I'm not following @tylercowen's argument here - I think we should expect a minimum wage and occupational licensing to have very different effects under monopsony! (1/10)
Here's how I'm thinking about it: start with your standard perfectly competitive labor market, with a welfare-maximizing equilibrium (2/10). 
Under monopsony, an individual firm will set wages and # employees below the competitive equilibrium, resulting in a welfare loss. (3/10)
Setting a minimum wage above the monopsonistic equilibrium (but below/equal to the competitive equilibrium) results in a welfare improvement - wages and # employees are closer to what they "should" be. (4/10)
Setting a minimum wage *above* equilibrium results in wages that are "too high", and employment that is "too low". (5/10)
How does occupational licensing work? We can represent occupational licensing as a quantity control. (6/10)
If you set quantity *below* the monopsonistic equilibrium, there's a welfare loss - you get even further from the competitive equilibrium.
If you set it *above* the monopsonistic equilibrium (which includes everything above the competitive equilibrium), the quantity restriction is non-binding, and has no effect - we stay at the monopsonistic equilbrium.
Note that I'm setting the quantity restriction to intersect with the labor supply curve at the same place the minimum wage intersected it earlier.
A minimum wage *can* improve welfare under monopsony (assuming you don't set it too high).
Occupational licensing/quantity restrictions can either have no effect, or reduce welfare.
Occupational licensing/quantity restrictions can either have no effect, or reduce welfare.
