Ferry Fares, Peak Capacity, and Distribution
An island ferry operator faces two daily demand segments. Peak demand is Qp = 14,000 − 1,500P; off-peak demand is Qo = 8,000 − 1,500P, where Q is passengers and P is the fare in euros. Marginal cost is €1.50 per passenger, fixed costs are €9,000 per day, and vessel capacity is 5,000 passengers in each segment. The current flat fare is €4.00. The regulator requires the operator to cover total costs but not to earn more than a normal return. Low-income residents make 35% of peak trips and have few substitutes; tourist demand is concentrated off-peak. The operator proposes raising the flat fare to €4.50 and adding a €1.00 peak surcharge. The ministry asks whether the proposal is efficient, whether capacity should be expanded, and how the burden falls on low-income residents.
1. Compute the unconstrained profit-maximizing fare and quantity in each segment. Does capacity bind? Show the marginal revenue expressions and explain the economics.
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Invert demand: peak P = 9.333 − Q/1,500; MR = 9.333 − Q/750. Setting MR = MC = 1.50 gives Q = 5,875 and P = €5.42. That exceeds capacity 5,000, so the capacity constraint binds: at Q = 5,000, willingness to pay is €6.00 and MR (€2.67) still exceeds MC. Off-peak: P = 5.333 − Q/1,500; MR = 5.333 − Q/750; MR = 1.50 gives Q = 2,875 and P = €3.42; capacity does not bind. At the current €4 flat fare, peak demand is 8,000, so 3,000 passengers are rationed by queuing or crowding, while off-peak demand is only 2,000. The unconstrained monopoly fare is not feasible at peak; the operator must either raise the peak fare to clear the market or expand capacity. The relevant comparison for expansion is the marginal cost of capacity against the marginal congestion or rationing cost, not against average cost.
2. Evaluate the proposed €4.50 fare plus €1.00 peak surcharge against a peak/off-peak structure that clears the peak market and covers total cost. Recommend fares and capacity, with welfare reasoning.
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At Qpeak = 5,000, the market-clearing peak fare is €6.00. The off-peak profit-maximizing fare is €3.42 with Q = 2,875. Revenue = 5,000 × 6 + 2,875 × 3.42 = 30,000 + 9,833 = €39,833; variable cost = 1.5 × 7,875 = €11,813; fixed cost = €9,000; contribution = €19,020. If the regulator allows only total-cost recovery, fares can be lowered until revenue equals cost, but the peak fare should still exceed off-peak because peak demand imposes capacity cost. The proposed €4.50 plus €1 peak surcharge gives peak €5.50 and off-peak €4.50: peak demand is 5,750, above 5,000, so rationing remains; off-peak demand is 1,250, so the off-peak fare is far above marginal cost and creates avoidable deadweight loss. A better structure is a peak fare near €6.00, an off-peak fare near marginal cost or lower if revenue-neutral, and congestion-based capacity expansion only if the marginal capacity cost is below the marginal benefit of relieving peak rationing.
3. Assess the distributional effects of the proposal and recommend how the ministry should separate efficiency from equity concerns.
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Low-income residents make 35% of peak trips, so a peak surcharge is regressive unless offset. Because their substitutes are few, their demand is less elastic; Ramsey pricing would put more of the fixed-cost burden on them, which may conflict with distributional goals. A two-part tariff with a lower peak surcharge for registered residents, or a lifeline off-peak pass, can preserve efficiency while limiting hardship. The ministry should separate efficiency (price peak at capacity cost, off-peak near marginal cost) from distribution (targeted transfers), rather than using a flat fare that creates peak overcrowding and off-peak underuse.