The airlines do not make the money from the taxes. Those taxes are airport taxes, which go to the airports that will be flown into, as well as there are taxes for international flights, and other taxes, as well. The airlines get none of that money, just like the stores do not get the sales tax.
As for fuel. Everybody knows how expensive fuel is. The airlines have to mark up their prices, to ensure that they can make a profit, over their cost for fuel, just like any company prices their products, or service, to ensure a profit. It would be nice if the airlines, and any company, for that matter, gave things away for free, or extremely cheap, but obviously that isn't going to happen, and it wouldn't make sense for the company to do so, from a business perspective. What most passengers do not understand, is that, even with the high cost of fuel, with inflation, you are spending the equivalent to what airfare was 20-30 years ago, if not less. The airlines could, and probably should be charging 2-3 times what they are, for airfare.
I can't speak for why there was a 300% mark up, on an infant ticket. I do know that for international flights, the cost for fuel, per passenger can get up into the $200 range. That, coupled with taxes, which again, don't go to the airlines, can easily cause a ticket that is only $80, to suddenly become much higher.
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