Why we need a mandatory living wage:

[Dystopia]

Also, they would probably be made redundant in this situation.

Well, there's protection if that happened. If someone buys the business they have to protect those jobs, and there's compensation etc.

Then if all businesses have to pay the higher wages then they're on an even footing, and there's no reason to fire people.

You are wrong. Here in Portugal you can fire someone without reason - But if you do so you are obligated by law to pay a compensation in money. Let's say the contract of the fired worker had 2 years left to go - You have to pay those 2 years - But if the employer owns the company, you cannot in any way force him to not fire someone, and if you do he will just find an excuse.

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Another problem with raising minimum wage that I believe no one has mentioned yet is that it can cause people to be fired - You can force employers to pay a minimum, you can't force them to not fire someone - If they reach the conclusion that the new minimum salary is too much, they'll fire people - That's how it works

That's one of the reasons that the welfare state exists. If you are actively searching for jobs (and can prove that) but haven't got one, in the UK we have something called "job-seeker's allowance".

I dislike the term 'welfare' state, I prefer 'social' state, it sounds better - Welfare sounds like charity to me. That largely depends, here in portugal you have people receiving welfare who refuse to work, it goes both ways and the system always seems corrupted.