i have this issue sometimes as well on newly purchased MBA.....
The first questions is relation to anything is run Disk utility, i can understand that for permission issues, but not for shut down issues.. ALmost as if Disk utility would be the silver bullet to solve everything....
I always find a clean install solves this... If you don't wanna do that, try a new account... DU can sometimes solve issues depending on the issue, but its certainly no magic cure. Apple think it is... but i have my doubts..
Its like saying check disk under Windows will get u back.
Usually if its only account related by a hang creating another admin account will fix the issue... All that would be then require to move everything across.... or just keep two accounts if u want.
Alternatively do a clean install.