3216 wrote:
you could never have a labor shortage unless there was an artificial ceiling on compensation
No, because market distortions other than compensation ceilings exist. Substantial barriers to entry exist in some fields (both in terms of time and cost). In some fields, the number of workers is restricted (availability of residency spots limits the number of physicians who can work in any given specialty, for example).
3216 wrote:
when people say "shortage" they usually just mean shortage of people willing to do X for the wage employers want to pay
Right, because that's really the most basic definition of what a shortage is. If people are willing to pay X for a good, and quantity demanded at price X is Y, there is a shortage if the quantity supplied is less than Y.
Really, though, "shortage" can be defined in different ways. The simple econ 101 version mentioned above is one definition. But you can also look at the socially optimal employment level in a given field considering all externalities. For an extreme example, the market for home invasion robbers might be efficient per the perfect competition model, but when you factor in externalities, there is obviously a surplus of home invasion robbers.
The distinction between definitions is relevant when discussing things like primary care physicians. Is there a shortage of PCPs in a neighborhood if quantity supplied equals quantity demanded, but there are still patients going untreated (i.e. the market is efficient in a basic supply-demand sense, but some people who need care can't afford it at the market clearing price)? It could actually be economically efficient for a poor neighborhood to not have any doctors (quantity supplied and quantity demanded are both zero for any positive price). But from a social perspective, most people would say that there is a physician shortage in a sufficiently large neighborhood that has no basic medical services.