If your car has TPMS do you have to pay more for new tires? Why and what would the cost difference generally be?
nothing special about the tires. It is a sensor on your rim usually tied like a band on the inside of the rim. The tire has no effect on it. The methods are mainly sensor on band inside rim, valve stem, and the counting of abs which is on older cars before the electronic ones came along.
I'm guessing an F150, being not a top of the line vehicle, would probably not have a tire pressure monitor. I could be wrong. Why don't you just go to an auto parts store or gas station and buy a gauge for a couple bucks? The max pressure will be labeled on the side of the tire. It will take all of a few minutes to check all four tires.
Tires cost the same either way unless the vehicle is equipped with Run-Flat tires in which case it is recommended the tires be replaced with Run-Flat technology tires.