Tyler Cowen and John Cochrane think that the minimum wage traces out a labor demand curve. It does not. There are many ways that a competitive labor market can comply with the minimum wage, and cutting employment is only one of them. E.g., change the composition of compensation, change the work schedule, change the location of employment, etc.
So labor demand could be wage-elastic but a socially costly minimum wage have no effect (or even a positive effect) on employment in a competitive labor market.
For a more detailed analysis, see also The Upside Down Economics of Regulated and Otherwise Rigid Prices.
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