It will happen much sooner then that.
"Much" sooner, yes. Soon enough to be significant, probably not.
-- The previous price hike happened 2 years ago, so chances are Netflix isn't moving to a "raise the price every year model", so we're probably safe assuming a worse-case of price hikes every 2 years from now on.
-- On the high end, assuming an 18% rate hike every 2 years, it will take 16 to 18 years for the price to increase from $13/month to $50/month.
-- On the low end, assuming a 10% rate hike every 2 years, it will take 28 to 30 years for the price to reach $50
-- Middle-road estimate, assuming a 13% rate hike every 2 years, it will take 22 to 24 years to reach $50
In all 3 cases, however, you're talking about it taking pretty much an entire generation before
future Netflix prices might reach
current cable package prices (& low-end packages at that).
And I can guarantee that Amazon will have raised its prices for Amazon Prime during that same period, so I highly doubt you'll ever see that much of a price gap between the 2 services.
And I can honestly say I'm not biased because I have both Amazon Prime & Netflix. There are aspects of both that I like & dislike (I.e. I like how Amazon's trailers work & their "Customers Also Watched" feature; I also like how Netflix puts all of the seasons of a show together instead of making them separate selections, and how I can like/dislike a show in Netflix while in the Roku channel), & there are movies & shows that I can find on 1 service that aren't on the other. But even with price increases they're still cheaper than cable or satellite packages.