Price Cap for a Monopoly Ferry
The only operator of a vehicle ferry between two islands faces demand P = 24 − 0.004Q, where P is euro per car and Q is cars per day. Its total cost is TC = 18,000 + 4Q. The regulator is considering a price cap of €8 per car. The operator says the cap will force it to cut sailings and reduce reliability; consumer groups say the current fare exploits captive users. The government cannot subsidise the route because of eurozone fiscal rules. There are 3,000 cars per day at the current unregulated fare. Fixed costs are sunk in the short run but must be recovered in the long run. The regulator must decide within three months. The ferry is the only practical route for freight.
1. Calculate the unregulated monopoly price, quantity and profit. Then calculate the quantity demanded and profit at a cap of €8. Explain whether the cap is likely to be sustainable.
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Unregulated: inverse demand P = 24 − 0.004Q, so MR = 24 − 0.008Q. MC = 4. Set MR = MC: 24 − 0.008Q = 4, so Q = 2,500. P = 24 − 0.004(2,500) = €14. TR = €35,000; TC = 18,000 + 4(2,500) = €28,000; profit = €7,000 per day.
At the €8 cap: 8 = 24 − 0.004Q, so Q = 4,000. TR = €32,000; TC = 18,000 + 4(4,000) = €34,000; loss = €2,000 per day. Price €8 is below average cost at Q = 4,000 (€8.50). In the short run the operator may still sail because revenue covers variable cost (€32,000 vs €16,000), but it cannot recover fixed costs. Over time it will cut frequency, quality or exit. The cap therefore creates a shortage and quality risk rather than a sustainable fare.
2. The regulator has three options: enforce the €8 cap, set a cap at average cost, or allow the monopoly and regulate service quality. Recommend one, using economic reasoning.
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The €8 cap is allocatively attractive because it is closer to marginal cost, but it is unsustainable: the operator makes a loss and will underinvest or exit. No cap gives €14 and restricts output to 2,500 cars, leaving a large deadweight loss. Average-cost pricing sets P = AC: 24 − 0.004Q = 18,000/Q + 4. Solving gives Q ≈ 3,823 and P ≈ €8.71, with zero economic profit. This expands output from 2,500 to 3,823, removes excess profit, and covers costs, but P is still above MC = €4, so some deadweight loss remains and the firm has weak cost-cutting incentives. Marginal-cost pricing P = €4 would give Q = 5,000 but a loss of €18,000 per day, impossible without subsidy under the fiscal rules. Recommendation: an average-cost cap with service-quality standards and periodic efficiency reviews, not the €8 cap. If affordability for low-income islanders is the goal, targeted vouchers are better than a universal below-cost fare. Publish accounts and consult freight users.