Q: The booking classes are A (first), D (business) and L (economy). If I buy a first class ticket and there is no first class on my flight, what happens?
A: That depends on what you mean by "no first class." If the seat inventory (A in this case, but the same goes for D) is not available for the flight you want and you can't get a flight that does have available inventory, you get downgraded to the next available inventory class (A goes down to D, and D goes down to L) and no compensation or refund is payable. Except on two class US domestic flights, if the plane is only one class (all economy) or two class (economy and business), then you get downgraded and no compensation or refund is payable. On two class US domestic flights, if you hold a D class ticket you can book into the A (first) inventory, if it is available, at no extra charge. On domestic flights on AE (American Eagle), AY, EI and LA (which are one class), all A and D tickets book into the Y (full fare economy) inventory bucket which means it is economy seating, but there should be plenty of availability.