That's only the case when profit margins are so low that the minimum wage extinguishes the marginal benefit of a worker. At the bottom of the wage spectrum tha

That's only the case when profit margins are so low that the minimum wage extinguishes the marginal benefit of a worker. At the bottom of the wage spectrum that's mostly not true. Profits would allow for higher wages, but the negotiating power of the employers is such that they can hold wages down. In these cases minimum wages do make sense and don't result in higher unemployment. And implementing minimum wage laws has shown that it does not affect unemployment in a big manner.