Haha sorry buddy, the 7870 editions that beat the PS4 are $200. You're right that they are better than the PS4 GPU, but wrong on the price. The 7850's get down to $150, but they're also benchmarking lower than the PS4 in synthetic benchmarks.
Also, a $50 price difference doesn't invalidate my answer of $600-$650 --- in fact you'll notice that it lands exactly in my stated error range of $50.
EDIT: My bad, I found a super off-brand cheap bad-warranty version of the 7870 for $170.
But speaking from experience, don't buy a shit card from a shit company with a shit warranty.