Leonardo Basso, Universidad De Chile, Sergio Jara-Diaz, Universidad De Chile, José Muñoz, Universidad De Chile


Optimal prices for container port services under different objectives are modeled and discussed. Access price acts as a proxy for a fixed fee to manipulate surplus; the other prices induce desired behavior on the shipping company and users downstream


The purpose of this work is to explore and compare pricing structures and the subsequent division of surplus in port containerized cargo services under different economic objectives: maximizing port profit, maximizing social welfare, and maximizing social welfare subject to cover port costs. In our model, operational restrictions relating to the capacity of ships and the port’s docking site are considered, so that congestion is a core element. For this, we propose a vertical structure model where agents move sequentially as follows: (i) the port selects its prices for its services of access, berth provision, unloading and forwarding cargo; (ii) based on these, a monopolistic shipping company determines its charges and service levels (frequency of ships and use of cranes) to serve users; (iii) finally, taking into account the sipping company prices and transport times, users decide on the number of containers to dispatch. Using reasonable values for all variables in the problem –that is, values that represent an actual route– we numerically obtain the subgame perfect Nash equilibrium, using the analytical solutions of the problem to help build intuition.

Our results show a strong trade-off between the benefits of the liner shipping company and those of the port, where one of the prices –the access price– is the preferred instrument to extract/inject surplus as it is the one that affects less other (marginal) decisions of the shipping company; in other words, it works as a sort of proxy for a fixed fee. A private port would then attempt to induce profit maximization downstream using the rest of the prices, while using the access price to extract those monopoly profits. In a sense, the use of a large vector of prices enables the port to diminish the double marginalization problem and force surplus up the chain. A welfare maximizing port will, on the other hand, choose to use some prices below the corresponding marginal cost to fight back allocative inefficiency caused by market power downstream –at the carrier level– while using the access price to recover costs and achieve exact self-financing. Importantly, the technical relations play a key role: when the level of demand and service conditions lead to a system saturation (that is, full ships and ports) the port is able to reach maximum social welfare making positive profit, as subsidizing to increase traffic is no longer desirable.


Association for European Transport