What is the purpose of having a minimum wage?
It's so business owners can't enslave you and give you money you can't live off of go read about the Meat Packers in Chicago during the early 20th century. The Jungle by Upton Sinclair is a historical fiction about it because he observed what happened in factories...
I know what the stated reason for it is. It has been posted here several times already. But what it has ended up skin is pricing low skill workers out of the market. In the past people with no skill could acquire a skill through an apprenticeship (low wage job), but now the only way to get a skill is through school (negative wage job). Progress!!
Skin -> doing
So companies aren't exploiting workers to make them essentially slaves which has been done historically.
Giving unions more money
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Lots of union jobs pay some multiple of the minimum wage.
Geoag is on the right track. Many union jobs pay is based on the minimum wage. If the min wage goes up, so does their wage.
So workers aren't completely exploited
It's to give the politicians a tool to get elected by the ignorance of economics in the masses.
A way of making some people feel virtuous without actually accomplishing anything.