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Karl Marx never provided a detailed description as to how communism would function as an economic system, but it is understood that a communist economy would consist of common ownership of the means of production, culminating in the negation of the concept of private ownership of capital, which referred to the means of production in Marxian terminology. Unlike socialism, which is compatible with a market economy, a communist economy consists of local or communal democratic planning.

also from wikipedia, http://en.wikipedia.org/wiki/Communism