The Gini index of demand imbalances in public transport

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.