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How would a society go from a purely communist system to capitalism, both with and separately without conflict?

Abbreviated Question: 
How would a society go from a purely communist system to capitalism, both with and separately without conflict?
Answer: 

You have asked an interesting (and open-ended) question to begin with. An issue with answering questions regarding capital and Socialism is that they get lost in the political thicket, although given the nature of the question, politics is inevitable at some point. No matter how much I appreciate the 'ark ship' narrative, I would like to answer without delving into it. [Opinion alert: The following piece will be subjective.]

What do economists think of the Lange model? Does it address the economic calculation problem?

Abbreviated Question: 
What do economists think of the Lange model? Does it address the economic calculation problem?
Answer: 

1.  A mainstream neoclassical synthesis economist would say that this system can be doable but it has what we would call a lot of incentive compatibility problems. It is not only the fact that the government needs to be accurate in timing and in calculation about when and in which market there will be a shortage (which itself is already probably slow, costly and might be inefficient compared to a pure market allocation) but is also that, if I understand properly, the government sets the producer sector to adjust based on the measures they have on shortage.