Fare Cap on a City Bus Corridor: Shortage, Revenue and Two Policy Options
A state transport authority caps the fare on a busy city corridor at ₹80 per trip. Before the cap, monthly demand and supply on the corridor were estimated as Qd = 1,200 − 4P and Qs = 200 + 6P, where Q is in thousand trips and P is the fare in rupees. The private operator's association immediately announced it would withdraw 15% of services, arguing that the cap 'destroys our revenue'. Within six weeks informal minibuses were charging ₹120 for the same trip and peak-hour queues had lengthened. The authority's own survey finds that 62% of corridor riders earn below ₹15,000 a month, and that the operator's cost per trip is roughly constant at ₹72 up to the current level of service. Two options are on the table: keep the ₹80 cap and pay the operator a per-trip subsidy, or withdraw the cap and give low-income riders a direct travel allowance. The finance department wants the cheaper option in budget terms and a defensible equity argument.
1. Find the pre-cap equilibrium, the quantity supplied under the ₹80 cap and the resulting shortage. By how much does the operator's fare revenue change, and is the association's claim accurate?
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Before the cap - set Qd = Qs: 1,200 − 4P = 200 + 6P, so 1,000 = 10P, giving P = ₹100 and Q = 800 thousand trips.
After the ₹80 cap - quantity demanded = 1,200 − 320 = 880 thousand; quantity supplied = 200 + 480 = 680 thousand. Shortage = 200 thousand trips a month.
Revenue - before: 800 × 100 = ₹8.00 crore; after: 680 × 80 = ₹5.44 crore, a fall of 32%.
Is the association right? Arithmetically yes, but revenue is the wrong metric and the claim actually understates the damage. With cost constant at ₹72, contribution margin falls from ₹28 × 800,000 = ₹2.24 crore to ₹8 × 680,000 = ₹54.4 lakh - a 76% drop. A supplier losing three-quarters of its margin will cut quality and capacity, which is precisely the announced 15% withdrawal. The revenue figure is not what drives exit; margin is.
2. Compare the per-trip subsidy and the targeted travel allowance. Which is cheaper, which is better on equity, and what does the ₹120 informal fare tell you about each?
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Subsidy route - restoring 800,000 trips at ₹80 at the old price of ₹100 costs ₹20 × 800,000 = ₹1.6 crore a month. But the honest basis is cost, not the pre-cap price: at ₹72 cost, ₹8 per trip (₹64 lakh) already covers cost. A regulator should pay audited cost plus a normal return, otherwise the subsidy is a windfall.
Allowance route - 62% of riders (about 496,000 trips) at ₹20 per trip costs roughly ₹1 crore, apparently cheaper.
The judgement - with the cap binding and supply stuck at 680,000, a cash allowance creates no extra trip. The ₹120 informal fare proves riders already bid well above the cap, so part of the allowance is capitalised into informal fares and queues rather than reaching riders as service. The subsidy buys availability but is costly and hard to police; the allowance targets equity better and costs less but leaves the shortage intact. The finance department's comparison is misleading unless it prices the deadweight loss of 200,000 unmet trips.
3. If the cap persists for five years, what happens to quality and to who actually gets served? How would a cost-of-service regime change your analysis?
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Persistent cap - the operator defers fleet replacement, so the ₹72 cost base creeps up as maintenance rises and vehicles age. Service quality degrades before quantity does: frequency, cleanliness, safety and staff conduct all slip, and those are harder for a regulator to measure than a fare. The queue rations the service to people with time rather than to people with low incomes, and the informal sector absorbs the excess demand at ₹120 - so the cap ends up subsidising the very operators it was meant to discipline.
Cost-of-service regime - price becomes prudently incurred cost plus a fair return, with the ₹72 audited rather than asserted, an asset-base valuation, and a service-quality index attached to the licence. The 15% withdrawal then becomes a compliance breach rather than a market response.
What would sharpen the decision - the price elasticity of demand for these specific riders and the supply elasticity of the informal sector, since together they determine how much of the cap's benefit reaches riders and how much leaks to informal operators.