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yard would be utilized in the first day, 40 percent in the second, 60 percent on the third, etc. Yet, a railroad that connected with more mines might receive 20 cars a day from five mines and send a trainload every day. It would still only need the 100-car yard, but would have five times as many cars to share in the coverage of the investment and operating costs of the yard.

Similarly, a full siding is necessary if one train a day will meet one other train coming in the opposite direction--but the same size siding would be necessary if four trains were meeting four trains at the same place. Crossing protection must be built and maintained in a densely populated area whether the railroad sends one train a day or three trains a day over the track at the crossing. The same is true for switches, fueling stations, and all other fixed plant investment. Once the plant is installed, a railroad can utilize it far more heavily with very little additional fixed investment cost. Also, a train of 40 cars, needs a crew of the same size as one of 60 cars. The ability to marshall cars of different shippers into a larger train also cuts other operating expenses. The engine power necessary for a longer and heavier train is not commensurate with the additional cars which have been added.

The statistical or econometric approach to analyzing railroad economies of scale has also had a long history. This history is rife with academic controversy and with steadily improving research methods. For example, some econometric studies found no evidence of rail economies of scale because they were founded on arbitrary allocations of costs between freight and passenger services. Other investigators failed to distinguish economies of scale from possible economies stemming from the geographic extent of a railroad's operations. Such studies incorrectly conclude that increasing returns to scale are absent from a finding that railroads covering more territory do not necessarily enjoy lower costs per ton-mile of freight.

Recent econometric studies in the United States have avoided these pitfalls and warrant several important conclusions. First, most of the rail system operates subject to increasing returns to scale and has elements of natural monopoly, whether considered in a single-product or a multiproduct setting. Second, as Fig. A. I indicates, unit costs decline sharply with density, but at some point between 25 and 40 million annual gross ton-miles per route-mile, depending on the commodity mix, the cost curve flattens out and a large part of the traffic in the system flows over this flat part. This represents the level of minimum efficient density, and one can think of this as the capacity of a single track between two points, the fundamental indivisibility in the rail cost structure. Higher traffic density can be served at approximately constant cost by adding segments of parallel track and signalling devices. Third, for very short-haul, terminal-oriented railroads, the long-run cost curve seems to flatten out much sooner (at under 2 million net ton-miles per route-mile). Fourth, there are considerable economies of longer hauls.

Overall, these studies establish the presence of substantial economies of scale in the freight operations of railroads. They indicate that pricing at short- and long-run marginal costs would recover