Equity and Efficiency Analysis of Pricing Strategies in a Bimodal Network with Heterogeneous User Groups

Document Type

Journal Article

Publication Date


Subject Area

land use - planning, ridership - commuting, ridership - demand, policy - equity, economics - pricing, place - airport, mode - rail


Welfare economics, Strategies, Strategic planning, Social justice, Social equity, Priorities, Pricing, Objectives, Mode share, Modal split, Kowloon (Hong Kong, China), Hong Kong International Airport, Heterogeneous users, Goals, Fairness (Social equity), Equity (Justice), Elastic demand, Efficiency analysis, Choice models, Bimodal rail-road transport systems, Bimodal networks


This paper investigates the equity and efficiency of pricing strategies in a bimodal transport network with elastic demand and heterogeneous users on the basis of logit-based discrete choice models. The network consists of a railway line and a parallel highway with a bottleneck that provide daily commuting services between a residential area and a workplace. On the basis of two user groups differing in values of time, first-best pricing is shown to remain possible through the use of anonymous charges under the stochastic user equilibrium condition. Second-best pricing is also examined, in which an equity constraint is introduced to ensure that some users, if not all, are at least not worse off from implementing the pricing at expectation level. The efficiency, equity, demand realization, and modal split resulting from various pricing strategies are investigated and numerically validated in a simplified real network connecting the Kowloon urban area to Hong Kong, China, International Airport. It was found that the equity-constrained second-best pricing can result in a win–win situation for society and users. The efficiency and welfare gains depend heavily on the values of time of user groups and the number of users in each group.