If "Basic Income" is implemented the way I understand it, the income from a part-time minimum wage job would stack on top of it (minus some amount of tax).
The idea isn't that you make more by not working. The idea is that you can live (not very comfortably) without working, and that every bit of work you do marginally improves your income and therefore your comfort level. This makes part-time minimum-wage jobs a reasonable target for people who want slightly more amenities than they can afford at the basic income level.
Based on the comments here, I don't think this proposal is for basic income. Rather, if you already make more than 20K, you don't get anything.
1) Stay unemployed and live off 20k/yr. 2) Work a min wage job and live off 40k/yr.
Many people will choose option 2.
Then who do you think is going to do the part-time minimum-wage jobs?
No one. They can just get more money for doing nothing.
Obviously, employers will start paying a lot more for part-time menial jobs, or go out of business. All of a sudden, Canadians will be asking "Why did everything get so expensive?" and "Why can't teens find jobs these days?"