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Why are bus fares so high?

When Lisa and I took the bus into Devizes in the evening a couple of weeks ago, we spent around 12 pounds for the return trip, and it would have been much more convenient and cheaper for us to drive. We live less than 6 miles from Devizes, and the bus journeys at the time we went are subsidised. If the fare was lower, perhaps more people would use the bus? Perhaps enough more people to actually increase the amount of money collected from fares. It turns out it's not that simple.

Let's see what happens if you try out fares for a journey from 1 pound to 5.50... 500 people will make the journey if you charge just a pound, but that will reduce to just 100 people using your service if you charge 5 pounds. It turns out that you'll have the highest farebox taking if you charge 3 pounds (a fair fare, perhaps), convey 300 people, and take £900.

Remember that - the fare for the maximum profit is £3.00

That's all very sensible. But now let's add in the concessionary fares scheme, under which older people don't pay at all to travel on the bus - their fare is paid by the local council to the bus company, at a certain percentage of the regular adult fare per journey. Now, very few older people are going to decide to catch the bus (or not catch the bus) based on what the taxpayer has to pay for them - they'll travel anyway.

So in addition to our fare paying passengers, let's say we know we're going to carry 800 OAPs, and we'll get paid 44% of the regular adult fare for each of them. By raising the adult fare, even though it discourages some of them from using the bus, the total income increases. If you continue to charge £3.00 and convey 300 of them and 800 seniors, your income will be £1956 ... but if you increase the fare to £5.00 and convey just 100 normal fare passengers, extra income from the concessionary fares will raise your total income to £2260.

So the concessioanry fare scheme forces up the adult fare from £3.00 to £5.00

I ran a Python course in the City of London yesterday (yes, I know it was Saturday) and it was all to do with financial modelling, so a I wrote a little Python example in the train on the way up - see [here] to illustrate the above - test out what I had been told. Am I surprised at the results? Yes. And also disappointed at the distortions in the system which were, I think, designed to get more people on the bus and yet are driving people away - apart from the elderly - onto other less sustainable modes.

Here are the full results...

fare in pence - number of fares - total fares - total fares with concessions

-bash-4.1$ python fares.py
100.00 500 50000.00 85200.00
150.00 450 67500.00 120300.00
200.00 400 80000.00 150400.00
250.00 350 87500.00 175500.00
300.00 300 90000.00 195600.00
350.00 250 87500.00 210700.00
400.00 200 80000.00 220800.00
450.00 150 67500.00 225900.00
500.00 100 50000.00 226000.00
550.00 50 27500.00 221100.00
-bash-4.1$


I have made lots of simplifications and assumptions there. The ratio of fare paying to concession varies widely; I have quoted for trunk hourly services, but on occasional routes there are very few full fares collected indeed. And I have assumed a linear passenger dropoff which is rather unsophisticated.

Other questions that arise

... "do we need to supply more buses if there are more passengers?" Alas, not on many routes. So changes will simply fill seats that would otherwise be empty

... "can we put up fares to £30.00, carry a single farepaying passenger (who perhaps is an employee we re-imburse) and make even more profit". Great theory, but you wouldn't be aloud to put fares up to more than the cost of a Wiltshire Rover, I don't suppose

... "Can we help our fare paying passengers by charging high for a single, and just 10p more for a return" ... ah, perhsps you're starting to see why return tickets are often just a tiny bit more than singles.

... "Do we need concessionary fares at all". I don't know how many OAPs would be in the bus if it wasn't free to them, but it would certainly be far fewer ... which would result in far less income for the bus company at whatever levels the other fares were set, which would result in far fewer commercial bus services, and either a need for a bigger "normal" subsidy for the network, or a slashing of the network. Of course concessionary fares are in themselves a form of subsidy, so it's down to the accountants as to how they look at things, and the politicians as to whether it's acceptable to cut out a bus service on which less than one seat in 5 is occupied.
(written 2013-08-18, updated 2013-08-24)

 
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