The relationship between the government of a country and its economy is referred to as its political economy.
Typically, there are two “extremes” to this:
Laissez-faire economy- an economy in which there is little to not economic regulation; minimal government intervention in markets.
This is typically associated with more capitalist societies
Command Economy- an economy in which the government controls everything; there is heavy regulation and the government usually runs most (if not all) industries
This is typically associated with more socialist societies