Describe each system.
Capitalism essentially is built on the premise that nations prosper the most when individuals are allowed as much freedom as possible to make their own economic decisions. These decisions include what to buy, what to produce, what to pay for a product and how much to charge for a product. Pure capitalism rarely functions today since government regulation in the form of labor laws, anti-monopoly laws, and restrictions against price fixing are in place. There is also significant government control over quality and safety guidelines.
Communism or socialism would be the other main economic system. In this system there is little or no individual control over the economy. The government determines what will be produced, how much can/will be charged for goods and services, what job an individual will work at and how much he/she will be paid. Additionally the government usually controls most or all of the industries and utilities considered vital to national productivity. These would include electricity, communications, media, road construction, military etc. As with capitalism, there is really no true 100% communistic nation in the world because it would self-destruct. China tried pure communism in the decades following World War II and nearly brought the economy to a standstill as the bureaucracy tried to micro-manage every aspect of the economy. Today they use a very capitalistic economic system while retaining communism in politics and social engineering.