Robo-taxi fleet economics napkin math

 Assuming $1 of monthly income supports $100 of expenditure, and that a robo-taxi costs $150k, a taxi needs to make $1500 a month (above operating costs). Marginal operating costs (beyond depreciation) can be assumed to be $.10/mile. Assuming 25 miles per hour (averaged over high speeds and waiting time), that's $2.50 in hourly operating costs or about $900 in monthly operating costs. So capital and operation is about $2400/month for a robo-taxi, or about $6.50 per hour. 

Of course a robo-taxi can make more than $6.50 an hour. A single Lyft trip reliable runs over $20. Assuming three trips per hour, $60 income versus $6.50 costs makes robo-taxi fleets a very attractive proposition. 

The counterpoint is that such a robo-taxi costs far more than a bus fare. The counterpoint to which is that we subsidize buses, so why wouldn't we subsidize robo-taxies? (For the sake of simplicity assume one pool of subsidy, and all operations are contracted out). Begs the question of how much it costs to provide service by bus. Costs varies wildly by service type - basic bus service is cheap, commuter bus is less so, demand-response (paratransit) is wildly expensive.

"UTA’s official published cost per passenger (per boarding) from its 2006 performance audit was $5.11 for buses, $3.51 for light rail, $36.82 for paratransit, and $3.53 for vanpool".

Add 57% for inflation (2006 to 2026) so it's about $7.25 per passenger for a bus. That's more than the capital + operations cost for P2P AV ($6.50), so our hypothetical subsidy provider would be better off switch many riders to subsidized AV. 

How many (and which routes) is a more nuanced question. Bus route productivity (passengers per service hour) varies widely. Removing the least productive routes would substantially reduce the average subsidy cost per passenger. $7.25 per passenger is $22 for 3 passengers per hour, so it would be far better to switch a lot of passengers to P2P AV. 

An intuition of averages suggest that would be a lot of riders. But that intuition is wrong. $7.25 per passenger is an average, and that average hides a staggering a range in productivity. There is one route that costs $40/passenger and another that costs $3/passenger. But the $3/passenger route has a low subsidy/passenger because it's transporting a lot of people. It's costing $150/hour to operate, but transporting 99 passengers/hour, which would cost $215 to do by PTP AV. In an economist's chart, the two lines in the napkin math would cross at about 75 passengers per hour. 

Assuming 15 mph for a bus, that's about 5 passengers per mile. Not a high standard. 

But a lot of transit agencies own some very expensive capital equipment (buses) that they can't resell, as the feds helped pay for it, and if they sell the buses they have to return the subsidy. So at best, agencies will shift to AV by not buying new buses rather than selling excess buses. So we'll see a lot of new PTP AV's serving marginal routes, as older and older buses serve the high-capacity routes. (Not a great outcome).

All of this assumes that bus costs remain fixed, and that the bus service provider doesn't also shift to fixed guideway AV vehicles. The advantage isn't as extreme for fixed guideway AV as for P2P AV, because the ratio of drivers/passenger is much lower. If it halved labor costs, the break-even point between fixed guideway and P2P AV shifts in favor of fixed route. This may be expected, and transit agencies are simply being quiet about it so as to not spook their driver's unions. (It will be a slow shift--a new bus has an operational lifespan measured in decades). 

It also assumes that P2P AV can only manage one passenger per vehicle. But even assuming extremely generous carpool standards (averaging 1.3/trip) it would only raise that number by a third. Most people don't start and end in the same location, and pairing up in even a portions of two trips requires them to coincide in time and space in an unlikely way. 

Finally, anyone providing services has to size their fleet (and supporting infrastructure) for the peak hour, whether that's 10 buses or 60 PTP AV vehicles. They also have to maintain sufficient 'spare' capacity to maintain that fleet capacity while part of the fleet is out of service and being repaired, which means 10-50% more vehicles than are actually in use even at peak. Which would substantially degrade the productivity we've assumed for AV vehicles. Vehicles achieving 3 trips during the peak hour are never going to achieve that outside of it. A key part of the economics of ride-hailing is part-time drivers who only work and accrue vehicle costs during the peak hour. In a 'fleet' context, that advantage vanishes. The operator wants to keep vehicles operating as close to constantly as possible, but the other 23 hours of the day are only ever going to be (at most), 90% of the peak hour volumes. So the operator will need to buy 110 P2P AV vehicles, of which only 90 will be operating 23 hours a day (10 spare, 10 idle for lack of demand). On which basis, the $6.50/hour operating costs looks a lot more like $8 an hour, further eroding advantage. 

[1] "But that's so much money!"---"Let me tell you about how much roads cost". 

[2]  In reality, assume the average fare is $2.00, so the subsidy is $5.50/passenger.