Difficulty will only drop if a lot of farms turn off their gear. It's likely that most folks will be mining at a loss for the first period after the halving. What sucks is, since mining only alters the total supply by a fraction at a time, the supply/demand curve won't be moved very much at all by the halving so it won't have much effect on the exchange rate.
So, the immediate effect is return halves for the same work. Miners are turned off. Blocks are found much less frequently but the day to day cost of power remains the same and not only is the payoff per block halved to 12.5btc but the payouts are less frequent. Sounds like a disaster. The next difficulty then will be an quick drop. Some miners are powered up again. Blocks are found more quickly than expected and difficulty goes up after a short duration?