Why aren't there more private roads?

[tolbiny]

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It causes a productivity loss compared to if the monopoly is abolished.

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Efficiency is not a static model, if one could predict and quantify the outcomes of these actions accurately then you would have a strong argument for central planning from an efficiency standpoint, whereby the state could produce goods and sell them at cost to consumers getting rid of all the "waste" that is profit. Unfortunately (or fortunately for lovers of liberty) profits work not just as rewards for those who receive them but as measuring sticks to view who is providing for consumers better and as encouragement for other entrepreneurs to invest in the same industry (or a warning to stay away). Groups can make high profits from industries which encompass what you are calling "natural monopolies" because clean water, roads, whatever are highly valued by consumers. The high profits signal others to invest money into that industry satisfying more and more consumers. Artificially limiting profits artificially restricts the amount of money directed into these markets which slows/prevents further invention and innovation which prevents future gains in efficiency.