I can guarantee that Netflix's primary demographic will not think "oh, Netflix raised its prices by a dollar, let's do piracy!"

From TFA: "Netflix now has [..] 48.35 million streaming subscribers worldwide"

"Netflix generated revenue of $1.07 billion in Q1 of 2014, compared to 1.02 billion in Q1 of 2013"

Don't think they have any short-term threat to their existence at this point.

What will probably end up occurring is the countries were torrents are legal will end up keeping the same price of $7.99... Where as countries that have laws against torrents, will most likely have an increase. Popcorn-time doesn't make it legal to torrent/stream videos without purchase in the United States, thus we can safely say that the price in the United States will increase.