(1) That I assume companies never have market power.
(2) That I suppose "market power" implies monopoly
(3) That my example was cherry-picked.
1. I did no such thing. I explicitly acknowledged market power several times.
2. Again, not correct. I explicitly mentioned oligopoly (assuming that 'imperfect competition' wouldn't land).
3. Of course it was. I acknowledged as much! I quite literally said the example doesn't generalize. The example serves to illustrate a 'there exists' claim. I felt a concrete example would be easier to follow than some kind of generalized model.
Your own comment claims that "actually competitive" markets can't have price discrimination. Sure, we can suppose the law of one price applies to perfectly competitive markets, but there's no sense in which a perfectly competitive markets "actually" exist at all! The obvious observation we can make is that such competitive dynamics imply that no one would make any profit!
My appeal to the airline industry as an example was not an accident. There's a very well-established literature on the relationship between competition and discrimination in the airline business. It's *certainly* not a settled question that discrimination decreases as competition intensifies. I included a classic from Stavins below that finds precisely the opposite of your claim.
My argument here isn't perfect. I can think of many flaws, many reasonable objections. But I don't think you're using any of them here.
---- Referenced paper from Stavins: https://www.bostonfed.org/publications/research-department-w...