This type of a political and economic system is typically called communism. When we are just talking about economics, they system can be called a command economy. However, when we add in the political system as well, it is called communism.
Communism holds that a free market economy, with private property and private ownership of the means of production, exploits the people who actually do the work. They believe that it is only just and equitable to have the workers also own the means of production. The government represents all of the people, so when it owns the means of production and holds the wealth, the people are the ultimate owners. In a communist system, there is little or no private property. Any property that is privately held is minor. Major property like factories, stores, and other economically important things are owned by the government.
The best answer to this question, then, is communism.