I was recently discussing the topic of minimum wages with a friend who favors them. (He is a prominent economist, whose name you would surely recognize, but conversations with friends are off the record). As justification for his view, he pointed me to this paper by Lee and Saez, called "Optimal minimum wage policy in competitive labor market."
What was notable to me about this paper is the incredibly strong assumptions they need to make their case. In particular,
Assumption 1. Efficient rationing: Workers who involuntarily lose their low-skilled jobs due to the minimum wage are those with the least surplus from working in the low-skilled sector.
Later they point out:
Finally, the desirability of the minimum wage hinges again crucially on the “efficient rationing” assumption. Under “uniform rationing”, where unemployment strikes independently of surplus, the minimum wage cannot improve upon the optimal tax allocation, a point formally proven in Lee and Saez (2008). Indeed, with efficient rationing, a minimum wage effectively reveals the marginal workers to the government. Since costs of work are unobservable, this is valuable because it allows the government to sort workers into a more socially (albeit not privately) efficient set of occupations, making the minimum wage desirable. In contrast, with uniform rationing, as unemployment strikes randomly, a minimum wage does not reveal anything about costs of work. As a result, it only creates (privately) inefficient sorting across occupations without revealing anything of value to the government. It is not surprising that minimum wages would not be desirable in this context.
Rather than providing a justification for minimum wages, the paper seems to do just the opposite. It shows that you need implausibly strong assumptions, such as efficient rationing, to make the case. I cannot see any compelling reason to believe that in the presence of excess supply of workers, the market will somehow manage to efficiently ration the scarce jobs.