Marginal Cost Pricing for Mass Transit

Twitter has a lot of virtues, but discussing policy issues in detail is not one of them. But I was saying earlier that to keep Metro running properly, WMATA-serving jurisdictions will need to pony up more tax money. Tim Carney asked:

@mattyglesias, why would higher taxes, rather than higher fares, be your solution for WMATA?

I replied:

@TPCarney It’s more efficient for prices to approximate marginal costs than average costs.

And he said:

@mattyglesias, (a) not sure I understand what you mean, (b) why should walkers, work@homers, & drivers subsidize metro-riders?

So I promised I would write a real blog post and explain myself. It’s below the fold:

In a perfectly competitive market, the price firms charge for a widget will be equal to the marginal cost of producing an additional widget. That’s because if the market price of widgets was less than the marginal cost of producing widgets, it would make sense for my firm to produce fewer widgets — after all, we’re losing money on each sale. Conversely, if the market price is higher than the marginal cost of producing widgets, I’m going to ramp-up production since each sale is profitable. And this is a good thing. As Greg Mankiw writes on page 152 of his Principles of Economics, in a perfectly competitive market: “the forces of supply and demand allocate resources efficiently. That is, even though each buyer and seller in a market is concerned only about his or her own welfare, they are together led by an invisible hand to an equilibrium that maximizes the total benefits to buyers and sellers.”


In the real world, of course, competition is often not perfect. And certainly there’s no competitive market in DC-area subway systems. Metro is a monopolist. So what about monopolists? We turn again to Mankiw’s Principles, this time page 323 (emphasis in the original):

We begin by considering what the monopoly firm would do if it were run by a benevolent social planner. The social planner cares not only about the profi earned by the firm’s owners but also about the benefit received by the firm’s consumers. The planner tries to maximize total surplus, which equals producer surplus (profit) plus consumer surplus. Keep in mind that total surplus equals the value of the good to consumers minus the costs of making the good incurred by the monopoly producer.

Figure 7 analyzes how a benevolent social planner would choose the monopoly’s level of output. The demand curve reflects the value of the good to consumers, as measured by their willingness to pay for it. The marginal-cost curve reflects the costs of the monopolist. Thus, the socially efficient quantity is found where the demand curve and the marginal-cost curve intersect. Below this quantity, the value of an extra unit to consumers exceeds the cost of providing it, so increasing output would raise total surplus. At the optimal quantity, the value of an extra unit to consumers exactly equals the marginal cost of production.

If the social planner were running the monopoly, the firm could achieve this efficient outcome by charging the price found at the intersection of the demand and marginal-cost curves. Thus, like a competitive firm and unlike a profit-maximizing monopoly, a social planner would charge a price equal to marginal cost. Because this price would give consumers an accurate signal about the cost of producing the good, consumers would buy the efficient quantity.

So Metro is a monopoly. And it is, in fact, run by social planners. If they’re benevolent, they will set the price of a metro ride equal to the marginal cost of WMATA “producing” an extra ride. And think about the marginal cost. Suppose I walk out of the office right now, go around the corner, cross the street, and head down into the McPherson Square Station to hop on the Orange Line. What does that cost WMATA? Well, basically nothing. The train was going to run anyway and running a train with 100 passengers on it costs the same as running a train with 101 passengers on it.

So the optimal price will be very low.

But even though the marginal cost of Metro is very low, the total cost is high. Building a subway system costs a ton of money. Buying rolling stock also costs money. And the minimum level of personnel, electricity, etc. that’s required to keep the system running is fairly high. So if you look at WMATA’s entire ridership, you’ll see that the average cost per rider is pretty high. If you don’t want WMATA to receive subsidies, you need to make the fare equal the average cost, which is going to be much higher than the marginal cost and therefore inefficient.


So if you’re going to build a mass transit system, it ought to be largest financed by non-fare revenue sources. Of course that’s arguably just a case for not building a mass transit system. And obviously, we generally don’t build mass transit systems. Even big-time advocates of heavy rail mass transit such as myself will happily concede that it would be foolish to build them in the majority of America’s towns. Raising sales taxes, after all, introduces inefficiencies of its own so you have to ask yourself if the costs of building the system will exceed the benefits. Note, however, that this is also a question that needs to be asked of roads and highways.

So how should you finance Metro? Well you actually can start with fares. Right now, during rush hour Metro runs as many trains as it’s logistically capable of running on most lines. And the trains are crowded. When faced with that kind of objective overburdening of the system, it makes sense to use high fares to bring demand in line with the supply that can actually be provided. There’s also money to be made from selling advertising and WMATA could license in-station vendors of different kinds. And WMATA owns parking lots at some of the suburban stations that bring in money.

But beyond that, it’s good to use tax revenue. Ideally you’d be talking about tax revenue that bears some relationship to the goals of your mass transit system. So congestion pricing on highways in the area makes a lot of sense, as does taxes on transportation-related pollution like a gasoline tax. Last, you should probably tax land near Metro stations.

In the real world, of course, nothing is ever done in an ideal way so we have (a) higher than optimal fares, (b) higher than optimal property and income taxes, (c) lower-than-optimal congestion charges and gasoline taxes, and (d) fewer mass transit lines than would be optimal.