From my understanding, there are 4 main types of market economies. They are also known as Economic Systems. The 4 are Free Market, Mixed Market, Command and Traditional Economy. Please try to understand that there are various terms for them, and it can be different from one book to another. What is important is to understand its characteristics. The Free Market, just simply means let the invisible hand in the Economy work, while in the Command Economy, the invisible hand is the government. The mixed Economy has a mixture of both. Traditional economy is a bit different though, the economy only moves when an elder tells them to.