Fare Revision on a City Bus Route: Elasticity and Revenue
A state road transport corporation runs a 12-km city route on which it charges ₹20 per trip and carries about 40,000 passengers a day. Facing a deficit, management proposes a uniform fare of ₹24. A consultant's survey splits the ridership into two segments: 22,000 peak-hour commuters travelling to work, with an estimated own-price elasticity of demand of 0.35, and 18,000 off-peak travellers (shoppers, students, casual trips) with an estimated elasticity of 1.6. Auto-rickshaws on the same corridor charge about ₹35 for the trip, and a metro line is scheduled to open in 18 months. The corporation's fixed costs are ₹4 lakh a day and its variable cost is about ₹11 per passenger trip, mostly fuel and crew. The board meets next week and wants to know whether the uniform hike will close the gap, or whether it should restructure fares instead. Two board members have already argued that any fall in passenger numbers must mean lower revenue and therefore a worse deficit.
1. Estimate the effect of the proposed uniform ₹4 increase on (i) daily passenger revenue and (ii) the corporation's daily operating surplus. Does the hike close the deficit?
Read the worked answer
Baseline at ₹20
- Revenue = 40,000 × 20 = ₹8,00,000
- Variable cost = 40,000 × 11 = ₹4,40,000, so contribution = ₹3,60,000
- Fixed cost ₹4,00,000, so surplus = 3,60,000 - 4,00,000 = -₹40,000 (a loss)
After a 20% fare rise to ₹24
- Peak (elasticity 0.35): quantity change = 20% × 0.35 = 7% fall, so 22,000 × 0.93 = 20,460 riders. Revenue = ₹4,91,040; variable cost = ₹2,25,060; contribution = ₹2,65,980 (up from 22,000 × 9 = ₹1,98,000).
- Off-peak (elasticity 1.6): quantity change = 20% × 1.6 = 32% fall, so 18,000 × 0.68 = 12,240 riders. Revenue = ₹2,93,760; variable cost = ₹1,34,640; contribution = ₹1,59,120 (down from ₹1,62,000).
Totals: revenue = ₹7,84,800, a fall of ₹15,200; contribution = ₹4,25,100; surplus = 4,25,100 - 4,00,000 = +₹25,100.
Judgement: revenue falls but the deficit is closed, because the riders lost are off-peak riders who were contributing only ₹9 each, while each retained peak rider now contributes ₹13. Revenue is the wrong scoreboard; contribution (revenue minus variable cost) is the right one. The board members who predict a worse deficit are using a revenue rule of thumb that fails whenever demand is inelastic.
2. Explain why the two elasticities differ so sharply, and what the ₹35 auto fare and the coming metro imply for the corporation's pricing power.
Read the worked answer
The standard determinants of price elasticity of demand are: availability of close substitutes, share of the consumer's budget, whether the good is a necessity or a discretionary purchase, the width of the market definition, and the time allowed to adjust.
- Peak commuters: the trip is a necessity with a fixed time window, walking or cycling is not realistic at 9 a.m., and ₹20 is a small share of a day's wage. Few substitutes and no time to adjust make demand inelastic (0.35).
- Off-peak travellers: trips are discretionary and postponable, shared autos, walking and cycles are available, and a fare rise can be avoided by combining trips. Many substitutes and elastic demand (1.6).
Cross elasticity. The auto fare of ₹35 is a close substitute, so the cross elasticity of bus demand with respect to the auto fare is positive and large, especially off-peak. The bus's pricing power off-peak is therefore capped: the current gap between ₹35 and ₹24 is the room it has, and closing that gap pushes riders to autos.
The metro. A new substitute makes demand more elastic in the long run, mainly for peak commuters who value speed and reliability. Today's 0.35 is a short-run estimate; after the metro opens, the same fare rise may lose far more riders, so a fare structure that is profitable now may not be in 18 months.
3. Recommend a fare structure, with numbers, and state one risk that could make your recommendation wrong.
Read the worked answer
Option A - peak-only hike (peak ₹24, off-peak ₹20). Peak contribution ₹2,65,980 + off-peak contribution ₹1,62,000 = ₹4,27,980; surplus = 4,27,980 - 4,00,000 = +₹27,980. This beats the uniform hike (₹25,100) by ₹2,880 and the status quo by ₹67,980.
Option B - cut the off-peak fare to ₹18. With elasticity 1.6, a 10% cut raises ridership about 16% to 20,880; contribution = 20,880 × (18 - 11) = ₹1,46,160, which is worse than ₹1,62,000. So do not cut the off-peak fare either.
Recommendation: raise the peak fare to ₹24, freeze the off-peak fare at ₹20, and offer a peak monthly pass to lock in commuters. This earns more than the uniform hike while avoiding the loss-making off-peak price rise.
Risk. The elasticities are survey-based, not revealed by actual sales. If peak elasticity is really 0.5, ridership falls 10% to 19,800 and peak contribution is 19,800 × 13 = ₹2,57,400 - still above the status quo (₹1,98,000), so the direction survives but the size changes. The metro is a second risk: it will shift the whole demand curve. Phase the hike, review ridership monthly, and keep a mid-course correction open.