Hope this question is not too elementary. I have an Economy seat on a domestic flight in a few days. I want to upgrade to a seat in First by paying, not with miles. At the moment the price to upgrade is $157 per segment. At the moment there's still a good supply of seats available, or at least unassigned, in First. Will the price go down if I wait and try to buy it from the machine at the airport, the morning of the flight? Or will people have been upgraded into those seats by then?