What stocks do we buy to profit off this?
MU all the way. NAND shortage is supposed to turn around by the end of the year but DRAM ASPs are screaming upwards. MU also has the added benefit of a possible paradigm shift in memory products with 3DXP.
source for second graph: http://seekingalpha.com/instablog/9577541-electric-phred/4951812-dram-spot-update-inaugural-day
MU has an analysts day first week of February, at which I expect a sizable positive increase in guidance for the current quarter. DRAM spot prices are up over 20% since first week of their current quarter.
I lied - one more important point: China's Tsinghua is rumored to be building $30bn in NAND fabs. I don't expect significant output for at least two years but, as stated prior, the NAND shortage will not last very long (well, unless the extra capacity finally prompts a full HDD replacement, at which point supplies will be limited again).
China is expected to actually start production by end of 2018 which means in the mean time, shortage. The shortage will actually end before china is a big player because by this time next year every major player with have large capacity 3D NAND is full production and the production will outstrip demand but there will still need time the beat down all the pent up demand.
Expect HDD prices to stay stable as well with Seagate lowering production and WDC spending more on growing their new SSD business.
Toshiba will also likely sell a large part of their NAND production shares to WDC this year so WDC is poised to make a killing in the next 2 years from NAND shortage