## 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!