Arguments for and against the minimum wage

I follow a lot of libertarian blogs, which are of course against increases in the minimum wage (and usually against a minimum wage entirely). And then I also occasionally read articles in the New York Times on the minimum wage, and the comments on those articles. The New York Times and it's readership usually skews very liberal, so they're in favor of increases in the minimum wage. There's lots of  talk about inequality, how increasing the minimum wage will help the poor, etc.

The comments highlight various studies, some of them finding that increases in the minimum wage do NOT increase unemployment, and some finding that they do. Everybody, both the pro and the cons side, has an ax to grind, and provides only the research and data that supports their side.

I was trying to think of effective, non-confrontational ways of convincing people that the pro-minimum wage argument is fatally flawed, and that passing a law making it illegal for people to accept a job paying less than $15 an hour is not a good thing. (Notice how I framed the argument artfully to support my point of view there, i.e. "making it illegal for people to accept a job paying less than $15 an hour" vs. something like "forcing fat cat employers to pay poor people a living wage".)

It's challenging, and frankly I don't see how somebody with any background in economics can not understand that making something more expensive makes it less likely that people will purchase it. Labor is a product very similar to other products.

But here's a thought experiment for the minimum wage supporter, who doesn't believe that increasing the minimum wage increases unemployment. Think back to those times when you were actually an employer. For me, this comes mostly from when we still needed babysitters for the kids. If I could have hired a trustworthy babysitter for about $5/hour, I would definitely hired babysitters far, far more often. But babysitters, especially reliable ones that I liked, usually charged far more than that. So, I didn't have them that often. I didn't purchase the labor that they were selling, because it was too expensive. Instead, I just did without the babysitters unless I really needed them.

The same thing applies when a minimum wage is set, or raised. Employers have options too. They'll invest in more technology instead of employees, or just not expand. One way or another, they'll do without the labor, if it's too expensive for them. Or they'll just go out of business.