Robert Murphy reviewed some of the literature regarding the minimum wage on Econlib. I found the article helpful and interesting.
Simple supply and demand economics suggests that any price floor, including the minimum wage, will create a surplus. The quantity demanded will decrease and quantity supplied increase relative to the equilibrium levels.
However, the conventional wisdom on the quantitative magnitudes is that the demand for labor is highly inelastic. That means that while a higher wage reduces the amount of labor firms will hire, it doesn't reduce it much. Inelastic means that the reduction in quantity demanded is less than in proportion to the increase in the wage. "Highly" inelastic means much less than in proportion. Only "perfectly inelastic" demand would mean that there is no decrease in employment.
Murphy argues that even if the demand for labor is highly inelastic, a surplus of labor will be generated due to the increase in the quantity of labor supplied. He emphasizes that this surplus of labor will still make it difficult for some to find work. Say, for example, youths from impoverished backgrounds.
For example, Bobby middle class sits at home playing computer games. While he could get a job, the money isn't worth that sacrifice of leisure. Dave from the inner city, works at a low minimum wage for Pizza Inc. The minimum wage is increased. Bobby now finds it worthwhile to work. Pizza Inc. thinks Bobby is well spoken and clean cut. They never really liked Dave's gold tooth. So, Bobby replaces Dave. Dave needs a job still, and is especially interested in getting one now that the pay is better.
This story fits in well with the evidence that most minimum wage workers live in households with total income well above the minimum wage. However, there is another story that I find interesting as well. Suppose the D- students drop out of school and get minimum wage jobs. The minimum wage rises, and so now, the C- students drop out of school and get minimum wage jobs. What happens to the D- students? Do they stay in school? Or do they hangout on the street corner unemployed? Employment is not impacted, but the most disadvantaged employees get nothing.
Murphy mentions also that many studies suggesting that the demand for unskilled labor is perfectly inelastic or is even positively related to wages, focus on how higher wages reduce turnover. I think that point deserves more emphasis.
As before, Dave works for Pizza Inc. at a low minimum wage. After a year or two, he finds a better job that pays better than the minimum wage. Pizza Inc. replaces him by hiring Dave Jr. Dave Jr. works for a year or two, and then moves on to a job that pays better than the minimum age.
Now, suppose the minimum wage is increased. Pizza Inc. doesn't fire Dave. Rather Dave stays on with Pizza Inc. for five years. Eventually he moves on, but in the meantime, Dave Jr. is unemployed. Of course, Dave Jr. does eventually get hired when Dave goes on to a better job. But Dave III isn't being hired.
Instead of having low skilled workers pass through low wage employment in a way that provides training for more skilled work, all work is paid like the more skilled work and workers capable of doing the more skilled work do less skilled work. For those patronizing unionized grocery stores, we see the middle aged man supporting his family by bagging groceries. In Charleston, South Carolina, for the most part, teenagers bag groceries.
The story about Bobby and Dave suggests that "jobs" are being misallocated. They aren't going to the workers who need them most. But the story of Dave and Dave Jr. implies that labor is being misallocated. It isn't going to the most productive uses, and poor Dave Jr. is left unemployed.