Firstly, I don't see what bitcoin miners are producing other than bitcoin. Heat, perhaps? Bitcoin can be part of their revenue, but it is their production of it that pays their bills. Let's get this in order: first, their production (they are producing bitcoin and heat, nothing more) drops by 50% on the bitcoin front.
Why do you continue to persist when it is evident that it is their revenue that would fall first? Not until then miners have any reason to cut production (effort and time wise), since that would mean losing profits...
OK, we have a misunderstanding based on semantics. Revenue is the money they make. Production is what they make in order to sell and make money. You're confusing production as in "how much they produce" with production as in "how many resources are put into producing bitcoin". Assuming that their efforts at producing bitcoin (time, hardware, maintenance, etc) does not change, what will drop first is
how many bitcoin they produce, it will drop 50%.
Then their revenue (the money they make) will be affected by what they do with their reduced reward.
What makes more sense for them is to raise the price they sell at, because what they have to sell is a lesser amount, despite the fact that the cost of producing what they sell remains the same.
So the amount of bitcoins produced (production) is reduced by 50% first, and their revenue is affected in some manner, one which I am not comfortable speculating upon.