Reason for the strange meaning of "for any length of time"?
Consider the sentence [emphasis mine]:
Foreign producers cannot sell all commodities at lower prices than domestic producers for any length of time because the depreciation (or pressures for depreciation) of the importing country’s currency ensures that trade will flow in both directions.
Intuitively, the sentence should mean that foreign producers can never sell commodities at lower prices than domestic producers, because even one day is "a length of time," and the sentence asserts that it cannot happen for any length of time. Of course, that's not what it's actually saying. A more literal phrasing would be "for a very long time" or "for any great length of time."
This interpretation of "any quantity of X" does not carry over to other values of X. For instance,
I would not sell that to you for any amount of money.
means exactly what it looks like it means: that any quantity of money, either very low or very high, is not appropriate.
So my question is, where does this strange use of "any length of time" come from, and are there any other things besides time to which it applies?
Solution 1:
This isn't restricted to "any length of time." Googling, you can see that most uses for any distance mean any distance at all, but sometimes you get constructions like:
If you need to carry your laptop case for any distance ...
where it means any substantial distance. You have to distinguish between these two meanings by context. It just seems that any length of time almost always means any substantial length of time, where any amount of money almost always means any amount of money at all. I suspect that once most uses of any length of time started meaning any substantial length of time, people were more likely to use the phrase this way.
With some searching, you can find cases where any takes the opposite of the usual meaning in the phrases any amount of money and any length of time. For example
It's difficult to convince people to pay for stuff, especially if it costs any amount of money.
and
A great place to stay for any length of time!
Solution 2:
The word any can have different meanings depending on how it's used, from "more than nothing" to "every". The meaning of any in this case is not "an undefined", but rater "an extended".
An example of the meaning can be found here: http://www.merriam-webster.com/dictionary/any
appreciably large or extended "could not endure it any length of time"