Disincentive Pricing

While riding the rails around Portugal, I frequently saw passengers buying tickets directly from the conductor on the train.  It got me thinking about how high the penalty should be for not buying your ticket ahead of time.  That is, how much more should you be charged for a ticket purchased on the train than in the station?

You see, if a rider could evade the conductor at a consistent rate, it might make mathematical (if not ethical) sense to gamble on paying the higher fare every so often.  For example, let’s say you can successfully sneak a free ride once every three attempts.  If the ticket in the station costs \$5, then the price of the on-board ticket should be at least \$7.50 to discourage you from attempting this cheat.

I never found out the price difference in Portugal.  But I do know how it works on the Long Island Rail Road.

Returning from vacation, we were rushing from the airport to the train station.  We didn’t have time to purchase tickets from the machine beforehand as the train was literally pulling into the station as we arrived.  After a long day’s travel, we were happy just to make our connection and get home as quickly as possible.  We figured whatever increase we’d have to pay was worth it.

And it turned out to be nearly a 100% increase.  Instead of the usual \$6.25, the on-board charge was \$12.  I guess that means they think fare-evaders can get away with it a little less than half the time?

We were happy to get home in a timely manner.  And I was happy to have one more open mathematical question resolved!

Categories: Application

patrick honner

Math teacher in Brooklyn, New York

Ben · June 22, 2012 at 1:39 am

I think there may be another purpose to this large markup, namely, I think the MTA is trying to disincentivize purchasing tickets on-board altogether. Handling money slows down the conductors, which at a busy time increases the probability of a successful fare evasion elsewhere on the train (because after all, a ticket that is not collected can be used again, and is therefore almost as much of a loss as a person who doesn’t buy a ticket.) So, although I think that 50% is a high estimate for the probability of being able to ride without a ticket, it may make sense for them to have chosen such a high markup anyway. Another complicating factor in choosing the prices is that passengers on the train without a ticket have no choice about whether to pay the high price once noticed by the conductor. Demand for the higher-priced tickets is therefore fairly “inelastic,” so they can safely set the price a little higher.

Unrelated note: my computer crashed while I was writing this, and when I restarted Chrome all the text was still in the text box. Now that’s a good feature!

MrHonner · June 22, 2012 at 7:15 am

That’s an excellent point about the time wasted collecting fares on board–I hadn’t thought about the “loss” associated with not collecting a ticket. I wonder how often that happens?

In some sense, uncollected tickets might be a potentially bigger problem than fare evasion. Most people would not actively try to evade the fare, but I bet most people would be comfortable reusing an uncollected ticket, thinking “It’s their job to collect it, and if they don’t, I win!”

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