Optimal concession contracts for landlord port authorities to maximize traffic volumes

Abstract

This article analyzes optimal concession contracts offered by a landlord port authority to competing operators of container terminals. The port authority pursues traffic-volume maximization. Three contract schemes considered are fixed-fee, unit-fee, and two-part tariff. A two-stage game is constructed to characterize interactions between the port authority and two terminal operators. We discover that the fixed-fee contract is the best choice for the authority. Terminal operators’ congestion costs and competition modes have no impact on this contract choice. Our results demonstrate that port authority’s goal is an important factor in determining optimal concession contracts.

Acknowledgments

The authors would like to thank editor Kevin Li, responsible associate editor, and two anonymous referees for their valuable comments. We also appreciate the National Science Council of Taiwan (Project No.: NSC102-2410-H-305-51) for providing research fund.

Notes

1. Since c₂ ≥ c₁, we have . Together with , we have . On the other hand, is implied by and . And condition suggests .

2. There exist two problems if terminal operators are subsidized. First, citizens may not like the idea, especially as operators are foreigners. Second, using debts to exchange terminals throughput may threaten port authorities’ long run sustainability. Thus, we do not consider the subsidy case.

3. Constraint will require and . Similar arguments apply to the two-part tariff scheme.

4. Constraint is equivalent to requiring and for i = 1, 2.

5. If n ≥ 3, we have . The associated first-order condition is . First, unit fee r appears in the constant term. Second, by the implicit function theorem, we have , where and for i, j = 1, 2. Here by the stability condition, and since by the second-order condition and by the strategic complement of operators’ service prices. Thus, we get for i = 1, 2. Then, by (3) and (4) and Cramer’s rule, we can obtain for i = 1, 2. In sum, unit fee r is positively related to equilibrium service prices, and negatively related to equilibrium cargo volumes.