" Plenty of people at my kids school work 2x FT jobs and everyone talks openly about how the second is only to cover the school fees"
Anecdote. Fail. This also doesn't mean that they'll remove their children and send to state either.
@MrChips
If the IFS doesn't mention elasticity ( its a while since I read it) it is a failing, I think the PED for private schooling is going to be highly inelastic due to the fact that parents consider it a necessity, and this is backed by the data on the numbers rising during the last decade when fees rose at above inflation, and cumulatively over 50% during this time.
The spread across all schools is perhaps a little simple, but the impact of students leaving will be spread across the country, it won't be uniform, but it will be mitigated by the spread.
You've asked about a 5% fall in revenue and the impact on the employment of teachers? I think it will be negligible as the fall in demand will be spread across the entire school, rather than 5% of each year grouping. Even if it was 5% of each class, the smaller class sizes and smaller cohort sizes in private schools would indicate that there would be no redundancies for teaching staff, as classes won't be collapsed. Private secondaries will still need to have broad offers, and again won't be able to collapse classes enough to lead to staff redundancies. What may happen is what happens in state schools is that some schools will have non-experts teaching subjects to the lower school in order to fill timetables and reduce the need for new hires. The Smith's assumption that a 5% fall in demand leads to a 5% reduction in staff shows a glaring lack of understanding of how schools work.
What don't you understand about 2? Basically the Smith assumption is that people will work less hard in their 20s and 30s because they are going to choose state schooling in the future and that this is a loss to the exchequer. Frankly that's a ridiculous assumption
"You write a paper"
As said, you want evidence of how little effect this is going to have, go look at the numbers attending private school in the UK whilst there was an exponential increase in fees over the last decade. Whatever impact this has it will be negligible.