poor people must have money taken away from them
Wrong. They're not having money taken from them. They're working in a job which creates value... but less than NMW amount of value
Who sets that value? the wealthy.
No one has so far answered why a 20yo should get substantially less than a 21yo doing exactly the same role and being equally productive.
Employers must be allowed to offer the salary which matches the productivity generated. When the government sets a minimum, then you end up with distortions: the person's work doesn't create NMW worth of value, so the company would lose money if they employ them at NMW... so they don't. But the employment would have created a smaller amount of value. From that value, the employee would have got a salary (instead of being subsidised by other people from the value their work creates) the company would have made a profit, and the government would have got their cut of tax. If you distort the market with too high NMW and the person doesn't work - so the value isn't created - everyone loses
Why do you think we needed a NMW in the first place? opposed tooth n nail by the right, for exactly the same reasons as you're giving, incidentally, anything that favours the least well off, is always opposed by the 'right.... see also NHS, Open Uni, school leaving age increased, worker rights, HS at Work act, even rent reforms
Employers, if they could, would offer very little at all, whilst expecting their employees to claim benefits other tax payers fund.
One only has to look at the supermarkets to see this, people worked to the bone, who get paid the NMW or just above, whilst the employer takes huge profit (forget the margin, its still billions & a monopoly, all pretty much charge exactly the same across a basket of goods) for themselves, wages far too low to live on, even with FT and extra hours.