Is there any formal distinction those economists make, or is it just a matter of "pretend it doesn't exist by calling it by a different name"? Natural monopolies can and do exist in markets as close to free as we can get.

If you can come up with a historical example of a natural monopoly you’ll have done better than the entire economics profession at doing so. We have many examples of local monopolies, government granted monopolies and companies getting very large shares of an industry by driving up quality and driving down prices but no unambiguous examples of natural monopolies arising in competitive markets. Large fixed costs and low marginal costs are usually cited as preconditions of natural monopoly but the US supports DHL, FedEx, UPS and the US postal service. Many municipal markets have had multiple competing utilities for multiple decades.

How about Norfolk Southern?

The vast majority of economists agree that natural monopolies exist, and economic theory from Adam Smith on describes how they form. To believe that the "entire economics profession" has failed to find a single historical example implies not only that the vast majority are wrong, but they're willfully ignoring the evidence (presumably because they hate freedom).

Additionally, the fact that nobody has shown a monopoly that didn't involve government somewhere along the line isn't evidence that monopolies don't exist without government, because governments have been involved in every private company ever created. It's like assuming "people would live forever if they never drank water, because everyone who ever drinks water eventually dies".

A natural monopoly is an organisation in an industry where the minimum efficient scale is more than 50% of the industry, such that it is impossible to have lower unit costs than the natural monopolist. This has never happened, anywhere, as far as my limited research has shown me.

Norfolk Southern from a cursory look at its Wikipedia page may have a local monopoly on rail transport of coal on North Anerica’s East Coast. This will enable it to charge slightly higher than competitive prices. It will not enable it to charge profit maximising monopolist prices because other companies can build their own rail lines and coal can be transported by truck. Local monopolies are contestable. You may have no actual competition but the price you can charge is limited by the fact that if you charge enough potential competition will become actual competition.

The concept of natural monopoly does not depend on government or private companies. It depends on minimum efficient scale being more than half of a market. If even the monopoly on violence, the core characteristic of a state, is not a natural monopoly, what is?

The minimum efficient scale doesn't need to be more than 50% of the industry, it needs to be beyond a size at which competitors are willing to invest.

The evidence that no one has successfully contested Norfolk Southern is evidence that it's a natural monopoly. The burden is on you to show that it's possible and there's some other reason it hasn't happened (and why it's okay that the free market is allowing a monopoly to exist).

>If even the monopoly on violence, the core characteristic of a state

Not sure why you brought this up. Can you explain how this relates to your argument?

If competitors aren’t willing to invest because the return on investment would be too low to make it worthwhile that’s one thing. It’s quite different from minimum efficient scale being so high that you can only efficiently have one supplier in a particular market. A local monopoly is not evidence of natural monopoly. A local monopoly has to worry about potential competition, a natural one doesn’t. Rail services in North America look like a natural oligopoly, not a natural monopoly. There are no particular welfare implications in those since if you can’t legally enforce collusion it doesn’t last. Plenty of oligopolies are competitive. Intel worries plenty about AMD.

If you search for Norfolk Southern competitors the following names come up, Union Pacific, Canadian National Railway Company, CSX Corp, Canadian Pacific Railway and Kansas City Southern[0]. Whatever that is it isn’t a natural monopoly.

Violence has high fixed costs and relatively low marginal costs. If the efficient number of states, violence monopolists, is so much greater than one why would we expect anything else to be a natural monopoly?

[0]http://financials.morningstar.com/competitors/industry-peer....

No, it's not a matter of names; the Austrian school (not to be confused with economists from Austria) claims they don't actually exist, and that the examples usually given can be explained by governmental manipulation.

"There is no evidence of the "natural-monopoly" story ever having been carried out — of one producer achieving lower long-run average total costs than everyone else in the industry and thereby establishing a permanent monopoly."

https://mises.org/library/myth-natural-monopoly