Only if the price list is player-side info. I posit it should be - must be - DM-only, for a variety of reasons of which your point is one.
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You've walked right into my number one reason why magic item pricing is essential: to make treasury division equitable and fair.
I'll pull some prices out of my hat here, but they're not far wrong:
Axe +1 - 2000
Pearl of Power - 10000
Wand of Fireballs (fully charged) - 6000
Total value 18000, meaning each of our two intrepid heroes should expect to see 9000 worth come out of this. So the Barbie gets the axe, with Wiz gets the wand, and maybe the Pearl has to be sold with the proceeds divided such that each ends up with their 9000 in total value.
Otherwise, the Barbarian here is going to get hella ripped off.