This is a very common argument found in introductory classes and texts. Here's Mankiw's version:
Thinking at the margin works for business decisions as well. Consider an airline deciding how much to charge passengers who fly standby. Suppose that flying a 200-seat plane across the United States costs the airline \$100,000. In this case, the average cost of each seat is \$100,000/200, which is \$500. One might be tempted to conclude that the airline should never sell a ticket for less than \$500. But a rational airline can increase its profits by thinking at the margin. Imagine that a plane is about to take off with 10 empty seats and a standby passenger waiting at the gate is willing to pay $300 for a seat. Should the airline sell the ticket? Of course, it should. If the plane has empty seats, the cost of adding one more passenger is tiny. The average cost of flying a passenger is \$500, but the marginal cost is merely the cost of the bag of peanuts and can of soda that the extra passenger will consume. As long as the standby passenger pays more than the marginal cost, selling the ticket is profitable.
Do airlines actually do anything like the above? I think they don't as I have frequently been on planes with mostly empty seats (even before the current pandemic).
Mankiw says the marginal cost of another passenger is "tiny". Let's say it's \$30. Then if a flight has some empty seats 24 hours before scheduled take-off, why doesn't it offer the seats for say \$50 each and fill them all up? Why is it that, in practice and contrary to the above argument, the airline will usually prefer to leave the seats empty?
What, if anything, is flawed or incomplete about the above argument?