Currently miners are getting 1/8th the coins they did a year ago for the same hash rate.
But BTC has doubled in price.
Even so, that would mean that Bitcoins are still only at a quarter of their value,
and we should see prices increase to around 4x their current rate, or just above $2500?
(Obviously this won't happen, but it does mean prices have to increase eventually, right?!?!)
You have assumed miners are still using the same technology as last year.
You need to take into account that mining hardware is now far more energy efficient. The S9 is 5 or 6 times more energy efficient than last years S5. So the hash rate per unit of electricity is now far higher.
The hardware is 5 times faster and bitcoin has twice the value yet the hash rate is only three times higher. Even with the halving, running an S9 is more profitable now than an S5 12 months ago.
I would not look for mining to drive any price increase. Mining will follow any price change, not drive it.