The current debate about the effect of raising the minimum wage on employment poses an interesting question about how efficient the labour market is. According to the classical view of economics (and the Freshwater school) raising the minimum wage should decrease the number of people working because it will induce employers to shed workers to minimize costs. However, multiple studies of the effects of minimum wages seem to show that small changes do not decrease employment and sometimes even increases it (e.g. see here). If people were completely rational, equally competent and the market were efficient then raising wages should decrease employment. If it turns out that this does not happen then one or more of these assumptions is false. My take is that they are all suspect.
According to basic economics theory, the wages employers offer is set by the marginal cost of adding an additional worker. This means that they will select a wage such that the productivity gains for the last worker they hire is balanced by the cost of that worker. However, this assumes that there is a readily available pool of workers willing to take that wage and that the productivity of a worker is independent of the wage offered. Neither of these assumptions may be true. The argument of the Freshwater school is that during times of high unemployment there should be lots of people willing to take jobs at any wage. However, there is likely to be a distribution for the lowest acceptable wage. In fact, Keynesian theory is predicated on the fact that wages and prices are ‘sticky’ so in an economic downturn, neither fall fast enough for the market to clear. A person is probably unwilling to take a lower paying job because it may affect her prospects of securing a higher paying one in the future when the economy rebounds. Hence, employers attempt to set a wage at some point on the lower tail of the acceptable wage distribution so that the cost of waiting to find someone willing to take that wage plus the cost of hiring is balanced by the expected increase in sales. Increasing the minimum wage could then actually increase employment by forcing employers to hire at a wage point where the wait time is much shorter. The savings from the shortened wait time and possibly lower turnover balances the cost of the higher wage.
Employment may also increase if productivity scales with the lowest acceptable wage. By forcing employers to pay a higher wage, they may actually hire much more productive workers that increases sales enough to hire another worker. In fact, the employers may not even realize that increasing the offered wage would actually increase sales because they never sampled that part of the distribution. They could be stuck in a local minimum where they offer low wages to low productivity workers when they could have offered slightly higher wages to much higher productivity workers. In that scenario, the minimum wage would actually benefit the employers more than the employees.
Both of these situations are plausible indications of a market failure in the labour market. The market may be locally efficient in that the wages are optimal for small changes but not globally efficient in that there could be another more efficient fixed point somewhere far away on the wage curve. Government intervention could actually push the market to a more efficient point and this is not even accounting for the fact that the increased wages would be spent, which could cause a Keynesian multiplier boost to the economy. This is not to suggest that the government knows any better than the employers but just that unintended consequences can go both ways.