>Despite minimum wage, there is extensive child labor in agriculture in the US, because there is a gap in child labor law. Which suggest that minimum wage didn't make child labor obsolete, banning child labor did.

That is of course not true, because as you yourself point out, there is still child labor going on. Banning something has nothing to do with it existing, just look at drugs.

Minimum wage law made child labor mostly unprofitable, is what I should have said.

> That is of course not true, because as you yourself point out, there is still child labor going on.

In specifically the area where it wasn't banned.

> Banning something has nothing to do with it existing

Odd, then, that child labor has been vastly reduced in exactly the domains where it is prohibited, and not where it isn’t.

> Minimum wage law made child labor mostly unprofitable, is what I should have said.

Were that the case, and not prohibition being the limiting factor, you'd expect child labor to exist where minimum wage is inapplicable, but not where it is, even independent of whether it is allowed.

But in agriculture, where it is prevalent and not prohibited, minimum wage applies and hasn't limited it. Yet it's not found in most of the other places it existed before being banned, and where it is, in fact, prohibited. It's prohibition, not minimum wage, that did it in.

Although there is a technical sense where “minimum wage law” is the deciding factor, because it was actually the same law (though the applicability of the minimum wage and the child labor prohibition pieces differ) that implemented federal minimum wage and the child labor prohibitions and restrictions, the Fair Labor Standards Act of 1938.

> Were that the case, and not prohibition being the limiting factor, you'd expect child labor to exist where minimum wage is inapplicable, but not where it is, even independent of whether it is allowed.

Banning and prohibition are just ways of increasing the cost of hiring children: they now have to pay the wage + fine. And it only works if that is too expensive compared with the alternatives.