A free-market system is defined as one where prices for goods and services provided comes from supply and demand, often characterized as prices being set by the market.
In a command economy, the prices for goods and services are set by an individual entity, typically a government, regardless of the true cost as determined by the market.
In a mixed-economy, components of a free-market and command economy are combined allowing for government control of some facets and oversight of many economic sectors, however, often times prices for goods are determined in part by market pricing and trends.
