## Pricing fines for ticketless travel

In large mass transit systems such as those in Mumbai (or even Chennai), ticket checking turnstiles can significantly slow the flow of human traffic. The sheer number of passengers that use these transit systems daily makes it impossible to check the ticket of each and every traveler. Hence, the Railways, rather than checking the tickets of every passenger, instead relies on random checks. During these random ticket checking efforts, people traveling without a ticket are asked to pay a fine. This, the Railways hope, will be deterrent enough for people to purchase tickets before travel.

The very existence of this market, however, implies that fines for ticket less travel are not being priced properly. The math is fairly simple: if the price of the ticket is $p$ and the probability of your ticket getting checked is $frac {1}{N}$, then the fine for ticketless travel should be strictly greater than $Np$. If not, it works out cheaper for your to pay the fine each time you are caught rather than buying the ticket.
What should the Indian Railways do to drive these “informal insurance companies” out of business? Currently, if the fine is $S$, $S le Np$. From this equation, you can see that the Railways can do one of three things so that this inequality gets reversed – the price of a ticket can be reduced – but that would be equivalent to cutting off the nose to spite the face, for it would have significant adverse impact on the railways’ revenues. Next, N can be reduced, or in other words the frequency of surveillance be increased. This, too, is not easily implementable since the Railways will have to invest in additional resources to check tickets. The last option is to increase $S$, and there is nothing that prevents the railways from doing this!