This is a bit tricky.
A PSU will only pull the power needed to power your machine. So if you need 350 for your computer it will only provide 350W and not the 550W that its capable of. Did you see what I wrote? I said provide, not pull.
If a PSU is 100% efficient at converting AC electricity to DC, then you'll pull 350W from the wall to provide your computer with 350W of DC power. PSUs are not 100% efficient. An 80% efficient PSU will 437.5W from the wall. A 90% PSU will pull 389W, while those old 70% units from the P4 days will pull 500W.
I bring this up because you used the word "pay". What you pay will depend on how good your PSU is. The worse it is, the more you'll pay.