Austrians have a Monopoly Calculation

I am following the Cafe Hayek conversation on taxes and government.

The nearest they come to a formula is that the minimal government we need arrives from a spontaneous organization, so I am going to call it the Monopoly Calculation solution. Of necessity the private sector produces emerging monopolies by calculation and  the required monopoly arises naturally. We stop the emerging process, hopefully, when we reach the necessary government monopoly and no more.Let us assume a norm for collecting taxes, the  minimal emerging government would have a single median tax rate for all agents  The norm comes from the minimal emergence property, that is a minimum redundancy.
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However, by recursion,  emerging government units will collectively calculate the emergence of a higher level of government, we have hierarchical government.  Following the recursion, the local government would cover the median cost of a median service provided from the central government to the local government.

How do we get broad based taxes out of this? There is a variety of local governments with differing median tax rates. But each government pays the same median rate for central government services.
Define the total personal tax rate as (r + M/p) where r is the local tax rate, M the central government rate applies to the local government, and p is the population.

Local governments will adjust population size until the gain from government specialization is equalized across the total economy, we get a government channel.  Channel Theory once again is the math for Austrians.

Austrian have a math.