Economist Ed Glaeser runs the numbers for a hypothetical high-speed rail line from Houston to Dallas and concludes they don't add up. I think it's a closer call.

Here's the crux of his estimate:

I estimate benefits by comparing rail to air. A train going from Dallas to Houston at 150 miles an hour would take 96 minutes. Southwest Airlines takes an hour for the same route, but the need to arrive early could add on an extra hour. I’ll add on an extra 36 minutes for the driving time to the airports, which means that the train saves an hour. The per-passenger benefit from the high-speed rail line is the saved cost of the Southwest ticket ($80) plus an hour’s worth of time (let’s say $40, which seems generous), plus any added benefits from the comfort of the train (let’s say $20 more). All told, benefits per trip are $140. Since the variable costs are $72 for the trip (30 cents a mile times 240 miles), benefits minus variable costs come to $68 a trip. If these numbers were right (and I think that they are very kind to rail), then the system should be able to run a healthy operating surplus.

. . .

Now it’s just down to multiplying: 1.5 million trips times $68 a trip means $102 million for benefits minus operating costs. Annual capital costs came in $648 million, more than six times that amount. If you think that the right number is three million trips, then the benefits rise to $200 million, and the ratio between the per rider net benefits and costs drops to one-to-three. This is the cruel arithmetic faced by people, like myself, who would love to be pro-rail.

A couple of problems here. First, Glaeser underestimates the value of time for business travelers, who surely would be HSR's predominant users. I don't know where he got his estimate of $40 per hour, but it is belied by *t**he air fares travelers **already pay. *The walk-up fare for a one-way trip from Houston to Dallas (the fare business travelers pay) is $140. From airport parking lot to airport parking lot, the flight from Houston to Dallas takes about two hours. Add an average of one hour for travel to and from the airport, for a total travel time of three hours. By contrast, it is a four-hour drive from Houston to Dallas. The plane beats the car by one hour, which means the business traveler values his time at least at $140/hour. Even if we are generous and assume the plane is one and one-half hours faster, business travelers are willing to pay almost $100 to save one hour.

The saving per *business *traveler is thus $100 for the hour saved plus $140 for the Southwest ticket saved less variable costs of $72, or $168.

But Glaeser also underestimates the extra productivity a train allows *in transit. *A plane is more attractive than a car for a business traveler because it allows him to be more productive during the trip. Ditto with rail over plane. I am lucky to squeeze out a good half-hours' work on a flight from Austin to Dallas (comparable to the Houston-to-Dallas route). On a train, I'd get in at least one more hour of work. Glaeser doesn't count the value of that extra productivity; trains offer much more than mere comfort. That extra hour would be worth a lot, judging by the amount travelers are willing to save in travel time.

The average per-passenger benefit for HSR's principal clientele will thus be well over $168 per trip, and probably well over $200. That's much higher than his estimate of $68 per trip.

Glaeser's second mistake is assuming that demand for travel between Houston and Dallas is fixed. It is not, of course. Quicker trips will induce more trips. More comfortable, productive trips will induce more trips. And cheaper trips will induce more trips. The demand for travel between Houston and Dallas is not perfectly inelastic, in other words. (Southwest could probably tell us the elasticity to within three significant digits but I doubt it will volunteer its expertise for this analysis.)

I'm no expert on rail, but I imagine rail capacity scales up more cheaply than plane capacity. In other words, to increase a train's capacity by 150 passengers, you only need to add another car to the end of the train. To increase a plane's capacity by 150 passengers, you have to add . . . another plane. A rail line's ability to add capacity at low marginal cost -- much lower than an airline's -- should allow it to cover operating costs at lower ticket prices. Assuming travelers respond to prices (and they do), this means more travelers. Glaser's prediction of 1.5 million users per year is likely low. Three million may indeed be more realistic.

Three million riders per year times a $200 per-passenger benefit is $600 million/year, which is awfully close to Glaeser's estimate of $648 million total cost.

My $200 net benefit per trip could be high, I concede, but all of these numbers are just educated guesses. The average one-way fare passengers actually pay is less than $140 -- although not necessarily much less, since even Southwest sometimes charges more expensive fares. Yes, most leisure passengers value their time at less than $100/hour, but many business passengers value their time at much more than $100 per hour. (Calculate total savings for a $300-per-hour traveler.)

I'm not proposing that the state of Texas proceed with a $12 billion capital investment based on my back-of-the-envelope calculation. I do think the question is closer than the back of Glaeser's envelope suggests.

**Addendum: **When using the price of air fare to calculate the value of time, I ignored the cost of driving from Houston to Dallas, which is perhaps $50. But then I also ignored the cost of the "last mile" once the traveler gets to the airport, which is the cost of a taxi or rental car. That last leg from Hobby to downtown or Love to downtown costs around $25 by taxi, so I should have discounted my base estimate by $25.

**Update: **Ryan Avent has much more at DC Streetsblog.