The economics of the British Rail effort to close the Settle-Carlisle make for amusing reading. Some preliminaries: a railroad presents all sorts of problems of allocating common and joint costs. The starting point for such a problem is the existence of a sharable input. The track that supports a fixed-capacity Electroliner at 4.50 can support a 'Liner Follower of as many standard coaches as required at 5.00, a one car Kenosha Local at 5.10, and the ferry truck service at 5.30. The track can be used to provide different types of outputs at different times of the day, which makes it a sharable input, and we would say that there are economies of scope (this explanation has it part right; I resolved to finish some research papers this summer, thus no amendments headed to Wikipedia from me) in providing railway transportation if the cost C of providing the passenger and freight services together is lower than the cost of providing the same level of each output (non-economists just have to learn to think in ceteris paribus terms) with two kinds of railroads. Formally,
C(passenger, freight)(The hostility of Union Pacific to Amtrak suggests the folks in UP's headquarters believe the inequality points the other way.) Because the volume of passenger service and the volume of freight service are under the control of the railroad, one can speak of the opportunity cost of displacing a freight train by running a passenger train (that's the way Union Pacific thinks) or the converse (one of our 115 car unit coal trains takes paths away from five or six express passenger trains is how the Europeans would see it) which makes the cost of the track a common cost. There is a complexity, however. If the passengers all want to travel to work between 6 am and 9 am and return between 4 pm and 7 pm, there are some large windows of time during which there is no point in running any passenger trains; you might looking at something like the trackage into Grand Central Terminal or the Gloucester Branch of the old Boston and Maine, where there's scant reason to run a freight train. The track transports passengers for six hours of the day and sailboat fuel the other eighteen. In this instance, the input takes on properties of a joint cost in which the outputs are produced in fixed proportions (think of a joint of meat: a steer produces two sides of beef and a hide that can be used as leather. One cannot produce more beef without producing more leather. The economics of bulls or cows, which must be combined although not necessarily in fixed proportions to produce steers, is more complicated. In transportation, once a coach has been built with five third-class and three first-class compartments, or a jet with a division of seats between commuter coach and sardine can, something similar arises.) Off-peak pricing of commuter trains, highways (same caveat on this explanation), standby air fares, and roller coasters works because successful entrepreneurs recognize that bygones are forever bygones and any revenue that exceeds the avoidable cost of moving the seat makes the enterprise more profitable. Accountants struggle with all sorts of methods of allocating common and joint costs (any machine that is idle for part of the day, say, because hiring people to work the night shift is too expensive, qualifies) and those methods lead to a number of follies, including the old joke about losing a nickel on each widget but making it up on volume (treat your standard volume as 75% of the estimated daily capability of the machinery, then sell 110% of that estimate) or the depressingly familiar criticism of rapid transit ("Amtrak loses $6 on each passenger. If more people ride, the taxpayers lose more.")
<C(passenger, 0) + C(0, freight).
That brings us to two British Rail fiddles in their attempt to close the Settle-Carlisle. In 1982, the authors suggest (p. 62) that British Rail charged to the Settle and Carlisle the entire cost of two additional locomotives and 10 coaches account a re-routing of a Nottingham-Glasgow service over the Settle and Carlisle (absent the Settle-Carlisle, the train would run a different way; absent a train on the Settle and Carlisle, that stock would still have to be paid for.) At the end of 1987 (p. 155) British Rail did not credit the Settle and Carlisle with any division of the revenue from detouring trains or from passengers boarding or detraining beyond the line (the aforementioned Nottingham-Glasgow riders as well as Nottingham-Carlisle or Leeds-Glasgow riders.) Alas, there is no generally accepted economic principle for obtaining the opportunity cost of a sharable input; the best one can do is ask two questions. First, could an equally capable entrant operate a service offering only one of the multiple products more cheaply? That's a test for cross-subsidy; in light of the legal constraints on building railroads, not to mention the irreversibilities involved therein, it's not one easy to conduct, although if you ever hear management of a multiple-product business objecting to an entrant's cream-skimming, you're probably hearing a confession that there is some cross-subsidization going on. Second, would the entire enterprise be more profitable, or lose less money, absent one of the products, with the incremental cost of each product properly identified. That's a full employment provision for industrial economists, notwithstanding the easy formula involved.
Note that the costs of those diesels and coaches providing Nottingham-Glasgow must remain in both terms.
Incremental Cost =
C(existing network) - C(network without Settle and Carlisle line).
Incremental Revenue = Current Revenue - Revenue of smaller network.Here one must work out whether the Nottingham-Carlisles, not to mention Nottingham-Glasgows, would ride the longer way 'round in the same volumes.
There's also an interesting comment at p. 186 on the use of buses as substitutes for trains.
The trains would be replaced by National Express coaches, but painted in BR colours. The coach services would call only at the places served by the train and would run to generally similar times. It would be like having a train, but one which used roads as a cheaper alternative to tracks. Again, there seems to have been little thought given to exploiting the flexibility of buses and coaches.In British parlance, a bus offers urban transportation service, and a coach interurban service. In either instance, it is a rubber-tired vehicle with the ability to go, subject to weight and clearance restrictions, anywhere on the road network, something that a train cannot do. The train's advantage is in moving large volumes of people between locations that originate or receive large volumes of people, such as Naperville to downtown Chicago. To the extent that people migrate off the rail network, motor coaches (how's that for a compromise?) provide the transit authority with an ability to adapt to new traffic patterns until the emergent pattern of location offers sufficient volume for a fixed-guideway (generally rail) service.