Your example from Denmark at 17% is on a $5 price point item.The idea that minimum wage is not effective in a market driven economy isn't true. Prices may go up, but the question is really are the higher prices worth having living wages. A few examples:
The federal minimum wage has been around since 1938, and the US economy remained the strongest in the world from then until now, including the post-WW2 era of incredible middle-class growth, so it can't be that harmful to the economy.
Research shows $15 California minimum wage has big impact on pay, none on jobs.
Fast-food workers paid $20/hour in Denmark as compared to $8.60 in US (133% increase), but McDonald's Big Mac price only $5.60 vs $4.80 (only 17% increase). (Also note that Denmark has no minimum wage law but instead very strong unions that bargain for these wages, so minimum wage laws aren't the only way.)
Imagine if every item you purchased in a months time was raised 17%.
And I didn't say a minimum wage increase has a negative effect on the economy. The US is full of consumers at every economic level.
If prices go up, you STILL won't have "livable" wages.
Productive, skilled workers can do more for themselves than a government mandate can do for them.