The GFX requires a minimum of 18amps so if you ask me, I can go higher for it's maximum performance but my PSU has a maximum of 19amps, so in my opinion the PSU is not letting the GFX give it's best performance seeing as the highest it can go is 19amps.
You could have a 1000W power supply - it wont make a difference. You graphic card requires 300w which is what your giving it. If you installed a 1000W PSU it would still only use 300W.
A game requires several things to run - good CPU + good RAM + good gfx card. As an idea there are several fixes on the interwebs about this (gta:iv specific) which might help
My game runs slow then after 30-60mins runs faster fps. But remember after a few hours your gfx card and computer are getting HOT! so your computer runs harder to cool it self down which lowers resources to the game, as your fans are running harder via motherboard to lower its temp.
If you are insistent that it is the PSU then by all means go and buy one (400w should be cheapish) and re-try - but i wouldn't expect any miracles.
Talking from experience:I got a new gfx card thinking "Yeah this will make my games run great!" - computers do not work like that. Computers need everything to be good to work.
I got a new gfx card and a 1000W PSU. Due to the design of the case and PSU, the PSU gets hot (ofc) and that heat is blowed DIRECTLY on to my CPU. So it lowers my CPU performance due to the heat, which makes the computer run harder to displace the heat.
Going back I should have got a good 500W PSU and a new case (or at least another fan).
Did you build you pc? and why did you get that gfx card?