Historically, I would have said that taking taxis was fairly price inelastic. You knew it would be relatively expensive but you either didn't care or it was really the only practical way to get from Point A to Point B.

However, my sense is that for at least certain locations/demographics, that's probably changed with Uber/Lyft. I don't personally use them much but anecdotally a lot of people have started using them as an alternative to public transit or just because it's easier if they're going out for a night on the town. And I work with a lot of people for whom the reflex seems to be to pull out a smartphone anytime they need to go more than a few blocks while traveling. I expect those behaviors would change if the price suddenly went to 2X. (It also definitely makes a difference at the margins when renting cars and that's mostly a straightforward price calculation.)