As I continue in my futile quest to catch up with all the blog reading that I have let slip, this post from early last week at Angry Bear caught my eye (I added the link to the Atrios site):

Duncan [Black] also recommends Monopsony in Motion: Imperfect Competition in Labor Markets by Alan Manning:

Much of labor economics is built on the assumption that all the workers will quit immediately. Here, Alan Manning mounts a systematic challenge to the standard model of perfect competition.

Simply because my aim here is to inform as best I can -- at least about the things I think I am qualified to be informative about -- I think it worthwhile to point out that this doesn't really describe the state of modern labor theory.  For a description of that, I'll turn to Rob Shimer, one of the guys at the top of the list of people actively creating modern labor theory:

I begin by describing the simplest version of the Mortensen-Pissarides matching model...

A central feature of this model is that the matched worker and firm are in a bilateral monopoly situation. That is, an employed worker could always leave her job and find another employer; however, because search is time-consuming, workers are impatient, and all jobs are identical, she prefers to work for her current employer. Likewise, a firm could fire an employee and attempt to hire another one, but this will take time and will not yield a better match. There are many wages consistent with the pair agreeing to match, and so the model provides little guidance as to how wages are determined...

Rob's article -- which is quite accessible -- is must reading for anyone with even a passing interest in what labor theory is all about these days.  My point in highlighting this passage is, of course, that the challenge to the perfectly-competitive spot market view is already well under way (even in macroeconomic models).  And as you can see, that theory is not built on the assumption that "workers will quit immediately."  Nor is it built on the assumption that employers will fire immediately.

What, then, does modern labor economics have to say about the minimum wage?  A complicated question that.  Here is a sampling of abstracts, generated by my highly scientific method of typing "minimum wage matching model"  into Google --

From Adrian Masters (in a paper published in a good peer-reviewed journal), the argument that wages may indeed be too low:

This article focuses on wage formation in an equilibrium (two-sided) model of search with match-specific heterogeneity. Despite a large number (a continuum) of employers, search provides sufficient isolation to generate market power. By posting wages, employers, without collusion, capture most of the surplus that accrues to any match. The equilibrium wage is below that which maximizes employment...

But be careful. From Michael Pries and Richard Rogerson:

So what happens when a policy, such as a minimum wage, interferes with that equilibrium wage rate? If the imposed minimum wage is higher than what the equilibrium wage would be, says Rogerson, there will be cases in which firms no longer want to enter the match to test it out. 

The reason, says Rogerson, is that raising the minimum wage raises the minimal level of match quality that a firm will accept to test out the relationship. The firm will still enter into some matches at above-minimum wage, but only those that show a higher potential of being good matches.

Rogerson explains the phenomenon through a car-buying analogy. "Imagine that a law was passed that said you could no longer test-drive a car," Rogerson says. "That deprives you of an important source of information. Although you can get some information from looking at a car, you have a much better idea after test-driving it than before." So what would the outcome of a test-driving prohibition be? "People would be less likely to find the car that best suits their needs, implying a loss in economic welfare."

Policies like the ones Pries and Rogerson analyze -- minimum wages, unemployment insurance, dismissal costs, and taxes -- are not the same as imposing a ban on test-driving automobiles. But their effect is to make test-driving an employee (hiring him to see through experience if he will be a good match) more costly, which means that firms will do it less often.

...The effects of other policies by themselves, including dismissal costs, unemployment insurance, and taxes, are minimal, write Pries and Rogerson. But the effects of those policies combined (as they often are in the real world) are quite large.

In fact, we should probably be thinking about labor market policies as a collection of interventions, rather than taking the piecemeal approach that characterizes how many of our policies are actually implemented.  From Pierre Cahuc and Andre Zylberberg:

We analyze how wage setting institutions and job-security provisions interact on unemployment. The assumption that wages are renegotiated by mutual agreement only is introduced in a matching model with endogenous job destruction à,À la Mortensen and Pissarides (1994) in order to get wage profiles with proper microfoundations... the assumption of renegotiation by mutual agreement allows us to introduce a minimum wage in a coherent way, and to study its interactions with job protection policies. Our computational exercises suggest that redundancy transfers and administrative dismissal restrictions have negligible unemployment effects when wages are flexible or when the minimum wage is low, but a dramatic positive impact on unemployment when there is a high minimum wage.

Just to make things more difficult, observing outcomes that we generally interpret as negative -- such as rising unemployment -- need not mean that a policy is misguided. From Christopher Flinn...

... we analyze the effect of changes in minimum wages on labor market outcomes and welfare. While minimum wage increases invariably lead to employment losses in our model, they may be welfare-improving to labor market participants using any one of a number of welfare criteria... Direct estimates of the welfare impact of the minimum wage increase from $4.25 to $4.75 in 1996 provide limited evidence of a small improvement. Using estimates of the primitive parameters we show that more substantial welfare gains for labor market participants could have been obtained by doubling the minimum wage rate in 1996, though at the cost of a perhaps unacceptably high unemployment rate.

... and from a related paper (published in a very, very highly regarded journal):

Although minimum wage increases may or may not lead to increases in unemployment in our model, they can be welfare-improving to labor market participants on both the supply and demand sides of the labor market... We show that the optimal minimum wage in 1996 depends critically on whether or not contact rates can be considered to be exogenous and we note that the limited variation in minimum wages makes testing this assumption problematic.

So, is the minimum wage a good idea or not.  Our theories, and attempts to quantify them, speak clearly: It depends.

UPDATE: More links on the topic, at Economic Investigations.