There are at least three options for the ownership of a personal rapid transit system such as SkyTran:
The first option, private ownership of the tracks and vehicles by a single company, might be technically desirable in the early stages to ensure that responsibility and management were concentrated while the bugs in the system were worked out. However, if it continued for years, it would probably make that company very rich -- this is a tempting carrot for investors in the system, of course. If the current SkyTran company is able to use its patents and know-how to become a single monopoly that cities couldn't afford to refuse, we might even see something like the 19th-century railroad monopolies. This is a very attractive model for investors today, but IMHO it would greatly limit the potential uses of the system.
The economic term is "monopoly competition", when the "competition" the monopoly faces is people using alternatives (wagons and canals in the 19th century; cars and existing public transportation in ours) or doing without. Pricing theory says the monopoly should charge the highest price they can that doesn't lose them more revenue in customers who can't buy the product than the higher price brings.
A sneaky variant that's quite prevalent today as then is offering deliberately inferior versions at a lower price to capture as much as different segments of the market can pay. For example, coach airline travel where long lines and cramped seating are a feature, not a bug -- they persuade those who can afford it to buy more expensive versions of the same basic product -- travel from point A to point B. The 19th-century equivalent was "long-haul/short-haul" freight rates: railroads charged less for long trips that were a growth area for their market, subsidizing them by high rates for established areas that didn't have good alternatives. The incredible variation between the price of air travel offers for vacation spots with extra room, and what you pay if you are stuck in your destination city and absolutely have to fly home tonight -- is a modern equivalent.
Ownership of cars and track by the city would solve the problem of monopoly, but at the cost of bureaucracy. This would probably be somewhat better for the public. I'm currently living in Paris, which has the best metro system in Europe, I'm told. Using well-maintained evolutionary technology (and many facilities) a century old, it provides relatively excellent transportation that makes it feasible for a large fraction of the population to get around quite well without owning cars. However, for a system with so many potential uses (for instance, see SkyTranFreightDelivery, SkyTranEqualsElevator and LittleShopOfWonders), government ownership would have a high opportunity cost.
Highways and cars are probably a better model: the roads are publicly owned (so you don't get absurd fights about who can go where on whose network of roads -- they are guaranteed to everyone, and paid for as a public service), while individuals and companies own the vehicles that travel on them, allowing tremendous flexibility in how we use our cars.
Fundamentally, the largest concern would be making an automated high-speed transit system safe without centralized responsibility and control. This has many aspects -- for instance software, communication protocols and digital signatures to guarantee that essential information is transferred between the tracks and vehicles and interpreted consistently. For instance, in an automated system, it is crucial that a vehicle not try to exit if the ramp or the next section of track is blocked or out of order.
Another major difference with highways and cars is the potential to re-use vehicles many times in a day. Fleets of vehicles could be owned by different companies, like taxicabs. Delivery services like FedEx and UPS would have their own vehicles, not to mention companies that wanted to offer delivery for products, from pizza to office supplies. Tradesmen, ambulance companies, and many others would want specialized vehicles, not to mention individuals who wanted to travel in their own special vehicle (PimpMyPod, EmergencyServices, SuperConsultants).