I agree that number of busses will scale linearly with the number of riders, but if we consider a single bus, waste will not scale linearly with the addition of

I agree that number of busses will scale linearly with the number of riders, but if we consider a single bus, waste will not scale linearly with the addition of passengers. The situation I'm trying to capture is one where there's a relatively unpopular route; say we only have one or two busses on the loop. In these cases, more people taking advantage of free busing would only increase the efficiency of the system. Of course, the utilization of these routes must be high enough to justify the cost; obviously if there is only one passenger for the day it would be cheaper overall for him to just drive.