Pre script: This may seem like a troll post
but it’s not... honest.
There is a very simple way to have an economy with all resources and means of production centrally planned under one authority, only have one person.
Imagine a Robinson Crusoe style Island of Despair economy. All the resources are directed under one single plan to provide for all of the citizens of the Island of Despair, there only being one person.
Under this trivial solution is perfectly possible to have a centrally planned economy. Those who say having a centrally planned is impossible, are simply false.
Now if we introduce a second person, he also comes to the Island through shipwreck, there is Mr. Crusoe goes up to him and they come to an agreement to agree upon and decide the best use of the resources, deciding they can be more productive and prosperous together.
A boat of a dozen colonists arrive on the Island of Despair, Mr. Crusoe and his associate decide as the agreement between them had worked so well they would extent it to these new arrivals. This new agreement works well and they decide the best use of resources through a system of majority voting. There is a growing consensus they should rename the Island of Despair.
As the population of the Island grows larger there is increasing discontent. Those who know more about an issue, argue that they should have greater say than their one vote. They have more information which is only relevant in that specific place and time and the focus on having a single plan for all the resources is preventing them from experimenting and finding new ways of doing things with their expertise.
There is no agreement on how to increase the voting power of specialists and those with more information without it becoming unfair and encouraging vested interests. As the population grows further the time and place specific information larger and larger and becomes harder and harder to process for the authorities. The Island regains it former name.
To conclude, centrally planned economies are possible but as populations grow larger having one organisation grows increasingly harder. To re-work Coase’s point in “The Nature of the Firm” there are costs to operating between organisations and there are costs to operating within one single organisation. The optimal point of size of organisations is when the costs from acting within and outside the organisation are equal. If only there was a system whereby the planning undertaken for the means of production was undertaken by different organisations in some way where they voluntarily offered some sort of medium of exchange to convey their specific interpretation of information in expectation of receiving more of that medium of exchange in return, under some sort of rule of law. If only that this sort of system existed....
Coase, R., H., (1937) "Nature of the Firm"
http://courses.cs.washington.edu/courses/csep590/06au/readings/coase.pdf
