Re: shortage vs. lack I think both of them mean "not enough" but lack is a more general word, it collocates with most words. Shortage, on the other hand, is more restricted. It's used to indicate an inadequate supply of a commodity. So you could talk about a fuel shortage (supplied by the oil companies, used by everyone) or a shortage of qualified teachers (supplied by the universities, used by schools) but not about *a shortage of sleep because sleep isn't "supplied" or "used" by anyone. It's not a commodity.
If you look at words which collocate with lack but not with shortage, I think they generally fit this rule - ie they are not commodities : a lack of privacy / interest / a sense of humour /self-confidence.etc
So - the rule would be : if it's a commodity, both lack and shortage could be used. If it's not a commodity, only lack.
Does that fit the examples you were thinking of? |