In a Market Economy, the people decide what should be produced and in a sense, it is usually the goods that people need for living. An example of a country with a market economy is the U.S.A.. This type of economy has seen much success throughout the world
This is a command economy, one that relies on the government to decide what should be produced. In theory, it is a concept that should beat the U.S. economy in only a couple of years, but that is not the case, as the gov't can mishandle the wants of people. A notable country that has used the economy is the U.S.S.R., and is still used today by some countries, but it's less favorable to a market economy.
A mixed economy is, as the name suggests, a mixture of the former economies that we talked about. Almost every country in the world has a mixed economy, due to an ideal mix of gov't control and free market. This is one very popular choice of economy as it is also flexible.
So this is a funny one, this is a traditional economy, the most head-scratching of them all. This has been superseded by almost every other economy out there, even the command economy. Countries that still use this include Mongolia and parts of other countries, such as West China. The people depend on each other.