Correct. If the price doesn't go up, the miners would jump ship, and the difficulty would fall, essentially creating price/reward equilibrium. The first halving of BTC was an interesting time, because you saw a shift in mining technology. I'm pretty sure it's safe to assume that everyone who was mining BTC with GPUs(myself included) before the halving pretty much stopped in the following months when the price was stable. But the price jumped like 15x shortly after that, and then ASICs hit chain. So it was a really interesting time for BTC market dynamics. However, this summer should be a true indication of the effect the halving schedule has on market dynamics. Even if the increase is gradual, it will be very sharp when looked at from a longer timeline. Yes, month to month it's not going to look crazy, but over a 3-6 month span I'm almost guaranteeing that you will see a considerable increase in price following the halving. I don't think you'll see enough of a decrease in mining to equalize the price/reward ratio. Time will tell though which way it will go.
Finally someone who gets it ;-)
Do you really think the effect of the halving will show itself 'exactly on' of 'right after' the reward halfing?
Of course the effect will be spread out to a period starting well before the halving itself end ending well after it.
Let's look at last time:

I say it was halving-induced. Price went from $5 to ~$125, a 25x increase. So I think my earlier estimation of a 10x increase is conservative under these assumptions.
Again: not sure above does work like that for AUR.