GTX 1080 TI FE + I7 7700K on cheap 50$ 700w psu ?

Solution
Your parts are not overly power hungry.
700w is more than enough.
If you already own the psu, and it has not caused a problem, I would go ahead and reuse it.

If you are looking to buy new, I would look for a tier 1 or 2 unit from a list such as this:
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html

For a $50 budget, this tier 2 Seasonic 620w unit is a better buy:
https://www.amazon.com/Seasonic-S12II-620-BRONZE-SS-620GB/dp/B003BIEOCI/ref=sr_1_1?s=electronics&ie=UTF8&qid=1494603125&sr=1-1&keywords=seasonic+s12ii+620+bronze+ss-620gb+power+supply
Your parts are not overly power hungry.
700w is more than enough.
If you already own the psu, and it has not caused a problem, I would go ahead and reuse it.

If you are looking to buy new, I would look for a tier 1 or 2 unit from a list such as this:
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html

For a $50 budget, this tier 2 Seasonic 620w unit is a better buy:
https://www.amazon.com/Seasonic-S12II-620-BRONZE-SS-620GB/dp/B003BIEOCI/ref=sr_1_1?s=electronics&ie=UTF8&qid=1494603125&sr=1-1&keywords=seasonic+s12ii+620+bronze+ss-620gb+power+supply
 
Solution