Manuscrito
Optimal Departure from Marginal Cost Pricing in Public Transport
Fecha
2015Institución
Resumen
Cities differ in the way they price, spatially, their public transportation systems. Among the largest cities in the world, many cities in America (e.g. Mexico City, Sao Paulo, Buenos Aires, Rio de Janeiro, Bogota, Lima, Santiago, New York, Los Angeles, Chicago, and Toronto) and some in Europe (e.g. Istambul, Moscow) have flat fares. On the other hand, some other cities have fare structures based on zones or on distance. For instance, many cities in Europe and Asia (London, Paris, Madrid, Berlin; Shanghai, Beijing, Chongqing) and some in Africa (Cairo, Johannesburg) use different price zones. Likewise, there are some examples of cities such as Washington D.C., Philadelphia, Jakarta, Mumbai, Bangkok or Sydney where fares are proportional to the trip distance. Which city got it right? This is in fact an open space for debate. In cities like London, Beijing Vancouver, there is a strong discussion on whether per-distance fares should be embraced or abandoned, in most cases with arguments that have to do with where do poor people live, that is, a distributional argument, coupled with the fear that flat fares would induce revenue problems.
From the point of view of efficiency, the main argument in favor of implementing an increasing distance-based fare is that marginal costs rise with distance travelled and the principle of marginal cost pricing therefore calls for a positive relation between fares and distance (see, e.g. Cervero, 1981). Other authors have claimed that the relationship between efficient fares and distance is not necessarily positive (see, e.g. Mohring, 1972; Turvey and Mohring, 1975). Their argument hinges on the presence of negative externalities such as boarding delays and crowding: a passenger that boards a full vehicle imposes higher costs due to the externalities and, for example, if load factors are higher closer to the CBD, this would call for an inverse distance-fare relationship. If this latter effect is strong enough,flat fares could be efficient even though marginal operational costs increase with distance. However, absent these externalities, marginal operational costs would dominate, leading to increasing with distances fare.
In fact, Brueckner (2005) showed that, for a monocentric city model where the cost of providing public transport is proportional, with constant k, to the number of passenger-kilometers, the per-
1 We gratefully acknowledge financial support from the Complex Engineering Systems Institute, ISCI (grant CONICYT FB0816), the Center of Sustainable Urban Development CEDEUS (grant CONICYT/FONDAP 15110020) and FONDECYT-Chile, Grant 1161032.
2 Universidad de Chile; lbasso@ing.uchile.cl
3 Pontificia Universidad Católica de Chile; husilva@uc.cl
2
kilometer fare that minimizes total use of resources is exactly k. In this paper, however, we show that if one considers a social welfare function that is the sum of the compensating variation of residents plus the absentee landlord rents, this is no longer the case. The efficient pricing is different from k dollars per-kilometer and is, under mild conditions, flatter spatially, and this does not come from externalities, which are assumed away, or differences in income, as we assume that all residents are equal.