[Helmet]

This is utterly incorrect and not at all what the neoclassical micro/marco economic laws suggest.

For the sake of brevity, you are not making the proper distinction between demand and quantity demanded - a change in the price of labor does not change the DEMAND for labor.

[lend000]

Poor choice of wording -- in the simplest sense, you are correct. However, labor markets are far too complex to be modeled as a single commodity with a supply and demand curve, and contrary to popular belief, both supply and demand can change in the wake of a price control.

This is because there is no single supply and demand curve for labor -- instead, there are dozens of curves for specific labor markets. For instance, the minimum wage does not really affect the SDE labor market in the US, but it can literally wipe out certain markets (farm labor, for example) that typically pay below the new minimum wage, resulting in a complex new supply and demand profile, automation, etc.

[mattmcknight]

It can if there are substitutes for labor.