This becomes nitpicking, but OK.
Consider the fixed group of people who will mine "before" and "after" the difficulty drop. Let X be a randomly chosen miner in that group.
For some choice X (say, Alice), the production will maybe increase, but for another choice of X (say, Bob), the production has to decrease.
Somebody has to switch of mining equipment to have the difficulty go down, otherwise it wouldn't go down.
A miner is an entity that is hashing in an attempt to find a block and he is spending resources to hash.
If you treat Bob as two entities (Bob and Bob' where Bob keeps mining while Bob' quits) your problem reduces down to miners that keep mining and miners that quit.
A miner (or part of a miner) that quits gets 0 while spending 0 resources while the others spend the
same amount of resources for a larger share (basically the amount of bitcoins earned by the now stopped miner is distributed proportionately to the hashrate over all remaining miners).
The set of miners that stopped mining should not be a part of the group you want to sample because they are doing nothing.
Like I said before I can create an infinitely large group of non-miners and they have 0 effect on the bitcoin network.
Including them in any calculation on miners is incorrect because you are altering the total number of miners by including non-miners.
What you are trying to do is include non-miners (well miners that stopped) in the set of miners.
[edit] by the way I am totally ignoring the fact that difficulty lags behind hashrate changes and that hashrate is not fixed so the actual model is more complicated but overall it more or less follows the described mechanism.