Has a market labor shortage ever occurred? A true labor shortage is when no labor is available for a task at any price. Surely this occurs all of the time if you consider markets that don't exist or could never exist, but has this ever happened otherwise?

Has there ever been a situation where a particular type of labor existed, and then dissapeared, leading to a situation where none of the labor in that sector was available at any price?
That very narrow definition of labour shortage, "when no labor is available for a task at any price", is rarely used, because it's a very rare phenomenon. Market forces kick in, raising prices sharply enough to suppress even relatively inelastic demand, long before the shortage becomes absolute. So the phrase is much more commonly used to mean that there is a temporary constriction in supply of a particular type of labour, usually leading to a large, rapid increase in its remuneration. Hence, when you hear the phrase, that's much more likely to be the intended meaning.

However, in the very narrow definition, the canonical example given is usually that of many trades in Western Europe, after outbreaks of the Black Death in the Fourteenth Century had halved the population.

However, even that example is problematic, as the evidence is that women were largely prevented from taking men's jobs, so the shortage was as much about culture as about physical limits:


  Labour scarcity should have opened up opportunities for females, but the regulations only added to their geographical and occupational immobility,