As can be seen by anyone watching the price of oil drop by half while airfare remains high.

It's complicated because as I understand it airlines hedge the price of oil far into the future.

However, big business are often corrupt so wouldn't surprise me equally if there was some sort of cartel. It's strongly in their collective interests to not drop the prices.

While the price of oil is an important part, it's not the only cost factor (personal, aircraft leasing, airport fees, etc) also play a part