Toll Tunnel Franchise and Congestion
A private consortium has built a toll tunnel linking a new town to the airport. It is the only direct route, and demand is given by a straight-line schedule: at HK$25 per trip, 20 million trips per year; at HK$20, 30 million; at HK$15, 40 million; at HK$10, 50 million. The tunnel's fixed cost is HK$300 million per year, and its marginal cost is constant at HK$5 per trip. The government granted a 30-year exclusive franchise but retained the right to regulate the toll. The consortium proposes HK$25. Consumer groups want a HK$10 cap. A transport economist recommends average-cost pricing. The government must also consider that a parallel ferry service carries 8 million passengers per year at HK$30, and congestion on the road outside the tunnel rises when traffic exceeds 45 million trips. The franchise contract does not mention subsidies.
1. Calculate the profit-maximising toll and annual profit. Show why HK$10 is not profit-maximising.
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Compute total profit at each toll. At HK$25, quantity is 20 million, total revenue is HK$500 million, total cost is HK$300 million plus HK$5 times 20 million, or HK$400 million, so profit is HK$100 million. At HK$20, revenue is HK$600 million and total cost is HK$450 million, so profit is HK$150 million. At HK$15, revenue is HK$600 million and total cost is HK$500 million, so profit is HK$100 million. At HK$10, revenue is HK$500 million and total cost is HK$550 million, so the firm makes a loss of HK$50 million.
The profit-maximising toll is therefore HK$20, with 30 million trips and profit of HK$150 million. HK$10 is not profit-maximising because it expands output into a range where the extra revenue from more trips is zero or negative while the marginal cost is HK$5 per trip. At HK$10 the firm loses money. The consortium's proposed HK$25 also earns less profit than HK$20, because it sacrifices too many trips.
2. Evaluate average-cost pricing as a regulatory rule, given the congestion threshold of 45 million trips.
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Average-cost pricing sets price equal to average cost. Average cost is HK$300 million divided by quantity plus HK$5. With the demand schedule, the lower break-even solution is approximately 47.3 million trips and a toll of about HK$11.3. At that point the firm earns zero economic profit and needs no subsidy. This is lower than the unregulated HK$20 toll and would increase output and reduce the deadweight loss from monopoly pricing.
However, 47.3 million trips exceed the congestion threshold of 45 million. The toll does not include the external congestion cost imposed on road users outside the tunnel. Average-cost pricing would therefore encourage too much traffic from a social perspective. Marginal-cost pricing at HK$5 would produce 60 million trips, an even larger loss of HK$300 million and more congestion. Average-cost pricing is better than the unregulated monopoly but is not first-best. A better rule would set the toll equal to marginal cost plus the congestion externality and cover the fixed cost through a two-part tariff or a targeted subsidy.
3. The consortium says the franchise is unfair because it cannot cover fixed cost at HK$10. Assess whether a subsidy is justified.
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At HK$10, the tunnel carries 50 million trips, revenue is HK$500 million, and total cost is HK$550 million, so the loss is HK$50 million. A subsidy of HK$50 million would allow the lower toll and increase output from the unregulated 30 million trips to 50 million. The deadweight loss at the unregulated toll is the triangle between demand and marginal cost from 30 million to 60 million trips: about HK$225 million. At HK$10 the deadweight loss falls to about HK$25 million. The subsidy therefore buys a large efficiency gain relative to its cost.
But the subsidy also encourages traffic beyond the 45 million congestion threshold, so part of the gain is offset by external congestion costs. A blanket subsidy could also be regressive if richer airport travellers gain most. Judgement: a subsidy is justified only if it is combined with congestion pricing and possibly a two-part tariff that charges heavy users more. The fixed cost is a natural-monopoly cost, so some public support may be efficient, but it should not be unconditional.