The Gini index of demand imbalances in public transport
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The Gini index of demand imbalances in public transport Daniel Hörcher1,2 · Daniel J. Graham1
© The Author(s) 2020
Abstract The paper studies a general bidirectional public transport line along which demand varies by line section. The length of line sections also varies, and therefore their contribution to aggregate (line-level) user and operational costs might be different, even if demand levels were uniform. The paper proposes the Gini index as a measure of demand imbalances in public transport. We run a series of numerical simulations with randomised demand patterns, and derive the socially optimal fare, frequency and vehicle size variables in each case. We show that the Gini coefficient is a surprisingly good predictor of all three attributes of optimal supply. These results remain robust with inelastic as well as elastic demand, at various levels of aggregate demand intensity. In addition, we find that lines facing severe demand imbalances generate higher operational cost and require more public subsidies under socially optimal supply, controlling for the scale of operations. The results shed light on the bias introduced by the assumption of homogeneous demand in several existing public transport models. Keywords Public transport · Demand imbalances · Gini coefficient · Optimal pricing · Subsidies
Introduction Short-run supply optimisation has a long-standing history at the boundary between transport planning and economics. The elementary principles of microeconomic theory suggest that, no matter which mode we consider, capacity variables1 such as road width or service frequency should be increased up until the point where the marginal operational cost of further expansion equals the marginal benefit delivered to users. The outcome of this capacity rule in combination with usage fees capturing the marginal social cost of travelling ensure that supply maximises the economic efficiency of service provision (Small and Verhoef 2007). 1 Throughout the paper, we use ‘capacity’ as a collective noun of frequency and vehicle size instead of the maximum passenger load per vehicle. We refer to the latter as ‘physical capacity’ or ‘capacity constraint’.
* Daniel Hörcher [email protected] 1
Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
2
Budapest University of Technology and Economics, 3 Műegyetem rkp., Budapest 1111, Hungary
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Transportation
In public transport, multiple variables can be considered as a representation of capacity, and the evolution of the underlying literature follows the discovery of the links between new capacity variables and the corresponding user costs. First, the tension between the cost of service frequency and average waiting time is investigated by Mohring (1972, (1976). In the second phase the literature recognises that not only waiting time, but also the in-vehicle travel time may depend on service frequency through the time required to board and alight at intermediate stops (Jansson 1980; Jara-Díaz and Gschwender
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