In 1946, Stigler did not believe minimum wages could be any good.
Wages represent marginal profit, so imposing a minimum wages equals increasing marginal productivity, or discharging unproductive employees.
It should be noted that a discharged employee can always go to a sector with a lower minimum wage, until there is only the national minimum wage or migration left, in which case unemployment because likelier.
But my thoughts are the following: is it not a much simpler explanation to consider the market as imperfect. In a supply and demand framework, one would be to the left of the equilibrium. Employers might hire more employees in order to optimize profit, but for some reason they don't do it. They all prefer to higher a few workers less, as if it was a collusive decision to keep a pool of workers unemployed, reasoning unemployment will increase their value (schooling, reduce aspirations, increase motivation, etc.). Certainly, as for many companies, the pool of possible employees is actually well known. They are aware of the fact that the emptier the pool, the higher the likelihood that the pre-estimated productivity will be wrong. Therefor, they rather select one worker when there are 20 more available in a town, then when it is the last one.
As a result, increasing the minimum wage literally changes nothing. Well, it does increase the labour supply and puts some limit on labour demand, but it may well be the case that from the point out of equilibrium one was in, the minimum wage is payable and not even touching marginal productivity, which moves with the labour demand curve. Actually, this should be the case. We know what there is to prove: minimum wages do not alter employment. The only question remaining is why the equilibrium is not regarded as an optimal position.
Stigler refers to this in the paragraph on Employer wage determination. Arguably, multi-employer collective agreements speak in favour of this option. However, he believes this wage cannot be above marginal productivity. Again, this might be wrong: there can be wage compression within firms or industries, by paying high-wage earners below marginal productivity, which is quite possible for the very same reasons as stated above. Don't these employees start their own business instead to obtain a higher income? It seems that risk aversion acts as a barrier to such movements.
