In the former case, you're competing with a bunch of alternatives that you're happy to substitute given a better/cheaper option. Maybe you take less public transportation or don't ask for a ride or don't drive yourself and use Uber.
AirBnB, on the other hand... Yes, some people will travel more/stay longer given cheaper lodgings but there are a lot of other costs associated with travel (including, for most, vacation time) so it's harder for me to believe that AirBnB will dramatically increase lodging days to the same degree that Uber could potentially increase taxi or private car-like service miles.
Also, AirBnB doesn't only compete with hotels... a lot of the market share in my country (Uruguay) was actually taken from real estate agencies for short-term vacation rentals, not hotels.
Edit: same in Portugal and Ireland, see https://news.ycombinator.com/item?id=12732874
That's not market elasticity though. That's shifting from one booking agency to another. When my family rented a vacation home we used various small vacation home services. I have no doubt we'd consider using AirBnB today if we still had the place.
I don't doubt that lower prices, where they exist, make a difference at the margins. I'm just skeptical that the effect is big. And, as the business traveler that I am most of the time, I mostly want predictability and a 24-hour desk from a hotel.
> Option 1. They didn't lose market share across the board, and instead cherry picked non-representative markets for their 13 region hotel comparison.
(from higher up this comment chain)