By that logic, all businesses with economies of scale are "natural monopolies". That's nonsense, because it assumes that everything else (particularly income per ride and cost per ride) are the same, or at least that they can be the same at a whim.

And in practice, we see smaller companies competing successfully with larger ones all the time.

Indeed, a lot of businesses with economies of scale and network effects can become monopolies. If we want to experience the benefits of free-market and competition, from a consumer point of view, we need to implement it through regulations. Peter Thiel explains it quite well, businesses want monopolies because they can reap a higher share of the value. Competition redistributes value to the customers. Once we recognize this, we can ask where, as a society, it makes sense to foster competition.

Which businesses have become monopolies through economies of scale? Can you give me some examples?

There's a huge liquidity advantage, relatively unique to this market, that is difficult to compete against.

Presuming you can block your drivers from working for rival services simultaneuosly.

Hardly difficult. Once you have a monopoly position you just add a clause to the terms and conditions that you may only use Uber if it's the only service you're signed into at the time.

I always thought Uber avoided such a clause now and would continue to do so in the future, regardless of monopoly status, because their contractors being reclassified as employees would be disastrous to their business model.

But how do you get the monopoly position in the first place? Also, that assumes the law doesn't invalidate those clauses.

As I said in the original post, by using VC cash to undercut competition and drive them out of business.

And others can't get VC cash, why?

VC cash isn't infinite, and the amount available today won't last indefinitely. And are many VCs really likely to invest in a new startup when Uber just got over a billion dollars of cash? You can be as innovative and disruptive as you want, you're still going to have an extremely hard time beating a company with $1.2bn in the bank.

Anti-trust violation

On-demand business maybe. But pre-arranged car service business (where majority of transactions is airport pick-ups/drop-offs) is very fragmented, and Uber is just another player there.

If you don't need on-demand availability, Blacklane.com or Limos.com are consistently cheaper than Uber Black.

And if you are okay with waiting for maybe an hour or so, Sidecar is usually a better deal for longer distances.