rationing under price controls is never perfect. Under rent control, for example, apartments do not automatically go to those who value the apartments the most. The misallocation due to imperfect rationing makes the actual welfare cost of price controls much higher than the standard deadweight loss triangle.
Suppose that the minimum wage is $10. You have one worker who would be happy to work for $8 and another worker who would be happy to work for $10. If the second worker is the one who happens to get the job, you lose $2 of surplus due to what Greg is calling “imperfect rationing.”
I remember being taught the equivalence between tariffs and quotas. But it seems to me that such an equivalence fails by the same reasoning. The quota may be imperfectly rationed, unless rights to sell within the quota are tradable.
The supposed equivalence between tariffs and quotas is a somewhat unfamiliar topic for me. I doubt you can find anyone claiming the equivalence is perfect. I think this post needs more fleshing out, more substance, to be interesting. Perhaps the intent was for the comments to yield more substance.
Here is a stab:
http://www.franke.nau.edu/eastwood-j/eco486/hwk-text_exercises/hwch07.htm