The problem is that we don't have a free market. So either side can claim the benefits. That's why we need to reduce things to certain undeniable facts.

1. Human action is based on improving our position.
2. People that want to work for a certain amount of pay think that their position will be improved.
3. Employers will only pay as much as the employee can return in productivity.
4. Minimum wage forces low productivity workers to be unemployed.
5. If we didn't have minimum wages then employers would compete for employees and their wage would tends towards their productivity level rather than a race to the bottom, etc, etc.

These are all facts so therefore we can deduce that minimum wage only hurts low productivity workers. You know who tends to favor minimum wage workers? Unions, because it keeps competition out of the market. Instead of hiring a bunch of guys with shovels that can compete with a bulldozer operator without minimum wages, employers don't have that option so they hire bulldozer operators. Who loses? We do through higher prices, the unemployed low productivity workers lose because they don't have a job and employers lose because their costs are artificially raised.

Oh yea, even if this wasn't all true, it's still immoral to prevent adults from interacting however they want, be it gay sex or low wage work.