by more than revenue in percentage terms because the cost is fixed - the same ₦520,000 is now spread over fewer passengers.
Interpretation to state in words. Passengers had no ready alternative during the two weeks, so they absorbed the fare rise; that is exactly what a low elasticity figure means.
2. Using the same elasticity, estimate what a further rise to ₦300 would produce, and explain why that estimate may mislead the owner in this particular case.
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Mechanical estimate. A rise from ₦250 to ₦300 is +20%. With PED constant at −0.73, %ΔQ = −0.73 × 20 = −14.6%, so Q ≈ 3,400 × 0.854 ≈ 2,904 passengers. Revenue ≈ 2,904 × 300 = ₦871,200, and profit ≈ 871,200 − 520,000 = ₦351,200 - apparently better again.
Why the estimate is fragile here.
- Extrapolation. The elasticity was measured over a narrow 25% fare band and a two-week window. Elasticities are not constants; they normally rise (in absolute value) as the price moves further from the customary level.
- New substitutes. Two tricycles at ₦150 arrive at the gate next month, and a second route opens. Both increase the number of substitutes, which pushes demand towards elasticity - the −0.73 figure will not survive.
- Time horizon. Two weeks captures captive, routine travellers who have not yet rearranged their journeys. Long-run elasticity is almost always larger.
- Capacity bias - the strongest objection. If buses already leave full at peak, the observed 3,400 may be limited by seats available rather than by willingness to pay. A supply ceiling makes demand look less responsive than it really is, so the measured 0.73 may understate true sensitivity.
Judgement. The ₦300 proposal is not safe on this evidence. At best it adds about ₦21,000 of daily profit; at worst, once the tricycles and the new route bite, revenue could fall outright. Holding at ₦250 while monitoring load factors is the prudent position, and a fare reduction is unlikely to pay since demand is inelastic.
3. What evidence would you gather before advising the owner, and how would you use it?
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1. A longer and better observed price history. Collect passenger counts for at least a full term across previous fare changes, so that seasonal effects (vacations, examinations) are not mistaken for price effects. Two weeks is a single observation point, not a trend.
2. Capacity data. Record seat-kilometres offered and load factors by hour. If peak buses run at 100% load, the recorded passenger numbers measure supply, not demand; the elasticity should be recalculated only from off-peak, uncongested journeys.
3. Cross-elasticity with the tricycles. Compare passenger numbers on days when the tricycle fare changes. A large positive cross-price elasticity tells the owner that ₦300 will trigger switching.
4. A controlled trial on one route. Change the fare to ₦300 on a single route for four weeks while leaving the others at ₦250, and compare. This isolates the price effect from the new route and the new tricycles.
5. Willingness-to-pay survey. Ask regular passengers their intended response to ₦300 and to ₦350; survey evidence is weak on its own but useful for spotting the fare at which resentment turns into switching.
6. Cost structure check. Confirm that the ₦520,000 really is fixed; if fuel varies with trips, cutting frequency to match 2,900 passengers would release savings and change the profit arithmetic.
How to decide. Set the decision rule in advance: raise to ₦300 only if the trial shows total revenue above ₦850,000 after the tricycles and the new route have been operating for four weeks. Otherwise hold.