Hong Kong does not have a minimum wage. Last time I checked they have one of the freest economies and are one of the most wealthiest nations.
A little thought experiment: if the United States abandoned all minimum wages, do you think everyone would be working for pennies? Why are there currently so many jobs that pay above the minimum wage?
As for why minimum wages are bad... Well, they are good for some people, and not good for others. Kaju has already shown how it's not good for some people (such as unskilled workers, who happen to be the poorest ironically, since minimum wages are supposed to help the poor). I'll leave to figure out for whom minimum wages are good.
And as an aside, it's also not about wages/prices and how much money you have, it's about purchasing power.