If you've ever taken a taxi in a market like South Africa, China, or Chile, it's so cheap it's insane. Almost unbelievable.
In many cases the cars are more or less the same, the gas costs more or less the same, so the only variable that's different is the cost of labor which Waymo eliminates.
My point is really that Waymo is eliminating what is unquestionably the highest marginal cost component of a ride.
I own a Pacifica PHEV, so I can come up with some numbers there: it has a 32-mile electric range off of roughly 13 kwh of charge. So, at 10¢/kwh, you're at about 4¢/mile for electricity. The vehicle can be charged from empty in two hours (on a level-two charger); so if you assume roughly 30 MPH average speed, the vehicle can be on the road ~1/3 of the time. So, assuming 240 miles per day * 365, you're at 87,600 miles per year. Assuming five years of vehicle life (not a stretch for this vehicle, especially in electric mode), you're at 438k miles out of a $50,000 vehicle; you'll probably need a new battery at 200k miles or so, so throw in $10k for that. So we're at ~14¢/mile for depreciation and battery replacement. Now we're at 24¢/mile—double it to factor in other maintenance (tires, cleaning, suspension, etc.), insurance, and to account for my likely optimistic usage pattern. We're still under 48¢/mile.
Keep in mind that this is for a massive seven-seat PHEV minivan. With a smaller, pure-electric vehicle (hybrid really isn't needed for this use-case), you're getting longer range and better mileage. Bump up the charge speed (level 3 charging is much faster than level 2), and you can probably get your run:charge ratio above 1:1.
So dramatically increasing the number of miles you drive per year reduces the actual total cost per mile. Using fleet management services and having deals directly with the manufacturer, as well as buying in bulk will generate huge savings, particularly since you almost wipe out the dealer fee.
This is why I think driverless taxis will be much bigger than many people expect, but also why this industry is going to get monopolized like none other. Bigger players will be able to get taxis to you faster, offer them cheaper, and still show bigger profit margins than smaller players. And without scaling labor costs... whoever wins this industry is going to be making a completely ridiculous amount of money. Consider that in 2016 3.2 trillion miles were driven in the US alone. 10% of those miles is 320 billion. A profit margin of a nickle above operating costs is a net of $16 billion. That's at operating on a nickle per mile, with 10% of 2016's mileage, in a single country.
On the other hand I expect all the players will realize this, so we should see and benefit from some insane competition as long as the market remains relatively free.
With Uber, as it is today, you have the strong forces of a network effect (where drivers are stuck because the passengers are there, and the passengers are stuck because the drivers are there). This effect is historically very difficult to break, a canonical example would be craigslist.
While rolling out self driving cars, simply requires money. If for example, San Francisco has 1000 Uber drivers active at any time today, all you need is to roll out 1000 cars yourself in the city, and the service you provide is equivalent to Uber.
In other words, if self driving technology becomes common, the market is going to be commoditized to the point where there is very little profit margin for any player (such as in the airline industry).
In a commodity market you win with combination of price and brand.
When it comes to price, a player with a fleet of a million cars can wage a pricing war for longer than a player with a fleet of 10 thousand cars because economies of scale mean that it costs them less, per car, to provide the service.
If this is a new entrant, the incumbents also have an accumulated war chest from past revenues they can use to outprice the competition.
And they also have more money to out-advertise the new guy. GM spends $3 billion a year on advertising which is why, not counting Tesla, the youngest surviving car company was founded in 1925.
It's also why Kellog dominates in cornflake space, coca-cola in soda business etc.
Which is why there will be a mad rush to grab the market share early on. Once someone reaches significant scale, it'll be virtually impossible to catch up with them.
It's not so bad (or maybe wouldn't be if cars themselves weren't so expensive.)
Assuming some even distribution of avaialable vehicles in an area, time-to-pickup scales like (area/vehicles), so the returns to scale diminish fairly quickly.
And "evenly spaced vehicles" might be the worst case depending on user preferences. It might be better to have fast pickups in some places and really slow pickups in others than average times everywhere, so long as users know the pattern -- slow from my house, fast from my work etc.
There are people who only buy Volvos because of the reputation for safety they've built up.
I'm guessing 35 cents is a bottom-up estimate that is just the marginal cost of gasoline (and maybe maintenance).
That said, if self-driving cars actually produce the expected reduction in collisions, then I would expect (self-)insurance and repair costs to go way down for self-driving cars versus human-driven cars.