The Hyperloop was recently introduced by Elon Musk as an alternative to the Californian High Speed Rail Authority's $68 billion dollar proposal for a new high-speed rail linking San Francisco and Los Angeles that, so far, has only secured about 1/6th of the necessary funding for construction. Due to Elon Musk's desire for the Hyperloop transportation system to be crowdsourced, many may speculate that the system will be introduced as a public good; however, this may not be the best scenario for the social benefit of society.

The Hyperloop is an idea for a transportation system comprised of multiple capsules traveling through a contained low-pressure environment proposed by Elon Musk, founder of Tesla and SpaceX, in place of the planned California High-Seed Rail. The capsule, "features a compressor at the leading face to ingest oncoming air for levitation and to a lesser extent propulsion". Levitation of the Hyperloop capsule occurs from the expulsion of compressed air from the bottom of the capsule rather than electromagnetic levitation because of the higher initial costs and running costs associated with an electromagnetic system. Rail support is also not an option due to the extensive "frictional losses" that would require a more sufficient onboard engine and ultimately demise the project to no more than smaller contained locomotive. The onboard compressor creates lift as well as maintains speed. For acceleration and deceleration, a series of electromagnetic arrays both push the capsule during departure and acceleration and also capture the energy to recycle back into the system from deceleration rather than wasting energy during traditional braking. Top speed for the Hyperloop system is 760 miles per hour, "for aerodynamic considerations," and the gravitational load on the capsule and its passengers, both in acceleration and horizontal loading, does not exceed .5 G as it, "is deemed the maximum inertial acceleration that can be comfortably sustained by humans for short periods." Filling these constraints, the Hyperloop transportation system would be able to, "transport people, vehicles, and freight between Los Angeles and San Francisco in 35 minutes." The summation of passengers the Hyperloop would be able to transport each year would amount to 7.4 million. The total estimated cost of the human transportation project is $6 billion, although some have estimated this number to be off by tens of billions.

Individual passengers on any journey attach different values to their trips that vary based on multidimensional perceptions of how their journey is affecting their time as well as the time of those around them; this variation in valuation can predict what form of transport a traveler will consume for a particular journey. Below are predicted cost equations for four substitute forms of transportation, where x is the individual's valuation of 1 hour of their time, λi is the individual's perception of safety, βi is the individual's desired freedom, ρi is the individual's altruistic beliefs concerning Climate Change, and ωi is the individual's desire for technological advancement and futurism in society.

Airplane = $58 + 2x + λ1

Automobile = $45.72 + 5.33x + λ2 - β2

High Speed Rail = $105 + 2.67x + λ3 - β3 - ρ3

Hyperloop = $α + .583x + λ4 - ρ4 - ω4

βi was not included for either an Airplane or Hyperloop journey because there are no stops or changes within the route, and thus β14 = 0. Assuming an individual just wants to get from San Francisco to Los Angeles, or vice versa, without any stops (βi = 0), an airline would be the most direct substitute a consumer would have for the Hyperloop.

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If either a publicly funded Hyperloop or High Speed Rail is introduced into society as an option of transportation, the airlines running between San Francisco and Los Angeles will be crowded-out of the market, possibly to the extent of creating a natural monopoly for the land based competitor. Not only will a land-based high-speed transport system crowd-out airline alternatives, but some automotive travelers with a particular valuation of freedom (βi), who would not have before justified the opportunity cost of an airplane's lack of freedom, would choose to instead take the Hyperloop or High Speed Rail and rent a car at their destination.

If the desire to revert Climate Change (ρi) and the desire to increase technological advancement and futurism (ωi) in society by the people of California was high enough, the justification for a publicly funded Hyperloop would be enough to account for its construction. Californian voters agreed on their desire to fight Climate Change and offer an alternative to airlines, "when California voters approved Proposition 1A in 2008"; this proposition, "allocated nearly $10 billion of an estimated $45 billion to build a train from San Francisco to Los Angeles." The $10 billion dollar valuation of reversing Climate Change through offering a new form of transportation would be enough to fund a Hyperloop system between the two major Californian cities, assuming the correct initial cost of constructing such a system would amount to just $6 billion, and would even be enough to fund the system's operating costs with the $4 billion left over, as long as an assumed constant operational cost is less than $120 million each year with an assumed annual interest rate of 3%.

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The public's valuation of a new High Speed Rail included the train's affect on Climate Change, but it also included almost no effect on technological advancement and futurism (ωi), therefore a public valuation of a Hyperloop would be greater than voters' $10 billion approval of Proposition 1A. Elon Musk's desire for technological advancement and futurism in society (ωi) by way of introducing the Hyperloop was so high that he decided to give the idea away and crowdsource the Hyperloop without any possibility of a direct monetary benefit though its construction.

Because of the nature of extensive public infrastructure, such as highways, roads, airports, and railroads, to be relatively non-excludable public goods, firms can sell more efficient tools, such as bikes, cars, airplanes, airplane tickets, and train tickets, to the consumer for traversing such infrastructure in a relatively competitive manner to where if the rivalry of transportation increases, the competitive market will generally respond with an increase in supply of tickets. If the Hyperloop was expected to reach a level of adoption to the point of expanding throughout the country, wherein the level of available freedom for a passenger (βi) would also increase, a publicly funded tubing and station network would benefit society through its comparative efficiency relative to multiple firms building multiple competing Hyperloops to traverse the same distance. However, the Hyperloop is still completely new and undiscovered technology that will only begin by traversing two locations and will require a large amount of communication between each capsule and the tubing network. Creating a completely public Hyperloop system would crowd-out other forms of transportation to the point where the rivalry between consumers for the Hyperloop would escalate beyond the point of non-excludability. Since the government is not able to enlist a Lindahl pricing strategy, where the consumers respond honestly and pay exactly for how much they value the Hyperloop, in order to pay for the Hyperloop, some consumers that value a journey via the Hyperloop more than others may be excluded from partaking and will thusly become an inefficiency of the transportation network.

The Hyperloop is a theoretical invention of Elon Musk that utilizes a low-pressure environment to transport capsules across a distance. Individuals value different modes of transport based on how those modes affect their time as well as the time of the people they surround; aggregating these values and comparing them to new forms of transport can determine how a society will value construction of a new system. A purely public induction of a Hyperloop system will crowd-out airlines and traditional rail as airline and rail transport are not fast enough to keep up with the Hyperloop's speed. The non-excludable nature of public infrastructure allows firms to sell more efficient tools for traveling across this infrastructure, yet the Hyperloop's infrastructure will not be comparatively extensive for a considerable period of time.

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I would recommend a private corporation's induction of the Hyperloop system between San Francisco and Los Angeles until the system reaches a point of viability for national expansion wherein the network be publicly funded, while the capsules are privately owned.