It is a pure command economy (also called a command-and-control economy). The government owns all the resources and makes all the decisions of what to produce with them.
The idea is that the government will prevent injustice from happening by making all the decisions. They would listen to workers and make decisions off of that. Yet ironically, in a pure command economy it is the government that assigns jobs to workers, and gives orders to factories and farmers.
The most obvious problem is that it alters the incentives both producers and consumers face. If a government really tried to implement the Marxist slogan “From each according to his abilities, to each according to his needs”, it’s likely that most people would eventually work less hard as they did under a capitalist framework.
Another principle of the socialist system is fair distribution. Workers use resources to make goods and then the goods are distributed fairly among other people. And even though it might be “more fair” than a capitalist system, it means there will be far fewer goods to be distributed. People won’t be willing to work hard if they get the same amount of goods no matter how hard they work.
There is also the problem of who will do the “dirty work”, like cleaning. In a market economy, people might want to collect trash because it allows them to afford a nice lifestyle. They might also want to do it because the cleaning job pays them more than some other job requiring the similar education and experience. In the socialist system it is often “fixed” by cutting hours, adding more benefits, making the job more appealing. Yes, this helps to get more workers take this job, but there is a bigger demand than there should be and other jobs start lacking workers. There is also the solution of forcing people to do undesirable jobs, but that would not do any justice, not only because they would not be willing to work much, they might also not be right for the job. Socialist rulers wouldn’t have been able to identify the potential output of Bill Gates when looking at him at 20 years old; how would they know who should be a cleaner and who shouldn’t?
In the market economy, the allure of financial rewards causes the best to rise up from the crowd and demonstrate their talents and ambition.