I wonder if prices will drop that much. Is owning and maintaining a massive fleet of driver-less cars really that much cheaper than just paying a bunch drivers that own and maintain their own car?

First, efficiency of utilisation: Driverless cars can be driven around the clock (modulo maintenance and refueling time), so car depreciation/maintenance gets amortised amongst more passengers.

Second, efficiency of scale in maintenance: It is extremely unlikely that the maintenance costs that uber drivers take on - buying parts retail and taking their car to the nearest garage for repairs - are lower than what would be a dedicated factory-like maintenance shop for thousands of automatic cabs.

And third of course: direct wage costs of the driver once you subtract car maintenance from fares is still a lot bigger than zero, so eliminating that saves money.

So in theory can normal cars. Many taxi companies (and I'm assuming at least some Uber drivers) share one car between 2-5 drivers to maximize the time on the road.

The other aspect you're not considering is that even after you take economies of scale into account a driverless car will almost certainly cost more than the market price of the current median Uber car. I'm guessing that $3000-5000 will get you a perfectly Uber-worthy car that will give you years of fairly trouble free use. What will a driverless car cost?

And that is ignoring the fact that most Uber drivers would have owned and maintained a car even if they had had a different job, so the only 'cost' is the marginal cost of extra maintenance being used as an Uber car causes.

Also I wouldn't be surprised if maintenance costs will also be higher at least in the short-to-medium term due the complicated and experimental nature of the components involved.

So even if there are long term savings I imagine that they will take a long time to materialize and even longer to show up in fare-prices, unless Uber decides to subsidize driverless fare to kick start the market.

And if they are not first with driverless cars, big national cab-companies are also in the run.

Many (most?) jurisdictions differentiate between for-hire-vehicles and taxis, and Uber doesn't operate unlicensed taxis as far as I know. I don't want to claim to know everything about Uber - but services like their black car and UberX service are not considered taxis in most jurisdictions that I'm aware of, for a number of reasons including because they accept only rides that were arranged in advance, they have no special paint job or advertising, etc. According to Quora, Uber does operate "UberTaxis" and those are actual medallioned taxis: https://www.quora.com/What-is-the-difference-between-an-Uber... - so it seems to me that Uber's classic services were never regulated by taxi laws to begin with, and the actual taxi services they have now comply with them.

I'd like to learn more about this topic though, since I find the boundary between business and law interesting in this case, so I will be glad to review further details if someone can provide them. (I have no connection to Uber nor that industry except as a once-in-a-while customer.)

Googling 'uber pays lawyers to drivers' also gives matches for NA although I didn't look the details.