The people making between £1,587 and £2,000 are getting £206 or less though. That's not an unsolvable expansion, especially because those people probably do in fact need the help.

> That's not an unsolvable expansion

So your solution is "spend a lot of extra money on social security", which is fine, but it doesn't satisfy the constraints.

You said you didn't want to "unilaterally extend benefits to a whole bunch of people", not that the cost couldn't increase even the tiniest amount.

But even so, smoothing out the curve some might be better overall even if the max amount drops.

Also you could extend the curve so that 'benefits' go negative at the high end. Now your budget is fine...

Your plan both massively increases the number of people on benefits and also increases costs by 20% on your 50% proposal, which in the UK means £15b-ish. Reconciling this with "even the tiniest amount" is impossible.

> Also you could extend the curve so that 'benefits' go negative at the high end

You've just invented tax, congratulations.

> massively increases the number of people on benefits

You have a very different definition of 'massively' than I do.

> You've just invented tax, congratulations.

Positive taxes can balance out negative taxes, ~tada~.

Dylan, just note that the problem as originally posed is not solvable. Your „solution“ is one that violates one of the constraints and then says „but it’s minimal“. Sure. But that was exactly the point of the comment above: by the nature of things, any change you make leads to an undesirable consequence. Either people who need the benefits don’t get them, or the „marginal tax rate“ is very high, or you extend the benefits to more people (which is costly). You’re stuck on the horns of a trilemma, and that’s the solution the UK has chosen, and any „improvement“ you suggest will be worse on at least one of the dimensions.

> Dylan, just note that the problem as originally posed is not solvable.

The original constraint was not a $0 increase. I did not violate the original constraint.

And even if you did take it to be $0, it said you can't "just afford to" increase. Proposing a tax to make up the difference meets that critera.

But even inside a hard "no more spending" constraint, it's not nearly as unsolvable as you make it out to be. It's quite possible that giving less money to people mildly below the old cliff edge, while giving more money to people mildly above it, is a net positive. That doesn't screw over people at the bottom, and it doesn't increase total cost.

Going from a hard cliff to a 90% marginal rate was obviously better, right? And going from 90% marginal rate to 85% was obviously better, right? They decided to stop at 63%. It doesn't mean that going further is a priori wrong.

And on top of all of that, smoothing out the curve to 50% very likely motivates more people in the range to work, reducing the amount of benefits they use.