In the following exchange, "you may well ask" is used after a question has been asked.
‘What’s all the noise?’ ‘You may well ask.’
But I'm wondering whether "may well V" is normally used after the action denoted by V is completed or the above sentence should be treated as a fixed expression.
It seems correct to say "You may well do this or that" when giving advice. The action denoted by "do this or that" has not yet been completed.
The usual usage of "you may well ask" is like this, said by one speaker:
" 'What's all the noise', you may well ask."
This is the speaker expressing that they think that another person may have noticed all the noise, and they expect a question about it.
As an exchange, as you have quoted it, it would mean that someone has noticed the noise and is asking about it. The person they are asking answers to say they think it is a justified question. But that phrase is much less likely as a reply than in the use shown above.
You may well ask is best treated as an idiom.
Normally may well means something like it is very likely that, eg
I may well go to the post office on my way home.
means more than just that I may go, but I think it is likely that I will go.
But You may well ask has a range of special meanings. At the least, it means "I thought you would ask that". But it often implies something like "That is an important question, and either it has the following surprising or annoying answer, or else nobody can find out the answer". In that sense, it usually has a connotation of annoyance, but not with the person who is asking the question.
