I'm confused by "pay the last few times." Again, I just bought a new MBA 13 from B&H PhotoVideo which included a free copy of PD8. I don't remember if I had already installed PD8 on my old MBA 11. Regardless, when the new MBA arrived I did install the free PB8 on it and ran the computer in that manner for about a month. I finally got around to doing one last Time Machine backup with my MBA11. After doing so, I hooked my new MBA13 up to my Time Machine HD and did a restore or recovery of all my programs/data to the new MBA 13. When the restore/recovery was completed, I booted up the new computer and all my programs that I know of got transferred to the new MBA13. Parallels 8 seemed to run fine.
Then a couple of days later (actually today) I went into Parallels on the new computer and it asked me for my activation key which came on the free installation disk. After entering that number, everything seems fine. So based on what I've seen, at least PD8 runs fine with the new beta OS X Mavericks. Whether this will be true with earlier editions of Parallels I haven't a clue. And yes, I expect that I'll have to pay the usual $29 or whatever Apple charges for the regular edition of Mavericks.
Fine with me as I don't want to open a can of worms by trying to go back to Mountain Lion.