1. Ian Savage (1997). Scale economies in United States rail transit systems. Transportation Research A 31(6):459-473.
[Published Version]  [Journal Website]

The research uses Federal Transit Administration "Section 15" data to investigate the operating costs of 13 heavy-rail and 9 light-rail urban mass transit systems for the period 1985-91. A transcendental logarithmic technology is used to investigate various types of economies of scale. The principal findings are:

• Large economies of density. Adding additional trains, and passengers, to an existing network leads to a less than proportionate increase in short-run variable costs for nearly all systems. Estimates of economies of density incorporate the effect of changes in output on average load factors. The exceptions are three larger systems that have track that is heavily utilized and offer a relatively flat level of service across the day and serve markets where passengers undertake short trips. When the cost of way and structure maintenance and capital costs of way, structure and rolling stock are incorporated, economies of density become more pronounced for all systems.

• Constant returns to system size in short-run variable costs. A similar pattern of system size economies persists when the cost of way and structure maintenance and capital costs of way, structure and rolling stock are incorporated. The sole exceptions are newer heavy-rail systems catering to longer-distance commuter traffic. These systems have a high ratio of peak to off-peak service. Diseconomies of system size are found for these systems.

• In making these calculations allowance was made for the effects of different levels of peaking of service and average journey length. Correction was also made for the use of light-rail technology. Newer systems which invested in automation, such as automatic train control and automatic ticketing systems have reduced their variable cost by 27% compared with comparable traditional systems.

There are four major public policy implications:

• Calculated economies of density can be used to estimate marginal cost. When comparison is made with fares, most of the least expensive systems are able to price at, or in excess of, marginal costs. However, more expensive systems are unable to pass these costs along in prices.

• There has been considerable controversy about the accuracy of cost and revenue estimates used when seeking funding for extensions to existing systems and the building of entirely new systems. The equations estimated in this paper provide a possible method for the federal government to evaluate operating cost estimates.

• Currently some smaller communities are proposing limited light-rail schemes. These very small schemes should be able to operate with similar average costs to those systems found in larger cities.

• The constant economies of system size for large systems suggests that there would not be cost disadvantages if the larger systems -- Boston, Washington, D.C., San Francisco, Chicago, and New York -- were divided into smaller operating units to permit privatization.

2. Ian Savage (1988/9). The analysis of bus costs and revenues by time period. Transport Reviews 8(4):283-299 and 9(1):1-17.
Part I: [Journal Website]  [Manuscript Version]
Part II: [Journal Website]  [Manuscript Version]

Bus operators serve many markets characterized both spatially and temporally. An objective of these companies is to tailor fares and service provision to these myriad markets. The past 20 years have seen an unprecedented desire by bus companies to analyze costs and revenues at the micro level to permit this tailoring. This was initially on a route-by-route basis and later on a time-of-day/day-of-week--or time period--basis. The methodology was developed in three stages: (1) Apportioning methods for allocating costs and revenues to route level were developed in the UK and the US in the period 1968 to 1974; (2) Further developments post 1974 were chiefly in the US and Australia and concentrated on prediction methods for incremental costs resulting from expanding/contracting service at particular times of day; and (3) There was a resurgence of interest in the UK post 1979 with analysis of both allocated and incremental costs and revenues. This assumed great practical interest with deregulation of the industry in 1986.

The first part of this two-part paper traces the development of the literature over the period, and indicates that costing methodologies have been extensively analyzed but revenue methodologies are still in their infancy. On the costing side, two methodologies, one from the United Kingdom and one from Australia, are available. The second-part of the paper describes these two techniques and in comparing them identifies a trade-off being predictive accuracy and simplicity of application. The paper concludes that the development of micro-level analytical techniques has proved to be both practical and desirable. Areas for potential future research are also identified.