A Question of Spell Costs

As I understand it, the resource point cost of a spell is determined by the spell obstacle and whether or not it has a caret (^) attached to it.
Non caret spells cost two times their obstacle in resource points in character burning.
Spells with caret cost four times their obstacle in character burning.

I ask this as the costs for the spells “Witch Flight” and “Witch Key” (page 223) seem to be switched:
Witch Flight: Ob 3^ lists Resource Points: 6
Witch Key: Ob 3 lists Resource Points: 12
Is this simply a mistake, or were they priced as such for a reason?

Should we apply the formula over the book in such cases as these?

I think you’re probably right in this case.

Thanks for the answer!

Add it to the wiki: http://www.burningwheel.org/wiki/index.php?title=Burning_Wheel_Gold_Errata#Sorcery_Spells