By making a city's public transportation system completely free of charge for all users, at all times, one can dispense with fare boxes, card readers, turnstiles, and inspectors. For buses or trams, this would enable much faster boarding, and therefore vehicles would spend less time at stops. Further speedups are possible by providing wider doors, and boarding by rear doors.
Less time spent at stops means faster trip times, especially during rush hours. When each bus or tram can make more round trips in a given time period, fewer vehicles will be needed to transport the same number of people. This represents savings in both capital and operating costs.
How much speedup can be anticipated, and how many fewer vehicles would this entail? A related question would be: in going to a free public transportation system, how many more riders would use the system, and how would this vary based on the amount of trip speedup?