Free market economy
An economy where all resources are allocated by the price mechanism. There's NO government intervention.
E.g. Hong Kong in 1960s is a close example
Command economy
An economy where all resources are allocated by the government.
E.g. Cuba or North Korea in the 1980s
Mixed economy
An economy where some resources are allocated by the price mechanism, and some are allocated by the government.
E.g. the UK
Adam Smith
He described the price mechanism as an "invisible hand".
He argued that free markets were very efficient and that the government should only intervene in cases of market failure (e.g. externalities).
Karl Marx
He argued that free markets would lead to capitalism and inequality.
Capital owners would make huge profits, but workers would be paid low wages.
So he supported command economies, where a government can fairly allocate resources between everyone.
Hayek
He described the price mechanism as a "communication network".
Changing prices told producers what consumers wanted and what they didn’t want, eliminating excess supply and demand.
He criticised Marx's ideas for a command economy. He argued that a government would not have enough information to work out how to allocate resources effectively.