To what degree can governments control prices or quantities of goods and services exchanged?

Governments have two main mechanisms for controlling the prices or quantities of goods and services exchanged, subsidies and taxes. Subsidies can be used to manipulate supply by rewarding supplies for producing, or not producing a target good. For internal trade, taxes can be used to manipulate demand by raising the cost of goods sufficiently that the potential pool of willing buyers is reduced. For external trade, tariffs offer similar effects.