market failture question

[Lovextreme]

Romp, Mike and Han are 3 players in cabal that plans to go to ft2 togerther, each has a budget of 400m with utility functions U=XY, they both need amp pots and GM buff in order to run this dungeon, amp pots cost 1m ea and GM buff cost 100m per day. calculate utility under 1)private solution 2) public solution 3) if GM[Kato] offers to join his membership club which the GM buff will only cost $36m, wats the max amount they would pay under the public solution?