Public transportation companies may have the ability to raise fares arbitrarily based on market demands, for examples British buses outside London and American freight railroads. Or they may be subject to regulations capping the fare, for example Japanese railroads. Mixed systems exist as well, such as British rail fares. In Britain, the privatized, mostly deregulated approach is so commonly accepted that a Conservative recently called Labour dangerous socialists for proposing municipalizing bus systems, as in such socialist states as the US, Japan, Germany, etc. In reality, in the case of rail specifically (and perhaps buses as well), there’s a theoretical case with some empirical backing for why reasonable fare caps as in Japan can lead to more investment and more capacity, whereas wholly unregulated fares lead to hoarding and capacity cuts to create shortages.
I’m stealing the economic model for this post from Paul Krugman, who used it to explain the California blackouts of 2000-1. The demand curve is inelastic: the demand is 1,000 units at $20/unit, decreasing to 900 units at $1,000/unit, at which point the curve goes flat. The supply curve is a constant $20/unit, but the market is oligopolistic (say, there are very high barriers to entry because building your own power plant is hard), and there are 5 producers, each with 200 units. If the price is regulated at $20/unit, each producer will supply 200 units. If the price is unregulated, then each producer alone gets an incentive to hold back production, since 100*1000 > 200*20, and then production will be curtailed to 900 units.
The model is simplified in a number of ways: real supply curves slope up; the part about demand going flat at 900 units is unrealistic and exists purely to avoid dealing with optimizing where at 800-something units each producer has an incentive to go back to producing more; capacity constraints involve escalating production costs rather than a God-given restriction on the number of suppliers and their capacity. But with all these caveats, it fits markets that have the following characteristics:
- There are steep barriers to entry, for example if large amounts of capital are required to enter (to build a power plant, set up a rail operating company, etc.).
- Demand is highly inelastic.
- Adding new capacity is expensive.
The issue of capacity
In rail, we can start plugging real numbers for both demand elasticity and the cost of new capacity.
In the above model the price elasticity is -0.0244 in the 900-1,000 units range, which is ridiculously inelastic, on purpose so as to highlight how the model works. TCRP Report 95 says the elasticity in a number of large cities studied is about -0.18, and a VTPI review in a mixture of cities and circumstances (peak vs. off-peak, bus vs. rail, etc.) asserts a short-term average of about -0.3. Unregulated fares will lead to supply reductions if the elasticity times the number of producers is more than -1 (or less than 1 if you flip signs); if no producer has <18% of the market, there will be supply restrictions under unregulated fares, just as a monopolist will hold back supply and raise fares if demand is inelastic.
The cost of new capacity of course depends on the line and the characteristics of competition between different railroads. It’s higher in Japan, where separate railroads run their own lines and trains, than in Britain, where different companies franchise to run trains on the same tracks. But even in Britain, getting a franchise requires a commitment to running service for many years. The significance of this is that the long-run public transport ridership elasticity with respect to fare is more elastic (VTPI recommends a range of -0.6 to -0.9), with a few estimates even going below -1.
For the purposes of this section, we do not distinguish capital from operating costs. Thus, the cost of new capacity is not given in units of capital costs, but in units of operating costs: if increasing service by 1% raises operating expenses by 2% counting the extra investment required, then we say the supply elasticity is 2. Note that supply curves slope up so the elasticity is always positive, but the elasticity can be below 1, for example if economies of scale are more important than the need to invest in new capacity.
Set the following variables: u is quantity of service, r is total revenue (thus, fare is r/u), c is total costs. The railroad is assumed profitable, so r > c. We are interested in the change in profit based on quantity of service, i.e.
The important thing to note is that price controls keep dr/du higher in an oligopoly (but not in a competitive environment, like housing – a single landlord can’t meaningfully create a housing shortage). With price controls, we get
whereas without price controls, with elasticity , we get
And likewise, with supply elasticity , we get
Note, moreover, that price controls as construed in Japan let operating companies recover profits, letting them raise prices if they invest in more capacity, so that dr/du is actually higher than r/u.
The real world
I do not know to what extent the lack of fare regulation on many British trains contributes to capacity shortages. However, there is some evidence that the same situation is holding back investment in the United States, on Amtrak. Amtrak is a monopolist facing some fare regulations, for example congressional rules limiting the spread between the lowest and highest fares on a given train, but within its ability to set its own capacity in the medium run, it has relatively free hand, and in fact a strong incentive to maximize fares, in order to subsidize money-losing trains outside the Northeast Corridor.
Amtrak generally runs the trains it has on the Northeast Corridor, without explicitly holding back on capacity. However, this is in an environment with very low utilization rates. There are 20 Acela trainsets, but only 16 run in service at a given time, giving them the moniker “hangar queens.” There is no real interest within Amtrak at raising speed just enough to be able to run consistent service intervals, for example hourly with two trainsets coupled to form a 16-car train south of New York. Nor is there any interest in making small investments to permit such long trainsets to run – most Acela stops from New York to the south have platforms long or almost long enough for such trains, but the rest need to be lengthened, within right-of-way so that the cost is positive but low.
In the future, capacity cliffs may prove serious enough to stymie American passenger rail development. Right now the main obstacle are Amtrak itself and obstructive commuter railroads such as Metro-North, but assuming competent, profit-maximizing investment plans, it is not so expensive to invest in capacity and speed so as to permit around 4 long high-speed trains per hour north of New York (or even New Haven) and 6 south of it. But then the next few trains per hour require further bypasses, for example four-tracking most of the Providence Line. High supply elasticity – let’s say around 2 – is plausible. Then eventually a dedicated pathway to intercity trains through New York becomes necessary, raising supply elasticity even higher. In an environment with uncapped, profit-maximizing fares, a rational Amtrak management may well just keep what it has and jack up prices rather than build more capacity.