Although the term "free market" is used liberally, no completely free market exists. Some regulation must be enforced on the economy, carried out by the government. A command economy places all control with the government; a market economy lets the market decide. Even in the United States, a largely pure market economy, organizations such as the Environmental Protection Agency place regulations on businesses. Regulations arise out of benefit for the majority, such as reducing smog. Because businesses have so much control in market economies, beneficial regulations are sometimes delayed or eliminated completely.
"The Invisible Hand" is an idea produced by Adam Smith in his 1776 book "An Inquiry Into The Wealth of Nations." He believed that markets would naturally regulate themselves because poor people were the consumers, and they dictated the products invested in by the wealthy. This dynamic was so inherent, it was invisible to those leading the market. The Invisible Hand concept chastises poor people for expecting more of the wealthy, asserting any aid by the wealthy must be met by additional effort from the poor. However, Smith didn't take into account problems with the idea -- such as abuses of subsidies, in which taxpayer money is provided to businesses by politicians needing support.
Price is the determining factor of supply and demand. When price decreases, demand often increases because the product or service becomes available to a wider range of people. Additionally, those who could afford the item before the drop in price then have the ability to buy more of the item, further increasing demand. When price increases, supply often increases because people aren't willing to pay more money for a product or service.
The factors of production refer to resources necessary to run an economy. They include capital, land and labor. Control and lack of control of these resources forms two markets within a market economy: sellers and buyers. Those who lack control sell their services to those who control production. In return, producers pay workers, which gives them the ability to buy products from various producers, creating a cyclical exchange of money. Forming this type of mutually beneficial environment is the ideal of market economies.