What are the advantages of a market economy?

The major advantages of a market economy are that such an economy provides the greatest personal freedom for its people, gives them with the greatest possible variety and quality of goods and services, and offers those goods and services at the best possible price. By doing these things, the market economy allows a country to be richer and freer than it otherwise would be.
In a market economy, people have the right to do more or less with their property as they wish. The government allows people to start businesses doing whatever they want (outside of illegal things like drug dealing). It does not tell them what they must do with their money and it does not create companies of its own that prevent private enterprise from growing. If we believe personal freedom is good, then a market economy is better than other types of economies because it allows people to be free to do whatever they want with their property.
When people are able to do what they want with their property, consumers benefit. When entrepreneurs are free to create businesses, they will try to figure out what consumers want to buy so they can make money by supplying those goods or services. For example, Apple created smartphones because it thought it could make money selling them. Because Apple was free to do this, consumers around the world have benefited from the use of smart phones. 
In a market economy, products will be made at the best possible combination (or combinations) of quality and price.  Companies will compete with one another for customers. If the quality of Apple’s smart phones cannot keep up with that of another company, Apple will lose market share. The same is true if Apple’s phones are just as good, but are more expensive. When companies compete, they force one another to provide the best possible goods at the lowest possible prices. This is much better for consumers than an economy in which (for example) one government-owned monopoly provides all telecommunications services and therefore does not have to worry about satisfying customers more than a competing company.
In these ways, market economies have definite advantages.  These economies allow greater personal freedom while simultaneously providing consumers with more goods and services that are high quality and as inexpensive as possible.
https://www.nyu.edu/projects/ollman/docs/china_speech2.php