Minibus Congestion Charge in the City Centre
A city centre is served by 10,000 minibus trips a day at an average fare of $2.00. The regulator estimates marginal private cost as MPC = 1 + 0.0001Q and marginal external congestion cost as MEC = 0.0001Q, where Q is trips per day and costs are dollars per trip. Demand is P = 4 - 0.0002Q. Minibus operators set fares competitively and currently ignore congestion. The city proposes a congestion charge equal to the marginal external cost at the socially optimal output. Operators say the charge will be passed fully to passengers, hitting low-income commuters who have no car alternative. Taxi and ride-hailing services are exempt, and some trips would divert to them. The city's transport department wants to know whether the charge will reduce traffic, how large the efficiency gain is, and whether a fuel tax would be better.
1. Calculate the private equilibrium, the social optimum, the congestion charge and the deadweight loss.
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Private equilibrium: set MPC = demand. 1 + 0.0001Q = 4 - 0.0002Q, so 0.0003Q = 3 and Q = 10,000. P = 1 + 1 = $2.00 (or 4 - 2 = $2.00). At Q = 10,000, MEC = 0.0001 x 10,000 = $1.00 per trip. Social marginal cost is MSC = MPC + MEC = 1 + 0.0002Q. Social optimum: 1 + 0.0002Q = 4 - 0.0002Q, so 0.0004Q = 3 and Q = 7,500. P = 4 - 0.0002 x 7,500 = $2.50. MEC at 7,500 = $0.75, so the congestion charge is $0.75 per trip. DWL at the private equilibrium is the triangle between demand and MSC from 7,500 to 10,000: at Q = 10,000, MSC = $3.00 and demand price = $2.00, so the gap is $1.00. DWL = 0.5 x 2,500 x $1.00 = $1,250 per day.
2. Evaluate the congestion charge against a fuel tax. Consider targeting, coverage, evasion and administration.
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A congestion charge is directly targeted at the external cost. At $0.75, the private cost curve shifts up to meet MSC at the social optimum, reducing trips from 10,000 to 7,500 and eliminating the $1,250 daily DWL, if enforcement is perfect. A fuel tax also raises private cost, but it is a second-best instrument: it penalises fuel use rather than road space at peak times, and the required rate is uncertain because fuel per trip varies. It would also affect off-peak and non-congesting trips. The charge can vary by time and location and can raise revenue for bus services or pedestrian improvements. However, exemptions for taxis and ride-hailing would divert trips and weaken the effect; if those services are close substitutes, the traffic reduction will be smaller than 2,500 trips. A fuel tax may be cheaper to administer and harder to evade. Judgement: the charge is better on efficiency grounds if coverage is broad; a fuel tax is a rough fallback. Combining the charge with better public transport would improve both efficiency and equity.
3. Assess the distributional effects. Are low-income commuters likely to be worse off, and how should the city respond?
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The charge raises the fare from $2.00 to about $2.50 at the new equilibrium; the full $0.75 is not passed on because lower trip volume reduces marginal private cost. Low-income commuters with no car alternative may be hit hardest, since the charge takes a larger share of their budget. But they also gain from shorter journey times and more reliable buses, and the revenue can fund concessions. If taxis are exempt, higher-income travellers may escape the charge while bus users pay, which weakens both efficiency and fairness. A pure charge is regressive unless revenue is recycled. Options include a residents' rebate, free transfers, or using revenue to subsidise minibus frequency. The efficiency case is strong, but the distributional judgement depends on how the revenue is used. The city should not treat the charge as a pure revenue measure; it should link it to a visible transport improvement.