shortage vs. lack
 

How would you explain the difference between a shortage of something of a lack of something? I can't seem to find a clear pattern.

a lack - is not having the thing/part to complete something

a shortage - is not having enough of something

in both cases of not enough, either can be used but only a "lack of" can be used when you don't have any at all.

but I would say "a lack of sleep" not "a shortage of sleep"
"The student performed badly on the test due to a lack of sleep."

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?

Re: shortage vs. lack
 

I fully agree with "lack of" sleep, privacy, interest and self-confidence.