First rule of Working Tax Credits club...

… don't talk about Working Tax Credits unless you know about Working Tax Credits.

Ben Jamin' politely pointed out here that with a flat tax on incomes of 20%; a flat tax on housing you own of 3.5%; and a flat Citizen's Income at current Income Support rates, a low earner on £13,500 a year paying £90 a week in rent would be about £4,460 a year better off compared to the current tax/welfare system. You can check his workings here.

Numpty Ingliz replied: "No, that is wrong, as there is £52.68 per week in working tax credits you would lose."

Well, firstly, the YPP tax reform proposals which Ben is basing all this on takes Working Tax Credits into account. We're not completely stupid.
-------------------------------------------
Secondly, no single earner receives anywhere near £52.68 a week Working Tax Credits, it is mathematically impossible.

From here, 2014-15 rates:

Basic Element (16 hours or more) - £1,940
30 hour element - £800

That adds up to £2,740, which is indeed £52.68 a week. What our numpty overlooks is this bit further down…

Income threshold - £6,420
Withdrawal rate - 41%.

So if you earn a steady £13,500 a year, you lose the lower of

a) £2,740 (the most you can theoretically get), and
b) £13,500 minus £6,420 = £7,080 x 41% = £2,903.

In other words, you get no Working Tax Credits whatsoever. Nothing, nix, nada.
-------------------------------------------
On £13,500, you are also paying £1,365 in PAYE (income tax and Employees' NIC); and suffering/paying Employer's NIC (£765) and VAT of approx. 10% of your earnings (£1,350), comes out at £3,480. Let's assume that Council Tax is economically borne by the landlord, or that makes our system even more favourable.

Under the flat tax system, a single earner receives a flat CI of £72.40 x 52 = £3,765 and pays £2,700 in flat 20% income tax, net tax paid negative £1,065.

All of which means that our low earner tenant in this example is £4,400 to £4,500 a year better off (depends slightly on how much Employer's NIC is borne by employees). Which covers his £90 a week rent, so there's no need for Housing Benefit, which in this case would only be a few quid, let's not bicker over small change.

Suffice to say, our low earner is not only a lot better off anyway but a) he doesn't have to fill in endless stupid forms or worry about benefits being clawed back etc and b) his marginal tax/withdrawal rate is 20% and not around 50%.