The current government is proposing large increases in fares to reduce how much the tax payer funds the railways, if there were bigger increases in the child leisure travel then it could slightly reduce how much the increase is for adult essential travel.
It is very dependent on how many children no longer decide to travel by train. The revenue from child fares is
n * x/2 where
n is the number of children and
x the full adult fare.
Let's now say that
a is the percentage of
n that no longer travel by train (expressed as a decimal). The revenue is now
n(1-a)*x.
If we set the two equations above equal we see that a = 0.5 = 50% which means, as you say, a loss of 50% will cause revenue to break even. I am acting under the assumption that fare evasion will not change.
Yet if 75% were to leave the railway then the revenue will be 0.25nx which equates to have the revenue currently obtained (0.5nx).
Should this happen and the railway lose revenue then it will either be relying more on the taxpayer or the full fare will have to rise possibly creating a vicious cycle for those who must travel by train.
As I said before I suggested a few different suggestions for discussion. In response to the suggestion of getting rid of child fares people quite a few people responded saying that will significantly reduce the number of children travelling so I thought it was worth pointing out how an up to 50% reduction in child travel would be advantageous if children paid adult fares.
That is true, the maths bears it out. I would like to see some kind of independent survey done before it is rolled out nationwide though simply to check how many would no longer travel by train (taking into account the bias such a question would no doubt incur)
Currently an 18 year old studying full time for A Levels with no job pays full fare while a 15 year old with a weekend job pays half fare.
Many would argue that's not fair. Also currently an adult can pay full fare to stand while a child can pay half fare to sit.
Which is why I'd like to see any child fares extended to those in full time further education (in much the same way students of any age can get the 16-25 railcard).
A child being able to sit rather than an adult is unfair but to state that the level you pay determines whether or not you get a seat would set a dangerous precedent IMO. Children today, railcard holders (including senior railcards perhaps?) tomorrow, advance ticket holders the day after and then those travelling off-peak.
A left wing view for fairness could be for child fares to be means tested. A child with rich parents pay full fare, while a child with unemployed parents gets free or significantly reduced fares. While a more right ring view of that would say that's not fair as the parents who have done well in their careers are being penalised.
Means testing would be nice yet it's not cheap to do. From working on means tested benefits it's a lot more complicated to process means-tested than non means-tested (OT - universal credit is going to be an administrative nightmare!). Perhaps if a child is eligible for free school meals then they are also eligible for free/reduced fares but done a term at a time in case their circumstances change, especially if the LEA issues the pass.
I am unashamedly left-wing although I don't like using the link between parental income and the child's benefit since there is no guarantee the child is getting anything off their parents. EMA was a good example - I know a few people who didn't get it but (they stated) they didn't get £30/week off their parents.